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INTERNATIONAL SERIES IN PHYSICS 
F. K. BICHTMYER, CONSULTING EDITOR 



APPLIED X-RAYS 



INTERNATIONAL SERIES IN PHYSICS 
F. K. RICHTMYER, CONSULTING EDITOR 



Backer and Goudnmit 
ATOMIC ENERGY STATES 

Clark 
APPLIED X-KAYS 

Condon and Morse 
QUANTUM MECHANICS 

Hardy and Perrin 
THE PRINCIPLES OF OPTICS 

Hughes and DuBridge 
PHOTOELECTRIC PHENOMENA 

Pauling and Goudsmit 
THE STRUCTURE OF LINE SPECTRA 

Ruark and Urey 
ATOMS, MOLECULES AND QUANTA 

Williams 
MAGNETIC PHENOMENA 



APPLIED X-RAYS 



BY 

GEORGE L. Cj^AEK, PH.D. 

ProfcHNor of Chemistry, University of Illinois 



SECOND EDITION 



McGRAW-HILL BOOK COMPANY, INC. 

NEW YORK AND LONDON 
1932 



COPYRIGHT, 1927, 1932, BY THE 
MCGRAW-HILL, BOOK COMPANY, INC. 



PRINTED IN THE UNITED STATES OP AMERICA 

All rights reserved. This book, or 

parts thereof, may not be reproduced 

in any form without permission of 

the publishers. 



THE MAPLE PRESS COMPANY, YORK, PA. 



TO 

MY WIFE 



PREFACE TO THE SECOND EDITION 

In the six years which have passed since the manuscript of 
the first edition of " Applied X-rays " was completed, the signs 
envisioned in 1926 of a rapid growth of pure and applied x-ray 
science have become accomplished facts beyond all expectations. 
A great group of earnest research workers all over the world 
has pushed out the boundaries of the science until these men 
themselves stand in wonderment at the progress which has 
been made. 

Since 1926 physicists in their investigations among other 
phenomena of the origin of x-radiation have refined their measure- 
ments of wave lengths and energies until the Bohr theory, 
or in fact any mechanical model of the atom, no longer is adequate 
to account for experimental fact. X-ray tubes have been 
designed and operated successfully at millions of volts. Medical 
science, still confronted with the enigma of cancer, has improved 
vastly its knowledge, applications, and results with x-ray therapy, 
until the future seems certain to bring forth greater triumphs. 
Perhaps the branch which has made the greatest advance of 
all is the chemists' diffraction analysis of the fine structures of 
solid and liquid materials and the evolution of a new crystal 
chemistry scarcely dreamed of a few years ago. And industry 
what has it done with a research tool which seemed promising 
but largely untried six years ago? No one can deny that x-ray 
testing and research have become important and often indis- 
pensable adjuncts to the programs of progressive industries. 
Baffling problems have been solved with the aid of the x-ray 
"supermicroscope"; improved quality of products and rational 
standardization of manufacturing processes have resulted; 
patents based on x-ray data have been issued. And yet all 
would agree that only the barest beginning has been made. 

Confronted by such an extraordinary expansion in subject 
matter in a comparatively short time, it is self-evident that the 
task of revision resolved itself into one of a completely new 
creation. With the exception of a few paragraphs in the early 
chapters which could be retained, the book is entirely changed. 

vii 



viii PREFACE TO THE SECOND EDITION 

Material could be selected from a great fund of information, 
in contrast with the missionary effort in 1926. Lessons taught 
by the experimental first edition have enabled a more logical 
arrangement and presentation. And yet there have been 
retained the original plan arid purpose of sketching the record of 
achievement and of depicting the promise for the layman in 
the industry and in the class room, while digging a little deeper 
than heretofore in the interest of clarity for the benefit of the 
inquisitive experimentalist in the laboratory. Again the treat- 
ment is suggestive rather than exhaustive. Several new and 
revised treatises on various phases of the science are now avail- 
able, and from these valuable information and suggestions have 
been gained. A large number of original papers has been con- 
sulted. The author's series of papers on " X-ray Metallography 
in 1929 " published in Metals and Alloys, and his chapter on 
"Some Practical Results of X-ray Researches on Colloids" 
in Alexander's "Colloid Chemistry," Vol. Ill, have served as 
the basis for the same topics in this book. 

A list of those whose inspiration, encouragement, and sugges- 
tions have been of inestimable value in the preparation of 
this revision would be of formidable length. It was a fond hope 
of the author to include as a slight token of respect photographs 
of some of the great contributors to x-ray science, but regretfully 
on account of space limitations the plan could not be carried 
out. To Professor F. K. Richtmyer of Cornell University most 
grateful acknowledgment is given for his painstaking examination 
of the manuscript, his suggestions for improvement in Part I, 
which have been incorporated as fully as possible, and for the 
honor involved in his recommendation for the inclusion of this 
book in the International Series in Physics. Sincere thanks 
are due especially to graduate students at the University of 
Illinois, particularly Doctors Lucy Pickett, H. A. Smith, W. A. 
Sisson, K. E. Corrigan, and J. C. Zimmer, for their help in 
establishing new facts many of which are published here for 
the first time; to Misses Winifred Johnson, Frances Johnson, 
and Dorsie Baize, and Mrs. Edna Evans for efficient secretarial 
assistance; and to Mr. Paul Evans for his painstaking help in 
the preparation of illustrations and index. 

GEORGE L. CLARK. 
URBANA, ILLINOIS, 
September, 1932. 



PREFACE TO THE FIRST EDITION 

The primary motive underlying the preparation of this book is 
the presentation of x-rays as a new tool for industry. 

The thirty-year-old science of x-rays is now broadening from 
the stage of pure or academic science to that of applied or indus- 
trial science. It has already to its credit a notable record of 
practical achievement. 

There are, therefore, several interwoven phases of the science 
of x-rays, none of which can be neglected in the consideration of 
practical applications. The spectroscopy of x-rays, involving 
the measurement of radiation wave lengths, has been of immeas- 
ureable assistance to the physicist in his searchings of atomic 
structures and of the interrelationships between matter and 
radiant energy. This phase of the science has found excellent 
expression in several books, particularly the authoritative 
exposition, recently translated into English, of the master 
experimenter and Nobel Prize recipient, Manne Siegbahn. 

Scarcely more than twelve years ago, von Laue and the Braggs 
reasoned that the use of crystals should make it possible to 
measure wave lengths of x-rays, and hence that x-rays of known 
wave lengths might render possible the analysis of crystals of 
unknown ultimate structures. The complete verification of this 
prediction has led to the foundation of a chemical, physical, and 
engineering science of the solid state, which has yielded beyond 
all expectations exact knowledge of a previously little known 
subject. On this phase of the science of x-rays, again, excellent 
books have been written by the great pioneer Braggs, Ewald, 
WyckofT, and others. 

Now the science enters the industrial phase. This book aims 
to tell what this new tool is, how it may be used, what results 
it produces, why it can be applied to practical problems of every- 
day life and how industry is beginning to use it now. The book 
is the expression of a conviction that x-ray research and control 
methods can now and in the future be of invaluable service in the 
solution of problems of constitution and practical behavior of 
metals and alloys of every kind, of catalysts, textile fibers (cotton, 

ix 



X PREFACE TO THE FIRST EDITION 

flax, jute, ramie, sisal, hemp, silk, wool, rayon), rubber, balata, 
gutta percha, resins, varnishes, lacquers, paints, pigments, dyes, 
enamels, carbon black, inorganic and organic chemicals, waxes, 
greases, soaps, oils, liquids of all kinds, dielectrics, storage 
battery oxides, colloidal metals and gels, patent leather, glass and 
its substitutes, gelatine, adhesives, abrasives, lime, plaster of 
paris, cement, ceramics, sugars, starches, biological systems, 
coal, gems, and numerous other substances. 

I have tried to give the reader, whether he be the industrial 
executive or research director who is seeking to learn of a new 
method of attacking his problems, or the inquiring student or 
layman, a true and understandable survey of x-ray science as it is 
known to-day. This is not a handbook for the complete and pre- 
cise determination by experts of wave lengths or crystal struc- 
tures, but nn outline of information for the intelligent inquirer 
who may himself never conduct a single x-ray experiment. I 
have hoped to make of it a missionary, which must speak an 
understandable language and have at hand the foundation facts 
to support its case. 

The subject matter falls into a natural arrangement in three 
parts. The first eight chapters present the fundamental physics 
of x-rays; Chapters IX to XII cover the properties and appli- 
cations of the radiation as such; the remaining chapters are con- 
cerned with the application to the study of crystalline structure. 

Free usage has been made of most of the published books on 
x-rays. These include, besides those already mentioned, the 
excellent little monograph by Becker "Die Roentgenstrahlen als 
Hilfmittel fur die Chemische Forschung," Hirsch's "Principles 
and Practice in Roentgen Therapy," and the texts by de Broglie, 
Cermak, and Kaye. A large number of original papers, particu- 
larly the most recent contributions, have been consulted. Finally 
many experimental studies from my own laboratory, most of 
which have not been published, are included. The fact remains, 
of course, that in this rapidly growing science important advances 
have been made even during the preparation of the manuscript 
of this book. 

I am deeply indebted, first of all, to Professor William Duane 
of Harvard University, pioneer and distinguished maker of light 
in the science of x-rays, whose inspirational guidance made 
possible an enthusiastic acquaintance with this research tool; 
also to Professors W. K. Lewis, R. T. Haslam, and W. G. Whit- 



PREFACE TO THE FIRST EDITION xi 

man of the Massachusetts Institute of Technology, who as 
engineers had the vision of x-rays in industry, and the faith to 
install an x-ray laboratory and to provide the facilities for the 
task of writing this book; to my able assistant in authorship, Mr. 
Robert Landis Hershey; to my associates in x-ray research, 
particularly Dr. R. H. Aborn, Mr. E. W. Brugmann, and Dr. 
Marie Farnsworth; to my friend, Mr. J. P. Kelley, author of 
" Workmanship in Words/ 7 who has generously examined the 
manuscript with a critical eye on its English; and to rny wife for 
her never-failing encouragement and for her assistance in the 
reading of manuscript and proof. 

GEORGE L. CLARK. 

CAMBRIDGE, M ASSACHUSETTS, 
November, 1926. 



CONTENTS 

PAGK 

PREFACE TO THE SECOND EDITION vii 

PREFACE TO THE FIRST EDITION ix 

PART I 

GENERAL PHYSICS AND APPLICATIONS OF 
X-RADIATION 

CHAPTER I 
X-RAYS, LIGHT, AND THE ELECTROMAGNETIC SPECTRUM . . 3 

CHAPTER II 
THE GENERATION AND PROPERTIES OF X-RAYS 9 



CHAPTER III 
X-RAY TUBES 12 

CHAPTER IV 
HIGH-TENSION EQUIPMENT 40 

CHAPTER V 
X-RAY SPECTRA 49 

CHAPTER VI 
CHEMICAL ANALYSIS FROM X-RAY SPECTRA 82 

CHAPTER VII 
THE ABSORPTION AND SCATTERING OF X-RAYS 91 

CHAPTER VIII 
RADIOGRAPHY 108 

CHAPTER IX 

PHYSICAL, CHEMICAL AND BIOLOGICAL EFFECTS OF X-RAYS. 131 

xiii 



xiv CONTENTS 

PAGE 

PART II 

THE X-RAY ANALYSIS OF THE ULTIMATE 
STRUCTURES OF MATERIALS 

CHAPTER X 
CRYSTALS AND X-RAY DIFFRACTION ^ 171 

CHAPTER XI 
EXPERIMENTAL X-RAY METHODS OF CRYSTAL ANAI/YSIS . . 185 

CHAPTER XII 
THE INTERPRETATION OF DIFFRACTION PATTERNS 208 

CHAPTER XTII 
THE RESULTS OF CRYSTAL ANALYSIS: ELEMENTS AND 

INORGANIC COMPOUNDS 231 

CHAPTER XIV 

INORGANIC CRYSTAL CHEMISTRY: FUNDAMENTAL GEN- 
ERALIZATIONS FROM EXPERIMENTAL DATA 259 

CHAPTER XV 
THE STRUCTURE OF ALLOYS 279 

CHAPTER XVI 

RYSTAL STRUCTURES OF COMPOUNDS OF CARBON AND 
THEIR PRACTICAL SIGNIFICANCE 307 

CHAPTER XVII 

THE INTERPRETATION OF DIFFRACTION PATTERNS IN TERMS 
OF GRAIN SIZE, ORIENTATION, INTERNAL STRAIN, AND 
MECHANICAL DEFORMATION 335 

CHAPTER XVIII 
PRACTICAL APPLICATIONS OF X-RAYS TO PROBLEMS OF 

METALLURGICAL INDUSTRY 388 

CHAPTER XIX 

THE STRUCTURE OF COLLOIDAL AND AMORPHOUS MATERIALS 
AND OF LIQUIDS 426 

CHAPTER XX 

THE STRUCTURE OF HIGHLY POLYMERIZED ORGANIC SUB- 
STANCES FOUND IN NATURE 438 

INDEX 463 



PART I 

GENERAL PHYSICS AND APPLICATIONS OF 
X-RADIATION 



CHAPTER I 

X-RAYS, LIGHT, AND THE ELECTROMAGNETIC 
SPECTRUM 

In 1895, during the course of some experiments with cathode 
rays, which are streams of electrons in evacuated tubes, Roentgen 
discovered the radiation which bears his name. 1 

The investigations of the discoverer and of other early experi- 
menters demonstrated that there were certain striking similarities 
between these new rays and ordinary light. 2 Both x-radiation 
and light moved in straight lines, passed through space without 
apparent transference or intervention of matter, affected a 
photographic plate, excited fluorescence or phosphorescence in 
some substances, and ionized gases. Both were unaffected by 
electric or magnetic fields, indicating the absence of electric 
charges, and both exhibited polarization, or different properties 
in different directions at right angles to the line of propagation. 
Finally, convincing evidence was obtained, which has since been 
rigorously confirmed, that the velocities of the propagation of 
light and of x-rays were identical. 

On the other hand, there were some respects in which x-rays 
and light seemed to differ. Roentgen and his contemporaries 
were unsuccessful in all their efforts to observe deflection of the 
new rays from mirrors, prisms, and lenses, to obtain diffraction 
by gratings, or to obtain double refraction and polarization in 
crystals. These phenomena in the case of light were, of course, 
well known. As a matter of fact, it has been within only a very 
few years that Duane and Patterson, A. H. Compton, Davis, 
Siegbahn, and others have demonstrated that x-rays may be 

1 The designation "x-rays" is now in more common usage among phys- 
icists and chemists in England, France, and America; but in medical science 
"Roentgen rays," "roentgenology," and similar terms are favored. Desig- 
nation by the discoverer's name is practically universal in Germany. 

2 For an excellent account of the history of experimental discoveries which 
led to the discovery of x-rays arid to the establishment of the nature of the 
radiation, see Wiltshire and Pullin, "X-rays Past and Present," D. Van 
Nostrand Company, New York, 1927. 

3 



4 APPLIED X-RAYS 

totally reflected at very small glancing angles from mirrors, 
refracted in prisms, and diffracted by finely ruled parallel lines 
on glass or speculum metal. 

According to the classical theory, derived largely by Maxwell, 
light consists of waves of electromagnetic origin which are 
propagated in the ether. Maxwell conceived of an electric field 
whose intensity or direction might vary periodically so as to create 
waves. Since action at a distance between electric charges is 
not instantaneous, these waves can be produced by giving an 
electric charge a rapid oscillatory motion. Each of these electric 
waves must be accompanied by a magnetic wave propagated 
with the same velocity; the periodically variable electric and 
magnetic fields must be perpendicular to each other and to the 
direction of propagation; hence, transverse. But such a condi- 
tion is actually found in light waves, which are, therefore, elec- 
tromagnetic waves. As an experimental verification, Hertz, 
by using oscillating electric discharges, was able to produce waves 
similar to light, in that they could be reflected, refracted, dif- 
fracted, and polarized. Thus all radiation throughout the 
spectrum finds its origin in what may be termed the unrest of 
electric charges. 

In 1912, Laue, reasoning from the electromagnetic-wave theory, 
predicted that x-rays should be diffracted by crystals, which 
serve as three-dimensional gratings, just as light is diffracted by 
the finely ruled lines of an ordinary optical grating, which is 
essentially two-dimensional. The complete experimental veri- 
fication of this prediction established beyond question the 
identical nature of x-rays and light. They are distinguished 
only by the fact that x-rays have a wide range of wave lengths 
shorter than those of light. Table I shows that the known x-ray 
range lies between 0.06 A.U., or even shorter, and 1019 A.U., 
thus overlapping the ranges of both y-rays and ultraviolet rays. 
In the laboratory for crystal analysis an average wave length 
employed is 1 A.U. or a value about one six-thousandth the wave 
length of yellow light in the visible region. Not only are light 
and x-rays thus closely related, but also included in the electro- 
magnetic spectrum are the 7-rays from radioactive disintegra- 
tions, possibly the cosmic rays, which, if they are finally proved 
to be like light rather than high-speed electrons, should have the 
shortest wave lengths thus far recognized, the ultraviolet rays, 
which are just shorter than visible light, the infrared or heat rays, 



X-RAYS, LIGHT, AND THE ELECTROMAGNETIC SPECTRUM 5 

the long range of radio or Hertzian waves, and finally the very 
long electric waves such as are associated with alternating cur- 
rents. All of these waves, seemingly so different in properties 
and produced by such vastly different methods, are actually identi- 
cal in every respect except length. All have the same velocity 
of propagation, namely, thirty billion centimeters per second. 

The spectrum of electromagnetic waves is presented in Table I. 
The ranges in octaves and in Angstrom units (one Angstrom 
unit, A. U., = 10~ 8 , or one one-hundred-millionth of a centimeter) 1 
and brief statements of the methods of generation and detection 
are included in this table. 

The simple facts of the fundamental mutual similarity of 
electromagnetic waves and of the essential difference only in 
wave length suggest immediately the general practical properties 
and the uses which may be made of x-radiation of average wave 
length as compared with ordinary light. Since their wave 
lengths X are so much shorter, or their frequencies v greater 
(X = c/v, where c is the velocity of light), x-rays may be expected 
to penetrate materials which are opaque to light and to be 
intimately related to a far finer subdivision of matter than is 
possible for light waves. Even under the ultrarnicroscope the 
examination of matter with the aid of visible light rays can 
reach only a definite limit of size which is still far removed from 
that of the ultimate constituents. The ultraviolet microscope 
so successfully developed by Lucas 2 and by Barnard 3 discloses a 
fine structure which appears perfectly homogeneous under visible 
light rays, but here again a limit is reached. Beyond this, 
x-rays are able to take the investigator on to the ultimate 
molecules and atoms, even on to the universe within the 
atom, if he but interprets his information properly, the reason 
lying in the fact that in solid crystalline matter the spacings of 
the ultimate particles of mass (which may be ascertained from 
density, the molecular weight, and the mass of the hydrogen 
atom) are of the same order of magnitude as the wave length of 
the x-rays, namely, 10~ 8 cm. 

1 Another unit frequently used for x-rays is 1 X.U. = 10~ 3 A.U. = 10~ u 
cm. 

2 An Introduction to Ultraviolet Metallography, Pamphlet 1576E, Am. 
Inst. Mining Met. Eng. (June, 1926), followed by several later publications. 

3 For the Beck- Barnard microscope and its use see Martin, /. Roy. Soc. 
Arts, 79, 887 (1931); Wyckoff and Ter Louw, /. Expt. Med., 64, 449 (1931). 



APPLIED X-RAYS 
TABLE I. RANGE OF ELECTROMAGNETIC WAVES 



Type 


Oo- 
taves 


Wave length range 

in A.U. 
(1A.U. - 10- 8 cm.) 


Generation 


Detection 


Cosmic' 




0.00008-? 


Cosmic condensa- 


Observed day and 








tion of 4 H to 1 


night. Uniformly 








He and atomic syn- 


in space. Pene- 








thesis in depths of 


trate 18 ft. of lead. 








space. (Millikan.) 


Discharge electro- 










scopes. 


"y-rayo 




0.01-1.4 


Emitted when 


As for x-rays, but 






0.06-0.5 used in 


atomic nuclei dis- 


more penetrating. 






radiology 


integrate (radio- 










activity). 




X-rays 


14 


0.06-1019 


Emitted by sudden 
stoppage of fast 
moving electrons. 


a. Photography. 
b. Phosphorescence. 
c. Chemical action. 










d. lonization. 










e. Photoelectric ac- 










tion. 










/. Diffraction by 










crystals, etc. 


Ultraviolet rays . . . 


5 


136-3900 


Radiated from very 
hot bodies and 


Same as x-rays a to 
e: reflected, re- 








emitted by ionized 


fracted, and dif- 








gases. 


fracted by finely 










ruled gratings. 


Visible rays 


1 


3900-7700 
Violet 3900-4220 


Radiated from hot 
bodies and emitted 


Sensation of light; 
same as ultraviolet 






Blue 4220-4920 


by ionized gases. 


rays. 






Green 4920-5350 










Yellow 5350-5860 










Orange 5860-6470 










Red 6470-7700 






Infrared rays 


9 


7700-4 X 10 


Heat radiations. 


Heating effects on 










thermocouples, 










bolometers, etc. 










Rise in tempera- 










ture of receiving 










body. Photog- 










raphy (special 
plates). Reflected, 










refracted, d i f - 










fracted by coarse 










gratings. 


Solar radiation 




Limiting wave 










lengths reaching 










earth 2960-53000 






Hertzian waves . . . 


28 


1 X 10to3 X 10' 4 






Short Hertzian 


17 


1 X 10to 1 X 10" 


Spark-gap discharge 
oscillating triode 


Coherer. Spark 
across minute gaps 








valve, etc. 


in resonant receiv- 










ing circuit. Re- 










flected, refracted, 










diffracted. 


Radio 


11 


1 X 10" to 3 X 10' 4 


Same. 


Coherer. Conver- 


Broadcasting band 




2 X IQi* to 5.5 X 
10 12 




sion to alternating 
current. Recti- 










fication with or 










without heterodyn- 
ing and production 


Electric waves 




3 X 10" to 3.5 X 
lOie 


Coil rotating in 
magnetic field. 


of audible signals. 
Mechanical. Elec- 
trical. Magnetic. 










Thermal effects of 










alternating c u r - 










rents. 



* Measurements by A. H. Compton during the summer of 1932 in various parts of the world 
teem to prove that cosrnio rays are more intense the nearer to the earth's magnetic poles, the 
higher the altitude, and in daytime as compared with night. The conclusion is that cosmic 
raye are high-speed electrons and not rays similar to light. The theory also has been 
advanced that they are streams of neutrons, or particles formed from closely coupled positive 
and negative charges. Future progress in experimental measurements alone can settle finally 
the question of the nature of these rays. 



X-RAYS, LIGHT, AND THE ELECTROMAGNETIC SPECTRUM 7 

In the consideration of radiation as continuous electromagnetic 
waves in the ether, the fact must not be dismissed that radiation 
also appears to be propagated in discontinuous bundles or quanta 
in accordance with the laws first enunciated by Planck more than 
a quarter century ago. In diffraction, refraction, polarization, 
and in phenomena involving interference, x-rays, together with 
all other related radiations, appear to act as waves, and X has a 
real significance; in other phenomena, such as the appearance of 
sharp spectral lines and of a definite short wave-length limit of 
the continuous spectrum, such as the shift in the wave length of 
x-rays scattered by electrons in atoms, and such as the photo- 
electric effect, the energy seems to be propagated and transferred 
in quanta defined by the values of hv, where h is the Planck 
action constant, and v the frequency of the rays. Such a cor- 
puscle or quantum is called a photon. 

Radiation, however, is not alone in displaying these dual 
properties. Electrons long considered to be definitely corpuscu- 
lar were shown first by the Americans Davisson and Germer in 
1927 and later by G. P. Thomson, Rupp, and others to possess 
definite wave properties in that they could be diffracted by 
crystals in very much the same way as x-rays. The electron 
diffraction patterns for metal foils, for example, are formed of 
concentric rings just like the familiar Debye-Scherrer x-ray 
powder photographs, and diffraction by single crystals is observed 
just as it is for x-rays. From the positions of the diffraction inter- 
ference maxima and the lattice spacing of the crystal it is pos- 
sible to deduce the wave length of the waves causing them; this 
is in agreement with the theoretical expression due to de Broglie, 
\ = h/mv, where h again is the Planck constant always associated 
with quanta, m the mass, and v the velocity of the electron. 
Hence electrons behave as though guided by a train of waves. 
Another triumph was registered in 1930 when Dempster proved 
that hydrogen atoms are diffracted by crystals, so that even the 
combination of a proton and electron constituting the corpuscular 
atoms acts as though guided by a train of waves. The dual 
aspect of the ultimate building stones of the universe as waves 
and particles must, therefore, be very fundamental, although it 
is obviously impossible to construct a satisfactory model of 
electrons, radiation, or atoms. Sir William Bragg has indicated 
the situation in stating that we may consider these as particles 
on Monday, Wednesday, and Friday and as waves on Tuesday, 



8 APPLIED X-RAYS 

Thursday, and Saturday. The mathematics of the new quantum 
and wave mechanics so wonderfully developed by de Broglie, 
Born, Heisenberg, Schrodinger, Dirac, and others is alone 
adequate to define the atom, the electron, and radiation. Mean- 
while the astronomer studies the universe of stars and suns and 
planets by the radiation which they emit or reflect ; the physicist 
assigns energy levels to the electrons in the atom from a study of 
the radiation emitted or absorbed characteristically by the atom ; 
the physician uses radiation to diagnose and cure disease; the 
biologist applies it as a vital principle in life processes; the 
chemist uses it to disclose the mysteries of matter and to institute 
chemical change; industry accepts ultraviolet rays and x-rays as 
great new tools of practical value; distance and isolation upon 
the earth are annihilated by long-wave radiation. By their own 
radiations and by means of radiation are all things in the universe 
bringing themselves to the knowledge of men. 



CHAPTER II 
THE GENERATION AND PROPERTIES OF X-RAYS 

Cathode Rays. The complex phenomena involved in the 
conduction of electricity through gases were recognized for half 
a century before the discovery by Roentgen of x-rays. In 1859, 
Plucker discovered that in a highly evacuated glass tube fitted 
with two metal electrodes "cathode rays" proceed in straight 
lines from the negative electrode or cathode. Hittorf made 
further advances in 1869. These rays produced fluorescence 
in the glass walls; they were intercepted by obstacles which 
cast a shadow, and they were deflected by electric and magnetic 
fields. Crookes believed that the rays consisted of negatively 
electrified particles. J. J. Thomson proved this to be the case, 
and found in addition that each of the particles, or electrons, as 
they came to be known, had a mass about one eighteen-hundredth 
as great as that of the hydrogen atom. 

The existence of electrons as the units of negative electricity 
has now been established as a fact by such classic researches 
as those of Thomson, Rutherford, and Millikan, the latter of 
whom by means of measurements with minute oil droplets 
determined the unit charge of the electron to be 4.774 X 10~ 10 
electrostatic units. Cathode rays, or streams of rapidly moving 
electrons, are always identical, regardless of the kind of gas or of 
the material of the cathode. This is but one of the evidences 
that electrons are a fundamental constituent of all matter and 
of atoms. They are spontaneously emitted by the radioactive 
disintegrations of heavy atoms and are called /3-rays. They are 
liberated as photoelectrons under proper conditions when radiant 
energy visible light, ultraviolet rays, x-rays, etc. impinges 
upon matter. Glowing-hot wires produce thermionic emission 
of electrons; heated gases dissociate into electrons and residual 
ions; free electrons course through metallic conductors as a 
flow of electric current. 

Lenard, in 1894, succeeded in bringing cathode rays out of the 
discharge tube through thin foil windows into the outside air, 

9 



10 APPLIED X-RAYS 

The success of the cathode-ray tube perfected by Dr. W. D. 
Coolidge has led to a great increase in knowledge of the physical, 
chemical, and biological effects of these rays. Finally the 
discovery by Davisson and Germer in 1927 of diffraction of 
cathode rays by crystals proved that the difficulties of physics 
in the earlier years of this century were due to ignorance of the 
dual particle and wave aspects of electrons as well as light. 
Generation of X-rays. X-rays are emitted whenever matter 
is bombarded by cathode rays; in other words, the sudden stop- 
page of swiftly moving electrons by the atoms of matter is 
accompanied by the generation of x-rays. In addition to this 
process it will be shown that under certain conditions primary 
x-rays will themselves generate secondary x-rays upon being 
absorbed in matter. The essential parts of an x-ray generating 
apparatus are, therefore, (1) a source of electrons proceeding from 
a cathode, (2) a target or anticathode or anode in the path of the 
cathode-ray stream, and (3) a means of applying a potential 
difference between the cathode and the target which will acceler- 
ate the electrons to the requisite velocity during passage across 
the intervening space. 

?The Properties of X-rays. Many of the properties of x-rays 
are mentioned in Chap. I. For the purpose of a general sum- 
mary of these and as an introduction to other properties which 
will be discussed in detail in later chapters, the following tabula- 
tion, essentially in the chronological order of discovery, will 
suffice. 

X-rays, then, are: 

1. Invisible, and pass through space without transference of 
matter. 

2. Propagated in straight lines. 

3. Unaffected by electric or magnetic fields; hence non- 
electrical in nature. 

4. Reflected, diffracted, refracted, and polarized just as is 
light. 

5. Propagated with a velocity of thirty billion centimeters per 
second, as is light. 

6. Transverse electromagnetic vibrations. 

7. Characterized by wide range of wave lengths (approxi- 
mately 0.01 to 1000 A.U.). 

8. Produced by the impact of cathode rays upon matter. 

9. Capable of blackening the photographic plate. 



THE GENERATION AND PROPERTIES OF X-RAYS 11 

10. Capable of producing fluorescence and phosphorescence in 
some substances and of coloring some stones and minerals. 

11. Able to ionize gases and to influence the electrical properties 
of liquids and solids. 

12. Differentially absorbed by matter. 

13. Able to liberate photoelectrons. 

14. Capable of acting photochemically, of activating catalysts 
in some cases, and of flocculating colloids. 

15. Able to stimulate or to kill living matter. 

16. Emitted in a continuous spectrum, whose short wave- 
length limit is determined only by the voltage on the tube. 

17. Emitted also with a line spectrum characteristic of the 
chemical elements in the anticathode. 

18. Found to have spectra characteristic of the chemical 
elements and of three kinds emission, absorption, and ionization. 

19. Diffracted by crystals acting as gratings in accordance 
with the fundamental equation n\ = 2d sin B, to which a correc- 
tion for refraction must be applied for very accurate work. 

20. Diffracted by optical gratings and totally reflected at 
very small glancing angles. 

21. Found to act in interference and related phenomena as 
waves; but in other phenomena as discrete quanta of energy 
which may be scattered by single electrons. 



CHAPTER III 



X-RAY TUBES 

There are two general types of x-ray tubes which fulfil the 
requirements for generation outlined in the previous chapter. 
In the first type, the so-called gas or ion tubes, the residual gas 
plays an important part; in the second or electron type the tubes 
are exhausted of gas to such an extent that no discharge takes 
place when a large difference of potential is applied. 

X-ray tubes are also classified according to the use to which 
they are put, which in turn depends upon the penetrating 
quality of the rays and the applied voltage. 

TABLE IT. CLASSIFICATION OF X-KAY TUBES 



Class 


Type 


Kilovolts 


1. Special high- voltage tubes 
2. Deep therapy. 
3. Industrial radiography 

4. Diagnostic 


Electron 
Electron 
Electron 
( Electron 
/Ion 


3000 (Lange and Brasch) 
Average 160 to 400 
100 to 300 
Average 50 to 110 


5. Diffract ion 


( Electron 
/Ion 


Average 25 to 50 


6. Superficial therapy or Creiiz ray 


( Electron 
/Ion 


Average 10 



Gas Tubes. The gas tubes were the first to be developed for 
practical use. They still find wide application both for medical 
and for purely scientific purposes, but the electron tubes now in 
operation undoubtedly far outnumber the older type. In the 
gas tube, the gas molecules are split up into electrons and residual 
ions when the voltage is applied. These positive ions are then 
hurled against the cathode by the electric field, so that electrons 
are set free in the bombardment. The cathode-ray stream thus 
generated bombards the positive electrode, or anticathode, and 
the x-rays are produced. 

12 



X-RAY TUBES 13 

The cathode-ray tube used by Roentgen in the discovery of 
x-rays is diagrarnmatically represented in Fig. 1. A flat disk 
served as cathode and the cathode rays impinged upon the 
opposite glass wall with the production of strong fluorescence, 
while the new rays passed through the glass. It is not surprising 
that it was thought that the source of the new rays resided in the 
fluorescence until Becquerel proved that this was not the case. 
The result of Becquerel's study was the discovery of radio- 
activity in 1896, only two months after Roentgen's discovery. 
Roentgen very soon constructed a tube with a special anticathode 
of platinum and a concave cathode for focusing the electron 

dnoafe 

Ccrf h ode 




t Support 



FIG. 1. Diagram of cathode-ray tube used by Roentgen in the discovery of 

x-rays. 

stream. Other tubes had both an anode and an anticathode 
bound together, with the idea that greater stability and less 
pitting of the anticathode would be attained. 

At the present time, several manufacturers in the world still 
supply ion tubes of similar design, with sharp focus for medical 
diagnosis and for superficial therapy: the General Electric 
X-ray Corporation in America, Gundelach in Thtiringen, C. H. F. 
Miiller in Hamburg, Phoenix (Siernens-Reiniger-Veifa) in Thurin- 
gen, Radiologie A. G. in Berlin, Gaiffe, Gallot and Pelon in 
Paris, Cossor in London, and others. Some water-cooled tubes 
may be operated at 25 ma. for harder rays and 40 to 50 ma. 
for softer. Others with special radiation cooling of both elec- 
trodes may be operated momentarily up to 150 ma. The fact 
remains, however, that for medical purposes the electron type 
tube has displaced practically completely the ion tubes, largely 
because the former are free from complications and from the 
dependence of intensity and quality of the x-rays. 



14 APPLIED X-RAYS 

The older varieties of the ion tube were provided with a device 
with which it was possible to add small amounts of fresh gas. 
The "hardness" of the x-ray tube (by which is meant the pene- 
trating quality of the x-rays produced) is determined by the 
amount of the residual gas, since the lower the gas pressure, the 
higher the voltage required for production of x-rays. During 
operation the hardness of the tube increases as the amount of the 
available gas diminishes owing to adsorption on the glass walls, 
etc. Consequently, in order to maintain constancy, gas must be 
admitted by diffusion through thin metal, or by heating or passing 
a spark through a small cylinder of some substance in a side tube. 

Very recently, several modifications of the old gas-type tube 
have been made in Europe and America with such success that for 
many types of investigations of x-ray spectra and crystal struc- 
ture these are competing favorably with the electron tubes. 
Seemann, Shearer, Hadding, Siegbahn, Miiller, Wever, Becker, 
Wyckoff, and others have constructed tubes largely of metal, with 
interchangeable targets (iron, copper, and molybdenum usually), 
thin foil windows, water cooling, and permanent connections with 
vacuum pumps by means of which the gas pressure may be 
readily regulated thus eliminating special devices for controlling 
hardness. These tubes are very simple and rugged and may be 
operated with such large energy that the time of photographic 
exposures is greatly reduced from that normally required. 

Another advantage of great importance for precise spectro- 
scopic and diffraction work is the purity of the spectrum, since it 
has been found easier to build a controllable gas tube than to 
prevent tungsten (from the hot-cathode filament) sputtering in 
one of the electron type. 

Probably the most familiar of the gas-type tubes for diffraction 
is the so-called Hadding-Siegbahn metal tube. Figure 2 shows 
this tube diagrammatically and Fig. 3 shows such a tube produced 
by the firm of Seemann. The body of the tube is entirely of 
metal, which permits self-protection for rays except as they pass 
through windows of thin foil. The entire metal part and the 
target are grounded and connected directly with the water mains 
for cooling. The cathode of aluminum, which is at high poten- 
tial, is insulated through a porcelain cylinder. This cathode may 
be cooled with an insulated water or oil circulating system or 
simply by blowing compressed air through the cooling system. 
Tubes of this type, particularly for operation with copper targets 



X-RAY TUBES 



15 



when long wave lengths are required, have been in successful 
operation in the writer's laboratory for many years. A recent 
improvement in the Hadding-Siegbahn tube as manufactured 
by Leiss is to be found in interchangeable cathodes for operation 





FIG. 2. Diagram of Had- 
ding-Siegbahn gas-type x-ray 
tube used in crystal analysis. 



FIG. 3. Seemann gas-type tube. 



as either ion or electron tube, and a whole series of interchange- 
able metal targets. Four sheets of metal are mounted on the 
four sides of a hollow copper rod with square cross section. By 
rotating the rod 90 deg. the various targets may thus be brought 
into alignment with the cathode. A needle valve is built in as an 



16 



APPLIED X-RAYS 



integral part of the tube. These tubes are ordinarily used with 
rectified high-tension current. Some of these tubes are so 
designed and operated that they are self-rectifying just as electron 
tubes may be, the most familiar being the Shearer tube. 1 A 
similar but even simpler and very efficient self -rectifying gas 




FIG. 4. Wyckoff-Lagsdin gas-type tube with evacuative and regulative 
system. A, anode; /?, glass tube connecting and insulating two ends (4 in. for 
voltage up to 40,000); C, cathode with fins for air cooling; a, interchangeable 
target; e, thin foil window for x-ray beam; D, automatic regulator; E, mercury 
diffusion pump; F, G, rubber connections for leakage; H, flask for increasing 
volume of system. 

tube is that designed by R. W. G. Wyckoff and used almost 
exclusively at the Rockefeller Institute for Medical Research for 
biological, chemical, and physical investigations. It has also 
been found very satisfactory in the writer's laboratory for many 
purposes, particularly for long wave-length studies. Figure 4 
shows the assembly of the tube and the evacuating system. 2 

1 Manufactured by A. Hilgcr, London. 

2 WYCKOFF and LAGSDIN, Radiology, 15, 42 (1930). 



X-RAY TUBES 



17 



For continuous operation over many hours such as is desirable 
in diffraction work, a suitable automatic regulator of gas pressure 




FIG. 5. Detail of gas pressure regulator D of Fig. 4. Automatic regulator 
for gas-type tube. When the iron core n floating on mercury is lifted by the 
solenoid, the mercury level in p drops and connection is established between q 
and r through slots w. Adjustment is made by raising or lowering s and by 
altering the current through the solenoid. 

(and thus of operation) is valuable. Such a regulator constructed 
by Wyckoff and Lagsdin and embodying the best features of 



18 



APPLIED X-RAYS 



earlier models is shown in Fig. 5 with the circuit for operation in 
Fig. 6. 

Electron Tubes. The Coolidge Tube. In the electron-type 
tube it is necessary to have an independent source of electrons, 
since there is insufficient gas present to enable passage of the 
current. For an x-ray tube to operate with a pure electron dis- 
charge it is necessary to evacuate to the highest attainable 
vacuum, usually 0.01 bar or 0.0075/z of mercury. These electrons 
may be supplied by application of the Edison effect, i.e., emission 
from a hot-wire cathode, or by oxides heated on the cathode, by 



Auto- trcxn<s former 




FIG. 6. Electrical circuit suitable for the operation and control of a gas-type 

x-ray tube. 

illumination of the cathode by ultraviolet light, or by LilienfekTs 
autoelectron-emission method. The first of these is the basis of 
the very familiar Coolidge tube which is now being manufactured 
on a large scale for deep therapy, diagnosis, diffraction analysis, 
and superficial therapy. The original Coolidge tube consisted of 
a glass bulb into which were sealed a solid metal target and a 
spiral of tungsten wire backed by a focusing shield of molybdenum 
as cathode. The emitting wire was 0.216 mm. in diameter, 33.4 
mm. long, and wound in a flat spiral of 5% turns with a diameter 
of 3.5 mm. The spiral is heated to incandescence by a current of 
3 to 5 amp. at 1.8 to 4.6 volts supplied in an independent circuit 
from storage batteries or step-down transformers. Under these 
conditions the wire has a temperature of 1890 to 2540 Abs. 
Electrons are liberated, and upon application of voltage to the 



X-RAY TUBES 19 

terminals of the x-ray tube they are drawn across to the target. 
The ordinary commercial Coolidge tubes are usually supplied 
with tungsten or molybdenum targets. In the "universal" type 
the target is not cooled and becomes white hot. 

Most of the electrons in the bundle of cathode rays strike a 
limited portion (1 sq. cm.) of the target called the focal spot 
which is usually visibly defined as a pitted or etched area on the 
target face. The size of this spot is determined by the position 
of the filament in a cylindrical focusing shield of sheet molybdenum. 

The necessity for cooling the target is explained by the follow- 
ing example: at 200 kv. and 3 ma. the kinetic energy of the 
electrons, which have a velocity of 220,000 km. per second as 
they strike the target, is transferred to the target at the rate of 
150 cal./sec., or enough energy in 10 min. to raise a liter of water 
from 10 C. to boiling. Only about 2 per cent of this energy is 
transformed to x-radiation and the remaining 98 per cent goes 
into heat. 

Obviously only metals can be used which will not melt under 
these conditions. In order that the energy may be dissipated, 
special radiators for air cooling are fixed on the end of the target 
arm; for continuous operation and for loads above 1 kw., water 
cooling of the target is resorted to. When the temperature of the 
target is maintained below that at which thermionic emission 
occurs, the terminals of the high-tension transformer producing 
low or moderate alternating voltages may be attached directly 
to the Coolidge tube, for it is then self-rectifying. Current will 
flow only during the half-time period during which the hot wire is 
negatively charged with respect to the target. If the target is 
at a sufficiently low temperature (during the time it is negative), 
there are no electrons available for the reverse current. 

One great advantage of the Coolidge tube is the independence 
of the current through the tube and the voltage. One may be 
altered without affecting the other, while in gas tubes it is obvi- 
ous that the number of the electrons and, hence, the current will 
increase with the voltage. The current in the electron type 
depends upon the number of electrons N, and this in turn depends 
upon the temperature of the hot-wire filament, by the Richardson 
relationship N = CT 2 e~ d/T , where C and d are constants depend- 
ing upon the metal (1.86 X 10 11 and 4.95 X 10 4 , respectively, for 
tungsten), and T is the absolute temperature. On account of 
the building up of a space charge, since the tube current does 



20 



APPLIED X-RAYS 



not increase so rapidly as does the number of electrons when the 
temperature of the filament is increased but the voltage held 
constant, a maximum or saturation current is reached at a point 
expressed by the equation deduced by Langmuir, 



V_2 

47T 



m x' 




Here e and m are the charge and the mass of the electron, V the 

voltage, and x the distance between 
electrodes. This relationship has 
enabled investigators to predict correct 
design for tubes. 

Deep-therapy Tubes. Most of the 
tubes designed for deep therapy to 
operate up to 220 kv. under ordinary 
conditions retain the original Coolidge 
features, namely, glass bulb, spiral 
filament, and massive tungsten target. 
Thifi plate targets enabling more rapid 
dissemination of heat are a more recent 
development (Fig. 7). Some prom- 
inent manufacturers are the General 
Electric X-ray Corporation, Westing- 
house X-ray Company, Allgemeine 
Elektrizitats Gesellschaft (A. E. G.) 
in Berlin, Phoenix in Thliringen, 
Radiologie A. G. in Berlin, Gaiffe, 
Gallot and Pelon in Paris. These 
tubes are pumped to the proper vacuum 
at the factory by the very special 
technique involving pumping, bak- 
ing, and operation under increasing 
voltages in order to remove the 
gas which is occluded in metal 
parts. 1 Such tubes fail very often 
from development of gas during operation and large currents 
begin to pass. Even if the operation is normal, however, with 
good care there is a limit to the life. The glowing filament 



FIG. 7. Deep-therapy tube 
of conventional design with thin 
plate target ( Westinghouse) . 



1 See TERRILL and ULREY, " X-ray Technology, " pp. 49-54, D. Van 
Nostrand Company, New York, 1930. 



22 



APPLIED X-RAYS 



vacuum tight and can be fused with glass. A photograph and 
diagram of a Metalix tube are shown in Fig. 9. These may be 
obtained in various sizes up to 240 kv. at 8 ma. with water cooling. 








-c 




D 



FIG. 9. Photograph and diagram of construction of the Metalix tube, 
showing the central chrome-iron cylinder to which the glass anode and cathode 
arms are fused. 

The familiar Miiller Metwa therapy tube is similar to the Coolidge 
design except that the bulb is replaced by a chromium-steel 
cylinder. These tubes provide radiation in the desired direction 
only and require no special mountings and protection. 



X-RAY TUBES 23 

Special Tubes for Very High Voltages. There are many points 
of interest in operating x-ray tubes at increasingly higher voltages. 
Since the effective wave length decreases as the voltage increases, 
the point might be reached where x-rays in the wave-length range 
of 7-rays or even cosmic rays might be generated with an output 
equivalent to thousands of grams of radium or with millions of 
times greater intensity than observed for cosmic rays. The 
advantage in therapy and in biological action is obvious, even 
supposing that the kind of biological action might be anticipated 
as independent of wave length. The intensity of radiation in the 
voltage range of modern deep therapy with usual filtration 
increases with a high power (at least third) of the voltage. The 
gain in intensity with mounting voltage and constant current 
makes possible material reductions in time of irradiation even 
with stronger filtration and increased distance from focal spot to 
patient, and a far higher percentage depth dose is attained. The 
physicist is also interested in the spectra of radiation excited at 
the highest attainable voltages and in the test of theories of 
atomic structure. 

Serious difficulties have been encountered, however, in attempts 
to operate x-ray tubes of usual design at voltages very much 
higher than 220,000, not because power plants are not available, 
since 1,000,000 volts can easily be attained in commercial 
machines, but because of electrical phenomena within the tubes 
which prevent a satisfactory "life." In the first place the auto- 
electronic effect, or the release of electrons from metallic points or 
sharp edges in the electric field, produces a discharge in the tube 
operated above a critical voltage. Momentary currents of 
several amperes may pass, followed by high-frequency electric 
oscillations which may result in ruin of the transformer and of the 
x-ray tube, especially if the discharge strikes the glass walls. 
In less severe cases, the natural distribution of potential along 
the tube is affected and gas is liberated from the glass walls in 
certain areas. This difficulty may be counteracted, so that 
higher potentials may be applied safely, by careful rounding of 
the cathode. 

The second group of phenomena which introduces difficulties 
is the back diffusion of electrons from the anode to the inner glass 
walls which become negatively charged. Next the outer glass 
wall becomes charged almost to the potential of the cathode, so 
that a high difference of potential is set up between the glass and 



24 



APPLIED X-RAYS 



the anode. A stream of ions will travel from the anode, through 
the glass, then through the air to the metal anode cap. It has 
been demonstrated that gaseous electrolytic products are liber- 
ated as a result of the passage through the glass of the current, 
even though smaller than 10~ 5 amp. The result again may be 
destructive discharge, depending on the potential and also the 
current. In order to avoid these effects so that a tube may 





Fio. 10. Design of electrodes in new 400-kv. deep-therapy tube (Siemens- 
Pan tix). 

operate with safety, the glass must be shielded from the second- 
ary electrons. 

A new commercial Siemens-Pant ix deep-therapy tube just 
announced to operate at 400 kv. effective and 5 ma. embodies the 
rounded cathode and the shielded anode in a highly satisfactory 
manner. 1 The design of the electrodes is shown in Fig. 10, and 




Fio. 11. Siemens-Pantix 400-kv. deep-therapy tube with protective rings on 

caps. 

the tube itself with protecting rings on the metallic caps is illus- 
trated in Fig. 11. These rings involve the principle of a sphere- 
gap in which discharge takes place at higher potentials than 
between points (or small diameter caps) at the same distance. It 
is possible therefore to cut down the over-all length of the tube, 
particularly since the glass really serves as an insulator when the 
secondary electrons are screened off internally. 

1 MILLER and ZIMMER, Fortschritte auf dem Gebiete der Rontgenstrahlen, 
46, 341 (1932). 



X-RAY TUBES 25 

Within the past year unusual interest has been aroused by the 
high- voltage tubes constructed by Lauritsen 1 at the California 
Institute of Technology (600,000 volts and one more recently 
to operate at 1,200,000 volts); by Coolidge 2 for the Memorial 
Hospital of New York (900,000 volts) operating by the cas- 
cade method (three steps of 300,000 volts each); by Tuve and 
associates 3 at the Carnegie Institution in Washington who used 
15 cascades to attain nearly 2,000,000 volts; by Lange and Brasch 4 
of Berlin (2,600,000 volts). The first three employed the usual 
principles of tube construction including hot-filament cathode, 
but with great length and special types of insulation with con- 
ducting rings. The German physicists succeeded in building a 
tube of alternate rings of paper, rubber, and aluminum which has 
been tested at 2,600,000 volts, continuing for an interval of a 
millionth of a second. Electrons are so speeded in this tube that 
they drill holes an inch deep in a brass plate. The x-rays pro- 
duced penetrate lead a yard thick. 

The new x-ray tube is less than a dozen feet long, despite the 
high voltage it withstands. It is estimated that an ordinary 
x-ray tube to withstand such voltages would need to be 50 ft. 
long. 

In their work on the new-type x-ray tube Lange and Brasch 
discovered that the most effective tube is short and crooked, so 
as to break up surface leakage. For this reason they made the 
doughnut-like layers of paper insulation, rubber, and aluminum 
of different diameters inside. 

Instead of using a hot-cathode source of electrons to be speeded 
up in the x-ray tube, the scientists actually obtained sufficient 
electricity for their purpose from a small porcelain tube, normally 
regarded as an insulator. 

In Berlin a new 7,000,000-volt surge generator is being built 
to be used with a Lange-Brasch tube. This tube will be devoted 
to cancer research and physical experimentation. It is planned 
even to impress upon such a tube the high potentials of the 
natural electrical discharges in thunderstorms (these experi- 
menters have already measured discharges in the mountains of 
16,000,000 volts) ; if successful, there will be produced gamma rays 

l Phys. Rev., 32, 850 (1928); 36, 988, 1680 (1930). 

2 Am. J. Roentgenology, 19, 313 (1928); 24, 605 (1930). 

3 Phys. Rev., 35, 66, 1406 (1930). 
* Z. Physik., 70, 10 (1931). 



26 APPLIED X-RAYS 

equivalent to a hundred thousand grams of radium, which is at 
least a thousand times as much radium as there is now available. 
When this experiment is performed, the super-x-rays obtained 
will equal the cosmic rays in penetration and the experiments 
projected should settle the question of the nature of the cosmic 
rays. 

Spectra and biological effects from the 600,000-volt tube in 
Pasadena have thus far shown no unexpected or anomalous 
results. 

Fine-focus Tubes for Metal Radiography. For deep therapy 
a broad focus is usually desired but such a beam does not give 
good definition for photographic purposes. With the great 
increase in the industrial application of examining heavy metal 
castings, etc., for interior defects, high-voltage rays are required 
for penetration but with fine focus. The finer the focus (the 
smaller the focal spot), the more intense the localized energy 
effects in metal targets and the more serious the cooling problem 
becomes. Such tubes for metal radiography as a special class of 
the so-called deep-therapy division are now available for con- 
tinuous operation at 240 kv. at 8 ma. The new 400-kv. tubes 
also should have excellent use in this field. 

Diagnostic Tubes. The essential attributes for this type of 
tube are as follows: 

Very sharp definition of photographs or shadows of objects in 
the x-ray beam. 

Fine focus (small focal spot). 

Intermediate voltage (50 to 110), minimum wave lengths 0.25 
to 0.11 A.U.). 

Large currents for high intensity and greatest rapidity. 

Coolidge concentrated the electron beam by means of a hemi- 
spherical shell of nickel about 25 mm. in diameter around the 
tungsten filament instead of the molybdenum cylinder used in 
deep-therapy and "universal" tubes. The anode was cooled 
either by radiation from external copper fins or by water cooling. 
The problem is, of course, the protection of the target while the 
largest possible current and the finest possible focus are 
maintained. The latest tube of conventional design for fluoro- 
scopic work (Fig. 12) requires no radiator, since the target is a 
disk of tungsten with maximum surface. 

The newest developments in construction of these diagnostic 
tubes, which apply also in general to the tubes used for diffrac- 



X-RAY TUBES 



27 



tion with which this book is primarily concerned, may be sum- 
marized as follows : 

1. Tubes of the usual Coolidge type with glass bulb and water 
or even radiator cooling through which currents of 150 ma. may 
be passed for 1 sec. are now fairly common (Fig. 13). 




FIG. 12. FIG. 13. 

FIG. 12. Fluoroscopic tube of conventional design (Westinghouse). 
FIG. 13. Air-cooled diagnostic tube (General Electric) . 

2. "Dofok" tubes (Phoenix tubes of Siemens-Reiniger-Veifa 
and also General Electric Coolidge tubes) have two hot spirals in 
the cathode, the one for fine focus and lower loads, the other for 
larger focus and higher loads. 

3. Tubes with elongated focal spot for fine focus but high 
intensity. The desire to increase the load and intensity of 
x-radiation from such tubes in order to cut down exposure time 
to a minimum is opposed by the fact that greater energy input 



APPLIED X-RAYS 



in a small focal spot results in melting and destruction of the 
target. Increase in size of the focal spot in all directions causes 
diagnostic photographs to lose sharpness. Hence it is necessary 
to change the focus so that the cross section through the x-ray 
bundle at the focal spot is as small as possible. The line-focus 
filament of Goetze employed in the Media tubes of Mliller is a 
successful solution. A long cylindrical spiral of very small 



Appearance on the 
anode surface 




Appearance in the direction 
of the primary becrm 



^_ k p nmc ,ry beam 




FIG. 14.- Diagram showing operation of a line-filament cathode. 

diameter produces a line focal spot on the target which by virtue 
of length can take up a very considerable amount of energy 
without damage to the target. The face of the target is inclined 
at an angle of 71 deg. to the tube axis, so that the line focal spot 
in the principal direction of emergence of the x-rays appears 
shortened to a small point. The focal spot is actually about 2 
mm. wide and 16 mm. long but from the front appears fore- 
shortened to a spot 2 mm. square (Fig. 14). The 10-kw. Media 



X-RAY TUBES 29 

tube is rated at 250 ma. at 40 kv. effective for 1 sec. or 370 ma. at 
40 kv. for 0.1 sec. 

Another modification which serves a similar purpose is the oval 
focus of Kiese wetter. The "XP" General Electric tubes have a 
20-deg. anode and an elongated focal spot as introduced by 
Benson in 1916. 

4. Cone targets. For large current capacities but fine defini- 
tion a Philips tube uses a target with cone-shaped hole. The 
filament is made of 1 J< turns of wire and of sufficient diameter for 
x-rays to pass back through it. The electron stream is focused 
into the conical recess in the target with its larger surface but 
small effective focal spot. 

5. Autofocus tubes of Mtiller are unique in that the focal spot 
automatically becomes larger as the current is greater. A small 
metal rod through the middle of the spiral filament is connected 
directly with the negative high-tension terminal, while the filament 
is connected through a high resistance so that the rod is always 
at negative potential to the filament. Depending upon this 
difference of potential determined by the tube current, the elec- 
trons will be repelled and thus increase the focal-spot area. 

6. The ro tat ing-anode tube (Philips Metalix) is a very recent 
and notable attempt to solve the problem of large energy input 
without damage to any one spot on the target. The anode, a 
heavy body of copper, forms the rotor of a small induction motor 
whose stator is a wound ring surrounding the tube. Anodes 
mechanically rotated through tight bearings have also been 
described. 

7. Special tubes, particularly for dental radiography where 
they must be brought close to a patient or specimen, have the 
electrodes at right angles. Lead glass bulbs may have a window 
of ordinary glass opposite the target, and at 40 to 50 kv. this is 
sufficient protection. 

8. Self-shielding tubes. For diagnostic purposes it is particu- 
larly desirable to eliminate the non-focal x-rays arising from 
portions of the anode outside of the focal spot and constituting 
10 to 15 per cent of the beam. Coolidge was the first to solve 
the problem inside the tubes by surrounding the target with a 
molybdenum cylinder with two openings, one for the cathode 
rays and one for emergence of the x-rays. In this manner the 
diffuse cathode rays producing the extraneous rays were screened 
off and at the same time all the rays in directions other than that 



30 



APPLIED X-RAYS 



desired. The target cap has been frequently used in commercial 
tubes. The General Electric X-ray Corporation self-shielding 
tube is rated at 100 ma. at 85 kv. for 10 sec. or 350 ma. at 55 kv. 
momentarily. Mliller tubes are protected by an outer housing 
(Pertinax) and the rays emerge from a small window. The 
Philips Metalix tubes with chrome-steel cylinder and the Miiller 




ode stem 



^ Target 

,'E/ectron 
V S+reatm 

Focus/ng 
cup 



-Radiation 
w/nofow 

FIG. 15. FIG. 16. 

FIG. 15. Photograph of new Westinghouse radiographic tube. 
FIG. 16. Diagrammatic construction of tube pictured in Fig. 15. 

Media Metalix tubes are similar in design to the therapy tubes 
and are very successful for medical purposes. The new General 
Electric XP tubes have an independent cylindrical lead sheath 
and interchangeable water- and air-cooled radiators. 

9. Helium- and neon-filled tubes. Following experiments by 
Janitsky, the Mliller tubes of all varieties contain a small amount 



X-RAY TUBES 



31 



of helium gas which is admitted after the tubes are exhausted 
and degassed. Westinghouse tubes contain neon. This gas, as 
well as helium, does not disappear upon operation of the tube 
like air and its high ionization potential prohibits action as an 
ion tube, while at the same time it permits pressure and operation 
to remain constant over long periods of time. 




FIG. 17. End window of Westinghouse radiographic tube showing ring filament 
through which x-rays from target pass. 

10. "Gun "-type tubes. Westinghouse radiographic tubes 
have a unique construction in which the x-rays pass back through 
a ring filament and out of a window in the end of the tube, as 
illustrated in Figs. 15, 16, and 17. Pyrex glass is used throughout. 

Diffraction Tubes for Fine-structure Examination of Materials. 
In this great new branch of x-ray science the diffraction of rays 
by a suitable grating is used as a means of discovering the 
ultimate fine structures of crystals and materials of all kinds. 



32 APPLIED X-RAYS 

While it was found that for determination of the gross struc- 
ture of materials the medical deep-therapy or diagnostic tubes 
could be used, special attributes are desirable in tubes for 
studies of fine structure. 

Moderate voltages, 25 to 50 kv. 

Largest possible tube currents so as to cut down exposure 
times. 

Continuous operation, since diffraction photographs may 
require many hours or days. 

Medium or fine focus. 

Small dimensions so that distance from target to specimen may 
be a minimum. 

Minimum absorption of beam in desired directions. 

Target usually not tungsten, but molybdenum, copper, iron, 
etq., and preferably easily interchangeable. 




FIG. 18. Cooli'to*' jpe diffraction tube (General Kloctru-y. 

Multiple bearr^ ii'om same target for routine examination of 
numerous specimens ; hence flat target at right angles to cathode- 
ray beam, from which rays at grazing angles may be defined 
radial 1 /. 

..Numerous modifications of the hot-cathode tube have been 
made, largely aimed at making it more adaptable for use in x-ray 
diffraction work with crystals, where interchangeable targets, 
small dimensions in order to approach as closely as possible to 
samples and spectroscopic apparatus, and general flexibility 
and ruggedness are required. Some are constructed largely 
of metal, some of quartz, and some of porcelain. The Coolidge 
water-cooled molybdenum-target tube with glass bulb is very 
generally used, in x-ray crystallographic investigations. It is 
shown in Fig. 18. The design has been carefully developed 
to meet many conditions which are excellently outlined in a 



X-RAY TUBES 33 

paper by the inventor W. D. Coolidge 1 with a later improve- 
ment due to Davey in which electrodes are brought much 
closer together. This tube is operated usually at 30,000 volts 
and at 20 to 30 ma. It may be connected directly with the 
alternating-current high-tension transformer. It is most con- 
venient to have the positive-target end of the tube and the end 
of the transformer secondary at earth potential so that direct 
connection may be made with the water mains. A positive 
potential, however, may be applied satisfactorily with an insulated 
water system (Ford radiator and pump, thermosiphon, etc.), or 
even by connection with the water mains through an insulating 
column of water in glass or rubber tubes from 40 to 60 ft. long for 
ordinary city water. Since the target of this tube is perpendicu- 
lar to the axis of the tube, the latter may be placed with the long 
axis perpendicular, and the x-rays emitted at grazing angles 
from the target may be defined radially around a complete circle. 
Hence, as many as 18 or 20 diffraction photographs may be 
taken simultaneously around one tube. It will operate con- 
tinuously under practical conditions for several thousand hours, 
although the life of some tubes is less than this. Somewhat 
longer life is obtained by the use of rectified high tension and by 
intermittent use. After a time gas develops and the tube must 
be repumped or entirely rebuilt if the filament has burned out. 
A water pressure of 20 or 30 Ib. is maintained, and it is essential 
to have automatic cutout switches (the "Mercoid" type is best) 
to save the tube should the water supply fail. A ball-valve 
shut-off in the line can be used very satisfactorily if the pressure 
becomes too large and threatens to burst any rubber-tubing 
connections in the water-cooling system. 

The best features of the diagnostic tubes in which require- 
ments are similar have been embodied by various manufacturers, 
particularly Miillor, Philips, and Seemann in diffraction tubes of 
the electron type. The most important of tht.se are as follows: 

1. Line-focus filaments for great intensity and sharp focus. 
In such a tube tw r o diffraction photographs may be made simul- 
taneously with opposite beams from the line focal spot on a target 
at right angles to the cathode rays. 

2. Cross-focus filament (Mtiller) which has the same 
advantages as the line-focus type but four equally intense 
beams may be defined at right angles. Figure 19 shows the 

1 J. Franklin Inst., 199, 619 (May, 1925). 



34 APPLIED X-RAYS 

Muller cross-focus tube for structure determinations. Four 
windows of Lindemann glass (containing boron, lithium, and 
beryllium instead of silicon, sodium, and calcium in ordinary 
glass), through which the beam passes with little absorption, thus 
permit the study of four specimens simultaneously. 

3. Demountable tubes. Besides the several varieties supplied 
by the manufacturers already pumped and permanently sealed 
off, it is convenient to be able to interchange targets in the same 
tube for diffraction research and particularly for spectroscopic 
analysis in which the unknown substance must constitute the 
target and must be mounted or pasted on a suitable backing. 
This, of course, means that such tubes must be pumped during 
operation. To one skilled in high-vacuum technique this does 
not present great difficulty, since equipment combining oil- 
backing pump, mercury-diffusion pumps in one or more stages, 
and liquid-air traps is well standardized. 




Fio. 19. Muller diffraction tube with cross-focus filament and four Lindemann 

windows. 

Several tubes made largely of metal are in the market and many 
have been designed and built in various laboratories. As prob- 
ably the best examples of such a tube are the new Siegbahn 
tube made by Carl Leiss which may be operated as either an 
electron or an ion tube, and the Ott-Selmayr tube. A photo- 
graph of one of the latter in the writer's laboratory is presented in 
Fig. 20. The body of the tube is essentially a heavy triangular 
block of metal into which the electrodes are fitted at an angle of 
120 deg. The cathode arm is of glass and the filaments inter- 
changeable spiral or line focus. The targets of various metals 
are easily removable and interchangeable. The window of thin 
aluminum (or, better, beryllium) foil is only a few millimeters 
from the focal spot and the specimen for structure analysis can 
thus be placed very close to the target. The result is a tube 
which provides radiation of extremely high intensity. 1 

' l For a description of this tube with improvements see Clark and Corrigan, 
Ind. Eng. C^m., 23, 815 (1931). 



X-RAY TUBES 



35 



4. High-intensity tubes. X-ray apparatus and technique 
have been passing rapidly through the stage of development and 
improvement within the past very few years. The diffraction 
method of testing materials has been expensive, not only on 
account of the initial expenditure for equipment but also because 
of the time required for photographing a diffraction pattern 
sometimes many days and always many hours. Part of the 
difficulty was alleviated by construction of multiple apparatus, 
such as the familiar and excellent General Electric unit with 




liu. liU. rtiutogntph of installation of high-intensity diffraction tube (Ott- 
Selmayr type) at the University of Illinois. 

which 12 or more exposures can be made simultaneously from the 
same x-ray tube. This time factor, however, has precluded the 
possibility of using the diffraction method as an industrial control 
or for exhaustive studies of uniformity. Furthermore, it has 
been impossible to use specimens undergoing change over rela- 
tively short periods of time, unstable compounds, or specimens at 
very low or at high temperatures. A very logical development, 
therefore, has been directed toward the designing of x-ray tubes 
which will produce beams of so much greater intensity that times 
of exposure can be materially reduced. 

Several workers in the diffraction field have recorded results 
obtained in very short periods of time. Ott published a descrip- 



36 APPLIED X-RAYS 

lion of a high-intensity tube mentioned above in 1926. l In 
October, 1929, Mark and von Susich 2 published typical results 
obtained with this tube in fraction of seconds, e.g., a single crystal 
of pentaerythritol in 0.1 sec., diamond in 0.04 sec., and the 
progress of mercerization of cellulose at 1-min. intervals. See- 
mann and Schotzky 3 pointed out that as early as 1916-1917 
Lane had shown with a Seemann x-ray tube "a complete spectral 
diagram" could be seen without difficulty on the fluoroscope. 
They showed moving picture films where the exposure times 
were /iso sec. and oscillograms for times as little as }2500 sec. 
Later the same authors 4 showed that the direct beam of the x-ray 
tube could be recorded on a film with an exposure time as short 
as 1/1,200,000 sec. with an x-ray oscillograph. 

The purpose of investigations in the writer's laboratory has 
been to discover whether such tubes as the Ott-Selmayr described 
above are actually practicable for use in the x-ray research 
laboratory devoted to fine-structure studies, whether they are 
easily constructed and economically operated, whether they 
make possible fields of investigation otherwise impossible, and 
whether they may be expected to displace the more familiar 
types. 

Some of the more typical experiments, selected at random 
are as follows: 

1. The first indication of this tube's extreme intensity came 
while the tube was first being tested out. A thick piece of lead 
glass with a fluorescent screen behind it was placed in front of 
the window for protection and to observe the intensity of the 
beam. After operating for some time it was noticed that a 
brown spot had appeared on the glass at the point struck by the 
ray. When another spot was exposed a colored area the full 
size of the window was obtained in l hr. and a very distinct spot, 
the size of the focal spot, was obtained in a few minutes. 

2. It was found that an ordinary fluorescent screen, ordinarily 
free from all after effects, would glow brightly for several minutes 
after the ray was turned off. 

3. Lane patterns of calcite were obtained in 0.5 sec. even with a 
precision pinhole system only 0.020 in. in diameter. 

l Physik. Z., 27, 598 (1926). 
tNaturwixsenschaJten, 17, 803 (1929). 

3 Naturwissenschnflcn, 17, 960 (1929). 

4 Naturwissemchaften, 18, 85 (1930). 



X-RAY TUBES 37 

4. Several independent observers have been able to see Laue 
patterns clearly on the fluorescent screen without special prep- 
aration of the eyes by remaining in the dark. An obvious 
extension is visual observation of changes in the patterns with 
physical or chemical changes in the specimen. 

5. Diffraction spectrograms of wool (whose crystallinity is 
only very rudimentary) requiring on the average 4 to 5 hr., and 
in some cases as much as 12 hr. with other tubes, were obtained 
in 10 min., and in some cases in as little as 2 min. In addition 
these pictures, which are very difficult ordinarily to measure, 
were found to be clear and sharp, and in every case the exposure 
was accompanied by far less fogging and general scattering than 
with the other tubes. The central spots due to incipient fiber 
structure as a result appeared more clearly, and changes in these 
central spots could be followed more easily. 

6. Liquid paraffins were investigated by cooling down and 
taking a short exposure. Clear pictures were obtained in inter- 
vals short enough to neglect the warming up of the sample. 

7. The disintegration of a sugar crystal through the liquid 
phase and its subsequent charring to carbon was followed on a 
strip of moving picture film. This crystal was mounted on a 
brass pinhole and the brass heated with a hand torch. In spite 
of usual difficulties attending the use of motion picture film, as 
mentioned above, the successive patterns showed a disappearance 
of the Laue spots as the temperature was raised, on account of 
the thermal agitation of the molecules, to a point where no pattern 
appeared though the outer form of the solid crystal still was 
maintained; then followed the appearance of a liquid type of 
diffraction pattern, upon melting, which gave way to a pattern 
characteristic of carbon upon charring. 

Numerous problems carried out under these most promising 
conditions suggest themselves and are under investigation. 
Meyer and Mark have shown how the mercerization process in 
cellulose takes place step by step by the use of a high-intensity 
tube. Other problems are: 

1. Efflorescence, deliquescence, dehydration, etc., of crystals stepwise. 

2. Unstable compounds such as KI 3 for which patterns can be made in a 
few minutes, long before disintegration; phase rule studies of unstable 
alloys. 

3. Crystals, tissues, and any other type of substance cooled to liquid-air 
temperature can be studied before sufficient warming has taken place, 
without special or complicated apparatus. 



38 APPLIED X-RAY R 

4. Any type of chemical reaction taking place over seconds or minutes 
followed as to velocity and mechanism, such as vulcanization of rubber, 
xanthogenation, nitration, methylation and acctylation of cellulose, poly- 
merization of resins, setting of cements and plaster, etc., oxidation, ozoniza- 
tion and photochemical changes of plastics, rubber, varnish, and patent 
leather. 

5. Steps in any process of heat treatment, as annealing of metals, and the 
mechanism of recrystallization; changes with gradual application of deform- 
ing forces. 

6. Transitions between solid and liquid at melting points, appearance of 
anisotropic liquid phases, allotropic transformations, etc. 

7. Experiments on structures of fresh and living tissues such as those of 
("lark, Bucher, and Lorcnz, and of Boehm and Schotzky. 1 Patterns of 
living electrically contracted frog muscle (excited by an applied voltage 
to tetanus contractions) on account of the long exposure necessary have 
been procurable at great sacrifice. As each muscle remains fresh only 
3-2 min., several hundred muscles have been required. With special tubes 
it has been possible to obtain photographs with a total of 2 to 6 min. with 
only 6 to 12 muscles. 

Superficial Therapy and Long-wave-length Tubes. Skin 
reddening or erythema develops much more rapidly with very 
soft x-rays than with rays of the usual range of hardness. Hence 
a logical development has been the design of tubes to operate 
at only 8 to 10 kv. corresponding to wave lengths of 1.2 to 2.0 
A.U. On account of the great ease of absorption these tubes 
were successful only after the development of windows of 
Lindemann glass and of cellophane. Medically, the soft rays 
are known as Grenz rays for no particularly good reason. The 
tubes involve no unusual features of construction except in so 
far as the small dimensions are concerned. The Miiller tube 
employs the cylindrical chrome-steel body of the tube as anode 
and the Lindemann window is thus directly opposite the cathode 
filament, which is screened off by a metal shield directing the 
electrons to the side walls. 

Rays with long wave lengths have great interest from the 
standpoint of spectroscopy and atomic structure, and more 
recently for diffraction studies where very large grating spacings 
are involved. Clark and Corrigan 2 have constructed an x-ray 
tube and camera in a single unit for operation in vacuum, with a 
magnesium target supplying rays with a principal wave length of 



1 See Chap. XX. 

2 Lnr rif 



X-RAY TUBES 



39 



9.86 A.U. For special studies of natural materials such as 
cellulose, rubber, and insulin, new information concerning 




FIG. 21. Long-wave diffraction tube (magnesium target) with integral 
camera (Clark and Corrigan). 1, body of tube and camera; 2, cathode; 3, 
pinhole system; 4, film holder; 5, camera sliding into 1. 

structure has been obtained which will be considered in Chap. 
XX. The long- wave diffraction tube is pictured in Fig. 21. 



CHAPTER IV 
HIGH-TENSION EQUIPMENT 

Of the various methods of producing the difference of potential 
across an x-ray tube, the alternating-current high-tension trans- 
former is now of greatest practical importance. Static induction 
machines and induction coils operating on direct current with 
interrupters were used widely for many years after the discovery 
of x-rays. The latter are still to be found in many laboratories 
and hospitals, particularly where gas tubes operated at moderate 
voltages are used. 




FIG. 22. 100,000-volt storage battciy m Crult Laboratory, Harvard University. 

Storage Batteries. The high-tension storage battery is, of 
course, the ideal source of power, since the voltage across the 
tube remains perfectly constant and no rectifying devices are 
required. Storage batteries have the disadvantages of being 
very expensive, difficult properly to insulate, and dangerous to 

40 



HIGH-TENSION EQUIPMENT 41 

the operator, since very large currents may be instantaneously 
drawn from them, and of requiring constant attention. A 
43,000-volt storage battery made from test tubes gave excellent 
results for more than twenty years at Harvard University. With 
it the precision researches on x-rays by Duane and his students, 
particularly the most accurate evaluation of the Planck constant 
h, were made possible. 1 A new 100,000- volt plant (Fig. 22) with 
the cells in pint jars has much greater capacity and every possible 
improvement. This battery will operate a tube for two weeks 
before recharging is necessary. 2 

Transformers. The usual modern equipment includes a 60- 
cycle oil-immersed transformer stepping up an alternating 110- or 
220- volt current to the required high tension. The secondary 
voltage is controlled by regulating the primary-current input by 
resistances, autotransformers, or combinations of the two. 
For a filament-heating current in Coolidge type tubes, the trans- 
former may contain a separate winding which will step down the 
primary voltage. For moderate voltages between 30 and 60 
kv., the electron tube can rectify the alternating voltage, as 
explained in the description of the tubes. Usually under these 
conditions the positive terminal of the x-ray tube and one end 
of the secondary of the transformer are grounded. Most of the 
x-ray power units on the market are designed for therapeutic and 
diagnostic use at voltages up to 250 kv. These commercial 
machines are all similar in general operation but differ in details 
of design, They usually include : 

A 60-cycle 110- or 220- volt alternating-current closed-core 
high-tension transformer. 

A separate transformer for filament current (insulated storage 
batteries may be used). 

An autotransformer for controlling input. 
A device for stabilizing and controlling the tube current. 
A device for rectifying the alternating high-tension current, 
of either a mechanical or electron-tube type. 

Rectifiers. Mechanical Type. The mechanical full-wave 
rectifiers are cross-arm arrangements revolving on the shaft of 
the alternating-current generator or driven by a synchronous 
motor. This rotating switch connects the terminals of the 

1 /. Optical Soc. Am., 5, 213 (1921). 

2 A complete description of the installation is given in a paper by Arm- 
strong and Stifler, /. Optical Soc. Am., 11, 509 (1925). 



42 



APPLIED X-RAYS 



secondary alternately to opposite ends of the x-ray tube in 
synchronism with the alternations of the current. Only a 
portion of the top of these waves is applied to the x-ray tube, 
since the contacts are intermittent. The tube is, therefore, 
r excited by pulses which are alike (see Fig. 25) . 

* Kenotron Type. The Kenotron electric 

valve, which is a familiar type of electron-tube 
rectifiers, is a vacuum tube operating on the 
same principle as the x-ray tube. In one 
type a tungsten- wire filament is at the center 
of a coaxial cylinder of sheet molybdenum. 
The filament is heated by a current from 
storage batteries or step-down transformers. 
Current passes through the valve, of course, 
in one direction only, since the hot wire is the 
only source of electrons. During the time 
of flow of current from hot cathode to anode, 
a difference of potential of only a few hun- 
dred volts at the most exists. During the 
other half period when the cathode is positive- 
ly and the anode negatively charged, the 
entire difference of potential on the x-ray tube 
is impressed on the valve tube, so that it must 
be constructed to withstand this. In another 
type the filament consists of three or more 
hairpin loops of wire and the anode is a cup 
or disk. The filament heating current is 7.8 
to 8.2 amp. at 12 to 14 volts and such a tube 
passes a current of 300 to 400 ma. Glass 
tubes are made by all the prominent 
manufacturers. The new Miiller Metalix 
valve tube (Fig. 23) has two metal cylinders 
which are fused on both sides of an insulating 
PIG. 23. M u 1 1 c r glass cylinder. The upper metal cylinder 
Metalix valve tube. serves as ano d e w i t h radiator fin cooling. 
The heating voltage is 15 volts and the emission at 8 amp. passes 
600 ma. or at 8.5 amp. 1100 ma. A new valve tube (Siemens- 
Supra) for operation at 400 kv. is illustrated in Fig. 24 as it 
appears in a complete power plant. The anode is carefully 
rounded, the filament has a protecting spool, and the end caps 




HIGH-TENSION EQUIPMENT 



43 



have the protective rings. The elongated oval glass bulb is also 
an important feature. 

Numerous types of circuits involving transformers and valve- 
tube rectifiers with auxiliary equipment are employed for various 
x-ray purposes (Fig. 25). Some of the more important may be 
listed as follows : 

1. Self-rectifying Coolidge type x-ray tube; half-wave recti- 
fication; for diffraction and other equipment up to 60 kv. where 
loss in power is not so important as simplicity and economy. 




FIG. 24. 550-kv. power plant showing 400-kv. valve tubes in position with 
protecting rings (Siemens). 

2. Single Kenotron; half -wave rectification; with or without 
condensers gives impulses; for use with gas- or ion-type tubes 
up to 80 kv. primarily. A unit of this type is shown in Fig. 26. 

3. Two Kenotrons; full- wave rectification. The circuit is 
shown in Fig. 25 with condensers. If two opposed Kenotrons 
are connected to the end of the transformer secondary whose 
potential is oscillating between +V and V then the total 
difference of potential across the plates of the condenser and 



44 



APPLIED X-RAYS 



LWWWVWW 

-wvwww 



WVWWWAr 1 



fens ion 
transformer 



X-ray tube 



n 



Time 




Voltage On transformer 

Voltage on tube during 

passage of current 

(A) Circuit for Self-Rectifying 
X-Roiy Tube (Half-Wave) 



Time \ I 



Voltage on transformer 

Voltage on tube during 

passage of current 

(B) Circuit with One Vcifve Tube 
(Half-Wave) 



High tension 
transformer 

s/vwwwvw 

I VWWWW 




Voltage on transformer 

Voltage on tube 



(C) Circuit with Mechanical Rectifier 

FIG. 25. Diagram of various x-ray machine circuits showing wave form produced. 



ime 

Vr 8 Transformer voltage 
V c * Voltage on condenser 
V R Tube voltage 

(D) Constant Potential Circuit 
with Two Valve Tubes 



HIGH-TENSION EQUIPMENT 



45 




Fio. 26. Photograph of Standard power plant with single Kenotron used in 

diffraction work. 




Fio. 27. Power plant for producing radiographs in ^{20 sec. at 1000 ma. 

(General Electric). 



46 APPLIED X-RAYS 

the terminals of the x-ray tube will be +V ( F) = 2V. 
The rectifiers must be able to withstand this voltage. Four 
Kenotrons give better performance. Figure 27 shows a Victor 
four-Kenotron apparatus with which radiographs in ^20 sec - 
at 1000 ma. are obtained. 

4. The most desirable is obviously a constant-potential 
direct-current (c.p.d.c.) machine. Only with such a condition 
is it possible to reproduce accurately dosages in therapy or to 
conduct scientific researches of the highest accuracy. Voltage 
and current ripples are smoothed out to less than 1 per cent. 
This is accomplished with 2 or 4 Kenotrons, a 500-cycle (or 
more) primary current, and condensers whose correct capacity 
depends upon the frequency. A highly satisfactory c.p.d.c. 
installation due to Duari^ at the Huntington Memorial Hospital 
in Boston operates on 20100 cycles with condensers of 0.0081-mf . 
capacity. With 60-cycle current no ordinary condenser capacity 
suffices to suppress the ripple, but a typical and usually unsym- 
metrical wave form is observed with an oscillograph. In any 
case this is subject to line fluctuations so that it is necessary to 
resort to separate generators. 

Measurement of the Voltage. The various methods of deter- 
mining the peak or effective voltages applied to the x-ray tube 
are as follows: 

1. Voltmeter reading of the transformer primary with known 
transformation ratio; a method accurate only with constant- 
potential apparatus. 

2. Sphere gap; the method most commonly used and the 
simplest, but giving only very approximate readings. 

3. Electrostatic voltmeter; one type consists of large balls 
charged with high voltage and small balls on a bifilar suspension 
turning in the electrostatic field. This instrument requires 
calibration and is then very satisfactory, not only as a measure 
of the voltage but also of the constancy of the potential. 

4. Measurement by ammeter of the current through a very 
high known resistance, 10,000,000 ohms, for example. 

5. Spectrometric method; this consists in determining the 
shortest wave length in the spectrum of a beam of x-rays reflected 
from a crystal of known planar spacing, and substitution of this 
value in the very accurate quantum equation V = hc/e\, where 
V is the voltage (peak), e, h, and c are constants (respectively, 
the charge of the electron, the Planck action constant, and the 



HIGH-TENSION EQUIPMENT 



47 



velocity of light, so that hc/e = 12,350), and X is the short wave- 
length limit of the spectrum. This method is extremely accurate 
but, of course, requires special equipment and skilled technique. 
A special Seemann wedge spectrograph with spectral oscillo- 
graph is manufactured in Germany for the use of roentgenologists 
in determining accurate therapeutic dosage. 

The importance of an accurate knowledge of the voltage, 
particularly in deep therapy and in quantitative studies of 
crystalline structures, will become apparent in later sections on 
intensity measurements. 

Electrical Precautions, The installation of x-ray equip- 
ment involves adequate protection for the operator both from 
the high-tension electrical power plant and leads and from the 
x-rays themselves. The following are recommended electrical 
precautions: 

1. Wooden, cork, or rubber floors or coverings. 

2. High-tension leads concealed in an assembled unit with 
outside grounded; for exterior leads, preferably metal tubes or 




FIG. 28. Coolidge tube used in shock-proof unit (General Electric). 

rods or tightly stretched insulated wire, suspended by the best 
quality of shellacked silk fishline. 
3. Efficient earthing of all metal parts. 



48 



APPLIED X-RAYS 



4. Safety switches and fuses no heavier than absolutely 
necessary. 

5. Magnetic circuit breakers to break contact with any unex- 
pected surges. 

6. Shock-proof equipment. One of the best recent develop- 
ments in commercial medical x-ray equipment has been in shock- 
proof equipment. The x-ray tube of the type shown in Fig. 28 
is enclosed in the transformer itself with outer grounded and lead- 
covered cases. Such a unit, manufactured by the General 
Electric X-ray Corporation, is pictured in Fig. 29. 




FIG. 29. Shock-proof medical x-ray unit in which both transformer and tube 
are enclosed in the movable head (left center). 

The protective measures to be used against the x-rays are 
considered in Chap. VII, page 104. 

For further information concerning the electrical-engineering 
aspects of x-ray installations and their operation, the reader is 
referred to such excellent works among others as Terrill and 
Ulrey, "X-ray Technology, " D. Van Nostrand Company, New 
York, 1930; Brenzinger, Janitzky, and Wilhelmy, "Allgemeine 
Grundlagen, Physik und Technik des Rontgenverf ahrens, " 
Thieme, Leipzig, 1931 (an excellent treatise on European equip- 
ment and practice); and literature supplied by manufacturers. 



CHAPTER V 

X-RAY SPECTRA 

Spectra from Crystals and from Ruled Gratings. All x-ray 
investigations, whether they are concerned with the radiation 
itself and the information thereby obtainable on chemical and 
biological effects and on subatomic structure or with crystalline 
matter whose ultimate structure is sought by means of the x-rays, 
involve two factors, the quantity and the quality of the x-rays. 
By quantity is meant the intensity of a given beam, as it is 
variously measured. This factor is considered in ('hap. IX. 
By quality is meant the constitution of the beam with regard to 
wave length. Ordinary white light is proved to be a mixture 
of many rays of visible light of different wave lengths and 
corresponding to pure colors, because the beam is spread into 
a spectrum from violet to red by refraction in a prism or by 
diffraction by the finely ruled lines of a grating. In analogous 
fashion the spectrum of a beam of x-rays whose constitution 
previous to analysis is unknown identifies the quality. 

Glass prisms or diffraction gratings consisting of finely ruled 
parallel lines on glass or metal can be used only under very 
special conditions for the spectra of x-rays, because these have 
wave lengths many times shorter than light. Crystals, however, 
are natural gratings in which parallel planes of regularly marshaled 
atoms are spaced from each other at distances which are of the 
same order of magnitude as x-ray wave lengths. 

The analysis for quality is made, therefore, with the crystal 
spectrometer originally designed by the Braggs. It is a device 
upon which crystals of known interplanar spacings are mounted 
and rotated; the quantities measured are the angles at which the 
various components of the beam are reflected by the crystal 
planes. Upon the photographic plate or plotted from ionization- 
current readings is the spectrum of the beam. The analysis 
is complete because the whole process is governed by a simple 
law n\ = 2d sin 9, where X is a wave length, n is the order of the 

49 



50 APPLIED X-RAYS 

reflection, d is the known distance between the parallel planes in 
the crystals, and is the spectrometrically measured angle of 
incidence of the ray upon these planes (or 2O the angle of diffrac- 
tion or reflection). 

The crystals ordinarily used in spectrum analysis are rock salt 
(NaCl) in which the planes parallel to the cube surface (100) 
planes are spaced 2.814 A.U. apart; or calcite with a spacing of 
3.029 0.001 A.U. Gypsum, (d = 7.584), sugar (d = 10.57), 
mica (d = 9.93), quartz (d 4.247), and other crystals are also 
used. Of these calcite is recommended as the primary standard. 
Siegbahn and his associates in the measurement of long wave 
lengths introduced the use of crystalline lauric (d = 27.268 
A.U.), palmitic (d = 35.49 A.U.), and stearic (d = 38.7 A.U.) 
acids and lead melissate (d = 87.5 A.U.). The use of organic 
crystals has been practically discarded, however, in favor of the 
ruled gratings. The design and operation of spectrometers and 
the mechanism of the interaction between x-rays and crystals 
in accordance with the above Bragg law will be considered in 
Chaps. XI and XII, which are concerned with the use of x-rays 
in determining the structure of crystals. 

It is obvious that some other method of absolute wave-length 
measurement is needed to substantiate thoroughly the assump- 
tions and calculations made with crystal gratings. The funda- 
mental grating spacing of some one standard crystal (calcite) had 
to be calculated as a basis for wave-length measurements of 
x-rays which were then applied to the determination of the 
grating spacings of other crystals. For calcite, a rhombohedral 
crystal, the distance between face planes is 



where V m the molecular volume = M/pNo (M = molecular 
weight, p = density, and JVo is Avogadro's number or number of 
molecules per mole); <^(j8) = volume of calcite rhombohedron 
with unit distance between these face planes = (1 + cos /ft) 2 /sin 
(1 + 2 cos fl) = 1.0962, with = 101 55'. The most uncer- 
tain quantities are p and N ; repeated measurement has given 
p = 2.7102 as most reliable and with the accepted value for 
No = 6.061 X 10 23 , the grating constant comes out 3.029 
0.001 A.U. 



X-RA Y SPECTRA 



51 



Several experimenters, notably Thibaud in Paris 1 and A. H. 
Compton and Bearden 2 in America, have made notable contribu- 
tions with wave-length measurement by means of ruled optical 
gratings. At grazing tangential angles such gratings produce 
excellent diffraction spectra for x-rays and the measurement of 
wave length is obviously an absolute check upon crystal spec- 
trometry. X-rays have an index of refraction jj, which is some- 
what smaller than unity or * 

/x = 1 - a (5 of the order of 10~ 6 ). 

It follows that a ray tangential upon a plane mirror or grating 
undergoes total reflection when the angle of incidence 6 is 
smaller than a definite limiting value 9 m = \/2d. On a photo- 
graphic plate appear a central maximum for the primary beam, 




FIG. 30. X-ray spectrum from ruled grating. K series of copper. (Thibaud). 

another for the total reflection, the distance between these 
being 20; finally there is observed a diffraction spectrum of 
sharp lines for the x-ray beam. In Fig. 30 is shown such a 
result for x-rays from a copper target. The measurement of 
these lines and calculation of the wave lengths have yielded 
results in approximate agreement with those derived from the 
Bragg expression for crystal diffraction and the value of Avo- 
gadro's constant; the difference though small presents a funda- 
mental problem as yet unsolved. Furthermore, by means of 
such gratings Thibaud has bridged the gap between the x-ray 
and ultraviolet regions and obtained in many cases the same wave 
length for a chemical element from the spectrum of a beam from 
an x-ray tube and from an ultraviolet spark spectrum. This 

l Physik. Z., 29, 241 (1928). 

*Phys. Rev., 37, 1694 (1931). 



52 



APPLIED X-RAYS 



region of long waves which are easily absorbed can be studied 
with the crystal spectrometer only in vacuum with the greatest 
difficulty. There are still some discrepancies, however, between 
crystal and ruled-grating data. The latest precision comparative 
measurements have been made by Bearden 1 with the following 
results : 



Spectral lino 


Crystal X 


Grating X 


CuK/i 


I 389 1 4 


I 39225 


CuKa 


I 53838 


1 54172 


OK/;! 


2 08017 


2 08478 


OrKa 


2 28590 


2 29097 



It is at once clear that x-rays may serve as an aid in the solution 
of chemical problems along two lines: (1) the analysis of the 
emission or absorption spectrum of a substance by means of a 
known crystal analyzer (X unknown, d known) ; and (2) the 
determination with an x-ray beam of known wave lengths of 
unknown grating spacings of crystals (-X known, d unknown). 
The first yields information concerning the element which is 
absorbing or emitting rays; and the second, information concern- 
ing the structure of the crystal lattice. The present discussion 
is concerned with the first of these, and Part II with the second. 
The first involves largely the measurement and study of x-ray 
wave lengths which are characteristic of the chemical elements, 
hydrogen to uranium. At present the shortest characteristic 
wave length measured by strictly x-ray methods is 0.1075 A.U., 
the K absorption limit of uranium. This is the shortest possible 
characteristic value unless, of course, a heavier element should be 
discovered. Rays with much shorter wave lengths have been 
generated and measured but these are independent of the target 
metal. 

The Continuous Spectrum. Two kinds of x-radiation are 
known, (1) the general, "white," or continuous spectrum x-radia- 
tion and (2) the characteristic x-radiation, which is composed of 
several monochromatic rays grouped in Series, with wave lengths 
depending upon the atomic number of the emitting element. 
The continuous spectrum may be generated in a tube at suffi- 
ciently low potentials over certain ranges of wave lengths without 

1 Phys. Rev., 37, 1694 (1931). 



X-RA Y SPKCTRA 53 

characteristic lines under certain conditions, but the characteristic 
spectrum is always superposed upon a background of the general 
radiation. The outstanding property of the general radiation 
is that the smooth curve obtained by plotting intensity against 
wave-length or spectrometer reading has a sharp short wave- 
length limit (zero intensity), which does not depend upon the 
material of the target of the tube but upon the voltage applied 
to the tube, according to the fundamental Planck-Einstein quan- 
tum equation Ve = hv$ = hc,/\o, where V is the constant poten- 
tial, e is the charge on the electron, h the Planck action constant, 1 
c the velocity of light, v the maximum frequency, and Xo the 
minimum wave length occurring in the spectrum. This law 
was first applied to x-rays by Duane and Hunt in 1914, and it- 
has been proved subsequently to be rigorously true, far more 
so than the other famous equation, n\ = 2d sin 0. 
According to this equation 



\ = ^1 = 6 ' 556 >OO-^_X_3_X_10 10 = 12,350 
~ eV, 1.59 X 10- 20 X Ko T ' 

where F is in volts. Thus at 300,000 volts, the highest 
now employed in deep therapy, the minimum wave length 
is 0.04 A.U., while Lange and Brasch's new tube at 2,600,000 
volts must generate rays with a minimum wave length of 0.005 
A.U., in the extreme 7-ray region of the electromagnetic 
spectrum. 

It is obvious that precision researches on the general radiation 
spectrum should be a very exact method for evaluating the 
constant A; X can be spectrornetrically evaluated from nX = 
2d sin 6; V can be measured very accurately, particularly if the 
source of high potential is a storage battery, by reading the 
current after passage through carefully calibrated high resist- 
ances; and e is the well-known value of Millikan. The latest 
measurements in the laboratory of Prof. William Duane at 
Harvard 2 gave a value of 6.556 X 10~ 27 erg-sec. Several other 
investigators have obtained nearly the same value, which agrees 
well with evaluations by entirely different methods, such as the 
photoelectric effect. 

1 h has the dimensions (L*mT~ l ) of a moment of momentum: [action] = 
[energy X time]. 

2 J. Optical Soc. Am., 6, 213 (1921). 



54 APPLIED X-RAYS 

Furthermore, the law of Duane and Hunt leads to the most 
accurate evaluation of peak voltage which is directly calculated 
from the sharp limit of a crystal spectrum : 

_ he _ 12,350 

-v ~~~ (\ 7 J 

<?AO id . ~ 
sin Go 
n 

where 26 is the experimentally measured angle of the limit. 

While the short wave length of the spectrum is entirely 
independent of the target element, the intensity is a function 
of the atomic number of the target element. The relationships 
are, however, quite complicated and remain still in doubt. The 
curves rise sharply to an intensity maximum, defined roughly 
by X = 1.3X , and then fall away more gradually. 

The question of the mechanism of the production of the general 
radiation is one of the most difficult in x-ray science, and a 
completely satisfactory answer has not been given. If cathode 
rays are accelerated in an x-ray tube by the voltage V, the kinetic 
energy Ek will be Ve = E k . If the electrons are stopped instan- 
taneously at the target, the kinetic energy is transformed into 
the maximum possible radiation energy or Ek V^e = hi>Q = 
hc/\o. If the stoppage of the electrons is stepwise as they 
penetrate the target, then the rays will have a variety of wave 
lengths longer than the limit. While the quantum law governs 
the general radiation, the explanation of the actual emission 
process, which can indeed be made simply upon the basis of the 
electromagnetic or wave theory as a forced vibration of electrons 
in bombarded atoms, is one of the great difficulties confronted 
by the modern theories of spectral emission by quantum 
processes. 

The general radiation is of practical importance since it is 
employed in the Laue method of crystal analysis. In all 
applications at high voltages including therapy, radiography, 
etc., it comes prominently into play. The spectrum can be 
profoundly modified by filtration, inasmuch as rays of short wave 
lengths are absorbed far less than are those of the long wave 
length. The effect of filtration in the absence of characteristic 
effects is, then, to sharpen the curve and to shift the maximum 
to the shorter wave lengths, without in any way affecting the 
value of X . Filtration and the measurement of effective wave 
length of general radiation will be considered in Chap. VII. 



X-RAY SPECTRA 



55 



Characteristic Emission Spectra. In addition to the con- 
tinuous x-radiation, rays which have wave lengths characteristic 
of the anticathode elements are recognized. If the potential on 
the x-ray tube is sufficiently high, the spectrum of the emitted 
beam will show sharp lines (or peaks if the ionization current 
measured with an ionization spectrometer is plotted) superposed 
upon the continuous background. These same characteristic 








44' 48' 5Z' 56' 2<o 30' 34' 
295 296 

Crystal Table Angles 
FIG. 31. A' series emission spectrum (rhodium). 

x-rays are emitted as fluorescent rays if a beam of primary x-rays 
with sufficiently short wave lengths falls upon an absorption 
screen containing the same element as the tube target. The 
characteristic emission lines appear in groups designated as the 
K, L, M, N, 0, etc., series (beginning with the most penetrating or 
shortest wave-length group), following the nomenclature of 
Barkla who discovered the characteristic emission in the course 
of his absorption measurements. 



56 



APPLIED X-RAYS 



Kach of the series of emission lines contains several definite 
lines of different wave lengths. Probably the most remarkable 
characteristic of the x-ray range of the electromagnetic spectrum 
is the uniform simplicity of these spectra. The K series of all 
the elements except the lightest consists of four principal lines, the 
7 (also designated /3 ? ), P (really a close doublet p\ and /3 3 ), and 
the doublet, a\ and 2 , in the order of increasing wave lengths. 
The typical appearance of this spectrum is shown in Fig. 31. 
Practically, this is the most important series, since it is now used 

A 



0.\J 

2.8 
2 A 

2A 

jk* 

iz.o 
IJ.B 
| u 

j 1.4- 
.9 L2 

J i.o 

J - 8 
0.6 
04- 
0.2 



1! 

FIG. 3 


o 


tjl 










0.8 
0.1 
Ok 
0.5 
0.4 
03 
0.? 
O.I 

A 

spo 












\ 



































\ 


--> 

J 

v~ 

-L a 


















i. 

n 

59 

2.- 




- 










2 

: 












h 


) 









-- 


- 


_. 


- 




A 

i 










* 




-\ 




* 

J^ 


/. 




n 

V/f 


y* 

5 1 " 
ctr 


u 


J 


i 






1. 






5' 15' 25' 35' 4' 
61 

orios emission 


5' 15' 25' 35' 45' 
61 

um (tungsten). 



almost exclusively in crystal analysis. The more numerous 
L series lines, illustrated in Fig. 32, are in three groups 7, 0, and a, 
corresponding to the three L absorption discontinuities. About 
thirty have been identified. Because of the long wave lengths, 
measurements of the M and N series have been largely confined to 
the heaviest elements. 

Characteristic Absorption Spectra. There are also absorption 
discontinuities observed in x-ray spectra whenever a beam of 
x-rays undergoing spectroscopic analysis passes through absorb- 
ing material; the wave lengths corresponding to these discon- 
tinuities or edges are also characteristic of each of the chemical 



X-RAY SPECTRA 57 

elements. All rays with wave lengths shorter than that of a 
given discontinuity or edge will be absorbed by the element to a 
markedly greater extent than rays with wave lengths longer 
than this critical value. In other words, an absorbing screen 
which is relatively " opaque' 7 to x-rays of a range of wave 
lengths up to a characteristic value is "transparent" to longer 
rays. Similarly, if a beam of x-rays is absorbed by a gas in which 
the ionization current is being measured, sharp discontinuities 
occur which correspond to wave lengths characteristic of the 
elements in the gas. A single absorption discontinuity is 
associated with the K series, three with the L, five with the M, 
probably seven with the N, and five with the 0. Absorption 
bands which are observed on all photographs correspond to the A' 
discontinuities of silver and bromine; the intensities as compared 
with the ionization curves are, of course, reversed because the 
absorbed energy blackens the emulsion to the greatest extent. 
The Relationship between Characteristic Emission and Absorp- 
tion Discontinuities. It is a singular fact that all the lines in 
the K series emission spectrum are excited simultaneously when 
the energy conditions permit. Thus the a doublet of the K 
series with definitely longer wave lengths cannot be made to 
appear without the 7 and /3 lines, by adjusting the value of the 
voltage in the equation Ve = hc/\ Ka . It is true that the spectrum 
obtained under such conditions will show the presence of rays 
with the same wave lengths as the Ka lines, but this spectrum is 
due only to general radiation and is not characteristic of the 
chemical element on the target. Nor will the K series lines 
appear when \ Ky , corresponding to the emission line of shortest 
wave length, is substituted in the energy equation. An exami- 
nation of the value of the wave length corresponding to the K 
absorption discontinuity for a given element serving as an 
absorber discloses the fact that this value is slightly shorter than 
the wave length of the characteristic Ky line emitted by this 
same element serving as a target. When the voltage on the 
x-ray tube is adjusted so that Ve = /ic/X Xah8 , then the entire 
emission series appears. It follows, also, that fluorescent x-rays 
can be emitted only when the primary x-ray beam contains rays 
with these critical wave lengths numerically the same as those 
which correspond to the absorption discontinuities; or shorter 
(i.e., rays generated by a definite minimum voltage or higher). 
The energy represented by Ac/X abs must be vitally related, there- 



58 



APPLIED X-RAYS 



fore, to definite processes which are occurring in atoms when 
electrons in the cathode-ray stream strike them, or x-rays pass 
over them. The L series can be generated in three groups, 
since there are three quantum wave lengths or absorption 
discontinuities. 

The effect of voltage on characteristic spectra differs markedly 
from that on the continuous spectrum. The latter is produced 
at any voltage but the short wave-length limit moves to smaller 
values as the voltage is increased. An emission series appears 
only at a critical voltage, and the only effect of a further increase 
of voltage is to increase the intensity of all the lines without 
altering them in position or in relative intensities. 

THE EXPERIMENTAL RESULTS OF THE MEASUREMENT OF 

WAVE LENGTHS 1 

Characteristic Absorption. The wave lengths of the K 
absorption limits have been measured for the elements with few 



K lines 



8 

fi 



L lines 




Jb'io. 133. Spectrum from tungsten-target x-ray tube, showing the absorption 
edges of silver and bromine in photographic emulsion, (de Broglie.) 

exceptions from magnesium (12) to uranium (92); of the three 
L limits for those from rubidium (37) to uranium (92) ; of the five 
M limits for tungsten (74) to uranium (92). The characteristic 
absorption discontinuities were observed by Barkla in his 
absorption measurements with screens before- the discovery of 
the use of crystals as diffraction gratings. De Broglie in his 
first spectral photographs discovered the sudden changes in the 
blackening of the photographic plate due to the characteristic 
absorptions of silver and bromine in the photographic emulsion 
(Fig. 33) ; in both cases the plate was blacker on the side nearer 
1 For the detailed results of x-ray spectroscopy the reader is referred to 
"International Critical Tables," Vol. VI, pp. 36-44; Siegbahn, "Spektro- 
skopie der Rontgenstrahlen," 2d ed., Berlin, 1931. 



X-RAY SPECTRA 



59 



the zero direct-beam line, a phenomenon which accords with 
the definition of critical absorption wave length as the one such 
that the absorbing element absorbs x-rays of shorter wave 
length than the discontinuity to a greater extent than x-rays 
of longer wave length. 

TABLE III. CRITICAL ABSORPTION WAVE LENGTHS, K SERIES 



12 Mg 
13 Al . 


9 5112 
. 7 9470 


35 Br 
40 Zr 


9182 
6874 


56 Ha.. 
74 W . 


. 3308 
. 0.17807 


17 Cl . 


. 4 3938 


42 Mo 


61842 


78 Ft . 


. 1581 


24 Cr 
26 Fe 


2 0663 
. 1 7405 


47 Ag 
53 I . 


4852 
3738 


79 Au.. 
82 Pb . 


. 1534 
1410 


29 Cu 


1 3790 






92 II 


1075 



TABLE IV. CRITICAL ABSORPTION WAVE LENGTHS, L SERIES 



Element 


Li 

(Ln) 


LII 

(Lu) 


/'in 

(L M ) 


47 Ag 
53 I 


3 2474 
2 3839 


3 5067 
2 5475 


3 6908 
2 7139 


56 Ba 


2 0620 


2 1993 


2 3568 


74 W . 


1 0205 


1 0713 


1 2116 


78 Ft 
82 Pb 
92 IT 


8921 
7806 
5687 


9321 
8136 
5920 


1 0709 
9500 
7216 



The values in A.U. of the K absorption limits for a few of the 
more commonly used elements are as shown in Table III. 

Some values of the L absorption limits are given in Table IV. 

M absorption limits for thorium and uranium are given in 
Table V. 

TABLE V. CRITICAL ABSORPTION WAVE LENGTHS, M SERIES 



Element 


w 


() 


A/, 2 


(> 


(A/v) 


Th 
U 


2 388 
2 228 


2 571 
2 385 


3 058 
2 873 


3 552 
3 326 


3 721 
3 491 



Emission Spectra. The K Series. In the wave-length region 
above 0.1 A.U. lie four groups of emission lines, the K y L, M, 
and N series. Each group in general retains the same appearance 



60 APPLIED X-RAYS 

from one clement to the next, with a given line simply dis- 
placed to a shorter wave length in passing from one element to 
a heavier. The K series, as first photographed by Moseley in 
1914, seemed to consist of two lines, ft and a, but these were later 
resolved into four lines 7 (ft% in I.C.T.), ft,ai, and a 2 . For the 
light elements the spectra are more complex. The ft line, in 
experiments of great precision, is further resolved into a doublet 
(ft\ and 0a). Very recently several more faint lines have been 
found in the K series; e.g., Kftz, Kft'", and K-TI are satellites of the 
line Kft\. 1 The wave-length difference between a\ and 2 varies 
from 0.0044 A.U. for tin' to 0.00484 A.U. for hafnium and the 
remaining heavy elements. 2 The separation of the ft doublet is 
about 0.00076 A.U. although there is a considerable variation; 
that of 70 - 7 T varies from 0.00955 A.U. for tin to 0.0048 A.U. 
for the elements above tungsten. 

The relative intensities of the K lines have been the subject 
of several investigations. Duane and Stenstrom found the 
following relative values for the K lines of tungsten: 

3 a< 2 Oil 01 7 

4 50 100 35 15 

The ratio ai/a 2 = 2/1 seems to be generally true for practically 
all the elements. Allison and Armstrong 3 have obtained 
precision measurements for the following ratios: Mo-X/3/ 
Mo-A'a = 1/7.7; Mo-A'fr/Mo-Afr, - 2/1 (the resolved doublet) ; 
Cu-Kft/Vu-Ky = 42/1 ; Cu-Ka/Cu-Ka s a 4 = 100/1. The appear- 
ance of lines and the relative intensities are, of course, of utmost 
importance in their bearing upon the structure of atoms and 
the levels of energy within them. 

The K emission wave lengths are now known with considerable 
accuracy for most of the elements between carbon (6) and 
uranium (92). In Table VI are the most probable values for 
the elements most commonly employed as targets in x-ray tubes. 

The lines are designated both by the Greek symbols and by the 
difference between two energy levels which will be explained in a 
later section. 

1 Cf. RICIITMYER, Phil. Mag, 6, 64 (1928). 

2 COHK-STEPHANSON, Phyx. Rev., 27, 138, 530 (1926). 
*Proc. Nat. Acad. Sci., 11, 563 (1925). 



X-RAY SPECTRA 61 

TABLE VI. CHARACTERISTIC EMISSION WAVE LENGTHS, K SERIES 





K - #21.22 


K - M-2> 


K - .1/21 


K - L 22 


K. />21 


Element 














7(02) 


0i 


0J 


Oil 


2 


24 Or 


2 0667 Otf 5 ) 


2 0806 




2 28503 


2.28891 


26 Fo 


1 74080 (0 6 ) 


1 753013 


I 75616 


1 932076 


1 936012 


28 Ni 


1 48561 


1 49705 




I 65450 


I 65835 


29 Cu 


1 37824 


1 38935 




1 53739 


1.54123 


42 Mo 


619698 


630978 


631543 


707831 


712105 


45 Kb 


53396 


54449 


54509 


61202 


61637 


47 Ag 


486030 


496009 


49665 


55828 


56267 


74 W . 


17898 


18422 




20862 


21345 


78 Pt 


15887 


16370 




18523 


19004 



For the lightest elements as many as twelve or more lines may 
appear in the 7\ series instead of the usual four or five. Wentzel 
first claimed that these lines are due to multiple ionization of the 
relatively simply constructed atoms and, therefore, are related 
to the ordinary lines (7, ft, a\, c*o) as the spark lines are to the arc 
lines in optical spectra. Thus an 3 a 4 line or doublet and 
other "non-diagram" lines appear in all elements below zinc, 
in addition to the regular a\a^ doublet. In the past three years 
great progress has been made on the interpretation of "satellite" 
or non-diagram lines by Richtmyer, Langer, and others as due 
to two-electron jumps in an atom. 1 The longest K series line 
recognized by "International Critical Tables" is the unresolved 
a line of carbon, average 44.79 A.U. 

It will be observed from the foregoing data that the wave 
length of the Ky emission line is only a fraction of a per cent 
longer than that of the K absorption limit. It is a point of 
great interest whether there are any additional lines between Ky 
and the limit. Larsson measured a K/3 line for molybdenum at 
0.61825 A.U. One of the most interesting recent discoveries in 
x-ray science is that of Duane in 1931. K series x-rays were 
examined by means of a Bragg spectrometer, the Moseley photo- 
graphic method being employed. The incident ray and that 
reflected by the crystal to the photographic plate through dis- 
tances of 4,725 mm. passed through long metal tubes, exhausted 
of air in order to reduce the absorption. The Kp doublet lines of 
molybdenum (AX = 0.00056 A.U.), examined by photometric 
curves, appear separated 0.88 mm. No third line lay in the 

1 A complete account is found in Siegbahn, 2d ed., pp. 370-378, 



62 



APPLIED X-RAYS 



immediate neighborhood of the ft doublet. Between the 7 line 
and the short wave-length limit of the series appeared a marked 
blackening that represented several lines close together. They 
were not in the position of a line reported by Leide. The new 
lines may be due to O electrons falling into the K level, but a 
better explanation is, perhaps, that the lines were produced by 
falls into the K level of conductivity electrons which may from 
time to time lie in outer atomic energy levels. Several photo- 
graphs produced by long exposures showed a fainter single line, 
roughly halfway between the ft and the 7 lines. It did not 
correspond to a known x-ray line of any chemical element reflected 
in the first or second order. Ross 1 has also found this line which 
he calls ft 4, with an intensity of 1/1000 that of Ka, another, 5 , 
and two groups of still fainter lines near 7 and ft lines. 

The L Series. The complexity of the L series, which has 
already been referred to, prevents its extensive use for practical 
purposes. It is interesting to note, however, that the new 
elements, hafnium (72), rhenium (75), illinium (61) and (87), 
were all discovered by means of analysis of their L emission 
lines. More than twenty lines in the a, ft, and 7 groups have 
been identified for uranium; this number decreases with decreas- 
ing atomic number, as is to be expected upon the basis of atomic 
models in which outer shells of electrons disappear. Measure- 
ments of the tungsten L series give the following values: 

TABLE VII. WAVE LENGTHS, TUNGSTEN L SERIES 



74 


Ln C/21,22 


1 02047 


07 


L-22 ^43,44 


1 2208 


79 


Ln - Nu 


1 0439 


011,12 




1 2354 


73 


Ln - Nv 


1 05965 


02 


L-2-2 Ns'2,33 


1 24191 


72 . 


Ln - N n 


1 00584 


03 -.. 


Ln ~ A/22 


1 26000 


76 . . . 


Lzi O S >2 


1.0720 


0i 


/,21 - .1/32 


1 27917 


7s 


Lzi On 


1 079 


06 


L 22 -Nn 


1 2871 


7i 


Lzi - N 3Z 


1 09553 


04 


An - M*i 


1 29874 


75 


L 2 i Nil 


1.1292 


0ii 


Ln Mil 


1 3344 


09 




1 2021 


77 .. 


/>2i Mn 


1.4177 


08 


L IL - M 3S 


I 2034 


Oil.. . . 


L 2 -2 A/33 


1 47348 


010 




I 2094 


2 . . 


A'22 A/32 


1 48452 


05 


Li'2 ^32,33 


1 2125 


/. 


A 2 2 Mn 


1 67505 



The relative intensities of the lines Lai/La^ are l %] the 7 lines 
are in the order 71:72:73:74:75:76 = 100:14.0:22.3:7.0:3.0:2.3; 

s. Rev., 39, 536, 748 (1932). 



X-RAY SPECTRA 63 

for the j8 lines fa :fa:fa:p*:fa:p6:p7:p*:p9:pio = 100:49.3:15.0: 
7.7:0.47:2.0:0.4:0.68:0.60. ^ 

The L series wave lengths are known more or less completely 
for all the elements from vanadium (23) to uranium (92). 

With remarkable ingenuity in using, as diffraction gratings 
in their vacuum spectrograph, crystals of palmitic and stearic 
acid, Siegbahn and Thoreaus made measurements upon the very 
long wave length a and ft lines in the L series spectra of zinc, 
copper, nickel, cobalt, and iron, the values ranging from 11.99 
to 17.66 A.U. The longest L line recognized by I.C.T. is the 011,2 
line of vanadium at 24.200 A.U. Practically all measurements 
are now being made with ruled gratings rather than with organic 
crystals. 

The M and N Series. The M series was discovered by Sieg- 
bahn in 1916, and later measurements were made by Stenstrom 
and Karcher. The researches of Hjalmar with a vacuum spectro- 
graph extended knowledge of this scries in a remarkable way. 
In 1931, Lindberg using ruled gratings determined with great 
completeness and accuracy the wave length of the M scries lines 
for elements from uranium (92) to cerium (58), with values 
ranging from 2.440 A.U. for the M U O IV line of uranium to 14.030 
for the M v N vt or a r line of cerium. For tungsten the wave 
lengths of the strongest M emission lines are 6.076 (7 or M m N v ), 
6.743 (P or M IV N vliVll ), and 6.969 A.U. (a or M V N VU ). 
Hjalmar also photographed lines belonging to the N series of 
uranium, thorium, and bismuth. The line at 13.805 A.U. for 
thorium was the longest wave length spectroscopically measured 
prior to the studies of Siegbahn and Thoraeus using stearic acid 
crystals as gratings. 

The Measurement of Long Wave Lengths by Methods Other 
Than X-ray Spectroscopy. Many investigators have attempted 
to measure wave lengths of the soft x-rays, particularly for the 
very lightest elements, by locating the discontinuities in the slope 
of the curves representing the photoelectric current as a function 
of the exciting voltage. Essentially the method consists in 
allowing radiation from the target of a highly evacuated x-ray 
tube to fall on a plate within the tube, which is connected to an 
electrometer. The current is kept constant and the voltage 
varied in steps. The various potentials corresponding to dis- 

1 Increasing subscripts refer to decreasing intensity. 

2 ALLISON and ARMSTRONG, Proc. Nat. Acad. tici., 11, 563 (1925). 



64 



APPLIED X-RA Yti 



continuities in the curve are considered to be the limiting volt- 
ages for the K and L series. Important values so obtained are 
H-# 912, Ile-K 493, C-K 42.6-45.4, N-/ 33.0-35.1, 0-X 23.8- 
25.8, Na-L 35.3, Al-L 100, Al-M 326, etc. i 

Reference has been made on page 51 to the use of ruled 
gratings. Thibaud's measurements with crystal and grating 
were in good agreement. In the range of very long wave lengths 
the same lines were obtained from an x-ray tube and from an 
ultraviolet vacuum spark. Grating results are as follows: 
O-Ka 23.8, N-Ka 31.8, C-Ka 44.9, B-Ka 68.0, Fc-La 17.7, Fe-Lr? 
19.6, Fe-L / 20.1, Mo-M 65.0, 54.9, Ta-AT 58.3, 61.4, W-N 56.0, 
59.0, I>t-N 48.0, 51.0, Au-N 46.8, 49.4. These values have been 
a powerful aid in the establishment of energy levels. Besides 
checking the measurements on the doublets of Ta, W, Pt and 
Au, del Rosario 1 has extended them to Hg and Ir and proved that 
the origins are transitions in the N shells, for example N lv N V19 
contrary to the principle of selection discussed below. 

X-ray Spectra and Chemical Valence. Since characteristic 
x-ray absorption and emission are processes in which the inner- 

TABLK VI II.- PRINCIPAL AND SECONDARY ABSORPTION EDGES FOR CL AND S 

(LlNDIl) 



Absorber 


A', 


A', 


Absorber 


A^, 


K* 


C1 2 


4 3938 


4 3816 


8 monoelmie 


5 0090 


4 9946 


HCl 


4 3853 




S rhombic . 


5 0086 


4 9938 


Chlorides 1 


4 3829 


4 3600 


S crystal 


5 0088 


4 9941 


Chlorates 


4 3769 


4.3574 


Sul fides . . 


5 0093 


Depends on metal ion 


Perchlorates 


4 3698 


4 3478 


Sulfites 


4 9960 


4 9881 








S0 2 


5 0040 


4 9964 








Sulfates 


4 9879 


Depends on metal ion 








S +4 ~ (organic) 


5 0068 










S 4+ (organic) 


5 0019 










S 6f (organi(;)- - 


4 9939 





1 The different edges for chloride, chlorate, and perchlorate "enable an analysis for purity 
of any salt. 

most electrons in the atom are concerned, it is reasonable to 
suppose that the external or valence electrons have little or no 
effect upon the wave lengths. For many years it was generally 
agreed that the characteristic wave lengths were entirely inde- 
pendent of the state of chemical combination of the element ; thus 

*Phy*. Rev. 41, 136 (1932). 



X-RAY SPECTRA 65 

sulfur or manganese as elements, or exhibiting various valences in 
compounds, were thought to give always the same critical 
absorption or emission wave-length values. Precision researches, 
largely in the Siegbahn laboratory, have now demonstrated that 
for lighter elements there are small but distinct variations in these 
values depending upon the state of the element in the absorbing 
screen or target of the x-ray tube. Furthermore, a fine structure 
is found for the limits of certain elements. Lindh investigated 
both the emission lines and the absorption edges of chlorine, 
sulfur, phosphorus, and other elements. Wave lengths of the 
absorption edges of chlorine and sulfur are assembled in Table 
VIII (Ki and Jf 2 principal and secondary edges, respectively). 
These values have been verified and extended by Stelling and 
others. Complete data are tabulated 
in the second edition of Siegbahn, 
" Spektroskopie der Rontgenstrahlen," 
pp. 278-306. Hanawalt 1 has made the 
most recent experimental study of the 
dependence of x-ray absorption spectra 
upon chemical and physical state. 
Spectra with a simple edge and with 
secondary absorption are shown in Fig. 
34. Monatomic vapors exhibit no 
secondary structure at a distance from 
the main edge greater than the ioniza- FlG- 3 4. ^-absorption 

tion potential. Polyatomic vapors spectra showing: a, simple 
11 i i i L edge; 6, edge with secondary 

usually have a secondary structure absorption . (Hanawalt.} 
similar to that exhibited by the same 

molecule in the solid state, but there is often additional structure 
observed for the solid state. The contention that completed 
outer electron shells are associated with the absence of secondary 
absorption is not verified, since Br absorption in the photographic 
plate and others show a secondary structure. The usual theories 
of secondary absorption are those of multiple electron transitions, 
transition of electrons in multiply-ionized atoms (Wentzel), 
and energies of excitation of vibrational states of " structure 
electrons " (Richardson). Further research and even greater 
experimental resolution are required for a final conclusion. 2 

l Phys. Rev., 37,715 (1931). 

2 For a general summary with complete bibliography of 60 references see 
Stintzing, " Rontgenstrahlen und Chemische Bindung," Fortschritte der 
Rontgenforschung, Leipzig, p. 275, 1931. 




66 APPLIED X-RAYS 

Methods of Obtaining Homogeneous Monochromatic X-rays. 

The beam of x-rays produced by any ordinary x-ray tube is 
obviously heterogeneous and contains many wave lengths. The 
general radiation is a continuous band and upon this is superposed 
above certain voltages the characteristic spectral series. In 
many applications of x-rays it is highly desirable to have a 
homogeneous beam of known wave length. This is particularly 
true for the analysis of the fine structure of materials. Even 
at very high voltages for deep therapy, the effort is made to 
homogenize the beam by filtration through sheets of metal so 
that dosage can be reproduced. 

There is only one method of assuring a monochromatic ray, 
and this is the use of the double spectrometer. At a given 
angular setting of a crystal grating with constant d, only 
those rays with a certain wave length X can be reflected at the 
definite angle 2 from the primary undeviated beam. Con- 
sequently the second spectrometer or other apparatus can be 
adjusted to receive the purely monochromatic beam. 1 Davis, 
Compton, Allison, and others have made excellent use of the 
double spectrometer to measure wave lengths accurately, to 
study the natural widths of spectral lines, etc. For practical 
purposes the method has the disadvantage that a loss in energy 
occurs in every reflection or diffraction process and the intensity 
of the radiation is thus diminished. 

The second method of rendering a beam homogeneous is by 
the use of the characteristic absorption edges. Suppose that a 
molybdenum-target tube is excited at 30 kv. : the spectrum 
shows the K series lines superposed on the smooth general 
radiation curve. If, however, the first part of this band and the 
Ky and Kfi lines could be suppressed, and the Ka doublet left 
in essentially undiminished intensity, a useful " dichromatic" 
(since the doublet cannot be separated satisfactorily) beam would 
result. It is necessary only to discover an. element whose K 
absorption edge wave length lies between the Kf3 and Ka wave 
lengths of molybdenum (i.e., between 0.631 and 0.708 A.U.) and 
use this for a filtering screen. Table III shows that zirconium 
has a K critical absorption wave length of 0.6874 A.U.; a thin 
screen interposed in the molybdenum-target beam will cut out 
practically completely radiation with wave lengths shorter than 

l Cf. COMPTON, Rev. Sci. Inst., 2, 365 (1931); ALLISON, Phys. Rev., 41, 1 
(1932). 



X-RAY SPECTRA 



67 



this value but will be nearly transparent to the most intense <* 
doublet. 

The following table presents some representative examples of 
selective absorption for obtaining homogeneous rays : 

TABLE IX. FILTERS FOR OBTAINING MONOCHROMATIC X-RAYS 



Target 


Lowest approxi- 
mate voltage for 
K series, 
kilovolts 


X for 
Kct 

doublet 


Filter 


Thick- 
ness, 
(milli- 
meter) 


Grams per 
square 
centimeter 


Chromium 


6 


2 287 


Vanadium 






Iron. . . 


7 


1 935 


Manganese 


005 


004 


Copper 


9 


I 539 


Nickel 


007 


0067 


Molybdenum 


20 


710 


Zirconium 


03 


020 


Silver 


25 


560 


Palladium 


0.03 


036 



The third method of generating a nearly monochromatic ray 
is largely of theoretical interest only. Reasoning from the 
probable mechanism of the excitation of the continuous spectrum, 
Duane conceived the idea of bombarding a very thin stream of 
mercury vapor and liquid with cathode rays so that there would 
be little chance for stepwise slowing up of the electrons. Under 
ideal conditions a single line for the short wave-length limit, 
instead of a continuous band, would be obtained. This ideal 
was very nearly realized by Duane in obtaining a very narrow 
sharp peak with a maximum only slightly longer than the X 
defined by Ve = hc/\ (] . 

GENERALIZATIONS FROM X-RAY SPECTROSCOPIC DATA 

The Moseley Law. The brilliant young Englishman Moseley, 
who was called from his remarkable researches to lose his life 
in the Dardanelles in 1915, was the first to recognize the essential 
simplicity of the K emission series. He showed that the wave 
lengths of a given spectral line varied continuously step by step 
in proceeding from one atomic number to the next, and not 
periodically as is the case with so many atomic properties. 
Even in optical line spectra there are definite relationships for 
chemically similar elements doublets for the alkali metals, 
singlets and triplets for the alkaline earths and spectra of 
increasing complexity in passing from left to right in the periodic 
table. The periodic properties such as these optical spectra ; 



68 



APPLIED X-RA Y8 



atomic volumes, etc., must find their origin in the outermost 
parts of the atoms; the non-periodic properties such as the x-ray 
spectra must be ascribed to the interior. The original Moseley 
K series spectra for several neighboring elements beginning with 
arsenic (33) are reproduced in Fig. 35. 

Moseley went further and 
showed that if the square root 
of the reciprocal of the wave 
length (or of the frequency or of 
the wave number, which is the 
frequency divided by a funda- 
mental frequency constant R, 
the Rydberg constant) of a given 
x-ray line, K/3, Ka, La, etc., were 
plotted against atomic number, a 
practically straight line resulted. 
Precision researches have demon- 
strated that the curves are very 
slightly concave upward. For 
a K line the curve is characterized 
by the equation \/ v/R = \/% 
(Z 1), where Z is the atomic 

number, or v = R (Z I) 2 
\ 

is of 



Hh 



Sr 



/I 1 \ 

( p - 2 )' 
V / 



FIG. 35. K series spectral lines for 
several neighboring elements, illustrat- 
ing the continuous wave-length progres- 
sion and the Moseiey law. great significance in its analogy to 

that expressing the frequencies of the ultraviolet Lyman spectral 
series of hydrogen. Similarly an L series line frequency is 



given approximately by v = R(Z 7.4) 



2 ( ^ ^A 



which is 



analogous to the expression for the Balmer series for hydrogen. 
A remarkable extension of the Moseley law has been made 
in the region of optical spectra by Millikan and Bowen in their 
experiments with stripped atoms. Working with elements in 
the second horizontal row in the periodic table, they have 
compared the spectra of sodium, magnesium 4 " (one electron 
removed), aluminum 24 ", silicon 34 ", phosphorus 44 ", sulfur 54 ", and 
chlorine 64 ", all of which, therefore, have exactly the same number 
of electrons and differ only in the mass and charge of the nucleus. 
The spectra are identical in appearance, and the square roots of 



X-RAY SPECTRA 69 

the frequencies of a given line are a linear function of atomic 
number. Richtmyer has demonstrated also that Moseley rela- 
tionships hold true for non-diagram or satellite lines. 

Applications of the Moseley Law. The simplicity of 
the relationship between spectral line frequency and atomic 
number, which according to present conceptions repre- 
sents the net positive charge on the nucleus, and also 
the number of non-nuclear electrons, suggests several valuable 
applications. 

1. The law proves that a fundamental relationship exists 
among all elements from hydrogen to uranium; that these are all 
constructed of the same building units in definitely progressing 
complexity; and that if x-ray spectral lines are to be ascribed to 
the innermost electrons in atoms, as is indicated by the high fre- 
quencies and consequently large energy changes, these inner 
electrons must be essentially the same in number and disposition 
in all atoms, regardless of the number of electrons constituting 
the outer portions, or of the state of chemical combination of the 
element. 

2. The law has been the fundamental basis upon which the 
discovery and identification of the recently discovered new eft- 
ments has depended. Interpolation of the -\/ v atomic number 
curves, or calculation, gives the wave length which should be 
expected for a given K or L or M line in the spectrum of an 
unknown element. In every case the process of discovery has 
been the matching of experimental lines from material used as 
the target of an x-ray tube with the theoretical values. In this 
way Coster discovered hafnium (72); Tacke and Noddack 
masurium (43) and rhenium (75); Hopkins and his students in 
1926 identified the rare earth illinium (61). In this last case the 
measured wave lengths of strong lines were 2.2781 and 2.0770 
A.U., corresponding to the predicted values for the Lai and L/? t 
lines of the element 61, respectively, of 2.2777 and 2.0730 A.U. 
Finally in 1931 Papish announced the presence of element 87 in 
the mineral samarskite with the characteristic x-ray wave lengths 
Mod = 4.517 Lai = 1.026, La 2 = 1.038, L0 2 = 0.853, and Lrj 
= 0.944 A.U. 

3. Qualitative and even quantitative analysis of any unknown 
substance is, of course, directly possible by analysis in similar 
fashion of the emission lines. Analytical applications of x-rays 
will be considered in Chap. VI. 



70 APPLIED X-RAYS 

The Combination Principle. While the Moseley law gives the 
relationship among elements of varying atomic number from 
the standpoint of any given x-ray spectral line, another principle 
observed from experimental data gives important information 
concerning the relationship between lines and absorption discon- 
tinuities in different series for the same element. Thus the 
frequency of the K/3 line equals the sum of the frequencies of the 
Ka and La lines. The differences between the K critical absorp- 
tion frequency and two of the L critical absorption frequencies 
equal, respectively, the frequencies of the Ka emission lines; and 
the difference between the K absorption frequency and one of the 
M critical absorption frequencies is equal to the frequency of 
the Kfi emission line; thus the differences between values of 
v/R, where v is the frequency and R the Rydberg constant, 
of the absorption discontinuities of tungsten are equal to v/R 
values for emission lines, as follows: 

K - L m = 4.367 -> Ka, = 4,3682. 
K - L u = 4.268 - Ka* = 4.2693. 

In the same way the frequencies of L and M absorption discon- 
tinuities give the frequencies of certain L emission lines. Thus 
the combination principle, long known in optical spectra, applies 
simply to x-ray spectra. In addition, Sommerfeld, Siegbahn, 
and others have noted important relationships between doublets 
in x-ray spectra. As an example may be cited the following 
pairs of values of the wave numbers (v/R) for tungsten: 



J 


642 78 1 




712 39 Ly b 


831 81 


LI 


... . 544 03 / 




613 85 L0 6 


733 76 














98.75 


. . 850 07 j 


98 54 


98 05 
4368 5 


L0b 




. . 751 56 1 




4270 













98 51 98 5 

Here are at least six doublets with the same difference, which is 
simply that between two L absorption limits: L n 849.59 
L m 750.88 = 98.71. The wave-length differences correspond- 
ing to these values for each of these doublets (regular or rela- 
tivity) remains practically constant for all the elements. Another 
type of doublet (irregular or screening) is that observed by Hertz, 
where the difference in -\f v/R values for pairs of critical absorp- 



X-RAY SPECTRA 71 

tion values (L n and L x ) is constant from one element to the next. 
These two types of doublets occur alternately in the structure; 
thus L m and L u are relativity, L u and L l are screening, M v and 
M IV relativity, M lv and M ni screening, and so on. Such facts 
as these indicate at once the possibility of definite levels of energy 
in atoms, the differences corresponding to the frequencies of 
emitted or absorbed radiation, and doublets to a doubling of 
energy levels. 

The Facts of X-ray Spectra to Be Explained by a Theory of 
Atomic Structure. Any comprehensive theory of atomic struc- 
ture must be able to account for the following facts of x-ray 
spectroscopy : 

1. Critical absorption wave lengths. 

2. Critical ionization wave lengths. 

3. Sharp characteristic emission lines. 

4. Grouping of spectral lines in series. 

5. Critical excitation potentials for groups of lines. 

6. The Moseley law, continuous, non-periodic progression in 
wave lengths. 

7. The combination principle, regular and irregular doublets, 
and the relation between emission and absorption. 

The Bohr Theory of Atomic Structure. Before outlining very 
briefly the Bohr theory of atomic structure, by means of which a 
very useful mechanical model could be constructed and processes 
related to radiation clearly pictured, it must be frankly stated 
that the model rs deficient and unable to meet the demands of the 
newest experimental physics. However, new quantum or wave 
mechanics theory, in which the mechanical model of the atom is 
replaced by a mathematical equation has not advanced as yet to 
the stage where any very satisfactory geometrical model can be 
visualized in terms of the facts of x-ray spectra. Hence the 
Bohr theory of the planetary atom still is worthy of presentation 
and use as a qualitative tool, particularly as it utilizes funda- 
mental quantum laws. Sir William Bragg advises that science, 
must not be criticized for dropping one theory in favor of another, 
as a carpenter is not scolded for dropping his saw to use his 
chisel. In a word, science can neither believe wholly in the Bohr 
atom nor do without it. 

In addition to some of the experimental facts of x-ray spectros- 
copy, there were in 1916 four other great factors, which were 
largely unrelated and even discrepant, to be taken into considera- 



series 



72 APPLIED X-RAYH 

tion by any theory. These were: the classical electromagnetic 
(wave) theory of radiation, the Planck quantum theory of radia- 
tion, the Rutherford nuclear atom, and the empirical (optical) 
spectroscopy of Balmer, Ritz, and Rydberg. The last factor 
refers to the relationships such as the following for the optical 

of hydrogen: Lyman series, v\ = v () ( 12 )' % = 

2, 3, 4, ; Balmer series, */ 2 = v ( [ - , )' "2 = 3, 4, 5, 

\z- // 2 -/ 

; Paschon series, V A = v ( \ V n% = 4, 5, 6, ; 

\.v n- A "/ 

etc., or in general v = vo[ 

\m- n- 

The fundamental assumptions of the original Bohr theory are 
as follows: 

1. The atom consists of a positively charged, extremely minute 
nucleus which accounts for practically all the mass, and of nega- 
tive electrons as satellites. The number of these electrons is 
equal to the net number of positive charges on the nucleus, and 
this number is the atomic number. The table of elements is 
constructed by the addition of one net positive charge and one 
non-nuclear electron for each element, beginning with hydrogen 
with one positive charge on the nucleus and one electron. 

2. The atom is a dynamic system, for the electrons are in 
rapid orbital motion. 

3. Three laws govern this atom: 

a. An Acceleration Law. In a simple atom like hydrogen, 
with the assumption that the mass of the nucleus M is infinitely 
great in comparison to the electron so that the electron remains 
in fixed position, the coulomb force of attraction between positive 
and negative charges is opposed by the centrifugal force required 
to keep the electrons revolving in a circle; in other words e' 2 /a 2 = 
mv 2 /a, where e is the electric charge (+ or --), a the distance 
between two charges, m the mass of the electron, and v its 
velocity. 

b. A Momentum Law. The angular momentum is governed 
by the equation mva = nh/2Tr, where n is an integer and h is a 
constant. In other words, the motion of the electron is very 
definitely restricted to orbits whose angular moment multiplied 
by 2w is equal to nh. The possible configurations under this 



quantum condition are called stationary states because no radia- 
tion is emitted while the atom remains in such a state. 

c. A Frequency Law. While an electron is revolving in any 
definite orbit of definite energy W\, it is conceived to be non- 
radiating, for otherwise energy would be lost and the electron 
would be pulled gradually into the nucleus. Another orbit 
W2 would correspond to a different energy level. It is only in 
the process of transition of an electron from one orbit to another 
that radiation may be emitted or absorbed; in other words, the 
energy difference W } W* = hv, where v is the frequency of 
the radiation and h the Planck action constant. Ordinarily an 
atom exists in the stationary state of lowest energy but by absorp- 
tion of radiation or some kinds of collisions it may be " excited" 
to a higher energy state. Radiation is emitted during the transi- 
tion from a higher to lower state of energy. 

A combination of these simple laws gives the equation 

27r 2 eW 1 1 \ /I 1 \ 

v = , , I ., ,., )> or v = vji , ]j 

h* \n 2 n 2 / \n 2 n 2 / 

where v is a fundamental constant frequency, the Rydberg 
constant already mentioned, and n and n' whole numbers; the 
equation expresses the frequencies of the spectral lines of hydro- 
gen. There is thus immediate explanation for the empirical 
spectroscopic formulas of Balmer, Ritz, and Rydberg. 

After the simple Bohr theory of hydrogen was announced, 
many corrections and additions were made. Briefly enumerated 
these were as follows: 

1. Allowance for the mass of the nucleus (in ionized helium 
the mass 4 must be introduced). 

2. Allowance for the revolution of the nucleus around the 
common center of gravity. 

3. A relativity correction, taking into account the variation in 
mass with the velocity of electrons. 

4. The introduction of elliptical orbits, in addition to Bohr's 
circular ones, to account for the fine structure of spectral lines. 
These orbits, in order to have energies which differ from those of 
the circular ones and thus to account for the complexity of 
apparently single lines, must undergo precession around the 
nucleus. 

5. The most striking characteristic of the quantum theory of 
atomic structure is the frequent occurrence of integers and half 



74 APPLIED X-RA YS 

integers; it is essentially a theory of numbers which are combined 
in all possible ways. The types of elliptical orbits, upon which 
the electrons in the complicated atoms revolve, may be charac- 
terized by quantum numbers n, k, j. The number n is related 
to the size of the orbit, k to its shape, and j to its position in the 
atoms relative to other electronic orbits. For convenience a 
particular orbit is referred to as Ukj. The larger the value of n 
the more loosely is the electron bound to the atom. 1 Thus the 
innermost electron "shell" consists of a single circular orbit 
In, the second of two ellipses, 2n (most eccentric) and 2 2i , 
and a circle 2 2 2, and so on. 

6. By combination of x-ray, spectroscopic, and chemical infor- 
mation the complete arrangement of electrons in various shells 
or orbits has been derived, most satisfactorily in 1925 by Stoner 
and Main-Smith, for all the elements from hydrogen to uranium. 
As an example may be cited the structure for the rare gases of the 
atmosphere, which, except helium, always have eight outside 
electrons: 
2. He l n (2). 

10. Nel 11 (2);2 11 (2);2 21 (2);2 22 (4). 
18. A l u (2); 2 n (2); 2 2 ,(2); 2 22 (4); 3 U (2); 3,(2); 3(4). 
36. Kr l n (2); 2 n (2); 2 21 (2); 2 22 (4); 3 U (2); 3 21 (2); 3 22 (4); 3 M (4); 

3 S3 (6);4n(2);4 21 (2);4 22 (4). 

54. Xe, same as Kr and in addition 4 32 (4); 4 33 (6); 5n(2); 5 2 i(2); 

5 22 (4). 

86. Rn, same as Xe, and in addition 5 32 (4); 5 33 (6); 6n(2); 6 2 i(2); 

622(4). 

This system explains many chemical and spectroscopic facts, 
the similarity in such homologous elements as Li, Na, K, Rb, 
and Cs, the chemical similarity of the triads Fe, Co, Ni; 
Ru, Rh, Pd; and Os, Ir, Pt; and the place of the 14 rare earths 
(57 to 71). Here the successive electrons are added in the 4 43 
and 4 44 orbits, previously unoccupied, though electrons are being 
added in the fifth shell beginning with rubidium, atomic number 37. 

The Explanation of the Facts of X-ray Spectroscopy by the 
Bohr Atom. It is now certain that the fundamental orbit of 
the x-ray K series is a one-quantum orbit (n = 1), that of the 
L series a two-quantum orbit (n = 2). 

The existence of individual, widely separated spectral series 
leads directly to the fundamental conception that a number of 

1 A third subquantum number takes into account electron spin. 



X-RAY SPECTRA 75 

electron groups are present in the atom which differ considerably 
from each other with respect to orbital energy and the distance 
between the electrons and the nucleus. Therefore, a single 
series arises from the transition of an electron from one of the 
outer groups (e.g., the L, M, or N groups) to one of the inner 
groups (e.g., the K group). The fine structure of the individual 
lines is due to the energy differences within a definite group; 
e.g., the Kai and Ka% lines are to be explained by transitions from 
two somewhat different L orbits to a single K orbit. 

The energies of the various orbits or shells or levels are desig- 
nated by the hv values of the experimentally measured critical 
limits, IK, 3L, and 5M, and presumably IN, 50, and 3P, dis- 
cussed on page 56. As a matter of fact, these are the energies 
required to lift an electron in its particular orbit out of the atom. 
For this reason the various levels may be designated either by 
reference to the letter K, L, etc., or to the quantum number 
Ukjy or now even to the terms used analogously in optical spectra; 
for example, the following are synonymous: 

K L! L n L m M l M u M ul M lv M v . 

In 2u 2 2 i 222 3n 821 822 832 3 3 3, etc. 

Is 2s 2p 2 2pi 3s 3p 2 3/^i 3d 2 3d. 

The orbital energy is expressed by \/U/Rch = Z*/n where (7 
is the orbital energy of an electron, R is the Rydberg constant, 
c the velocity of light, n the principal quantum number, and Z* 
the effective nuclear charge; this is less than the true nuclear 
charge Z by virtue of the screening effect upon the electron in 
question, which other electrons of the atom with interpenetrating 
orbits exert upon the full attractive force of the positive nucleus. 
When Z*/n is plotted against Z, the curves show that Z* in the 
different levels, particularly for heavier atoms, does not vary in 
the same way with increasing Z. It is considerations such as 
these, indicating when electrons are added to a new shell before 
an underlying one is completed, which have led to the assignment 
of complete electron structures to all the elements; measurements 
of energy levels from experimental values of x-ray critical 
absorption limits have been one of the most valuable contributions. 
The Bohr theory, therefore, explains the facts of x-ray spectra 
as follows : 

1. Critical Absorption Limits. Energy required in primary 
radiation quantum, or collision with cathode rays, to lift elec- 
trons from a given energy level out of atom. 



76 APPLIED X-RAYX 

2. Critical lonization. The frequency is the same as that of 
critical absorption, since only with energies greater than those 
corresponding to this frequency can ionization and electric 
current increase occur. 

3 and 4. Sharp Emission Lines in Series. When a K electron 
is removed, L electrons may fall into the vacancy producing Kai 
and Kaz from two of the three L levels corresponding to circular 
and elliptical orbits. The K/3 doublet results from the transition 
of electrons from two of the five M levels, and Ky, an unresolved 
doublet, from transition from two N levels. If electrons in the L 
level are removed, the L series results by the transition from the 
higher M, N, etc., levels to the L level. With three L and five M 
levels there are thus possible 15 lines from this one type. How- 
ever, not all the lines so predicted appear. The spectra are 
governed by a partly empirical rule of selection which states that 
n in the quantum number Ukj must change, that k must change 
by one unit and that j may change by one unit or remain 
unchanged. Recently a number of "forbidden" lines have been 
discovered, but they are very faint. Newly measured lines of 
very long wave length whose origins are transitions within the 
N shell (An = 0) have been mentioned on page 64. Energy- 
level diagrams have been constructed for all the atoms to show 
how spectral lines in x-ray and optical regions are related to these 
transitions. Optical spectral lines are produced, of course, by 
electronic changes between the orbits farthest removed from the 
center. The complete energy-level diagram, as designed by Meg- 
gers, Foote, and others, is given in Fig. 36; each point represents 
an orbit characterized by an n k - } value, and the lines joining these 
points represent electron transitions resulting in spectral lines. 
The diagram is a remarkably terse and complete expression of 
the origin of radiation and its relationship to atomic structure. 
It is independent of conceptions of orbits and the mechanism of 
electron jumps so holds useful in spite of deficiencies in the 
Bohr model of the atom. 

5. Critical Excitation Potentials. The K series lines are not 
excited separately but appear together only when the kinetic 
energy of the bombarding electron stream in the x-ray tube is 
equal to or greater than the value given by the equation 
E k Ve = hv KAlnt . Similarly K series secondary fluorescent 
x-rays are excited only by primary rays with energies equal to or 
greater than hv K&iMt . Only under these conditions is it possible 



X-RA Y SPECTRA 
2 3 



77 




FIG. 36. Complete energy-level diagram, showing the origin of x-ray spectral 
lines. (From Siegbahn, "Spectroscopy of X-Rays") 



78 APPLIED X-RAYS 

to impart sufficient energy to the K electron to remove it 
entirely from the atom (not to the L or M levels, for example). 
The vacancy is supplied then by an L, M, or N electron; 
the new vacancy is filled from a still more distant shell. The 
atom returns to a neutral state by a process which, in general, 
takes place as a series of steps; but jumping over several steps 
and even the direct return of an outer electron to the K ring is 
not unusual. 

6. The Moseley law is a consequence of the fact that the inner- 
most levels in atoms, which take part in the production of x-rays, 
are all similarly constituted as regards number and disposition of 
the electrons. 

7. The combination principle is a direct consequence of differ- 
ent energy levels with definite values. The same wave-number 
difference may be obtained by several combinations of the wave 
numbers of critical absorption limits and emission lines, when 
these are pictured as distinct jumps from lower to higher levels or 
vice versa (Fig. 36). The principle thus affords several checks 
for numerical evaluation of the energy levels. 

Happenings to an Electron in an X-ray Tube. In the light of 
the foregoing considerations of atomic structure, evidently at 
least four things can happen to an electron which is hurled at the 
anode in an x-ray tube: 

1. It can be reflected from the anode surface. 

2. It can pass through one or more atoms. The electric fields 
in the interior of the atom diminish the speed of the electron so 
that it loses part of its energy. This has been imparted to the 
atom whose kinetic energy is increased; thus the lost electron 
energy has been transformed not only into x-rays but also into 
heat, and the temperature of the anode rises. The slowed-up 
electron then may pass through another atom with further 
diminution in speed and so on until it is stopped. 

3. It is stopped completely by impact with the atom nucleus. 
In this case only is the initial electron energy transformed com- 
pletely to radiation as E k = hv with a continuous spectrum as 
explained above. The stoppage in steps explains why from an 
x-ray tube operating at absolutely constant potential rays of 
different wave lengths are emitted. It is evident that x-rays are 
generated not only upon the surface of the anode but also in 
the interior of the metal. The thickness of the layer in which 
x-rays arise depends on the voltage and on the anode material; 



X-RAY SPECTRA 79 

with a tungsten target this is only about 0.001 mm. or a layer 
2000 tungsten atoms deep. 

4. In its impact on an atom in the anode the electron which has 
traveled from the cathode may eject an electron out of its energy 
level (or quantum orbit) in this atom either to another level, 
thereby producing an excited atom or entirely out of the atom, 
thereby producing an ionized atom. Characteristic x-rays are 
emitted as the atom returns to the normal state. The electron 
proceeds with smaller kinetic energy to any one of the four 
possible occurrences just enumerated. 

X-rays and the New Quantum Theory. Heisenberg 1 cites the 
following as the most important experiments from which may be 
deduced concepts of present physics: 

a. Wilson photographs by the cloud-track method showing 
that a and ft rays may be regarded as streams of minute 
particles. 

b. Diffraction of ft rays or electrons, showing wave-like proper- 
ties, discovered by Davisson and Germer in 1927. 

c. The diffraction of x-rays showing form of wave motion, 
and the photoelectric ejection of electrons when x-rays strike 
matter, showing corpuscular properties. 

d. The Compton-Simon experiment, in which x-rays passing 
through supersaturated water vapor are scattered by molecules, 
producing both recoil electrons and photoelectrons, the first 
by a collision of a photon (light particle) with an electron in a 
molecule and the second as a result of the collision of this photon 
moving in a new direction with a second molecule. 

e. Collision experiments of Franck and Hertz leading to the 
conclusion that atoms in a gas through which a beam of slow 
electrons passes can assume only discrete energy values and 
" stationary states" as originally postulated by Bohr. 

In simplest terms the essential facts involved underlying the 
new theories which have displaced the Bohr model are as follows: 

1, Matter, including free electrons, and radiation possess a 
remarkable duality of character, since they sometimes exhibit 
the properties of waves, at other times those of particles. A 
phenomenon cannot be a form of wave motion and be composed 
of particles at the same time. It is experimentally certain only 

1 "Physical Principles of the Quantum Theory/' University of Chicago 
Press, Chicago (1930). 



80 APPLIED X-RAYS 

that light sometimes behaves as if it possessed some of the 
attributes of a particle, but there is no experiment which proves 
that it possesses all the properties of a particle; similar statements 
hold for matter and wave motion. 

2. Language is incapable of describing processes occurring 
within atoms, for it was invented to express the experiences of 
daily life which consist of processes involving exceedingly large 
numbers of atoms. Furthermore, it is almost impossible to 
modify language so as to describe these atomic processes, since 
words can only describe things of which we can form mental 
pictures and this ability is a result of daily experience. Mathe- 
matics is not subject to this limitation. 

3. Contradictions between theory (Bohr) and experiment 
have led to the necessity of demanding that no concept which 
has not been experimentally verified should be involved in 
scientific formulations. 

4. The principle of uncertainty shows among other things 
that the position and velocity of an electron (say in an orbit) 
cannot be known simultaneously. Determinism is dropped out 
of the latest formulations of theoretical physics. 

5. The new theory removes discrepancies between the orbit 
theory and the facts of spectroscopy, particularly fine structure. 
The power of the new quantum mechanics in giving better 
understanding of events on an atomic scale is becoming increas- 
ingly evident. The structure of the helium atom, the existence 
of half-quantum numbers in band spectra, the continuous spacial 
distribution of photoelectrons, and the phenomenon of radio- 
active disintegration are items which baffled old theories but are 
successfully accounted for by the new. 

6. As nearly as may be visually conceived, the new model of 
the atom spreads the electron from a point charge moving in 
orbits to diffuse shells of negative electricity with increasing 
density the closer to the nucleus. Henoe the orbits are smudged, 
in the words of G. P. Thomson, but the electrons retain in a 
sense their individuality. However, Dirac regards waves or 
particles of light or electrons as two useful abstractions for 
describing the same physical reality but he warns the student 
against combining them into a mechanism that behaves like 
familiar things. 

7. The Bohr atom is, therefore, welcomed today as an indis- 
pensable model, expected to remain so for many years to come, 



X-RAY SPECTRA 81 

and admitted to be inadequate. Even the most advanced 
mathematical physicists still speak of "orbits" and "electron 
jumps." Nor has the final word been said with the new mathe- 
matical models. 

8. Finally, in the words of Jeans, "the Great Architect of the 
Universe now begins to appear as a pure mathematician." 



CHAPTER VI 
CHEMICAL ANALYSIS FROM X-RAY SPECTRA 

Since definite x-ray wave lengths, both emission and absorp- 
tion, are characteristic of the chemical elements, it follows that 
x-ray spectroscopy may find practical application in qualitative 
and quantitative analysis. The Moseley law, of course, is of 
splendid assistance, more particularly in the qualitative discovery 
of new elements in complex mixtures, since the wave lengths for 
these elements may be accurately predicted. 

The five general procedures employed in analysis are as 
follows : 

1. Measurement of primary spectral emission lines (K or L or 
M series) in which the unknown substance undergoing analysis is 
made the target of an x-ray tube. 

2. Measurement of secondary fluorescent emission lines in 
which the unknown is so placed on some device inside the x-ray 
tube that it is screened from the cathode rays but directly 
irradiated by the primary x-ray beam. 

3. The same except that the unknown is irradiated outside 
the x-ray tube; on this account the intensities are greatly decreased 
and the time required for photographic registration of the 
spectrum increased. 

4. Measurement of wave lengths of characteristic absorption 
edges in which the unknown serves as an absorbing screen. 

5. Use of a cathode-ray tube with thin windows for passage 
of rays, with bombardment of unknown outside and spectro- 
graphic analysis of x-rays generated. 

Apparatus. The essential apparatus for analysis comprises 
the x-ray tube and power plant and a crystal spectrograph. 
Special demountable tubes are required for methods 1 and 2. 
In the first case the sample must be pasted or fused on a cooled 
metal surface serving as anode. The tube so prepared is then 
pumped continuously. Any of the demountable electron or ion 
tubes described in Chap. Ill are used. For method 2 either a 
second target or some other special holder is required inside the 

82 



CHEMICAL ANALYSIS FROM X-RAY SPECTRA 



83 



tube which must then be pumped. One of the best designs due to 
Stintzing is shown in Fig. 37. Both the vertical cone-shaped 
anode opposite the hot-filament cathode and the fluorescent-ray 
plate, horizontal left, are rotated. Another tube for method 2 
which has been used with great success by Coster, Hevesy, and 
others is shown in Fig. 38. 




FHJ. 37. FIG. 38. 

FIG. 37. X-ray tube for chemical analysis by secondary fluorescent rays 

(Stintzing) . 

FIG. 38. X-ray tube for chemical analysis by secondary fluorescent rays 

(Hevesy) . 

For methods 3 and 4 any standard x-ray tube with ordinary 
targets can be used, operated at requisite voltages for the 
excitation of the secondary radiation. Vacuum spectrographs 
are very largely used for analyses, particularly where minute 
amounts of substances are involved. Standard equipment such 
as shown in Fig. 39 is available in which the high vacuum of the 
tube is separated from the moderate vacuum of the spectrograph 
by aluminum foil. A calcite crystal with cleavage face as reflect- 
ing plane is used as grating. Registration of the spectra is 



84 



APPLIED X-RAYS 



almost always photographic, although measurement of ionization 
currents with the ionization chamber spectrometer is easily 




FIG. 39. Seemann high-vacuum spectrograph shown attached to x-ray tube 

(vertical) . 

possible without vacuum. The crystal is best oscillated over a 
small angle by means of a motor and heart-shaped cam. 



ADVANTAGES OF X-RAY ANALYSIS 

1. Over chemical methods. 

a. Analysis of extremely minute amounts triumph of discovery of 
elements 72, 43, 75, 61, and 87 (Papish 1931). 

b. Analysis of rare earths, platinum metals, etc., where separations are 
difficult or impossible. 



CHEMICAL ANALYSIS FROM X-RAY SPECTRA 85 

c. Material used in any available form without special preparation 
and independent of chemical combination and without loss; hence 
valuable for rare metals, gems, etc. 

d. Greater safety, since no separation of elements is involved; hence 
much less work and great saving of time. 

e. Permanent record on plates, largely independent of personal 
equation. 

2. Over optical spectroscopy. 

a. The great simplicity of x-ray spectra, particularly the K series 
emission, as compared with the great complexity of optical spectra 
(notably iron). 

b. Absolute independence of x-ray spectra (number of lines and relative 
intensities) from excitation conditions; optical spectra are affected 
by differences in arc and spark spectra, changes in capacity and 
induction of the current for ultraviolet causing disappearance or 
strengthening of lines, etc. 

c. Independence of x-ray spectra from chemical combination or 
valence, since only atoms and not molecules are involved; optical 
spectra are affected by kind of chemical combination, band spectra 
of molecules, presence of foreign substances, etc. 

DISADVANTAGES 

1. Cannot be used for analysis of lightest elements, since characteristic 
wave lengths are too long for measurement by usual crystal gratings; the 
practical limit is calcium (Z = 20). 

2. Somewhat expensive and special equipment, much of it commercially 
available only in Europe. 

3. Very special technique, including selection of proper voltage, etc., 
for accurate quantitative analysis. 

4. Somewhat limited accuracy for quantitative work involving compari- 
son of line intensities with standards. The line intensities are not propor- 
tional strictly to the weight proportions of elements in the preparation for 
several reasons noted below. Intensities also depend on the particle size 
of the substance undergoing analysis, and minimum size is essential for 
true values. 

5. Selective volatilization of constituents of mixture from focal spot of 
target for primary emission method, with erroneous results; this difficulty 
is partly alleviated by rotating the anode in order to present fresh surface, 
or by using the fluorescent-spectra methods. 

6. Great decrease in intensities and prolongation of time for fluorescent- 
spectra methods. 

7. A serious difficulty for quantitative analysis is the effect of absorption 
edges on emission lines; if in a mixture one element has one characteristic 
absorption edge of longer wave length than the emission lines of other 
constituents of the mixture, these lines will be selectively absorbed. Such 
difficulties are avoided, when standardizing substances are used, by not 
mixing but by using a rotating target with the samples contiguous and 
excited to emission separately but, of course, registering on the same photo- 
graphic plate. The effect of the absorption edges of silver and bromine 
in the plate must be taken into account also. 



86 APPLIED X-RA YS 

8. Line coincidence 1 may occur and cause difficulties; avoided only by 
greater resolution of spectra and use of higher orders of reflection. 

9. Appearance of foreign lines, such as mercury, from diffusion pump; 
tungsten from metal sputtered in target from hot cathode, fluorescent metal 
lines from slits, traces of material from previous experiments on surface of 
anode, etc.; these can be checked with blank runs of apparatus. 

10. In certain mixtures characteristic rays of one element can be excited 
by the characteristic rays of another element arid thus produce a strengthen- 
ing of intensity of lines for the first. Gunther, Stransky, and Wilckc 
observed that a mixture of chromium and copper in the ratio of 46:54 
appeared to have the ratio 60:40 on account of characteristic rays of chro- 
mium excited by copper rays. Dilution with ground quartz produced true 
results. 

11. Varying sensitivity of the photographic emulsion to different wave 
lengths; long-wave lines are blacker in proportion to intensity than shorter. 



Qualitative Analysis. For the case of qualitative analysis of 
materials most of the foregoing disadvantages of the x-ray 
method are unimportant and the method is straightforward for 
the analysis, particularly of rare earths and alloys of every kind. 
The fluorescent method which has been hampered by low 
intensities and long exposure times is coming int o almost universal 
use with the advent of high-power tubes producing very intense 
radiation. 

Quantitative Chemical Analysis. Methods of quantitative 
analysis using the emission spectrum have been described by 
Coster, Stintzing, Gunther and Wilcke, Hevesy, Glocker, Gold- 
schmidt, and others. In general these methods depend upon 
the comparison of the intensities of corresponding spectral lines 
of two neighboring elements in the periodic table, the assumption 
being made that the intensities of, say, the K lines of two such 
elements would be the same because of the similar electronic 
configurations, provided the elements were present in the same 
amounts on the an ti cathode, and provided also that the excess 
of the potential on the tube over the potential required to excite 
these lines was great compared with the difference between the 
characteristic excitation potentials of the two lines. (In the 
first approximation the intensity of a spectral line is proportional 
to the second power of the difference between the potential used 
and the characteristic potential.) 

1 GLOCKER, " Materialpriifung mit Rontgenstrahlen," p. 119, Berlin 
(1927). 



CHEMICAL ANALYSIS FROM X-RAY SPECTRA 87 

The actual procedure in all these methods consists in deter- 
mining, photographically, the emission spectrum of a mixture 
containing an unknown amount of the element for which the 
determination is being made and a known amount of the reference 
element. The intensities of the two corresponding lines of these 
two elements which have been chosen for comparison are then 
measured, and the elements are then, on the previous assump- 
tions, present in amounts proportional to the intensities of their 
respective lines; or the amount of the reference material may be 
changed until the two intensities are equal, when their atomic 
amounts are also equal. 

The differences in the methods mentioned are mainly differ- 
ences in the technique of measuring the line intensities. Coster 
used a Siegbahn spectrograph and measured the relative line 
intensities with a Moll microphotometer. Gunther and Wilcke 
used spectrograms made with very small times of exposure, the 
lines being hardly visible to the eye. By using a microscope of 
800 magnification, they then directly counted the reduced silver 
grains in the film. The choice of the time of exposure is very 
delicate with this procedure, for too long a time causes agglom- 
eration of the grains, making counting inaccurate and difficult. 
Stint zing mentions the use of a microphotometer and also 
suggests a simpler method. He proposes the use of several 
superimposed photographic plates to record the spectrogram, 
the intensities of the several lines being indicated by the number 
pf films they penetrate. 

Coster and Nishina, indeed, found the assumption of equal 
intensity of the lines for equal atomic concentration to be valid 
only under certain conditions. For instance, in analyzing 
zirconium ores for hafnium, tantalum was added as the reference 
element, and correct results obtained if the tantalum was used as 
the dioxide. If, however, the pentoxide was used, the tantalum 
lines were 2\^ times as weak as the assumption would predict. 
Furthermore, the presence of only a small amount of Lu 2 O 3 caused 
the dioxide to give results similar to those obtained with the 
pentoxide. These differences led Coster and Nishina to the 
adoption of an entirely empirical method in which any two 
lines near each other in the photographic plate may be used. 
Thus Hevesy and Jantzen used the Lu-L/3i line and the Hf-L#2 
lines, which are 0.004 A.U. apart, in analyzing for hafnium. The 
method of Coster and Nishina has been used for the analysis of a 



88 



APPLIED X-RAYS 



large number of zirconium ores for their hafnium content. The 
determinations are said to have been made to 0.1 per cent with 
an accuracy of 10 per cent. 

Because of the inherent difficulties of the emission-spectrum 
method, Glocker and Frohnrnayer have developed a method 
which depends upon the relative intensities of the general 
radiation on each side of a characteristic absorption discontinuity 
of the element for which the analysis is being made. An ordinary 
Coolidge tube may be used; the sample may be in a number of 
different forms and may even be used without change if neces- 
sary. A photographic absorption spectrum is obtained in 
the usual way and the relative intensities determined by a 
microphotorneter; or an absorption spectrum may be determined 
by using an ionization chamber. The relation between the 
intensities and the amount of the element in the sample is given 
in general by the equation 



where /2 is the intensity of the radiation leaving the absorption 
screen on the short- wave-length side of the discontinuity, and I } 
is the intensity of the long-wave side; c is a coefficient which must 
be experimentally determined, and p is the amount of element 
present. 

The following data include values of c and of the smallest 
mass, m, in milligrams per square centimeter for the production of 

'FABLE X. MINIMUM MASS OF ELEMENTS REQUIRED FOR ABSORPTION 

EDGE 



Element 


c 
K edge 


c 
LI edge 


m 
K edge 


m 
LI edge 


42 Mo 


69 




0.7 




47 Ag 


45 




1.1 




50 Sn 


34 




1 5 




51 Sb 


31 




1 6 




56 Ba 


24 




2 1 




58 Ce 


22.5 




2.2 




74 CV 


8 




6 




82 Pb 


5 7 




9.0 




90 Th 


3 2 


50 


16.0 





92 H 




45 




1 1 



CHEMICAL ANALYSIS FROM X-RAY SPECTRA 



89 



a true absorption edge (5 per cent intensity difference in two 
sides). 

This method has been used by Glocker and Frohnmayer in 
the successful analysis of barium in glass, antimony in a silicate, 
salt mixtures of antimony, barium, and lanthenurn, bismuth in 
alloys, etc. It cannot be used to advantage for elements below 
molybdenum. 

Hevesy 1 has made a very careful study of the factors which 
determine the results by analysis with fluorescent secondary 
rays. Characteristic primary rays ordinarily give six or seven 
times more intense secondary rays than rays with a continuous 
spectrum. For greatest intensity a metal must be chosen for 
target whose characteristic rays are 0.15 0.20 A.U. shorter 
than the absorption bands of the elements undergoing analysis. 

Especial attention also has been paid to the distorting effects 
upon emission-line intensity of absorption edges of a foreign 
element between comparison lines, or lines of a foreign substance 
between the edges of the elements being compared, etc. The 
general conclusion is that the comparison element should be 
chosen so that the lines and absorption edges are as near as pos- 
sible to those of the element being determined. The following 
table is an example of correct choice: 



TABLE XL COMPARISON ELEMENTS FOR QUANTITATIVE ANALYSIS 



Element 
analyzed 


Lino X, A.U. 


Edge X 


Comparison 
clement 


Line X 


Edge X 


Pt . 


La, 1 310 


1 070 


Ta 


L0 3 1 303 


1 058 


In 


La, 3 764 


3.313 


Cd 


Lfti 3.730 


3 322 


Cd 


7^3.948 


3 496 


Ag 


L0! 3.927 


3 505 


Mo 


Lai 5. 394 


4 914 


Ch 


L/3, 5 480 


5 012 


Rb 


La, 7.303 


6 841 


Si 


Ka, 7 109 


6 731 


Ge 


K@, 1.126 


1.115 


Ta 


La, 1 135 


1 112 


Zn . 


K&! 1.293 


1 281 


Hf 


L0 2 1 324 


1.293 


Ni 


K$, 1 497 


1.489 


Er 


L/3, 1 511 


1 480 


Ti.. 


K$, 2.509 


2 494 


Cs 


L 2 2 506 


2.466 


8 


K fr 5. 021 


5 012 


Mo 


L|8, 4 909 


4 904 


Al . . 


Kfli 7 941 


7 947 


Br 


LfrS.108 


7.727 


Mg. . 


Kft } 9 535 


9 511 


As 


Lp, 9.394 


9 300 



1 "Chemical Analysis by X-rays and Its Applications," McGraw-Hill 
Book Company, Inc., New York, 1932. 



90 APPLIED X-RA YS 

Fortunately the distorting effect is appreciable only when there 
is a considerable amount of a foreign element present ; in ordinary 
cases it may be neglected without seriously affecting the quantita- 
tive analysis. An important application of secondary-ray 
analysis is that of complex minerals down to 0.1 per cent of a 
constituent or even 0.001 mg. of any element. Another is in 
tests of preparations for purity, in which concentration of impuri- 
ties of 1 part in 10,000 may be found. Kiddy, Gaby, and Turner 1 
were able to find 1 part of iron in 300,000 parts of zinc. 

1 Proc. Roy. 8oc. (London), 124, 249 (1929); 127, 20 (1930). 



CHAPTP]R VII 
THE ABSORPTION AND SCATTERING OF X-RAYS 

The fact that x-rays are absorbed in matter in accordance 
with definite laws is, of course, of very great practical importance. 
Differential absorption by heterogeneous matter of varying den- 
sity is the fundamental basis of the entire science of radiography 
both in medical diagnosis and in the examination, for example, of 
metal castings for defects, inclusions, pipes, gas pockets, etc. The 
laws of absorption determine the protection which x-ray workers 
must utilize against the harmful effects of the x-rays. Similarly, 
absorption must precede any effects of x-rays upon chemical 
action or biological functions. 

X-ray science owes much to absorption measurements, since, 
properly interpreted, they give valuable information upon 
atomic structure. They were the sole method of investigating 
the quality of x-rays from the time of Roentgen's discovery down 
to 1913 when Lane and the Braggs introduced crystal analysis. 
By absorption measurements with screens of various materials 
Barkla discovered the absorption and emission of x-rays w^ith 
wave lengths which are characteristic for each chemical element. 

The Absorption Coefficients. In traversing matter of all 
kinds, x-rays are absorbed in accordance with the usual exponen- 
tial equation 7 = 7 e~ M * where 7 is the intensity after passage 
through homogeneous matter of thickness x, 7 ( , is the initial inten- 
sity, and IJL is the absorption coefficient. One of the most useful 
applications of this formula is the expression of absorption proper- 
ties in terms of the "half-value thickness 77 II or that which dimin- 
ishes the intensity of a parallel bundle of rays to one-half the 

initial value; thus 5 = e~^ , 77 = ^-^ = ~ 6 -- When the 
'2 ' MM 

intensity of a monochromatic beam of x-rays is plotted against 
the thickness of absorbing material (presupposing no character- 
istic absorption effects), a curve of the form illustrated in Fig. 
40 is obtained. If values of log 7 are plotted against a*, a linear 
relationship holds, as shown in Fig. 41, always provided that the 

91 



92 



APPLIED X-RAYS 



beam is strictly homogeneous. The slope of the line is an indica- 
tion of quality or wave length : the steeper the slope, the softer the 
ray. 

Practically always, however, the absorption formula appears as 

-t* 
I I () ep P where p is the density, and /i/p, the mass-absorption 



80 
60 

M 

40 
20 



\, 




















\ 






















\ 






















\ 






















\ 






















\ 






















X 


s^ 






















^ 


^ 













































100 
80 
60 

40 



20 



4 6 

X inm.m 
FIG. 40. Intensity of x-rays plotted 



2 4 6 8 10 02 4 6 8 10 

X in m.m. 

FIG. 41. Semilogarithmic graph for 
us a function of thickness (.r) of an absorption of x-rays; I and III repre- 
absorbing screen. sent beams with the same wave 

length but different initial intensities, 
while II has the same initial intensity 
as I but a longer wave length. 

coefficient, denotes the absorption by a screen of such thick- 
ness that it contains unit mass per square centimeter. Only in 
this way is it possible to compare rationally the absorption coef- 
ficients of different substances and the properties of the atoms 
themselves. This /x/p is a simple function of atomic number 
while M is not. The mass coefficient is independent of physical 
state, state of aggregation, and temperature and for chemical 
compounds is in the first approximation additive from the mass 
coefficients of the constituent elements. By multiplying /z/p by 
the absolute mass of an atom, which is the atomic weight A 
divided by the Avogadro number No = 6.063 X 10 23 , the 
atomic-absorption coefficient is obtained. Since this refers to a 
screen which contains 1 atom per square centimeter, it leads to 
some interesting information concerning atomic structure. 

It is now definitely established that JU/P is really the sum of two 
coefficients r/p, the true or fluorescent-ray mass-absorption coef- 
ficient, and er/p, the mass-absorption coefficient due to scattering. 
The latter is usually much smaller in value than the coefficient for 



THE ABSORPTION AND SCATTERING OF X-RAYS 



93 



the absorption due to fluorescence. For light elements o-/p has 
a practically constant value of 0.17 independent of the wave 
length for intermediate ranges. For heavier elements its experi- 
mental value changes in a complicated fashion. Some repre- 
sentative values for n/p and <j/p are as follows : 



TABLE XII. VALUES OF 



AND 





M/P 


0-/P 




X - 0.12 A.U. 


X - 0.71 A.U. 


X = 0.12 A.U. 


X = 0.71 A.U. 


c 


151 


68 


14 


18 


Al 


18 


5 35 


14 


20 


Cu . 


46 


53 7 


18 


29 


Ag 


1 60 


28 5 


35 


47 


Ph 


5 2 


140 


67 


82 



In all cases a/p has a very small value for very short wave 
lengths. Barkla obtained the approximately constant value of 0.2 
in his pioneer experiments. When this value is equated with the 
J. J. Thomson theoretical value of scattering by electrons in 
accordance with the classical wave theory, the result comes out 
that the number of electrons per atom is half the atomic weight. 
Subsequent developments have proved that this deduction is only 
approximate. 

The true or fluorescent coefficient may be written as a function 
of 'the cube of the wave length, i.e., K\*. The atomic-fluores- 
cent coefficient of absorption refers to a process of actual trans- 
formation of x-rays in the absorbing screen. It is a function of 
both the atomic number Z and the wave length; thus r/p -A /No = 
CZ 4 X 3 (law of Bragg and Peirce). C for each element is constant 
only over certain ranges and then changes abruptly at wave 
lengths which are characteristic of each element; the same is true 
of Kin 

fjL/p = r/p + d/p = K\* + a /p. 

The latest values 1 of the constants for six metals in the equa- 
tions for the mass-absorption coefficients above, K K , and below, 
K L , the first discontinuity (the characteristic K absorption), 
are given in Table XIII. 

1 RICHTMYER, Phys. Rev., 27, 1 (1926). 



94 APPLIED X-RAY X 

TABLE XIII. VALUES OF CONSTANTS IN ABSORPTION EQUATION 





Mo (42) 


Ag(47) 


Sn(50) 


W(74) 


Au (79) 


Pb(82) 


K K 


375 


545 


595 


1870 


2230 


2570 


K L 


50 


70 


90 


330 


395 


476 


K K /Ki 


7.5 


7.8 


6 6 


5 65 


5 65 


5 40 


T/1 (10~ 21 ) 


13.3 


11.0 


8 90 


3 19 


2 57 


2 37 

















Of especial interest are the precise equations deduced by 
Duane and Mazumdar for aluminum and copper which are so 
commonly used as filters for x-rays: 

AL/ = 15.5X 3 + 0.147; 

P 

Cu, M = 193X 3 + 0.13. 

p 

Allen 1 has found that the empirical formula 



(A/No) 



- 

P 



where A is the atomic weight and No the Avogadro number, 
applied to his experimental results on carbon, paraffin, sulfur, and 
16 metal elements from aluminum to uranium for wave lengths 
0.56 to 0.08 A.U. (the important range in therapeutic uses of 
x-rays) gives values of <r/p which increase with atomic number, 
becoming about 1 for heavier elements. The values of C for 
all values of Z and for values of X from 0.08 to 1.0 A.U. are 
0.0132 for the so-called K (or hardest) series of x-rays and 0.00181 
for the L series. 

Another empirical formula, suggested by A. H. Compton, has 
the form 

M/P = (rv# 4 X 0.32Z)/(A/#o). 

Since the mass-absorption coefficient of a chemical compound 
may be represented as the sum of the coefficients for each of the 
atomic species present in the compound, the equation may be 
written in the summation form 



= (compound) = (CX 8 2 4 + 0.32 2Z)/2(A/N ). 
ALLEN, Phys. Rev., 27, 266 (1926). 



THE ABSORPTION AND SCATTERING OF X-RAYS 95 

In precision researches by Havighurst 1 this equation has been 
found to agree excellently with experimental results on various 
powdered salts containing elements with atomic numbers greater 
than 5. Measurements by Windgardh on some of the same 
salts in solution arc also in agreement. 

Jonsson has utilized the idea of absorption coefficient "per 
electron 77 

ii - - . A - r<tt - C(7 \V (Z ' X) 
PC vF~r r/ iA>6 A; , 

p I\ Q/j /J 

where A is the atomic weight, Nn the Avogadro number, and Z 
the atomic number. Out of this has come a universal absorp- 
tion curve 2 in which 



log [GO* x No] = log 



is plotted against log (Z\). This linear graphical method is 
surprisingly accurate and is applied directly if X is smaller than 
the K absorption limit; if X lies between X A - and X Ll the numerical 
value from the curve must be multiplied by v L J V K , etc. 

Mechanism of Absorption.- When a beam of x-rays impinges 
upon matter, the radiation energy is partly transformed, as 
already indicated, and partly scattered. Figure 42 indicates 
the principal phenomena which have been identified, though 
others have some experimental proof. 3 

Fluorescent Characteristic X-rays. The energy of these 
secondary rays is accounted for in the term r/p in the mass- 
absorption equation JJL/P = r/p + <r/p. Upon analysis with a 
spectrometer the rays arc shown to be identical with those 
which would be emitted if the absorber element were used as an 
x-ray tube target, in that the line spectra in the K y L, Mj etc., 
series are obtained with the same wave lengths. This presup- 
poses that if the K series spectrum appears, the exciting primary 
beam must contain rays with a frequency equal to or greater 

1 Proc. Nat. Acad. Sci., 27, 477 (1926). 

2 KIRCHNER, Allgemeinc Physik dcr Kontgenstrahlen, "Handbuch dor 
Expcrimentalphysik," Vol. XXIV, Part 1, p. 252. 

3 The most complete and recent treatise on the whole subject is to be 
found in Kirchner, Allgemeine Physik der Rontgenstrahlcn, "Handbuch 
d* Experimeritalphysik," Vol. XXIV, Part 1. 



96 



APPLIED X-RAYS 



than thai which is characteristic of the K critical absorption limit 
of the absorber element. Fluorescent x-rays are unpolarized. 

Primary x-ray quanta with an energy equal to or greater than 
^absorber K limit remove electrons from characteristic levels in the 
atom just as effectively as the cathode rays in an x-ray tube. 




jfc 



%v 



^""er, 



'**-"*<, 

'"""ftfer 



- Un&bsorbed Primary Rays 




Primary X-RayS 



FIG. 42. Phenomena occurring when x-rays impinge upon matter. 

Scattered X-rays Unmodified. These rays have the same 
wave lengths as the primary beam; for instance, if the primary 
beam contains the tungsten characteristic rays, then the spectrum 
of the scattered x-rays will show the tungsten lines; thus reflection 
from crystals is essentially a special case of scattering. If the 
primary x-rays are transferred in energy quanta, the scattering 
is produced by atoms or groups of atoms which are too massive 
to be sensibly affected by the radiation quantum. These rays 
are polarized, usually completely; thus no reflection from a 
crystal occurs, when the primary rays are linearly polarized, 
if the direction of the reflected ray coincides with the electric 
vector of the incident ray. 

Scattered X-rays Modified by the Compton Effect. One of 
the great contributions in physics in recent years was the dis- 
covery by Compton and by Debye that the spectra of scattered 



THE ABSORPTION AND SCATTERING OF X-RAYS 97 

rays, characteristic of the primary rays and not of the secondary 
radiators, show not only lines with the same wave length as 
those in the primary beam but also, on the long wave-length side 
of these lines, other lines which indicate that in the process of 
scattering a distinct change has occurred. These modified lines 
were shown to be quantitatively explained upon the basis of a 
purely quantum phenomenon. A primary quantum of x-radia- 
tion energy hv Q strikes an electron and imparts to it a certain 
amount of kinetic energy resulting in recoil. The radiation 
quantum is changed in its direction and proceeds with an energy 
hv, smaller by the amount involved in the recoil of the electron. 
Consequently the wave length will be longer. The so-called 
shift from the unmodified wave length is expressed by 
the equation b\ = (h/mc)(\ cos </>) = 0.0242(1 cos </>) = 




. 4'i. Diagram showing Oonipton effort. 



7 vers </>, where is the angle between the incident and the 
scattered ray. At $ = 90 deg., the shift will therefore be 0.0242 
A.U. This increase in wave length is, therefore, independent of 
the wave length and of the scattering element and depends only 
on the angle </>. 

The Compton effect is well illustrated in the diagram in Fig. 
43. Here hv Q is the primary quantum scattered by the electron e. 
The length of the arrow hv$ measures the energy magnitude. 
According to classical or unmodified scattering, the scattered 
quanta will always have the same hv n value independent of the 
direction. This can be represented by the dotted semicircle 
with radii hv Q . Actually there is a wave-length change and this 
is represented for five directions 1, 2, 3, 4, 5, as full lines, the 
lengths hv being smaller the greater the scattering angle, and the 
energy changes being the vector difference between the dotted 



98 APPLIED X-RAYS 

and full positions of each radius. This energy change is 
accounted for in the kinetic energy of the recoil electrons repre- 
sented by the arrows in the smaller curve; T is because for the 
scattering angle deg. no energy is available; 2', which is too 
small to show, corresponds to 2, 3' to 3, etc. 

The ratio of the intensities of modified and unmodified rays 
in the Compton effect, however, varies with the atomic number 
of the radiator element, from co for lithium (all energy modified) 
to 5.48 for carbon, 1.91 for sulfur, 0.51 for iron, 0.21 for copper, 
and decreasing values for heavier elements to practically zero 
for lead. The Compton effect has been the subject of consider- 
able controversy, as the result of which careful researches by 
numerous investigators throughout the world have estab- 
lished it as a fact and as a powerful support to the conception 
of radiation energy in quanta. No such change in wave length 
has been observed in the reflection of x-rays by crystals, or 
in the scattering of rays of light. As independent proof the 
tracks of the recoil electrons have been photographed by C. T. R. 
Wilson's cloud-expansion method. 

The energy distribution 

ri , a. vors (/> 2a cos 2 O 

= hv 



'-'kmotic '*" 11 , 'tr /^ . ^r^ ^ oTV" 

1 + a vors <t> (1 + a)~ a 2 COS 2 B 

where a = 7/X, is verified experimentally. 

It is interesting to calculate how much energy is involved in 
the recoil electrons for a practical case of irradiation of the human 
body from a tube at 200 kv. (average wave length 0.04 A.U.) : 

E kinetic = ^("0 V). 

If the average increase in wave length (</> = 90) is 0.024 A.U., 

E k = h( j- - f nv>i ) '> expressing E in volts the recoil electrons 
\AO AO -r O.UZ4y 

have a velocity of about 50 kv. Thus 5 ?2oo or %5 per cent of 
each quantum in the human body goes into the energy of recoil 
electrons. For rays generated at 200 kv., 2.5 per cent of the 
x-ray energy in each part of a tissue is transformed into the 
energy of photoelectrons. Of the fraction of primary energy 
which is scattered (12 per cent), 3 per cent (25 per cent of 12 
per cent) goes into recoil-electron energy. 

Scattered and Characteristic 0-rays. X-rays which are 
impinging upon the surface of a secondary radiator eject photo- 



THE ABSORPTION AND SCATTERING OF X-RAYS 99 

electrons. If the radiation is monochromatic (frequency v), 
then the kinetic energy of some of the liberated (scattered) elec- 
trons will be Ek = hv, independent of the secondary radiator. 
The electrons are those so loosely bound in the atoms that the 
work required for their removal is negligible. In addition, 
however, other photoelectrons are ejected with kinetic energies 
which depend upon the particular kind of atom from which they 
are liberated; hence, their removal has involved a certain amount 
of work W. If a beam of these electrons is analyzed by causing 
them to bend in a magnetic field, then all electrons with the 
same value of Ek = hv W will register a sharp spectral 
line on a suitably disposed photographic plate. By means of 
these characteristic /8-ray speclra, de Broglie showed that the 
energy necessary to eject an electron from an inner atomic shell, 
which is involved in the correction term W, is simply the quantity 
of energy representing the energy levels A', L, M, N, etc., which 
is in turn measured by the frequency values of the critical 
absorption limits. These /3-ray spectra, therefore, constitute 
another important method of measuring energy levels. In one 
photograph for photoelectrons ejected from a silver plate irra- 
diated by the ^-radiation of tungsten (and of course producing 
the secondary fluorescent silver K-radiation), de Broglie obtained 
six lines, corresponding to six different kinetic energies. He 
showed that these were: 

1. hv AKKa , L AK (where L/ AK is the energy required to remove an L 
electron from the silver atoms, or hv AoLeLbs ). 



3. hv^t - M AK . 6. fc? WA - K AK . 



More recently Robinson and his associates 1 have made notable 
contributions to the field of magnetic spectra of secondary elec- 
trons. By means of greatly improved experimental methods the 
values of energy levels have been determined for many of the 
chemical elements, including measurement of absorption limits 
in the range of long wave lengths in which the crystal-grating 
method is impracticable. This new work has also included 

1 For further detailed information see "International Critical Tables," 
Vol. VI, p. 2. The data of Ilobinson, together with all references, are given 
in Siegbahn, " Spektrokopie der Rontgenstrahlen," 2d ed., pp. 413-428. 



100 APPLIED X-RAYS 

measurement of energy levels in multiply-ionized atoms. The 
magnetic spectra not only yield energy values of secondary 
electrons which are ejected from inner levels by action of the 
primary x-rays; the secondary fluorescent x-rays generated in the 
radiator are also effective in liberating electrons. The process 
may be pictured as follows: a K electron is ejected through the 
agency of the primary x-rays, followed by the transition of an L 
electron, for example, to fill the vacancy. Normally a Ka ray is 
emitted as a consequence of liberation of energy. However, this 
energy so released can be transformed in the atom into forms 
other than the quantum of radiation. For example, the transi- 
tion L > K may lead to the ejection of an M electron with a 
kinetic energy represented by the difference between the first 
energy (L > K) and the work required to remove this M electron 
from the atom. This work is greater than that which normally 
corresponds to the M level, because an electron is missing from 
an inner level with the result that there is diminished screening 
of the positive nucleus. Therefore the work of separating an 
outer electron is equal to that required normally for the element 
of next higher atomic number. Such processes have been 
experimentally verified in Robinson's work. 

Atomic Structure from Intensity of Scattering by Gases. 
One of the most promising recent developments in physics has 
been the use of data from the scattering of x-rays by gases to 
determine electron distribution in atoms and to test data calcu- 
lated from wave mechanics. Compton 1 has shown that the 
density of electrons is represented by a Fourier integral of the 
form 



U(r) = Zr Q B sin (wrx)dx, 

where V(r) represents the number of electrons per Angstrom 
unit at a distance r from the center, Z is the atomic number, B 

/ _ \\ VL 

(depending on intensity of scattering) = 27r.r< ~r -yV , where 



S is the scattering per electron at x = 4/X sin (0/2). 

Wollan 2 has determined the distribution in helium, neon, and 
argon and found the curves for U(r) against r in good agreement 

1 Phy*. Rev., 35, 925 (1930). 

2 Phys. Rev., 37, 862; 38, 15 (1931); see also JAUN-CEY, ibid., 38, 1. 



THE ABSORPTION AND SCATTERING OF X-RAYS 101 

with similar curves derived from waves mechanics. For neon 
the data actually are able to separate the K and L electrons, 
as shown in Fig. 44. 

Filtration. The x-ray beams directly from a tube target are 
not of greatest usefulness as they are. The rays contain a large 
proportion of very soft components which are absorbed in the 
uppermost layers of any absorbing substance. For medical 
diagnosis and deep therapy they are obviously useless; par- 
ticularly as they may cause harmful skin reactions because the 
absorption per unit volume for the soft rays is relatively so great. 
The necessity presents itself in medical and other uses of working 



-N20 



\ 



K \ 



\ 



\ 



0.2 




1.4 



0.4 0.6 0.8 1.0 
(Angstroms) 

FIG. 44. Electron distribution in neon gas as derived from experiments on x-ray 
scattering (Wollan.'} 

with the most nearly homogeneous rays possible, namely, those 
for which the relative ratios of components of various wave 
length do not change during penetration of the irradiated object. 
The effect of filtration is illustrated by the following example: 
A mixture of rays consisting of 3 parts, soft, hard, and very 
hard constituents with equal intensity is filtered through 5 mm. 
of aluminum. For the very hard ray, ju = 0.405, 80 per cent 
penetrates through, for the hard ray, ju = 1.08, 60 per cent, and 
for the soft, /* = 6.75, only 4 per cent. Thus out of a continuous 
heterogeneous mixture actually generated, a beam less and less 
heterogeneous and with greater and greater average hardness 
(shorter wave length) results from greater filtration. Actual 
experimental results showing the effect of passage through 1, 5, 



102 



APPLIED X-RAY 8 



and 10 mm. of aluminum are illustrated in Fig. 45. When the 
absorption results are plotted logarithmically as in Fig. 46, it is 




as 

FIG. 45. Curves showing; effect of filtration of heterogeneous x-ray beam 
through 1, 5, and 10 mm. of aluminum. 

seen that the slope of the curve for small thicknesses changes 
continuously instead of being constant as is true for mono- 
chromatic rays (Fig. 41), showing that the quality of the beam 

is changing. Finally a point is 
reached where the curve becomes 
linear and below this homogeneity 
point no further change in quality 
occurs. This does not mean that 
the beam is monochromatic or 
even homogeneous when filtered 
through other materials. A beam 
generated at 200 kv. and filtered 
through 1 mm. of copper behaves 
as though it were homogeneous 
when passed next through water 
or the human body, for the curve 

FIG 46.-- Semi-logarithmic curve j g Kn but the game fi l tered 

illustrating the homogenizing of a 

beam of x-rays by filtration through beam passed through more COpper 

copper (compare with Fig. 41 for ig b n() means homogeneous, 
monochromatic rays). ^ 

These different behaviors are, of 

course, determined by the relation between values of ju and a. 
Hence filtration for the purposes of homogenizing is easily 
accomplished with a substance of higher atomic number than 
that of the object or body in which the rays are to remain homo- 



80 
60 

4-0 
20 






















y 


















\ 


















\ 




















\ 


















\ 




















\ 


"V 




















\ 


X 


X 


s 




) 2 4 6 8 
mm 



THE ABSORPTION AND SCATTERING OF X-RAYS 103 



geneous. In general medical practice copper is used as the 
homogenizing filter and aluminum as the test filter. If the 
radiation is homogeneous in aluminum, it will be so in the human 
body. 

Measurement of Quality by Absorption Methods, Since 
absorption depends so definitely upon the nature of the absorber 
or filter and upon the wave length of the ray, a practical measure- 
ment of the quality or hardness of an x-ray may be based upon 
it; for example, by comparing the absorption power of layers 



u/w 
































































j 


































rv -19 






























+ 
/ 






























































} 




028 




























/ 




n?A 


























/ 






























/ 




























































/ 












\\ 
















,-f-' 


^x 1 




























,+' 




























^ 






















0.12 








/ 
























fi fiR 
































































f\ n/\ 
































































o 


































D 


t 


V 


( 


!> 


1 


2 


1 


<b 


'L 





I 


4 


'I 


& ^ 



uw 








\ 






















\ 














032 





__ 







\ 


V 












t 












V 


TZ. 

jC. 








026 
-- 














M 








cn 

C 9 A. 














\ 












N 












\ 






'^020 


- 




1 


% 


a 






\ 


~A 


- 


+- A t. 








\| 


s. 






\ 

-\ 






<i 










\ 


s j 


p 








^-i 
& n i? 














S k 




\ 




^ 
















N 


4- 
1 




005 
















*k 


4- 






























































































Thickness of Aluminum /'n millimelers 
leni lo 1 millimeter of Copper 



20 40 60 

Percen-Voige of X-Rausihccf passes 
Ihrou^h 1 mm ,of Copper end 4mm of Aluminum 

a ft 

FIG. 47. Methods of evaluating effective wave length of a heterogeneous 
beam of x-rays. (Duane.) (a) Curve showing the thickness of aluminum 
having the same absorbing power as 1 mm. of copper for a beam of heterogeneous 
x-rays; (/>) curves showing the percentage absorption in 1 mm. of copper and in 4 
mm. of aluminum as a function of wave length. 

of aluminum to that of fixed thicknesses of silver, as judged by 
the fluorescent or photographic power of the emergent ray, a 
scale may be constructed and used without reference to wave 
lengths. Roentgen himself used such a device, and the Benoist 
penetrometer, consisting of a thin silver disk 0.11 mm. thick, 
surrounded by 12 numbered aluminum sectors from 1 to 12 
mm. thick is still widely used, particularly in the measurement 
of dosage in x-ray therapy. 

In many cases an x-ray beam with a variety of wave lengths 
may be used, and the simple absorption equations cannot be 



104 APPLIED X-RAYS 

used directly. Duane has suggested, however, the determina- 
tion of the " effective" wave length, or the wave length of a 
monochromatic ray which has the same absorption under given 
conditions as the whole polychromatic beam. An experimental 
curve has been constructed, based upon the fact that the thickness 
of aluminum which has the same absorbing power as a given 
thickness of copper depends upon the wave length of the radia- 
tion; for soft or long wave-length x-rays the thickness of alumi- 
num must be large, and for hard x-rays small. Experimentally, 
the percentage of the beam absorbed in 1 mm. of copper is first 
measured by the ionization produced in a gas, or by the effect 
on a fluorescent screen or photographic plate; then the absorp- 
tion in increasing thicknesses of aluminum is measured until it 
has the same value as for the copper. The wave length as a 
function of this equivalent thickness is read from a graph such 
as is shown in Fig. 47a. Another method consists in the suc- 
cessive measurements of absorption in 1 mm. of copper and 4 
mm. of aluminum. The wave length may then be read from 
the curves in Fig. 476. 

Protection from X-rays. The definite laws which govern the 
absorption of x-rays also permit an exact determination of the 
thickness of protecting material which must be employed in all 
work with these rays in order to prevent dangerous physiological 
effects such as burns and anemia. Of the more readily available 
materials, lead is the best for protective purposes. Table XIV, 
from the work of Kaye and Owen, lists the thicknesses of lead in 
millimeters which are equivalent to 1 mm. of several protective 
materials in common use for x-rays generated by a Coolidge 
tube operated at 100,000 volts. 

TABLE XIV. PROTECTIVE POWERS OF MATERIALS RELATIVE TO LEAD 

Lead glass 12 to 20 

Lead rubber . 25 to . 45 

Bricks and concrete 01 

Woods ... 001 

Barium sulfatc plaster 05 to 13 

Steel . . . 0.15 

Adequate protection is a factor of vital importance which 
must be considered in the installation of x-ray equipment. 
Undue exposure to the radiation may lead to a lowering of the 
white blood-corpuscle count (leukopenia), to low blood pressure 
and anemia, as well as to the skin burns which were so fatal to 



THE ABSORPTION AND SCATTERING OF X-RAYS 105 

the early workers. For those engaged in x-ray researches a 
dental film carried in the pocket for 2 weeks will give a quick 
index of excessive exposure; if it is then definitely fogged, pro- 
tection should be increased. Blood-corpuscle counts at intervals 
are advisable. Shortening the hours of work and increasing 
the amount of fresh air and recreation are effective in removing 
symptoms. A "tolerance dose' 7 which the human body may 
withstand without ill effects has been determined as 1 X 10~ r> 
rVsec. for 200 working hours per month. 2 

An International Safety Committee under the auspices of the 
International Congress of Radiology has functioned for several 
years in standardizing requirements for adequate x-ray protec- 
tion. As higher and higher voltages are being used in therapy, 
such standards become increasingly important. A new advisory 
committee formed in the United States has prepared a unified 
and detailed set of safety recommendations (x-ray and high- 
tension protection, storage of inflammable film, etc.). 3 

The following minimum equivalent thicknesses of lead for 
protection are recommended as adequate : 

TABLE XV 

X-rays Generated by Peak Voltage Minimum Equivalent Thickness of 

Not in Excess of (Kilovolts) Lead, Millimeters 

75 1 

100 1 5 

125 2 

150 2 5 

175 3 

200 4 

225 5 

300 90 

400 15 

500 22 

600 34 

In the x-ray laboratory at the University of Illinois which 
is devoted primarily to researches on ultimate structures of 
materials, the x-ray tubes are enclosed in lead-lined containers 
through which are adjusted the necessary slits and pinholes. 
Sheet lead ^ in. thick gives a large factor of safety for a molybde- 
num-target tube operated at voltages up to 30,000 volts, and a 

1 The ' V unit of dosage is denned on p. 163. 

2 MUTSCHELLER, Am. J. Roentgcnology , 13, 65 (1925). 

3 Bureau of Standards, Handbook 15 (1931). 



106 APPLIED X-RAYS 

thickness of }/ in. suffices for tungsten-target tubes operated at 
voltages up to 150,000 volts. The new metal self -shielding 
x-ray tubes, which permit passage of rays only through very 
small windows, also simplify the matter of protection of the 
research worker. For radiographic examination of metals and 
in x-ray therapy, the rays from a tube cannot be so narrowly 
defined, and it is sometimes essential to line an entire room with 
sheet lead and to place the control instruments outside the room. 
Such equipment may be seen at the Watertown Arsenal and in the 
Physics Department of the Massachusetts Institute of Technology. 

Some Practical Applications of Absorption Measurements. 
Aside from the value of characteristic absorption edges in 
qualitative and quantitative analysis (Chap. VI), the simple 
exponential law / = /o^" MX is the basis from which valuable 
information may be obtained. Filtration, for the purpose of 
homogenizing beams for therapy, and the determination of 
quality and effective wave length have been considered already. 

Other possibilities which have found interesting practical use 
are as follows: 

1. Determination of the true thickness x of various specimens. 
As an example may be selected the classification of hides and 
finished leather. Because of the biological variable, constant 
quality and thickness are out of the question and mechanical 
micrornetric methods are ineffective. For such a classification 
the beam from an x-ray tube, which is operated so that wave 
length will be compatible with absorbing power of a specimen 
(soft rays for leather), is passed through a specimen and the inten- 
sity / as well as the initial intensity 7 is measured, best from the 
ionization current produced in a gas, which in turn is measured 
by the deflection of an electrometer or electroscope. The 
brightness of a fluorescent screen or darkening of a photographic 
plate could also be employed. With constant 7 and ju for the 
given material it follows that the values of x from one sample to 
another may be ascertained with great accuracy. Other known 
examples are glass lenses, thin metal foils, paper, paint and 
varnish films. 

2. Uniformity of gage. Variations in thickness in a sample of 
material are, of course, indicated by irregular results when the 
sample is moved around in the x-ray beam. 

3. Composition of mixtures and solutions. In such cases 
quantitative analysis of the unknown composition of two or 



THE ABSORPTION AND SCATTERING OF X-RAYS 107 

more substances mixed as powders or melted together, or dis- 
solved, may be made if standard measurements of absorption as 
a function of known composition are available for comparison. 
Aborn and Brown 1 showed that the amount of lead tetraethyl 
in gasoline could be determined by measurement of the absorp- 
tion of x-rays, generated under standard conditions, in a standard 
thickness of the solution and comparison with standard experi- 
mental curves showing absorption as a function of lead tetraethyl 
concentration. This method is, of course, best adapted for pairs 
of substances whose absorbing powers are widely different. 
Alloy composition, amount and uniformity of distribution of 
impregnating agents in wood, heavy metal content of glass, 
loading of silk fibers with tin dioxide, concentration of colloidal 
metal sols, and fillers in rubber are among the examples of this 
process. 

4. Determination of porosity. The actual absorption measure- 
ments of a substance of certain apparent thickness depend, of 
course, on whether the substance possesses maximum density or 
whether the density is affected by a porosity, even microscopic, so 
that the absorbing power is smaller than the value predicted for 
the measured thickness. Charcoals, drying agents such as mag- 
nesium perchlorate, sodium silicates, and other substances have 
been studied in this way. 

5. Detection of counterfeit coins; differentiation of true and 
imitation gems, such as diamonds, and of soft and lead glass; 
and 'other similar test in which specimens may be compared 
side by side have depended upon the absorption laws for x-rays. 
The advantage is found in the extreme rapidity with which 
identification can be made, presupposing the availability of 
suitable apparatus. 

6. Finally, the examination of all materials for gross interior 
structure, the discovering particularly of inhomogeneities and 
imperfections, depends upon the differential absorption of x-rays. 
This constitutes the familiar and extremely important and practi- 
cal science of radiography to which the next chapter is devoted. 

1 Ind. Eng. Chem., analytical ed., Vol. I, p. 26 (1929). 



CHAPTER VIII 
RADIOGRAPHY 

Although x-rays, because of their short wave lengths are able 
to penetrate matter, still they are differently absorbed by differ- 
ent substances; that is to say, all materials are not equally trans- 
parent to x-rays. These facts are the basis of the science of 
radiography. Broadly defined, the experimental technique con- 
sists in passing a beam of x-rays through the object to be examined 
and, by means of a fluorescent screen or photographic plate, 
recording the varying intensities of the emergent beam and thus 
obtaining a shadow picture of the interior of the object. ^ Prob- 
ably the first practical uses of x-rays were of a radiographic 
nature, and radiography today is a most useful tool to the 
medical and industrial diagnosticians. 

MEDICAL DIAGNOSIS 

In the discovery and location of internal defects of the human 
body, radiography has become indispensable. The use of x-rays 
to examine fractured bones preparatory to setting, to study con- 
ditions of the teeth as an index to subsequent treatment, and to 
locate bullets, swallowed pins (Fig. 48), and the like has become 
so routine that everyone is acquainted with it. Not so well- 
known, perhaps, are the uses of x-rays in the diagnosis of tumors, 
of incipient tuberculosis of the lungs and joints, of diseases of 
the alimentary tract, of stones in the kidney and the gall bladder, 
and of diseases of the liver and the pelvic organs. 

In the examination of the alimentary tract the use of barium 
sulfate or bismuth salts or emulsions and other similar agents, 
mixed with the food to produce opacity in the part to be examined, 
has become a science in itself. Similarly, the injection of gases 
and iodized oil into affected parts enables these to be thrown 
into relief for diagnosis from radiographs. The application of 
such schemes is continually extending the field of x-rays in 
medical diagnosis, and wider and wider applications are certain 
to be found. 

108 



RADIOGRAPHY 109 

An exceedingly interesting outgrowth of medical diagnosis 
has been the x-ray photography of mummies taken through 
wrappings. Some very interesting anatomical comparisons of 
ancient Egyptians with modern man have been made possible 
and the same evidences of disease and malnutrition in bone 
structures obtained as are common today. The Field Museum 



it: 




FIG. 48. Typical medical diagnostic radiograph for location of foreign bodies. 

including one in which the ancient embalmer had perpetrated 
a hoax entirely unsuspected from the exterior of the mummy by 
connecting the head and the legs with a stick since the trunk 
of the body is entirely missing. 

Still other applications are the fitting of shoes; identification 
of skeletons by radiographs of the skull which are as highly 
individualistic as finger prints; scientific studies of the diet as it 
affects bone and tooth structures of rats and test animals, or 
produces rickets; and identification of cause of diseases in fish 
such as the knot-head carp in the Illinois River radiographed in 
the writer's laboratory. 



110 



APPLIED X-RAYS 




FIG. 49. Exterior view of modern industrial x-ray installation for radio- 
graphic examination of welded pressure vessels. (Courtesy Henry Vogt Machine 
Company, Louisville, Ky.) 




FIG. 50. Interior view, showing two x-ray tubes and two Kenotrons, of new 
installation for metal radiography. (Courtesy General Electric X-Ray Cor- 
poration.) 



RADIOGRAPHY 



111 



INDUSTRIAL DIAGNOSIS 

Just as the inside of the opaque human body may be observed 
on the photographic film or fluorescent screen by virtue of the 
differential absorption of penetrating x-rays, and without damage, 
so also may any metal object be radiographed for the purpose of 
determining the gross structure and the presence of inhomogeneity 
or defect. The immeasurable importance of this information is 
evident in terms of the satisfactory behavior or failure of metal 
or other objects of practical utility and of the safety of human 
life which is so frequently involved. 

General Principles and Technique of Radiography Applied to 
Industrial Materials. 1. The 
technique for preparing radiographic 
pictures is comparatively simple. 
A tungsten-target x-ray tube of the 
Coolidge or Metalix hot-filament 
type is ordinarily employed. The 
filament is heated to incandescence 
by a separate circuit and this con- 
stitutes the cathode in the high-ten- 
sion circuit, with the target as the 
anode. A closed-core, oil-immersed, 
high-tension transformer which may 
produce up to 300 kv. is almost 
invariably the modern equipment. 
The alternating high-tension current 
is rectified by mechanically rotating 
disks or by vacuum-tube Kenotrons. 
The targets may be water-cooled by 
an insulated circulating system and 
thus enable the passage of large cur- 
rents through the tubes. Since 
radiographic exposures are usually 

of short duration, X-ray tubes of the FIG. 51. General arrangement 
i , . i . i , 1 i . for photographic radiography. R t 

universal type, in which the targets x . ray tube; ^ protecting cy i in der; 

become hot, are Ordinarily #, diaphragm; W, specimen, F, 
i i rro. i_ j. !_ i_ j. photographic plate; B \. lead screen. 

employed. The object which is to * * 

be radiographed is placed at some distance from the tube so that 
the rays proceeding from the focal spot on the target are essentially 
from a point source. Radiographs are merely shadow pictures 




112 



APPLIED X-RAYS 



produced by radiation traveling in straight lines from a point 
source. The most recent types of industrial installation for the 
examination of high-pressure vessels are shown in Figs. 49 and 50. 
2. Registration of the radiograph is either photographic or 
visually observed on the fluorescent screen (calcium tungstate 
usually, or barium platinocyanide, zinc silicate, cadmium tung- 
state, etc.). The general arrangements for the two methods are 
shown in Fig. 51 for the photographic method and in Fig. 52 
for visual observation. In the latter case a mirror is arranged 
so that the observer will not be in the direct path of the x-rays. 




FIG. 52. Two arrangements for x-ray fiuorosoopy ; R, x-ray tube; SV, pro- 
tecting cylinder; /?, diaphragm; W , specimen; L, fluorescent screen; 8, mirror for 
observation of fluorescent image without direct exposure to x-rays; A, eye. 

3. For each material and each thickness there is a certain 
optimum voltage for excitation of the x-ray tube: e.g., 80 kv. 
for 4 cm. Al, 110 kv. for 10 cm. Al, 200 kv. for 6 cm. Fe, 230 kv. 
for 6 cm. brass. 

4. Secondary and scattered radiation plays a large part in the 
results obtained and, for the certain identification of small 
imperfections in an object on the plate, must be eliminated. A 
grid such as a Bucky diaphragm consisting of narrow strips of 
lead or other metal edgewise with free space between each strip 
is often placed between the object and the plate. The primary 
rays pass straight through the gaps between these strips, while 
the secondary rays at various oblique angles from the specimen 
are entirely cut off. Such diaphragms must be moved slowly 
across the plate. Secondary rays also arise from the walls of 
the room and other objects, so that the film must be thoroughly 
protected by covering the back and edges with sheet lead. 



RADIOGRAPHY 



113 



5. Tubes with the sharpest possible focal spots are necessary 
for sharp definition and contrast on photographs at the boundaries 
of portions indicating different densities. 

6. Careful photographic technique must be employed in 
order to assure distinction between the smallest differences in 
blackening of the plate. Experiment has indicated that the 



optimum blackening is 8 0.7 to 



.9 (K = log %, 



the photo- 



metrically measured light intensities before and after passage 
through the photographic layer). The normal eye can detect 
with certainty a minimum blackening difference between adjacent 
areas of 0.02. 

7. The amount of exposure is defined by the product of the 
milliamperage through the x-ray tube and the time of exposure in 




"0 10 20 30 40 50 60 70 80 

Thickness of Iron in Millimeters 
FIG. 53. Exposure chart for radiography of iron or steel specimens. 

seconds. Very complete and useful data have been obtained by 
Berthold 1 for iron, aluminum, copper, and brass. The chart for 
iron in thickness up to 80 mm. is reproduced in Fig. 53. This 
shows the log of milliampere seconds (m.a.s.) against thickness of 
iron in millimeters, for voltages from 120 to 200 kv. for both small 
field (less than 3 cm. 2 ) and large field (50 to 100 cm. 2 ), focal 
distance 50 cm., two intensifying screens with Agfa films, 
absolute blackening 0.7. 

1 "Grundlagen der technischen Rontgendurchstrahlung," Leipzig, 1930. 



114 



APPLIED X-RAYS 



8. For practical use of the fluorescent observation, at least a 
dose 5 X 10~ 3 r l per second must fall upon the screen. 

9. The practical limits of penetration and satisfactory radio- 
graphic examination of aluminum, iron, and copper are listed 
in Table XVI for the following conditions: 200 kv. non-pulsating, 
15 ma., 50 cm. focal distance, two intensifying screens, Agfa 
film, blackening S = 0.7, without screens for eliminating 
scattered radiation. 

TABLE XVI. LIMITS OF THICKNESS IN MILLIMETERS FOR RADIOGRAPHIC 

EXAMINATION 



Element 


Photographic, 
small field 


Photographic, 
large field 


Fluorescent 
screen, 
small field 


Fluorescent 
screen, 
large field 


10 min 


60 min. 


10 min. 


60 min. 


Aluminum . . 


240 


280 


355 


415 


120 


175 


Iron 


59 


70 


73 


86 


30 


40 


Copper 


39 


46 


46 


56 


20 


25 



Berthold has conducted experiments with a Phoenix tube up 
to 350 kv. in order to determine what advantage would be gained 




200 



300 



350 



250 
Tube Volfage in Kv 

FIG. 54. Curves illustrating penetration of iron as a function of tube voltage. 

(Berthold.) 

by such unusual technique over more common procedures. The 
results are graphically shown in Fig. 54. Increasing voltages 

1 The r unit of x-ray quantity or intensity is considered on p. 163, in the 
next chapter. 



RADIOGRAPHY 



115 



have increasingly smaller increments in the limit of penetration, 
so that above 300 kv. the increase in material thickness limit of 
iron is inappreciable. With these very short wave lengths, 
scattering and recoil coefficients become very important in 
relation to the true absorption coefficient. 

10. The limit of recognition of inhomogeneities in a material 
of certain thickness is practically measured by the smallest 
sharply defined difference in thickness of this same material 
which can be recognized. Blowholes and gas pockets have little 
or no absorbing power, so that this definition accurately holds 
for such cases. This limiting difference in blackening of a film 
is of the order of 2.4 per cent. 

Thus: / = 7 e~ MZi , For a 10 per cent difference in 

blackening, 

/ 



/o 



= 0.976 = e-" 
- 0.024. 



h 



= 0.89 



- 0.115. 



Since ju is constant, xz/x\ 4.8. By means of such absorption 
calculations, taking into account scattering which serves to 
obscure the sharpness of delineation of defective areas, it is 
possible to calculate the limits of failure recognition and experi- 
mentally verify these data, such as are shown in Table XVII. 

TABLE XVII. REQUIREMENTS FOR RECOGNITION OF FAILURE RADIO- 
GRAPHICALLY 



Kilo- 


Ma tonal thickness, 
millimeters 


Smallest thickness 
difference, 
millimeters 


Per cent of irradiated 
material 


volts 










Al 


Fe 


Cu 


Al 


Fe 


Cu 


Al 


Fe 


Cu 


80 


72 






42 






6 






120 


173 


23 


12.7 


2 7 


11 


058 


1 6 


48 


46 


160 


247 


41 


25 


12 


30 


14 


4 9 


73 


56 


180 


290 


54 


34 


30 


55 


25 


10 


1.0 


73 


200 


355 


73 


46 




1 20 


49 




1 6 


1 05 



Conditions: Milliampere seconds 9000 (10 min. at 15 ma ), field < 100 cm.-', 50 cm. focal 
distance, constant non-pulsating potential, blackening 7, no scattered ray screen, film 
with two intensifying screens 

For observation of inhomogeneities on the fluorescent screen, 
a difference in brightness of two adjacent areas of the shadow 



116 APPLIED X-RAYS 

must be 15 per cent, and a blowhole or gas pocket in aluminum, 
iron, or copper must be 5 to 7 per cent of the total thickness of 
sound metal for certain conclusions. 

11. Special technique is required for specimens of irregular 
shape in order that parts of the radiograph will not be over- or 
underexposed. Cylindrical bars or other specimens with circular 
parts should be placed in suitable holders of the same material 
so that the x-ray beam will pass through a constant thickness. 
Immersion in liquids, such as methylene iodide, having nearly 
the same opacity to x-rays as the piece to be examined, removes 
this difficulty. Otherwise, sheet lead of varying thickness, lead 
shot, lead oxide paste, barium sulfate paste, and other absorbing 
materials can be used with irregularly shaped pieces and for the 
prevention of the undue fogging of the film by scattered radia- 
tion or halation from direct rays at the edges of the specimen. 

12. Intensifying screens have played a most important part in 
bringing this branch of radiography to its present high state. 
The ordinary calcium tungstate screens are usually employed. 
It may be mentioned here that a metal screen may also be used, 
lead foil being sometimes employed. The intensifying factor 
of such screens is lower than that of calcium tungstate screens; 
they have, nevertheless, some advantages over the tungstate 
screen. They absorb some of the secondary radiation from the 
under side of the piece being examined and, hence, reduce the 
fogging of the film; they produce finer-grained and, hence, 
more sharply defined images and are, therefore, especially useful 
for the examination for fine cracks in the metal. For thick 
pieces, where a higher intensifying factor than a lead screen 
provides is necessary (i.e., above 2 in.), the two kinds of screens 
may be used together with the lead one next to the film. Metal 
screens may find an increasing usefulness as higher-powered 
tubes come to be used for thicker sections, because of their 
ability to reduce fogging. 

13. The microphotometer has come into increasing usefulness 
for quantitative interpretation of radiographs on films, since the 
curves indicate at once the relative densities and hence dimensions 
of any imperfection. An example from the tests of Schwarz is 
shown in Fig. 55. The microphotometer is an instrument which 
has become practically indispensable for any kind of x-ray photo- 
graphic work. The general principle of its operation is as 
follows: A light of constant intensity passes through the film 



RADIOGRAPHY 



117 



which is moved slowly and at constant speed. The light of 
varying intensity, depending upon the density of the photographic 
layer, then falls upon a delicate thermocouple (thermopile, 
photoelectric cell, etc.) which is connected with a galvanometer. 




The deflections of the mirror which are a function of the thermo- 
electric current, the light intensity, and the photographic density, 
are then indicated by causing a reflected beam of light to register 
on sensitized paper on a slowly moving drum. 

Spectral lines on the film are thus converted into peaks and the 
completed curve gives a method of quantitative measurement. 



118 APPLIED X-RAYS 

An instrument of special design in the writer 's laboratory is shown 
in Fig. 56. The microphotometer is useful in the following 
types of investigation : 

a. Accurate measurement of wave length and of relative 
intensities of spectral lines; indication of resolution of doublets, 
etc. The photometric curves measure position, fine structure, 
intensity from height of peak, and inherent breadth of lines. 




FIG. 66. Microphotometer for quantitative measurement for x-ray spectra, 
diffraction patterns and radiographs. 1, constant source of light; 2, slit; 3, lens; 
4, driving screw for slow movement of film holder; 5, film holder for moving film 
over narrow beam of light; 6, sensitive silver-bismuth thermocouple registering 
intensity of light transmitted through successive positions of film; 7, galvanom- 
eter lamp (galvanometer not shown); 8, rotating drum for sensitized paper 
(cover removed) registering deflections of galvanometer mirror. 

b. Indispensable in quantitative chemical analysis, for which 
line intensities or height of absorption edges must be accurately 
compared with standards; indications of very faint foreign lines, 
etc. 

c. Quantitative representation of radiographs. 

d. Position and intensities of lines in diffraction photographs. 

e. Indispensable in measurement of colloidal-particle size 
from widths of diffraction lines. 



RADIOGRAPHY 119 

/. All other cases where automatic graphical measurement of a 
photographic plate in film would be useful. 

14. Stereoscopic radiography for industrial diagnosis is often 
as valuable as it is in medical diagnosis. The depth and angular 
disposition of an inhomogeneity in any material may be ascer- 
tained much more certainly. Two radiographs are made, in 
each of which the tube has been shifted about 1.25 in. on either 
side of the center of the object. The two films are then viewed 
in the stereoscope which fuses the two pictures into one with the 
appearance of three dimensions. 

PRACTICAL APPLICATIONS OF RADIOGRAPHY 

1. Metal Castings. This is the most important application of 
x-ray radiographic diagnosis simply because of the wide use of 
castings and because of the uncertainty of gross structure with 
empirically developed foundry practice. The following defects 
may be radiographically detected on the interior of castings 
without in any way destroying or marring the specimens, although 
the diagnosis may be confirmed by "post mortem" incisions: 

(Jas cavities. 

Due to gases liberated from the hot metal. 

Duo to gases from the mold. 
Sand inclusions. 
Slag inclusions. 
Pipe or shrinkage cavities. 
Porosity. 

Due to small gas cavities. 

Due to small shrinkage cavities. 
Cracks. 
Metal segregations. 

Figure 57 shows the interior gross structure of a steel casting 
1.25 in. thick which is characterized by every type of defect noted 
above, particularly gas cavities, non-metallic inclusions, and 
shrinkage cavities. The photographic reproduction is a negative 
and the spots of smaller absorbing power show up da rker than the 
surrounding metal. Figure 58 shows typical gas cavities in cast 
steel 1 in. thick and Fig. 59 demonstrates with remarkable clear- 
ness the presence of internal cracks entirely unsuspected in 
cast steel 1.5 in. thick. These radiographs have been supplied 
through the generous cooperation of Dr. H. H. Lester of the 
Watertown Arsenal, a leading authority on metal radiography. 



120 



APPLIED X-RAYS 




FIG. 57. Interior gross structure of a steel casting with all types of defects. 




FIG. 58. Radiograph of cast steel showing blowholes. (Lester.) 



RADIOGRAPHY 121 

It is now possible with commercially available equipment to 
radiograph satisfactorily 3.5 in. of steel, while the Woolwich 
Arsenal in England reports penetration of 4.5 in. of steel showing 
an internal flaw 0.3 in. in diameter. The limiting thickness of 
metal is at present determined by the inability of available x-ray 
tubes to withstand voltages higher than about 280 kv. 

The value of the x-ray method of inspection of castings to 
insure soundness and safety in operation is readily apparent. 




FIG. 59. -Radiograph of cast steel showing internal cracks. 

The method may seem too expensive to utilize in the examination 
of every piece, but even in such cases it may be employed to 
tremendous advantage in the derivation of a proper foundry 
technique and changes in the design of core and mold or in the 
process of gating. Many progressive foundries have adopted 
this practice, although the great majority still cling to the old 
empirical methods and uncertainty whether a casting will survive 
or fail. On the other hand, it is the part of wise economy often 
to radiograph every unit of cast metal in an installation or every 
piece which is intended for expensive machining operations. An 
outstanding example in which extensive radiographic tests were 
used as specification for acceptance of parts is that of the high- 



122 APPLIED X-RAYS 

pressure steam installation in the Edgar power plant of the Boston 
Edison Company at Weymouth, Mass. The pipe and fittings 
for the 1200-lb. steam line and the cast shell of a 3000-kw. 
steam turbine were all examined and many rejections were made 
upon the basis of the radiographs before acceptance. The 
justification lies in the fact that not a single failure or break of 
any kind has occurred since installation, even though the 
conditions represented are extreme. Examples of this type are 
being multiplied rapidly at the present time and radiography 
must be considered an indispensable and thoroughly scientific 
testing and control method in the foundry industry. The 
Aluminum Company of America, for example, has considered 
as a sound and necessary investment the installation in all plants 
of radiographic equipment for the examination of aluminum and 
other light-alloy castings. 1 

2. Welds. Closely allied to the problem of testing metal 
castings for soundness is that of welds. Here again there is no 

positive assurance by the usual 
methods that a weld has been 
made perfectly. With the 
agency of x-rays the smallest 
defects, such as pipes or gas 
inclusions, are indicated direct- 
ly, with the result that a vast 
improvement in the technique 
of welding has taken place in 
the space of a very few years. 
n n D A- u * j * A - u Welds are now made with 

I< IG. 60. Radiograph of defective weld. 

certainty of safety where they 

would never have been attempted previously. Figure 60 shows 
the actual condition of a typical weld which appeared perfect on 
the outside. The radiography of welds in locomotive parts sub- 
jected to vibrations and stress is widely used, particularly in Ger- 
many. In Fig. 61 is shown standard equipment on a German 
railroad for testing welds of locomotive fire boxes. 2 The writer 
recently advised the installation of an x-ray plant by a large manu- 
facturer for the continuous inspection of welded rod to be used in 

1 See FINK and ARCHER, A.S.S.T. 1929; 108 references to radiographic 
applications are given. 

3 HERR, "Ergebnisse der technischen Rontgenkunde," Vol. I, p. 181, 
Leipzig, 1930. 




RADIOGRAPHY 123 

the drilling of oil wells. Here is a case where these rods hundreds 
of feet long depend entirely upon the strength of the weakest welded 
joint, for with a break the rod falls to the bottom of the well. 
Consequently, the manufacturer did not dare to market the 
product without the assurance of sound joints. Since the rodding 
was only about 1 in. in diameter, it was found possible to use 
visual inspection with a fluorescent screen as the welded pieces 
moved along on a belt. The inspector was protected from the 
radiation by observation of the screen by means of a series of 
mirrors arranged in baffle fashion through heavy lead glass. 

A very comprehensive radiographic, macro- and micrographic 
study of butt and lap welds of all kinds is reported by Lefring. 1 




FIG. 61. Standard x-ray equipment on a German railroad for radiographic 
examination of locomotive parts and welds. 

The failures are divided into bonding and layer deficiencies 
and gas pores. Such a study, of course, leads directly to estab- 
lishment of the best possible technique. 

3. Automotive and Aircraft Parts. It may be truthfully 
stated that the remarkable dependability of automobile and 
aircraft motors in races and endurance flights such as those 
of recent months may be ascribed primarily to the assurance of 
soundness promoted by radiographic testing. This is particu- 
larly true for propellers, in which soundness is absolutely neces- 
sary. Not only internal defects but also surface cracks which 
have escaped attention are immediately detected. Pistons 

1 "Ergebnisse der technischen Rontgenkunde," Vol. II, p. 313, Leipzig, 
1931. 



124 APPLIED X-RAYS 

have been surprisingly prone to disclose serious though unsus- 
pected defects. All parts of an airplane may be inspected 
with x-rays from the cast cylinders to the spark plugs and the 
wooden framework. And where the safety of life is so utterly 
dependent upon sound mechanism and faithful performance 




FIG. 62. Radiograph of rolled sheet steel containing slag inclusions. 

it would seem little short of criminal not to use this positive 
method of specification and selection. 

4. Rolled and Drawn Metal. Figure 62 is the radiograph 
of a rolled sheet of steel containing slag inclusions which have 




FIG. 03. Radiograph of overdrawn aluminum rod. 

been fibered with the metal in the rolling process. The very 
poor quality of such a sheet is clearly demonstrated by entire 
failure in forming operations. Figure 63 shows how an alumi- 
num rod is affected by extreme cold drawing. The structure 
is such as to render the specimen worthless. 

5. Miscellaneous Applications of Metal Radiography. Among 
a large number may be mentioned the inspection of insulated 



RADIOGRAPHY 125 

wires and cables and coated metals for breaks, of metal tubes 
and capillaries for clogging, of intricate assembled objects for 
proper adjustment of parts, of projectiles for proper location 
of caps and fuses as well as for complete filling by explosive, of 
gun barrels for rifling and defects, of molten metals inside furnaces 
for melting point and surface tension (Fig. 64), of ball bearings and 
of all fencing foils at the University of Illinois for soundness, 
of electric insulators for the presence of metallic particles, of 
metal radio transmission tubes for proper position of grid and 
filament, of all sorts of sheets suspected of corrosion, and of steel 
Dewar flasks used for liquid air or oxygen, where corrosion may 




FIG. 64. Radiograph through furnace showing solid and liquid copper in 
equilibrium at the melting point. (Libman.) 

result in great decrease in wall thickness. This last test is a 
standard procedure in the German railway shops. 1 

Miscellaneous Practical Applications. Besides innumerable 
metal products, numerous other practical applications of radiog- 
raphy have been made and some of these are briefly enumerated : 

Arc electrodes for soundness. 

Coal for classification as to foreign mineral content (Fig. 65), 
and for control of cleaning by flotation (Fig. 66). 

Rubber tires for imperfect bonding to cords. 

Reclaimed rubber for nails and other foreign bodies. 

Golf balls for centering of core. 

Complicated glass, hard rubber, and bakelite pieces of various 
kinds with internal seals, etc., for improper fabrication. 

1 SCHWARZ, IOC. dt. 



126 



APPLIED X-RAYS 




FIG. of coal pure coal (lower 

containing (('lark and 




FIQ. 66. Radiograph showing steps in cleaning of coal by flotation. Upper left, 
maximum content of impurities; lower right, nearly pure coal. 



RADIOGRAPHY 



127 



Wood for cracks, wormholes, rot, knots, embedded nails, 
etc., as employed in aircraft frames, special lumber, telephone 
poles, etc. 

Railway ties for compression or erosion under the plates (after 
soaking in mercuric chloride solution to increase x-ray absorp- 
tion). 

Shells and cartridges for improper filling. 

Porcelain insulators, thermocouple tubes, spark plugs, etc., 
for internal cracks (Fig. 67). 

Location of pipes and wires in building walls. 

Contraband goods in trunks with false bottoms, and suspicious 
packages for bombs, etc. 




FIG. 67. Radiographic detection of defects in porcelain tubes. (Courtesy 
Cloud S. Gordon Company.} 

X-rays and Art. One of the most striking applications of 
x-rays has been in the field of art. A well-established branch 
of radiography is now that of the examination of old paintings 
and art objects for evidences of retouching, or of original paint- 
ings covered over with others, and for distinguishing true master- 
pieces from copies. Important court cases have been decided 
upon the base of the x-ray evidence. The old paint pigments 
consisted of inorganic substances which are heavily absorbing 
to x-rays as compared with modern organic dyes. Excellent 
x-ray laboratories are now to be found at the Fogg Art Museum 
of Harvard University, Metropolitan Museum of New York, and 
the museums at Chicago, Philadelphia, Minneapolis, and else- 
where. An example is reproduced in Fig. 68 from the paper by 
Dr. Alan Burroughs, 1 an outstanding authority on this subject. 
The x-ray photograph represents a portion of the painting 
"Mars and Venus" by Veronese. The painting shows the head of 

1 Smithsonian Rept., 529 (1927). 



128 



APPLIED X-RAY '8 



Venus upright while the x-ray photograph shows two heads, the 
one more inclined to the right having been painted out very 
likely by the master himself. 




FIG. 68. Typical result of application of radiography in examination of old 
paintings; from "Mars and Venus" by Veronese. The head at the right was 
painted out and disclosed only by x-rays. (Burroughs, Smithsonian Report, 
1927.) 

The Cost of Radiographs. Several attempts have been made 
to estimate the cost of radiographic examination of materials 
in order to justify its adoption as an industrial method of testing, 
control, and research. The cost, of course, depends on many 
factors, among which are the nature, size of the specimens, the 
number per hour, amortization, and overhead. Fink and Archer 
estimate an average cost of $2 per square foot of film, although 
for several small specimens on one film this may fall to well 
below $1. In other cases for very large specimens the cost may 
well rise to much higher values. Berthold has made the most 
extensive calculations for German practice and has constructed 
a series of curves of basic cost against specimen thickness for 
three kinds of apparatus operating at 120, 180, and 200 kv. and 
for aluminum, iron, and copper. A few data read from these 



RADIOGRAPHY 



129 



graphs for the cost of 1 RM (about 24 cts.), to which must be 
added the cost of photographic materials, are as follows : 



Metal 


Kilovolts 


Thickness, 
millimeters 


Al 


120 


145 


Al 


180 


248 


Fe 


120 


16 5 


Fe 


180 


43 5 


Fe 


200 


62 5 


Cu 


120 


10 


Cu 


180 


26 5 


Cu 


200 


39 



The indications, therefore, point to a considerably lower cost 
now than in the past, due to the newer high-power tubes, stand- 
ardized equipment, and technique. However, it is probably 
still too expensive for ordinary routine examination of every 
unit, except when safety is involved or where the pieces are 
especially valuable, or the raw material is to be subjected to 
expensive fabrication. 

Radiography by the Use of Gamma Rays. The presentation 
of this subject would be incomplete without mention of the 




FIG. 69. Radiographs of wrench and defective weld, with y-rays. (Mehl and 



remarkable radiographic results obtained by Mehl and his 
associates with the 7-rays from radium emanation. Since the 
wave lengths of 7-rays are shorter than x-rays as generated under 
practical conditions, it follows that they should penetrate thicker 
sections. Successful photographs were made through 10 in. or 



130 APPLIED X-RAYS 

more of steel, utilizing only a small bulb of radium emanation at 
a certain distance from the specimen and a photographic film. 
Exposures of 10 or 12 hr. were necessary but, of course, this is 
not a serious handicap, since no attention is required. The 
method is very promising for the examination of structures in 
position and because of the extreme simplicity and absence of 
all machinery. The 7-radiographs of a wrench and a weld are 
shown in Fig. 69. 



CHAPTER IX 

PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS OF 

X-RAYS 

I. SOME PHYSICAL EFFECTS 

lonization. Of physical phenomena the ionization of gases 
through which x-rays pass is the best known and probably the 
most fundamental. It was recognized soon after the discovery 
of x-rays and has ever since been the subject of much extensive 
and intensive study. Although C. T. R. Wilson, with his beauti- 
ful cloud-condensation experiments, was able to demonstrate 
the mechanism of the ion formation some years ago, accurate 
information concerning the variation in ionization with changes 
in the gas and x-ray conditions has become available only very 
recently and is even now incomplete. 

When the x-rays pass through the gas, they liberate photoelec- 
trons (which, as will be explained, are known to cause the ioniza- 
tion) ; they excite those characteristic radiations of the gas whose 
critical absorption frequencies are less than the frequency of the 
incident x-ray beam; they produce scattered radiation of the 
frequency of the incident beam; and they may produce recoil 
electrons and the accompanying secondary radiation (Compton 
effect). lonization experiments are usually conducted so that 
the ionization is measured by the electric current passing through 
the ionized gas, under a definite potential difference. The gas is 
held in an ionization chamber between two electrodes which are 
connected to the source of electric potential. Many of the early 
experiments were valueless because the incident radiation was 
allowed to impinge upon these electrodes, where it caused second- 
ary phenomena similar to those mentioned above and conse- 
quently altered the electrode potential. It is obvious that the 
secondary radiation excited in the gas, even when the electrodes 
are protected from the incident beam, may cause like disturb- 
ances. The difficulty of measuring ionization and ionization 
only is very great. 

131 



132 APPLIED X-RAYS 

The mechanism of the ionization is now agreed to be the follow- 
ing: The high-speed photoelectrons released by the x-ray beam 
have too much kinetic energy to be at once absorbed by adjacent 
molecules, and they consequently break down the molecules with 
which they come in contact into pairs of ions. Thus they pro- 
gressively dissipate their kinetic energy until it becomes so small 
that the electron is absorbed either by a molecule to form a 
negative ion or by a positive ion to cause neutralization. All this 
was very excellently shown by the experiments of 0. T. R. Wil- 




FIG. 70. Tracks of /3-rays liberated in gas by x-rays. (C. T. R. Wilson.} 

son who, by condensing water on the ions at the moment of 
formation and simultaneously photographing them, was able to 
obtain actual photographic records of the paths of the photo- 
electrons. One of Wilson's photographs is reproduced in Fig. 70. 
Thus it would be expected that in a layer of gas insufficiently 
thick to absorb the x-ray beam completely, the degree of ioniza- 
tion would be proportional to the density of the gas or, if the 
temperature were constant, to the pressure on the gas, provided 
the x-ray beam remained unchanged. This has been borne out 
by experiment, Crowther and Owen having found the ionization 
to increase proportionally with pressure, and Crowther having 
shown that temperature over a range from 180 to +148 C. 
has no effect on ionization if the density is kept constant. It is 
reasonable to assume that, after the density became sufficiently 
great to absorb the x-ray beam completely, no further increase 
in ionization with increasing density would be observed. There 
are, however, no high-pressure experiments to test this point. 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 133 



The relative ionization of the gases, except hydrogen and 
possibly ethyl bromide, is not changed by a change in wave 
length of the incident ray, so long as the range over which the 
wave length changes does not include a characteristic absorption 
discontinuity for any of the gases. 

Several recent experiments seem to prove quite satisfactorily 
that within certain wave-length limits, at any rate, ionization 
is independent of the wave length of the exciting x-ray beam, 

TABLE XVIII. RELATIVE IONIZ \TION PRODUCED IN VARIOUS OASES BY 
HETEROGENEOUS X-RAYS 







Ionization 


relative to 




Density 


air 


i 


Gas or vapor 


relative to 








air = I 


Soft x-rays 


Hard x-rays 


Hydrogen, Jl2 


07 


01 


18 


Carbon dioxide, CO 2 . . . . 


1 53 


1 57 


1 49 


Ethyl chloride, C 2 H 5 C1 . . . 


2 24 


18 


17 3 


Carbon tetrachloride, CC1 4 . . . 


5 35 


67 


71 


Nickel carbonyl, Ni(C()) 4 .. . . 


5 90 


89 


97 


Ethyl bromide, C 2 H 5 Br 


3 78 


72 


118 


Methyl iodide, CH 3 I 


4 90 


145 


125 


Mercury methyl, Hg(CII 3 ) 2 . 


7 93 


425 





TABLE XIX. RELATIVE IONIZATION PRODUCED IN VARIOUS G\SES BY 
HOMOGENEOUS X-RAYS 



Element 


Ionization relative to air = 1 


emitting 
characteristic 
radiation 


H 2 


2 


CO, 


SO, 


C 2 H 5 Br 


CH.I 


Fe 


0.00571 


1 37 


1 58 


11 3 


41.2 




Ni 




1 35 


1 55 


11 6 




162 


Cu . 


00573 


1 38 


1 55 


11 8 


42 


152 


Zn 


00570 


1.42 


1 54 


11.5 


41 6 




As 


0.00573 


1.27 


1 51 


11.7 


42.2 


158 


Se . . . 




1 31 


1 53 


11 8 


41 7 




Sr 




1 28 


1 53 


11 8 


153 




Mo 




1.28 


1 54 


11.5 


213 


188 


Ag 




1 32 






272 


198 


Sn 


0.04 


1.29 






335 


205 


Sb . 




1 28 










I . . 












211 


Ba 












251 



134 APPLIED X-RAYS 

provided that the number of photoelectrons liberated is the 
same (see page 192). 

Kulenkampff and Kircher and Schmitz have calculated the 
energy necessary for the production of one pair of ions in the ioni- 
zation of air, and the former finds it to be 35 volts, while the 
latter find 21 volts. The energy is here expressed as the number 
of volts necessary to impart to a single electron a kinetic energy 
equal to the energy in question. KulenkampfFs value is the 
more likely and is generally accepted. The Compton effect 
explains the lower value. Recoil, or Compton, electrons in 
addition to the photoelectrons are excited by the shorter wave 
lengths, and these electrons, though having little ionizing power, 
absorb much of the energy in the x-ray beam; longer waves excite 
only the photoelectrons, which produce the ionization. 

The ionization of gases by x-rays is much used in measuring 
x-ray intensity. A more complete description of such use will be 
found on page 161. 

The Effect of X-rays on the Electrical Conductivity of Solids 
and Liquids. Although there have been few experiments directly 
aimed at studying ionization in solids and liquids, it is certain 
that the increase in electrical conductivity of certain solid dielec- 
trics when exposed to x-radiation is exactly the same phenom- 
enon. This effect has been known for many years and has been 
studied in several different dielectrics. The experiments have 
generally been found to be in good agreement. The most 
exhaustive experiments are reported by Roos, 1 who studied 
sulfur, paraffin, hard rubber, and amber. 

The conductivity of sulfur was found to increase rapidly to a 
constant and reproducible value, if the raying was not continued 
over a period of more than about 2 min. In such cases, also, the 
conductivity fell to its original value almost immediately 
after the raying was discontinued. If, however, the dielectric 
was exposed to the rays for a somewhat longer period of time, the 
conductivity first rose, then gradually fell off, and did not drop 
immediately to its original value after cessation of the raying. 
It was found that the current through the sulfur was propor- 
tional to the voltage imposed for the whole range of voltages 
employed. These results are in agreement with those of Grebe, 2 
who used potentials up to 200 volts. Both experimenters found 

1 Z. Phyaik., 36, 18 (1926). 

2 Z. Physik., 17, 295 (1923). 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 135 

that the effect was also proportional to the x-ray intensity, a 
result also obtained by many of the early experimenters (see 
Roos's paper for references). 

The influence of x-ray wave length on this effect was studied 
by both Grebe and Roos by comparing the ionization produced 
in air with the increase in conductivity. Grebe found the ratios 
of the currents through the ionization chamber to the current 
through the sulfur to be equal for different waves and, from this 
fact and from the discovery that the ratio of the absorption 
coefficients for air and sulfur remains constant for wave lengths 
less than the K absorption discontinuities, he concluded that the 
change in conductivity of sulfur was due to a kind of internal 
photoelectric effect, similar to the effect that produces ionization 
in air, 

The action of paraffin, hard rubber, and amber strengthens this 
conclusion; for while the same relationship between x-ray inten- 
sity and the effect holds for them as for sulfur, they also show 
definite saturation currents, just as does air, though no such cur- 
rent was found for sulfur. 

After this saturation current is reached, it is no longer permis- 
sible to speak of the change in conductivity of the dielectric but 
rather of the change in ionization. It is also interesting to note 
that Gudden and Pohl, 1 who studied the effects of ultraviolet 
light on the electrical properties of crystals, came to the conclu- 
sion that these were the results of an internal photoelectric effect. 
It may be concluded that those solids which are strong dielectrics 
undergo an ionization exactly similar to that of gases. Indeed 
it is probable that this phenomenon is of fundamental importance 
in every direct effect of radiation, and that a more complete 
knowledge of it will lead to a better understanding of the many 
and diverse ways in which x-rays react upon matter. 

The fact that saturation currents can be reached for amber, 
hard rubber, and paraffin make these dielectrics more suitable for 
practical insulation in x-ray apparatus than sulfur, unless pro- 
tection is provided against the x-radiation. Thus for thin insu- 
lator layers the conductivity of sulfur is appreciably higher than 
that of the others. In this connection it is interesting to notice 
that Grebe found in his experiments that monoclinic sulfur was 
approximately three times as conductive as rhombic sulfur when 
radiated with the same beam. 

1 Several papers in Z. Physik. (1920-1924). 



136 APPLIED X-RAYS 

An effect somewhat similar to the one just discussed is the 
well-known change in the electrical resistance of selenium crys- 
tals, when illuminated with ordinary light, ultraviolet rays, or 
x-rays. Although McMahon found that an increase in pressure 
on the crystal increased the effect, the change in sensitivity with 
wave length has not been determined. 1 This phenomenon of 
resistance decrease, which must find its explanation ultimately in 
the peculiarities of the structure of the selenium crystal, has been 
explained upon the basis of several hypotheses, one of the most 
promising being that of resonance. By this theory the electrons 
in the crystal which have radiation frequencies in approximate 
correspondence with the frequency of the exciting radiation are 
temporarily loosened from their atomic bonds and become 
available for the transfer of electricity. In a practical way this 
phenomenon has found some application in estimating x-ray 
intensity. 

The conductivity (0) of insulating liquids exposed to x-rays has 
been investigated a few times. A few typical results are as 
follows for 

C = lO^ohm" 1 cm" 1 : 

Carbon tetrachloride 8, carbon disulfide 20, amylenc 14, benzene 
4, liquid air 1.3, petroleum ether 15, vaseline oil 1.6. 2 

The Excitation of Luminescence in Irradiated Substances. 
The excitation of luminescence in many substances, when irra- 
diated by x-rays, is a property which has played an important 
role in the history of the science. As a matter of fact, the 
fluorescence of neighboring objects led to Roentgen's discovery 
of the radiation. 

The phenomenon depends upon the ability of substances to 
absorb the rays and transform the energy into radiation of longer 
wave lengths in the ultraviolet or visible regions. 

Schuhknecht 3 was the first to study the fluorescence of mate- 
rials under x-rays, with the quartz spectrograph. Because of 
the excellence of his work, the results are presented in Table 
XX, showing the spectral regions and the wave lengths of the 
intensity maxima, in A.U. 

Schuhknecht observed that the spectral distribution of the 
luminescence was profoundly influenced by minute amounts of 

l Phys. Rev., 16, 558 (1920). 

2 "International Critical Tables," Vol. VI, p. 6. 

3 Arm. Phy,nk, 17, 717 (1915). 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 137 
TABLE XX. WAVE LENGTHS OF FLUORESCENT LIGHT EXCITED BY X-RAYS 





Region, 
A.U. 


Position of 
maximum, 
A.U. 


Fluorspar 


3640-2400 


2840 


Fluorspar and iron spar 
Srheelitc (Ca tungstate) 
Zinc sulfide ... 
K platinocyanide .... 
Ba platinocyanide ... . 
Ca platinoryanide 


3900-2310 
4800-3750 
5090-4120 
4900-4120 
5090-4420 
5090-4550 


2800 
4330 
4500 
4500 
4800 
4800 


IT NH 4 fluoride 


4400-3800 


4100 


X-ray tube glass . 


5090-3000 


3750 



impurities, as is well known for fluorescence under visible 
light. 

Nichols and Merritt 1 found that the intensity distribution in 
a fluorescent band was independent of the exciting radiation, 
x-rays, ultraviolet light, or cathode rays. More recently Wick 2 
has studied the fluorescence of uranium salts, and Newcomer 3 
that of about five hundred chemical compounds (mostly organic). 
The latter found sodium bromide very strongly fluorescent in the 
ultraviolet, and benzoic acid and naphthalene and their deriva- 
tions in the yellow green. 

All workers with x-rays are probably familiar with the fact that 
when the radiation strikes the eyes, there ensues a sensation 
of luminescence which may continue for several seconds after the 
exciting source is removed. This latter phenomenon is an 
example of phosphorescence; with x-rays phosphorescence, in 
general, is usually more pronounced than with light because of 
the deeper penetration of the former, and hence of a greater 
volume effect. Gases and many solids are phosphorescent. 
Even powdered rock salt is easily visible in a darkened room for 
a half hour or more after its exposure to x-rays. 

There are several practical uses of fluorescence under x-rays. 
The property may be used to differentiate between chemical 
substances, e.g., diamond and a glass substitute. It may serve 

l Phys. Rev. (1), 21, 247 (1905); 28, 349 (1909). 

2 Phys. Rev. (2), 5, 418 (1915). 

3 /. Am. Chem. Soc., 42, 1997 (1920). 



138 APPLIED X-RAYS 

as the basis of invisible inks and identification marks on objects 
which are developed under a beam of x-rays. It may be used 
as a means of measuring intensities of x-rays, as discussed later 
in this chapter. It is the basis of the science of fluoroscopy or 
visual radiography, as outlined in Chap. VIII. Tarada in 1915 
used a fluorescent screen in order to see Laue diffraction patterns 
of crystals; more recently Hauser and Mark have proved by 
such a visible examination that the diffraction pattern of stretched 
rubber appears instantaneously; with the advent of high-power 
x-ray tubes diffraction patterns may be easily visually observed. 
The property of fluorescence may be utilized to intensify 
x-ray photographic exposure, as will be shown in a subsequent 
paragraph. 

Finally, the newest and most remarkable application of 
fluorescence of substances irradiated by x-rays is that discovered 
by McDonald and associates in cancer researches in Philadelphia. 1 
Living cells comparatively resistant to the direct action of x-rays 
were treated with solutions of organic compounds which fluoresce 
in the ultraviolet range when irradiated with x-rays. Under 
the action of these ultraviolet rays (2000 to 2500 A.U.) the 
cells were observed to become violently agitated and then 
killed in an astonishingly short interval of time as the result of 
specific photochemical action on the nucleus. This discovery is 
recognized as one of major importance in the further development 
of x-ray therapy. 

Fluorescent Intensifying Screens. A very practical use of the 
property of fluorescence is the intensifying screen, used with 
photographic films in x-ray radiographic and crystal diffraction 
applications in order to cut down the time of exposure, sometimes 
to a twentieth of the usual value. For these screens calcium 
tungstate serves best because of its intense blue-violet fluores- 
cence. The screens are usually placed behind the photographic 
plate or film, and the fluorescent portions add their action on the 
sensitive emulsion to the direct x-ray effects. Unless care is 
used, difficulties with the screens may arise as follows: 

1. If the calcium tungstate is not pure, the screen may have 
an appreciable hangover or phosphorescence. In the writer's 
laboratory some of the best commercial screens have produced a 
distinct effect on a photographic plate for as long as 3 months 

Reported at the Denver meeting of the American Chemical Society, 
August, 1932. 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 139 

after their exposure to x-rays. Hence, this extraneous action of 
previously used screens may lead to misinterpretation of newly 
obtained x-ray photographs. 

2. Unless the screen is very carefully prepared for uniform 
particle size and is placed in the closest proximity to the sensitive 
emulsion, it may reduce the definition of the photograph by 
broadening the image. This effect is observed easily, even when 
only the thickness of the glass of a photographic plate separates 
the emulsion and the luminescent image. 

3. The intensity of fluorescence depends upon the wave lengths; 
although quantitative data on this point are lacking, de Broglie 1 
showed that a screen had no intensifying effect upon rays with 
wave lengths of 1.25 A.U. but displayed a gradual increase in 



m 




7,000 6,500 6,000 5,500 5000 4,500 4,000 3,500-*- A.U. 
Red Yellow Green Blue Violet Ultra- 

viol e+ 

FIG. 71. Curves showing spectral ranges of maximum sensitivity of the eye 
and photographic plate, to which should correspond, respectively, the fluorescent 
screen and the intensifying screen. I, fluorescent screen; II, calcium tungstate 
intensifying screen; III, silver bromide of photographic emulsion; IV, human 
eye. 

effectiveness up to the critical absorption wave length of tung- 
sten at about 0.179 A.U., at which point, corresponding to 
greater absorption, a sharp increase occurred for the shorter wave 
lengths. For this reason fluorescence cannot serve satisfactorily 
as a means of measuring x-ray intensities. 

An interesting comparison is given in Fig. 71 of the spectral 
ranges of sensitivity of the eye, the fluoroscope screen (containing 
as the most important constituent zinc silicate), the silver bromide 
emulsion, and the calcium tungstate photographic intensifying 
screen. Very properly the first two and the last two show 
sensitivities over the same spectral range. 

II. CHEMICAL EFFECTS OF X-RAYS 

There are several points of interest in the study of the chemical 
effects of x-rays which may be enumerated as follows: 
1 Compt. rend., 177, 849 (1920). 



140 APPLIED X-RAYS 

1. Pure photochemistry, the mechanism and rate of reactions, 
the stability of chemical bonds, etc. 

2. Light thrown on therapeutic effects by study of chemical 
changes. 

3. Discovery of reactions which could be used as suitable 
dosimeters for quantity or intensity of radiation. 

The casual observer could well believe that x-rays by virtue 
of their penetration and energy should have innumerable pro- 
found chemical effects, but as a matter of fact the examples of 
considerable chemical change are extraordinarily few in number. 
Systems which undergo change in ultraviolet light are apparently 
unaffected. The photographic effect, a few oxidation-reduction 
reactions, and some condensations of organic compounds are 
almost unique among the large number of experiments already 
empirically tried. However, the hope remains that other chemi- 
cal effects may be discovered which might serve the purpose even 
of a convenient dosimeter. 

The Mechanism of Chemical and Biological Action. It has 
already been indicated that absorption of radiation energy must 
precede any physical, chemical, or biological effects which may 
be observed. In pure absorption the energy of an x-ray quantum 
is transformed to that of electrons (photoelectrons) liberated 
from atoms, together with the net potential energy of the 
irradiated atom (ionization). In the latter case the atom remains 
in the ionized condition only a very short time (10~ f>> sec.); one 
of the electrons in the outer orbits falls into the vacancy created 
by the photoelectron. In so doing, the potential energy of the 
ionized atoms becomes the energy of secondary characteristic 
rays. The ionized action by virtue of its changed condition can 
also enter into chemical reactions. Since secondary character- 
istic rays produced by return of the ionized atom to the normal 
state are softer than the primary rays, especially so in the human 
body on account of the light elements, they will be easily absorbed 
by one of two processes. The quantum of radiation may leave 
the mother atom and be absorbed by a neighboring atom, or it 
may actually remain in the mother atom so that its energy is 
used for the liberation of a second electron (photoelectron of the 
second kind). This effect or process of inner absorption can 
also be considered as a radiationless transition of an electron to a 
deeper orbit, in which the energy difference is imparted as 
kinetic energy to another electron. 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 141 

The photoelectrons account for the second portion of the 
energy following absorption of a primary quantum (or x-ray 
photon). The variations in velocities as determined in 0-ray 
spectra have already been considered and it follows that the 
kinetic energy will have nearly the same value of the primary 
x-ray quantum for light elements or for outer electrons of heavier 
atoms, in which the work required to free the electron is small. 
The photoelectron is now free to liberate secondary electrons 
by impact with atoms, which, of course, have lower velocities, 
thereby ionizing the atoms, or the impact may serve only to lift 
the electron to a higher energy level in the atom which becomes 
therefore excited. 

Still another mechanism in the absorption of x-rays by atoms 
in molecules is the transformation into heat. An increase 
in energy of motion of atoms in molecules in position results in 
nothing more than local elevation in temperature. Of course 
in an irradiated body the transformed x-ray energy is so small 
that a measurable increase in temperature is almost impossible 
to observe. The phenomenon is of interest in the light of 
Dessauer's point-heat theory of biological action. 

It is certain that in a biological or chemical medium the 
photoelectrons possess large initial velocity with a velocity 
distribution corresponding to the x-ray spectrum. The fate of 
the photoelectrons is widely varied but in general it is the same 
as that observed for the impact of cathode rays on the anti- 
cathode of the x-ray tube (see page 78). Between the first 
and last (heat) steps in the chain of transformations the widest 
variety of effects must be possible. 

These high-speed electrons can bring into reactive form 
by impact other atoms and molecules which have been abso- 
lutely unaffected by the primary radiation quanta; in fact 
the proportion of atoms and molecules activated by the photo- 
electrons may be very much larger. This mechanism differs 
from the chemical effects of ordinary light in which energy suffices 
only to excite atoms by lifting electrons to higher energy levels. 
X-rays also differ from ordinary light in that they may have 
chemical action because of scattering and recoil electrons and 
yet undergo no fluorescent absorption, a process unknown for 
light. 

Besides the process of true absorption, the energy of a quantum 
of x-radiation can also be transformed into electron kinetic 



142 APPLIED X-RAYS 

energy that of the recoil electrons in the Compton effect. The 
velocity of these is considerably smaller than that of the photo- 
electrons and, of course, depends on the scattering angle. Their 
chemical and biological effects are consequently smaller. How- 
ever, it must be noted that at 200 kv. 2.5 per cent of the x-ray 
energy goes into photoelectrons and 3 per cent into recoil electrons. 
At higher voltages the latter figure becomes even more significant. 

Experimental Tests of Theories of Chemical-reaction Mecha- 
nism. -The above theory of chemical action due very largely to 
Glocker has been subjected by him and by others to experimental 
test. Glocker and Risse 1 have studied the decomposition of 
hydrogen peroxide and potassium persulfate in very dilute 
solutions. The amounts decomposed corresponded to the energy 
of the secondary electrons liberated in the system during passage 
of x-rays; 70,000 cal. (electrons in motion) are required to 
decompose 1 mole of H 2 O 2 in VBOO normal solution and 2.45 
times as much for potassium persulfate. The dependence of 
chemical effect upon x-ray wave length is a question entirely of 
how much energy during passage of an x-ray beam of certain 
wave length through matter of certain composition is transformed 
into the energy of secondary electrons. Taking into account the 
complications of scattered and fluorescent rays which may form 
secondary electrons, Glocker and Risse have obtained complete 
verification of the theory, and further substantiation has been 
obtained by other workers for other systems. 

In general, the exact mechanism and kinetics of chemical 
reactions, though due to activation by electron impact, have been 
explained only in a very few instances. The photographic action 
is unusually simple, in that the silver and bromine ions are 
converted endothermically into neutral atoms through the energy 
of the secondary electrons. The evolution of hydrogen chloride 
from chloroform is the best example of a reaction where far 
greater change is observed than can be accounted for by electron 
impact. It is, therefore, a chain reaction: a residual chloroform 
molecule disturbed by electron impact can react with an 
unchanged chloroform molecule, the product of this reaction 
with another unchanged chloroform molecule, and so on. Such 
reactions, together with side reactions with atmospheric oxygen, 
account for the extreme sensitiveness toward x-rays of iodoform 
solutions in chloroform. Because of the common mechanism 
1 Z. Physik., 48, 845 (1928); Z. physik. Chem. (A), 140, 133 (1929). 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 143 

some chemical effects of x-rays would be expected to be the same 
as those with ultraviolet light, but not necessarily the same 
as thermal reactions. Barium azide decomposes into nitride 
with x-rays but never with heat. 

The Photographic Effect. In their action on the photographic 
plate x-rays seem similar to ordinary light, for there are no 
known plates sensitive to x-rays which are not also sensitive to 
the visible radiation. Examination of microscopic sections 
through the sensitive layer of exposed plates has shown, however, 
that x-rays, unlike light, produce an equal distribution of grains 
of reduced silver throughout the whole thickness of the layer. 
Consequently a greater blackening of the plate, when exposed to 
x-rays, can be obtained by increasing the thickness of the sensi- 
tive layer. Here, indeed, is found the chief difference between 
ordinary photographic films or plates and those manufactured 
for x-ray use; the latter are provided with a thicker sensitive 
layer and are usually "duplitized," or coated on both sides with 
the sensitive silver bromide emulsion. 

The laws of the blackening of photographic plates have been 
quite thoroughly studied. The frequency and intensity of the 
incident rays and the time of exposure are the important factors. 
Rays of differing frequencies do not have an equal quantitative 
effect. Kulenkampff has made calculations, based on some new 
intensity and ionization measurements, which appear to show 
that equal blackening will result from equal energy absorption 
regardless of wave length. Furthermore, rays of frequencies 
higher than the critical absorption frequencies of bromine and 
silver are very highly absorbed and produce a large photographic 
effect, while rays of slightly lower frequency produce a relatively 
lower effect, though the incident intensities may be the same. 

With monochromatic rays of constant intensity, the blackening 
is approximately linear with time, for short periods of time. 
With longer exposures the blackening increases less rapidly than 
this proportionality demands and finally, with very long exposures, 
approaches a constant value. Over a certain range, then, 
Bunsen's law, that equal products of time and intensity produce 
equal blackening, is fulfilled. A long exposure with a low 
intensity, however, produces a less blackening than a shorter 
exposure at a correspondingly higher intensity. 

Eggert has worked out with great care the optimum conditions 
for practical photography in radiography. Films are classified 



144 



APPLIED X-RAYS 



Re 



s 



a 



i 



s 



a 



3 



S 



s 

a 

o 



H 

b 

O 



< 



X 
X 



PQ 

H 



Energy relation 



S 



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PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 145 



ROSEVEARE, J. Am. Chem. 
Soc., 52, 2612 (1930) 


WYCKOFF and BAKER, .4m. /. 
Roentgenology and Radium 
Therapy, 22, 551 (1929) 


QUIMBY and DOWNES, Radi- 
ology, 14, 468 (1930) 
REIXHART and TUCKER, Ra- 


diofcw, 12, 151 (1929) 
STEXSTROM and LOHMAXX, /. 


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PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 147 



according to their threshold sensitivity and the steepness of 
gradation of the blackening log time curve and the double 
emulsions and use of intensifying screens improve these. The 
photographic blackening effect depends on voltage. Under the 
same conditions the exposure time is smaller the harder the rays. 
The same blackening, for example, is obtained at 25 kv. in 25 
m.a.s., 50 kv. in 3.2 m.a.s., and 80 kv. in 1.6 m.a.s. For radiog- 
raphy, however, the best contrast and less disturbance due to 
scattered rays but longer exposure time are obtained with soft 
x-rays. Proper technique, therefore, involves using the lowest 
voltage consistent with a practicable exposure time. Intensify- 
ing screens (shortening time but decreasing definition) and 
screens to eliminate scattered rays improve contrast. 

As a chemical effect the blackening of the photographic film 
has been quantitatively studied. 1 For a wave length 0.45 A.U. 
about one thousand silver atoms are set free per quantum as 
compared to one silver atom per quantum of ordinary light. Of 
course, the absorption of a quantum takes place on one molecule 
of silver bromide so that the additional action is accounted for 
by secondary electrons. The Einstein equivalence law is not 
obeyed, since the x-ray quantum is about ten thousand times 
greater than a light quantum and yet has only one thousand 
TABLK XXIL PHOTOLYSIS OF KN0 3 











Incident 


Energy 


Experiment 


Exposed 
area, centi- 
meter 
squared 


Thickness 
of layer, 
centimeters 


Weight of 
0.001 N 
thio, grams 


energy per 
centimeter 
squared 
per second, 


absorbed 
per centi- 
meter 
squared per 










r 


second, r 


1 


15 48 


1.62 


4117 


2.56 


0.80 


2 


15.90 


1.04 


2702 


2 32 


0.490 


3 


12.91 


1.12 


2291 


2 40 


0.535 



Total energy 
absorbed (10 hr.) 


Molecules react- 
ing per 


Molecules per 
ion pair (M/N) 


Energy, calories 
per mole 


445, 680 r 
280, 476 r 
248, 400 r 


5 58 X 10 11 
5 83 X 10 11 
5.58 X 10 11 


2-0.3 
2-0 3 
2-0 3 


1 31 X 10 7 
1 25 X 10 7 
1 31 X 10 7 



1 EGGERT and NODDACK, Z. Phynik., 43, 222 (1924). 



148 APPLIED X-RAYS 

times greater chemical effect. The discrepancy is due to scatter- 
ing of energy as heat. The dependence on wave length is 
determined by the number of absorbed quanta, i.e., the absorbing 
properties of the photographic plate or film. 

Energy calculations have been made for several chemical 
systems; these may be illustrated for the case of the photolysis 
of potassium nitrate, studied by Clark and Pickett. These 
calculations depend upon ionization, or the formation of ion 
pairs. 

Fairbrother makes the assumption that a given amount of 
radiation will produce approximately the same number of ion 
pairs in a dilute aqueous solution as are produced in the same 
weight of air, inasmuch as the atomic numbers of air and water 
are not very different. To allow for relative densities of air and 
dilute solution, a factor of about 1000 is involved. If this 
assumption is adopted, the number of molecules of potassium 
nitrate which react for each ion pair may be calculated, as follows : 

Total energy . . ,. , 

j. ^ = ion pairs per cubic centimeter in 

Charge on electron 

10' 
air = 7-774 = 2.1 X 10 9 ion pairs per cubic centimeter in air, or 

approximately 2 X 10 12 ion pairs per cubic centimeter in the 
solution; 

Molecules reacting , , . 

. 2 = molecules per ion pair. 

Ion pairs 

Using the data given above, the values for the latter are between 
0.2 and 0.3 for this endothermic decomposition of potassium 
nitrate. The number of molecules per ion pair may be calculated 
independently from the energy in calories per mole and the work 
required to form one ion pair (35 volts): (1.313 X 10 7 cal./mole 
KNO 3 ) / (23,000 X 35 cal./mole ion pairs), or approximately 0.1 
molecule of potassium nitrate per ion pair. This is in satis- 
factory agreement with the value calculated above, considering 
experimental difficulty, and with the order of magnitude to be 
expected thermodynamically. 

In order to express results in terms of absolute energy, the 
absorption coefficients and the fraction of the absorbed energy 
which is converted into the kinetic energy of electrons and thence 
into the work of formation of ions must be known. The absorp- 
tion coefficient 0.228, as calculated from the above data, agrees 
very closely with the value for absorption of the same wave 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 149 

length in water interpolated from a series of values given by 
Glocker. The fraction of the total absorbed energy converted 
into work of formation of ions is the ratio of the values of the 
absorption coefficients for the energy given to recoil and photo- 
electrons to that of the total absorption coefficient. Using values 
recorded by Glocker, this fraction for the effective wave length 
used is 0.263. 

The absorbed energy as measured in r may be converted into 
ergs by the use of the formula proposed by Rump 1 and Kulen- 
kampff's experimental value of 35 volts as the work required to 
form one ion pair in air 



rw) 



i 0.36' 

where E/i = 1944 ergs/r, p = density, e = 35 volts, and 
r + ov = absorption coefficient attributed to recoil and 
photoelectrons. 

Thus the total energy absorbed in experiment 1 is 445,680 X 
1944 ergs, the fraction 0.263 of which is transformed into work 
of ionization. At the same time 4.117 X 10~ 7 mole of potassium 
nitrate is transformed. Thus the energy rate is 1.313 X 10 7 
cal./mole of reactant. 

The heat of decomposition of potassium nitrate calculated 
from band spectra of oxygen and thermochemical data is 1.03 
X 10 5 cal./mole. Thus it seems evident that not more than 0.8 
per cent of the energy absorbed and utilized in formation of ions 
in the solution appears as chemical dissociation of the molecule 
of potassium nitrate. 

With these results is to be contrasted the very efficient photo- 
chemical-chain reaction between mercuric chloride and potassium 
oxalate, studied by Roseveare. The energy efficiency in this case 
is 1.32 cal./mole or 0.91 X 10~ 16 erg per molecule; since it takes 
35 volts or 56 X 10~ 12 erg to produce an ion pair, there are 6 X 
10 5 molecules reacting per ion pair. 

The Flocculation of Colloids by X-rays. The action of x-rays 
in flocculating colloids, now a well-recognized phenomenon, is 
another subject which appears promising for the research worker. 
Fernau 2 noticed the coagulation of cerous hydroxide, Ce(OH) 2 , 

*Z. Physik, 43, 254 (1927). 
2 Kolloid Z., 33, 89 (1923). 



150 APPLIED X-RAYS 

sols under x-radiation ; and a similar effect in the case of albumin 
sols. Here again the effects can be produced by hydrogen per- 
oxide and ozone, and the production of these is supposed to be 
the first step in the coagulation. The positively charged 
Ce(OH) 2 is then coagulated by the electrons released when the 
hydrogen peroxide reverts to water. Wels and Thiele 1 found that 
aggregate formation in globulin solutions occurred on either side 
of the isoelectric point and, hence, is independent of the charge 
which the molecules bear. Dognon reported a peculiar phenom- 
enon in the flocculation of gum-mastic suspensions. Whereas 
homogeneous rays caused flocculation, a heterogeneous beam 
caused very little or none. 

Crowther and Fairbrother 2 have performed numerous experi- 
ments on colloid flocculation and dispersion under x-radiation. 
They contend that positively charged colloids are coagulated. 
Clark and Pickett, however, found that colloidal lead was 
stabilized to a slight extent. This metallic sol is of unusual 
interest because of the discovery by Blair-Bell in England that 
injection into the tissue before therapeutic irradiation resulted in 
a much greater effect than observed for tissues alone. This 
might be due to secondary radiation from the heavy metal 
particles, or to a specific chemical effect. Clark and Pickett have 
experimentally demonstrated that the latter must be true, since 
colloidal gold, equally efficient in production of secondary rays, 
has no beneficial effect whatever. These authors have also 
shown that the flocculation of clay slips by x-rays, measured by 
viscosity charges, is a direct function of the amount of organic 
protein matter present. The whole matter of flocculation or 
dispersion of colloids under x-ray treatment is of greatest impor- 
tance in its bearing on the therapeutic effect on cancers. At 
present the results are still so conflicting, due to large effects of 
impurities, sensitiveness to hydrogen-ion concentration, and other 
unknown eccentricities such as internal photoelectric action, that 
no definite conclusions or rules can be established. 

The Effects of X-rays on the Activity of Catalysts. The effects 
of x-rays on catalytic reactions have been studied in the decom- 
position of hydrogen peroxide by platinum and catalase, and in 

1 Arch. ges. Physiol (Pflugcr's), 209, 49. 

*Phil. Mag. (7), 4, 325 (1927) 6, 385 (1928); Brit. J. Radiology, 1, 121 
(1928). 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 151 

the production of sulfuric acid by contact of sulfur dioxide and 
oxygen with platinum. 

Schwarz and Friedrich 1 studied the decomposition of H 2 02 
under x-ray influence and found that the rate of decomposition 
was decreased. Subsequently, Schwarz and Klingenfuss 2 studied 
the catalytic oxidation of SO2 by contact platinum, which had 
been x-rayed. They found a temporary increase in activity of the 
catalyst. The increased activity toward S()2 was explained as 
due to a photolytic action on the moisture present, producing an 
activated form of oxygen or a peroxide, which then becomes the 
oxidizing agent. 

Clark, McGrath, and Johnson 3 studied the effect of x-rays on 
contact platinum catalysts for the SO 2 oxidation. Some experi- 
ments were made with thoroughly dried gases and very little 
conversion was obtained, whether the catalyst had been previ- 
ously rayed or not. The conversion in these cases was constant 
at about 3.25 per cent for both rayed and unrayed catalysts. 

Experiments with moist gases and those in which the catalyst 
was rayed in the presence of moisture showed, however, a decided 
increase in the catalyst activity. Thus for a run after the first 
irradiation of the catalyst, the conversion at a constant tempera- 
ture of 300 C. increased from 88 to 94 per cent. After about 
five hours the activity dropped very markedly to something less 
than the original value, subsequently increased to about the 
original value, and then slowly decreased, until the conversion 
became constant at about 84 per cent. A second 3-hr, irradiation 
of the same catalyst produced another increase in activity, but 
only to about 87 per cent, followed by fluctuations similar to 
those described for the first run. 

After raying, the catalyst always contained more oxygen as 
measured by the amount of iodine liberated from potassium 
iodide solution. 

Coloration of Glass and Minerals. It is a well-known fact 
that x-ray tubes made of glass containing manganese are colored 
violet after the tube has been in use for some time. Lead glass is 
colored brown. Barium platinocyanide and some other plati- 
num compounds undergo color changes probably by a process of 
dehydration under x-ray illumination. The extent of this color 

1 Ber., 65B, 1040 (1922). 

2 Z. Elektrochem., 28, 472 (1922); 29, 470 (1923). 
3 Proc. Nat. Acad. Sci. 9 11, 646 (1925). 



152 APPLIED X-RAYS 

change is used as a means of estimating intensity in x-ray therapy. 
Some substances, e.g., fluorspar, undergo a change, but exposure 
to sunlight effects the return of the original color. 

Bayley 1 has investigated a large number of alkali halides with 
respect to this change. Most of them showed a temporary 
coloration, though some did not. The colors faded logarithmi- 
cally with time, upon exposure to sunlight. Halite, which was 
colored amber and showed an absorption band from 0.3 to 1.3/x 
with a maximum at 0.46^, and silvite, which showed a similar 
band at 0.55^, faded most rapidly when illuminated with rays 
whose wave lengths corresponded roughly to these maxima. 

Dauvillier 2 has pointed out that these effects are always asso- 
ciated with ions. The x-rays release electrons, which attach 
themselves to positive ions; the neutral atoms, so formed, prob- 
ably form colloidal aggregates which cause the color change, while 
the subsequent illumination by light restores the electrons to 
their original positions. In a few cases, such as the conversion 
from red to green oxide of chromium, colloidal phenomena are 
evidently not involved. 

This change in color with exposure to x-radiation has been 
employed in the production of colored candles, of artificial ame- 
thysts from manganese glass, of special pieces of glassware, and 
it is perhaps the irony of progress that the purple-glass windows, 
so colored by years of exposure to sunlight and often so highly 
prized by antiquarians, can be produced cheaply, rapidly, and 
genuinely by x-radiation. 

The Transformation of Metastable into Stable Solid States 
by X-rays. In their remarkable studies of the allotropic modifica- 
tions of sulfur trioxide Smits and Schoenmaker 3 attempted to 
demonstrate the differences between the icelike form, the low- 
melting asbestos-like form, and the high-melting asbestos-like 
form, by photographing the x-ray crystal diffraction patterns. 
The films were identical, the pattern being that of the stable 
third form. The radiation thus converts metastable to stable 
modifications. On distillation of a portion of the intensively 
dried, high-melting, asbestos-like form, different states having 
abnormally low vapor pressures and abnormally high initial 
melting points were obtained, thus showing that this particular 

l Phys. Rev. ,24, 495 (1924). 
2 Compt. rend., 171, 627 (1922). 
3/. Chem. Soc., 1926, 1120, 1603. 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 153 

form behaves as a mixture of pseudo-components which have 
very different vapor pressures and melting points. At room 
temperature these states do not alter but at 50 changes take 
place in the direction of inner equilibrium. The x-ray diffraction 
patterns for the unchanged state and that changed at 50 were 
identical. It was proved experimentally that the x-rays actually 
effect a very rapid increase in vapor pressure to a value exactly that 
of the high-melting, asbestos-like form in inner equilibrium. An 
entirely new field of investigation is opened in this work and in 
that of Cohen on the metastable states. 

III. BIOLOGICAL EFFECTS OF X-RAYS 

It has been indicated that in all experiments designed to deter- 
mine the direct action of x-rays, the variables are difficult to 
control. In the study of the action of x-radiation on living 
matter, certainly the most interesting and important both 
practically and theoretically, the additional variable of life 
produces complexities which have so far defied satisfactory 
interpretation. This statement made in 1926 in the first edition 
of this book must still stand in 1932. As Dr. James Ewing 1 in his 
masterly Caldwell lecture, " Tissue Reactions to Radiation," put 
it: "Ultimate knowledge of the mode of action of radiation still 
eludes our grasp." Speaking of action on human tissues, he says : 

More than a decade ago one could trace in detail the nuclear and cyto- 
plasmic reactions following irradiation, the preliminary hyperemia, cell 
liquefaction and necrosis, the appearance of phagocytic cells, the growth 
of granulation tissue, the extreme overgrowth of lymphocytes and 
plasma cells, the healing by supple scar tissue. . . . The very volu- 
minous contributions of the past decade have served to clarify many 
details . . . but no new and fundamental principles of reaction have 
been established. 

The subject, by its enormity and by the vast number of largely 
uncontrolled and unrelated observations recorded in the litera- 
ture, ranging all the way from a single-cell nucleus to a complete 
human system, is appalling, particularly in light of the urgent 
need to have the ultimate knowledge which will permit accurate, 
scientifically founded radiation therapy. 

For many years, the supposed rule gained wide circulation 
that small dosages tend to activate and stimulate various func- 
tions and chemical reactions in biological colloidal systems, 

1 Am. J. Roentgenology and Radium Therapy, 15, 93 (1926). 



154 APPLIED X-RAYS 

while larger dosages destroy, either instantly or after a latent 
period. This idea has been tested on seeds, eggs, single cells, 
and organisms of every imaginable kind. It found practical 
applications in the destruction of tobacco-worm larvae, cotton- 
boll weevil, the flour weevil (tribolium confusum), etc. The 
experimental evidence for stimulation with small doses is 
extremely meager and the rule is considered now invalid. A 
measure of acceleration in cellular metabolism has been observed 
repeatedly but this is proved to be a transient phase of reaction 
invariably followed by inhibition of function and cellular degen- 
eration. 1 Again as the result of primary degeneration of certain 
radiosensitive cells a secondary and indirect stimulation may 
sometimes be observed. It has been demonstrated very recently 2 
that x-rays do not kill cancer cells instantly, but accelerate 
the process of normal living and dying characteristic of each cell. 

Numerous studies have been made on bacteria. Among these 
Clark and Boruff 3 found that x-rays act like sterilizing agents on 
cultures of B. coli (from sewage) and Erythrobacillus prodigiosus 
(from bread mold), in that the curves are characteristic steriliza- 
tion or death-rate curves, showing that the total counts decrease 
logarithmically with time. B. coli showed no mutations with less 
than lethal dosages but the other organism showed a tendency 
toward lack of ability to produce its characteristic red pigment, 
although this is recovered in 12 hr. when a white colony is trans- 
ferred to an agar slant. Wyckoff and Luyet 4 have shown that 
yeasts can be injured without being killed outright, and that 
injury is followed by development of an extraordinarily large 
number of two-celled colonies which on prolonged incubation 
ultimately die without further budding. 

Genetics and X-rays. One of the most important new develop- 
ments has been in the study of mutations after the irradiation of 
parent organisms. In 1927, Prof. H. J. Muller of the University 
of Texas discovered that when fruit flies (Drosophila) were 
irradiated, the processes of evolution were speeded up over 1500 
per cent. The second generation of offspring showed abnormali- 
ties such as rudimentary wings, no wings, white eyes, etc. These 
sensational results were the inspiration for further researches all 

1 DESJARDINS, Science, 76, 569 (1932). 

2 ISAACS, Science News Letter, 22, July 9, 1932. 

3 Science, 70, 74 (1929). 
'Radiology, 17, 1171 (1931). 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 155 

over the world in this field of genetics, on other insects, worms, 
mice, rats, larger animals, roses, corn, and many other plants. 
In all cases the effect of x-rays on the chromosomes has been 
fully substantiated. Obviously these dosages were smaller 
than those producing death. The obvious application is to 
the human race. Before these discoveries x-rays were being 
rather widely, and entirely ignorantly, used by some physicians 
for the purpose of producing sterility. The condition, however, 
is ordinarily temporary only; the first generation after such 
treatment may appear normal, but what abnormalities might 
appear in succeeding generations can only be guessed. Certainly 
as a means of birth control x-rays are to be most surely shunned, 
except as recommended and applied by men of unquestioned 
authority. 

Among diseased cells which show a pronounced sensitiveness 
to the action of x-rays are those of hyperplastic connective tissue 
and young rapidly growing cells of the embryonal type. 

The Effect of X-rays on Tissue. As inquiries into the ultimate 
nature of the action of rays upon tumor and normal tissue 
cells become more fundamental in terms of physics and chemistry, 
they become less satisfying in terms of biology. Since such 
tissues are not merely aggregates of cells but are highly complex 
systems of related and interdependent structures, purely chemical 
or physical data can never explain their behavior. And yet it is 
highly important to review briefly a few of these observations. 

First, the cell and nuclear membranes become more permeable. 

The marked swelling of irradiated nuclei and the ballooning of the 
cytoplasm are most easily and probably correctly interpreted as an 
increased capacity of these structures to absorb water, through an 
altered cell membrane. The nature of this cell change escapes us, but 
again assuming the simplest cause, one must suppose that intracellular 
chemical changes produce new electrolytes by decomposition of salts, 
proteins, and fats and that water is drawn in by simple osmosis. 

One of the gross effects is the actual closing of blood vessels and a 
disturbance of the vascular supply. Unfortunately there are no 
simple chemical studies comparing normal with heavily irradiated 
tissue. Again, radiation inhibits cell ferments. Hussey has 
shown that simple solutions of pepsin or trypsin are inhibited in 
action. Theories of splitting or ionization of cell constituents, of 
colloidal coagulation by points of radiation heat (Dessauer), 



156 APPLIED X-RAY 8 

increase in hydrogen-ion concentration, alterations in the disper- 
sion phase, changes in the electric charge of the colloidal con- 
stituents, disintegration of lipoids, changes in albumin, increase 1 
in the ratio Q = K(H 2 PO4 + HPO'O/Ca are among the observa- 
tions and theories which may be laying the basis for the solution 
of the problem. Certain it is that tissues must be considered as a 
whole. 

There is, however, a dominating fact which has become a 
recognized law in radiology, namely, the specific sensitiveness 
of each kind of cell to radiation. According to Desjardins, 2 
although the factors responsible for such specificity have not 
yet been determined, the sensitiveness peculiar to each kind 
of cell appears to be related to the natural life cycle. Thus the 
lymphocytes, whose metabolic cycle is the shortest, are also 
the most radiosensitive, and the nerve cells, whose life cycle is 
longest, are also the most resistant to irradiation. 

General average values of the sensitivity coefficients of normal 
tissues to x-radiation of medium hardness, referred to the skin 
as unity, are assembled in Table XXIII. 3 

TABLE XXIII. "RELATIVE SENSITIVITY OF A NORMAL TISSUE TO RADIATION 

OF MEDIUM HARDNESS (SKIN = 1.0) 
Leucocytes: Blood vessels: 

2 5 Lymphocytes 1 5 Endothelium (intima) 

2 . 4 Polynuclear 

Epithelial cells of salivary glands Dermal structures: 
Germinal cells: 1 4 Hair papillae 

2 . 3 Ovarian 1 3 Sweat glands 

2 2 Testiculnr 1 2 Sebaceous glands 

Blood-forming organs: 1 . 1 Mucous membrane 

2 . 1 Spleen 1 Skin 

2 Lymphatic; tissue 9 Serous membrane 

1 .9 Bone marrow Viscera: 

Endocrines: 8 Intestine 

1 8 Thymus 0.7 Liver, pancreas 

1 7 Thyroid 0.6 Uterus, kidney 

1 6 Adrenal Connective tissue: 

5 Fibrous tissue 

4 Muscle, fibrocartilage 

0.3 Bone 

0.2 Nerve tissue 

0.1 Fat 

1 KROETZ, Biochem. ., 161, 449 (1926). 

2 Loc. cit. 

3 HIRSCH, "Principles and Practice of Roentgen Therapy," p. 240, 
American X-ray Publishing Company, New York, 1925. 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 157 

X-ray Therapy. X-ray therapy is indicated when it is desirable 
to produce the following effects. 1 

1. Stimulation. It is now doubtful if there is a true stimula- 
tive effect. The change due to a so-called stimulating dose may 
be really processes of repair following an injury caused by irradia- 
tion. Treatment of skin diseases characterized by sluggishness or 
dryncss, or of glands deficient in function, has given conflicting 
results. 

2. Inhibition of the growth or function of glands and cells. 
Differentiated cells such as those composing glands and hair 
follicles, physiologically active cells, young cells, cells about to 
divide, lymphoid tissue, and tissue of embryonic type are all 
markedly radiosensitive. This fact is the fundamental basis of 
therapy. Skin diseases characterized by hyperactivity of the 
glands, hyperthyroidism, diseases which can be cured by check- 
ing ovulation, leukemia, and many other conditions are success- 
fully treated by irradiation. 

3. Solution of hyperplastie connective tissue, such as in uterine 
fibroids. 

4. Reduction of lichenification. The effect of x-rays on over- 
growth of cells of the epidermis is due to inhibition of cell division 
and activity. 

5. Anodyne effect. The relief of itching has been very 
frequently accomplished. The relief of pain, except when due to 
a lesion which can be cured by irradiation, is less certain, though 
many writers have reported an analgesic effect upon neuralgic 
pain. 

6. Reduction of inflammation. There is a favorable experience 
in treatment of carbuncles, pneumonia in certain stages, erysipe- 
las, etc. The rate and mode of reaction of inflammatory lesions 
indicate that the rays act chiefly by destroying the infiltrating 
lymphocytes, the exceptional sensitiveness of which has already 
been pointed out. Evidently these cells contain protective 
substances which enable them to neutralize bacterial or other 
toxic products which give rise to the inflammation; when the 
cells are destroyed by irradiation these protective substances 
are liberated and become immediately available for defensive 
purposes. 

7. Destruction of fungi. 

1 ERSKINE, " Practical X-ray Treatment," Bruce Publishing Company, 
Milwaukee, 1931. 



158 APPLIED X-RAYS 

8. Destruction of benign and malignant tumors. 
Desjardins 1 summarizes this subject in part as follows: 

The specific sensitiveness of different kinds of cells constitutes the 
most important single factor in the treatment of neoplasms. The 
value of roentgen rays or radium in different varieties of tumor depends 
mainly on this feature. The susceptibility of tumors to irradiation 
agrees closely with the radiosensitiveness of normal cells of the same 
kind as those from which the tumors are derived and of which they are 
largely composed. Thus, the inordinate hyperplasia of lymphoid 
structures which characterizes Hodgkin's disease, lymphosarcoma, 
and lymphatic leukemia retrogresses under irradiation at the same rate 
as normal lymphocytes are known to be destroyed by similar exposure. 
In fact, so striking is the parallel that irradiation is now being used 
daily as a means of distinguishing such conditions when their clinical 
features do not permit absolute identification. In some cases, indeed, 
the radiothcrapeutic method of diagnosis is more accurate and depend- 
able than microscopic examination. 

Knowledge of the relative radiosensitiveness of different cells has 
enabled Ewing and others to distinguish a group of bone tumors from 
other neoplasms which affect the skeleton. Ewing has designated 
this tumor as endothelial myeloma, because endothelial cells are a 
prominent feature. Among the malignant tumors of bone they are 
the most sensitive to irradiation. In fact, the other malignant growths 
which attack bone can hardly be said to have any sensitiveness; rather 
they are noteworthy for their resistance. Endothelial myeloma, on 
the contrary, is distinctly sensitive, and large tumors of this kind melt 
away with astonishing rapidity. The only other bone tumor which is 
radiosensitive is the usually benign giant-cell tumor, but its reaction 
to irradiation is unlike that of any malignant neoplasm. Instead of 
being followed by rapid or slow, but steady regression, irradiation of 
such growths causes them to swell and become tender. The patient 
and the uninitiated physician may naturally conclude that exposure to 
the rays has stimulated the tumor to increased growth, and the limb 
may be unnecessarily sacrificed. Such inflammatory reaction is a 
transient phase which lasts two or three weeks and is followed by slow 
regression and repair of the tumor by deposition of new bone. This 
characteristic reaction of giant-cell tumor constitutes at once a valuable 
means of identification and treatment and furnishes additional evi- 
dence that tumors of this kind, at least at the outset, are not true neo- 
plasms but chronic inflammatory lesions. 

Many other examples might be mentioned, but the foregoing are 
sufficient to illustrate the important bearing on medical diagnosis and 

1 Loc. tit. 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 159 

treatment of the radiosensitiveness of cells and tissues. Heretofore, 
for some reason, biologists have seldom made use of radiation for experi- 
mental purposes. As soon as they begin to realize its possibilities, they 
will find in the method a means of acquiring much valuable information, 
and such increase in knowledge will help to extend the diagnostic and 
therapeutic applications. 

The most recent important contributions to our knowledge of 
the mechanism of cancer is that of McDonald of the University of 
Pennsylvania. 1 As a result of careful researches it is definitely 
established that, in order to have a cure for cancer, conditions 
must be produced which will accomplish the following: 

1. Alter glycogenolysis towards normal from the cancer 
type; in tumor tissue for every 13 sugar molecules attacked, 12 
are split up into lactic acid and 1 oxidized, while in normal tissue 
this ratio is 1:1; hence the cancer cell as an energy adapter 
follows a different mechanism from normal. 

2. Produce conditions of biological equilibrium towards normal 
from the alkaline state (pH 7.47 or 8.7 per cent more alkaline in 
internal untreated cancer blood plasma; the more alkaline, the 
quicker the disease kills). 

3. Reduce high blood glucose. 

4. Produce a calcium-like effect (cancer cells have less calcium 
than normal). 

5. Reduce or prevent a potassium-like effect (the virulence of 
the tumor increasing with potassium content). 

These remarkable facts so newly established should give a clue 
to the satisfactory treatment of cancer by x-rays or 7-rays. 
The mechanism, aside from specific radiosensitiveness of cells, 
by which radiation is accomplishing these necessary changes 
and others still unknown, remains largely a mystery. But 
in the meanwhile, in spite of ignorance and inefficiency, x-rays 
are proving one of mankind's greatest aids and hopes in the 
evolution of the most important problem of our time, namely, 
cancer. The literature abounds with case reports of cures, 
some even for the advanced stages of the disease. In other 
cases where cure is hopeless, comfort and alleviation of pain 
and prolongation of life are made possible. However, the under- 
lying principle of successful cancer treatment by radiation therapy 
is early diagnosis. People must be educated not only to the 

* Science, 74, 55 (1931). 



160 APPLIED X-RAY8 

desirability but to the necessity of complete physical examination, 
in which x-rays shall be applied in their other great medical 
province, that of radiographic diagnosis. Internal cancer may be 
well advanced without the disclosure of symptoms; and yet a 
radiographic examination alone may show its presence. 

The earlier the discovery of such a condition, the greater the 
probability of a genuine cure under the careful and intelligent 
ministration of a trained roentgenologist. Ignorantly used, 
however, this great therapeutic agency may actually become a 
curse. 

IV. THE MEASUREMENT OF X-RAY INTENSITY OR DOSAGE 

Besides the measurement of quality or wave lengths of an x-ray 
beam, which has been discussed in Chap. V, the measurement of 
the intensity of x-rays is of importance to all x-ray workers, 
whether in the pure science or in its applications. The physicist 
must know the energy distribution in the x-ray spectrum and 
must have a ready and accurate method of measurement of the 
absolute intensity if he is to discover the underlying natural 
laws he seeks. The x-ray spectroscopist and the student of 
crystal structure need reliable intensity measurements if they are 
to obtain the utmost benefit from their data. The roent- 
genologist requires a simple and easily usable method to estimate 
x-ray dosage. Intensity is measured not as radiation energy 
directly, but by means of the following effects: heat, ionization, 
darkening of the photographic plate, other chemical effects, 
fluorescence, color change, change in the conductivity, and certain 
biological effects such as skin erythema, killing of Drosophila 
eggs, etc. 

Heat Methods. If a small beam of x-rays is allowed to 
impinge upon a metal block of such size that practically complete 
(97 per cent or more) absorption of the beam occurs, the net 
effect of the absorption will be an increase in the heat content of 
the block. That is to say that essentially all secondary rays, 
photoelectrons, etc., are absorbed in the block and their energy is 
converted into heat. This fact is the basis of present methods 
of accurately determining the total energy content of an x-ray 
beam. Such methods have been used to study the distribution of 
energy in the x-ray spectrum, the dependence of intensity upon 
the potential on the x-ray tube and upon the current through the 
tube, the relation between the energy input to the tube and the 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 161 

x-ray energy produced, the relation between energy, wave length, 
and ionization, and the relation between energy and photographic 
darkening. 

The instruments employed generally consist of two elements, 
one heated by x-rays and one by electricity, which are balanced, 
by several different methods, against each other; the electric 
energy input is measured directly and, since the heat effects in the 
two elements are the same, is equal, after the instrumental cor- 
rections have been applied, to the x-ray energy input. 

Terrill 1 has used the method to determine the total energy 
of x-rays from a tungsten-target tube excited by constant 
potential direct current at 30 to 100 kv. The total output 
of the tube was thus found to be from 0.00025 to 0.00192 times 
the input. Plotted against the square of the voltage these 
values give a straight line to 69.3 kv. where a change of slope 
occurs, probably due to the selective absorption of the target 
itself. 2 

All these heat-measuring devices require the most careful 
construction and manipulation, the chances of experimental 
error being very great as the measured effects are usually very 
small; hence, they are not available for routine intensity 
measurements. 

Ionization. Except for heat methods involving complete 
absorption, the actual extent of various other effects of x-rays 
including ionization depends on radiation intensity and also on 
wave length and on this account a different fraction of the initial 
radiation with varying intensity for different wave lengths is 
transformed in the irradiated medium into other energy forms. 
The action is independent of wave length only when the beam of 
given initial intensity, inclusive of secondary rays arising there- 
from, is completely absorbed in the irradiated material. Hence 
the ionization current is a measure of the absorbed, not the 
incident, radiation intensity. The difference in the dependence 
of the sensitiveness of different methods of measurement upon 
the wave length is demonstrated in Fig. 72. If different 
homogeneous rays fall simultaneously with equal intensity upon 
an air ionization chamber, a fluorescent screen, and a photo- 
graphic plate, the brightness of the screen changes much less 
with wave length than the ionization current; the photographic 

l l*hys. Rev., 28, 438 (1926). 

2 The K series tungsten rays are generated only above 69.3 kv. 



162 



APPLIED X-RAYS 



sensitiveness changes with sudden jumps at 0.49 and 0.91 A.U. 
Since these wave lengths coincide with the discontinuities in 
absorption coefficients of silver and bromine, the two effective 
constituents of the photographic emulsion, the photographic 
action is closely connected with absorption. Hence the action of 
the rays changes with wave length in the same way as the inten- 
sity of the absorbed portion of the incident rays changes; excep- 
tions occur in the rays of very short wave x-rays when the 




Fio. 72. Effects of x-rays of different wave lengths. 
i _ iomzation 

/ ~~ incident ray intensity' 
// _ fluoreaopnt screen briKhtnesB^ 
/ incident ray intensity ' 

<S _ photographic blackening 
E incident ray energy 

Compton effect is appreciable and in the case of the excitation of 
characteristic fluorescent rays of the irradiated material. The 
general rule holds for each known physical and chemical effect: 
that the effect changes with wave length in the same way as the 
fraction of the incident radiation energy transformed into the 
energy of photoelectrons and Compton electrons. The values 
may be calculated for certain chemical compositions of a material 
from physical data (absorption coefficient, recoil coefficient, etc.) 
and Glocker has found excellent agreement between theory and 
experiment for ionization. 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 163 

The aim of practical dosage measurement, particularly for 
therapy, must consist in the selection of a radiation effect which 
can be measured and which changes with wave length in the 
same way as a given biological reaction, e.g., skin erythema. 
Repeated experimentation has proved convincingly that a 
complete parallelism between skin erythema and air ionization 
exists independent of the quality of the radiation. Since the 
absorption coefficient depends not only on wave length but also 
upon the density and upon the atomic number of the elements 
constituting a material, so it is to be expected that air consisting 
of the light elements oxygen and nitrogen should possess the same 
absorption properties as tissues consisting of organic compounds 
of carbon, nitrogen and oxygen, or water. At the second Inter- 
national Congress of Radiology in 1928, therefore, the measure- 
ment of air ionization was accepted as the basis of international 
dosage measurement, and a definition was given of the unit of 
dosage, designated the roentgen unit and written as "r, " as 
follows : 

The absolute unit of the x-ray dose, one roentgen or r, is obtained 
from that x-ray energy which, when the secondary electrons are 
fully utilized and secondary radiation from the wall of the 
chamber is avoided, under standard conditions C. and 760 mm. 
of mercury pressure, produces in 1 c.c. of atmospheric air such a 
degree of conductivity that the quantity of electricity measured 
at saturation current equals 1 electrostatic unit. 

The physical dose is the electron energy (kinetic energy of 
photoelectrons and Compton electrons) liberated by the action of 
x-rays in a volume element of an irradiated body during the time 
of exposure divided by the size of the volume element. 

Glocker 1 has proposed a change in the definitions of the roentgen 
unit, to provide for the entire range of wave lengths. The 
absorption edge of argon found in air at 3.86 A.TJ. has the conse- 
quence that the absorption of x-rays in air changes discontinu- 
ously at this wave length and the dose measured for wave lengths 
greater than 3.86 A.U. is 18-20 per cent too small whereas 
the same phenomenon does not take place in tissues or water. 
Glocker, therefore, suggests that carbon dioxide gas be substituted 
for air in the definition. 

Several types of ionization chambers have been designed 
for the determination of intensities in therapy, even in absolute 

1 Radiology, 17 (in press). 



164 APPLIED X-RAYS 

units. The Duane ionization chamber or iontoquantimeter is one 
of especial merit. It consists simply of a series of aluminum 
sheets about 5 cm. long and 2 cm. broad held parallel to each 
other and 5 mm. apart by hard-rubber frames. Alternate sheets 
are connected together, thus forming a small condenser with 
layers of air between the sheets. The condenser is joined in a 
simple electric circuit with a battery and sensitive galvanometer 
which is calibrated by means of a Weston standard cell and resist- 
ance. By comparison of the deflection with the known current 
to the deflection produced by the current produced by the ioniza- 
tion of air by the x-ray beam in the chamber of known volume, 
the intensity of the beam in r units may be calculated. Glasser 
at the Cleveland Clinic, Taylor at the Bureau of Standards, and 
others have designed large air ionization chambers for standard- 
ization purposes. 

Friedrich has introduced the use of an ionization chamber made 
of horn, the chemical elements in which are those found in the 
body, containing only 1 c.c. This has the advantage that 
intensities in absolute units may be read on a scale of the deflect- 
ing electroscope. Dauvillier has devised a spherical gas chamber 
containing xenon as the absorbing gas. Several other similar 
devices of bakelite, graphite, etc., are manufactured by equip- 
ment builders. 

An unusually simple and efficient portable instrument is the 
Victoreen /-meter, consisting of a small ionization chamber rigidly 
connected with a string electrometer, the scale of which is cali- 
brated in international units. The chamber is exposed for 1 rnin. 
to the rays and the scale read, the figure being r per minute. 
This instrument also serves readily in all kinds of absorption 
measurements including the determination of effective wave 
length. 

Meanwhile, by using a properly designed ionization chamber 
and by recording simply the ionization-chamber current as the 
index of intensity, the method becomes very valuable for many 
kinds of work, particularly in the analysis of crystal structure 
by the ionization spectrometer (sec p. 190), where only a relative 
measure of intensity is needed. The ionization chamber should 
be large enough completely, or nearly completely, to absorb the 
rays; the electrodes must not be exposed to the incident rays; 
a gas of quite heavy molecular weight is most satisfactory, 
methyl iodide or ethyl bromide being often used. Sulfur dioxide 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 165 

has also been used; air usually does not show enough effect. The 
use of heavy gases is also helpful in insuring complete absorption 
of the rays without the use of excessively large pressures or 
large chambers. 

There are several accepted ways of measuring the current 
through the ionization chamber. Some experimenters use an 
electroscope and time the fall of the leaf. Others use a quadrant 
or string electrometer; recently it has been suggested that the 
current might be amplified by the use of three-element electron, or 
ordinary radio, tubes; and indeed such an arrangement has been 
developed by the Siemens and Halske Company 1 in Germany in 
an instrument designed to measure dosage in x-ray therapy, 
usually in conjunction with the small Friedrich ionization 
chamber. This amplifies the current to such a magnitude that 
it may be measured by a microammeter. The General 
Electric Company has developed also a special amplifying 
tube for this purpose (see page 193). In every case the poten- 
tial across the chamber is provided by a battery of electric 
cells and must be high enough to insure reaching the saturation 
current through the chamber. A potential of 90 volts is usually 
sufficient. 

Photographic Methods. The limitations in the photographic 
method for determining absolute or even relative intensities 
have already been indicated on page 143. The wide varia- 
tion in the speed of different emulsions, the complications 
introduced by the absorption edges of silver and bromine (Fig. 
29), and the dependence of blackening on voltage are some of 
the difficulties. 

Other Chemical Methods. Table XXI (page 144) lists a few 
chemical reactions which have been suggested as dosimeters 
and have been calibrated in r units. The most promising and 
practical of these are: 

Mercuric chloride + ammonium oxalate (Eder's solution) > 
precipitate of mercurous chloride (calomel) which may be 
weighed; 0.58 mg. mercury per cubic centimeter for 840 r (I 
threshold erythema dose). 

Oxidation of ferrous sulfate to ferric sulfate; 0.0027 mg. FeS04 
per cubic centimeter per 1000 r. 

1 VON HAUSER, K. W., R. JAEGER, and W. VAHLE, "Siemens and Halske 
Catalogue, Rohrengalvanometer," Siemens and Halske Company. 



166 APPLIED X-RAYS 

Both of these reactions are relatively simple but will scarcely 
compete as dosimeters with commercial ionization equipment. 

Fluorescent Methods. For measuring intensity of x-rays by 
fluorescence methods, the fluorescence of a screen is compared 
with the fluorescence produced by a standard radiation. This is 
obviously a comparative method and is open to the objections 
that the fluorescing salt becomes "tired" under the action of 
the rays, and that the screen may not be of uniform fluorescing 
power. The objections to using fluorescence methods to deter- 
mine absolute intensity are that the relation between fluores- 
cence and the x-ray intensity is unknown and that certain rays 
will excite a characteristic fluorescence. Further shortcomings 
of fluorescent screens are covered on page 139 in the present 
chapter. The method is not used except in medical work, and 
then rarely. 

Coloration Methods. With the medical profession the 
color change in barium platinocyanide "pastilles" as an index 
of intensity has been utilized. The pastille is placed at a speci- 
fied distance from the anticathode of the tube and the color 
matched against a set of standards. The color changes from 
yellow green to brown, and periodic comparison with the standard 
indicates the total energy absorbed. The method gives hardly 
more than qualitative information since wave lengths of all 
kinds are measured by a surface-color change. Exposure to 
light brings the pastille to its original color. 

Selenium-cell Method. Furstenau has developed a selenium- 
cell method of measuring intensity which is used in x-ray therapy. 
This is dependent upon the fact that x-rays cause a change in the 
electrical resistance of selenium. The method is only qualitative, 
and the cells must be frequently checked against a standard, 
since they change characteristics during usage. 

Biological Methods. The method of estimating dosage from 
skin reddening or erythema is familiar to all x-ray workers. 
This can never serve as an accurate method because of the widely 
varying sensitivity of the skin of different individuals to radia- 
tion. Glasser and Portmann 1 compiled data from 40 clinics 
on the number of r units for average erythema reaction in deep 
therapy. These varied from 500 to 1,250 r, or an average of 
930. The threshold value of erythema is commonly taken to 
be 840 r. 

1 Radiology, 14, 346 (1931). 



PHYSICAL, CHEMICAL, AND BIOLOGICAL EFFECTS 167 

A much more accurate "biological ionization chamber/ 7 as 
designated by Wood 1 are Drosophila (fruit fly) eggs. Invariably 
50 per cent of the eggs are killed by 180 r and 90 per cent by 
500 r. The points for the effect of radium fall directly on the 
curve experimentally determined for the percentage of eggs 
hatching as a function of r-units. 

1 Radiology, 12, 461 (1929). 



PART II 

THE X-RAY ANALYSIS OF THE ULTIMATE 
STRUCTURES OF MATERIALS 



CHAPTER X 

CRYSTALS AND X-RAY DIFFRACTION 

The Solid State of Matter. Knowledge of the crystalline 
state of matter was decidedly limited prior to the discovery 
by Laue and the Braggs that x-rays could be applied to the 
analysis of the internal structure of crystals. The great and 
relatively aged science of crystallography had been built up to 
the conclusion, from careful observations with microscopes and 
optical goniometers, that apparently almost all true solids were 
really crystals, either single entities with pairs of parallel bound- 
ing surfaces disposed in definite geometric fashion at angles 
which could be measured, or aggregates of these single crystals. 
While regularity of exterior appearance indicated some kind of 
regular internal arrangement of unit building material, whatever 
that might be, yet without experimental methods of investiga- 
tion and without adequate conceptions of atomic and molecular 
structure and the forces holding atoms and molecules together, 
physicists and chemists were unable to find points of useful 
contact with the essentially applied geometric science of crystal- 
lography. Concerning the gaseous and liquid states of matter, 
much more was known in the sense that their behavior could be 
explained by simple hypotheses. They are characterized by 
disordered arrangement of atoms or molecules which are rela- 
tively free to move, even in liquids. Since all directions are 
alike, it is possible to calculate with considerable accuracy the 
behavior of gases and liquids in very practical phenomena. 
Chemists have worked very largely with gases and liquids because 
the freedom of motion of the molecules has permitted reactions 
more readily. But in solids great complications arise because 
the atoms and molecules are bound together tightly by their 
mutual forces. It is evident that the exercise of these forces 
should tend to produce regularity of arrangement. X-ray 
analysis has shown that such a regularity does exist in practically 
every solid substance. 

171 



172 APPLIED X-RAYS 

The great practical importance of scientific knowledge of the 
ultimate structure of solids, which are crystals in the natural 
state, is self-evident, when consideration is given to the definition 
of desired physical and chemical properties. The strength of 
steel girders, the corrosion of aluminum alloys, the wearing prop- 
erties of case-hardened steel, the plasticity of lime, the dielectric 
capacity of materials, the lubricating properties of long-chain 
paraffins or of graphite, the stretching of rubber, the covering 
power of pigments, and innumerable other practical phenomena 
of everyday life all depend upon ultimate crystalline structure. 
Bragg has shown clearly that as a matter of fact the only prop- 
erties of solid bodies which are not directly and obviously 
related to crystal structure are those, few in number, which 
depend upon atomic characteristics alone, such as weight. With 
few exceptions every aspect of the behavior of a solid substance 
depends on the mode of arrangement of its atoms and molecules. 

A clear distinction must be made relative to the ultimate crys- 
talline structure of materials. Sir William Bragg speaks in the 
following inimitably clear fashion of the three types of assemblage: 

The simplest is that of the single atom as in helium in the gaseous 
state, in which the behavior of every atom is on the whole the same as 
the behavior of any other. The next is that of the molecules, the 
smallest portion of a liquid or a gas which has all the properties of the 
whole; and lastly, the crystal unit, the smallest portion of a crystal 
(really the simplest form of a solid substance) which has all the proper- 
ties of the crystal. There are atoms of silicon and oxygen, there is a 
molecule of silicon dioxide, and a crystal unit of quartz containing three 
molecules of silicon dioxide. The separate atoms of silicon and oxygen 
are not silicon dioxide, of course, in the same way the molecule of 
silicon dioxide is not quart/; the crystal unit consisting of three mole- 
cules arranged in a particular way is quartz. 

The first aim of the x-ray analysis of crystals is to determine 
the arrangement of the atoms and molecules in the crystal unit, 
and to account for the properties of the crystal in terms of that 
arrangement. The interference of x-rays in gases and liquids 
has made possible more recently fine-structure determination 
even for these states. 

Fundamentals of Crystallography. In Part I attention has 
been given primarily to the fundamental properties of x-rays 
which are to be used subsequently simply as a tool in the analysis 
of fine structure of matter. The crystal grating of known con- 



CRYSTALS AND X-RAY DIFFRACTION 



173 



stant by which it is possible to analyze x-radiation and measure 
wave lengths has been taken more or less for granted. It is 
now appropriate to take the radiation for granted and to inquire 
into the reasons for the satisfactory action of crystals as gratings 
and for the fact that the analysis of x-ray spectra from each 
crystal leads directly to the interpretation of how a particular 
crystal is built from ultimate atomic units. 

Entirely apart from x-ray data a systematic science of crystal- 
lography has been developed which serves as the basis for rational 




(110) Planes 



(100) Planes 



(211) Planes 




(310) Planes (111) Planes (321) Planes 

FIG. 73. Typical sets of parallel pianos in a cubic lattice. 

interpretation of x-ray data. The steps in the development of 
this information may be summarized briefly as follows: 

1. The important properties of a crystal visible to the eye are 
the planar bounding faces and the symmetry. The first logical 
step is to measure the angles between faces with the goniometer. 
In order to express then the positions in space of these planes 
relatively to each other, it is essential to derive a system of 
coordinates. The planes may then be indexed in terms of their 
intercepts upon the axes of a system of coordinates; upon each 
axis a unit distance is chosen and then the distances from the 
origin of the given plane along the three axes are measured; the 
reciprocals of these intercepts are then the indices of the plane. 



174 



APPLIED X-RAYS 



Thus a plane intersecting the X-axis at unit distance from the 
origin and parallel to the F and Z axes has the intercepts 1, >, 
oo and the indices 100 (see Fig. 73). Other cubic faces have the 
indices (010) and (001) and the planes which bisect diagonally 



C H 




FIG. 74. Directions and planes in a cubic lattice. 

the cube faces arc (110), (101), and (Oil). In addition there are 
the similar planes with negative indices where the intercepts are 
in other quadrants. A single specific plane or crystal face is 
usually designated with parenthesis, thus (100), a family of 

ABC 
c 



7 




FIG. 75. The coordinate axes of crystal systems. (A) Triclinic, a 7* b 7^ c, 
a ^ ft j y j 90. (B) Monoolinic, a^b^c, a = j = 90, ft ^ 90. (C) 
Rhombic, a^b^c, = = 7 = 90. (D) Tetragonal, a = b ^ c, a = 
ft = y = 90. (E) Cubic, a=b=c,a=0=7= 90. (F) Hexagonal, a = 
b ^ c , a = ft = 90, 7 = 120. 

parallel planes <100> or 100, and a direction or normal to a 
side of parallel planes [100] (Fig. 74); if the faces of a crystal are 
completely developed then the form is designated { 100} to include 
the six cubic faces, etc. A crystal in the cubic system may have 
the form { 100 } , cubic shape, or { 1 1 1 ( , an octahedron. In Fig. 73 



CRYSTALS AND X-RAY DIFFRACTION 



175 



are shown six of the various sets of planes into which a cube 
may be imagined to be sliced up. 

Now an immense amount of experimentation has proved that 
all angle measurements and indexing of plane faces are accounted 
for by seven systems of coordinates (Fig. 75). In other words, 
there are seven crystal systems: triclinic, monoclinic, orthorhom- 
bic,* tetragonal, hexagonal, rhombohedral (often classed under 
hexagonal), and cubic. As an example of these relationships 
whereby a crystal is characterized, the case of tetragonal tin 
(Schiebold) is represented in Fig. 76. The outer form of a 
single crystal is represented on tetragonal axes, a, a, c, a = = 
7 = 90. The most characteristic faces are designated p the 




FIG. 76. Diagram of faces of a single crystal of white tin, after Schiebold (see 
text for method of indexing face planes). 

indices being (111), (ill), (TTl), (Til), (111), (UT), (TTT), (III), 
or the form {111}. The other faces can also be symbolically 
represented, so that the crystal habit is completely described as 
follows : 

p = {a, a, c} = {111} ;r = {a/3, a/3, c} = {331}; 

m = ja:a: oo c } = {110} ; 

s = {a, oo a, c} = {101}; t = {a/3, oo a, c} = {301}; 

a = {a: oo a: oo c} = {100}. 

From the angle between the faces s:a = 68 54', the axial ratio 
can be calculated to be a: c = 1:0.3857. 

Another important property is illustrated by this figure, 
namely, that several faces intersect in parallel edges stats, 
prmrp, etc. The aggregation of all faces or planes which 
intersect with parallel edges is called a zone and the common 



176 



APPLIED X-RAYS 

II III 




IV 




VII 



I 


f 

,Vb 


t 


7 


t 


p 




r 


*/ 
t. 




X 

, \ 


~^l 


"7 

X 


', ). 

f 

,' ,' 

' '14 


) , 

. 

*. ' 


,' 

L< 



VITI 



IX 



XI 




XII 



XIII 



XIV 



a 2 



V 



7 



FIG. 77. Space lattices. I, triclinic; II, simple monoclinic; III, end face- 
centered monoclinic; IV, simple rhombic; V, end face-centered rhombic; VI, 
body-centered rhombic; VII, face-centered rhombic; VIII, hexagonal, IX, 
rhombohedral ; X, simple tetragonal; XI, body-centered tetragonal; XII, sim- 
ple cubic; XIII, body-centered cubic, XIV, face-centered cubic. 



CRYSTALS AND X-RAY DIFFRACTION 177 

edge direction a zone axis. It follows that every possible crystal 
face must belong to at least two crystallographic zones. 

2. As a further result of the experience of two hundred years 
it is now definitely assured that the indices of all the plane faces 
of crystals are always small whole numbers (z.e., 100, 321, 568, 
etc.) the law of rational indices. If this is true, then only a 
definite lattice in three dimensions formed by the intersection of 
three sets of parallel planes can explain the rational intersections 
on axes. These lattices are, of course, considered to be built 
on the above seven systems of coordinates, and there are 14 of 
these spacial patterns geometrically possible (Fig. 77). 

3. To the systematic classification into seven crystal systems, 
the experimentally founded law of rational indices and the 
consequent hypothesis of space lattices, may be added other 
types of information enabling an approach to the subject of 
symmetry. Some of these are velocity of solution of different 
crystal faces, etch figures, birefringence, optical activity, piezo- 
and pyroelectric properties. In general, it might be expected 
that two crystals, which gave identical measurements of angles 
between faces indicating identical disposition of planes, should 
also have identical properties. It soon becomes evident, how- 
ever, that the formal classification of crystals thus made has 
not been extended far enough. Mark 1 points out that angle 
measurements class both barium antimonyl tartratc and calcium 
molybdate as tetragonal, but this in no sense explains why one 
has optical activity and the other has not. Account, therefore, 
must be taken of different symmetries. 

4. The symmetry of an object is an expression of the fact 
that the object has equal properties in different directions. 
Two positions of a crystal, in which the equivalent directions 
may be brought into coincidence, say by a simple rotation around 
an axis, are not distinguishable by any physical-chemical means. 
Now the following symmetry operations may be performed to 
bring equivalent points in space into coincidence: 

a. Axes of symmetry (cyclic operation). Points in crystals 
may have one-, two-, three-, four-, or six-fold axes by which is 
meant coincidence of equivalent points by rotation of 360 (every 
point has this identity operation), 180, 120, 90, or 60 degrees. 
The fact that there is no five- or seven-fold axis (although five- 

*Z. Metallkunde, 20, 342 (1928). 



178 



APPLIED X-RAYS 



fold symmetry is found in nature in starfish) is further indica- 
tion of a space-lattice structure. 

b. Plane of symmetry (mirror operation), in which points on 
one side of a plane are mirror images of points on the other. 







h i j k 

FIG. 78. Ornamental figures illustrating crystal symmetry. (After Schie- 
bold.) a, plane of symmetry, hornblende; b, two planes of symmetry, aragonite; 
c, ornament with a plane of symmetry; d, two-fold axis of symmetry, gypsum; e, 
three-fold axis of symmetry, quartz; /, four-fold axis of symmetry, wulfenitc; g, 
six-fold axis of symmetry, apatite; h, ornament with mirror and rhythmic sym- 
metry; ?', planes of symmetry and three-fold axis, tourmaline; j, planes of 
symmetry and four-fold axis, tinstone; A-, planes of symmetry with three-fold 
rhythmic symmetry, caloite. 

c. Center of symmetry or a combined rotation and reflection 
across a plane perpendicular to the axis. 

These symmetry elements are well illustrated by the orna- 
mental figures selected by Schiebold, shown in Fig. 78. The 
symmetry planes, axes, and center for a cube are illustrated in 
Fig. 79. 



CRYSTALS AND X-RAY DIFFRACTION 



179 



When now these symmetry operations are combined in every 
possible way, using the seven systems of coordinates, it develops 
that there are 32 point-groups which define 32 crystal classes 
in terms of symmetry. A combination of goniometric and 
physical measurements makes it possible to classify crystals as 
to system and as to the finer subdivision of class or point-group. 
But it is to be observed that this is still a macroclassification, and 
the idea of the lattice, except as an explanatory hypothesis, or 
of the ultimate units from which crystals are built, does not enter 
in. 

5. The final step in the further refining of classification of 
crystals was taken as a result of the work 
of Schoenfliess in 1890, with the three- 
dimensional lattice theory and the idea 
of atoms at the points of the lattice as 
a basis. In other words, by combining 
the 32 classes of symmetry around a 
point with translation in three directions 
to other equivalent points, arranged 
according to a definite spacial pattern 
(the lattice), at a distance of the order 
of 10~ 8 cm. or atomic dimensions apart, 
other symmetry operations involving i 
this translation become evident, namely, four-fold; triangles, three- 

, ,1 / j r i j fold; ellipses, two-fold. 

two-, three-, four-, and six-fold screw 

axes of symmetry, involving rotations about and translations along 
an axis, and glide planes of symmetry in which a figure is brought 
into coincidence by reflection in a plane combined with translation 
of a definite length and direction in the plane. These were called 
by Schoenfliess " microscopic symmetry elements. " When these 
are included in the process of placing each of the 32 point-groups 
at the points of the 14 lattices, the result is a total of 230 com- 
binations or space-groups. The definition of a crystal by its 
space-group is unique. A recent extension of the space-group 
theory by Weissenberg takes into account the existence in space 
of the molecule (in the sense of Avogadro) defined as " island 
point-group," "dynad," and " micro-building unit." 

It is obvious in the macroclassifications depending upon 
reflections of visible light by different faces, and other physical 
measurements, why this final refinement depending upon the 
arrangement in space of atoms, and the differentiation between 




180 



APPLIED X-RAYS 



axes and screw axes of symmetry, was impossible. Herein lies 
the great province of x-rays, as first predicted by Laue in 1913, 
with wave lengths of the same order of magnitude as these lattice 
spacings. X-ray studies of fine structure have thoroughly 
confirmed the geometrical theory of space-groups, so that now, 
vice versa, the theory of space-groups is an indispensable aid in 
the interpretation of x-ray spectra obtained from any given 
crystal in terms of the ultimate fine structure of that crystal. 

X-ray Diffraction by Crystals. If crystals are built up of 
atoms and molecules marshaled in definite rows and in parallel 
planes with their mutual forces restraining them to relatively 
fixed positions in the rigid solid, and if x-rays are scattered by 
atoms, then these crystals are potential three-dimensional diffrac- 




Fio. 80. Derivation of Bragg law. n\ = 2d sin O. 

tion gratings for x-rays. Such was the prediction in 1913 of 
Laue, after he had accepted the work of Schoenfliess and Federov 
leading to the conception of space-groups and had calculated 
from the density, molecular weight, and weight of the hydrogen 
atom that the distances between regularly disposed particles 
of mass in crystals must be of the same order as the wave length 
of x-rays (10~~ 8 cm.). Friedrich and Knipping verified the predic- 
tion using a crystal of zinc blende. The original analysis by 
Laue was of considerable mathematical complexity but the 
Braggs were able to reduce the interaction between x-rays and 
crystals to terms of great simplicity, by considering primary 
x-rays to be reflected by the face of a crystal. As a matter of 
fact, the mechanism is far more complicated, since planes and 
atoms far below the " reflecting" surface are concerned, and since 
the emergent " secondary" x-rays have been emitted as a conse- 
quence of electronic changes in the atoms across which the 



CRYSTALS AND X-RAY DIFFRACTION 181 

primary beam passes. Experiments have shown that the whole 
phenomenon appears to be simple reflection of the primary beam 
in accordance with a simple equation n\ = 2d sin 6. The simple 
relations among X, d, and 6 are at once seen from Fig. 80, which 
shows the incident beam 7 reflected at O t and 2 . The line ab 
is perpendicular to the reflected rays Oil and 2 2. The length 
or 'path OiOjb is greater than the length of the path O t a by the 
length of the broken line r0 2 6, the line Oc being perpendicular 
to Oi0 2 . The length of the broken line cO> 2 b is, obviously, 2d 
sin 9. The condition that there should be a reflected beam is, 
therefore, that the reflected train O 2 2 shall be exactly one wave 
length or an integer multiple of wave lengths n behind the train 
Oi^ or that 

n\ = 2d sin O. 

This is the fundamental equation of x-ray spectroscopy and 
of the analysis of structure of crystalline materials. For ordinary 
purposes it may be considered as rigorous; slight departures 
from it, observed particularly at higher orders of reflection, are 
due entirely to refraction, for 5, in the expression for refractive 
index ju = 1 5, is not zero but of the order of 10~ 6 . 

Regardless of the experimental method of analysis (con- 
sidered in the next chapter), the information vouchsafed by 
interference patterns of crystals is essentially the same. This 
is the determination of a series of values of d for different sets 
of planes by use of the Bragg equation. Now if a crystal is 
really a lattice, it follows that planes of three sets in the principal 
directions will enclose a small unit cell the smallest possible 
subdivision which has the properties of the visible macrocrystal 
and which by repetition or translation of itself in all directions 
actually builds the crystal. It is the size of this fundamental 
architectural unit which may be determined directly from the 
experimental values of di, d 2 , and dv the respective edge lengths 
of the small parallelopipcd. This presupposes some previous 
information about the crystallographic system, whether the 
axes are at right angles or not, or are of equal length or not. 
As previously indicated, this may easily be obtained by goniom- 
eter measurements of angles between faces. But if optical 
data are not available, the angles between the axes and axial 
ratios may be measured by reflection of x-rays from a crystal 
mounted on a goniometer head just as readily as by the optical 



182 APPLIED X-RAYS 

method. Assuming this to be the process employed, the steps 
in analysis are as follows: 

1. Goniometric determination of crystallographic system. 

2. Determination of dimensions and volume of unit cell. 

3. Determination of the number of atoms or molecules in each 
unit cell. This involves a measurement of the density of the 
crystal and the use of the volume of the unit cell in the following 
formula : 

pV 

n = -YJ j 
Mm 

where n is the number of atoms (of an element) or molecules per 
unit cell; p is the density; V is the volume of the unit cell (d 3 for 
a cubic crystal, or in general 

V = abc -\/sin 2 a + sin 2 ft + sin 2 7 2 cos a cos ft cos 7 , 

where a, 6, and c are edge lengths, and a, ft, and 7 the angles 
enclosed by the edges); M is the atomic or molecular weight, 
and m is the absolute weight of the hydrogen atom (1.663 X 
10~ 24 g.). 

4. Further classification as far as possible according to sym- 
metry observed, measurement of the intensities of lines, 
appearance or non-appearance of certain reflections, and the 
identification of interference maxima with the indices of planes. 

5. Application of the theory of space-groups. Each of these 
space-groups is characterized by certain diffraction criteria, 
such as the apparent halving of spacings due to non-appearance 
of odd order (n = 1, 3, 5, etc.) interferences. Screw axes and 
glide planes can be detected; for a screw axis causes all orders 
of reflection from the plane normal to it to disappear except that 
corresponding to a multiple of the screw translation, as, for 
example, in quartz with a trigonal screw axis only the third, 
sixth, ninth, etc., orders appear. Glide planes halve whole sets 
of planes hko, where h + k is odd. A great service has been per- 
formed by Astbury and Yardley 1 in tabulating and graphically 
representing these criteria. 

6. Determination of the symmetry of the molecule from the 
space-group of the crystal, the number of entirely unsymmetri- 
cal molecules theoretically required, and the number of mole- 
cules per unit cell actually found. 

l Phil. Trans. Roy. Soc. (London), 224A, 221 (1924). 



CRYSTALS AND X-RAY DIFFRACTION 183 

7. An analysis of the structure factor from intensity measure- 
ments, defining the positions within the unit cell of the diffract- 
ing centers, and even of the symmetry and positions of atoms 
in molecules if these are the lattice units. This is the most 
difficult, least direct, and yet the most interesting stage in 
crystal analysis. Briefly put, the process consists in assuming 
uci*tain values for parameters and upon the basis of known 
laws of scattering and interference in calculating from these 
the theoretical intensity of reflections from a set of planes. 
These results are compared with observed intensities, and the 
process of trial and error continued until there is an agree- 
ment. Bernal has likened the process to the solution of a 
cross-word puzzle. The cell and space-group provide the 
square and pattern, the atoms the letters, and the intensities 
the clues. 

8. A coordination and test of the completed structure with 
other known physical and chemical properties, such as atomic 
or ionic radii, optical activity, polarization, etc. 

Types of Information Obtainable from X-ray Diffraction 
Data. From the foregoing development of the subject it might 
be concluded that the lattice-type and unit-cell dimensions 
of crystals, together with the consequent explanation of certain 
properties, are the only facts to be gained from x-ray diffraction 
data. Suppose that we know that a whole series of samples of 
metal has exactly the same lattice structure, characteristic of 
iron or copper, etc. Is there any further differentiation possible 
upon the basis of x-ray diffraction patterns? 

The dependence of x-ray interferences upon the condition 
as well as the kind of lattice makes it possible to detect very 
minute changes in atomic position or in lattice constituents. 
Consequently a fund of purely scientific and technological 
information is obtained from this fine-structure method which 
is almost universal in its scope. 

Following is a tabulation of the principal types of information, 
each of which will receive discussion : 

a. Crystalline or non-crystalline. 

6. Crystallographic system, space-group, unit-cell dimensions, 
parameters of atoms or molecules. 

c. Deduction of crystal unit (atom, ion, molecule), of size of 
unit, of type of binding, and of general properties of solid to 
be expected. 



184 APPLIED X-RAYS 

d. Chemical identity, chemical and crystallographic changes 
and stability. 

e. Allotropic modifications. 

/. Type and mechanism of alloy formation. 

g. Single crystal or aggregate. 

h. Crystallographic orientation of single crystal or of grains 
in aggregate. 

i. Random or fibered aggregate and relative degree of pre- 
ferred orientation in intermediate stages. 

j. Grain size in an aggregate (particularly in colloidal range). 

k. Internal strain or distortion. 

I. Extent of deformation and mechanism of fabrication in 
rolling, drawing, etc. 

m. Analysis of effect of heat treatment, grain growth, control 
and mechanism of recrystallization, and the establishment of 
scientifically correct annealing technique. 

n. Differentiation between surface and interior structure. 



CHAPTER XI 

THE EXPERIMENTAL X-RAY METHODS OF CRYSTAL 

ANALYSIS 

The several methods of analysis of crystal structure by x-rays 
involve the following essential differences: single crystals or 
powders; monochromatic or polychromatic x-rays; photographic 
or ionization-current registration; and reflection or diffraction 
from a single set of parallel planes, or from many different sets 
simultaneously. It is evident, therefore, that the information 
obtained will differ somewhat, depending upon the combination 
of these variables. The proper selection of the method for the 
material under investigation, and for the type of information 
wanted, is of utmost importance. To this end the five more 
important methods have been compared and contrasted in tabu- 
lar form (Table XXIV) under the heads: kind of x-rays, beam 
definition, sample (single crystal or powder), mounting, method 
of registration, pattern, interpretation, chief usefulness, modi- 
fications. Representative photographs or ionization-current 
curves obtained by each method are shown in figures indicated 
in the table. 

Special Notes on Apparatus. 1. The Laue Method.- -The 
experimental equipment here is relatively so simple, as shown 
in Fig. 81, that little additional explanation is required. Typical 
symmetrical and unsymmetrical Laue patterns are illustrated 
in Figs. 82 and 83. The design and construction of the pinhole 
for defining the beam are most important. With a single orifice, 
of course, a pinhole image of the target is obtained by the pinhole 
camera* effect. The longer the collimator, which is simply a 
pinhole in a solid block or two apertures in metal plates separated 
by a fixed distance, the more nearly parallel is the x-ray beam. 
The diameter of the pinhole is of importance from the standpoint 
of detail in the diffraction pattern. The interferences become 
sharper the smaller the diameter. This is well illustrated in 
Fig. 84 for patterns of an aluminum wire (not a single crystal) 
taken respectively with pinholes of diameters 0.060, 0.040, and 

185 



186 



APPLIED X-RAYS 




Lead 
Pmholes 



Specimen 



Main X-R<xy Beqrn 



Photoqraphi'c 

PI*& 



'' Lead Box 
FIG. 81. Diagram of the Lauc and monochromatic pinhole x-ray methods. 




FIG. 82. Symmetrical Laue photograph of an iron crystal. 



X-RAY METHODS OF CRYSTAL ANALYSIS 187 




FIG. 83. Unsymmetrical Laue photograph of an iron crystal. 




FIG. 84. Diffraction patterns for aluminum wire showing effect of pinhole 

diameter. 



188 



APPLIED X-RAYS 








3 


>> .^ i 

1 o g g, 


S 5 bb ti 2 jj "3 

a^-s^^i , 


o ,^ 


^ 


3 22 * _, 


i ^ o ^ d C* 


11 


J oo 


2 S |^ 

-tj w 43 -4J 

l_i (^ rt ** 

a .2-3.1 


6 fcj _ CD fci 

! !M-!| 


Monochr 
pmhole ( 


nochroma 
lole (Fig. 


8 " S S i. 

1 iss-i 

r I ll'Sl 


& I^S|?-a - 
a a||*3 a 5 gf 
s | S | g | fc -5 ^ 




% CU 


o5 c * cs ^ X 

^ Jf< Lu * ^ 


^^oggc^o^ 

fefe 'J 


^ 


1 


II 


-llfie 


U, 


1 


a 55 

o - 


^ It "S s 






o s 




fc 73 




08 a 


d * M C ^ 


Powd 
(Hull-Debye- 


Monochromat 
Hull, slit ;Debj 


2 as 

^ i 

fl - 
D D fH on 

' (H *S -O 

O 4> c3 - rf 
43 T3 ti 13 S 

S 1* O) 1> I-" O 

ft z &23^ 

PH "'fe 


- a s ^ 
a s ^ -3 - 

1 S i fl o 
g tJ o a, 
ft ft " - 1 

? 03 ft GO O> 

2 43 S M 
fc -u K ^ 

S r a o c i^ 
x * 3 "* c 


i! 

b"o 


o 
^2 




T3 T3 A T3 C 
M o fl "S oa o 

I llf-SS 

iS o ^ C 4; fl 

a ^ -? c 


5 fe S3 g fc^ 

^i-l'&l! - 


^ 


-3 cj 


-* -. ^ S a o 


1 * 1 s 5 


Rotating 
(Schiebold- 


Monochroma 
Pinhole usu 


5^-2 s * fe 

~ "J5 83 'O S W 

U! s^llS 

s si s s s h 

.g| o>E 2 


II ^ gl 
? s l|l1a! 

U^rfcfloE 1 ^ 

"E ? Q ^^^^ j: 






s g 4 Iss 


a s & 






g B g -B -g oo 


^ !2 fe < 






a $ g g ts a M 


- 2 a ^ c 




o 


8 1 1 5 5 1 & 


o g 2 g ( 

C 03 "^ fl u. 


I 


Monochromat 
Slit 


llb-!i-sl 
^i^lfl 
iJsi*l 

| g . -5 -3 g 


1 i 1 , ' 

f, is - ^ f 

g> tj "3 

s ! S ! ^ 

S '3 g 

!2r s 




D 

Q 


<d 

0) C3 


s l^li 






t) 


3 -g o M 




c 


2 


o _o -M ft, ( 


OJ 


00 


M J2 

d >3 


43 ^ jj fl3 ^ c 
ft ft "S ft u 
c? S t 


rt 


Polychromat 
Pinhole (Fig. 


3 "S-a 

OQ O -^ 
1 & 
5 | ll 

s a * a 

73 fe 


S ^ SJ T-J X 

S ! i 

o ^3 T) "3 - 
43 a; oo ;; c 

ft a g ss 

1 P 2 








d 








o 


"8 


' 




n <* 
03 C 


1 


a a 

0) g) 


g S 


2 "^ 




& a 
? $ 


1 1 
I J 


2 fi i 

1 l 1 




x 


73 rf 


t> PH H 



. 

* 



s-s 

'C^ 



4 8 

a ? 

fl 

lfc 



a 






a I I 2 S 

03 fl ^ "g e 



fl 

g M .2 o -g 

"*s s a -^ ^ 

4 "8 S ft So 



X-RAY METHODS OF CRYSTAL ANALYSIS 



189 





Monochromatic 
pmhole (Fiber) 


Sol J & "S * ^ 

gQ-2|.fla'33 
o .3!Sfl'o i6 J2l& 

Sl-sSSSsagsS-s 

PS X " * -0 ~ 13 

t&is|1J|ls*| 

. ** 15 -, fe 5 J3 t* S "S 

t-ojcSoS-S" o C a 
O d w o3^ l *-'cnt-.'+- 1 -*>dc: 
**"* ""'cp G Ocpo "o 

Jllllillllla! 


Cylindrical film with 
axis perpendicular to 
beam or coaxial with 
beam. Reflection from 
surface at fixed angle 


(Fig 99); back reflec- 
tion (described in later 
section) 







feMf s-lis 

2 r * S en" 


o & i g i 

3 & -3 & 
o> d -s *j JT; 


X5 . S 


1 

5 

<) 

3 

5 
J 


ll 

^Q 

3 


5^^ 11 2 1 1 

g S'cl'co 2, 43 he's 
on ^ CT oj cp 
bC ^ 03 *^ - 
a) ^>cp ^43>>'" 
^Sf3d^d^cp 

-*^03d^ ftOJ^jd 

f -,ap'-5o3^^3 
.5 *- 4i t< CT ft 
^3 en "o T3 - S 

^^^b^c* 
^t?-2 S 13 s ^ 


Bohlm-Westgren m 
has slit, flat sai 
and film on same 
cumference permi 
focus and rapid ( 


sure by reducing 
sorption of rav 
specimen to a mini 
(Figs 100, 101) 


3 
D 




i ^?~ d TJ 


i -a > 




XH 

H 
) 


3 & 


^ 1 o 






H 


II 


^5 S 5 .3 
* ^ "S ^ rt 


ilts 




^ 

D 


j| 


^ si II 


l|s 




J 

^ 


"o J: 


"d '2 IS 

5 13 t? b 

g a ^ ? 


"3 1 -g S 

Z V XI C- 




XH 
XH 





d >- >, c -, -= 

s 8-a-S 

^ 


a| 




s 






C/2 




H 

q 




CP *C g 






jH 




5 w 










"S S 






5 
^ 




^5^ | 








bo 


3 -d * 






3 


s 


^ i o a 






1 


PQ 


^ "~- 3 






I 




C 2 M J3 co 

O d fl T3 

igi^g 










g o> a o 2 






9 




^ *i 00 i M. 






> 










H 
t 




^ d a o *o i 1 

bC d 43 ** 


oo 
d 




< 




* s g * co ^ 


CP 




3 




cp ^ | * -S "o 

o <u S - a cp 


1 




-1 

5 


CP 


^ M o ^ d ^ g 


1 




3 


<S 


isf^f |1 


C 








43 *o g cp bC _O 


d co 
d 








Sill s &1 

^ d g *Q ^ no 1 


Is 




1 




CO " ^ 


^ 




i 


"8 










1 




I 






^ 


CP 
en 


s 










cp 








1 


1 








6 


S 





190 APPLIED X-RAYS 

0.020 in. On the other hand, the time of exposure increases 
with increase in length or decrease in diameter. Voltages are 
usually not higher than 60,000 volts, since higher values merely 
complicate the range of wave lengths which in this method are 
unknown except in so far as there is a short wave-length limit 
corresponding to each voltage, so that in the interpretation of the 
patterns all lower values of X can be at once eliminated. 

The average length of exposure with ordinary equipment 
for a Laue photograph of a single crystal without heavily absorb- 
ing elements is 30 min. to 1 hr. The new high-powered tubes 
described on page 35 enable reduction of time to a matter of 
seconds or minutes. 

2. The Bragg Method (Spectrometry) . Since the Bragg method 
of crystal analysis involves direct angular measurements of 
9, the use of monochromatic radiation, and reflection from a 
single set of planes, the significance of the results is readily 
understood in terms of the preceding development. By succes- 
sive resettings of the crystal so that the planar distances for 
various set of planes, which have a common zone axis, are ascer- 
tained, it is usually possible to arrive at something like a complete 
structure; the difficulty arises in the tedious repetition of measure- 
ments and the accurate orientation of the crystal specimen on 
the spectrometer. 

Because of the great value of intensity data in this method, the 
ionization method is preferable for the investigation of an 
unknown structure. The ionization spectrometer consists essen- 
tially of a crystal table, which rotates about the axis of the spec- 
trometer with reference to a fixed scale graduated in degrees and 
minutes; readings to seconds of arc may be made by means of a 
vernier or with microscopes with micrometer eyepieces. A 
separate movable arm carries the ionization chamber, whose 
angular position can be read on a second concentric scale. Two 
or more slits define the x-ray beam impinging on the crysta.l n ~A 
another slit is adjusted in front of the ionization chamber. 

The ionization chamber is simply a container for a gas or 
vapor and two electrodes; reflected x-rays pacing ;**<ATr-tl*c ^as 
ionize it; with a sufficient difference of potential between the 
electrodes, a current results, which is measured by the speed of 
discharge of a gold-leaf electroscope or the deflection per second 
of a quadrant electrometer. In an experiment the ionization 
chamber is adjusted so as to receive the reflection from the 



X-RAY METHODS OF CRYSTAL ANALYSIS 



191 



crystal face. Then the crystal and ionization chamber are moved 
step by step (the latter at twice the rate of the former), and the 
ionization current measured for each step. When the ionization 
current is plotted against the angle 0, or angular scale reading, a 




ionization spectrometer with quadrant electrometer. 



Gurve is obtained showing the characteristic peaks, which 
appear as spectral lines if a photographic plate is substituted for 
the ionization chamber. 

The theory of ionization and the practical utilization of air 
lonization as a measure of x-ray dosage in tissues have been 



192 



AWL1EI) X-RAYX 



considered in Chap. IX. Recently Allison and Andrew 1 made 
an experimental test of the ionization-chamber method of 
measuring the relative intensities of x-ray spectrum lines. With 
suitable precautions it was proved that the saturation current 
obtained from a given volume of any gas is proportional to the 
fraction of the x-ray beam transformed into /3-rays within it, 
provided the p-rays come to the end of their ionizing range within 
the volume. 




rdCsi 
S5 7 



L_ 



s 



r 




^'I'l'l'l'l'l'l' 

+ 9O t"45 



TAH 

I'H 



LH|,|II 



=- 10 



Fio. 86. Potentiometric control of quadrant electrometer used to measure 

ionization currents. 

1, Single-pole, double- throw switch for charging needle; 2, Reversing switch 
for potentiometer circuit; 3, 2- volt 20-a.mp.-hr. storage cell; 4, 400-nhm general 
radio potentiometer; 5, Earthing key controlled by silk fishline for distance; 
0. Quadrant electrometer fixed quadrants; 7, Movable needle of electrometer* 
8, Dry-cell radio "B" battery (90 to 150 volts) ; 9, Ionization chamber; l,p,^artn. 

The photograph of a precision spectrometer equipment in 
the writer's laboratory is reproduced in Fig. 85. TTno^j^be spec- 



trometer, built (by the Soci6t6 Genevoise d' Instruments 
sique) with circular scales which may be read to 0.2 sec. of arc, 
is mounted an ionization chamber of the original Duane design, 
consisting of a long glass tube, containing a cylindrical electrode 
Rev., 38,441 (1931). 



X-RAY METHODS OF CRYSTAL ANALYSIS 193 

connected with a battery and a central insulated-rod electrode 
running along the axis of the tube and connected with a pair of 
quadrants in an electrometer. The electrical connections of the 
system are shown diagrammatically in Fig. 86. The electrom- 
eter is of the Compton-Stryker type with sputtered quartz 
fiber suspension; it has proved eminently satisfactory. A source 
of light is reflected by the mirror upon a large scale upon the side 
of the wall, so that extremely accurate readings of the speed of 
deflection are possible. The make-and-break switch consists of 
two fine longitudinal platinum wires, stretched on stirrups which 
are supported on quartz rods and make contact at right angles; 
from the standpoint of stray and induced e.m.fs. the arrangement 
is by far superior to any other. The quadrant or string electrom- 
eter may be used as null instruments, so that readings of potential 
are made by inducing such an opposite charge on the collecting 
system as to return the needle to the neutral position. 

Numerous attempts have been made to displace the quadrant 
electrometer, string electrometer, or gold-leaf electroscope as 
measuring devices for ionization currents. Fonda and Collins 1 
have described an amplifying system for ionization currents 
employing a new four-element vacuum tube characterized by a 
very high input resistance. The deflection of the galvanometer 
is taken directly as a measure of the relative intensities of the 
x-rays entering the chamber. 

Many modifications of the Bragg spectrornetric method have 
been made; chief among these are the remarkably precise instru- 
ments of Siegbahn, who has preferred the photographic method 
originally developed by de Broglie. Depending upon the range of 
wave lengths to be used, a somewhat different type of spectrom- 
eter has been devised by this master experimenter; the vacuum 
type for the spectroscopy of very soft x-rays, which are easily 
absorbed in air, is perhaps of the greatest interest and impor- 
^onop. These spectrographs are fully described in Siegbahn's 
book. 

For the photographic registration the setting of crystal angles 
by.J^3*K,j '^W^nvenient and a mechanical method of oscillating 
the crystal over a certain angle is desirable. This consists of a 
cam and small motor. A spectrograph for use on, a multiple 
diffraction unit is shown in Fig. 87. The crystal is mounted 
flat on the circular table which is oscillated in a vertical plane, 

!/. Am. Chem. Soc., 63, 113 (1931). 



194 



APPLIED X-RAYS 



since slits are horizontal in such units. This Bragg spectrograph 
is applicable not only for single crystals but for all thin films of 
long-chain organic compounds in which parallel diffracting planes 
are built up from molecules oriented perpendicular or at some 
definite angle to the planes (see Chap. XVI). 

The photographic modification of the Bragg method in which 
diffraction from only a single set of planes is registered !, of 
course, only a special case of the general single-crystal spectros- 
copy in which a crystal is oscillated or rotated in the x-ray beam. 




FIG. 87. Oscillating spectrograph for Bragg method. 

The simultaneous registration of all possible reflections from a 
crystal rotated around an axis produces the so-called complete 
spectral diagram. This technique is considered separately under 

the rotation method. ^, ^. 

f' 
The ionization spectrometers have been primarily used with 

known crystals for the accurate evaluation of wave lengths, 
energy levels, etc. The double spectrometer^^i*i^ 
monochromatic beam is formed by reflection from a crystal*^ 
a special modification for very refined physical measurements, 
spectrum line breadths, resolution of doublets, etc. For the 
accurate measurement of intensities of reflections from both 
single crystals and powders, which is so important for the com- 



X-RAY METHODS OF CRYSTAL ANALYSIS 



195 



plete analysis of crystalline structure, no instrument can compare 
with the ionization spectrometer. The best experimental 
measurements of the so-called F curves for various atoms have 
been made by Wyckoff and his associates. The method and 
results will be considered in the next chapter. 

Rotation Method. The most powerful method of crystal 
analysis is undoubtedly the rotation method which is known 
in several modifications. Ordinarily the single crystal is mounted 
and rotated around a principal axis. Three such photographs 
around the principal axes make possible almost complete informa- 




Fio. 88. Two views of camera for rotating crystal and Dcbye-Rcherrer pow- 
der diffraction methods. Left, complete camera; upper right, film holders of 
two sizes; lower right, adjustable case with pinhole and clockwork top for rotation 
of sped nen held in chuck. 

tion. In the usual method a stationary film is used, either flat 
at., 4P&3U -vflr!r<je from the crystal or preferably bent on the 
circumference of a circle with the crystal at the center. A 
satisfactory design of rotation camera or spectrograph is shown 
in Fig. 88 either for special units or for commercial multiple 
apparatus. Frequently it is desirable to mount the crystals 
on a goniometer head by means of which the angles between axes 



196 



APPLIED X-RAYS 



may be measured. If, for example, a rational layer line pattern 
for the rotation method is obtained for one orientation of an 




FIG. 89. Complete diagram (Secmann-Schiebold-Polyani) for benzil crystal 
taken with a M tiller spectrograph. (Hilger.) 

orthorhombic crystal another will be obtained when the crystal 
is shifted 90 deg. and again rotated, and still another after it is 
shifted 90 deg. in the third direction. In all cases a complete 




FIG. 90. Complete spectrum pattern of nx-k-Milt crystal by Seemann 

angle method 

spectral diagram for all possible reflections from a given crystal- 
line zone (the rotation axis) is obtained, such as appears in 
Fig. 89. By a special modification employing a widely divergent 



X-RAY METHODS OF CRYSTAL ANALYSIS 



197 



fan-shaped beam Seemann has obtained patterns of the type 
shown in Fig. 90. 

A complete diagram for rotation around 360 dog. is, of course, 
the summation of a series of diagrams which may be prepared by 
oscillating the crystal over fixed angles, 1 to 20 deg., 20 to 40 deg., 
etc. The apparatus employs the heart-shaped cam described 
under the Bragg method. This interpretation of a complex 
rotation pattern is often greatly simplified by these oscillation 
diagrams. 

Aside from the arrangement of the photographic film and 
the method of mechanically rotating or oscillating the crystal, 




P 

FIG. 91. Principle of slitless speo- 
trograph with specimen mounted 
between m and /i. 



FIG. 92.- Principle of wedge spectro- 
graph with wedge at S. 



the principal variable in the simple method is the method of 
beam definition. Here as in the Bragg spectrometer the most 
common equipment is a pair of slits for rendering the rays parallel. 
These are made of lead, lead alloy, gold, or even brass for softer 
ray^! 7 oi utr% very small crystals the slits may be so short 
as actually to be pinholes, as is the case of the rotation camera 
pictured in Fig. 88. The smaller the slit width or pinhole diam- 
eter, the sharper are the interferences. There are also the 
so-called slitless spectrographs which have been devised by 
Seemann and others for widely divergent rays. The slitless 



198 



APPLIED X-RAYS 



method is illustrated in Fig. 91, and the wedge spectrograph in 
Fig. 92. These methods make it possible to bring the crystal 
very close to the x-ray source and thus permit very rapid photo- 
graphic exposures. A very complete comparison between the 
various methods of beam definition is given by Seemann. 1 

For increasing accuracy and sensitiveness special modifications 
of the rotation method are employed as follows: * 

a. Displacement of the film parallel to the direction of the 
axis of rotation of the crystal (Weissenberg goniometer). 

b. Displacement of the plate or film parallel to the o>axis 
(Dausar). 




FIG. 93. Weissenberg-Seemann goniometer. 

c. Displacement of the film parallel to the direction of the 
primary beams (Kratky). 

d. Rotation of the photographic plate or film around the 2-axis 
(Seemann, Mark, and Wigner). 

e. Rotation of the plate around the ?/-axis (primary beam) 
(Schiebold). 

/. Displacement of two photographic plates in dilations 
parallel and perpendicular to the axis of rotation. 

Of these the first is most generally employed, largely because 
of the simplicity of interpretation and because of the availability 
of an excellent commercial instrument. Figure 93 shows such a 

1 Ann. Phyxik, 5, 6, (1930). 



X-RAY METHODS OF CRYSTAL ANALYSIS 



199 



Weissenberg goniometer as designed by Bohm and built by 
Seernann. The cylindrical film, coaxial with the rotating crystal 
fragment, is gradually displaced during the exposure in the direc- 
tion parallel to the axis. The principle of the apparatus is 
shown diagrammatically in Fig. 94, and in Fig. 95 is reproduced 
a diffraction pattern; the line spectrum above is that obtained 
by the ordinary rotation method. In the Weissenberg diagram 
the spectra of the various surfaces of the zone of rotation are not 
superimposed but are arranged in hyperbolas which enable 
relatively simple assignment of indices. When several lattice 
planes are equivalent, such as (110), (HO), (TlO), (110) in a 
rhombic crystal, and have the same lattice spacing d and the 
same diffraction angle 20, they will all register on a stationary 
film the same interference point, 
whereas in this modification with 
moving film each set of planes will 
register its own interference lying on 
a vertical line. 

The Diffraction of X-rays by 
Powders. Thus far the considera- 
tion of the reflection or diffraction of 
x-rays by crystals has assumed essen- 
tially single crystals. On account of 
the fact that so many interesting 
chemical substances, including practi- 
cally all metals, cannot be obtained 
in the form of sufficiently large single 
crystals, one of the great contribu- 
tions to x-ray science has been the 
discovery, independently by Debye 
and Scherrcr in Elurope and by Hull 
in America, that fine powders, or 

, iv i r 11 i j FIG. 94. Principle of operation 

crystalline aggregates of all kinds, of tho Welter* goniometer. 




may be analyzed for ultimate crys- 
talline structure in a most satisfactory way. The diffraction 
depends upon* the fact that in a fine powder the grains are arranged 
in an entirely chaotic manner. There should be enough particles 
in this array, turned at just the right angle to the incident primary 
beam of monochromatic x-rays, to enable strong reflection from 
one set of parallel planes; other particles turned at another angle 
will produce reflection from another set of planes (the same set in 



200 



APPLIED X-RAYS 







Fia. 95.- Typical Weissenberg diagram compared with oidinary rotation 

spectrum above. 




FIQ. 96. Monochromatic pinhole diagram of ateel ribbon showing continuous 

rings. 



X-RAY METHODS OF CRYSTAL ANALYSIS 201 

many particles cooperating). Thus a beam passing through a 
powder specimen will fall upon a perpendicular flat photographic 
film (Fig. 81) as a series of concentric rings (Fig. 96), each uni- 
formly intense throughout, and corresponding to one set of 
planes of spacing d. A horizontal section cut through this 
diagram has, therefore, the appearance of a line spectrum (Fig. 
97\. This same result may be obtained by bending a narrow 



FIG. 97. Powder diffraction patterns for a-iron (body-centered cubic) and 
platinum (face-centered cubic). 

film in a cassette on the circumference of a circle, at the center of 
which is the specimen. In the so-called Debye-Scherrer camera, 
now purchasable on the market, the film is bent around 360 deg. 
and the beam, defined by pinholes ; passes through a hole in the 




FIG. 08. Monochromatic pinhole diagram of chrysotile (asbestos) showing 
almost perfect fiber structure. 

film; in other modifications where larger dispersion is desired, the 
film may occupy only a quadrant or semicircle. In contrast 
a pinhole pattern for a fiber, instead of a random aggregate, 
is shown in Fig. 98. 



202 



APPLIED X-RAYS 



The sample may have one of various forms, the essential 
point being random orientation of grains; powders of 200-mesh 
or smaller size may be placed in fine capillary tubes of glass or 
celluloid, pasted by collodion on ribbons or threads, or pressed 
into slabs. Metals may be used in the form of fine wires or as 
small beveled plates with the beam grazing the blunt knife-edge 
at a small angle and passing through a sharp edge. Reflection 
from the surface of a sample at a fixed angle with respect to the 
x-ray beam can be used, as illustrated in Fig. 99. 

For powders of heavily absorbing substances such as lead it is 
desirable to use a non-crystalline diluent such as gum tragacanth 
or powdered starch. A complete table of proper proportions 



Phologr&phic Plaie 




-Lead Box 
FIG. 99.- Diagram of surface reflection method. 

has been worked out by Davey. The volume of the diluting 
material with 1 volume of a chemical element varies from 1 for 
elements 10 to 26, 3 for 18 to 28, 5 for 29 to 44, 6 for 36 to 46, 7 
for 47 to 53, 8 for 54 to 57, and 9 to 10 on up to 92. 

On account of the complexity of the spectrum it is desirable 
that the beam of x-rays should be as nearly monochromatic as 
possible. With molybdenum rays the zirconium filter eliminates 
all but the Ka doublet, and a nickel filter serves for copper, etc. 
(see page 66). 

The accurate measurement of the crystal powder spectrum 
lines is, of course, of great importance in analyses of unknown 
mixtures. Where semicircular cassettes or cylindrical cameras 
are used, the undeflected beam strikes the center of the film and 
diffraction lines are registered on both sides of this zero position. 
Uncertainties as to this are eliminated by measuring from one 



X-RAY METHODS OF CRYSTAL ANALYSIS 203 

line to the corresponding line on the opposite end of the film. 
If, however, the zero position is at one end of the film as in the 
case of quadrant cassettes, greater resolution is possible but it 
is often necessary to run a calibrating spectrum for known pure 
crystal powders such as sodium chloride on the same film, either 
mixed with the unknown or 
placed in half of the small cap- 
illary tube. Since the spacings 
for each of these lines are accu- 
rately known and, hence, the 
necessary displacement on the 
film, the zero position may be 
accurately determined as well 

as all evidences of film shrink- FlG loo.-Seemann-Bohlin powder 
age and inaccurate alignment of diffraction camera, with slit, specimen 
ii and film on same circumference, similar 

ine specimen. to type uscd in studics of alloys by We8t . 

By its very nature the powder gren and coworkers. 
method requires more energy to 

produce a suitable photograph than is necessary for single 
crystals; consequently a greater time of exposure is required 
and this may well run into a hundred hours or more for some 
substances on usual apparatus. High-powered x-ray tubes, 
of course, can be used to advantage. The Seemann-Bohlin 
camera (Fig. 100) employs a divergent beam of x-rays and a 




FIG. 101. Pattern for sheet steel with Seemann-Bohlin camera. 

focusing principle. Here the focal spot of an x-ray tube, the 
specimen in the form of a ribbon or flat surface, and the photo- 
graphic film are on the circumference of the same circle. Spectra 
such as illustrated in Fig. 101 are registered very rapidly and the 
method has proved of greatest value in technical examination of 
materials such as alloys, not only at room temperatures but 
also at low and high temperatures. 

Multiple Apparatus. The most familiar and useful apparatus 
for metallurgical and chemical applications is the multiple 
General Electric diffraction apparatus. This consists of a 
transformer operating at a fixed potential of 30,000 volts, with 



204 



APPLIED X-RAYS 



an enclosed filament transformer, an operating switchboard 
with filament current stabilizer, a water-cooled molybdenum- 
target self-rectifying Coolidge tube, a slit system which permits 
12 simultaneous exposures radially around the vertical tube at a 
grazing angle of 5 deg. upon the target, and quadrant cassettes for 
the Hull powder method. Interchangeable slits and pinholes 
made of bakelite impregnated with lead oxide give the apparatus 
greater elasticity, since oscillating reflection spectrographs (Fig. 

87), flat cassettes (Fig. 102), 
and other specially con- 
structed devices may also be 
mounted. In the writer's 
laboratory every one of the 
methods including modifica- 
tions may be used on the 
General Electric apparatus. 
Figure 103 shows the table top 
with quadrant cassettes for 
the powder method and a 
spectrograph combining the 
Bragg method (oscillation of 
the specimen) and the pinhole 
surface reflection method 
(diagrammatically shown in 
Fig. 99). A new multiple- 
diffraction unit designed and 
constructed in the writer's 
laboratory is shown in Fig. 
104. It is distinguished by 
a small lead-covered bakelite 
cylinder around the x-ray tube, external pinholes adjustable in 
all directions (as shown in Fig. 105, looking down from above), 
and an integral control switchboard. 

A new Philips "Metalix" crystal analysis unit weighing only 
54 Ib. is shown in Fig. 106. The Metalix tube and two Debye- 
Scherrer cameras are shown in position. 

Another ingenious universal spectrograph which, however, 
cannot be used with the General Electric apparatus, is the Mtiller- 
Hilger instrument. It has interchangeable parts which adapt it 
for all of the methods of crystal analysis. As shown in Fig. 107 a, 
6, c, it is set up respectively for the Bragg method (oscillating 




Fia. 102. Flat cassette and holder 
for pinhole method used with multiple 
apparatus. 



X-RAY METHODS OF CRYSTAL ANALYSIS 



205 




FIG. 103. Top of General Elct-tiic multiple-diffraction apparatus with various 
types of cassettes in position. 




FIG. 104. New multiple-diffraction unit with Standard transformer and integral 
control board designed and built at the University of Illinois. 



206 



APPLIED X-RAYS 




FIG. 105.- 



-Multiple-diffraction unit illustrated in Fig. 104 as viewed from above, 
showing completely adjustable pinholes and slits. 




FIG. 106. Philips Metalix diffraction apparatus with Mctalix tu 
horizontal covering and two Debye-Scherrer cameras; weight 54 Ib. 



X-RAY METHODS OF CRYSTAL ANALYSIS 



207 



crystal), for the Lane and rotating crystal methods (showing the 
goniometer head), and for the Debye-Scherrer powder method. 

Numerous spectrographs and cameras of all types combining 
special features have been described in the literature, particularly 



Z 



w u 




FIG. 107. Muller-Hilger Universal Spectrograph as set up respectively for 
Bragg, Laue and rotating-crystal, and Debye-Scherrer powder methods. 

those of German design and manufacture. Many of these, such 
as the Seemann spectrograph, are most ingeniously combined 
with steel mercury vapor pumps and demountable x-ray tubes. 
A diagram of a typical unit is shown in Fig. 39, page 84. 



CHAPTER XII 
THE INTERPRETATION OF DIFFRACTION PATTERNS 

Once the diffraction effects from any material have been 
observed by one or more of the experimental methods described 
in the preceding chapter, the interpretation must be made as the 
step in x-ray science which requires most knowledge and experi- 
ence. The problem may involve the complete structural analysis 
of an unknown crystalline substance by the successive steps which 
are outlined on page 182. Or again the interpretation may 
involve the condition of a substance of known structure in terms of 
grain size and orientation, internal strain, purity, or other proper- 
ties listed on page 183 concerning which information is vouchsafed 
by diffraction patterns. Exhaustive treatment of the matter of 
interpretation is obviously impossible in this book but the attempt 
is made in this chapter to consider briefly, first, the most funda- 
mental aspects of the general subject, the position of interferences, 
and their intensities; second, characteristic details of measure- 
ment of patterns from each of the most important experimental 
diffraction methods for structural analysis; and, finally, the inter- 
pretation of the exact condition of any specimen whose ultimate 
crystalline structure may be known. 

1. The Positions of Diffraction Interferences from Crystals. 
As explained in Chap. X, the simple law which governs all 
diffraction phenomena is n\ 2d sin 6, where n is an integer, 
the order of the reflection, X is the wave length, d is the distance 
between the set of planes at an angle O with respect to the incident 
beam. Thus for a known wave length X, the ratio d/n can be 
calculated for any diffraction spot or line, independent of any 
assumptions as to the grating structure, since the experimental 
measurement in diffraction science is that of 0; actually the 
measurement is made not of the angle of incidence but of the 
angle of diffraction 20. This relationship is easily seen when it is 
understood that a beam of x-rays impinging on the face of a 
crystal at the angle will appear to be reflected from this face at 
the equal angle 9 between the face and the beam, but the total 

208 



THE INTERPRETATION OF DIFFRACTION PATTERNS 209 

angle between the undiffracted primary beam and the reflected or 
diffracted beam will be 29. On a flat film placed at right angles 
to the primary beam the displacement of the interference from the 
zero primary beam (a) divided by the known distance from speci- 
men to film (6) gives 26 = tan" 1 a/6. From this sin 9 is 
obtained and the calculation for d/n (usually d/l) is made. For 
a filai bent on the circumference of a circle with the specimen at 
the center, x/r = 29 n in radians, or 360.r/27r, where x is the dis- 
placement of the interference on the film and r is the effective 
radius of the curved film. 

If it is known that the crystal is cubic, a single measurement of 
the spacing of planes parallel to the cube face dioo (or ao) on the 
spectrometer leads at once to the volume of the unit cell; if 
orthorhombic, three measurements of d 10 o, rfoio, dooi, are made at 
right angles, etc. However, in most of the methods numerous 
other interferences appear which must be identified before com- 
plete analysis is possible, or the crystal system may be unknown 
and must be deduced from the x-ray data. It is evident that all 
the hkl planes in a crystal must be related in such a way that all 
the spacings can be calculated in terms of a fundamental value a 
together with information concerning axial ratios and angles. 
By the method of direction cosines or by pure lattice geometry it 
can be easily shown 1 that for a cubic crystal 



i* 



sn 



where a is the lattice constant or length of the unit cube edge, 
and ft, k, I, the indices of any planes. Hence 



Vh* + k* + I* 

If an unknown crystal is cubic, all the diffraction interferences 
must be related in this way; the usual method is therefore to 
correlate calculations with experimental values. In the same 
way equations may be derived for all other simple lattices. In 
general 

2a 

n\ = 2d hkl sin G n = > IT7 ^ n . sin 9 n , 
\/F(hkl\ abc; a/3y) 

where abc are unit lengths in three dimensions, and afiy are axial 
1 WYCKOFF, "The Structure of Crystals," 2d cd., p. 78. 



210 



APPLIED X-RAYS 























Sen 
^ 










^_^ 


73 03 












O O 










1 


r-H 










1 


f 










8 


^ ^J 








a 


O 


c o 


TO. 8 ~ 


XJ 




3 

o 


cr 


o o 1 * 
















a o - 1 


3 ^ 




00 


-f 


i^^ 


^ 8 








--0 <M 




O3 O) 


*^3 




1 


-C; -i^ "^ 


c* Tj. 





S 

^ 




y 


-f + 


03 02 




O ' I O 










"" O O 




J 
* 


^ 


02 


vS CO 

<vi O 


+" 


O2 
^00 




^ 


(N 


o 






4 

< 

4 


1 + 


^ 


1 ''' ? 


r/3 C/J 

O O 




X, 






^ *> N "w 






tf 


^> \ 


^3 




<* 8 




4 


'o ' .J |~ 




r ' -^ 


02 






1 ^ ,M 




r--J 







H 


+ + ^ i "^ 




t H- 


' 




c< 
D 


Ss <? Ss + 




^ ^ 


^-^^ 




7; 


Q + 4- ^ ^ 




T~ ^ 


e 




D 


<M -1 ^ O 




^ ^^ 


^-^ 






"^ > ^> ^> 




x^ ~^ 


-^^ 




4 


< ? r < 




* ^ 


^ 




j 













J 
-) 






g 






S 


S b o II 

Ci Ci Cs . 
<>* 




C 

C 


n. \ 

"> CQ. C 


I 




> 

4 


ii ii H 

* ^ ^ 8 

II II II || 


\ 

<> 

1 


o^ 1 

. 8 
ii > 


Ik 
Ik 




4 

4 




o: 


1 <^ c 


Q. 




C 


II II II I) 


1 


II 


fk 




H 


8 S S S 


5 


J 






O 





*- 


"I ^J 


- 




e 


^ ^ e - 




, O 


^ 




1 


^o 

p-1 ^ 


1 
1 


i 
3 

' H 






C/3 


C O 

& i 

I 8 

o H o a 


^ 

1 

^ 
PC 


5 ii 
! i 

^ o 
S S E 


| 

3 

H 





THE INTERPRETATION OF DIFFRACTION PATTERNS 211 

angles. Table XXV lists the formulas for dhki in convenient 
form. 

From the mathematical expressions n\ may be calculated 
by substituting the values of dhki in n\ = 2d sin 6. For the 
cubic system therefore 

2a 

", ~ v/P + A 2 +t 2 Sri T " 
Squaring, 



snr 



All the possible values of sin 2 B n may then be calculated when 
the cube edge length a () and the wave length are known, assigning 
all values of hkl. These values are then compared with the exper- 
imental sin 2 6 values for the interferences appearing on the pattern 
and the crystallographic system is thus established. The inter- 
ferences may be those on different photographs for different zones 
or all on the same film as in the powder method. 

It is clear that with decreasing symmetry the number of pos- 
sible interference maxima increases. The derivation of the 
quadratic form from the x-ray data therefore becomes different 
except in the cases of highest symmetry. In a cubic lattice it is 
possible to have 48 planes of the same form (hkl) where h, k, and I 
are all different, with the same spacing, and hence cooperating to 
produce only a single interference maximum; whereas in the 
triclinic lattice there are 24 different spacings and hence 24 
reflection lines or spots corresponding to these hkl planes. Theo- 
retically possible maxima may overlap and thus render deriva- 
tion of the quadratic form and the crystal system practically 
impossible. 

Modes of Atomic and Molecular Arrangement from Intensity 
Data. While the dhki equations just considered give the posi- 
tions of all the possible reflections for a given lattice, and no 
crystal of a given system can produce any additional inter- 
ferences, it does not follow that they will all appear. Whether 
they all appear, or what are the possible reflections, is determined 
by the arrangement of atoms in the unit crystal cell. This is the 
most important aspect of the general problem of the effects of all 
variables on intensities. 



212 APPLIED X-RAYS 

Consider a series of planes all alike in a single crystal. If 
reflection is observed, the path difference from successive planes 
is 2w or an integral multiple. The ratio of the amplitude of the 
wave scattered in a given direction by the electrons in the atom 
to that which would be scattered by a single electron in similar 
circumstances is designated by F. Now consider two parallel 
planes, one bearing P and the other Q atoms, and disposed 
from each other at a fraction a/x of the lattice constant or 
distance between P planes, and Q planes. The contribution 
from P planes with path difference 2irn will be F P and from 
the Q planes F Q . The secondary x-ray waves from P and Q 
have a phase difference. If Q planes are exactly halfway 
between P planes, then waves from them will be exactly out of 
phase with waves from P when n is odd. The resulting amplitude 
or structure factor F' or S is the difference of the contributions 
from P and Q atoms or F P F Q . It is a function, of course, of 
atomic numbers of P and Q and also of x. If other interleaving 
planes are present, the phase relationships between the waves 
from the various sequences of parallel planes may be very com- 
plicated but F' is determined by a summation of the F values, 
Fp, F Q , F R , etc., for each of the atoms modified by a phase factor 
<t>p> 4>Q> <t>Rt etc., expressing the distance of the atomic plane from 
the parallel geometric plane (e.g., a/.r). From optics it can be 
shown that the square of the structure factor F' is the sum of 
squares of cosine and sine terms : or 

F'* = A 2 + B' 2 , 
where 

A = F r cos fa, + F Q cos Q + F R cos <t> R , etc. 
B = F P sin fa, + F Q sin <t> Q + F K sin <j> R , etc. 
For a cubic crystal simple equations for planes show that 
<t>p 2irn (hxp + ky p + /z/>), etc., 

where 2irn is the phase difference between waves from geometri- 
cally like planes which reinforce, and the parallel plane passes 
through the atomic coordinate position x p y p z p . Hence for 
crystals containing parallel planes of P, Q, and R atoms 

A = F P cos 2irn (hx P + ky r + lz r ) + F Q cos 2trn (hx Q + ky Q + 

lz Q ), etc. 

B = F P sin 2irn (hx p + ky p + lx p ) + ^Q sin 2/rn (hx Q + ky Q + 

fe Q ), etc. 



THE INTERPRETATION OF DIFFRACTION PATTERNS 213 



From wave optics an experimental form may also be written 

ni(hxp-\-kvp+lz P } \ 



If a lattice cell has two atoms of the same kind with coordinates 
xyz and x l y l z l , the intensity of the interference from the planes 
hkl will be proportional to F f ' 2 . If the atoms have the coordinates 
000. and }<^ }^ l /2 (cubic as for iron, tungsten, etc.) 



(/< + A- 4-0 



F' = 



e 2 "" + e 



the structure factor for a body-centered lattice of an element 
(Fig. 108). Now when h + k + I is an even number, the latter 
factor will be 1 and F' = 2; if h + k + I is an uneven number, 



> 

<x- 

f 


\ 
\ 
t- 

1 

i- 


1 

-k-- 

\ 
4 



.<y' 
Y" 

FIG. 108. Body-cen- 
tered cubic lattice 
(tungsten type). 



\\/ 



jfe^--- 



^ 



V / 



FIG. 109. Face-cen- 
tered cubic lattice (cop- 
per type). 



F r = 0. Thus all reflections will be missing on the diffraction 
pattern for planes, the sum of whose indices is an uneven number. 

n\ 
First the expression sin 2 9 = v 2 (h 2 + k 2 + Z 2 ) gives all the 

possible reflections for the cubic lattice, while the structure factor 
F 1 = 1 + e &+ k + l ) shows which of these will be missing from the 
particular variety of the cubic lattice known as body centered; 
e.g., 100, 111, 210, 221, etc., will be absent. 

For the face-centered cubic lattice (aluminum, copper, gold, 
etc.) the four atoms in the unit cell have the coordinates (see 
Fig. 109) 000, M 1 ^, }0>, 0>^. Thus 

pt _ j i grni(h + k) i grm(h+l) i grm(k+l) 

If all three indices hkl are even numbers (including 0) or all odd 
numbers, F r = 4 and the interferences will appear. If, however, 
the indices are mixed, partly odd and partly even numbers, F' = 
and interferences for these planes 001, Oil, 012, 112, 122, 003, 013, 
023, etc., will not appear. 



214 APPLIED X-RAYS 

To consider one more example we may select the cesium 
chloride type lattice, body-centered cubic with two kinds of 
atoms (Fig. 108) with P at 000 and Q at 1 / 2 1 A 1 A 

F' = F P (1) + /V rt(A+ *- H) ; 

when h + k + /is an even number F' = F P + F Q (for a lattice with 
only one kind of atom F' = 1 + 1), while for h + k + Z an^odd 
number F' = 7 y V F Q . It is at once evident that if the scattering 
powers of P and Q were approximately the same, or in other words 
the effective atomic number the same as in Cs^ I~ crystals, for h 
+ k + I an odd number F 1 = F cs+ P\^ = 0, and thus reflections 
will be totally missing where they would be observed for CsCl 
or CsBr. 

In this way structure factors may be derived for all the various 
lattice types and the atomic positions in the unit crystal cells 
properly interpreted. It is possible to ascertain the value of 
F' accurately from intensity data but the actual values of F's 
which contribute to F' and which measure the atomic scattering 
powers are still incompletely known. However, even with 
limited experimental data astonishingly satisfactory practical 
results are being obtained. Wyckoff has undertaken the task 
of determining the F curves for the atoms and lists the values so 
far available. 1 If all electrons in an atom were at the exact 
center point and scattered independently, the F curve would 
have a constant value equal to the number of electrons. But 
actually the electrons are distributed in space around this center 
and F must decrease as the diffraction angle 2O increases. In 
order to calculate F values the fundamental intensity equation is 
applied. 

The work of Darwin, Compton, Bragg, James, Bosanquet, 
Hartree, and others has led to the following formula for the 
absolute intensity p of integrated reflection by the face of an 
imperfect crystal : 2 



" / ~2 M mV 1 sin 29 2 

1 "Structure of Crystals," 2d od., p. 100, 

2 Diamond is the only crystal which has given reflections agreeing with 
theoretical deductions for ideally perfect crystals, the intensity varying 
with the first power of F. In most cases the reflections are too intense 
but correspond to those from an ideally imperfect or mosaic crystal. It 
is for this case that the equation is derived. The majority of crystal 
specimens lie somewhere between the two ideal conditions. 



THE INTERPRETATION OF DIFFRACTION PATTERNS 215 

Here Eu/I is the experimental measurement on the ionization 
spectrometer, E the total ionization, co the angular velocity of the 
crystal in radians per second, and / the power of the incident 
x-ray beam (obtained by measuring a known crystal). The 
other symbols in the above formula are: ju = linear absorption 
coefficient of the crystal; n number of unit crystal cells in 
1 c.c.; X = the x-ray wave length; e and m = charge and mass 
of the electron; c = velocity of light; = the angle of incidence; 
and e ~ Beni ^ Q is the Debye factor, a correction term for tempera- 
ture effects usually small and included in F. The symbol F 
stands for the ratio of the amplitude of the wave scattered by 
all atoms in the unit cell in the given direction, as compared 
with the wave scattered by a single electron in similar circum- 
stances. Mathematically this can be stated: 



C D ^ /2miz\ 

= Z p(z) cos ( rT }dz, 

JD/2 \ U / 



where Z is the atomic number, D is the grating space, and p(z)dz 
is the probability that an electron will lie at a height between 
Z and Z + dz above the atomic layer. The value of F varies 
with the direction of the incident and scattered x-ray beam as 
above explained and hence F curves against sin 6/X are plotted. 
The contribution of each atom to the scattered wave will depend 
on the arrangement of the electrons in the atom, and the com- 
bination of these contributions into a single scattered wave 
will depend on the relative positions of the atoms in the unit cell. 
In practice, therefore, the values of F' for a number of crystal 
planes are calculated from the observed intensities by x-ray 
reflection; from these values the atomic positions may be directly 
deduced. For example, in rock salt F' = F Nft F cl for planes 
with all odd indices, such as the cube diagonal planes 111, and 
for other planes F' = F Na + F rl . These lead directly to the 
curves for F Na and for F ri . 

It is evident from all the foregoing discussion that the actual 
intensity of a given x-ray diffraction interference depends upon a 
number of factors. A general expression is as follows: 



j 

L sin 2 cos 9 

F is the structure factor just considered. H is the cooperation 
factor taking into account the number of equivalent planes of 



216 APPLIED X-RAYS 

the same kind which cooperate to produce a single diffraction 
maximum varying from 2 for triclinic to 48 for (hkl) planes in 
certain cubic crystals. D is the Debye factor taking into account 
the increasing oscillations of atoms from a mean plane or position 
with temperature and is equal to e ~ BBlll ' where B is a constant 
aT/\ 2 with a calculated from the theory of specific heat. P is a 
factor which takes into account polarization of scattered radiation 
and is equal to 1 + cos 2 2B. L is the Lorentz factor taking into 
account overlapping reflections or departures from sharp reflec- 
tions at the angle and is expressed by sin 2 O cos 0. 

Two other effects on intensities have particular bearing on the 
discrepancies which have been observed between calculated and 
observed reflection intensities from actual crystals. These have 
been termed primary and secondary extinction. The first is the 
abnormally great absorption of an incident x-ray beam resulting 
from the fact that crystal fragments act as perfect crystals and 
upper layers of atoms shield the lower layers of the same homo- 
geneous fragment from the intensity of the primary beam. 
Secondary extinction is a loss in intensity due to the fact that 
reflection from atomic planes in the interior of imperfect crystals 
is decreased by reflections from the tiny crystals making up 
the imperfect crystal nearer the surface. These effects are 
avoided by finely powdering the crystal before intensity measure- 
ments for F values are made. 

Finally, the most recent method employed in analyzing diffrac- 
tion effect is that of Fourier series, although the applications to 
periodic wave motions in sound and light have long been known. 
The suggestion was made by Bragg in 1915 and worked out by 
Duane first in 1925 with further development by Havighurst, 
Compton, 1 and others. If the amplitude of reflection in a number 
of orders is measured experimentally, a curve representing the 
electron distribution in sheets parallel to the geometric planes 
can be constructed by adding together the terms of the mathe- 
matical Fourier series. Such an equation has the form 



= N/d + 2(F l '/d) cos2ir*/d + 2(F 2 '/d) 

cos Qirz/d + etc., 



where N is the number of electrons in the atom, p(z) is the 
probability that one will be in a plane at the distance z from a 

1 For the best treatment see Compton, "X-rays and Electrons," New 
York, 1926. 



THE INTERPRETATION OF DIFFRACTION PATTERNS 217 

geometrical plane, d is the interplanar spacing, and the F's are 
measured from reflection intensities in several orders. The 
curves calculated from the above equation for electrons per A.U. 
plotted against height above a given plane have given good 
pictures of electron distributions in simple cases. 1 Extension 
of the series to three dimensions enables calculation of electron 




FIG. 110. Lauc pattern of single crystal of carborundum. 

density along a given line in a crystal, and by this same method 
the variation in electron density in an atom from the center 
along the radius has been calculated. These are called U curves. 
Extensions to electron distribution in atoms of gases and liquids 
as well as solids from the intensities of scattering have been 
mentioned on page 100. Agreement of wave-mechanics calcula- 

1 As an excellent recent example of the application of the Fourier method 
may be cited Wyckoff's analysis of single crystal spectrometric data for 
urea, Z. Kryst., 81, 102 (1932). The F values of NH 2 agree with those of 
NH 4 in NH 4 C1; the experimental C + O curve is practically identical with the 
sum of the carbon curve from graphite and the oxygen curve from metallic 
oxides. 



218 APPLIED X-RA y,S' 

tions with these data has given strong support to the newest 
atomic theories. 1 

The Interpretation of Laue Photographs. The growing useful- 
ness of this historically first method for obtaining informa- 
tion, even as to the probable space-group characteristics of a 
crystal, makes desirable some further comment upon interpreta- 
tion, although detailed discussion is to be found in the several 
technical treatises on crystal analysis. A single Laue photography 
taken alone yields only a limited amount of information. It 
appears as a series of spots (Fig. 110) whose loci are symmetrically 
disposed ellipses, passing through the central direct beam image if 
the primary beam has passed through the crystal parallel to a 
principal axis. The galaxy of spots is an indication of the ability 
of the many families of planes, each at a certain angle G with 
respect to the primary x-ray beam, to pick out, from the assort- 
ment of rays of different wave lengths, the particular one for 
reflection according to nX 2d sin 0. The symmetry is a proof of 
the orderly arrangement within the crystal, suggested by the exter- 
nal crystalline form. Thus if the beam passes parallel to a cubic 
axis, with fourfold symmetry, the pattern has a fourfold symmetry. 

The spots 2 on any ellipse correspond to reflections taking place 
at a number of faces which have a common zone axis (i.e., a row 
of atoms through which various planes pass). If the incident 
rays are inclined at an angle 9 to the zone axis, the reflected rays 
will also make an angle with this axis, so that all the rays lie 
on a circular cone whose axis is that of the zone. The direction of 
the incident rays also lies on this cone; consequently the loci of 
the reflected spots are situated on the ellipse formed by the inter- 
section of the cone with the photographic plate. Important 
zones of the crystal structure correspond to those ellipses which 
are densely packed with spots in the Laue diagram. The 
symbol of the zone which corresponds to each ellipse can be 
found and, since each spot may be considered as lying at the 
intersection of two ellipses, the plane which reflects it can be 
identified by cross-multiplication of the zone symbols. 

1 An exhaustive treatment of the present status of the whole subject of 
atomic structure factors is given by Ehrenberg and Schafer, Physik. Z., 33, 
97 (1932), and especially Wollan, Rev. Mod. Phys. 4, 205 (1932). 

2 BRAGG and BHAGG, " X-rays and Crystal Structure," p. 279. 



THE INTERPRETATION OF DIFFRACTION PATTERNS 219 



It is much more convenient, however, to use a system of pro- 
jection in the assignment of indices to spots. The stereographic 
method converts the ellipses into circles. In Fig. Ill a crystal is 
at the center of a sphere which touches the photographic plate 
at the point N, where the direct beam SN is intercepted by the 
plate. The cone of reflected rays about any zone axis will cut 
the sphere in a circle which can be 
projected on the plate. A reflected 
spot appears on the plate at R. A 
line from S through Q, where the 
ray cuts the sphere, meets the plate 
at R' ', the projection of R. This 
spot will be on a circle with the pro- 
jections of the other spots originat- 
ing from planes with a common 



Rlf 




"Fio. 111. Method of stereographic 
projection. 



zone axis. 

A stereographic projection of 
potassium chloride is shown in 
Fig. 112. The Lane pattern of this simple cubic crystal is char- 
acterized by spots with perfectly regular distribution of intensi- 
ties, at every intersection of circles. The Laue pattern for 
sodium chloride, on the other hand, differs in that the spots which 

021 




FIG. 112. Stereographic projection of Laue pattern of KC1. 

for KC1 have odd and even indices (e.g., 341) are absent. Thus 
the face-centered cubic lattice for which the structure factor 
predicts this very fact may be assigned as the underlying arrange- 
ment of the heavier chlorine atoms in rock salt. 



220 



APPLIED X-RA F*S' 



The gnomonic projection is even more valuable for the com- 
plicated types of Laue patterns. The essential process involved 
is shown in Fig. 113; R is the Laue spot and OQ the zone axis 
of the plane which is perpendicular to the plane of the paper. 
The perpendicular to this plane strikes the plane of projection and 

P'S = P'O cot 6 and PR = PO tan 26, 

where P'S is the distance of the gnomonic projection from the 
center, P'O is the radius of projection, PR is the distance of the 
Laue spot from the center, and PO is the radius of the Laue 
film (i.e., distance from specimen to film). P'O and PO may be 
different but usually both are made 5 crn. Thus any Laue 



> Photographic Plate P 



ff 





Plane of 
Projection 



FIG. 113. Method of giiomonic projection. 

spot and its projection lie on a straight line passing through the 
common center. On this account the plotting of the gnomonic 
projection is most simply and rapidly accomplished with a 
suitable ruler. The left side is divided in millimeters for measure- 
ment of the distance of the Laue spot PR and the right side is 
graduated in accordance with the expressions P'S = 5cotO 
and PR = 5 tan 2O to measure corresponding projected lengths 
P'S. This method has been widely used with success by Wyckoff 
and by Schiebold. It is evident that the closer the reflected 
Laue spot, the farther from the center is the projection. Planes 
parallel to a zone axis lie on a straight line, which is the inter- 
section of the plate and a plane through parallel to the zone 
axis. It results that the gnomonic projection of a cubic crystal 
is based on a network of squares whose sides are equal to the 
distance from the crystal to the plane of projection (usually 
5 cm.) ; for an orthorhombic crystal the network will be rectangles, 
the lengths of whose sides are in the same ratio as the axial 



THE INTERPRETATION OF DIFFRACTION PATTERNS 221 

ratios; for a rhombohedral or hexagonal close-packed lattice, it 
will be parallelograms with an angle of 120 deg. between sides, 
and so on. The indexing of the planes corresponding to each 
spot is usually not difficult, particularly when the axis of a 
crystal is normal to the plane of projection, say the Z or I index. 
This will then always be /, and X and Y (or h, fr) can be read 
directly from the coordinates on the network. Thus for a cubic 
crystal in which the Z axis is perpendicular to the plane of pro- 



: \ Ni/x^\ *^V" \ \ - V \ 

v-r "\ V'\" 
v"\ >-c\,\ 

\ >-' \ \.-\ ^ 




FKI. 114. Gnomonic projection of an unsynnnetricsil T^iuc pattern of Kl. 

jection, or paper, a spot two squares to the right of the center and 
one square up would have the indices 211; a spot two to the 
right and one-half down is 412 [2 X (2, X 2 , 1)J, and so on. 

Wyckoff has used, with great success, unsymmetrical Laue 
photographs, obtained by inclining one of the crystal axes to the 
beam. Such a result with a crystal of iron is reproduced in 
Fig. 83 which is to be compared with the symmetrical diagram in 
Fig. 82. In Fig. 114 is shown the gnomonic projection for such 
a photograph of a potassium iodide crystal. 



222 APPLIED X-RAYS 

The dimensions of the unit cell may be sometimes estimated 
from these data, and, of course, for cubic crystals the values of 
n\ for each spot are given by sin and a and hkl from the 

equation nX-=J_ aine.. 



The fact that general radiation is employed, however, is always 
a complication. At moderate voltages, 50,000 kv., the maximum 
intensity in the spectrum is at 0.48 A.U., the characteristic absorp- 
tion wave length of the silver in the emulsion. If the voltage is 
known, X mm is, of course, at once established and this at once 
limits the possibilities of interpretation of Laue spots and elimi- 
nates some of the alternative possible unjit crystal cells. 

Intensity data from Laue patterns are not accurately deter- 
mined but simply classed relatively by visual comparison on the 
photographic negative. Numerous complications are involved 
as explained earlier and in addition absorption in the crystal. 
However, the Laue data even though very approximate are 
sometimes very important, since by this method alone are 
reflections from planes of high indices and complicated structure 
registered. The greatest usefulness of the method therefore lies 
in conjunction with other methods with which quantitative 
information can be easily obtained. 

The Interpretation of Bragg Spectrum, Rotation, and Oscilla- 
tion Patterns. When a single crystal is rotated around one of its 
principal crystallographic axes in the path of an x-ray beam 
defined by pinholes or slits, a very characteristic pattern is 
registered on the photographic film. It is called a layer line 
diagram because the interference maxima all lie on horizontal 
layers or lines. If a flat film is used, these lines are hyperbolas 
above and below a straight equatorial line. On a cylindrical film 
bent on the circumference of a circle at t>he center of which is the 
crystal the layer lines are straight lines parallel to the equator. 
Representative photographs are shown in Figs. 115 and 116. 
It follows that all the interference maxima lying on these layer 
lines are produced by planes with the same zone axis, namely, 
the common crystallographic and rotation axis. The spectrum 
is therefore " complete." The familiar Bragg spectra are, of 
course, produced by only one set of planes, the experimental 
arrangement of slits and crystal being such that other planes 
cannot register. The lines or spots lying on the equator of the 




THE INTERPRETATION OF DIFFRACTION PATTERNS 223 

oscillation or rotation pattern therefore are really the " Bragg 
principal spectrum." 

As explained in the preceding chapter, the angles between 
principal axes may be determined in many cases by reorienting 
the crystal on its goniometer 
head until sharp layer line dia- 
grams are obtained. With 
three such rotation patterns 
corresponding to the three 
principal axes, the dimension 
of the unit crystal cell may be 
directly deduced. These p;at- 
terns have the great advantage 
that one lattice spacing, 
namely, that for the atomic 
planes along the rotation axis, 
may be measured independent- 
ly of any assumption as to FIG. 115. Typical rotation pattern 
Crystal Systeni or planar (<*rysotilc) on flat film showing layer 

J J , Mines as hyperbolas. 

indices. It is necessary only to x 

measure the distances e\, e 2 . . . e n of the vertices of the 
hyperbolas on the tangent film (or the straight layer lines on a 
film which had been bent on a cylinder coaxial with the specimen) 
from the central zero point of the main beam. The distance 

from specimen to film, a, 
being known, the diffraction 
angles MI, M2 . . . Mn (Fig. 
117) may be calculated, since 
the tangents are e n /a. The 
identity period or spacing 
along the rotation axis is 
then simply calculated from 

/ = nX/sin /* n , 
/Q I 10 ' 1 ll6 -~ T J. pioa !, tation ,?*"?"} where n is the number of the 

(3.3 diammo-dimesityl) on cylindrical 

film. layer line (1, 2, 3, etc.) . Then 

identically the same value is obtained from all the layer lines. 
Three such values of I for each of the principal axes give the 
size of the unit cell. 

The process of assigning indices to the interference maxima 
lying on the layer line is usually straightforward. Thus on the 




224 



APPLIED X-RAYS 



equatorial line the index /t 3 in hihjiz is zero; in other words all 
indices must be h\h$\ h ?l must he 1 on the first horizontal layer 




Fi. 117. Diagrammatic representation of the rotation method. 

line, 2 on the second, etc. These maxima lie not only on hori- 
zontal layer lines but also on vertical loci which are zone curves 



Zone curve 
and H2 constant 




Layer line 
h^ constant 



Equator 



7 I V 

FIG. 118. Diagram of two types of layer lines on rotation patterns. 

(Fig. 118). Schiebold calculated these two types of layer lines 
(Schichtlinieri) of the / and II kind. Thus if the first maximum 



THE INTERPRETATION OF DIFFRACTION PATTERNS 225 

on the equator is due to 100 planes, then the spot on the first 
layer line lying on the common vertical zone curve is 101; if the 
second spot on the equator is 110, the spot above or below it on 
the first layer line and the second zone curve is 111. It is at once 
evident that oscillation photographs taken over a fixed angle are 
much simpler to interpret than a composite pattern made for a 
complete rotation around 360 deg. The matter of interpretation 
may become very complex, of course, if the number of maxima 
on a rotation pattern is large, or if the axis of rotation or oscilla- 
tion is not a principal crystallographic axis. Fortunately these 
cases in practical crystal structure analysis are rare. However, 
rigorous methods of indexing have been worked out by Schiebold 1 
and Bernal 2 employing the conception of the reciprocal lattice 3 
and graphical nets. Inasmuch as the great majority of experi- 
mental results can be interpreted by the very simple means 
described above, these more rigorous procedures will not be 
presented here, and the reader is referred to the original articles. 

Besides giving direct information concerning the crystallo- 
graphic system, and the dimensions and shape of the unit cell 
together with the number of atoms or molecules per unit cell, 
these spectrum photographs permit space-group assignment. 
When the interference maxima have been identified with the 
planar indices, the presence or absence of possible reflections can 
at once be noted and the criteria for a specific space-group 
set up. 

The advantages of the Weissenberg modification of the rota- 
tion method, in which the film is moved parallel to the axis of 
rotation, have already been noted. An important equation for 

1 A 90 
the interpretation of these patterns is a = jj&rj where <r 

L\i TTd 

is the angle between lattice plane normals, R is the translation of 
the films in millimeters during a revolution of 1 deg., A the differ- 
ence in abscissas of two interference points, Ar; the ordinate 
difference, and a is the distance of the crystal from the photo- 

1 SCHIEBOLD, Fortschritte Mineral., Kryst. Petro., 11, 113 (1923). 

2 BERNAL, Proc. Roy. Soc. (London), 113A, 117 (1926). 

3 In the reciprocal lattice originally worked out by Ewald, Z. KrysL, 66, 
129 (1921), the points, each of which represents a plane of the crystal, lie 
along normals through the origin to these planes at distances inversely to 
the spacings dkki- The mathematical calculations are greatly simplified 
obviously by representing planes as points. 



226 



APPLIED X-RAYS 



graphic film. Since only one layer line is used in the Weissenberg 
goniometer, the assignment of indices as illustrated in Fig. 95 is 
usually not difficult, particularly when a pattern with stationary 
film is used in conjunction. The great power of the method, 
of course, lies in the separation of interferences for planes of the 
same indices which would normally cooperate to produce the 
same diffraction maximum. Any overlapping interferences 
which render intensity estimation difficult can thus be separated. 
The Interpretation of Powder Spectra. This subject is 
practically completely covered in the first part of this chapter 
under the discussion of the positions and intensities of interfer- 
ences. In this method there is simultaneous registration of all 
sets of planes due to the random distribution of fine grains. If 
the crystal system and unit-cell dimensions are known from inde- 
pendent measurements with single crystals, the assignment of 



indices is not difficult, since 
cubic system dhki = 



or for the 



Under the discussion of 



intensities and stnicture factors a differentiation was found for 



1 




" 








II 






! 


1 


B 


'1 


S' 


Simple Cube 














1 












sf 


? 


Body Czniored Cube 




























1 


Face Centered Cube 




























1 


Diamond Cube 



FIG. 119. Diagrammatic representations of powder spectra for cubic lattices. 

simple, body-centered, and face-centered cubic lattices depending 
upon non-appearance of reflections for certain planes. The 
structure factor clearly indicates that if all possible values of 
hkl appear the crystal is simple cubic ; for the body-centered lattice 
the sum of hkl indices must be even and 110, 200, 211, 220, 310, 
222, 321, 400, etc., will appear, and for the face-centered cubic 
lattice the indices must be all odd or all even as in 111, 200, 311, 
222, 400, etc. The powder spectra are illustrated in a diagram in 
Fig. 119. It will be noticed that even for the cubic system lines 
related to \/7, A/^> \/23, A/28> \/31, etc., are absent, since in 
\/h 2 + k 2 + I 2 no sum of squares of integers will give these 



THE INTERPRETATION OF DIFFRACTION PATTERNS 227 

numbers. If values of a , etc., are unknown, trial and failure 
methods may be successfully used. Thus for a cubic crystal 

7 _ a __ 

~~ 



0n 
-- X2~~" = ' ~^" + ^ ' 

Any two powder spectrum lines must have sin 2 O n values which 
will be in the ratio of whole numbers, since (A 2 + k 2 + I 2 )n 2 is 
always an integer and a and X are constant. For other systems 
the ratio will not be that of whole numbers. In systems of lower 
symmetry than cubic (in which only the cube edge length need be 
known) the calculations from quadratic equations listed in Table 
XXV may become increasingly difficult, particularly when the 
crystal system is unknown. Numerous criteria have been set 
forth but most useful probably is the graphic method of Hull and 
Davcy 1 for the hexagonal, rhombohedral, tetragonal, and par- 
tially the orthorhombic systems. For each system the logarithms 
of the spacing d calculated for each set of planes are plotted 
against axial ratios. The experimental data are plotted to the 
same logarithmic scale and then moved over the graph until a 
match is found, thus identifying system and axial ratios as well as 
planar indices for each interference. 

The following facts are obvious in the interpretation of these 
line crystal spectra: 

1. Only definite lines in a definite pattern correspond to a pure 
crystalline substance. 

2. Foreign lines indicate the presence of other crystalline 
substances as impurities; each entity produces its own spectrum 
if present in sufficient quantity (above 0.2 to 1 per cent usually) 
and the comparison of intensities is a method of quantitative 
analysis. 

3. Solid solution is indicated by no change in the pattern of 
lines of a pure constituent, but in a shift in position of the lines, 
toward smaller angles (nearer the zero main beam) if the lattice is 
expanded by the addition of foreign atoms, or to larger angles if 
contracted. In many cases the lattice spacing is linearly related 
to atomic percentage of constituents of a solid solution alloy, as 
will be illustrated later. 

1 For example, Phys. Rev., 17, 266, 549 (1921). 



228 



APPLIED X-RAYS 



4. The powder method may be made very accurate in evaluat- 
ing the lattice constant of a pure substance and from this the ideal 
density of the material. The value for tungsten so obtained has 
been of utmost value in vacuum-tube applications where tungsten 
filaments are employed. 

5. The widths of the diffraction lines serve as a means of deter- 
mining grain size in the specimen as will be demonstrated in a 
later section. 

6. Any departure of the powder or aggregate from purely 
random arrangement, which results in continuous diffraction 

circles or lines of uniform in- 
tensity, is manifested by the 
patterns. Thus if the grains 
are too large to permit the 
probability of random arrange- 
ment, the lines become spotted 
and dashed due to reflection 
from individual grains (Fig. 
120). In general, the grain 
diameter must be smaller than 
10"" 3 cm. to prevent this. 
Most metals with grains which 
will pass through a 200-mesh 
sieve will give uniform lines. 
Again if the grains are 
sufficiently small but are 
oriented in some preferred 
direction, as by some deforming force, some lines may become 
shortened or disappear or assume localized intensity maxima. 
This process of fibering will be now considered. 

The Monochromatic Pinhole Method. Figure 98 taken by the 
monochromatic pinhole method is reproduced as an example 
of the structure of a natural fiber, asbestos. This mineral 
is not a single crystal, since otherwise it would give a Laue 
pattern of symmetrical spots. But neither is it constituted of 
grains in random arrangement, since this would mean a pattern 
of concentric uniformly intense rings. It may be seen, however, 
that circles may still be drawn through the diffraction maxima, 
although the more prominent loci are hyperbolas. These would 
be parallel straight horizontal lines (as in Fig. 116) if a cylindrical 
film had been used instead of a flat one. In this mineral, there- 




FIG. 120. Pinhole pattern illustrat- 
ing effect of large grain size (black 
diamond or carbonado used in mining 
drills) with pattern characteristic of an 
aggregate of diamond crystals. 



THE INTERPRETATION OF DIFFRACTION PATTERNS 229 



fore, the grains are oriented in a common direction with respect to 

the fiber axis. The pattern is typical of a fibered aggregate. 

It should be noted that the pattern obtained by rotating a crystal 

around a principal axis is a layer line diagram exactly like that 

produced by a fiber without rotation. With a fiber, of course, 

only one such result is obtainable, while with a single crystal 

three patterns corresponding to rotations around the three 

principal axes are possible. Now a fine-grained aggregate 

may be made fibered by rolling or drawing in one direction, as 

shown by Fig. 121 for cold-drawn aluminum wire. The desira- 

bility of a pattern 360 deg. 

in azimuth is at once appa- 

rent if the degree of fibering 

is to be estimated and if the 

actual location of the 

symmetrically placed 

maxima is to be used in the 

determination of the mecha- 

nism of deformation by 

mechanical work as explained 

in a later section. A fiber 

diagram has a great advan- 

tage over an ordinary powder 

pattern and this is that a 
measurement of a lattice 

spacing, namely, the atomic plane periodicities along the 
fiber axis, may be made independently of any assumption 
as to crystal system or planar indices. It is necessary only 
to measure the distances e\ 9 e 2 , e 3 . . . e n of the vertices of 
the hyperbolas (or of the straight layer lines on a film 
which had been bent on a cylinder coaxial with the specimen) 
from the central zero point of the main beam. Knowing the 
distance from specimen to film, a, the diffraction angle MI, 
M2 . . . Mn may be calculated, since the tangents are e n /a. The 
identity period or spacing along the fiber axis is then simply 
calculated from I = nX/sin Mn, where n is the number of the 
layer line (1, 2, 3, etc.). Thus identically the same value is 
obtained from all the layer lines. For the other lattice spacings 
it is necessary, of course, to interpret the pattern exactly as in 
the powder method since the Debye-Scherrer circles may still 
be evident. The degree of perfection of preferred orientation is, 




FIG. 121. Fiber diffraction pattern for 
cold-drawn aluminum wire. 



230 APPLIED X-RAY 8 

of course, indicated at once by the patterns, since there may be 
a continuous transition between the concentric circles for a 
random aggregate and the sharp horizontal layer lines for perfect 
fibering. 

While this method has come to be most generally associated 
with the fiber state, it follows that it is only a special case of 
the Laue method and of the powder method. It is generally 
employed in all of the metallurgical studies involving fibering in 
fabrication, internal strain, annealing, and recrystallization. 

The Complete Determination of Crystal Structure. From 
the results of one or more of the crystal-structure methods 
interpreted as briefly outlined in this chapter the complete 
analysis of a given crystal in terms of the exact coordinates in 
space even of the ultimate atoms in molecules may be made. 
The steps in this procedure have been outlined on page 182. 
Actually a considerable training and experience are required 
for the analysis of the more complicated substances which now 
occupy the attention of x-ray scientists, since probably nearly 
all of the simplest types of crystals have now been studied. 
The attempt will not be made here to carry through a complete 
analysis from experimental data, since this is not intended to 
be a technical handbook and since the chief interest is in gener- 
alization from results to date. However, in the chapter on 
organic compounds, the procedure employed by Mrs. Lonsdale 
in her painstaking and classical analysis of the shape of the 
hexamethyl benzene molecule will be outlined. All of the 
next chapter dealing with results, of course, has depended on 
carrying through analyses in the stepwise fashion already referred 
to. 



CHAPTER XIII 



THE RESULTS OF CRYSTAL ANALYSIS : ELEMENTS AND 
INORGANIC COMPOUNDS 

The Chemical Elements. By the methods of x-ray analysis 
outlined in the preceding chapter about 65 of the known chemical 
elements (the discovery of the last of the 92 was announced in 
November, 1931) have been assigned definite lattice structures 
in the solid state. Pure metals are, of course, chemical elements; 



o i 
H 



2 He 



3 iNe 



5 Kr 



6 



Xel 



Li 



No 



Rb 



7 Rn 



234- 



Be! 



Mgj 

Go] Sc i Ti 
I i 

Sri V !Zr 



Ac lib 1 



567 


a 


1 2345676 






He 






r T 
!Be : B 


[ c| 


ooooo^ > r--| 
Ng^O > F Nel 






1 I 


LJ 


IOOOCWN/ 1 






i M9 !B 


Si 


j[p| S Cl A | 


V !Cri ;Mn 


Efcs 


Cu ||Zn ;JGa j 


Qe 


!As ^Se| Br Kr | 


Cb Mo Md 
Ta W i Re 


^-"ii 

jRu iRh Pd 

Os |i Ir Pt 

1 ' ... 


Ag|!Cd:Mn~|: 
i 1 ' ! ^ 
AujSHglffi; 


Sni 




Bi j Po Rn 
:/wv 


Pn H 





6 LajjCejjPr Nd II Sm Eu Gd Tb Dy Ho JErj Tu Yb Lu 



Face -centered cubic 



KEY 



! ! Hexagonal close- packed 
[ | Body- centered cubic | | Diamond type 

F^l Arsenic type ^ ^ Selenium type 

FKJ. 122. Periodic table of chemical elements showing crystal structures. 

every metal except a few of the rarest in nature may be classified 
now according to the pattern by which its atoms form crystals, 
and according to the numerical values which define the unit 
crystal cell. Fortunately for practical purposes most of the 
metals are grouped in a very few crystal systems, the majority 
being face-centered and body-centered cubic and hexagonal close 

231 



232 



APPLIED X-RAYS 



fi 


Oo 1 ^J ^!Q^^: 












0) 

G 


















O 




u 


g^^ ^^_ rtO^ 


00 


ri 








G 




36 


"^8 rj ^8 c!^" fxw ^? 3 


^ 


^ rl 


<> 


co 






0) 


- d 


c^^ 1 I O N M: ^-' 


<N 


00 CD 


* 


CO 




ili 


0} 


O 


^^HO ^^^ ^ 0?D ^ 


^ 


T^CO 


<M 


w 





CO 









(M 


o" 






o 






"2 


H) ,-, oicli'-H "^ 


^ 


^ 


(M 


Or- 


,- 








I'M i O 
















g g 


SO i-l -H rH O 
rH . . 


O 


O <N <-" 





21 


|~| 






* 6 a 


,-T o" o ^ o o" '-' 





-o 
OO 


Q 


s'2 


I-HO' 








^ _ g ^ 





^ 




<=> 









Ibs'S 


^ n c-i QO 


TlH 


C^JCl 


CO 


<* 


^ 






C5 




















x; N -* 


s 


- t 


e* 5 


CSKr-N 


^ 









'N ^ 


(A 


f-l\ 


'3 


XfW 1 


s 






V 


- (N ^1 - ^" "* J^ 1 


G 


^^-T " 


13 


r-f\ ' 


c^\ 






~ as 


'> -N CO ^ 


hf x^ 


V ^ ^ 




\ " ^ 


c7 c 






f-l 




o ^ 


^r,\ + + 


^ 


r-rO-.f 


o+l 


s 




< O 
O 


"^ ^. ^ 2o 


GO 


o - - r " rx 


O 


of 


cst 


+1 ft 
























8 8 8 ^ 


,x^0 


^aa^ 


^ 


8^ 


v '" CO 






G G 


*.%* ? ^4* 




% 












03 


















si 

G > 




"OJ 


g 




6 








<u<a 
6-6 

<p O 


QCL i ^H ^fjj ^ ,03. tiE~ ' ^ ^ 


'$ 


PH 

S ~ 




0) 








36 


H a)l ~ H .. ~r* - '"5 *"* 






H 


a 










>^ Qj,jQfG CD^ ^ I , 03 C3 -^^ | 

tiio^ji, p_( ^H ^ o ^ y ^ oOE~ | r v Q 


CO 


S3 




cd 


ffi 


O 




^ g u, 


OO CO -^ 








^ 










rH S ^J ^ 
















0-3-61 



















ft^ eS ^ 


i i iM CO ^ 


in 


COt- 


00 


O 




"- 




H >>c5 


^ -* ^ -r; 


^ 


-rj ^ 


j 


-^ 


^ 


'I 




00 "K 


















Aft 


V 


^ 


'- u> 


c 


, 


01 







03 

at* 


6 6 Q O 


Q 


QQ 


n 


Q Q 


Q 


Q 




-/: M 


















Space lattice 

1 


- 1 I s 

73 a ^Oi n 
GO ^ ^0 

^ gO -ojW fe 

^r^i i>^ ST? .S be 
a>W ?*> 05 ^ 3* 

fiH TJ a ^-S 5 
tS- 5 a ^ K a h^ 


0, 



PQ 

^ 
IS 



Q 


ragonal 
FC tetragonal 
BC Rhombohe- 
dral (deformed 


simple cubic) 
Hexagonal (de- 


formed simple 
cubic) 
Hexagonal 


Rhomb ohedral 


Tetragonal (sim- 


13, 










cs 


















c 












G 






o 










G 








hi 


o 
















oj 


^2 








I 

15 


" 

^ g sS 


I 




m 


rt 








ft 


g I 

(- ^ S o 




S 


g 
3 


5 


>> 


g 




^ 


s. sal 


c 




'3 


a 


o 


.2 






3 a 

o H ^ Q 


S 


II 


0) 

1 


a] 

(H 




1 


-3 
O 





THE RESULTS OF CRYSTAL ANALYSIS 



233 



TABLE XXVIa. NEW UNCLASSIFIED TYPES FOR INCOMPLETELY ANALYZED 

STRUCTURES 
(See Table XXVII for details) 



Type element 


Space lattice 


Space- 
group 


Iodine. 


Rhombic 


TV 8 


a-Manganese, y-chromium 


BCC (special) 


7V 


ft- Manganese 


Cubic 


0\ O 7 


a-Nitrogen 


Cubic 


T * 


^-Tungsten 


Cubic 


O 2 or Oh 3 


Sulfur 


FC rhombic 


v h 


Se (monoclinic) . 


Monoclinic 


cv 


Parahydrogen . 


Hexagonal 


? 


Oxygen 


BC rhombic 


? 


White phosphorus 


Cubic 


? 





FIG. 123. Hexagonal 
close-packed lattice (zinc 
type). 



FIG. 124. Tetrahedral cubic 
lattice (diamond type). 



packed. In addition, some of the metallic as well as non-metallic 
elements crystallize in more than one modification, iron being 
an outstanding example. In Fig. 122 the periodic table of 
elements is used as a basis for a graphical representation of 
lattice types. These types are further listed and denned in 
Table XXVI and finally Table XXVII presents in detail the 
most recent and reliable data for the elements alphabetically 
arranged. 1 

1 From an excellent and painstaking summary by Neuberger, Z. Kryst., 
80, 103 (1931). This paper gives complete formulas for calculating distance 
between atoms, atomic radius, atomic volume, packing density, volume of 
the unit cell, etc. 



234 



APPLIED X-RAYS 



O 



S 

H4 



k> 

^ 
X 

H 

a 







T8 






13 








"rt 




CO 




1 


"3 

i 




1 
o 


I 






1 


1 


S3 




o 


JD 





S 




J3 






o 


o 


0> 




"2 


S 


^ 


" 


g 






l_ 


g 







CD 

'a 








"ft 


O 






0) 

ft 


o 











^ 




O 






s 


O 






cc 




*^ 


m 


fa 






CQ 


fa 


ij^ 


<*< 


5 




05 


35 







^ 


o 




o -e ^ 






















322^ 




























^ 




as 


00 






CO 


Tt< 






o 


n 




















o 






o 


o 




















CO 
























00 








00 


< 




II 


II 




II 


II 






II 


|| 






3 


3 




3 


3 






3 


3 


00 





CO 

d 












1 
d 




i 

d 


i 




e w 


+1 


+1 


+1 


o 






+1 




+1 


+1 


.S 


S 




CO 


+1 


,_, 


O5 


iO 




O5 


00 


Sc " 


S 


S 


{ 


^ 


12 


fo 


o 


S 


t^ 





W 


T*< 


T*< 


CO 


o 


-* 


o 


iO 


CM CO 


TJH 


CO 




II 


II 


II 


II 


H 


II 


II 


II II 


II 


II 




c 


e 





o 


o 





a 


e o 





c 


1 1 3^ 






















S ^ s -3 


^ 


Oi 


00 


"& 


<M 


00 


^4 


(N 


CM 


00 


h 3 * fc 






















/^ "o ft 






















g a o> 




_ 






^ 








^ 




s a 

O >j 




i 






"8 






13 


8 




03 <U Cj 




o 






^o 









8 




ft S * 


s^ 


1] 


;^ 


s^ 


^ 


S ^ 

^ "^ 


o^ 


||" 


1 = 


g h. 

5 ^ 




fa 


tf 




fa 







tt 


w 






*1 2 









>o 






O5 


co 






oa ^W) ^3 


CO 


CO 




CO 


t^- 




10 


00 


t>- 




01 g J 


CM 


CO 




iH 


>o 




CO 


-H 


O5 




o to 






















i|s 


05 


o 




05 


CO 
05 




CO 

CO 


S 







< 1 ^ 


S 


s 




% 


s 




co 


05 







O It 

II 

g 


CO 


^H 




00 


CO 

co 




SI 


^ 


co 

00 




*? 3 






















< G 
































o 












*2 c 






















fl 
















cu 






J -J3 


<} 


rr> 






+3 












S 3 

S -5 

43 O 

W 6 


1 

a 
1 


timony, 




a" 


O 

I 


j 


03 

PQ 
S 

3 


6 


CQ 
j 

1 






1 


(3 




^ 


^ 










S 





RESULTS OF CRYSTAL ANALYSIS 



235 



1 














^ 


4) 






O 
















00 








: 


isD 

o ^5 rt 


CO 

00 


S 


s 





l-H 

00 


CO 


(N 

CD 


< 2 : ' 


" 


11 








rH 


11 


<N 


- S 

* ! 
















w 


CO cjD 





8 










S 


CH 


fl +1 




+1 








O 


^flJ ^ 






f^ 








+1 








C5 










M 


l^ 

OS CO 


5o 


s 


00 00 


.H 


2 


o 


w 


^ '0 


10 


co 


CM CD 


CO >O 


10 


CD 




II II 


II 


II 


II II 


II II 


II 


II 



















o 


O 


U, 00 ^ 


01 


. 


00 


* 


<N 


*< 


e, 


5 o S 
















i ? s 


(73 








c 




O 






aai 

CQ OB 


rt "^ M 

a 


g aq 


o ^ ^ 
o ^ 


a 


4" 

a 


fe " 1 


* C 

PQ 


"S a> 2 
en M -C 
C ^ ft 


s 


S 


10 


2 


00 


s 


s 


a> d as 


00 




CO 


* 


CD 


CO 




Iro 


rH 


S 


i 


> 
> 
> 


fv 


J 


00 


O >r1 OS 


















S 


s 


<> 


i 


C 

T 


} 
4 


S 


1 1 


00 





cc 


3 


(X 

f 


! 


s 


-d a 
















Element an 
modificatio 


Cadmium, Cd 


Calcium, Ca . 


Carbon, C 
Diamond . . 


Graphite . 


Cerium, Ce 
a 







a 

1 



236 



APPLIED X-RAY8 



1 
































o> 
















o 

| S S ^ 

2 * 7 1 < 

t, t* * 


^ 


25 

CO 


iis^ 


ii 


1 


! 


! 


a 3 
































-f 3 
















^ oS 
















1 

W) jj 









0* 


8 

o 









c 


4-1 






4-1 41 


4-1 


41 




1 

W 


oo 

00 


r^ oo 

<N ^ 


00 


^ "O 


iO 


CO 


co 


CO CO 




II 


II II 


II 


II II 


II 


II 


II II 













O ^ 


a 


c 


<" 


** ti 






00 




*< 






X^ a 






>0 










|9& 






S 










5 &: 




13 




13 






13 


o 4 S 

o c^ 




a 


c 


ti 








c 


08 e8 


a CN 














OQ & 


83^ 

m 


W 


^ " 


M Q *r< 
<y ~S i 

w 


z s * 


8 ^ ^ 


W 


>> rt ^ 
















Ifi 


S 


o 


U5 


'0 


CO 


CO 


OS 


Q|E 


^ 


co 


^ 


00 


00 


00 




Hi 




o 




O5 







CO 














CO 


b- 


^ ^ 




1C 




c 




co 


co 


M 

| S 




cs 




b- 

<N 




. 


i 


'O fl 
















C 
05 ~ 


IH 














*J 08 

fl 

S3 ya 


g" 






8 




<3 


H 


S^ 

4 O 

S s 


3 

8 





- 


V 


oi 


1 


Erbium, 



RESULTS OF CRYSTAL ANALYSIS 



237 



00 










ffl 






93 










CM 






S 

& 










J8 




a 


.-, 










^ 




S 












CM 




M) 

HH 


His 


CM 


CM 
CM 
CM 


i 


1 




CM 

CO 


rH 05 
iO CO 
CO t- 


*t 2 *- 
















If 
















00 






o 









III 

















o o o 


















C . 








-fl fl 






41 4-1 -ft 








CM 










M a " 


iO >O 


CO 





o ri 

CM O 


S 


00 CO 
>0 00 


>o >o o 

OS 'O 00 


w 


^ t- 


o 




CO iO 


CO CO 


^ ^ 


rti t^ 05 




II II 


II 


II 


II II 


II II 


II II 


II II II 







CJ 


C 


C <- 





O VJ 


e ^ 


IJjjl 


00 


00 


* 





. 


* 


00 


Space lattice 
space-group 
lattice type 


Tetragonal 

/)4A 16 

A 11 


FCC (diamond) 
Oh 7 
A 4 


gs q 


Hexagonal 

Z>6fc 4 

A 3 


Hexagonal 
t 

? 


Tetragonal FC 
D^' 
A 6 


Rhombic 
V h 
charactenstic 
type 


6 
















> -3 






,_, 




O5 






a 85 
-s ft 


CM 

O 


CO 


o 

CO 





oo 
O 


co 


3 


0) g g 


CO 


'O 


O> 


CO 









|s- 


CM 


i 


CM 


CO 


I 


00 


CO 
05 


-2 s 2 


Ol 


CM 


j^ 


00 


,_! 


f 


CO 


- 


CD 


^ 


2 






^ 


CM 


|| 






Oi 






O5 


CO 


3 S 


CO 


CO 












'O a 



















OS 

-w 09 
fl 


03 

O 






w 


w 

rj 


d 




<u ya 
S 3 

si 


e 
o 


'S 

93 

o 


-o" 

3 
O 


Hafnium 


H 

3 a 
" 


S 

^5 
a 

I-H 


S 

1 



238 



APPLIED X-RAYS 










1 
















MS 


"oS 












00 




TS 


OJ ^ 












jj; 




o3 


a 












03 

a 




X 


5 "S 


o 


00 






1 


0> 






CJ 


el 


o 


<j 






o ' 






O -j 


82 


o 


o^ 






g 






^ 2 


M X 


rH 


CN 






>-H 






<? ^ 


?^ 


3j 


-P 









o 

o *3 "* 


CO 


CO 
CN 


CN 


a 


Oi 


CO 
00 


s 


8 


5 2 I? 


rH 


" 


rH 


" 


" 


" 


" 


" 


a 


















JJ c 


















^ 03 


















1 


CN 

8 

o 


CO 

-flo 











CN 

8 

O 


S 

o 


JU 


+1 


8 


-H 








+' 


4-1 




CO 




^J 












hC 




oo 




CO 

<o 


s 


CN CO 


3 


CO 


3 


CO 


CN 


CO 


CO 


1C 


CO CO 




CO 




II 


II 


II 


II 


II 


II II 


H 


II 




e 


e 


Q 


e 


a 


a <~ 


e 


o 


II! 1 


. 


CN 


* 


* 


CN 


- 


CN 


5 o 
















^ ? 










ri 
o 










o CN 












a a "3 

02 ~* 


X 


tt 


s s " 


fa 


W 


g j:: 


86^ 



















>> c ' 




00 












s 8J3 


00 


00 


i2 


CO 


s 


CO 


s 


If I 


CN 


^ 


00 


CO 


CO 


2 





Jfl 


r ( 

CO 


o 
*o 


o 
do 


oo 

co 


i 



**< 
OS 

CO 


CJ * 














11 





8 


8 


1C 


CN 

00 


CO 


^ 3 














"^ C3 














ts a 
g 2 








J 






rt 














Element 
modifica 


Indium, Ir. 


; 

C M W 

o f* 


c 


Lanthanum 


e 


Lithium, Li 



THE RESULTS OF CRYSTAL ANALYSIS 



239 







3 


| 





2 










"S 


1! 


"2 


1 I 






J3 




ft 


& 


ft ^ 


-8*1 






03 
0) 




6 

o 
o 


3 

s 

o 



, room tern 
ttrapolated 


ll-S 
<| 

V IN -S 

s*y 




oc 






< 


^5 


< 3 


M rt fe 




ff. 





^ 


IN iN 00 N. 


Tt< >O 


^^ 


00 







2 s ;-> 


s 


co ^ 06 t< 

O O 1-1 IN 


00 <> 





OS 


^ 


! 


< (H >- 


























<N CO 
















CO ^ 






3 3 










O 00 
















h~ os 






! 










II II 
















3 3 








(N CO 


>0 








CO 




X 




8 


i 


8 8 




o 




fee w 


6 o 





o 


o o 








ti 


+i +i 


+1 


+1 


+1 +1 








W) 


CO CD 


Tf 

os 
oo 


8 

CO 


1^ <N 


r- oo 

OS 'O 





<N 


S 


CO 

II II 


oo 
II 


CO 


co co' 


II II 


co 
II 


^ 




o 


o 


O 


e 


o e 


o 


O 


1 i a 
















111 1 




s 


8 


^ 


r-l Tf 


<N 


^ 


& s 




u 





y 


13 






-So 




1 


1 


S 


s 






1 If 


a 
o 


| & 


o 

o o S s, 


a 

Ss 

ofl *: ^ 




a 2 


<N 




ft || 


* Q ^ 


g | S 


o ^ 


4> ^ 


JQ% 


85-^ 


8 S ^ 




W 





u 


H 


PS 





fa 


6 
















>> c ^ 
















5 to ,3 


^ 


tj 


>o 

(N 


JN 


a 


CO 


^ 


d "S * 




























o 




Q 8 , 










" 






O ^J 


M 

CO 




CO 
05 




CO 





oo 


< & ~* 


s 




S 




8 


s 





S "2 










O 





o 


2 1 


H 




<N 




00 


^ 


r " 1 


^ a 




























o 




*g _, 


M 


d 








<^ 




c o 
















5 
*J 03 

d w 


S 


- 






bO 

w 


I 

gj 




S c 

S -6 
o> 5 

w s 


3 

8 

a 


s 

CJ . 

08 . 

bO 

5 








g 
& 


! 


jS 

1 




g 








s 


S 





240 



APPLIED X-RA Y8 



a 


jjijj 


; 

i 




2 






"3 .2 .. S c 










S 


d oo-o "I 

o M o . { 


a 

j 











x 5 "S ~^ ' 


3 




cl 








3 
^ 




< 




lis^ 




CO 





S 


CO 
CO 


+* "2 < *f* 




,_, 


^i 





,-H 


< 2 - ' 












'"1 












OQ 




8 


i 




11 


*i 












O O 


c *t 




+1 


+1 




-H +1 


*> 




^ 


CO 






a " 


S N 


iO 


CO 


g 


^ co 


13 

w 


w rf 


00 


00 


o 


<N ^ 




II II 


II 


II 


II 


II II 




13 <j 


c 


o 


o 


CJ V 


^ ao ^, 












la 1 


W 


: * 


<N 


00 


<N 


in 








o 
-D 

C 






"3 






5 


3 


o o 13 


G 
O 








2 <u 


S3 



aaS 


" 


o "* *" 


o ** w 


J * S S 


S 1 s ro 
















ffi 


fe 


W 





ffi 


" T 


~" 










>> a 'o 


Q 







<N 


'S 


In 


oo 


00 


00 


- 


a 


III 


S 

oc 




CO 


00 

8 


OJ 

o 




5 




0> 


^ 


O5 


II 


S 




g 


N 


S 


< a 


















3 






o d 








^J 




Element an 
modlficatio 


TS : 

Q 


. 


Niobium, Nb ( 
umbmm, Cfc 


5 

d 

0) 

1 


Osmium, Os 



o 

-H 



to co oo 
II II II 



2 



THE RESULTS OF CRYSTAL ANALYSIS 



241 





a, 


"as 

















"8 


"c 












j 


j 





'T3 i 










t-l 

03 

g 


5 9 




8 




o 










i 


0) 


&>& 


^ 


a 










**< 




co 


V 



















-ft 
a 


(H 










9 


JjSiJ 




GO 


^ 

CO 


8 

CO 


CO 
CO 


CO 


CO 


11 -^ 




O 


^ 


04 


*" 


rH 


CM 


a 8 




CO 


I 












< 




II 


II 
















3 


3 




















8 


>o 


* | | 




03 








S ' s 







o 

















4-1 


o 


^ -0 








Cl 


41 


H 41 


^ 


-H 












CO 'O O 












CO 










3 


- 





>o 


O5 

CO 


'0 

II 


II II 


CO 

II 


CO 
'O 







o 





(3 







13 


o 


u. ao ^, 

s s s 


















"s ^ T 


CO 


<N 


00 


* 


<N 


o, 


<* 


N 


^ *o ft 


















ft. 




a 












5 o S 




S 

(U 












""" i 










03 

3 
















o 
















W "i CO 






JQ -2 





O Q Tl 


g*^ 


|Si 


cd 5 

a 


gs. 


w 


o 
















>> fl ^ 






'0 






1 t 




S M J3 


} 


00 
CO 


00 


00 


^ 


CO 


00 

IQ 


















Q g 2 


(N 











g 


a 




6 |jw 

48" 


8 

co 


CO 
01 

>o 

OS 


s 

CO 


CO 


OS 




<*" 


o ** 














II 


12 


00 


OS 


s 


o 


IN. 

CO 


11 




j 


w 


<u 


tf 


s 


11 

w a 


S o 


a 

a 
ta 


a 

00 

1 


a" 
^ 

s 

0> 

43 


a 

1 


a 
1 

,3 

3 







(^ 


s 


tf 


rt 






I 



o 



<M 

co 

OS 



OQ 

H 

S5 
<) 
H 

03 

O 

o 

a 

o 



^ 



> 
X 
X 
s 

9 

H 



242 



APPLIED X-RAYS 



J? 
















01} 












< 




4> 












o 










02 






3 


* 


O 

1 1 .s tj 


i 


s 




co 


3 


S 


00 


^ 2 ^ 


J ~ t 


1-1 




"^ 


""* 


11 


N 


a J 






10 










3 8 

















<n 


6 6 


II 

d d 




6 





6 

o 


d 


fl 


-fl +l 


-fl fl 




fl 


CD 


+i 


-fl 


S 


>0 CO 
OS ^ 
CD 01 


CO Os 


O b- 

>o oo i> 


00 


O 







S 




II II 


^H 00 00 

II II II 


II 




T 


CD 




CJ O 


y o 


O rO O 


o 


o 





e 


OJ g "3 
















f 1 =5 


0) 


CO 


'N 


00 


^ 


<N 


* 


5 ^ 






co 










^ ^ a 
















g 4 g, 








i 

























5 p>f 


'd 
G 


7 Q 


o 

s 


1 








o o :; 
s} 03 4j 




rt ^S M 





S*i 


3^ ^ 


r 1 


<N 


^H 


a a ^ 


SQ^ 


q ^ 


fl ,* 

O <0 c^ 


8 o ^ 


^j 6 ^ 


8 o -i 


O ^ ' 




ffi 


W 


rt 


fe 


fe 


PQ 


fe 


6 
















>> c -^ 
















'S to -a 


00 


00 


10 


CO 


S 


OS 


>o 





(N 














(N 


o o M 

(H 
















||| 


O 


OS 

b- 


8 

00 
<N 


o 

t> 

o 


IN 

os 
OS 

(N 
<N 


CO 
tD 

t> 

00 


|| 


5 


co 


I ( 


5? 


" 


00 

CO 




a 












S 1 


D4 










^ 


*i 03 
fl w 

0) O 


a 
1 

o 


CQ "3 '3 

ll 1 


J/? 

c 


bC 


o3 

a 


w 

5 


3 s 


^5 

i 


I s ^ 


o 
o 


1 


S 


fl 



THE RESULTS OF CRYSTAL ANALYSIS 



243 



si 


oft 
















tf 


1 


















"o 
















H" 




! 


CT> 
CO 


o 


f 


- 


o 


! 


|| 


















J 




CO 

8 

d 








i 

c> 







g) o 




+1 








+l 




+1 4! 


CU pJ" 
bO G 


i-H t>. CO 

CO 00 >O 


S 


lO (N 


S3 

^ 10 


00 


rt 

o 


CO 


00 ^ 


W 


rH ^H (N 


CO 


<* iO 


CO >O 


"t 


o 


CO 


lO CO 




II II II 


II 


II II 


II II 


II 


II 


II 


II II 




O JS <J 


C5 


e 


O J 





C3 


O 





1 1 a^ 


00 
















6 1 S 1 




<N 


CO 


<N 


-* 


<* 


00 


^ 


X *o a 


















0> 














5" 

d 





5 o >, 

c3 ^ ** 


O 




- 5 


^_ 






o 

s 


13 


g II 


V 

' ~ 
S ^ 


<N 


G n 


a 1 ^ 00 


o 

c3 * 


^ 


^ 


3 


a 


CQ - 


3*- 




ffl 


3 ^ 

a 


<D ^ < 


g " 1 


fo^ 


g ** 


gQ ^ 


6 _ 


















^ S 'pS 








CO 
(N 


00 


28 


CO 


1-4 

00 


O3 
CM 


fi -S ft 

0)^03 
Q Q K 

t-c 




CO 


CO 


^ 


^ 


JH 





** 


o >( j 




CO 




O5 




(N 


c 


5 


d 'yj CO 




CO 


iO 


CO 




1-1 






O -j< C5 




^ 


J^ 


^ 




(N 


01 


D 


^ 5S ^ 


CO 


00 


^J 


<N 




CO 
(N 




H 


"i| 
1 


CO 


CO 


g 


00 




i 


s 


I 


^ c 


















T3 d 


















Element an 
modificatio 


03 

O. 
O) 


Tantalum, Ta 


Tellunum, Te 


Thallium, Tl 
a 


x 


Thorium, Th 


d a 


ft (white) . 



244 



APPLIED X.RAYS 





















CJ 












d 






C 












^ 






<D 












1 




- 


O 

c 2 S ^ 

S "s << ** 


? 


! 


8 


O5 


! 


00 


CO 


! 


-3 jB 


















Jr C 


















^ Ci 


















GQ 

bO <_, 

a 


o a 

-fl H 


CO 


-fl 






i 

d 

-fl 


6 
o 


CO >O 

88 

O 
H -fl 


0.002 
0003 






CO 














1 


? 05 


S 

co 


I 


CO 

co 


o 

CO 


00 
CO 


38 

CO 05 


CO CO 

co <o 




II II 


II 


II 


II 


II 


II 


II II 


II II 




e ^ 


a 


C3 


a 


a 


a 


^ 


o <* 


a> t! 


















-2 c " 


















II r 


(N 


c, 


00 




CM 








&& 






o 
.D 

(R 












S - 

- ., 

0) 4) 


13 

o 




!S 








13 

fl 


1 

o 


III 
CC ^ 


ffi 


PQ 


o 


85" 

PQ 


PQ 


^ 


X Q ^ 

w 


S 1 3* 
3-* 
w 


>> 6 - 




CO 














S S^ 





(N 


05 


^ 


CO 


CD 


o 

(N 


S8 


a> ^ c9 


^ 


05 


DO 


O5 


CO 


CO 


l^. 


CO 




















^ 
3 r; i ' 








2 


O3 


<M 


S 


CM 


IIS 


S 


2 


00 

CO 


S 


1 


>o 

CO 


O5 


<3 

11 


(N 


S 


8 


CO 


S 




co 


o 


iJ 3 
















*s fl 
















'O fl 
















C 
















fl '^3 


H 





JJ 


"* 






CSJ 


c w 

si 

0) O 

K S 


S 

c 

03 


1 : : 



Q QQ. 


1 

1 


oS 


fl 



S 


fl 

o" 

c 


z 

c 
o 

z 




H 


H 


*5 




X 


t5 


c3 



THE RESULTS OF CRYSTAL ANALYSIS 245 

Inorganic Compounds. Several hundred inorganic compounds 
have now been subjected to crystal-structure examination and 
more or less complete analysis by x-rays. l These data are readily 
available for reference in the International Critical Tables, Vol. 1, 
Wyckoff s "The Structure of Crystals/' 2d ed., New York (1931), 
and especially in the monumental u Strukturbericht " of Ewald 
and Hermann which appeared serially in the Zeitschrift fur 
Krystallographie and in book form late in 1931. Hence, only 
the general types and relationships need be considered here. 
Ewald and Hermann's type classification evidently will be 
adopted as a standard so this method is followed here. The list 
docs not include a hundred or more compounds which have been 
subjected to crystal analysis but for which results are still incom- 
plete owing to extreme structure complexity, such as some of the 
natural silicates or to very complex or poorly defined chemical 
formulas. Alloys are considered separately in Chap. XV. 

A general impression to be gained by such a table is that the 
field of inorganic chemistry is a hopelessly complex one from the 
structural standpoint. Thus for the various classes of compounds 
there are the following definitely classified different types, to 
which must be added numerous highly characteristic structures 
for individual compounds: 

AB. 13 

AB 2 (A*B) .16 

A x B y . . . . . 8 

. 5 

. 8 

A t (mB n )y . . 20 

The 878 pages of the " Strukturbericht " are eloquent evidence 
of the industry and ingenuity of x-ray diffraction research workers 
all over the world whose interest lies in trying to discover how 
nature builds its vast number of chemical compounds. They 
have succeeded in finding already 70 definite architectural plans 
according to which one or more compounds are constructed, plus 
as many more which are not so definitely known. Out of the 
complexity a great step forward has been made in the classifica- 
tion alone. Similarly constituted compounds of chemically 
similar elements tend to crystallize in the same way. Certainly 

1 In the valuable "Tables of Cubic Crystal Structure," by Knaggs, 
Karlik and Elan (Hilger, London, 1932) there are listed 513 cubic elements 
and compounds, and 156 cubic alloys. 



246 



APPLIED X-RAYS 





!-J-?** : g ^~ 1 


a 




^ ^ ^ ^ g . M .Q * 


&* 




~" ~ *" 1 ! ^ ^ T3 ^ S 


.-^ CQ 


1 


*?riS^ ^1 rf| ? 


5 * 


n O 


u . S S ^' ^ ^- N o N 


.. 


3 


fe ^J Q , N -H" OH <|> ^ Q 


fc 


3 


2 ^ r ffi '~ V ^5 c 


.. B 


I 


& b ^- ^ . - ^ a ^ 


^ ^ S 


S 


-bOf Oc ^^h2^ H ^ .QT^ 1 ^ 


X .; 'd 




rt*""^"* * -? (^^^ffl^Sci 


.0 ^ 


;> 




o ^ ' _r 


^ 


X " ^. H X jB ~ . jS , '- 


o - S 


-i 
< 


^S^Bggg" g?lg5 


* ^ 


3 






-* 


iO 


>O 'O 


n 

5 


oS cs o o 


O'-iOOscoO'-'TticOcbOiO'OcO 




M 2 fM CO CO CO O 


CO >O CO h- CO 'O ^f Oi O ^ CO >O (M CO jfj 


c CQ 


CO r-i ^ 


"- 1 ft) cO 




10 ^ II 'I H II 


II II II II II II II II II II II II II II 10 


3 CQ 


e w e o 


eocowoO'oQ^o^c^ 


H *"O 

j d 


v -v-' ^-^ 


^^ ^^ ^^ w^ ^^ ^^ ^~s 


3 3 






5 a 






2 a 






j O . 

< O J J 

2 >> s a 

N 5 3 ^ 


- + 


A 

c 

CO 'O CN| CO <N (N^ M3 

i ( ^ 


^ X o 

s C 




^ 


' 3 ga 




* 


3 h-J ft 


"% *^ C T3 






O O ^ <J ^ 


vj o Q Q Q Q vj 


3 CO S) 

3 






3 



^ SJoqqSlOU ^ 


^IM F 


3 

* o> 


uio^^^a 


po^ojL ^ 1 


H 03 

-I j 

-4 


3 ^ oj 03 

1 . 8 II 1 ! 


oj 13 TS "3 g g^^^ 

C C B (3 g Smt^O 
O O O O g. 2, 08 ^3 JO 
bC &C bC M 3* *r p. fl 

SSsS--2| 


< 


& Q ffi W 


ffl W W ffi H HccBo^ 


^ 






3 73 




^ 


J a 




- i 2 


teal compoui 


OJ i i 

1 S B 

S 

^ fa C 

2 > d 


a a I is 

1 1 I *- 9 *, 

3 S ^ ^ 73 OJ -S 


a 


O a? so 

5? a s s 5 


u. u. ^^ J2 <5 ^ - 

5 5 5 g^ o 

l_ t-, y S^KH ^ T3 

2 (3^A, S 


a 






H 


ci co' -* 10 


O rH <N CO 




QQ CQ CQ CQ Cq 


QqcqoqoqcqcQCqflQ 



RESULTS OF CRYSTAL ANALYSIS 



247 





w > p 
\; J 1 JQ ^ 






N <5 ^ o DO 






o" 4 5 ^ 






n - -^ fe ^ 
U ^ H ^r .?g 






^ CO * ^ ^ ^ 


w 


s 

1 


9o ^^ ^Ir 

tfi . & fc 3 ^ ^ 

^ eg ^ O ^> 


O 


* O 


^ X " O fl * t 







o": ^8 


6 




73 T J3 ^ ^' k ^ CO 

o^p,^ P^C^ 6^- o 





' 


--q^a q^^ 2?^ o 


cf ^ 






PQ ^ 


J 


J ^ fi rf , w -< t V " ^ VT ^ 9 


8 M ^ 


2 


rf 9 1 c .7 q ^ ^ ^ g | ^ 


o" ^' 


% 



B^85S ^^^ 


w ^ << 


j 






J 






i 


Tfl >OO5t^CO<MOO'-iCOOOCOO 


b CO iM t t>- CO CO 

rf OiM'OCOOOCO COCO 


3 05 


10 ^ro^^fNcooi^cocoe^Tt^oio 


LO^iOoO-tf^COcO^ T*<N 


^ N 

_j "3^ O 


^ CO 'N rH 


^H rH 


H ^J 


II .c ..- ^ II II II II II II II II II II II 


II t, II II II II II II 2 II II 


$ $ 


2^ iyi/ 2^ 2^ 2^Z 2. 


vi ^vW 2^/ 2^ 2^ 


% & 


< 

v ^-V 


Q. 

^v< 


D ^ 






H $ 






> fl n 






3 3 g J 






y* s pQ O 

S 2 s a 


Tjt ^^<N<N^^(N CO 


00 ^ <N <N CN 


Q pT ^ v_ 

S x ^ 






q O 








*to 


9 


4 CU ft 

S E & ! 


"< 3 Q 

o EH^OQQOQ * 


"a ** 155 2 * 

Q g ^ Q 
to 


C< 


>_l 

CP 




D 




13 


1 1 

ts 


1111 1 

M M 2, ? s, a 


1 ill 
o o J o 


3 H-) 


000^ g S rt rf 


.2 S S S 


J 


a .s! 1 xs^? a 






3 3S34) cy cucjcu <D 
O OOOH EH W"^W W 


90 o> -fl cy 
O W H H 


H 

H 
H 

" 






4 

a 


1 


6 -Tf 

^ 9 


Typical com 


s" 1 1 1 i So 

I 1 14 I , I 1 
1 6 ^ 3 2 

fe ^OO-t1O^ O* 


1 ? 

i i 

>jj 

cj S 00 W 


1 






H 


r-i S'' M ' r * 1l0t0t>> 


O r-4 (N CO 




O OOOOOOO O 


O O O O O 



248 



APPLIED X-RAYS 







1 








c 








9, A 

\t~ * 








n C 




fa O 




O j 




*H ^ 




H 




o ^ 







e 

JO 


c 

O 

s 




-o 3 
O X ^ 


O 






M *O 




2 w '""' 
S fc =" 




c a 




s*1 




1 1 C t' ^ 




5 j? ^ 




t-i * ^3 O O 

* PQ W o CM oj e ' 




S r* 1 C 
C fa fcsj 




^ i I 1 ^ i o s J 




<N 00 00 CO 








O 00 10 t^ t^ CO 10 O >0 

r-< i* O 00 O CM CO ^ CO 




IS S S S 2 S ~ 




'O 00 jyj CO Tf* 'O ^t* CO 't* O 1( ^ 




lOOOCO^ ^ 00 '^ ^^S 


(3 


O CO 


e 


rH r-l CM ^ 




II II ,, II II II II II II II co 


QQ 
g 


10 00 CM II II II II II H II 






CO 








1 




,_, 














JO 

a a 


Tf 00 ^ "^ CM rH 


s 

O 

u 


^ 00 00 CJ <M rH CO 


X o 








2 g- 


^. 4) " -" fi in 


1 I 


,, 


08 o 


s -^ c -s %, -^ s 








Q O S, Q H^ U- Cj 

^CD_ 




&i E^ E^ C) Q q o 




3 




"M 
S -3 


2 

"S 

i-j 


1 1 1 c, | 

o a a -s -2 

8 1 2 ff a a 




000-^1 I c 

^2^3 S c?^ 




S ^ ^3 oo 








WO H H P4 P4 




OOOH cc<^; wd 


c 








o 
ft 






o 




CO 




W '"' 


2 


fa 




ffl 'I 


"3 







oT | 


o 


-< 




c ^ 


a 






-^ 2 Is 


H 


^ O O fa ^ O 




jj -? ^ 9, ^2 q q 

5 r^ fl M ^ r^ JQ 

XOww OO h'l r fi 


1 


': 




_; ^ ^ ^ w ^ 




O O O O 




QQQQ QQ QC) 



THE RESULTS OF CRYSTAL ANALYSIS 



249 









5 





4 




1 5 


Js 


-0 




X li 


^ 


s 




X 








00 ^ O 




^ 




< V X 




1 




X P 




c 








N 


C1 


^ ^ 




W) 




J? OS ., 






s 


^ > 




^5 


-- 


U ,7 ^ 




- 


^ 






5 03 


^ 


d 55 




U X 


f 


W X W 






s 








H 
Tj 






CO O 


(/; 


t- <M t^. i-i C-l Oi 




O5 00 




CO Oi ' <O <X> t-~ r-< 




oo oo ! 


Jj 


Q Oi 00 'O CO ?0 >O 


o 






CO 




II II oo oo 


rt 


,o 11 II H H II II 




o a 


^ 


s^w viv^ ivw 






2 








"S 








S 




J3 7$ 

s a 


TO >o >o 


J-H 
x; 
H 


^ 00 rH -^ rH 


3 ^ 








X o 




C3 








i 




S * 


- 'H 


p 


- T3 ^ 


a 2 
rn to 


S ^ 


H 


^ ^ C) t* 




<uSfl <^Ss ^ fl 


.ti 




o 


^i-slfS-BjII 

rQflj H^CP rjJSCC 

o*-iajCo^ajH^^4 

6^ ^^^^3 - >> 


cc 


oS 

e "o 
o X o o 


HH 


|! a!|I sl||l 


1 


o 2? " S 1 2* 

^ 03 C 03 C3 

^ 43 ^0 43 43 
H P4 H H 


H3 




\> 


CO 


G 






4) 


3 






fe 


g 









O 






oT 


O 






B 


s, 


* 1 3& 

N ^2 5 




! 1 51 i 1 




1 o do 




3 ^ M 


0) 

a 








EH 


oo oo 8 S 




^ JU S Sj CO 




Q Q Q Q 




ft, fe, t, fe, fe, 



250 



APPLIED X-RAYS 



I 






a? d 

1 

p cj 



0! ^ 

O 

* I 



CQ 

H 







|d 










c o 










CO M ^J 










* - 

^Ofe 








p 










03 


$2% 








'* 


o - ^ 









n 


W O fa 









O 

o 

g 

fl 

^ 6 

aS 


N -ss 

625 W 

^ fa" 
9 ^ ^ <5 S 
? 6 o w 


i, Pb)(NO) 2 






N < 


^ 6 3 5 . j 


a 






M . 


'So PH O O 








<^ r fe 


O ^ - 08 M 


cc 






08 08 
O O 


o ^ <5 o o a 

x fe w ^ ^ 


s 








"tf (M 






e 


CD "* 

CO 


"' s s 


B 1 ^ 
00 


O5 C5 




co H 


II II co o co 


CO t"- 


II II 




v^ 


rO 

-v ' 




V^v^ 


<jj J2 

"a a 


c, * *- 


V p. 


5 ^ &d 35 1 


O 3 


li 


8 


2 

00 


1 


1 


^H 


2 








2 




O 




o 


G 


33 








O 


>-3 


a 


a .262 


1 .s 


W) 




o 


O JD O 42 












43 3 









PS tf O 


tf O 


W 


nfl 






6 




G 
3 




o 





x^ 


Typical compo 


6 
o 

6 
1 

|S 
"a3 


8 OH 
6 %v 

fa <o 

S w .-a 
2 -a E 

g | | 


jtf 

3 

^"'S 

11 

"S 43 


eryl, Be 3 Al 2 (SiO 




O 


< x a CM 


Q P^ 


PQ 


1 










^ 


to 


<N 00 ^ O 

to to to to 


tt Ch 


ro 
to 





6 




G 




6 




o 




a 




f- 2 




o 




- CQ O 


CM 

CM 


O5 O5 00 -^ -l "t> O5 


CO 


co co oo 10 r> co 'O 


e 
^-^ 


II II II II II II II 


, * 




^ ^ ^ 




^ N C) 




a 




o c? fl 




3 3 a 




a a 




o o is 




-G 43 




W PH EH 




O 




N 




" j? cT 








CO C/2 o 




PQ N 




i <N CO 




Hj llj ftj 



THE RESULTS OF CRYSTAL ANALYSIS 



251 





& o 








3 5^1-2 


4 




- , >d3 








^ a B m B 


B 




S N " ^ 








5 -5 jj ^ "o 


o 




k> o j3 








o P ^ 1 ^ 


O 




^ 05 ^ 








^ fa 






o 5 3 fl - 

3 * . - N 


o 






<3 ""* ""^ "* 


2? 



1 

6 


XaIO4, KIO 4 (Ca, Ba, Pb) ( 
Pb)(WO 4 ) 
Including all spinels, FesCh, 
K 2 Cd(CX) 4 , K 2 Hg(CX) 4 , et( 
(Mg, Fe) 2 Si0 4 ; (Mg, Ca)SiO- 
Li 2 MoO 4 , Li 2 WO4, Be 2 SiO4< 
Li 2 BeF4 


KzPtCh, K 2 PdCl4, (XH 4 ) 2 Pd 


Ag 3 PO 4 , Ag 3 AsO4 
KH 2 PO 4 , (XH 4 )H 2 PO 4 


q 

(N 

d 

o 

If 


5 |^ " 
w w js ^ T 5 

B <o j^ >P j/5 


(K, Rb, (XH 4 )) 2 Pt(SCX) 6 

Ni(XH 3 ) 6 (XOa) 2 , Zn(BrO 3 ) 2 .6 
(XH 4 ) 3 (AlFe, FeFe, MoO 

[I, (C104) 3 ] 




^ oo 

<N CO 


"- O OJ r-t 


CO > 

^ Oi 


IQ 00 

^ 00 




cs 




' ^ <y> oo 


>O 00 CO ^ 


05 ^ ^ 


CO ^ l>> 


,-H CO 


t^ co o 


e 


O CO 




O5 


00 




CO ^ 05 ^ 




II H oo h- 


II II II II 


U7 II II 


r-l H II 


(N O 


>o II II o oo 




O VJ 


e o e u 


C3 <J 


^ Q 




v-^ 


o.g 


^ oo ^ co 


- 




00 01 


. .. 


- - -- 


|| 


^ 2 ". 


a 


s 


o ^ 




M " * 


&& 


<3 ^0 


C q 


^ 


O 


^ 00 


Q Q ^^ 


Lattice 


2 

1 . il 


1! 


"ea 

c 
o 


0] 


o 

'. 


1 IS 
o 

S o3 .2 2 




A 00 


K i3 

CP as 


g -g 


"i "" 


Is 'C " 


X XI X) 




HO tf PH 


W H 


H 


H 


HO 


tf B 










rt 


(M 




15 








6 


. 




Typical compou 


CaWO 4 
Spinel, Al 2 MgO4 

Ohvme, Mg 2 SiO 4 
Phenacite, BezSiO 


6 d 

P 


Ag 3 P0 4 
KH 2 PO 4 


Granite, Al>Ca 3 (Si 
K 2 CuCl 4 .2H 2 


I 9 
a 8 

- 5"d 

S O 3 * 
M S^ 

5 o w 


K 2 Sn(OH) 6 

K 2 Pt(SCX) 6 

Ni(NH 3 )e(XOs)* 
(NH4) 7 A1F 6 


H 


rH CN CO 


rji IO 

r-t i-l 


(N ^ 


CO T* 


CM T-H T-H 
T*< iO cO 


CN CO ^ -H 
CO CO CO !> 




Ju aj a; a; 


a: aj 


^ ^ 


tci as 


ft: as a: 


a: aj a: aj 



252 APPLIED X-RAYS 

the number of atoms in the molecule is of great importance; 
the size and shape of atoms and groups or the electron configura- 
tions would surely be a determining factor; the type of forces 
which hold the units in position in space must be considered. 
It is the province of the new science of crystal chemistry to take 
the great mass of experimental data which show how crystals are 
built and try by means of classification and correlation to general- 
ize and answer the question why a compound assumes the lattice 
structure which it does. What is it that causes simple binary 
compounds AB to have about 13 ways of crystallizing? What 
determines the fact that some of the dioxides crystallize like cal- 
cium fluoride and others like rutile? These and other questions 
which naturally arise are the subject of the next chapter on 
crystal chemistry. 

Some Practical X-ray Researches on Inorganic Substances. 
In order to identify a substance as it exists in a particular solid 
crystalline form, either alone or in mixtures, the chemist, mineral- 
ogist, ceramist, jeweler, or manufacturer must have recourse to 
optical methods or to x-ray diffraction results. In many 
problems the latter alone can be applied to practical problems. 
Several patents and patent litigations have been based solely 
and convincingly on x-ray results. It is possible here to enumer- 
ate only a few of the general problems which have been success- 
fully attacked. By way of suggesting further applications it is 
necessary to point out only that any problem of qualitative or 
even quantitative analytical identification of a substance in 
terms of the actual formula and crystalline forms, purity, 
chemical change, etc., is a potential x-ray investigation, 
entirely apart from the scientific value of unique space-group 
determinations. 

1. Qualitative Separations. The identity of the sulfides 
in the tin subgroup and of such compounds as HgNH 2 Cl, 
the invariable presence of crystalline BiOCl in Bi 2 S 3 , and 
numerous other similar problems have been investigated. A 
vast field for diffraction research still lies in classical 
qualitative analysis. 

2. Complex Formation. Many examples might be cited of 
studies of suspected complexes formed by inorganic compounds. 
For example, the compound dimethyl barium carbonate which is 
definitely reported in the literature is found to produce a dif- 
fraction pattern identical with that of pure barium carbonate. 



THE RESULTS OF CRYSTAL ANALYSIS 253 

Purple of Cassius is found to be a colloidal mixture, rather than a 
compound. 

3. True and False Hydrates. A true hydrate possesses a 
crystal lattice just as definite and characteristic as any pure 
anhydrous compound. Many so-called hydrates with stoichio- 
metric composition give patterns which indicate appropriate 
mixtures of lower and higher hydrates. Again some unsuspected 
cases of hydrate formation, such as the pentahydrate of sodium 
silicate, produce patterns proving their true identity. 

4. Unsuspected Chemical Reactions. Among many which 
might be cited are: formation of barium carbide catalytically 




FIG. 125. Reflection spectrograms from lead storage-battery plates (Cu-Ka 
radiation) showing lines for lead oxides, sulfate, etc. a, positive; 7>, negative. 

from barium oxide and carbon in thermally emitting electrodes 
at temperatures far below those predicted ; formation of mercurous 
chloride by absorption of mercuric chloride on charcoal; reduction 
of zinc oxide in methanol catalysts and formation of brass with 
copper; and identification of the composition and chemical 
charges in lead storage-battery plates as related to performance. 
Reflection patterns with copper radiation for used positive and 
negative battery plates (Fig. 125) show clearly the types of lead 
oxides, presence of lead sulfate, grain size, addition agents, etc. 
5. Inclusions in Metals. Proof of existence and analysis of 
nature are possible without dissolving or destroying a metal 
specimen. 



254 



APPLIED X-RAYS 



6. Mineralogy. This has become one of the greatest inor- 
ganic applications of diffraction analysis, particularly since the 
great steps forward in interpretation of silicate structures. An 
entire monograph upon this subject could be written, since 
possibly two hundred minerals have been already uniquely 
analyzed. The interest lies not only in identification and classi- 
fication even to evaluation of commercial ores, as a great aid to 
optical mineralogy, but to chemical questions of variations in 
composition, and in geological questions of origin. The great 
library of standard diffraction patterns for all minerals made by 
Professor Winchell at the University of Wisconsin is an example. 
Aside from unique analyses of crystal structures of asbestos 
minerals, mentioned in connection with silicates in this chapter, 
Clark and Anderson 1 made a study of eighty specimens from 
mines all over the world, and found the diffraction patterns often 
so distinctive as to indicate the origin. The effects of acid and 
heat treatment were also characteristically depicted in patterns. 
Clark and Ally 2 found for five chrome ores from different localities, 
that the length of the edge of the unit cube ranged from 8.283 to 
8.179, varying inversely with the A1 2 3 content of the ore. The 
theoretical densities also were calculated from the " average " 
molecular weights and x-ray data. 

The spinels both natural and synthesized have been the sub- 
ject of several investigations as regards identification and for the 
bearing on generalizations of crystal chemistry. The following 
data on these cubic crystals were obtained in precision measure- 
ments on carefully synthesized spinels, by Clark, Ally, and 
Badger. 3 

TABLE XXIX. LATTICE DIMENSIONS (A.U.) OF SYNTHETIC SPINELS 



Element 


Aliitninatcs 


Chromites 


Forritos 


Zn 
M 


8 062 OOi 
8 086 4- 003 


8 296 002 
8 305 + 001 


8 423 001 
8 366 f 001 


Fe. ... 
Mn ... 


8 119 002 
8 271 002 


8 344 003 
8 436 001 


8 374 003 
8 457 002 



The analysis of silicate minerals, which presented greatest 
difficulties until the rational assumption of coordination structures 

1 Ind. Eng. Chem., 21, 924 (1929). 

2 Am. Mineralogist, 17, 66 (1932). 

3 Am. J. Sci. t 22, 539 (1931). 



THE RESULT 8 OF CRYSTAL ANALYSIS 255 

was introduced, will be discussed in the next chapters. For 
specific results reference may be made to such excellent sum- 
maries as that of W. L. Bragg, 1 Schiebold on feldspars, 2 and 
numerous papers published in the past two years. 

An excellent mineralogical research combining x-ray, chemical, 
and microscopic methods has been conducted recently on phos- 
phate rock and apatite-like substances. 3 American continental 
phosphate rock consists of submicrocrystalline fluorapatite, 
Cai F2 (POOe, with excess of fluorine and some sodium. The 
compounds Ca 10 (OH) 2 (PO 4 )e, Ca 9 (H 2 0) 2 (PO 4 )c, and Ca 10 CO 3 
(POO e, H 2 O, all of which are identified in natural or artificial 
mixtures by means of diffraction patterns, form extensive series 
of solid solutions with fluorapatite some members of which occur 
in geologically recent rocks. Tricalcium phosphate hydrate, 
Ca 9 (H 2 0)2 (POO e, gives a pattern like apatite, disappearing 
after heating at 900 C.; it comprises phosphate rock from 
Curacao while hydroxy fluorapatite, Cai (F, OH) 2 (POO 9 is 
found native in Pacific islands. 

7. Bone. In connection with the research on phosphate rock 
just described it was proved that animal bone free from organic 
matter is a carbonate apatite, Cai C03(PO4)6.H 2 0, isomorphous 
with fluorapatite. Oxyapatite, Cai 0(P006, is formed by 
heating bone to constant weight at 900 C. Upon fossilization 
the carbonate group and the water molecules are replaced by 
fluorine. 

8. Zeolites, Permutites, Ultramarines, Etc. The permutites, or 
zeolitic silicates, are a group of remarkable alumino-silicates in 
which alkali atoms may be exchanged with other metallic atoms. 
They are the familiar agents used in water softeners, as hydraulic 
agents accelerating the setting of Portland cement, and as sub- 
stances which can take up or lose water without affecting the 
solid form in any apparent manner. The ultramarines, a group 
of famous pigments, are closely related to the permutites, con- 
taining sulfur in addition, and having similar atom-replaceable 
properties. The extraordinary properties make the problem of 
structure especially interesting and valuable. X-ray researches 

1 Faraday Soc. Mon., Crystal Structural and Chemical Constitution, 
p. 291 (1929). 

2 Ibid., p. 316. 

3 HENDRICKS, HILL, JACOB, and JEFFERSON, Ind. Eng. Chem., 23, 1413 
(1931). 



256 APPLIED X-RAYS 

by Jaeger 1 on permutites, minerals sodalite, nosean, garnet, etc., 
and ultramarines, and in the writer's laboratory on a whole 
series of natural and synthetic cement accelerating agents have 
thrown interesting light on the problem. Ultramarines give 
powder diffraction patterns identical with those of hauyne or 
nosean, (Naio A1 6 Si 6 O 3 2 S 2 ), apparently for a cubic lattice, a = 
9.11 A.U. One fact immediately becomes apparent, namely, 
that it is impossible to attribute to any appreciable number of the 
atoms in the molecule any definite fixed place in the unit cell. 
Sodium, aluminum, and sulfur atoms are " wandering " constit- 
uents, just as are the water molecules in zeolites. The sodium 
ions are situated in a cavity, 2.66 A.U. between six oxygen 
atoms, and thus have room to move freely in it and be easily 
replaced by Li, K, Ag, Tl and NH 4 , Zn, Mn, Ca, etc., ions with 
smaller diameters, or even larger ions, when the substance is 
brought into contact with solutions containing other ions. In 
the middle of the unit crystal cell is a large cavity with an edge 
length of 3.7 A.U. in which the wandering constituents may easily 
move, and into which water and solutions may easily pass. The 
walls of these cavities are electrically charged. This fact may 
help to fix electrically charged ions or water molecules. It is 
clearly evident that x-ray research has been necessary in order 
to clear up the puzzle of these peculiar substances although there 
is not yet agreement among all x-ray investigators. It is pos- 
sible that these structures account for the selective absorbent 
power of the soil, containing, as it does, permutites, and to the 
remarkable stimulating power of traces of zinc and manganese 
on plant growth, as well as the predominant part of calcium. 

9. Gems and Pearls. Numerous applications of diffraction 
analysis have been made to the identification and structure and 
perfection of natural and synthetic gems, particularly with Laue 
patterns. The distinction between a fine pearl and one cultivated 
with a mother-of-pearl nucleus is easily made without injury to the 
specimen from a diffraction pattern, since the typically crystalline 
center is disclosed at once. 

10. Cement. The analysis of the constitution and structure of 
cement is a problem of great importance and difficulty. Funda- 
mental x-ray studies beginning with structures of single pure 
constituents have been under way for several years at the Bureau 
of Standards and elsewhere. In a recent investigation by Brown- 

1 Ibid., p. 320. 



THE RESULTS OF CRYSTAL ANALYSIS 257 

miller and Bogue 1 28 samples were examined and the results found 
to agree with chemical and microscopical data; tricalcium 
silicate and 0-dicalcium silicate are the most abundant constitu- 
ents, while calcium oxide up to 2^ per cent is seldom found. 
Much remains to be done on setting, hydration, effects of addi- 
tion agents, and aging. 

11. Lime. The plasticity of lime is directly related to the 
appearances of additional diffraction lines, corresponding to 
Ca(OH) 2 and CaC0 3 in CaO, and to unchanged CaCO 3 in 
Ca(OH) 2 . PJvidently calcium carbonate may coat some of the 
grains of oxide and slow down the rate of hydration, thus decreas- 
ing plasticity. 

12. Ceramics. There are so many practical applications of the 
diffraction method to ceramic materials that it is not surprising 
that fruitful results have been obtained already. Merely as an 
indication of these results and of possibilities for further useful- 
ness, there will be cited a few examples of researches carried out 
in the x-ray laboratory at the University of Illinois. 

In an investigation of the effect of heat on china clays, 2 it was 
found that the chief crystalline constituent of the clay was 
kaolinite, whose lattice was destroyed upon dehydration. 
Mullite was formed at 950 C., and in Georgia clay free alumina 
was present from 950 to 1100 C. and cristobalite at temperatures 
above 1200 C. 

The x-ray method is of value in the detection of the various 
forms of silica in silica refractories, as found in a study of the zonal 
structure of silica brick from the roof of a basic open-hearth 
furnace. 3 After use to the point of fusion in an open-hearth 
furnace, the silica brick still retains quartz formation with increas- 
ing tendency towards cristobalite the higher the temperature. 

The identity of crystalline compounds present in sheet-steel 
enamels as opacifiers 4 is easily determined. SnO2 is the primary 
opacifying compound when it is used in any mixture; Sb2C>5 when 
commercial Sb 2 O 3 or sodium antimonate are the primary agents; 
sodium silicofluoride, fluorspar, and cryolite aid in the develop- 
ment of opacity when used with the above compounds, although 
no diffraction lines for them appear. When used alone, however, 

1 Concrete, 38, 85, 89 (1931). 

2 McVAY and THOMPSON, J. Am. Ceram. Soc., 11, 829 (1928). 

3 CLARK and ANDERSON, Ind. Eng. Chern., 21, 781 (1929). 

4 ANDREWS, CLARK, and ALEXANDER, J. Am. Ceram. Soc., 14, 634 (1931). 



258 APPLIED X-RAYS 

they produce opacity, NaF from cryolite and CaF 2 from fluorspar. 
Interesting cases of solubility, dissociation, and oxidation are 
thus involved in these. 

The problem of the constitution and structure of glasses will be 
considered in later chapters dealing with grain size, colloids, and 
liquids. 



CHAPTER XIV 

INORGANIC CRYSTAL CHEMISTRY: FUNDAMENTAL 
GENERALIZATIONS FROM EXPERIMENTAL DATA 

The complexities which confront the crystal analyst when 
he attempts to generalize on the modes of crystal construction 
have been amply demonstrated by the data of the preceding 
chapter. In spite of the immensity of the field, however, a 
brilliant chapter in science is being written by the Braggs, Fajans, 
Pauling, Bernal, and particularly Goldschmidt. From their 
work it is possible to advance a theory of why crystals are built 
as they are, which not only explains at least the simpler types of 
structures already known serniquantitatively but enables even 
the prediction of new structures and properties. Five years 
ago when the first edition of this book appeared no chapter with 
the above heading could have been written. The concepts of the 
new wave mechanics have assisted materially in these develop- 
ments, and great further progress may be expected of this infant 
branch of chemistry. The fundamental unit to be considered in 
these structural inquiries is, of course, the atom, which may be 
now pictured roughly (see page 79) as a nucleus surrounded by 
shells of diffuse negative electricity, which is denser the nearer the 
nucleus. Each shell is thought of as composed of a set of Bohr 
orbits on the older theory. Thus the atom has a size, and since it 
certainly is not rigid it must have a certain degree of compressi- 
bility and deformability. It has been amply demonstrated many 
times that the chemical and crystallographic properties of atoms 
depend on the size and particularly on the condition of the outer 
shell of electrons. Each ion or atom in a compound must be 
considered as forming a lattice of its own, the interpenetration of 
the various lattices resulting in the structure of the compound. 

1. Types of Crystals in Terms of Bonding Forces. A careful 
survey of all crystal-structure data leads to the conclusion that 
all crystalline substances may be classed under four principal 
types according to the types of combination of atoms into mole- 
cules and solid crystals : ionic or hetero polar, homopolar (sharing 

259 



260 



APPLIED X-RAYS 







6 




Typical crystals 




* o d w 


Ohvine, Mg2SiO4 
Cyamte, AhSiOs 
Garnet.R 11 ^ 111 ^! 
Spinel, Al 2 MgO 4 
Corundum, Al2Oa 


Diamond, C 
Zinc Blende, ZnS 
Wurtzite, ZnS 
Carborundum, CS 




i | g -i 


. 2 ^ s 


T3 1 


aJ 


* c 


i^ ; o 


M """ 




03 CJ *" 


^ u d 


rt m 3 


C 






.^ <n c8 




^ c -. "** "*"* of 


<S Q 


d g 


O 


~ 55 i> o ^ >> 


^ 4> k. ^ 






L *8 ^ d _< S3 c3 
















fc .S i <u -. 'o 


> ~~ "* 






.fl M ' TJ 


A W) - m -T3 &C 


, 43 _0 Q 


S'rt 
E 


-C " o 
T3 

"** - = 3 . 


.^f C ^ ^ ^ ' 


^ "S NO 

d * - S-3 

j| >- d-S 


S, 


^7 d S ? o 


> * o ^ 


3 , S ft a| 


1 H 

o. 


ft, ft - - 


S ft W) <** O*O 


&?1 > 11 










tn 


X + t *- 


i *- <u i M i c 


1 1 OQ ** 4j 


n 








" -3 


J3 TJ 53 




oj m K -5 'ea " 


1 * 

6 1 

W 


5 S S 

!* 5 a 


" s * 2 S ! * 


o3 "^ d o ^ 'O "o 




^ c: ^ 3 

d >H 'O 


S 'S ^ J 

d 2 sit 


o d * *> 3 


eS 


08 2 1 " 


_ -^ g "3 


> J (JO ^ o3 t3 


O 


O. "o, ** S 


o 3 2 wi 2 " 


S o,.fi ^ a o 

g ^ u ^ 




8 5: S,2 


d ^-ft^ TJ^ ^ 


^ 


d 


^^^o ^^^o J| 


^ i 


5-4-a u 


Is 


"3 d J ^"8 0-^^^ 


7^ o 1 


^2 - -5 






K * d 




*- 


5^ S ftg 3 MO^ 


-^^ * 2 


os 






eJ d ** 




1 


| i 5 c -s 5 a 


jy <jj 


tSJ"i 












rj 


15 i- 


& -^ 


OQ 


1 


C O OJ 

.2 f "5 


^g - 


3 


"S . 


, g 


- && i 


OQ 


o 2 


,_, d a* 
S "1 


^> 00 

- M - 




"a 




d 3 _j ^ 







],S5l 


|-1 


& 








3 






S 


1 




5 


1 


O 


a 





s 

o 




o 


02 


W 



INORGANIC CRYSTAL CHEMISTRY 



261 



^ 


es 

- 

s 
u 

q j 

S S 



-2 
Q^ 

3 


o 


-S c. 

&3 




|| 
ftG 1 






00 

cT 

."2 

o> 

s 


ahlertz, R u 2 SbS 3 


1 




-< 


S PM 


U 


o 




O ^ 


tS3 




^ 


u. 


^ 




ery soft, hard- 
ness increasing 


\\ith polarity of 
molecules 


o3 
S 1 

ll 


leaving readily 
in layers 


03 ^3 
f 

ll 


IH G 

4) TJ 
O 03 


W 
*& 

|s 
ii 


tic but yield 
by glide plane 
slipping when 
overstressed 


loderately 




-+j 

1 


Properties a 
mixture of 


O 
O ft 


K* 






u 




""' 






?* t 








"G 5 

Ip 

Z5 ^ 
"QJ 4) 


neutral atoms, 
rises with heav- 


|S 

| 
2 03 


molecules 
anous, similar 
to both molec- 


ular and homo- 
polar 


loderate to 
very high melt- 


51 

G 0" 

""" 
ft 

,0^ 

c 9 


interval 


a 
a> 


to vaporize or 


" a 

|: 

O bC 


peratures 


^ 






K* 










H 








Qj 0) 


3 | 

3 G 


o3 1> 
^ 1 


s s 

all 


o 
o 


2 ^ 
2 3 


^ 

<D C 

s. n 


^ -i J2 2 

<u o 'O G 

i: 02 C 2 

+* 03 

o f 


0) 03 

**^ o 





a i 
s 

o 




Insulators 
cept whe 


polar; s 
in non-io 


(molec 
solvents 


m _d 

C 3 ^O 
qi O ^Q 

> o3 


T3 

G 

OS ^ 

11 


Conduc 
c o n d 


tivity ini 
proporti 


u G .G W 

,0 " M 4> 

fill 


absorb 
electrons 
Medium \ 


conduc 


ll 


sition 


G a 


** G 


GO ^ 






o -^ 


> a 






^ 


G 


i 




Transpare 
optical prc 


erties due 
molecules a 


2 cr 

Is 


3 

eg o 

!"2 






w T5 

0" <u 

O *" 


with selecti 
reflection in 


1 


Opaque meta 


ft 
O 


M 03 
"^ > 

fl 


3 


~^ nQ 


^ G 

r s 


73 
r2 

3 


OQ O 


a 


' G 
03 o 


i -o 

DO G 




o 


03 


i M 




^ ! 




ft 

Ui 
03 


03 


g> 


o .-. 

*H 


a 


1 


O) 
Ui 


O 
ft 


^1 




(U 


OJ J3 


3 


*** O. 


o g ^ 




S o 




G 





03 J3 




S 

j! 


ll 


J 

"o 

a 


c3 O 


G W 

h- < 


111 


M rt 


P "" 
^ * 


1 


M 





11 




<n ^ 


S 




N 2? 




G 03 






"d 


O) 


T3 




O ^ 
OS 

SJi 


molecul 




i* 

>> G 


oo 

G 

O 

i 


M 
- G 






itoms ar 


*8 


03 
& 

2 o 






^ 




Sb 


c 


r ^ 






, 


Q 






II 


03 
1 




G 

O M 

02 ~ 


_rt 
ft 


(E -Q 

s 






1 


1 


m o3 




03 










O 






s 








o 
























O> 






V 


















O 

^f. 






3 




^ 






o> 









262 APPLIED X-RAYS 

of electron pairs), molecular, and metallic. This does not mean 
to say that the division lines are clear-cut, for many substances 
may be thought of as in the transition zone between two or more 
types. Bernal has therefore added three of the most important 
intermediate classes: silicates, layer lattices, and metalloids. 
The fundamental classification and properties have been assem- 
bled by Bernal 1 as shown in Table XXX. 

2. Important Concepts and Definitions in Classification of 
Crystals, a. Ionic or Heteropolar Combination. There remains 
little doubt that in a large number of crystals the atoms are really 
ions in the familiar chemical sense and that they are held together 
in space with requisite rigidity by electrostatic forces of attraction 
between positively and negatively charged particles, inversely 
as the square of the distance. When the outer electron shells of 
+ and ions are in close proximity, however, a repulsion sets in 
inversely at about the ninth power of the distance between them. 
Thus in a crystal like rock salt a condition is easily reached like 

Na Cl= Na+ 

Na+Cl-^Na+Cl-^Cl-Na+Cl- - 
Cl-Na+ Na+Cl-Na+ 
Cl-Na+Cl- 

and so on, till the whole single crystal is thus constructed. Thus 
sodium chloride diffracts x-rays in a way which leads to the 
assignment of a structure in which each sodium ion is not bound 
to a single chlorine ion as in the simple chemical molecule (vapor 
state) but exerts its attraction on six equidistant chlorine neigh- 
bors, and each chlorine ion is surrounded by six sodium ions. 
Thus each ion tends to surround itself with as many oppositely 
charged ions as possible. In the electrically neutral crystal 
there are not pairs of sodium and chlorine atoms or ions, but 
simply an equal number of oppositely charged ions. In a sense, 
the chemical molecule seems to be lost sight of and proper for- 
mulas would seem to be Na 6 Cl and NaCl 6 . However, an analogy 
cited by Sir William Bragg serves to clarify the situation. 
Several couples of men and women go in to dinner and are seated 
at a circular table. Each man now has a lady on either side and 
the identity of the original couple is obscured though by no 
means destroyed on account of the seating arrangement. 
1 Encylopcdia Britannica, 14th ed., Vol. 23, p. 857. 




INORGANIC CRYSTAL CHEMISTRY 263 

All physical and chemical properties, all knowledge concerning 
the scattering of x-rays since the original interpretations by Debye 
of experiments on lithium fluoride, all calculations from intensity 
data on electron distribution (see pages 100 and 211), and all 
mechanical data on breaking strengths of perfect crystals 1 are in 
agreement that the lattice units in solid salts are ions and that the 
bonding forces are electrostatic. 

b. Polarization. It is certain that ions are of very different 
sizes and it follows that some curious effects might be obtained by 
combining, for example, a small highly charged positive ion with 
a larger diffuse negative ion such as S~. This ion would be not 
only attracted but actually distorted, since the negative shell 
would be pulled toward the small positive ion and the nucleus 
repelled. This phenomenon which has been demonstrated in 
numerous ways particularly by Fajans is called polarization. 
Increasing polarization gradually merges with homopolar binding. 

c. Homopolar Combination. In terms of modern theories of 
valence this means that atoms are held together by sharing 
electrons, usually in pairs called covalences. The stable dia- 
tomic molecules such as H 2 , O 2 , N 2 , etc., and H 2 O, CO 2 are built 
up in this fashion in order to complete the various quantum 
electron shells. In organic molecules the carbon atoms form 
long chains by homopolar bonds. The best example is in dia- 
mond where each carbon atom is sharing electron pairs with four 
others, so that this linking is extended indefinitely in all directions 
to the limits of the crystal itself which thus may be considered a 
single solid molecule. The word "adamantine" has been ascribed 
to this class by Bernal. 

d. Molecular Combination. Organic compounds form the 
great class of crystals whose pattern units are the whole molecules 
in which, in turn, the atoms are linked together by pairs of elec- 
trons held in common. While in the ionic lattice the identity 
of the single molecule of potassium chloride, for example, is some- 
what obscured (though by no means destroyed) by the division 
of the bonding forces of one atom among six neighbors, in the 
molecular lattices the molecule of the chemists' formula and of the 
gaseous phase is built essentially unchanged into the solid struc- 
ture. By virtue of the residual stray fields of the electrically 
neutral molecules, it is possible for one molecule to lie up against 

'See JOFFE, "The Physics of Crystals/' McGraw-Hill Book Company, 
Inc., 1928. 



264 APPLIED X-RAYS 

another and form the regularly built-up solid. Thus there are 
two molecules of naphthalene in the unit crystal cell. Because 
the stray forces holding the molecules in their fixed position 
cannot compare in intensity with the strong polar or non-polar 
bondings between atoms, the substance easily melts or throws off 
single whole molecules in the process of sublimation. This type 
of combination will be considered in detail in Chap. XVI on the 
structure of organic crystals. In the case of electrically neutral 
inert gas atoms, the residual attraction is effective only at 
very close distances and consequently except at lowest tem- 
perature the substance remains a gas. Molecular lattices are 
also to be found among inorganic compounds, notably solid 
HC1, Snl^ 1 and the cubic forms 2 of arsenious and antirnonious 
oxides. 

e. Metallic Combination. Metallic combination occurs when 
atoms tend to lose electrons very easily. The positive ions are 
then held together by an electron gas produced from the discarded 
electron now no longer bound to particular atoms. 

/. Coordination and Primary and Secondary Valence Forces. 
The various types of lattices enumerated in Chap. XIII for inor- 
ganic compounds are distinguishable by their coordination num- 
bers as originally defined chemically by Werner, or the number of 
neighbors possessed by each ion; thus the following simple coor- 
dination types for the compounds AB and AB 2 may be recognized : 

AB. 1: single molecules and molecular lattices. 
2: double molecules, molecular chains. 
3: BN type. 

4: diamond typo lattices of zinc blende and zinc oxide. 
6: NaCl and NiAs types. 
8: CsCl type. 
AB2. 2 and 1: single molecules and molecular lattices. 

4 and 2: a. and ft quartz, cristobalite, tridymite, cuprite. 
6 and 3: anatase, rutile, brookitc, layer lattice Cdl2. 
8 and 4: fluorite. 

Each of these types is characterized by a definite energy sta- 
bility, which may be deduced theoretically and the constants 
evaluated from compressibility and related data. 3 

1 DICKINSON, /. Am. Chem. Soc., 46, 958 (1923). 

2 BOZORTH, ibid., 45, 1621-1629 (1923). 

3 Cf. BORN, "Problems of Atomic Dynamics," p. 176, Massachusetts 
Institute of Technology, 1926. 



INORGANIC CRYSTAL CHEMISTRY 265 

The point of greatest interest to chemists, possibly, is the com- 
plete verification by x-ray analysis of the remarkable Werner 
theory. This holds not only in the case of primary coordination 
of oppositely charged ions but also for the so-called secondary 
valence compounds, in which electrically neutral molecules, such 
as ammonia in the ammines or water in the hydrates, may be 
chemically bound by molecules of ionogens. For the compound 
Ni(NH 3 )6Cl 2 , for example, Werner postulated that the six 
ammonia molecules should be held around the central nickel ion 
at the corners of an octahedron. By x-ray analysis Wyckoff 
found this indeed to be the case for the complex ammonia complex 
compounds, potassium chloroplatinate (K 2 PtCl 6 ), zinc bromate 
hexahydrate, etc. Dickinson 1 studied potassium chloroplati- 
nite, KjjPtCU, and found again the four chlorine atoms equidistant 
around the platinum atom in the same plane. Upon these 
grounds primary and secondary valences are no longer separable 
sharply from each other. Even when neutral ammonia molecules 
are bound by nickel atoms, there is a sharing of electron pairs, 
both being present originally in the nitrogen atom. In the alkali 
polyhalides such as CsI 3 , the ionic lattice consists of singly posi- 
tively charged cesium atoms and a group or radical I 3 , retained 
intact, the iodine atoms being held in a string probably by the 
sharing of only single electrons. 2 

g. The Sizes and Shapes of Atoms and Ions. Since the dimen- 
sions of the crystal unit cells of the elements containing a definite 
number of regularly arranged atoms may be determined with 
great accuracy, by simple deductions it is possible to determine 
the distance of nearest approach of two atoms and the radius of 
the atom. By radius is, of course, meant the sphere of influence 
of the very open structure of electrons in diffuse shells around a 
minute nucleus which constitute the atom; however, the electrical 
forces holding atoms and ions in position are so strong as to render 
solids very little compressible, and, hence, the atoms act usually 
like solid spheres in the crystallographic sense. These radii, 
calculated from the best available crystal-structure data, are 
tabulated in Table XXVII in the preceding chapter. As has 
long been known, the atomic radii, as well as volumes, are dis- 
tinctly a periodic function of atomic number. 

1 /. Am. Chem. 8vc., 44, 2404 (1922). 
2 CLARK, Am. J. Sci., 7, 109 (1924). 



266 



APPLIED X-RAYS 







4 o> . ^ 










CO O2 O O 










Tt< CO 


^1 rH 


rt< Tf 






-}- "* ^ 


4 fl ^ ^ 


-}- ^ 






r*< O o o 


HH CO O O 


Tt< r^-H O O 






CM CM 


CM rH 


o o 








_1_ O5 00 


+ O O5 
r-H , 






co O o o 


CO rS 


CO H rH O 






CO Tft 


CO l> 


CM O 






_j_ 00 l> 


_L_ ^ O O5 


-f- ho 1 ~ l ^ 






CM CS3 O O 


CM rH 


CM W rH rH 






CO 


CO CO 


b- 






J- 3 - O5 


4 M *""! . 


+ 3 : n 






rn o : d 


rH -^ rH rH 




3 

^ 

< 




9 






s 

M 


4- . ^ 

CO CO O O 


_|_ ^ CO O 

co O d d 






H 


rt - K - 1 

C3 CM ^T 








H ^ 


^ O O 








3 P 


a | rH | Tf 


O O5 


05 O 




3 & 

1 rH 
Q r* 


1 * rH rH _j_ CO CO 

lOr^J^OO loOnOO 


.t> gd 


4.^ co t- 

10 O o o 




>xi r inv 

rnTrurv^ 


2 05 rH 

4- .<*-< 4-._ w "* 


+ .-SS 


_|_ ^ 00 00 


+ s 


H P^ 


^O^OO Tt< CO O O 


rt< H o o 


rfi N O O 


Tt< CJ rH rH 


3 


t-H 








< a 


^ 








H g 


I CM 1 iO iO 

co CQ d co <! o o 


_|_ 00 00 

CO CO O O 


SCO 
05 

CO >< rH 


+ .83 

1^ Co 
CO rH rH rH 




Tt< rH 00 O 

CMPQ oo CM^OO 


CO O5 

+ 03 05 

CM O rH O 


t^ co 

+ CM rH 
rH 
CM CO rH rH 


CO >O 


H 


00 O 00 to 

rHr3 OO rH/^OO 


CO CO 

_|_ co co 

rH rH rH rH 


O5 00 
_|_ ^ rjj rJJ 

rH HH rH rH 


rH O rH rH 


3 i 










o 










. w 


CM CM 


CM ' 






3 W 




05 


*H *" ' 


QJ CO 


< H 


O ffi rH O ^ rH 


O J rH ' 


O W w 


X CM 


<j 
^ 


I> 00 CO CO 

j CM O | CO CO 


| 00 00 


, .88 


CO 

| CM rH 






rH Q rH rH 






) 

4 

3 


CM O 

1 CO ^ 


1 t> 00 


rH 00 
| O5 O5 


rH rH 

| ^H CM 


-1 


CM O rH rH 


CM CO rH rH 


CM CO *-* rH 


CM H CM CM 




13 13 


13 


J : 


13 




a . o 







O 




'C ^ 'C r- 


*C ^-1 




'C r-H 




- a g 'a g 


a g 


*a g 


*a g 




C5 'r^ fl *r^ 


a-! 


a '43 


a '-2 




QJ g Q> g 


* o 




o g 




^ J ^ J 


:! 


rSj 


rd J 




a ^ a ^ 


S *" 


a +* 


a ^ 




-C bfl rC t 










OQ <3 05 ,2 


J^s 


M -S 


J 1 




2 3 23 


s 3 


2 3 


f * 




O f2 O r 


S r2 


O 


O c3 

O p.; 



INORGANIC CRYSTAL CHEMISTRY 



267 







4- o,^ 






co U o 






CO K^ rH 




00 


^ O CM 




CO tf 


CO H rH -^ H rH rH 




4- < 


1^0 ^ oo : 




CO rH O 


CO H rH ^ H 0* 




CO ^ O 


CO S rH Tfl PH rH O 


p 


+ cO 
(-1 

co O o 


4- >. *R 4- <u ? 

CO P rH* Tt< H 


o 


LO 

i ^0 


CO -^ 
' - + ^ ^ < 


^ 


CO > O 


CO r~* rH H/l hH O O 


g 


V 


05 

co H d 


rH l> IO 

-|_ ^ rH _j_ ^ CO CO 

CO O rH -HH O O O 





CM rH 


CO ^O CO 


<J 


4- ^ ^ ^ 


_]_ j^ rH _|_ 3 CO CO 


M 


CS PH rH T-H 


CO W rH H^ PH O O 


Q 


00 Oi 


CO *O t^- 


< o 


_|_ ._ t^ CO 


4- S * 4- . " 


p? 


(N X O O 


CO r/} T-H H/l 3 rH O 





+ s s 


oo co 
_|_ _j_ v co co 


pj 


CM O O 


CO PH ^ J^ O O 


s 

PS -<! 


CO >O 
CM rH O O 


_)_ rrj rH _^_ O CO CO 

CO r^ rH T^ 1^5 O O 




rH O 


CO O5 t>- 


J^ P 


4" w-i 


+ rH 1 Q CO CO 
VH . I p- 


frl 3 


<N r^< O 


CO PH rH *& /^ G> & 


o* )/3 


in!!!; 


OO CM O 
+ o - +> 

CO O rH <^*5OO 


r* O 


+ W^ : 


(M rH O5 

i csj i cO >O 


$0 




CO (-3 rH Tf K^ O O 


rH 





O CJ 




ac3 



1 1- 
s 11 




;g 


S 53 *C 




is s 


^ i a 




1 ' 

-g W) 


1 a * 

r| rd faB 










r 


03 "rt rf 




Si 


O O c3 
O O rS 



268 



APPLIED X-RAYS 



Numerous methods have been employed to calculate the radii 
of ions, but the most widely accepted values today are those of 
Goldschmidt, empirically determined from crystal-structure data 
and from Wasastjerna's values (optical) F~ = 1.33 and O = = 
1.32 A.U. Pauling has calculated theoretical radii from quan- 
tum-mechanics considerations and the agreement in general is 
excellent. The values are shown in Tables XXXIa, 6, c. 

TABLE XXXIc. RADII OF ANIONS 





F- 


ci- 


Br~ 


I- 


o- 


s- 


Sc- 


Tc- 


Goldschmidt 


1.33 


1.81 


1 96 


2 20 


1.32 


1 74 


1.91 


2 11 


Pauling 


1.36 


1.81 


1.95 


2.16 


1 40 


1 84 


1.98 


2 21 



It may be seen at once that the size of the positive ions in 
the same periodic group increases with atomic number, whereas 
it decreases in the same periodic series with increasing charge 
which tends to tighten the structure. In negative ions the 
increased size due to repulsion of the extra electrons is 
balanced by the greater electric field, so that doubly charged 
negative ions are no larger, and sometimes smaller, than singly 
charged ions. The tightening effect of increased charges is 
shown by comparing K + C1~ and Ca+^S^; although all four ions 
have 18 electrons, the interatomic spacing for KC1 is 3.14 A.U. 
and for CaS 2.84 A.U. 

3. The Laws of Formation of Ionic Crystals. Goldschmidt's 
first law of formation of ionic crystals is as follows: the crystal 
structure of a substance is determined by the ratios of numbers, 
the ratio of sizes and polarization properties of its components, 
which may be ions, atoms or atomic groups. The sizes of ions 
are obviously the most important property, since the coordination 
numbers which define crystal-structure types depend upon the 





Change in 


Decrease in 


Transition in lattice type 


coordination 


distance, 




number 


per cent 


CsCl-NaCl 


8~>6 


3 


NaCl-*ZnS 


6->4 


5.8 


CaF a -> TiO 2 (rutiie) 


8, 4 - 6, 3 


3 



INORGANIC CRYSTAL CHEMISTRY 



269 



packing radii. The influence of the coordination on distances in 
ionic lattices is shown in the table on p. 268. Thus the fewer 
the neighbors around an ion, the shorter the ionic distance, 
the charges being kept constant. Goldschmidt has shown 
from simple geometry that in order to arrange a certain 
number of spheres B so that they will touch around a central 
sphere A, the following ratios must hold: 



Number 
spheres B 


Arrangement 


Limiting 
RA/Rx 


2 


Opposite 




3 


Equilateral triangle 


0. 15 
Ooo 


4 


Cube diagonal (tetrahedral) 


zz 

n 41 


4 


Square 


41 





Cube normals (octahedral edges) 


n 7** 


8 


Cube diagonals (octahedral) 





Such simple relationships which determine possible arrangements 
in space for given ratios of radii hold true in remarkable fashion 
for the packing of ions in crystals. 

The way in which atomic diameter influences structure can 
be seen from the simplest ionic structure of the type AB, with 
equal numbers of ions of opposite signs. The simplest of these 
is the structure of rock salt, where sodium and chlorine ions 
occupy alternate corners of a cubic lattice. The coordination 
number is 6:6; i.e., each sodium has six chlorine neighbors and 
vice versa. Actually, the chlorine ions are so large compared 
to the sodium that they form an octahedron that encloses it 
almost completely. Simple geometry shows that this can only 
be the case if R A (radius of positive ion) : R B (radius of negative 
ion) = 0.73. This relation holds for all halides of the alkaline 
metals with the exception of the chloride, bromide, and iodide 
of cesium where the ratios R A /Rs are 0.91, 0.84, and 0.75 respec- 
tively. Now these last three are the only alkaline halides which 
do not belong to the sodium chloride type but to the cesium 
chloride type. Here the coordination number is 8:8 and there 
is, so to speak, more room for the larger cesium ion inside the 
cube of chlorine ions. Where R A :R B is very small, the factor 
of polarization comes in, and the structure ceases to be ionic 
and becomes adamantine or molecular. 



270 



APPLIED X-RAYS 



If we pass to the next simpler series, AB^ a similar situation 
occurs. Where R A : R B is greater than 0.73, the structure is of the 
fluorite type (see Fig. 126). Here the coordination number is 8 : 4, 
the calcium ions being surrounded by a cube of eight fluorine ions 
just as the cesium by the chlorines. A number of compounds (see 
Type Cl in Table XXVIII) belong to this type, which includes 
the fluorides of the alkaline earths and the dioxides of zirconium, 
thorium, praseodymium, cerium, and uranium. If RA'.RB lies 
between .73 and .41, a structure is formed analogous to rock 
salt. This is the rutile structure (see Fig. 127). Here the 
coordination number 6:3 cannot be satisfied in the cubic system 
and the octahedron of oxygen ions is placed on its side in a 
tetragonal structure. The two other forms of TiO 2 , anatase and 



199 A 





4.52 A 



FIG. 126. Lattice 
model for fluorite 

(CaF 2 ). 



7> 
00 

FIG. 127. Lattice model 
for rutile (TiO 2 ). 



brookite, are also built with the same coordination but with the 
octahedra distorted and differently placed. A large number of 
substances belong to the rutile structure: the fluorides of Mg, 
Mn, Co, Fe, Ni, Zn and the dioxides of Mn, V, Ti, Ru, Ir, Os, 
Mo, W, Cb, Sn, Pb, and Te. 

When RA'.RB hes between .41 and .22 the coordination number 
is 4:2, which is approaching a homopolar structure. This is 
the case for the different forms of silica (SiO 2 ), cristobalite, 
tridymite, and quartz. Though apparently different, these 
structures have the essential point in common that they are 
built from silicon ions completely surrounded by four oxygens 
in a tetrahedron. Each oxygen is shared between two tetrahedra 
and the different forms of structure are merely due to different 
arrangements of these tetrahedra. Thus the polymorphism 
of silica is not due to any change in the molecule. 

Such considerations as these may be extended even to the 
ionic compounds with complex cations such as Ni(NH 3 ) 6 " H " and 



INORGANIC CRYSTAL CHEMISTRY 271 

to atomic radicals such as sulfate, nitrate, chlorates, etc. The 
work of Zachariasen on the compounds ABO 3 , A 2 BO 4 , etc., is 
especially noteworthy. In anhydrous Na 2 SO 4 , the SO 4 ion is a 
perfect tetrahedron, and NaOe a deformed octahedron, with 
each tetrahedron sharing two edges with an octahedron. 1 

4. Layer Lattices. The most important influence, next 
to the size of the ions, in determining how a compound shall 
crystallize is the phenomenon of polarization, which includes all 
alterations which particles show under the influence of electric 
forces. The simplest case is the formation of a dipole under 
the influence of an electric field. The negative iodide ion is a 
typical polarizable ion. Cadmium iodide, by analogy with 
related compounds and the transition CdF 2 >CdI 2 and by 
consideration of the ratio of ionic radii fi Q1 ~ H ~/# I "~, would be 
expected to have a rutile structure, but instead it forms a distinc- 
tive type of its own. The coordination arrangement is such that 
any cadmium ion is surrounded symmetrically by six iodine ions 
rhombohedrally, but each iodine ion is in contact with three 
cadmium ions on one side, an ideal condition for polarization. 
The structure is built up in layers with the sequence iodide ion- 
cadmium ion-iodide ion layers being repeated. In each layer 
there is really a giant ionic molecule as large as the extension 
of the layer, whereas the layers are held together by secondary 
forces, which accounts for the very prominent cleavage. Of 
course, graphite is a prominent example among the elements. 
The transitions TiO 2 > TiS 2 and SnO 2 > SnS 2 also result in 
changes to layer lattices. 

5. Isomorphism, Morphotropism, Polymorphism. Gold- 
schmidt's great contributions have been the result of his experi- 
mental method of substituting one ion for another in compounds 
and observing what change in structure occurred. It is clear 
that analogy in size of ions is the most important attribute 
contributing to isomorphism. This accounts for unsuspected 
cases of isomorphism such as lead and strontium, and magnesium 
and cobalt or nickel, salts, and for lack of isomorphism among 
salts far more nearly related chemically, such as salts of magne- 
sium and calcium and even of sodium and potassium. In general, 
one atom or ion may be replaced by another without destroying 
the crystalline arrangement when the ionic distances do not differ 
by more than 10 per cent. This is also the degree of disarrange- 

1 Z. Kryst., 81, 92 (1932). 



272 



APPLIED X-RAYS 



ment thermally possible before a crystalline arrangement of 
planes is destroyed by melting; thus the isomorphic and thermal 
tolerances are the same. When by chemical substitution the 
limit of homogeneous deformation is surpassed, a new atomic 
arrangement in space takes place; such a process Goldschmidt 
calls morphotropism. This occurs in the series of dioxides when 
the ratio R A /K B reaches 0.7 and in numerous other series of com- 
pounds in which stepwise substitutions are made to points 
where sudden changes in properties occur. Polymorphism, the 
phenomenon in which the same substance under different thermo- 
dynamic conditions may have different crystal structures, is 
simply a case of morphotropism brought about not by substi- 
tution but by thermodynamic alteration (temperature, pres- 
sure, directed force, etc.) so that the substance is no longer 
isomorphous with itself. These are but a few simple examples 
of the rational explanations of crystal chemistry based on x-ray 
crystal-structure data. 

Goldschmidt has gone even further and used a model prin- 
cipally employing substitution of ions of the same size and shown 
that TiO 2 is like MgF 2 , ThO 2 like CaF 2 , SrTiO 3 like KMgF 3 , 
BaSO 4 like RbBF 4 , Zn 2 SiO 4 like Li 2 BaF 4 . Thus the properties 
of a very difficultly prepared salt may be anticipated by the 
study of a substituted model more easily available. 

6. Application of Crystal Chemistry Laws to Prediction of 
Properties. Goldschmidt has shown that the hardness and related 
cohesive properties of ionic crystals depend directly upon the elec- 
trostatic forces between ions. The hardness of crystals increases 
with decreasing distance between the ion centers, the charge being 
kept constant; and the hardness increases with increasing ionic 
charge when the distance is kept constant: for example, 



Property 


MgO 


CaO 


SrO 


BaO 


NaF 


MgO 


ScN 


TiC 


Distance 
Hardness 


2 10 
6 5 


2.40 
4.5 


2 57 
3 5 


3 3 


2 13 
3.2 


2 10 

6.5 


2 23 
7 to 8 


2 23 

8 to 9 



Partial correlations have been made between ionic structure 
and optical properties, 1 compressibility, 2 expansion coefficients, 
elastic constants, cohesion, etc. 

1 See for example WOOSTER, In Relation between Double Refraction and 
Crystal Structure, Z. Kryst., 80, 495 (1931). 

2 See Bridgman's great book "The Physics of High Pressure," 1931. 



INORGANIC CRYSTAL CHEMISTRY 273 

7. The Structure of Silicates. One of the most brilliant 
recent achievements in diffraction analysis is the series of 
remarkable studies of the complex silicates, which for a time 
defied complete interpretation on account of formulas which 
seemed unrelated to the usual valence laws of chemistry. A 
large number of ionic crystals which are of neither the simple 
nor complex ionic types are thus grouped together as the inter- 
mediate silicate type though not all contain silicon. W. L. 
Bragg was the first to show that the great complexities were 
dispelled when it was realized that these compounds consist 
essentially of the relatively larger oxygen ions in close-packed 
arrangement, either cubic or hexagonal. These ions are held 
together by strongly charged metallic ions which fit into the 
spaces between them. In tetrahedral spaces are to be found 
the smallest and most highly charged ions, Si ++++ , Be ++ , Ti++ ++ , 
Al + + + , Mg ++ , Fe ++ , etc. Larger ions, such as Ca +4 ~, Na+, 
and K^, introduce distortion into the structure. The symmetry 
of the particular silicate adjusts itself to fit these ions with 
minimum distortion, with the result that the unit crystal cells 
are large and complicated because of low symmetry. W. L. 
Bragg summarizes the features of the great work done under 
his guidance as follows: 1 

a. Whatever the silicon to oxygen ratio, silicon always is 
situated within the tetrahedral group of four oxygen atoms, 
which is very constant in form from crystal to crystal. 

b. The structures are typical coordination structures four 
oxygens at the corners of a tetrahedron, six of an octahedron, 
etc. The whole structure may be regarded as a fabric of which 
these groups are the stitches, the groups being joined together 
by sharing oxygen atoms. 

c. The coordination numbers among silicates are Be ++ 4, 
B+++ 3, 4, Na+ 6, 8, Mg++ 4, 6, 8, A1+++ 4, 5, 6, Si 4 + 4, Ca++ 6, 
7, 8, SC+++ 6, Ti 4+ 6, Mn++ 4, 6, 8, Fe++ 4, 6, 8, Fe+++ 6, Zn++ 4, 
Zr 4+ 8, Ba++ 6, 12. 

Pauling 2 has gone still further in discovering general principles 
of structures. The entire group of coordinated anions around 
each cation is to be considered as polyhedron (see Fig. 128). 
The presence of shared edges, and particularly of shared faces, in a 

1 Faraday Soc. Mon., Crystal Structure and Chemical Constitution 
(March, 1929). 

2 J. Am. Chem. Soc., 61, 1010 (1929). 



274 



APPLIED X-RAYS 



coordinated structure decreases its stability (since the positive 
ions would be brought into unusually close proximity) : the effect 
is large for cations with large valence and small coordination 
number and is especially large in case the radius ratio R A /R B 
approaches the lower limit of stability of the particular 
polyhedron. 

In limited space it is impossible to give a just picture of the 
great progress which has been made possible by means of these 




FIG. 128. Photograph of a model FIG. 129. Silicon-oxygen chains in 

illustrating coordination structures of pyroxene (diopside), above; and double 

complex compounds, and representing chains in amphibole, below. Mica is 

sodalite, Na4Al3Si3Oi2Cl. (Pauling.) built from a further extension of these 

The spheres indicate chlorine ions, chains into a sheet, 
and the tetrahedra have an oxygen ion 
in each corner and silicon or alumi- 
num at the center. 

simplifying conceptions. The service to chemistry, geology, and 
mineralogy is immeasurably great. Only a single example need 
be cited to show what simple relationships are now found to hold 
for substances which seemed hopelessly complex only a short time 
ago. The essential feature of diopside, a typical metasilicate with 
the formula CaMg (8103)2, is that each silicon atom is surrounded 
tetrahedrally by four oxygen atoms in the usual way. Two of 
these atoms are common to neighboring groups and two are not. 
The tetrahedra are linked by their corners into endless chains par- 
allel to the c axis of this monoclinic crystal as shown in Fig. 129, 
It is incidental that the Si0 4 groups are cemented sideways by 



INORGANIC CRYSTAL CHEMISTRY 275 

calcium and magnesium ions. Bragg and Warren, soon after the 
analysis of diopside, noted certain similarities with asbestos. 
Analysis has indicated that the Si0 4 single chains in diopside are 
now double chains in asbestos. Splitting can occur parallel with 
these double-linked chains. Now this process may continue until 
a whole sheet or network of the SiO 4 groups is made possible 
by sharing oxygens. This is mica whose cleavage in thin sheets 
is so familiar. 

8. General Relationships of Structure and Properties of Crystal- 
line Metals. The following conclusions may be drawn from a 
consideration of the data obtained by x-ray analysis of crystalline 
structure of metals: 

a. The periodic arrangement of elements is, in general, carried 
over into the types of crystalline structures; there is an easily 
observed tendency for elements in the same periodic column or 
family to crystallize in the same way. There are notable excep- 
tions, as, for example, the discovery in the writer's laboratory 
that calcium and strontium are face-centered cubic and barium 
is body-centered cubic. 1 Other complexities are the unusual 
structures of a and manganese, which have remarkable ana- 
logues among the alloys, and the cases noted above of entirely 
distinctive structures for white tin, etc. 

6. As noted in a preceding section, evidence, including the 
interpretation of the new quantum mechanics, points to the fact 
that true crystalline metals are built up from positive ions in an 
electron gas. This electron gas, so-called, is a primary determin- 
ing factor. In ordinary ionic lattices for chemical compounds in 
which electrostatic forces between positive and negative ions 
hold these at the points of the lattice, the elements mag- 
nesium, cobalt, nickel, and zinc are very similar, whereas in 
metallic crystals the similarity is retained only for cobalt and 
nickel. 

c. New evidence seems to indicate that metals are a state 
of matter rather than a type ; in other words, at sufficiently high 
temperatures and pressures such as may be attained on the 
interior of the stars, all elements and compounds may become 
metals in the sense of the fundamental properties such as con- 
ductivity by electron transport. 

1 CLARK, KING, and HYDE, Proc. Nat. Acad. Sci., 14, 617 (1928); 16, 
337 (1929); /. Am. Chem. Soc., 61, 1709 (1929). Also EBERT and HART- 
MANN,*Z. anorg. allgem. Chem., 179, 418 (1929). 



276 APPLIED X-RAYS 

d. The ratios in which metal atoms combine are often not 
capable of explanation on the basis of usual chemical rules but 
may be accounted for geometrically on the basis of coordination. 
In the series Cd 2 Li, Cd 6 Na, CdnK, the proportion of cadmium 
increases with the atomic volumes of Li (21 A.U. 3 ), Na (48 A.U. 3 ), 
and K (72 A.U. 3 ). Similarly miscibility or non-miscibility may 
be almost entirely a matter of atomic radii. 

The best method of arriving at definite conclusions as to the 
relation between characteristic properties and structure is to 
observe the transformations of one type of crystal structure into 
another in series of comparable alloys. This logic has been used 
by Westgren and by Goldschmidt to derive important generaliza- 
tions from a seemingly hopelessly complicated field. Some of 
these will be noted in the next chapter on alloys. It is certain 
that, for rnetals, atomic weights or atomic numbers are relatively 
far less important in determining the type of crystalline structure 
than the average concentration of valence electrons. In other 
words, the most important factors are the polarization properties 
of the atoms. Goldschmidt 1 draws an analogy between a radical 
such as ammonium (NH 4 ), which acts as a polynuclear pseudo- 
atom, and a single metal crystal, no matter how large, which is also 
a polynuclear pseudo-atom on account of the common electron shell 
(gas) around the positive kernels. In terms of modern theories of 
the structure of matter, this accounts for all those properties 
characteristically associated with the metallic state-allotropy, 
transformations, common behavior in polyphase systems, the 
solubility of hydrogen in solid metal crystals 2 (in the form of 
hydrogen kernels), the electron emission from heated metals as an 
ionization leaving the whole metal crystal as a macroscopic cation, 
electron isomerisrn, and passivity. Even molten metals are 
polynuclear pseudo-atoms, and only in vaporization do the single 
atoms regain their individuality. 

e. As might be anticipated, the problem of the metallic state 
is rendered so difficult by the fact that there are so many degrees 
of what may be termed metallic properties. It is impossible to 
find, for example, where metallic combination leaves off and 
homopolar begins, just as is true for the transition from ionic to 
homopolar combination in silicates. There is recognized, how- 

1 Ber., 60, 1263 (1927); Trans. Faraday Soc., 25, 253 (1929). 

2 Also helium in platinum, with x-ray evidence of compound formation: 
cf. Damianovitch and Trillat, Compt. rend., 188, 991 (1929). 



INORGANIC CRYSTAL CHEMISTRY 277 

ever, a class of half metals found in the B periods of the periodic 
table (Al, Zn, Ga, Ge, As, Cd, In, Sn, Sb, Hg, Tl, Pb, Bi). They 
are distinguished from true metals in part as follows: 

(1) Their structures are such that each atom is surrounded by 
8-n neighbors where n is the group number of the element in the 
periodic system (Hume-Rothery) ; in other words each atomhas 
as many neighbors as there are number of electrons required to 
fill up the rare gas shells. This leads to two-atom molecules for 
the halogens, chains for selenium and tellurium, layers for As, 
Sb, and Bi, and to the diamond structure for Ge and Sn. 

(2) True metals conduct electricity less readily in molten con- 
dition, while the half metals are characterized by the reverse. 

(3) Closest packing in crystal lattices is ordinarily absent in 
half metals. They can ordinarily dissolve only traces of the true 
metals, since an atom can be replaced only by one of similar 
electron configuration, while true metals can readily dissolve 
half metals if there is not too great a discrepancy in atomic 
dimensions. 

(4) Half metals are strongly diamagnetic (as is also true in the 
alloy structures); the atoms themselves (vapor) may be para- 
magnetic but the behavior of the solid indicates the great struc- 
tural effect. Very weak diamagnetism persisting after melting 
must reside in bonds of hornopolar nature. Very strong negative 
susceptibility is also a structural property. 

(.5) Electrical conductivity is at a minimum for stoichiometric 
combinations of half metals, but a maximum for true metals. 

(6) The compounds of the true metals with P, As, Sb, Bi, Si 
(Ge, Sn, Pb), S, Se, Te and with H, B, C, and N(O, F) are dis- 
tinguished at least for the first two groups as simple ionic, while 
the compounds with the transition metals, half metals, and heavy 
metals are homopolar or metallic. 

In a masterly paper on the problem of the metallic state, J. D. 
Bernal 1 summarizes the evidence concerning the metallic bond as 
follows : 

1. It must be capable of acting between identical atoms and 
at the same time between atoms of very different constitution 
(as in intermetallic compounds), the only limit being that the 
majority of atoms concerned should be metallic. 

2. It should be undirected, as is shown by its identity and 
almost equal efficacy in the liquid state, and unsaturated; i.e., it 

1 Trans. Faraday Soc., 26, 367 (1929). 



278 APPLIED X-RAYS 

should permit always of the highest coordination number steri- 
cally possible. This number in some alloys rises as high as 16. 

3. Its force must vary inversely as some high power of inter- 
nuclear distance as shown by its extreme weakness in the alkaline 
metals, with low melting points and very large atomic volumes, 
by the high value of the thermal energy of titanium, and by the 
low atomic volume of the platinum group. There must be some 
difference between the forces concerned with thermal and 
mechanical effects. 

4. In equilibrium with this force of attraction there must be a 
force of repulsion which is an atomic property as shown by the 
constancy of atomic volume in alloy formation. (This is the most 
difficult fact to explain on the theory that conductivity electrons 
belong to the lattice, as a whole, and not to single atoms.) 

5. The bond must allow a transfer of electrons from one atom 
to another to account for the electrical properties. 

Notable efforts have been made in recent months by Bernal, 
Slater, Mott, and others to take these factors into account in 
attempting to define the metallic state upon the basis of wave 
functions combining what amounts to both free and bound 
electrons. The great progress which has been made, the great 
mass of experimental observations on metals, half metals, alloys, 
etc., and the need of further development of modern wave 
mechanics are clearly indicated in two very recent publications 
by Bernal 1 and by Hume-Rothery 2 which present the entire 
subject of the metallic state as it is now known. 

1 "Fortschritte der Rontgenforschung in Methods und Anwenndung," 
pp. 200-239, Leipzig, 1931. 

2 "The Metallic State," Oxford University Press, New York, 1931. 



CHAPTER XV 
THE STRUCTURE OF ALLOYS 

1. Types of Alloys. The phenomena which occur when two 
metals are melted together and allowed to cool have long been 
known. Microscopic, thermal, dilatometric, and electrical 
methods have demonstrated the formation of " mixed crystals " 
or solid solutions, of eutectic mixtures, and of chemical com- 
pounds. In binary alloys all of these conditions are found in 
various combinations. 



FIQ. 130. Powder diffraction patterns illustrating solid solution: upper, a-brass, 
80 per cent copper, 20 per cent zinc; lower, pure copper. 

a. Alloys Formed by a Continuous Series of Solid Solutions 
(Substitutional) . In such alloys the atoms of one kind of metal 
which is being alloyed with another replace the atoms of the 
latter at the lattice points. In most cases this is a simple process 
but in other cases, as in copper-aluminum alloys, complex sub- 
stitution may involve replacing three by two atoms, etc. 

Microscopic evidence: only one kind of crystals appears in 
any specimen ranging from one pure component to the other. 

Thermal evidence: smooth continuous curve in phase dia- 
gram between pure components. Very slow cooling or careful 
annealing to permit diffusion is necessary to assure that all the 
crystals separating from the liquid phase are uniform in com- 
position since two " nicks " appear in cooling curves. 

X-ray evidence: only one type of diffraction pattern through- 
out, the only variation being a change in the lattice parameter. 
Figure 130 shows how the diffraction lines for a pure metal are 
shifted for a solid solution. 

Requirements: only two metals which have the same lattice 
structure (i.e., both face-centered cubic, for example) can form 

279 



280 APPLIED X-RAYS 

a continuous series of solid solutions. All pairs of metals with 
common lattice structure do not form continuous series (e.g., 
aluminum-gold) . 

Additivity relations: Vegard's law of additivity states that 
in a binary system forming a continuous series of solid solutions 
the lattice parameters are linearly related to atomic percentage 
of one of the components. In other words, upon a straight line 
joining the numerical values of the edge lengths of the unit crystal 
cells of the two pure metals, lie all the lattice values for all 
possible solid solutions of the two metals. 

Examples investigated by x-rays: gold-copper, gold-silver, 
gold-palladium, nickel-copper, tungsten-molybdenum, cobalt- 
nickel, nickel-palladium, iron-vanadium, platinum-palladium, 
potassium-rubidium, strontium-calcium (unpublished), etc. 

6. Substitutional Solid Solution over Limited Ranges.- It 
follows, of course, that other systems which do not form a con- 
tinuous series of solid solutions will show substitutional mixed 
crystals over limited ranges of B in A and A in B. 

c. Interstitial Solid Solution. The alloying atoms do not 
substitute for atoms of the original metal but enter the empty 
lattice spaces between the atoms; the best example is carbon in 
iron. 

X-ray evidence: the symmetry and the positions of the x-ray 
interferences of one of the fine metals may be entirely unaffected. 
With the entrance of new atoms in the interstices, of course, 
the relative intensities will be definitely affected. 

d. Systems with a Eutectic. Microscopic evidence : mechanical 
mixture of two kinds of crystals usually identified as the pure 
components. 

Thermal evidence: liquidus curve sharply discontinuous with 
separation of crystals at lower temperature than that for the 
pure metals or intermediate mixtures. 

X-ray evidence: diffraction patterns for both metals super- 
posed. 

Example: lead-silver alloys. In an alloy with 1 per cent 
silver, pure lead crystals will first separate until a composition 
of 2.5 per cent silver is reached, whereupon at 304 C. both lead 
and silver crystals separate together in constant ratio. 

e. Systems with Compound Formation. Microscopic evidence: 
doubtful, two kinds of crystals, unless the specimen has the exact 
constitution corresponding to a definite chemical compound. 



THE STRUCTURE OF ALLOYS 281 

Thermal evidence: maximum in the melting point curve. 

X-ray evidence : limited solid solutions of A in B and B in 
Aj or lattices of both A and B, compound A x B y with different 
characteristic lattice, and solid solutions or mechanical mixtures 
of A and A x B y and B and A x B y . 

Example: in the system lead-magnesium (Sacklowski), x-ray 
data show a series of mixtures, from to 81 per cent lead, of 
magnesium, and the compound PbMg 2 ; at 81 per cent lead a 
face-centered cubic lattice for PbMg 2 with an edge length of 
6.76 A.U., and at higher lead contents, mixtures of lead and 
PbMg 2 lattices. 

The elements may be arranged according to the ease with 
which foreign atoms enter the lattices: 

Group I, first kind: Cu, Ag, An, and the Fe, Pd, and Pt triads. 
Group II, second kind: Li-Be, Na-Al, K-V, Pb-Cb, Cs-Ta, 
Zn-Ce, Cd-Sn, Hg-Bi, non-metals, half metals (B, Si, As, Sb), 
rare gases, and hydrogen. 

Alloys of metals of the first kind form generally continuous 
solid solutions or wide ranges of solubility; intermediate com- 
pounds if any are of the overstructure type, appearing only after 
careful tempering. 

Alloys between metals of types I and II are characterized 
by a great array of intermediate phases, e.g., copper-zinc or brass 
(Fig. 131). Those phases which are rich in the metal of the first 
kind have a greater range of homogeneity than the others. 

Alloys between metals of the second kind, between metals 
and half metals or non-metals, are similar to the last class, 
although the greater the loss of metallic character, the more 
definite the chemical compound with no solution phenomena. 

/. Systems with Superstructures. Intermediate types between 
the foregoing principal types are, of course, to be expected, such 
as the solid solubility of a compound in the lattice of a pure 
metal. Or a foreign atom entering the two kinds of mixed crys- 
tals (substitutional and interstitial) may take up special positions 
and actually enlarge the lattice or lower the symmetry. Such a 
lattice is really a true compound. It is distinguished from the 
other compounds by the fact that it represents very slight 
deformation of the lattice of the pure metal; it is distinguished 
from a true solid solution or mixed crystal, in that new or super- 
structure lines appear in the x-ray patterns in addition to those 
characteristic of a pure metal, or in that normally single lines 



282 



APPLIED X-RAYS 






THE STRUCTURE OF ALLOYS 



283 



appear to be split. The surprising list of examples is shown in 
Table XXXII . These superstructure types do not usually appear 
with ordinary melting practice, but only after careful tempering. 



0,6 

i 



oc 



V) 
U) 



0,7 

i 



c 1 ? 

Sm* 
0,8 



0,9 



'I 

i 1 






18 






39 < 

79 
93 



^Siii'wi,*? iA*: v*y. i .; ' ; V'.f ^iSSl 

FIG. 132. 1'owcler piiotograms ol sn\ r er-aluimiiuiii alloys. (.wcsLyren and 

Bradley.) 

2. X-ray Results on Alloy Systems. The lattice types of the 
alloy compounds have been classified on the arrangement of 
Ewald and Hermann's " Strukturbericht " in Table XXXII. All 
of the types 5, C, and D have been listed in the classification of 



284 



APPLIED X-RAYS 

Q' * 

Sin 2 j 
0,6 0,7 0,8 



0,9 



K^W'k-^'Mf-'-^Tf^*^^ 

cu+ cu^l^Jjjf '--flll^ ;:f -r -in 

Cu 2 Mg[ ; '] || 



f 



I .1; ill 



FIQ. 133. Powder photograms of copper-magnesium alloys. (Ruiiquit>t, Arn- 
fclt, and Wcstgren.} 



0,6 




Sin 1 f 
0,8 



0,9 



^Hf "t'^^ 1 .",''' 1 ' 'T^? 1 ' ' 




in 

IV 
V 



VI ; 



VII 








' f" ^ -. - 







___ 

FIQ. 134. l ) o\vdei photogrums oi metals and alloys of the iron-tungsten and 
iron-molybdenum systems. I, Fe; II, Fe, saturated with W; III, Fe 2 W; IV, 
Fe 3 W 2 ; V, Fe 3 W 2 -f W; VI, W; VII, Fe 3 MO 2 . 



THE STRUCTURE OF ALLOYS 285 

inorganic compounds (Table XXVIII, page 246). A new type 
L, however, has been devised to account for the substitutional 
alloys of the superstructure types and L 1 for the interstitial 
superstructure types. 

While it is evident that a great many papers have been pub- 
lished particularly in the past two years and that most of the 
present information on the metallic state, valence, atomic struc- 
ture, and general analogies have been obtained from a knowledge 
of how metals combine, still the great part of the field is unex- 
plored. First in the field of alloy structure and constitution 
stands Prof. A. F. Westgren of Stockholm, who, with Dr. G. 
Phragmen and other co workers, has carried out a series of 



rs" 







FIG. 135. Rotation patti'ins around two axes for single crystal of CuMg2. 

experimental researches with x-ray methods which finds no 
superior in science. In the Stockholm laboratory have been 
perfected all the standard methods of analysis and interpretation. 
In the face of widespread doubt and criticism there were reported 
the large unit cells of 7-brass (52 atoms), 5-bronze (416 atoms), 
a- and 0-manganese, etc., only to demonstrate that these results 
were correct. It is one of the privileges of x-ray workers to pay 
tribute to the untiring skill and invaluable contributions of 
Professor Westgren. Diffraction patterns made in the Westgren 
researches, on the systems silver-aluminum, copper-magnesium, 
and iron-tungsten and iron-molybdenum are reproduced in Figs. 
132, 133, and 134, respectively. The camera used was of the 
focusing type with slit, specimen, and film on the same circumfer- 
ence, similar to the Seemann-Bohlin instrument shown in Fig. 100. 
Single crystal patterns for CuMg 2 are shown in Fig. 135. 



286 



APPLIED X-RAYS 



TABLE XXXII. CLASSIFICATION OF ALLOYS 

Alloys related to type Al (face-centered cubic): substitution superstructures 



L 10 


Tetragonal 


>4fc 


Al distorted along a 4-fold axis 


CuAu 


L 11 . 


Khombohedral 


Dd* 


A 1 distorted along a 3-fold axis 


PtAu 


L 12 


Cubic 


Ok 1 


A I with regulated substitution; 
planes with mixed indices 


AuCu 3 , PtCua, 
PdCua 








double A 1 




L 13 


Cubic 


Oh 1 


Superstructure; 100, 110 same as 


CuPt 








Al planes with 3 odd indices 










doubled 




L' 10 . 


Cubic 


Oh 1 


Planes 3 odd indices same as in 


Fe 4 N 








A 1; mixed indices planes 










doubled 





B 2 



L 21 



L 22 



L 1 20 



Alloys related to type A 2 (body-centered cubic) 



Cubic 



Cubic 



Cubic 



Tetragonal 



Oh 9 



CsCl structure 



Substitution superstructures; 
planes of even and two odd 
(110) indices same as A 2, of 
one odd and 2 even (100) 
doubled; all odd (111) quad- 
rupled 

Substitution superstructure; 
cube edge three times A 2 cell; 
contains 54 atoms 

Interstitial superstructures A2 
interferences for 100, 110 split 
into two and others into three; 
111 simple 



CuPd, CuBe, Cu- 
Zn, AgMg, Ag- 
Zn, AgCd.AuZn, 
NiAl 

CuaAIMn (Heu- 
sler alloy) 



Sb 2 Tb 



Martensite a 
Fe + 6 at. per 
cent C 



Other alloy types in Table XXVIII 



B 2 


(Cubic CsCl structure) 


CuPd, CuBe, CuZn, AgMg, AgZn, 






AgCd, AuZn, NiAl 


B 8... 


(Nickel arsenide) 


AuSn 


C 1 


(Fluorite) 


Mg 2 Si, MgaSn, Mg 2 Pd 


C 14.. . 


Hexagonal 


MgZna 


C 15 


Cubic 


Cu2Mg 


C 16 


Tetragonal 


CuaAl 


C 17 


Tetragonal 


Fe 2 B 


C 18 


Rhombic 


FeSz (marcasite), FeAs 2 , FeSb 2 


D 81, 82, 83, 84 




FesZnio, CubZng, CugAl^, CusiSns 









BRIEF SUMMARY OF CONCLUSIONS FROM X-RAY DATA ON ALLOYS 
Ag-Al: a. (Al in solution in Ag to about 19 per cent); ft' (Ag 3 Al, complex 

cubic with 20 atoms per unit cell); 7 (27 to 43 per cent Al, hexagonal 

close-packed); 5 (Al, no Ag dissolving). 

Ag-Au: Continuous solid solution very nearly obeying Vegard's law. 
Ag-Bi: No compounds; Bi in Ag to 5.5 per cent, expanding Ag lattice. 



THE STRUCTURE OF ALLOYS 287 

Ag-In: Again (hexagonal close-packed). 

Ag-Pd: Continuous solid solution. 

Ag-Sb: Sb in Ag to 6 per cent; 11 to 16 per cent Sb, hexagonal close-packed; 
Ag 3 Sb (rhombic). 

Ag-Sn: to 11 per cent Sn in Ag; Ag 6 ,7Sn, e and e' (Ag 3 Sn) (hexagonal close- 
packed). 

Ag-Zn:Like Cu-Zn. 

Al-Sb: AlSb (type B 3). 

Au-Cd: 7-phase like Au-Zn. 

Au-Hg: to 15 per cent Hg in Au; 25 per cent Hg, hexagonal; two other 
phases at 50 to 60 and 65 to 70 per cent Hg. 

Au-Pd: Continuous solid solution. 

Au-Sb: AuSl)2, cubic. 

Au-Sn: AiuSri (B 8 type), and AuSn 2 , AuSn4, and another intermediate com- 
pound (16 atomic per cent Sn) with hexagonal lattice 

Au-Zn: Like Cu-Zn, and Ag-Zn except two additional phases: 7' (75 atomic 
per cent Zn, AuZn 3 , cubic, 32 atoms per cell, ordinary temperature); 
7" (77.7 atomic per cent Zn, high temperature, cubic similar to 7'). 

Cd-Hg: Two phases to 20 per cent Hg (Cd lattice); 36 to 65 per cent Hg 
(tetragonal body-centered) . 

Co-Cr: 30 per cent Cr in Co, 25 per cent Co in Cr, intermediate hetero- 
geneous. 

Cr-C: See page 303. 

Cu-Ag: Incompletely miscible, no compounds; no silver lines below 6 per 
cent Ag and no Cu lines above 70 per cent Ag. 

Cu-Al: a (solution of Al in Cu to 20 per cent A 1), ft (Cu.jAl stable at high 
temperatures, cubic superstructure), 5, e, r?, (7') (all similar, D 83, 
Cu 9 Al 4 ); 6 (5), CuAl 2 (type C 16); K (e), solution Cu in Al in very 
small amounts. 

Cu-Al-Mn / Ileusler alloys; a, 0, 5 (7') structures of Cu-Al, while Mn pro- 

Cu-Sn-Mn) duces superstructures in ft. 

Cu-Au: Continuous solid solution nearly obeying Vegard's law; AuCu (type 
L 10) and AuCu 3 (type L 12) superstructures with very slow cooling or 
tempering. 

Cu-Be: a (15 per cent Be in Cu); 7 (CuBe, type L 20); 8 (CuBe 3 ). 

Cu-Co: 5 per cent Co in Cu, 8 per cent Cu in Co. Co always cubic in alloys, 
hexagonal when pure. 

Cu-Mg: Cu lattice expands 3.608 to 3.624 when saturated; Cu 2 Mg (C 15); 
CuMg2 (rhombic); Mg dissolves no Cu. 

Cu-Mn: Cu dissolves 30 per cent Mn with increase in a. 

Cu-Ni: Continuous solid solution. 

Cu-Pd: 38 atomic per cent Pd in Cu, 50 per cent Cu in Pd; compounds 
CuPd (type L 20); superstructure Cu 3 Pd from copper phase in temper- 
ing (type L 12). 

Cu-Sb: Cu 3 Sb like Cu 3 Sn; Cu 2 Sb like Fe 2 As. 

Cu-Si: a, Cu lattice; ft (high temperature) 14.5 atomic per cent Si, hexagonal 
close-packed, a = 2.588, c 4.176 A.U.; 7 (low temperature) 17 at. per 
cent Si, cubic same as /3-Mn, a 6.210 A.U., CusSi; 6 (high tempera- 
ture) 18 at. per cent Si, deformed 7-brass type; c (low temperature) 21 



288 APPLIED X-RAYS 

at. per cent Si, body-centered cubic, a - 9.694 A.U. 76 atoms per unit 
cell, Cu 15814; 17, 25 at. per cent Si, hexagonal nearly same as cubic p- 
brass type. 

Cu-Sn (bronze): a (0 to 8 per cent Sn in Cti); (15 per cent Sn, quenched 
from 700 deg. BCC); 7 (D 84, Cu 3 iSn 8 ); e (Cu 3 Sn, hexagonal close- 
packed with superstructure) ; rj CuSn (B 8 with superstructure a' = 5a) ; 
Sn (white Sn dissolves no Cu). 

Cu-Zn (brass): a (solid solution, types A 1-0 per cent Zn, a = 3.61; 38 
per cent Zn, a = 3.69). and (3 f (CuZn, type L 20: 46 to 48 per cent 
Zn, a = 2.945); 7 (Cu 5 Zn 8 , type D 82, 61 per cent Zn, a = 8.85); 
e (type A 3, 80 per cent Zn, a = 2.745, c = 4.294; 86 per cent Zn, a = 
2.761, c = 4.286); t\ (type A 3, solid solution Cu in Zn; 96 per cent Zn, 
a = 2.67, c = 4.92; 100 per cent Zn, a = 2.66, c = 4.94). Sec Fig. 131. 

Cu-Zn- Al: xCu^Zin^.y CiigAU. 

Fe-As: a (0 to 4 per cent As); e (Fe2As, tetragonal D 1 ^); rj (FeAs rhombic, 
deformed NiAs structure). 

Fe-B:Fe 2 B (C 16 type). 

Fe-Bi: Completely insoluble in each other. 

Fe-C: See page 296 for iron-carbon alloys. 

Fc-Co: 80 per cent Co in a-Fe; in FCC-Co 11 per cent Fe; hexagonal Co only 
with traces of Fe. 

Fe-Cr: Continuous solid solution obeying Vegard's law. 

Fc-Mn: 7-Fe in 7-Mn, continuous scries of mixed crystals; 35 per cent 7- 
Fe in 0-Mn (730C.); 37 per cent 7-Fe in -Mii (490C.); e phase, 12 to 
23 at. per cent Mn; solubility of Mn in a-Fe very small. 

Fe-Mo: Limited solubility; compound Mo 2 Fe.} (hexagonal, 8 molecules per 
cell). 

Fe-N: a (pure -Fe, N 2 insoluble); 7" (Fc 4 N, type L'10), e (hexagonal pack- 
ing Fe atoms); f (Fe 2 N, rhombic). 

Fe-Ni: Twenty-five per cent Ni in a-Fe: 65 per Fe in Ni. 

Fe-P: a (0 to several per cent P with no change in lattice of Fc); e (Fe 3 P, 
tetragonal 4 2 ); r (Fe 2 P hexagonal): 77 (FeP?). 

Fe-Sb: a (0 to 3 per cent Sb); (FeSb, type B 8); f (FeSb 2 rhombic typo 
C 18); t] (pure Sb, no Fe dissolving). 

Fe-Si: a. (0 to 30 per cent Si with decrease in lattice from 2.861 to 2.815); 
above 13 per cent Si superstructure (L 21), 7 (with 4 8 per cent Si and 
above 7-phase of Fe non-existent); e (FeSi, cubic), * (FeSi 2 tetragonal); 
t) (pure Si, dissolving no Fe). 

Hg-Sn: Tetragonal tin dissolves no Hg; 7 to 8 per cent Sn in Hg hexagonal. 

Mg-Al: Limited mutual solubility. 

Mg-Cd: No x-ray trace MgCd2.' superstructure at 50 at. per cent Mg, 
a 1 = 6a, c 1 = 3c of Mg. 

Mg-Si: MgoSi (type C 2). 

^ pi* [ Three phases, pure metals and Mg 2 Sn, Mg 2 Pb (type C 1). 

Mg-Zn: Three intermediate compounds; MgZn 2 (C 14 type). 
Mo-C: 30 to 39 per cent C, hexagonal close-packed Mo atoms. 
Mo-W: Continuous solid solution. 
Na-Cd: NaCd 2 . 



THE STRUCTURE OF ALLOYS 289 

Na-Pb: several compounds with complex structures; Na 4 Pb really Na 3 i Pb 8 
cubic, 78 atoms per unit cell, related to y-brass structure. 

Ni-Al: NiAl (L 20 type). 

Ni-Cr: Sixty-four per cent Ni in Cr, 65 to 85 per cent Cr rhombohedral phase. 

Pd-H: Pd 2 H (face-centered cubic metal atoms dissolve more H up to PdH), 
a (Pd) = 3.89; a (maximum H content) = 4.02 to 4.07; lose H in air 
to stable Pd 2 H. 

Sn-Pb: to 3.6 per cent Sn in Pb; both lattices beyond. 

Sn-Sb: 55 per cent 81), B 1 type with doubled cube edge. 

Tl-Pb: Tl dissolves little Pb, 4 per cent Pb giving both lattices; Pb dis- 
solves 80 per cent Tl. 

Tl-Sb: a (0-8 per cent Sb in -Tl); ft (soln. of Sb in 0-T1); 7 (Tl 7 Sb 2 , type 
L 22); 8 (Sb, with only small solubility of Tl). 

W-C: W,C cubic, WC (hexagonal lattice). 

Zn-Al: Solubility Zn in Al: 2.7 per cent 25; 5.2 per cent, 100; 7.4 per cent, 
150; 9.4 per cent, 200; 13.4 per cent, 250. Both lattices beyond. 

Zn-Hg: Two solid phases to 6 por cent, 12 to 35 per cent Hg (hexagonal 
close-packed). 

3. The Mechanism of Solid Solution. The two types of solid 
solution may be distinguished by density measurements, as 
illustrated by the following example from the work of Westgren 
and Phragmen: 

Austenitic steel with 12.1 per cent manganese and 1.34 per cent 
carbon has a face-centered cubic lattice with a = 3.624 A.U. 
The two possibilities are that these alloying elements are substi- 
tutes for iron atoms, or that the manganese atoms are substi- 
tutional and the carbon interstitial. The average atomic weight, 
calculated from the atomic weights of three elements, iron, 
manganese, and carbon, in given percentages is given by 



86.56 (%) JL2.1_(%) L34 

55.85 (at. wt. Fe) "^ 54.93 (at. wt. Mn) """ 12 (at. wt. C) 

= 53.13. 

Substituting this in the density formula (see page 182) 

Mn = 4 X 53.13 X 1.65 X IP" 24 - fi 

p ~ n volume unit cell (37624 X 1<H)" 8 

This is the density, therefore, on the substitutional basis. 

For the other case the average atomic weight for iron and 
manganese is 55.74. To each 55.74 grams (iron + manganese) 

1 34 
are added interstitially ^W X 55.74 = 0.757 gram of carbon. 



290 APPLIED X-RAYS 

The 
and 



- 

The average atomic weight is therefore 55.74 + 0.757 = 56.497 
nd 



_ 4 X 56.497 X 1.65 X 10- 24 _ QQ 
p -- (3^24 X 10- 8 ) 3 7 ' 83 ' 

The actual experimental density is 7.83, proving that the 
second alternative of interstitial carbon is correct. 

The interstitial type of solid solution is usually unstable and 
limited to only a few per cent of one component (the solubility 
of carbon in iron is about 0.1 per cent in body-centered and 1.7 per 
cent in face-centered cubic). Heat treatment may destroy this 
condition. There has been much conjecture as to whether the 
interstitial carbon atoms in iron alloys are fixed in position or are 
free to move. In a paper on the absence of allotropy in pure 
iron, Yensen shows how the thermal agitation of atoms is 
large at high temperatures and how the small carbon atoms may 
travel from one cube to another. If the concentration is low 
enough no distortion may result, but with increasing concentra- 
tions the lattice may change over because of distortions to face- 
centered cubic, in which the solubility is greater. At still higher 
concentrations (6.67 per cent) exceeding the powers of the 7-iron, 
the compound cementite Fe.*C is formed. Similarly nitrogen 
which has a maximum solubility of 0.5 per cent in a-iron may 
cause the lattice transformation and then the formation of Fe4N. 
Oxygen with a maximum solubility of 0.2 per cent may behave 
similarly. 

4. The Distinction between "Chemical Compound" and 
"Solid Solution." From the x-ray point of view the most inter- 
esting phases of alloy research are the intermetallic compounds 
and the solid solutions. The question which is still frequently 
agitated is just what is the boundary line between the two. 
Westgren and Phragmen, outstanding masters in the x-ray 
science of alloys, some years ago made the following differentia- 
tion: "In an ideal solid chemical compound, structurally equiva- 
lent atoms are chemically identical. In an ideal solid solution, all 
atoms are structurally equivalent." 

In the case of iron-nickel alloys, for example, the forces of 
combination of a definite number of nickel atoms with iron are 
not sufficiently strong to overcome the forces of diffusion. 
There is a geometric chance, however, for the compounds FeaNi 
(20 per cent nickel, face-centered cubic), FeNi (51 per cent), and 



THE STRUCTURE OF ALLOYS 



291 



FeNi 3 (76 per cent). Efforts have been made to identify these 
among the series of alloys, based upon Tammann's theory, but 
without avail; hence they may be regarded as very weak com- 
pounds or merely as stages in the continuous solid solutions. In 
one sense, an intermetallic compound may be regarded as a solid 
solution in which the forces of combination are stronger than 
those of diffusion. CuAl 2 , FeSi, and FeSi 2 have been clearly 
considered as chemical compounds, on the basis that structurally 
equivalent atoms are chemically identical. The explanation of 
the fact that the composition of such phases as these corresponds 



Cu i 

0/L 
1 

CUL 

1 

Cm. 



Affi 



CuAl CuAl 2 



<** 



j5/7 



.Sn 



S'A'/jW 

FIG. 136. Graphical representation by Westgren and Phragmen of structural 
analogies and common ratios of total number of valence electrons to total num- 
ber of atoms, for some copper and silver alloys. 

to simple stoichiometric proportions is sought therefore in the 
crystal structures. However, more recently some cases have 
been found where the composition corresponds with constant 
and simple stoichiometric proportions without reference to 
regularity in the crystal structure. Westgren and Phragmen 1 
point out the case of Ag 3 Al which has a crystal structure appar- 
ently isomorphous with /3-manganese, even to the relative inten- 
sities of x-ray interferences (see the pattern for the y phase, 
Fig. 132). Preston 2 has shown that the 20 atoms of manganese 

1 Trans. Faraday Soc., 25, 379 (1929). 
z Phil Mag. (VII), 5, 1198 (1928). 



292 APPLIED X-RAYS 

in the unit cell are divided into two groups, one containing 12 
and the other 8 equivalent atoms. Now in Ag^Al the 15 silver 
atoms cannot all be unequivalent to aluminum atoms, and any 
possible division of the two kinds of atoms into unequivalent 
groups will yield entirely different intensity relationships from 
those in ^-manganese. The inevitable conclusion, therefore, is 
that the silver and aluminum atoms are distributed at random 
and approximately uniformly over the two groups of structurally 
equivalent atomic positions. From the standpoint of constant 
and simple stoichiometric proportions Ag 3 Al is a chemical com- 
pound; from the standpoint of crystal geometry and the earlier 
definition of Westgren and Phragmen it is not. The explanation 
of proportions must, therefore, be sought elsewhere than in 
structural equivalence, and probably in the ratio of valence 
electrons to atoms as explained later. 

5. Analogies and Generalizations from the Study of Alloys. It 
is always the method of science to try to find a thread of generali- 
zation or correlation running through a mass of experimental 
facts. Alloy formation seems at first sight to be hopelessly 
complex, but x-ray investigations primarily in the laboratory of 
Westgren have disclosed orderly processes and relationships 
where other methods have fallen short. Some of these analogies 
summarized in a paper by Westgren and Phragmen, 1 together 
with more recent developments, are briefly outlined in the follow- 
ing paragraphs. 

a. In 1926 W. Hume-Rothery 2 suggested that the @ phases of the 
system Cu-Zn, Cu-Al, and Cu-Sn are analogous in structure. As their 
compositions correspond approximately to the formula CuZn, Cii2Al, 
and CiuSn, he also put forward the hypothesis that their structural 
similarity might be due to the fact that in each case the ratio of valence 
electrons to atoms is 3:2. X-ray investigations have confirmed the 
assumption that the said phases have the same type of structure. 3 In 
each case the atoms occupy the points of a body-centered cubic lattice. 
In the /3-Cu-Sn-phase the Cu and Sn atoms seem to be distributed at 
random over the lattice points, but in /3-Cu-Zn and /3-Cu-Al the different 
kinds of atoms are mainly oriented in networks of their own, forming 
what may be denominated " super-lattices." Phases of this structure 

1 Trans. Faraday Soc., 25, 379 (1929). 

2 HUME-ROTHERY, J. Inst. Metals, 35, 295 (1926). 

3 WESTGREJST and PHRAGMEN, Phil. Mag. (VI), 50, 331 (1925). 
PERSSON, Natnrwissenschaften, 16, 613 (1928). 
WESTGREN and PITRAGMEN, Z. anorg. Chem., 175, 80 (1928). 



THE STRUCTURE OF ALLOYS 293 

have been found in several binary alloys of Cu, Ag, and Au with other 
metals and, in fact, they all occur at concentrations making the ratio 
of valence electrons to atoms about 3 :2. 

b. In many cases a phase (7) of a complicated cubic structure has 
been found, having usually 52, but in some cases 8 X 52, i.e., 416, atoms 
in its elementary cube. When Cu, Ag, or Au is combined with a 
bivalent (Zn, Cd . . . ) the homogeneity range of this phase corre- 
sponds to formulas of the type CugAh. In these phases there are 21 
valence electrons to 13 atoms. The type of phase present in the Cu-Sn 
system has an extremely narrow range of homogeneity. It is homo- 
geneous at 32.6 per cent Sn, 1 as shown by Heycock and Neville, 2 corre- 
sponding to CusiSiig, which gives again 21 valence electrons to 13 atoms. 

c. Phases of the systems Fe-Zn, Co-Zn, Ni-Zn, Rh-Zn, Pd-Zn, Pt-Zn, 
Ni-Cd also give the same diffraction pattern as 7-brass arid correspond to 
the ratio 21:13 if zero valence is assigned to the transition (Group 
VIII) elements. 

d. The close-packed hexagonal structure (e), an atomic grouping 
which seems, moreover, to be connected with a certain concentration 
of valence electrons Ji, is also commonly present in these systems. 

e. Figure 136 gives a survey of the occurrences of analogous phases in 
some binary Cu and Ag alloys. The homogeneity ranges of the inter- 
metallic phases in the different systems are here indicated on one and 
the same scale, denoting the concentration of valence electrons. As will 
be seen, the homogeneity intervals of analogous phases all include, or 
come very close to, certain common concentration values indicated by 
vertical lines in the figure. 

/. In some cases when in an alloy the ratio of valence electrons to 
atoms is 3:2 and a phase having a body-centered cubic lattice might 
thus have been expected, the atoms have instead been found to be 
grouped in the same way as in /3-manganese. Just as this metal differs 
from its neighboring elements in respect to crystal structure, these inter- 
metallic phases, for some reason, form exceptions to the general rule. 
A phase of this kind is found in the Ag-Al system. 3 Its range of homo- 
geneity is so narrow that it may be denoted by a mere line in the equi- 
librium diagram. Its composition corresponds to AgsAl, from which it 
is evident that its ratio of valence electrons to atoms is 3:2. Other 
good examples are AugAl and CiuSi. 

g. In order to explain the facts of structures of binary alloys it is 
evident that the most important factor is the number of valence elec- 
trons per atom. Electron configurations in metal atoms and molecules 
in the vapor state are known from spectroscopic work but not for solids 

1 GLOCKER, "Materialpriifung mit Rontgenstrahlen," p. 281 Berlin 1927. 

2 HEYCOCK and NEVILLE, Phil. Trans., 202, 1 (1904). 
BERNAL, Nature, 122, 54 (1928). 

3 WESTGREN and BRADLEY, Phil. Mag. (VII), 6, 280 (1928). 



294 APPLIED X-RAYS 

unless new work on the fine structure of spectra of very soft x-rays bears 
out present promise of enabling energy-level determinations. The num- 
ber of valence electrons per atom in metals is most easily determined 
from magnetic susceptibilities. In a crystal like diamond with homo- 
polar or electron-pair bonds the coordination number is equal to the 
valence or number of outermost electrons in the case of carbon four. 
In a metallic bond, however, the coordination number, usually 8 or 12, 
is greater than the valence number of the atom, so that it is not possible 
to assign a certain pair of bonding electrons to a certain pair of atoms. 
Thus each of the bonding electrons in a metal lattice must encircle in 
the course of time all the atoms in the lattice in the same way, and thus 
transport an electric current through the lattice. These are the valence 
electrons in metallic bonding. It does not follow that all the electrons 
which belong to the outermost shell in the free atom act as valence elec- 
trons in the crystalline combination, for some of these must fall back 
into the second outermost shell, which in many metallic elements is 
uncompleted, when the atoms combine with a metallic bond. 

h. A general rule as stated by Dehlinger 1 is as follows: When in the 
fusion of two metals with different valence electron number per atom 
(for example, Cu, 1 and Zn, 2) concentrations are reached at which the 
resulting average valence electron per atom (or the ratio of the total 
number of electrons to the number of atoms) varies markedly from a 
whole number, an intermetallic compound is formed. 

i. Upon the basis of the foregoing generalizations it is possible to 
classify binary alloys in a new and fundamental way, as follows: 

I. Metallic compounds of metals with different valence electron numbers. 

1. Body-centered cubic lattice (#) with the average valence electron 
number j^; examples: CuZn, CiuAl, CiuSn, CoAl, etc., where the 
numbers arc Cul, Zn2, A13, Sn4, CoO. 

Similar lattices related to /3-Mri with number ^ as for Ag^Al and 
CWSi. 

2. -/-phase with average valence electron number 2 Ksj as in Cu 5 Zn 8 , 
CugAU, Cu 31 Sri s, Fe 5 Zn 2 i, etc. 

3. Hexagonal e phase with number %, as in CuZn 3 , CiisSn, AgsAla, etc. 

4. Other compounds, as CuPd, Ag&$b, FeZn 8 , Cu 2 Mg, Mg 2 Cu, etc. 
II. Alloys of metals with equal numbers of valence electrons without 

compounds. 

1. With continuous series of mixed crystals, as Ag-Au, Au-Cu, Mn- 
Ni, Mn-Co, Mn-Fe, Ni-Co, Ni-Fe, Co-Fe, Pt-Ir, Pt-Rh, Au-Ni, 
Cu-Mn, Cu-Ni, Ag-Pd, Au-Pt, Au-Pd, Cu-Pt, Cu-Pd, Fe-Pt, 
Ni-Pt, Bi-Sb. 

2. With intervals of non-miscibility in the solid state, as Ag-Cu, 
Ag-Pt, Au-Mn, Au-Co, Au-Fe, Cu-Co, Mg-Cd, Cd-Hg, Pb-Sn. 

1 Z. Elektrochem., 38, 149 (1932). 



THE STRUCTURE OF ALLOYS 295 

3. With intervals of non-miscibility in both liquid and solid states, 
as Ag-Mn, Ag-Ni, Ag-Co, Ag-Fe, Ag-V, Cu-Fe. 

4. Superstructure phases observed for some of these systems: Au-Cu, 
Cu-Pd, Cu-Pt, Mg-Cd, Ni-Mn, Fe-V, Fe-Cr, Au-Pt, Ag-Pt. 

III. Alloys of metals with apparently different valence electron numbers but 
forming no compounds: Sn-Al, Pb-Tl, Pb-Sb, Sn-Bi. 

IV. Alloys of metals with apparently the same electron numbers but form- 
ing compounds (usually with non-metallic properties): MgZn 2 , CdSe, 
HgTe, GaAs, InSb. 

V. Compounds with unknown numbers of valence electrons: Fc2\V, Fe 3 W2 
Fe 3 Mo 2 , Co-Cr, Ni-W. 

j. Miscibility and compound formation in metals depend much less 
on radius ratios than is true for polar salts (see page 268). Abnormal 
cases may involve specific influence of atomic kernels, including abnor- 
mally strongly bound valence electrons in Hg, Tl, Pb, etc., accounting for 
superconductivity, and the especially small influence of the kernel in 
silver so that this metal is similar to the alkali metals in many properties. 

k, Westgren 1 has shown that the divergence of the transition elements 
of Group VIII of the periodic system from other metals is manifested 
in three ways: these elements alone are able to form phases with NiAs 
structure; when combined with hydrogen, boron, carbon, or nitrogen 
they give products with metallic properties, which is not the case with 
other elements; and in the ft and 7 phases of alloys with Zn, Cd, Al, etc., 
they appear to have zero valence in maintaining the ratios 3:2 and 
21:13. 

6. The Systematization of Iron Alloys. From the viewpoint 
of crystal chemical generalizations the iron alloys form a unique 
series on account of the complications introduced by the poly- 
morphic phases. Sufficient x-ray data are now at hand so that 
some remarkable relationships have been observed by Wever. 2 
All the many iron alloys may be classified under four types: 
(a) open 7-field, illustrated by the iron-nickel system in Fig. 137. 
(6) the closed 7-field illustrated by iron-chromium; (c) the 
expanded 7-field (iron-carbon) ; and (d) the contracted 7-field 
(iron-boron). Figure 138 shows a periodic arrangement of the 
atoms and the description as to which type of binary alloy is 
formed. The open 7-field for alloys with metals of Group VIII, 
the closed 7-field in the center of the periodic table and insolu- 
bility for elements of Groups I and II are clearly apparent. 
That these differences are due primarily to atomic dimensions 

1 /. Franklin InsL, 212, 577 (1931). 

2 WEVER, Ergebnisse der technische Rontgenkunde, 2, 240 (1931). 



296 



APPLIED X-RAYX 



is shown by Fig. 139. The elements with largest atomic radii 
are insoluble in iron, and those with smallest radii are most soluble 
and form alloys which are characterized by open or expanded 
7-field, while intermediate elements narrowed the 7-phase. 



1,800 
1.600 

1,400 

? 

Q 1,700 



1,000 
800 
600 
400 
100 



10 20 30 40 50 60 70 60 90 100 
Nickel in Per Cent 



l,OUU 

1,500 
1,400 

1,300 
5) 
o 1.700 

c 

; 1,100 

| 1,000 

S. 900 
E 
600 

100 
600 


N* 












^ 




1 ^ 


^ 






\ 








^ 


>s 














r 


^ 






/ 


/- 


- 




j\ 

-a 




A 








\y 






















) 1 7 3 
PerCent C 



1,800 
1,600 

o L 400 
jtfOO 

I W 

2 800 
o 

SL 600 
E 
400 

200 

c 




10 70 30 40 
PerCent Fe 3 C 


1,500 
1400 










Fe^ 


62 



X 


















= 


_~ " 





===== 


MM> 


1,300 

CD 



1,200 

\ 1,100 

-f- 

\ 1,000 
tx 
E 




\ 




/ 


/" 


s; 


^1 


^ 


\^ 











/ 


































^ 

r 
^ 

cc 


\\ 











r 










- 


L 


- - 








- 












f_ 900 
800 












700 
ftnn 


cc 










- 














































) 10 20 30 40 50 60 70 80 90 100 02468 1C 
Chromium in Per Cent Per Cen+ B 



FIG. 137. Classification of binary iron alloys. 

Such generalizations are highly gratifying and rapid progress may 
be expected in classifying similarly other systems of binary alloys. 
7. Steel (Fe-C Alloys). The most important possible applica- 
tion of x-ray analysis to the structure of alloys is, of course, to 
the series of iron-carbon alloys. There are several reasons for 
this, aside from the practical utility of steel. The equilibrium 
diagram is one of great complexity because of the great variety 



THE STRUCTURE OF ALLOYS 



297 



of forms involving the four allotropic forms of pure iron; hence, 
there has been among metallurgists for a great many years the 
widest divergence of opinion concerning the actual constitution 
of many of the iron-carbon phases. The x-ray has been eagerly 
sought for a final answer to these mooted problems; while it 
has already given many hopeful signs, the results are still insuffi- 
cient to more than open the subject. 

The facts established by x-ray analysis of steel may be briefly 
summarized as follows: 

a. Austenile, formed by quenching Fe-C alloys from above 
the AS transformation point, has the structure of 7-11-011 (face- 





a 


b 


n b 


T 




fi 






r 








vnr 
a 


b 


I 


3 Li 


























1H 








2 He 


n 




4 Be 



12Ma 

A 

20Coi 

A 






5B 
O 




6C 

a 




7N 
a 




80 




9F 








10 Me 


m 


11 Na 








13 Al 




14 Si 




15P 




165 





17CI 








18A 


w 


19 K 

A 






21 Sc 




22Ti 




23V 




24Cr 




25 Mn 




26Fe 


27Co 


28Ni 






29Cu 

a 




30Zn 
D 




31Ga 




32Ge 




33As 




34Se 




35 Br 








36 Kr 


* 


37 Rb 




38Sr 




39Yt 




40Zr 




41Cb 




42Mo 




43 Ma 




44Ru 


45Rh 


46 Pd 






47Ag 




48Cd 

A 




49 In 




50Sn 




51Sb 




52Te 




531 








54Xe 


YL 


55Cs 

A 




56Ba 

A 




58 Ce 



72 Hf 




73Ta 




74W 




75Re 




760s 


77 tr 


78 Pt 






79Au 
D 




80Hg 




em 

A 




82Pb 




83Bi 




84 Po 




85- 








86Rn 


m 


87- 




88Ro. 

A 




89Ac 




90Th 




91 Pa 




92 U 

















Open T-Fie 

Closed T- Field 



D Expanded y- Field 
O Contracfed y- Field 



A Insoluble 



FIG. 138. Periodic table showing effects of chemical elements in binary iron 

alloys. 

centered cubic). Carbon causes an enlargement of the lattice. 
Westgren and Phragmen found the dimensions of the unit cell 
to be 3.629 A.U. for a saturated solution (1.7 per cent) quenched 
from 1100 C., and 3.606 A.U. for a specimen containing 0.9 
per cent C quenched from 750 C. A specimen containing 12.1 
per cent Mn and 1.34 per cent C had a parameter 3.624 A.U. 
As already explained, the carbon atoms are placed interstitially. 
The carbon may be atomically and irregularly dispersed or the 
atoms may be more definitely arranged, in the sense that an 
atom of 7-iron may be replaced by a complex of an iron combined 
with one or more carbon atoms. In other words, austenite is a 
solid solution of carbon or Fe 3 C (cementite) in 7-iron. 



298 



APPLIED X-RAYS 



b. Cementite. The only definite compound formed by iron 
and carbon, Fe 3 C, crystallizes in the orthorhombic system. The 
unit parallelepiped has the dimensions 4.518 by 5.019 by 6.736 
A.U. or the axial ratios 0.671 : 0.753: 1. This compound is found 

75 



Inso/ub/e 

Narrowing of f- phase 

Expanding of p-phcxse 




AQ 50 

Atomic Number 

FIG. 139. Curve showing effect of atomic radius upon formation of binary iron 

alloy. 

in pearlite (the eutectoid mixture of a-iron and cementite formed 
by slow cooling of austenite from the transformation point), 
troostite (a-iron and cementite in colloidal dispersion), sorbite, and 
in the massive spheroidal condition. Meteoric cohenite has the 
same structure. 



THE STRUCTURE OF ALLOYS 299 



c. Ferrite has the body-centered cubic structure of pure a-i 
Carbon has a very limited solubility in it, since the diffraction 
lines for the numerous specimens have the same position as for 
pure electrolytic a-iron. A widening of the lines and the dis- 
appearance of the resolution of doublet lines may be taken as an 
indication of a slight increase (up to 0.3 per cent) in the lattice, 
but non-uniformly, since pure iron dimensions are still indicated. 

d. fi-Iron. There is no x-ray evidence of /3-iron, since there 
is no structural discontinuity between a- and 7-iron. 

e. Martensite. This interesting constituent found in hardened 
steel has received more attention than any other phase of x-ray 
analysis of alloys. Martensite is formed and retained at room 
temperatures when the y-a transformation is delayed by suffi- 
ciently rapid cooling until a temperature of 300 C. is reached. 
The cooling may be slower in the presence of retarding elements 
such as nickel and manganese. The simple facts were first 
established that martensite gives the spectrum of a-iron and that 
the diffraction lines are broad and diffuse. 

More careful technique in the preparation of samples and in 
photographing diffraction spectra has served to clarify the 
problem. Fink and Campbell 1 found evidence in drastically 
quenched eutectoid and hypereutectoid steels of a body-centered 
tetragonal structure. This was not uniform with lower carbon 
contents, but with 1.5 per cent carbon the value of a was 2.85 
A.U. and of c, 3.02 A.U. (body-centered cubic a-iron, a = 2.86 
A.U.). It was found to be less stable at low temperatures 
than the 7-iron lattice and disappeared on tempering at 100 C. 
Bain then showed that the face-centered cubic lattice can be 
considered as a body-centered tetragonal lattice with an axial 
ratio of \/2 and a = 2.54 and c = 3.60 A.U. Of this, the body- 
centered cubic lattice would be a special case with axial ratio 1. 
Hence, the martensitic tetragonal structure might represent an 
arrested stage in transformation from face-centered cubic 
(7) to body-centered cubic iron (a). This discovery was con- 
firmed by Seljakow, Kurdjumow, and Goodtzow, 2 who showed 
further that the axial ratio c/a increases with carbon content at 
constant heating and quenching conditions and with the tem- 
perature before quenching at constant carbon content. Honda 



1 Trans. Am. Soc. Steel Treating, 9, 717 (1926). 

2 Z. Physik, 45, 384 (1927). 



300 APPLIED X-RAY 8 

and Sekito 1 found still later that the outer layer of quenched 
carbon steel contains a body-centered tetragonal lattice, 0-mar 
tensite, and the inner portion a body-centered cubic lattice,a-mar- 
tensite, with a gradual change in the axial ratio from 1.07 to 1. 
Upon annealing, the tetragonal structure gradually changes to 
cubic without passing through a stage of an intermediate axial 
ratio. Kurdjurnow and Kaminskii, 2 however, maintain that the 
tetragonal structure exists on the interior of quenched specimens. 
There is some difference of opinion also concerning the actual 
positions of the carbon atoms (although it is most probable that 
two carbon atoms substitute for one iron atom) and concerning 
the exact mechanism of the transformation from face-centered 
cubic to body-centered tetragonal and then to body-centered 
cubic structures. At any rate, it may be concluded that marten- 
site is a supersaturated solid solution of carbon ina-iron, although 
austenitc is also almost invariably indicated by its diffraction 
pattern, and that the intermediate tetragonal structure together 
with inherent complex strains accounts for hardness. The vari- 
able parameters of course could account for the very diffuse x-ray 
diffraction interferences as well as distortion or very small grain 
size. 

8. The Problem of Hardness. Six views have 3 been presented 
to account for the hardness of martensite : (a) solid solution, (6) 
supersaturated solid solution, (c) fineness of grains, (d) distorted 
space lattice, (e) presence of minute particles of carbide, and (/) 
internal strains. These reduce to two general phenomena associ- 
ated with hardness: (1) distortion and (2) slip resistance by the 
keying action of small particles. 

Bernal 4 points out that a pure metal crystal, when stressed, 
yields not by cleavage or fracture but by the formation of glide 
planes in which layers of atoms slip over each other with little 
loss of energy. It is possible that in the ideal case of an abso- 
lutely pure metal with infinitely small stress it would lose no 
energy at all in gliding. Its behavior would, in fact, be that 
of a liquid, and a pure metal crystal would only differ from a 
liquid by the regular ordering of its atoms. Actually, however, 

1 Science Repts. Tohoku Imp. Univ., 17, 743 (1928); J. Study Metals, 6, 
380 (1928). 

2 Nature, 122, 475 (1928); Z. Physik., 53, 696 (1929). 
3 SAUVEUR, Tram. Am. Inst. Mining Met. Eng., 73, 859 (1926). 
4 Tram. Faraday Roc., 25, 370 (1929). 



THE STRUCTURE OF ALLOYS 



301 



when a certain amount of gliding has taken place, a hardening 
sets in which prevents further gliding. This hardening is almost 
certainly due to a distortion of the lattice elements. What 
appears to be an exactly similar distortion is produced by the 
presence of foreign atoms in solid solution. (It is, of course, 
to these properties of hardening 
by cold working and alloying i hat 
metals owe their technical impor- 
tance.) The distortion of the 
lattice manifests itself in a variety 
of ways; as well as the mechani- 
cal hardening there is always a 
very large increase in the electri- 
cal resistance, but what shows 
most clearly the nature of the 
change is the x-ray evidence. In 
a strained or impure metal crystal 
the reflection of a monochromatic 
ray in a crystal plane, instead of 
occurring extremely sharply over 
a width of a few seconds of arc, 
occurs more and more diffusely 
as the strain is increased. This 
is an indication that the atoms 
no longer lie in absolutely plane 
parallel layers but that there is 
a more or less irregular displace- 
ment of certain atoms from the 
average planar position. A 
similar but periodic displace- 
ment is produced by the tem- 
perature vibration of the atoms, 
and indeed on looking at an x-ray 
photograph of a metal which shows very blurred lines it 
is impossible without further information to know whether 
they are due to impure crystals, distorted crystals, or hot crystals. 
It is probable that the effects which Dr. Kapitza 1 has found in 
high magnetic fields are due to a similar distortion of the lattice. 
It is possible that solid solutions do not represent stable states 
but metastable ones; that given sufficient atomic mobility, or 
. Roy. Soc. (London), 123, 292 (1929). 




Soakmoj Time in Hov*" 

FIG. 140.- Curves showing age-hard- 
ening of copper-silver alloys. 



302 APPLIED X-RAYS 

sufficient time, all solid solutions would separate out into their 
constituent compounds, or form regular superstructures. Frorr 
this point of view the solid solution is a mere regular form of a 
glass. 

9. Age-hardening. Several alloy systems, notably Al-Cu- 
Si (duralumin), Au-Cu (intermediate state of AuCu), Ag-Cu, 
Cu-Be, Cu-Fe, low-carbon (armco) iron, etc., are characterized 
by hardening with time after a heat treatment. Figure 140 
shows the variation of hardness with time of mixed crystals of 
silver and copper as measured by Agnew, Hanan, and Sachs. 1 
The alloy was quenched from 770 C. and then held at a tempera- 
ture of 250 C. This age-hardening has great technical signifi- 
cance, since an alloy of steel in light metals may be formed while 
in easily worked condition and then the product subsequently 
strengthened is hardened with aging. Difficulties are, of course, 
encountered even at room temperatures if steel sheets, for exam- 
ple, are not used for a considerable period after manufacture so 
that they will form far less easily. The phenomenon of age- 
hardening therefore has been subjected to numerous investiga- 
tions. If gold-copper mixed crystals containing about 50 atomic 
per cent gold with entirely random distribution of atoms above 
425 are cooled, an intermediate state can be observed from x-ray 
patterns. The unit cell has the tetragonal form (AuCu) of the 
final equilibrium state but in a part of the lattice the copper and 
gold atoms have definite arrangement and in the remainder are 
completely random. This inhornogeneous irregularity is to be 
distinguished from the true homogeneous substitutional solid 
solution type. The intermediate state is characterized by great 
hardness. By long heating under 428 the much softer, entirely 
definitely arranged tetragonal state is reached. Diffraction 
lines for CuAl 2 have been observed after long heat treatment of 
duralumin. The theory of hardness has been based on the con- 
ception of separation of very small colloidal particles which tend 
to key slip on planes. However, newer x-ray researches seem to 
demonstrate that at the point of greatest hardness no new 
lattice is necessarily observed. There may be a slight broadening 
of x-ray lines, such as might be produced in very slight deforma- 
tion, but no change in lattice dimension of the old lattice is 
observed as ought to be expected from concentration changes, due 
to separation of a new phase. Upon the basis of magnetic meas- 

1 Z. Physik., 66, 350 (1930). 



THE STRUCTURE OF ALLOYS 303 

urements on copper-iron specimens Tammann has presented the 
hypothesis that, before the separation of a new phase, some kind 
of grouping within the coherent old lattice of the chemically 
different atoms occurs which in an unknown manner causes 
increase in hardness. This agrees with the actual observation of 
inhomogeneous atomic distribution in the intermediate state of 
AuCu and with the most recent observations on duralumin at 
maximum hardness by Hengstenberg and Wassermann 1 of 
increase in line intensity and decrease of fogging due to scattering. 
The dependence on temperature of the age-hardening process is 
still unexplained. 

10. Alloy Steels. The success attendant upon the complete 
interpretation of the highly complex x-ray diffraction patterns 
obtained with alloy steels within the past two years has been 
truly amazing. A rationally scientific explanation can now be 
given to the properties of various alloy steels in terms of ultimate 
constitutions and structure. Ranges of stability of phases are 
defined and predictions of the constitution and properties of new 
alloys are non-empirically made. A very few of all the facts 
which x-rays have disclosed are enumerated simply as an indica- 
tion of achievements and possibilities, other results being briefly 
noted in the tabular summary of alloys : 

a. The identification in the iron-tungsten system of Fe 2 W (hexagonal) 
and Fe 3 W 2 (trigonal, 40 atoms per unit cell) and of Fe 3 Mo2 corresponding 
to Fe 3 W2 in the iron-molybdenum system (Fig. 134). 2 

6. Studies of the iron-chromium-carbon system and stainless steel 3 with 
the following conclusions: 

(1) Iron and chromium form a continuous series of solid solutions. 

(2) Phases in the Fe-Cr-C system: 
a-metal. 

7-metal. 

Cementite (Fe, Cr) 3 C in which chromium may rise to 15 per cent. 

Cubic chromium carbide (Cr, Fe)4C in which chromium may be sub- 
stituted by iron up to 25 per cent. 

Trigonal chromium carbide (Cr, Fe) 7 C 3 with iron up to 55 per cent. 

Orthorhombic chromium carbide (Cr, Fe) 3 C 2 with only a few per cent of 
iron substituting. 

*Z. Metallkunde, 23, 114 (1930). 

2 ARNFELT, Carnegie Scholarship Memoirs, Iron and Steel Inst., Vol. 
XVIII, p. 1 (1928). 

3 WESTGREN-, PHRAGMEN, and NEGRESCO, /. Iron and Steel Inst., 117, 383 
(1928). 



304 APPLIED X-RAY 8 

(3) In annealed ball-bearing steel the chromium is contained in ccmentite. 
''Double carbide" causing rejection, due only to unequal distribution of 
eementitc. 

(4) Carbide in stainless steel is cubic chromium carbide saturated with 
iron (35 per cent). 

(5) Steel for dies (17 per cent nickel, 11 per cent chromium, 2 per cent 
carbon) contains trigonal chromium carbide with more than half of the 
chromium substituted by iron. 

(6) Ferro-chromium (60 per cent Cr, 5 per cent C) peritectic alloy of cubic 
chromium carbide with iron substituting partially, a-metal, and some 
trigonal carbide. 

c. The identification in high-speed steel of a true double carbide Fe 4 W2O, 
face-centered cubic, a = 11.04 A.U., containing 112 atoms per unit cell. 1 

d. The identification and proof of Fe^N, important in case hardening of 
iron by nitrogen, with the iron on a face-centered cubic lattice, a ~ 3.789 
A.U. and the nitrogen at the center. 2 

11. Crystal Structure and Magnetism. The fact that a-iron 
is magnetic and 0-iron non-magnetic, though x-rays detect no 
structural discontinuity between these, seems to indicate that 
magnetic properties are not functions of the arrangement of atoms 
in space. However, Persson 3 in Westgreri's laboratory has 
recently demonstrated that the magnetic Heusler alloys (copper- 
manganese-aluminum) always show the x-ray diffraction lines 
of the 0-phase. In this the basic lattice is body-centered cubic, 
upon which is superposed a face-centered cubic lattice of alumi- 
num atoms with twice the dimensions of the basic lattice. Hence 
the unit cube contains 16 atoms, of which 12 are copper + man- 
ganese and 4 aluminum. The formula (Ou, Mn) 3 Al is sub- 
stantiated by the x-ray results. It is further essential that the 
concentration of manganese must be above a limiting value in 
order that magnetic properties may develop. In other words, the 
pattern for the /3-phase may appear for non-magnetic specimens if 
manganese is insufficient. Further work will be awaited with 
interest. 

12. X-ray Studies of the Mechanism of Corrosion of Alloys. 
One of the most remarkable recent examples of the application 
of x-ray diffraction methods to metallurgical problems is the 
study made by Graf and Glocker 4 of the mechanism of corrosion 
of single crystals of gold-copper alloys. Carefully prepared 

1 WESTGREN and PHRAGMEN, Trans. Am. Soc. Steel Treating, 1928, 539. 

2 HAGG, Nature (Sept. 1, 1928). 

3 Naturwisscnschaflen, 16, 631 (1928). 

4 Metallwirtschaft, 11, 77 (1932). 



THE STRUCTURE OF ALLOYS 305 

specimens were analyzed by the rotation method, the patterns 
showing the characteristic solid solution and superstructure 
phases of this system. After etching with strong oxidizing 
agents, the specimen produced the interferences for pure gold in 
a surface layer oriented exactly like the original alloy layer. 
Thus with the removal of the less noble copper atoms from the 
mixed crystal lattice the remaining gold atoms apparently had 
grouped together into a pure gold crystal layer with entirely 
different lattice spacing from that of the underlying unattacked 
alloy. Weak oxidizing agents, sulfur-containing compounds, 
and corrosive gases had the effect of producing an outer layer 
of alloy much richer in gold than the original crystal. When 
gases attacked the surface at high temperatures, at which atoms 
diffuse easily, the copper atoms could all reach the surface and 
escape from the protective action of the gold atoms, so that 
the corrosion zone was pure gold. In order to explain these 
results a definite mobility of the gold atoms after the copper 
atoms are removed from the lattice is necessary, either by a direct 
way in which the gold atoms in unstable configuration are brought 
to new and stable lattice positions by the action of outer one- 
sided lattice forces in the layer, as in the case of weak oxidizing 
agents, sulfurizing compounds and gases at low temperatures; 
or indirectly by diffusion at higher temperatures or by ionization 
in the corrosive liquid agent such as a strong oxidizing agent. 
In the latter case the gold atoms exceed the wave potential which 
holds them in place in the solid lattice and they escape as ions. 
They return to the lattice by imparting the ionic charge to the 
remaining neutral, less noble, copper atoms in the interface 
between solid and solution, and thus displace them to form a 
copper-free gold layer. By attack of other agents at low tem- 
peratures only the copper atoms are ionized and separated from 
the lattice. The gold atoms left behind are sufficiently mobile 
in their unstable positions to regroup under the action of the 
one-sided lattice forces. A small fraction of copper atoms which 
had been completely surrounded and protected by gold atoms 
remains in the layer as is readily ascertained from the diffraction 
patterns. An interesting further observation has to do with 
limits of resistance to corrosion as a function of alloy composition. 
Tammann has stated certain rules, based on experiment, con- 
cerning these limits at which corrosive attack can occur in alloys. 
Resistance to corrosion begins at a remarkably definite content 



306 APPLIED X-RAYS 

of the noble metal component. Depending on the corrosive 
agent the various resistance limits correspond to contents ofr 
n/8 mole of the noble component. In the present case of gold- 
copper alloys, resistance to attack of weak oxidizing, sulfur- 
containing, and gaseous agents begins at 25 atomic per cent of 
gold (% mole), and the corrosion zone is a gold-rich solid solution. 
The alloy with 50 atomic per cent of gold (% mole) is the resist- 
ance limit for strong oxidizing agents, and the corrosion zone is 
pure gold. As a result of these observations a complete picture 
of corrosion and resistance mechanisms is afforded all based 
upon the interpretation of x-ray diffraction patterns. 



CHAPTER XVI 

THE CRYSTAL STRUCTURES OF COMPOUNDS OF 
CARBON AND THEIR PRACTICAL SIGNIFICANCE 

The examination of the crystals of organic substances repre- 
sents the newest phase of the still infant science of x-ray crystal 
analysis. This hesitancy among experimenters is in one sense 
surprising, inasmuch as the organic chemist long ago introduced 
the simplifying and logical conceptions of spacial arrangements 
of atoms which have been the strength of the science as compared 
with the great complexities with which inorganic chemists have 
been confronted; on the other hand, crystallographic exami- 
nation has shown that the great majority of organic compounds 
crystallize in the very classes of low symmetry whose diffraction 
effects are the most difficult to interpret; and good crystals for 
analysis are usually impossible to obtain. It stands to the 
matchless credit of Sir William Bragg, always in leadership, that 
he undertook the problems fearlessly. His skill in combining 
x-ray data with other authentic information, to show that whole 
molecules instead of atoms are the units placed at the points of 
the lattice and to arrive at a final solution of structural problems, 
has given to organic chemistry the solid experimental facts of 
structure which have been hoped for. 

Sir William Bragg 1 speaks of another point of interest in these 
compounds as follows: 

Apart from the interest in determining structures of this kind, there 
is also the question of the " minor" ties which bind the molecules 
together; not so much the ties that bind the atoms together in the mole- 
cule. The ties which bind molecule to molecule are perhaps of a 
different and weaker nature and yet must be of immense importance in 
the constitution of the world, for after all a great deal of nature's work is 
done at moderate temperatures and simply by the laying of one mole- 
cule against another. 

The Carbon Structures. The structure of the compounds 
of carbon must find ultimate prototypes in the structure of 
crystalline carbon; of this there are two varieties: the diamond, 

1 Chem. Ind., 45, 245 (1926). 

307 



308 



APPLIED X-RAY 8 



crystallizing in the tetrahedral cubic system with each car- 
bon very definitely at the center of four other equidistant, 
carbons at the corners of a tetrahedron; and graphite, with 
a lower hexagonal symmetry. " Puckered " six-carbon rings 
are easily identified in the diamond lattice (Fig. 141). After 
considerable controversy Bernal 1 succeeded in proving from 
x-ray data that the carbon atoms in graphite are flattened into a 
plane so that three of the carbon neighbors remain at somewhat 







G. 141. Comparison oi crystal models of diamond and graphite. 
Central Scientific Company.) 



(Courtesy 



smaller distance from the central atom than in the diamond 
tetrahedra (1.42 A.U. as against 1.54 A.U. in diamond), and 
the fourth is at a greater distance (3.40 A.U.) in the next layer 
(Fig. 141). In other words, in graphite the atom has three 
strong bonds coplanar or very nearly so with itself, and one weak 
bond at right angles to these bonds. This bond may be easily 
ruptured so that one layer will slide over another to account for 
the lubricating properties of graphite. The peculiar lamellar 
structure also enables special types of reactions to occur as shown 
by Hofmann and Frenzel. 2 Graphite reacts with alkali metals 
to form stoichiometric compounds of the type C 8 K and C i6 K. 
X-ray diffraction data show no change in the distance between 



l Proc. Roy. Soc. (London), 106A, 749 (1924). 
2 Kolloid-%.. 58, 8 (1932). 



THE CRYSTAL STRUCTURES OF COMPOUNDS 309 

carbon atoms in the same layers, but the distance between layers 
.increases from 3.38 A.U. in graphite to 5.34 in C 8 K. Treatment 
with mercury regenerates graphite. In graphitic acid this dis- 
tance between layers is 6 A.U. which increases to 11 A.U. by 
swelling with water. 

One of the most interesting questions in the whole science has 
been whether the carbon atoms in ring compounds, e.g., aromatic 
series, lie in one plane, as in graphite and as the organic chemist 
has represented structures on paper, or are staggered as in 
diamond. A satisfactory answer to this question has been given 
only very recently; even yet it cannot be maintained that the 
shape of the benzene ring found for some compounds is necessarily 
the same in all aromatic compounds. A few of the important 
steps leading to the final conclusion will be outlined. 

The Structure of the Benzene Ring. a. Bragg Analysis of 
Naphthalene and Anthracene. The first selections for complete 
crystal analysis were naphthalene and anthracene, since solid 
benzene cannot be easily prepared. Bragg found for the dimen- 
sions of the unit prisms of these monoclinic crystals, each con- 
taining two molecules, the following: 

Naphthalene, a = 8.34, b = 6.05, c = 8.69, ft = 122 49'. 
Anthracene, a = 8.7, b = 6.1, c = 11.6, ft = 124 24'. 

The a and b axes are very nearly the same, but the c axis is con- 
siderably longer for anthracene than for naphthalene. This 
difference in the c axis suggested the difference in the length of 
the two molecules, since anthracene is represented as three con- 
tiguous benzene rings and naphthalene as two. Bragg then 
assumed that the closed rings of six carbon atoms, which were 
definitely known to exist in diamond, were carried over essentially 
unchanged into benzene, naphthalene, and anthracene. The 
difference in length between the two, 3 A.U., was exactly 
accounted for by the extra ring in anthracene. The constancy 
of the cross sections of the two cells results from the fact that it is 
determined not by the length but by the breadth and thickness of 
a single ring and, hence, is a measure of the space necessary for 
side-by-side linking of the two molecules in each unit cell. Fur- 
thermore, the theoretical length of the naphthalene molecule, 
6.65 A.U. , agrees with the length of the c axis, 8.69 A. U., if allow- 
ance of 1 A.U. is made for a hydrogen atom at each end. Further 
consideration showed that the two molecules in the unit cell were 



310 APPLIED X-RAY8 

arranged so that one is the mirror image of the other. In the 
monoclinic prismatic class, there must exist a plane of symmetry, 
a twofold axis perpendicular to the plane and, hence, a center of 
symmetry. If the molecules lack symmetry, then there must be 
four of them in the cell, one obtained by rotation of another 
around 180 deg., and the two from the first pair by reflection in 
the plane of symmetry. Hence, the molecules must have a 
center of symmetry, since only two are found. The cleavage of 
these crystals is easily accounted for as coming only in the direc- 
tion where hydrogen atoms from different adjacent molecules 
touch; in all other directions the strong forces due to the carbon 
atoms are involved. 

b. Miscellaneous Aromatic Compounds. Structure investiga- 
tions on fully halogenated benzene derivatives have not been 
particularly successful from the standpoint of elucidating the 
structure of the nucleus itself. The compounds C 6 C1 6 , C 6 Br 6 , 
and Cele were found to be centrosymmetrical and monoclinic, 
just as naphthalene, anthracene, and benzene were observed 
to be centrosymmetrical. The tendency, of course, was to incline 
towards the puckered nucleus. 

Diphenyl was found to crystallize 1 in the monoclinic system 
with the space-group C^. The indications were that it is centro- 
symmetrical. Presumably then the rings are not flat, for in that 
case the molecule would be expected to have at least a plane of 
symmetry which it did not seem to have. This conclusion was 
based on the fact that there were two molecules per unit cell in 
the crystal, while four asymmetrical molecules are required by 
the space-group. It is clear, of course, that failure to realize that 
only the minimum molecular symmetry is fixed by the crystal 
symmetry may lead to erroneous interpretations as Hendricks 
and Hilbert 2 have shown. The explanation proposed by Berg- 
mann and Mark 3 for the possible isomerisrn of some derivatives of 
fluorene prepared by Schlenk and Bergmann is based on an 
assumed puckered benzene ring which was incorrectly said to be 
required by molecular symmetries of compounds. Geometric 
isomers of fluorene and optical isomers of diphenyl derivatives 

1 HENGSTENBERG and MARK, Z. Kryst., 70, 285 (1929). 
CLARK and PICKETT, /. Am. Chem. Soc., 63, 167 (1931). 

2 /. Am. Chem. Soc., 53, 4280 (1931). 

3 Ber., 62, 750 (1929). 



THE CRYSTAL STRUCTURES OF COMPOUNDS 311 

can be explained with the flat benzene ring, since these need 
not be coplanar in the same molecule. 

c. The Structure of Hexamethylbenzene. The classical research 
by Mrs. Lonsdale 1 on hexamethylbenzene has done most to 
clear up the controversy. She demonstrated rigorously from 
x-ray diffraction data that in this compound the benzene nucleus 
is flat and that the carbon atoms in the methyl group also lie in 
this same plane. The choice of compound was particularly 
fortunate, since only one molecule per unit triclinic cell is found 
and the intensity data may be very directly interpreted. The 
direct x-ray information on axial lengths and angles is as follows : 

a = 9.010 A.U. a = 4427' 

6 = 8.926 A.U. = 11643' 

c = 5.344 A.U. 7 = 11934' 

The facts that a and 6 are nearly equal and that the angle 
between them is nearly 2?r/3 immediately suggested hexagonal 
structure. The factors in the (001) zone should repeat themselves 
closely throughout the series of planes (100) > (010), (010) > 
(1TO), (TlO) -> (TOO). This was tested by a comparison of 
structure factors which were calculated from the observed inten- 
sities by the formula 



F> cc VI - r- X 



sin 

where (0.15 -f cos 2 20) is the measure of the polarization factor 
for Mo Xa-radiation; F is the scattering power of the atoms and 
e~ m is the temperature factor. Two sets of calculations were 
made corresponding to F values for diamond (Ponte) and graphite 
(Bernal), respectively. These proved conclusively the hexagonal 
arrangement and the graphite arrangement; there was a marked 
similarity in the intensities of various orders from the (001) 
cleavage plane and those from the corresponding cleavage plane 
of graphite. The structure factor was also larger than for any 
other plane in the crystal and almost independent of the order of 
reflections, proving that the carbon atoms lay in or near the (001) 
planes. The factors for planes (340), (470), and (730) also were 
very large and these gave a further clue, since these were small 
spacing planes and therefore any deviation of the atoms from 
these planes would cause a more rapid falling off of structure fac- 
i/Voc. Roy. Soc. (London), A123, 494 (1929). 



312 APPLIED X-RAYS 

tor than would a similar movement away from a plane of larger 
spacing. In other words, the carbon atoms must lie at or near 
the intersections of these planes. There are 36 such intersections 
and only 12 carbon atoms. Since, however, there is an hexagonal 
arrangement in the (001) zone, the problem was greatly simplified. 
Mrs. Lonsdale calculated structure factors for the first six orders 
of the (100) plane for each possibility and the true arrangement 
at once derived. 

The immediate deductions are as follows: 

(1) The molecule exists in the crystal as a separate entity. 

(2) The benzene carbon atoms are arranged in ring formation. 

(3) The ring is hexagonal or pseudohexagonal in shape. In 
order to answer the question as to the sizes of the atoms in the 
rings and the dimensions of the ring itself, and whether or not the 
ring is plane, variations of three kinds are made from the positions 
of the atoms established: (a) a variation of atomic dimensions, 
(b) a variation in directions along which atoms lie (ring rotation), 
and (c) shifting of atoms perpendicular to the (001) plane, or a 
puckering of the benzene ring. The effect of each kind of varia- 
tion upon the structure factors was then determined and corn- 
pared with experimental results, with the following further 
deductions. 

(4) Diameter of the nuclear carbon atom 1.42 0.03 A.U. 
Diameter of the side-chain carbon atom 1.54 0.12 A.U. 

(diamond). The aromatic nucleus is therefore exactly like 
graphite in dimensions. 

(5) Only the plane ring gives anything like agreement with 
observations, again as in graphite. 

(6) The side-chain carbon atoms are attached radially to their 
respective nuclear atoms and lie in the plane of the ring. 

(7) Three of the valences of aromatic carbon are coplanar 
certainly, but no direct information is afforded concerning the 
fourth except that it must be so disposed as to give the ring as a 
whole a center of symmetry. This condition eliminates the 
Kekule static model with three double bonds. 

d. Further Recent Information Concerning the Benzene Nucleus. 
Since the analysis of hexamethylbenzene, renewed interest has 
been taken in the questions of the shape of the benzene nucleus. 
The fact that in C6(CH,3)6 it corresponds so closely in structure to 
the graphite type of ring indicates that very little deformation 
can have taken place. The expectation is that in fully substi- 



THE CRYSTAL STRUCTURES OF COMPOUNDS 313 

tuted derivatives the structure of the nucleus should remain 
similar. However, some symmetry has been lost, for the graphite 
ring possesses true hexagonal symmetry while the benzene deriva- 
tives are only centrosymmetrical. 

Banerjee 1 has made a careful reinvestigation of naphthalene 
and has shown that the intensity data are consistent with per- 
fectly flat rings. Hendricks and Hilbert 2 have shown that in 
meta-dinitrobenzene the carbon and nitrogen atoms are all in 
the same plane. The failure of attempts to form rrieta or para 
rings of benzene compounds indicates that the valences are not 
easily deformed in direction and that the benzene ring is very 
rigid. Dhar 3 has subjected diphenyl to complete analysis, 
including structure factor data from intensities, and proved that 
the rings are flat and lie in one plane and that the molecules 
are inclined to cell faces. The distance between rings in the 
molecule is 1.48 A.U., which is a mean of 1.42 (in graphite) and 
1.54 in aliphatic linkages. 

There is still uncertainty as to whether cyclohexane and 
reduced compounds have plane or puckered rings. The cis- 
forms of CeHeCle and CbH 6 Br 6 have greater symmetry than 
benzene and the halogen atoms belonging to one molecule lie in 
two planes. In naphthalene tetrachloride and dichlornaphtha- 
lene tetrachloride, one ring remains unreduced and retains aro- 
matic character, while the other has been reduced and might be 
puckered. Considerably more research is required to discover 
whether the aromatic character is bound up with a graphitic 
arrangement or whether this can persist when aromatic properties 
are lost. If the ring is flat in reduced derivatives, then the aro- 
matic nature must depend more on the fourth valence bond than 
on the configuration of the bond. 

One interesting question is this: In derivatives with flat rings a 
considerably higher symmetry might easily be expected for the 
crystal lattice than is actually observed. Even hexamethyl- 
benzene has only triclinic symmetry. This would seem to indi- 
cate that the lower symmetry of the molecular arrangement in 
space is due to the hydrogen atoms in some way or to a distortion 
of the ring so slight as not to affect the structure factors markedly 
for the flat ring. Of course, reliable interpretation of data on 

1 Nature, 125, 456 (1930); Indian /. Phys., 4, 557 (1930). 

2 Loc. cit. 

3 Indian J. Phys., 7, 43 (1932). 



314 APPLIED X-RAYS 

crystallized benzene is still lacking. In the derivatives with 
more than one nucleus (naphthalene, diphenyl, etc.) the rings 
may be flat but still not coplanar. 

Some light on these questions is afforded by electron diffraction 
studies on benzene, cyclohexane, etc., vapors. The data best 
agree with a plane hexagonal ring with edge length 1.42 A.U. for 
benzene and a puckered ring with edge length 1.54 A.U. for 
cyclohexane. Just what happens when these molecules are 
condensed into crystals with a lower symmetry is still doubtful. 

There are evidences from both x-ray and electron diffraction, 
of course, that the aliphatic carbon atom is tetrahedral or sphe- 
noidal. Only in methane, CC1 4 , or other fully substituted deriva- 
tives is the regular tetrahedron maintained. If the carbon atom 
is unsymrnetrically loaded with halogen atoms, for example, 
tetrahedral symmetry is lost. But even CBr 4 crystallizes in two 
forms: tetrahedral symmetry at low temperatures and bi-mole- 
cules (monoclinic) at higher temperatures with deformation of 
the single molecules and a loss in symmetry. 

The Results of Crystal Analysis of Organic Compounds.- Six 
years ago all x-ray data on organic compounds could be con- 
sidered in very little space, and in fact the International Critical 
Tables, Vol. I, listed only about fifteen organic compounds for 
which space-groups had been assigned. With the great improve- 
ments in technique and in methods of interpretation a very large 
number of organic compounds have now been analyzed for crystal- 
line and molecular structures with results just as complete and 
convincing as the examples already cited. Ewald and Hermann 
have classified these into 26 main types already, with many others 
still to be fit into the scheme. Little would be gained in this 
book by presenting these experimental data, since even tabulation 
would be greatly extended, and since they are to be found in full 
in the "Strukturbericht." Consequently only some general con- 
clusions of general interest to the chemist will be considered 
briefly. 

1. Inorganic Types with Organic Substituted Radicals. The 
alkyl ammonium halides, principally studied by Wyckoff and 
Hendricks, are the chief representatives. In almost every case 
a very clear relationship exists between the structure of the 
compound and the simpler compound in which a metal atom has 
been replaced by a radical. For example, triethylamrnonium 
iodide is like wurtzite (ZnS), with the radical replacing Zn atoms; 



THE CRYSTAL STRUCTURES OF COMPOUNDS 315 

the length of the chain, of course, causes a large decrease in the 
axial ratio. Tetrarnethylammonium iodide is similarly related 
to phosphonium iodide (type #10), methylammonium iodide to 
rock salt, and methylammonium chloride to cesium chloride. 
A very curious result is that in these latter two cases the chains 
which replace one of the ions in the simple salts evidently must be 
linear rather than zigzag, in order to account for observed sym- 
metry and spacings. Several derivatives of hexachloroplatinates 
and hexachlorostannates, in which these ions are octahedrally 
coordinated, also have structures which might be predicted from 
the results on metal ion salts of these complex anions. The 
chief interest, of course, is in the effect on the symmetry of the 
ammonium group by substituting various combinations of 
alkyl groups. 

2. Symmetrical Methane Derivatives. The tetrahedral form of 
these compounds is the point of greatest interest. Methane 
crystallizes in the face-centered cubic lattice of parallel CHU 
tetrahedra; tetramethyl methane has the diamond cubic struc- 
ture, and tetraiodornethane is a simple cubic lattice of parallel 
tetrahedra. X-ray and electron diffraction researches have 
shown clearly the distortion of the tetrahedra which results when 
the hydrogen atoms are unsymmetrically replaced by halogens or 
other groups. Even carbon tetrabromide, which crystallizes in 
two modifications with a tetrahedral molecule for the lower 
temperature modification, loses symmetry at higher temperatures 
and forms a monoclinic lattice from bi-molecules. In tetranitro- 
methane, although cubic, one of the nitro groups evidently differs 
from the other three in space and the formula is perhaps correctly 
written O=-N O C(NO 2 ) 3 . 

Pentaerythritol, C(CH 2 OH) 4 , a tetragonal crystal, probably 
has the distinction of having been investigated more repeatedly 
than any other organic compound. It illustrates the case in 
which very slight differences in interpretation of x-ray and optical 
data lead to widely different molecular structures. In the early 
work it was concluded that the carbon atoms were all coplanar or 
formed a flat pyramid. Further work has demonstrated that it is 
impossible from the x-ray data to distinguish between symmetry 
classes C 4 or 84 (tetrahedral). Researches on crystal growth and 
solution, etch figures, pyro- and piezoelectricity have given pre- 
ponderance to the tetrahedral molecule and the space-group 
S 4 2 . Besides pentaerythritol, the tetracetate and tetranitrate are 



316 APPLIED X-RAYti 

also body-centered tetragonal with the same symmetry class but 
they differ in the orientation of the center molecule with respect 
to the molecules at the corners of the unit cell. The compounds 
C(C 6 H 5 ) 4 , Si(C 6 H B )4, Ge(C 6 H B )4, Sn(C 6 H B )4, and Pb(C 6 H B )4 all 
have the same tetrahedral molecular structure and lattice as 
pentaerythritol tetranitrate. 

3. Unsymmetrical Methane Derivatives without Cham Character. 
Chief representatives of this class thus far studied are iodoform, 
urea and its derivatives, and some formates. In iodoforrn the 
iodine atoms form an hexagonal packing of spheres. The carbon 
and hydrogen atoms enter octahedrally the holes in this lattice 
work, so that the molecule CHI 3 forms the unit. In urea 
OC(NH 2 )2, the molecule consists of a central atom circumscribed 
by an almost equilateral triangle of one O and two N atoms. 
There are thus chains of the molecules parallel to the c axis or 
networks perpendicular. Thiourea is orthorhombic with four 
molecules per unit cell, instead of tetragonal with two molecules 
per cell for urea, and the carbon atoms are surrounded by the 
sulfur and two nitrogen atoms in the form of a flat pyramid. The 
nitrogen atoms are equivalent, so that the correct formula in 

NH 2 NH 2 

the solid state is S=^( 1 <^ and not HS C<^ 

X NH 2 X NH 

4. Short Aliphatic Chains with Symmetry about a Central C C 
Linkage. Numerous compounds of this type have been investi- 
gated, of chief interest being ethane and its derivatives, and 
oxalic, maleic and furnaric, and tartaric acids and their derivatives. 
Ethane, C 2 H 6 , and diborane, B 2 H 6 , crystallize alike with hexag- 
onal cell (type Z)41). The dimensions for the former are 
a = 4.46, c = 8.19 A.U., distance C C in the same molecule 
1.55 A.U., C C, different molecules, 3.5 A.U., distance molecule 
center to center 4.46 A.U. Of the derivatives C 2 C1 G , 2 Br 6 , 
C 2 H 4 Br 2 (two modifications), C 2 H 5 F, C 2 Cl,Br 3 , and C 2 H 4 (CH 3 ) 2 
(two modifications) are isomorphous-orthorhombic, space-group 
V^ 16 ; C 2 (CH 3 )4Br 2 and C 2 Br 4 (CEU) 2 have isomorphous tetragonal 
structures; C2(CH 3 ) 5 OH is orthorhombic with eight molecules per 
unit cell. Further work is required to understand exactly the 
distortions of carbon tetrahedra caused by substituent groups and 
the temperature conditions of stability of polymorphic forms. 

Fumaric acid is distinguished from its isorner maleic acid in 
showing six molecules per unit cell, an unusual case of association 



THE CRYSTAL STRUCTURES OF COMPOUNDS 317 

or polymerization. Outstanding among early work are Astbury's 
analyses of d-tartaric acid and d/-tartaric acid (racernic acid). 1 
The first is monoclinic, a = 7.70, 6 = 6.04, c = 6.20 A.U., and 
18 = 100 17', with two molecules to the unit cell; the second is 
triclinic, a = 14.82, 6 = 9.74, c = 4.99 A.U., a = 8220', 
)8 = 12250', and a = 11152', with four molecules to the unit 
cell. Cleavage occurs in the [100] direction where the OH groups 
touch. 

The power of both crystals and solutions of tartaric acid to 
rotate the plane of polarized light is to be found in a spiral 
arrangement of the atoms. Tn the crystal two such spirals exist, 
one connected with the four central carbon atoms of the molecule, 
and the second resulting from the way in which the molecules are 
combined in the crystal unit. These two spirals are in opposite 
directions, so that the rotatory power of the solid is determined by 
the difference. In solution, of course, the second spiral structure 
is absent and the rotatory power depends only on the central 
carbon atoms. In racemic acid spirals are exactly balanced, so 
that there is internal compensation. 

5. Short Aliphatic Chains without Symmetry around a Central 
C C Linkage. Examples of this classification are metaldehyde, 
aldehyde ammonia, acetamide, basic beryllium salts of fatty 
acids, and other metal salts including acetylacetone compounds 
of trivalent metals. These last are isotrimorphoric : a, monoclinic, 
P, rhombic, and 7, rhombic. The iron compound of the 7-rnodifi- 
cation has 16 molecules per unit cell of the unusually large 
dimensions 13.68 X 15.74 X 33.0 A.U. 

6. Highly Polymerized Organic Compounds. These substances 
usually of natural origin, such as cellulose and rubber, will be 
considered in Chap. XX. 

7. Derivatives of Benzene. These have already been considered 
in sufficient detail to indicate the nature of the benzene nucleus. 
Reference should be made to Ewald and Hermann's "Struktur- 
bericht" for numerous interesting details for a large number of 
derivatives. 

8. Special Ring Compounds. Hexamethylenetetramine 
C 6 Hi 2 N4 was probably the first organic compound to be subjected 
to a complete structure determination. 2 It is cubic space- 
group TV 3 with two molecules per unit cell. The N and C atoms 

l Proc. Roy. Soc. (London), 102, 506; 104, 219. 

2 DICKINSON, and RAYMOND, /. Am, Chcm. Soc., 46, 22 (1923). 



318 



APPLIED X-RAYS 



form molecules of the same configuration as those of (Sb 2 3 )2 
(type Z>61) but the lattice is body-centered instead of diamond; 
a = 7.02 A.U., the distance C N in a molecule 1.58, C C 
between two molecules 3.37. 

9. Sugars. The principal x-ray research on sugars has been 
carried on by Hengstenberg and Mark, 1 Sponsler and Dore, 2 
Marwick, 3 and Astbury and Marwick. 4 

Essential data are tabulated as follows: 



Carbohydrate 


iSystem 


Dimensions of unit cell 


Density 


a 


b 


c 

7 9 
9 14 
11 1 
7 65 
5.67 
4 99 
9.12 
6 43 


ft 


Natural cellulose. 
Cellulose hydrate 
Cellobiose 


Monoclinic 
Monocliuic 
Monoclinic 
Monoclinic 
Orthorhombic 
Orthorhombic 
Orthorhombic 
Ort horhombic 


8 3 
8.14 
5.0 
11.0 
7.62 
10 40 
8 06 
6 12 


10 3 
10 3 
13 2 

8.7 
18 18 
14 89 
10 06 
18 24 


84 
62 
90 
103 5 


1 52 
1.56 
1 556 
1 588 
1 501 
1 544 
1 598 
1 654 


Sucrose 
Mannosc 


Glucose (a-d) . 
Fructose (d) 
Sorboso 



Astbury and Marwick have pointed out that the small varia- 
tion in density of these saccharoses suggests an approximate close 
packing of some molecular unit, and by further calculation of 
cross-sectional areas it becomes apparent at once that the 
dimensions of this unit the sugar ring and its side chain 
impress themselves in the various unit cells. For mannose as an 
example, the ring may be drawn 



H 



H 

o: 



'OH 



OH 




H 



"CH 2 OH 



The molecular dimensions so deduced are 7.27, 5.64, and 
2 X 4.58. Thus probably the sugar ring takes about 4.5 A.U. in 
thickness or normal to the ring (being puckered), about 5.5 A.U. 

1 Z. Kryst., 72, 301 (1929). 
*J. Am. Chem. Soc., 63, 1639 (1931). 
*Proc. Roy. Soc. (London), A131, 621 (1931). 
4 Nature, 127, 12 (1931). 



THE CRYSTAL STRUCTURES OF COMPOUNDS 319 

across the ring horizontally, i.e., in the direction of the chains in 
cellulose, and 7.5 A.U. across the ring vertically, in the direction 
of the side chain CH 2 OH. 

Long-chain Compounds. Out of the x-ray studies of the 
aliphatic series, conducted largely by Muller and Shearer in 
Bragg's laboratory and by Trillat and Thibaud in de Broglie's 
laboratory, have come some of the most striking results of the 
science; these have been achieved in the face of such difficulties as 
the inability to use the simpler compounds (which are liquid), or 
to obtain single crystals of the higher members of the series, thus 
necessitating the use of the powder method except in a few cases. 

The great simplifying phenomena discovered in the study of 
the higher paraffin hydrocarbons, acids, esters, salts or soaps, 
ketones, etc., were that the unit cells into which the molecules, 
long pictured by chemists as chains, are packed, have one side 
which is very much longer than the others, and that this side 
grows in a uniformly constant manner as the number of carbon 
atoms increases. This dimension must, therefore, correspond 
to the length of the molecule. The two other dimensions remain 
nearly constant throughout the series; hence, they must cor- 
respond to the essentially constant cross section of a chain of 
carbon atoms. 

For the usual diffraction experiments in which single crystals 
are not obtainable, a small flake of the substance is flattened on a 
glass or metal backing, or melted or poured on a flat surface 
and placed on an oscillating-type spectrograph. On the film is 
obtained a single strong line repeated through many orders, 
corresponding to the long dimension and varying with the number 
of carbon atoms, and lines corresponding to the smaller side 
spacings. The x-rays measure the perpendicular distance 
between successive identical planes in the crystal; since the 
principal spacing increases a constant amount for each addition of 
a CH 2 group, the conclusion is that the molecules are parallel and 
either perpendicular (in which case the interplanar spacing 
measures the actual molecule length) or inclined at a constant 
angle to these reflecting planes. Bragg uses the picturesque 
analogy of a carpet as a layer, the pile of the carpet as the 
molecules, and a stack of carpets as the crystal. 

This oriented film in a sense, therefore, acts like a single crystal 
which is oscillated in an x-ray beam and reflections from a set of 
planes registered by the Bragg method in accordance with n\ = 



320 



APPLIED X-RA 



2d sin (see page 180). The simultaneous appearance of the side 
spacings proves the powder nature of the specimen. Hence the 
oriented film consists of many crystal grains oriented exactly 
alike with respect to one axis but at random around this axis. 




,'* Defining pin hole 







y^ "/ ) 


^<z^ W/////////////A 


,,* 

Photog 
plah 


nap/uc 


< 

*'Lec*d 
scnoen 
[ 


/ ^^ ^/////////////^ 


^Liquid drop 


7777?. 


& 
I 


77771 






i 





FIG. 142. The tangent drop diffraction method. 

Another technique which has been used with great success by 
Trillat and by the writer is the use of a curved surface upon which 
the molecules of a film may orient. Inasmuch as the x-ray 




FIG. 143. Patterns for thin films of paraffin wax. Left, on glass plate and 
oscillation spectrograph; right, on mercury drop. The short lines or arcs at 
small angles are interferences in various orders for molecular length, while the 
long Pebye-Scherrer rings correspond to molecular cross section. 

beam may strike this spherical surface tangent ially at a whole 
series of angles, one position will be correct for reflection from the 
long spacings of the film. Hence oscillation of the specimen is 
obviously unnecessary. This method is illustrated in Fig. 142. 



THE CRYSTAL STRUCTURES OF COMPOUNDS 321 

Typical patterns for the same paraffin wax sample, respectively 
by the method of oscillating a film on a flat plate and of orienting 
a film on a mercury drop, are illustrated in Fig. 143. Orientation 
of film on water, metals, molten liquids, etc., will be considered in 
a later paragraph. 

Paraffin Hydrocarbons. In order fully to understand the 
results obtained from films of the hydrocarbons, a complete 



m 





Fiu. 144. Rotation spectra for single crystal of C29H60, showing sixty-sec ond- 
ordor reflection. (^fuUer.} 

structure determination obviously was necessary and, of course, 
this required a single crystal which could be analyzed by the 
rotation method. Mtiller 1 succeeded in obtaining a single crystal 
of C 2 9H 6 o and in completing a remarkably able analysis. A 
rotation photographic around the a axis and another showing 
0, 0,60 and higher reflections are reproduced in Fig. 144. The 
crystal is orthorhombic with the space-group V^ 6 ; the unit cell 

iProc. Roy. Soc. (London), 120A, 437 (1928). 



322 



APPLIED X-RAYS 



containing four molecules has the dimensions: a = 7.45, b = 
4.97^ c = 77.2 A.U. It is evident therefore that two molecules 
end to end are placed along the c axis, since a spacing d\ of 38.6 
A.U. is observed by the powder (thin-film) method together with 
d 2 = 4.13, d 8 = 3.72, d 4 = 2.98, d 5 = 2.48, and d Q = 2.35. 
These all correspond to the planar indices in the single crystal 
analysis respectively of 002, 110, 200, 210, 020, and 120. The 
analysis further shows that the CH 2 groups of the chain molecule 






FIG. 145.- 



Odd Even 

-Diagram of long-chain compounds with odd and even numbers of 
carbon atoms. 



lie equally spaced on two parallel rows, the lines between succes- 
sive centers thus forming a zigzag with an angle somewhat less 
than 92 deg. (slightly distorted tetrahedral angle) . The distance 
between two consecutive scattering centers on either row of the 
crystal molecule, i.e., from (CH 2 )o to (CH 2 ) 2 on one row, or from 
(CH 3 )i to (CH 3 ) 3 on the other, is 2.537 A.U., or the increment 
per CH 2 to the total length is 1.27 A.U. A gap of 3.09 A.U. 
exists between the ends of two consecutive molecules in the 
crystal. 

Hengstenberg 1 obtained results also for crystals of C 35 H 22 
which gave unit-cell dimensions of a = 7.43, 6 = 4.97, c = 46.2 

1 Z. Kry*t., 67, 583 (1928). 



THE CRYSTAL STRUCTURES OF COMPOUNDS 



323 



A.U. (single-chain length). Because of great intensity of the 
thirty-sixth and thirty-seventh orders, the vertical component of 
distance between neighboring carbon atoms must be 1.27 A.U. as 
Mtiller found. 

Of principal interest in these studies is the significance of the 
zigzag chain in explaining the well-known alternations in proper- 
ties for substances containing odd and even numbers of carbon 
atoms. Mliller's interpretation 1 is shown most clearly in Fig. 
145. In the odd molecule the pattern repeats itself every second 



40 



30 



D 

c 



"C 

c 
if 



1O 





1O 20 

Number of C Atoms 



30 



FIG. 146. Plot for normal paraffin hydrocarbons showing relationship of two 

modifications. 

molecule along the direction r, while in the even all successive 
molecules are identically situated. It would be expected in the 
actual crystal therefore that two molecules would lie along the c 
axis for odd-numbered chains and only one molecule in crystals 
containing even-numbered molecules. This prediction has been 
fully verified for dicarboxylic acids where the end groups are 
COOH instead of CH 3 in the paraffins. 

In order to test the effect of even and odd hydrocarbons, 
Muller investigated 2 a number of normal paraffins ranging from 

!Proc. Roy. Soc. (London), A124, 317 (1929). 
2 Proc. Roy. Soc. (London), A127, 417 (1930). 



324 



APPLIED X-RAYS 



C 5 Hi2 to C 3 oH 6 2 at liquid-air, room, and nearly melting tempera- 
tures. The higher members of the paraffin series crystallize in 
the normal form as found for C 2 9H 6 o, irrespective of whether the 
carbon content is an even or odd number. Thus for these long 
chains the effects of the end groups are not sufficient to differen- 
tiate the two series as predicted from Fig. 145. Differences in 
the behavior of even and odd members begin to appear, however, 
when the carbon content decreases. C^KUe, C 2() H4 2 and CisEUs 
exist in two alternative structures, the normal one near the melt- 
ing point and another structure at lower temperatures. The 
change from the normal form into another one also occurs in the 
series of odd members between CuH 24 and ( 1 9 H 20 . The results 
are expressed graphically in Fig. 146, in which the long spacings, 
varying from 7.35 A.U. for C 5 Hi 2 to 40.0 A.U. for C 3 oHo 2 , are 
plotted against the number of carbon atoms. There are two 
straight lines, the upper representing the normal crystal structure, 
the lower the second form appearing at low temperatures. In 
spite of this complication, the fact is demonstrated that these 
chains have a constant increment in length of 1.25 A.U. per 
carbon atom and that the x-ray spectrum is a powerful method of 
identifying any member of an homologous series and of determin- 
ing molecular weight. Hengstenberg's values of 46.2 A.U. for 
C 3 5H 72 and 78.2 A.U. for CeoHm are consistent. 

X-ray diffraction results with ordinary paraffin waxes are of 
unusual interest. In spite of the fact that these waxes may con- 
tain as many as 18 or 20 different hydrocarbons, both normal and 
branched-chain isomers, a single diffraction spacing corresponding 
to molecular length is obtained, together with the usual side 
spacings. Clark 1 first made x-ray measurements on a series of 
commercial waxes of varying melting points with the following 
results : 



Wax molting 
point, degrees 
Fahrenheit 


</, 


Number of C 
atoms indicated 


135 


39 42 


29 


130 


38 58 


28 5 


125 


35.22 


26 


120 


34.38 


25 



Science, 66, 136 (1929). 



THE CRYSTAL STRUCTURES OF COMPOUNDS 



325 



The spacing obtained varied, however, depending upon the 
method of preparing the specimen film (from 36.64 to 40.20 A.U. 
for the 135 wax), and especially the time given for molecular 
orientation. Furthermore, the presence of addition agents in 
very small amounts served to change the long spacing. Obvi- 
ously, possibilities of polymorphism, changing predominance of 
one molecular species over all others in the mixture, and changing 
tilts of molecules to the diffracting planes may explain the 
variations. 

Clark and Smith 1 next studied series of samples from carefully 
fractionated paraffin waxes derived from midcontinent petroleum. 

Some representative data are tabulated for one of the series. 



Fraction 


.1 


R 


C 


D 


K 


F 


Melting point, degrees Centi- 














grade 


59 9 


55 2 


47 1 


40 5 


35 . 2 


29 4 


Kefractive index, 80 C 


1 4303 


1 4306 


1 4330 


1 4550 


1 4359 


1 4380 


Molecular refraction 


122 7 


122 8 


126 5 


129 8 


128 4 


125 


Specific gravity 


770 


773 


779 


783 


786 


792 


Solubility in CjIIiCla (14 r , g 














for 100 c c ) 


115 


218 


82 


2 4 


5 7 


70 3 


Molecular weight 


366 


367 


379 


389 


385 


377 


Average value of n in Cull-in > 














indicated 


26 


26 


27 


27 6 


27 4 


26 8 


X-ray identity period, d\ 


42 3 


39 2 


42 3 


42 3 


45 8 


50 3 


Number of carbon atoms. 


31 


29 


31 


31 


34 


38 


Number of orders of reflection 


6 


4 


2 


2 


1 


1 


Molecular weight from rfi 


464 5 


430 9 


464 5 


464 5 


503 8 


552 8 



Some conclusions are as follows: 

a. No fraction is a single pure compound. 

6. In fractions from the same wax the identity periods corre- 
sponding to the predominating molecular length follow no 
regular order with melting point; thus the largest spacing was 
obtained with the fraction with lowest melting point. 

c. The number of orders of diffraction caused by the oriented 
molecules varies directly with the melting point of the fraction. 
This indicates that with the lower melting fractions the degree 
of perfection of orientation of the molecules becomes less, prob- 
ably owing to the interference of an increasing number of mole- 
cules with lower orienting tendency. Excellent agreement 
between observed and calculated molecular refractions proves that 



Ind. Eng. Chem., 23, 697 (1931). 



326 APPLIED X-RAYS 

these molecules must also belong to the paraffin series and 
are probably branched-chain molecules in view of the small 
variation in the observed molecular weight compared with large 
variation in melting point. This is further indicated by the 
fact that the side-spacing diffraction maxima corresponding to 
molecular cross sections become increasingly diffuse from A 
toF. 

d. Molecular weights calculated from the x-ray data are about 
25 per cent higher than values by the ebullioscopic method. 
This indicates that besides containing the molecules indicated 
by the identity period every fraction is also made up of lower 
molecular weight paraffins, either shorter straight chain or iso- 
paraffins or both. 

e. In 16 fractions only five spacings are observed corresponding 
to the values for pure hydrocarbons with 29, 31, 34, 38, and 42 
carbon atoms by interpolation on the straight-line plot of d\ 
against n. C^H 7 8 and C^Hsc were recognized as constituents of 
paraffin wax for the first time. 

Aliphatic Acids. The principal spacings vary from 6.66 A.U. 
for crystallized acetic acid, C 2 H 4 O2 (Saville), to 82.0 A.U. for one 
modification of lacceroic acid, C3 2 H 6 4O2 (Thibaud, powder 
method). The layers in any one acid have double the spacing 
displayed by the paraffin with the same number of carbon atoms ; 
hence they are two molecules thick with COOH groups together 
at the ends of two oppositely turned molecules. Until the 
remarkable photographs of Prins and Coster, showing as many as 
34 orders for palmitic acid, it was believed that the odd orders 
were generally more intense than the even. These new results 
prove that this is true to about the ninth order at which point 
even and odd intensities become equal; beyond this the even 
orders become more intense, reaching a maximum at the six- 
teenth. The thirty-fourth order spectral line is much stronger 
than any of the adjacent lines indicating a distinct periodic 
phenomenon in the fact that the spacing for one molecule (35.6 
A.U.) is thirty-four times the increment for a CH 2 group. The 
precision measurements of Trillat prove that the large lattice 
spacings (and hence the lengths of the molecules) for the fatty 
acids vary in proportion to the number of carbon atoms, but 
group the acids into two series, one for those containing an even 
number, the other for those containing an odd number of carbon 
atoms. 



THE CRYSTAL STRUCTURES OF COMPOUNDS 



327 



In addition the researches of Piper, Malken and Austin, 1 
Thibaud, 2 deBoer, 3 and others have demonstrated that there is a 
definite polymorphism of the higher fatty acids, each acid from 
palmitic (Ci 6 ) up, whether containing even or odd carbon atoms, 
having two forms. One form is obtained by melting the acid 
and forming a thin layer, the other by evaporating a solution. 



60 



70 



60 



o 

8. 



40 



30 



ZO 





A Pipers values 
o Thibaud^ values 

Even acid 

- Odd acid 



10 



15 20 25 

Number of C-Atoms 



30 



FIG. 147. Graph for normal aliphatic; acids showing effect of even and odd num- 
bers of carbon atoms, and of B and C modifications. 

These are called, respectively, the C or a and the B or ft forms. 
An A or 7 form with still larger principal spacing appears very 
rarely. A graphical representation of the variation of the 
spacings corresponding to molecular length with the number of 
carbon atoms thus requires at least four curves: odd acids B and 
C, and even acids B and C. The best data are plotted in Fig. 147. 
The increase of the chain's length per carbon atom is, respec- 

!/. Chem. Soc., 129, 2310 (1926). 

2 Compt. rend., 184, 24, 96 (1927); 190, 945 (1930); Nature, 119, 852 (1927). 

3 Nature, 119, 50, 635 (1927). 



328 



APPLIED X-RAYS 



lively, 1.327 and 1.146 A.U. for the B and C forms of the odd 
acids and 1.21 and 1.10 A.U. for the even acids. The polymor- 
phic transitions occur at definite temperatures and are accom- 
panied not only by a change in spacing but also in refractive index. 
Some representative data are as follows: 



Acid 


B Spacing 


C Spacing 


Transition 
temperature 


C n Hr2O 2 


30 1 


25 4 


17 (deBocr) 




35 1, 31 5 


29 8 


32 


C 16 II, O 2 


39 7, 35 9 


34 4 


44 




40 2 


38 7 


54 


' ' 1 2* 24^2 


30 6 


27 4 


10 (Thibaud) 




35 


31 2 


25 


('16H. 2 () 2 


39 3 


35 


40 




43 95 


39 9 


55 


Cie + ("is acids 

(y27Hf,4()2 .... 


41 (i 
(H) 


37 6 
(>4 


40 < T < 55 

82 5 



Excellent complete analyses of single crystals have been made 
on stearic acid and derivatives by Miiller, 1 and on lauric acid 
by Brill and Moyer, 2 and partial analyses on several others. 

Both the Ci2 and Ci 8 acids are monoclinic with four molecules 
per unit cell arid with double molecules lying with their long direc- 
tion almost parallel to the r axis. The zigzag aliphatic acid 




al093Q' 
FIG. 148. Form of zigzag carbon chain and cross section. 

chain can be represented essentially as an elliptical rod with a 
ratio of axes of 0.64 as represented in Fig. 148. 

Other Acids. Oleic, with one double bond, linolic with two, and 
linolenic with three when in thin layers on polished lead, demon- 
strate according to Trillat how chemical change may be followed 
by x-ray patterns. New lines appear as oxygen is absorbed at the 
double bonds. When the latter two become hard and dry, the 
x-ray spectra disappear as is the case with linseed oil. 

l Proc. Roy. Soc. (London), 114, 542 (1927). 
2 Z. Kryst., 67, 570 (1928). 



THE CRYSTAL STRUCTURES OF COMPOUNDS 



329 



Patterson 1 studied a series of phenyl normal saturated fatty 
acids. While benzoic acid is a purely aromatic acid, from e-phe- 
nyl-caproic acid (n = 5) onwards, the side chain tends to pre- 
dominate and the substances tend to be like the aliphatic acids. 
The lower acids thus represent the stage in which the properties 
go over from aromatic to aliphatic and these variations are 
quite complicated. 

The di-acids (succinic, adipic, pimelic, suberic, azelaic, etc.) 
diffract x-rays in the predicted manner from oriented films. 
Since there are two COOH groups in each molecule, the layers 
are only one molecule thick; the spacing of a Cs di-acid, for exam- 
ple, multiplied by four gives the observed spacing of the Cie 
fatty acid (with two molecules per layer). 

An alternation is observed in the films between chains with 
even and odd numbers of carbon atoms. Caspari 2 prepared 
single crystals and found the effect greatly pronounced in 
complete-structure analyses. In the following table the data 
are assembled for the unit-cell dimension of the monoclinic unit 
cell (c) corresponding to molecular length, the number of mole- 
cules per cell (2), and for comparison the principal spacings 
obtained by Henderson from films of the acids. 



Acid 


Number of 
C atoms 


c 


Z 


d (film) 


Adipic 


6 


10 02 


2 


6 90 


Pimelio 


7 


22 12 


4 


7 65 


Suberic 


8 


12 56 


2 


9.05 


Azelaic . . .... 


9 


27 14 


4 


9 56 


Scbacic . . . . . 


10 


15 02 


2 


11.20 


Brassylic 


13 


37 95 


4 


13 3 


Hexadecanodiearboxylic 


18 


25 10 


2 





Part of the discrepancy between single-crystal and film data 
may be due to polymorphism which has been observed for such 
di-acids as malonic, succinic, and glutaric by Latour. 3 However, 
these acids substantiate the theory of Miiller as to the effect of 
even and odd chains on properties. 

1 Phil Mag., 3, 1252 (1927). 

2 /. Chcm. Soc., 1928, 3235. 

3 Compt. rend., 193, 180 (1931). 



330 APPLIED X-RAYS 

Esters. Ordinarily there is a normal decrease in intensity; 
the layers are one molecule thick; this is true except for acetates 
CH 3 COO(CH 2 )nCH 3 with much greater spacings, suggesting 
doubling from the active double-bonded oxygen atom, while 
methyl esters CH 3 (CH2)nGOOCH3 are normal; the increase per 
carbon atom is 1.22 A.U. 

Soaps. The layers are one molecule thick, and the spacing is 
independent of the metal for any one acid. By the ingenious 
method depending upon the fact that the fatty acids on a lead 
support will form the lead soaps, Trillat has obtained the spectra 
for a series from the acetate, C 2 , d = 12.6 A.U. to the lacceroate 
C 32 , d = 92.0 A.U., the largest lattice spacing thus far measured. 
The increment per carbon atom is 1.3 A.U. 

For a whole series of potassium salts, Piper 1 observed two dif- 
ferent types with different lattice spacings, one for freshly pre- 
pared specimens and one for the same specimen after standing 
exposed in air which proved to be the acid salt. The acid-salt 
molecules evidently are perpendicular to the diffracting layer and 
the neutral-salt chains at an angle of 5454 / . 

Ketones.In general for CH 3 (( 'H 2 )mCO(CH 2 ) n CH 3 the layers 
are one molecule thick, but for ketones with the CO group sepa- 
rated from the end only by a methyl group, double spacings 
occur, indicating activity of the C()CH 3 group comparable with 
COOH for acids; the compound methyl heptadecyl ketone has 
double the spacing of the isomeric propyl pentadecyl ketone; 
the intensities of the normal di-ketones (oxygen in the middle of 
the chain) are strong in the odd orders and weak in the even, 
exactly as with acids, except that one molecule of a ketone acts 
like two molecules of the acid; if the oxygen atom is one-third 
along the chain, the third, sixth, ninth, etc., orders disappear; 
the increase in spacing per carbon atom is 1.3 A.U. 

The following conclusions and practical applications from the 
x-ray analysis of long-chain compounds may be drawn: 

1. Molecular Form. The molecules are confirmed as the long 
chains known to the chemists. The substances are truly crystal- 
line, since the side spacings are observed, although some of the 
soaps are obtainable in the mesomorphic srnectic state (see Chap. 
XIX). The increments in spacing, per CH 2 group added, are on 
the average either 1.05 or 1.27 A.U. In diamond an addition of a 
carbon atom to the zigzag chain lying in one plane increases the 

1 J. Chem. Soc., 1929, 234. 



THE CRYSTAL STRUCTURES OF COMPOUNDS 331 

length 1.26 A.U.; hence, for paraffins, ketones, etc., the increment 
is the same as in diamond, and the molecules may be considered as 
perpendicular to the layers; for acids, etc., with smaller incre- 
ments, molecules tilted at about 30 deg. may be the explanation. 
Weight to this explanation is given by the fact that measurements 
on single crystals of stearic acid show an angle of 30.3 deg. between 
the c axis and the normal to the c plane in the unit monoclinic 
prism. 

2. Polymorphism. The parallel arrangement of molecules and 
the tilt may be determined by preparation and working of the 
samples. Particularly with lower members of the series, depend- 
ing on whether flakes are pressed on flat surfaces or the substance 
is melted and solidified in a film, different spacings are obtained. 
Polymorphism is very common, though previously unsuspected, 
in many scries of compounds. 

3. Molecular Weight. The simple x-ray photographs may be 
used to determine molecular weights by interpolation of the 
observed spacing on the straight line relating number of carbon 
atoms to the interplanar spacing. Pure hydrocarbons will give 
results which fall on the curve while mixtures will not; isomcrs are 
clearly differentiated as they fall on different curves. This 
matter is complicated for normal saturated acids with four 
curves necessary. 

4. Isomerism. The position of ketonic oxygen atoms is accu- 
rately determinable in any compound from data on the intensities 
because of its greater scattering power for x-rays and the resultant- 
effect upon the intensities of various orders. 

5. Structural Formula. Alternative possible formulas may be 
tested; for example the ketones may be 



co 



or C n H 2 n+i.COC m H 2 m-fi, the length of the first being n + 1 
or m + 1, and of the second n + m + 1 carbon atoms; the second 
is proved correct. 

6. Film Formation. Numerous physical properties are 
explained; e.g., the comparatively strong black spot of very thin 
soap films is truly crystalline in the sense that it consists of a 
double layer of oleic acid molecules, with their carboxyl ends 



332 APPLIED X-RAYS 

turned in toward each other. The thickness of a layer of double 
molecules determined by x-ray diffraction corresponds to the 
various measurements on the thickness of the black spot and to 
the length of the molecule adsorbed in surface films. 

7. Chemical Analysis. Natural materials such as paraffin wax, 
glyceryl margarate, hydrogcnated soy-bean oil, spermaceti, 
Chinese wax, ceresin, lecithin, etc., all give lines and may be 
analyzed. Mixtures pressed together give lines for all constit- 
uents but, when melted together, may give lines for only one 
constituent which may actually be present in only a minor 
quantity. 

8. Lubrication. Flakiness, greasiness, and lubricating prop- 
erties are due to layer formation and ease of movement of one 
layer over another, particularly if methyl groups on the ends are 
in contact. Thin stratified layers of lubricant may thus be more 
effective than thicker unoriented layers. 

9. Chemical Reactions. These long-chain compounds are the 
best for following the course of chemical reactions. Small 
quantities of the acids melted on metals show superposed spectra 
of the acid and the soap formed by interaction with the metal 
base; the latter spectra are intense with lead, tin, and antimony; 
less intense with iron, copper, and bismuth; faint with nickel, 
zinc, and molybdenum; and absent with aluminum, palladium, 
platinum, and gold. The absorption of oxygen at the double 
bonds of lead oleate, formed by painting a film of oleic acid on 
lead, may bo followed perfectly by the gradual appearance of new 
spectrum lines and the disappearance of the oleate lines. 

10. Kpectroscopy of Soft X-rays. The large spacings character- 
istic of these stratified organic compounds made possible the 
spectroscopic measurement of long- wave lengths and the bridging 
of the gap between ultraviolet and x-rays. Ruled gratings are 
used now more commonly for these researches. 

11. Molecular Orientation at Surfaces and Interfaces. Finally, 
the theory of orientation of molecules at surfaces and interfaces, 
long well-known as the result of surface energy studies of 
Hardy, Harkins, Langmuir, N. K. Adam, and others could be sub- 
jected to the most rigorous direct experimental test by the 
methods discovered for the study of these long-chain organic com- 
pounds. In general, the x-ray study of the structure of thin 
films, surface and interfacial layers has fully substantiated the 
conception of definite molecular orientations such as fatty acid 



THE CRYSTAL STRUCTURES OF COMPOUNDS 



333 



molecules at the surface of water standing upright with the 
polar carboxyl group turned into the water. Obviously, mono- 
molecular films cannot serve as diffraction gratings but the results 
obtained with layers only a few molecules thick fully substantiate 
the picture. A wide variety of experiments have been conducted 
to show orientation. The excellent results obtained from very 
thin films on mercury drops have been noted already. Trillat 1 in 
a second paper reports a whole series of ingenious investigations 
on the surface structure of entirely solidified drops of fatty acids, 
diacids, paraffins, and triglyccrides, of films of these substances 



f l "' 



FIG. 149. Diffraction patterns showing molecular orientation in surfaces. 
Left, surface of solidified drop; center, surface of molten drop with invisible film 
cooled by jet of air; right, surface of liquid drop. 

obtained by cooling the surface of a liquid drop, the remainder 
being molten, and of films obtained by cooling in contact with 
heated water. An x-ray beam defined by a horizontal slit strikes 
tangent ially upon the surface in each case. The appearance on 
the diffraction photograph of the interferences in several orders 
corresponding to the molecular lengths at once proves that the 
chains must be preferentially oriented at interfaces between solid 
or liquid substance and air, and between water and air. Figure 
149 shows a series of patterns for paraffin made in the writer's 
laboratory by J. N. Mrgudich. Especially interesting is the sec- 
ond one made as follows : the paraffin is melted in a small cup by 
means of a carefully controlled current through a resistance wire 
in contact with the cup. A blast of air was directed on the sur- 
face so as to form a transparent film on the molten drop. The 

1 Ann. phys., 15, 455 (1931). 



334 APPLIED X-RAYS 

pattern shows a liquid halo and in addition sharp interferences for 
the oriented film. The orientation theories are thus entirely 
substantiated. Not only is this true of long organic molecules, 
but even in surface "skins 77 of other substances. Surface reflec- 
tion x-ray photographs have demonstrated conclusively an 
oriented molecular structure approaching the crystalline condi- 
tion in the surface of cast-glass cylinders, while a nearly amor- 
phous glass pattern is obtained for the interior. Organization and 
orientation seem to be inherent tendencies of matter, given the 
proper conditions of molecular mobility, or assisted by some 
mechanical unidirectional force such as stretching or drawing into 
a fiber. The orientation of molecules thus observed is true 
whether in the solid or liquid state. For example, molten lead 
oleate on metallic lead backing gives nearly as sharp inter- 
ferences as a solidified film. 



CHAPTER XVII 

THE INTERPRETATION OF DIFFRACTION PATTERNS IN 

TERMS OF GRAIN SIZE, ORIENTATION, INTERNAL 

STRAIN, AND MECHANICAL DEFORMATION 

The Scope of X-ray Diffraction Information. In the subject- 
matter thus far developed in this book in Part II, particular 
application of fundamental principles has been made to the 
analysis of crystalline constitution or ultimate structure. It has 
been shown that such analyses of solids may involve the use of 
single crystals or of specimens composed of many fine grains 
usually in random orientation. The various experimental 
methods employing either single crystals or aggregates have been 
outlined in Chap. XL It has also been indicated that numer- 
ous other types of information besides ultimate crystalline 
structure may be obtained from the interpretation of the x-ray 
diffraction patterns. It is at once apparent that a whole series of 
specimens may give identically the same known crystal pattern 
characteristic of body-centered cubic a-iron, and yet from the 
standpoint of practical behavior these specimens may vary 
enormously. If, then, x-rays told us only that all the specimens 
were a-iron, they would perform a notable service but fall far 
short of the greatest usefulness. Fortunately, by means of these 
rays it is possible to make fundamental and subtle distinctions 
between the specimens, which all have the same unit crystal cell, 
far beyond the powers of any other testing agency, and thus 
scientifically to account for actual behavior in service, and to 
enable rational establishment of manufacturing processes which 
will assure a desirable combination of properties in terms of a 
desirable structure. It is this information concerning grain size, 
internal strain, fabrication, heat treatment, etc., which is the 
newest contribution of x-ray science and at the same time the 
most important from the actual industrial point of view. In this 
chapter consideration will be given to the fundamental 
interpretation of x-ray patterns in terms of some of these 
properties, while Chap. XVIII will be devoted largely to 

335 



336 APPLIED X-RAYK 

actual examples and achievements of the x-ray method in 
metallurgical industry. 

Grain Size. 1. X-ray Evidence of Grain Size. In Figs. 82 
and 96 are shown the x-ray diffraction patterns for two extremes 
of grain size of a-iron, respectively, a single crystal grain and a 
random aggregate of very small grains. The former is distin- 
guished by a symmetrical array of Lane spots, the latter by a 
series of concentric, continuous Debye-Scherrer rings. Both 
patterns are definitely characteristic of crystalline a-iron and, in 
addition, each characterizes a particular condition of grain size. 
Of course, there may be every possible gradation in grain size 
between the extremes and also extending to grain sizes in the 
colloidal range smaller than represented by Fig. 96. In general, 
it may be stated that specimens with grains larger than 
10~ 3 cm. in diameter produce a fairly uniform peppering of 
diffraction spots which grow larger and fewer in number as the 
grain size increases or the number of grains in the path of an 
x-ray beam of constant cross section decreases. In the region of 
10~ 3 cm. these spots begin to lie on Debye-Scherrer rings as in 
Fig. 120 if the /fa-doublet of the radiation is present so as to 
exceed allotherrays in intensity (i.e., approaching monochromatic 
rays). As the size still further decreases, the spots lying on rings 
decrease in size and increase in number until individual spots can 
no longer be distinguished and the diffraction rings appear of con- 
tinuously uniform intensity and have maximum sharpness. There 
is a range of particle sizes between 10~ 3 and 10~ 6 cm. as 
limits which produce these sharp rings and which, therefore, 
cannot be accurately distinguished. As the grain still further 
decreases in size below 10" fi cm. into the colloidal range, the 
interference effects become less perfect as the number of 
parallel reflecting planes falls below a certain value. This 
manifests itself as a broadening of the diffraction rings, so that 
a measurement of breadth leads directly to an evaluation 
of grain sizes of colloidal dimensions, as will be illustrated 
later. 

2. The Measurement of the Size of Submicroscopic (Colloidal) 
Crystals. Since the x-ray method of evaluating particle size 
was first applied to submicroscopic or colloidal particles from 
10~ 6 to 10~ 8 cm., this range will be considered here first. 

Debye and Scherrer were the first to derive an equation con- 
necting particle size with an experimental measurement of the 



INTERPRETATION OF DIFFRACTION PATTERNS 337 
breadth of interferences at points of half-maximum intensities. 

^OScberrer 



_ o fc 2 X 1 

er A\ pv H^ f 

\ IT D X 



COS ^ 

where # is the breadth of a diffraction interference at points of 
half-maximum intensity, X is the wave length, D is the edge length 
of the crystal considered as a cube, x is the angle of diffraction, 
and b is the natural minimum breadth of the Debye-Scherrer 
diffraction line which is a constant depending upon the particular 
apparatus and size and absorption of the specimen. Scherrer 
first determined b by plotting measured values of B against 

for a sample of colloidal gold. The straight line drawn 
cos* 

through the points was then extrapolated to cut the ordinate axis 
which was the value of 6 = b r where r is the radius of the camera. 
This equation served for several years though comparatively little 
work was done on critical experimental test. Selyakov, by a 
considerably more straightforward proof, derived the equation 



1 




which differs from the Scherrer equation by less than 2 per cent. 
W. L. Bragg by remarkably simple reasoning and calculation 
utilizing the conception simply of n planes of thickness d arrived 
at the equation 

5 Br a = 0.89 g . ? + b. 
cos | 

Expressed in the same form, 

Ferrer = 0.94 ~ . + 6. 

cos I 

In 1926, Laue deduced from vector analysis a new equation which 
in its most general form is free from the limitations of the cubic 
system and permits size evaluation in different directions and thus 



338 APPLIED X-RAYS 

xhape of a particle. In the simplest rigorous form this equation 
is 



where 77 is a pure number, B is the measured width of the diffrac- 
tion maximum at points of half-maximum intensity, in radians, 
r is the radius of the cylindrical specimen, R is the value of the 
camera and film, and x is the diffraction angle. The quantity rj is 
related to the size and shape of the particle by the equation 



where 6 t - is the ground vector of the reciprocal lattice, h % are the 
indices of the reflecting planes, and w t are numbers which express 
how many times the elementary cell measurement is repeated in 
the direction i. This reduces to r? = X/4?r ma t for cubic crystals, 
where ma t - is the extension (or size D) of the crystal particle in the 
direction a^ or the magnitude to be calculated with all the other 
factors known or experimentally measurable. 

A simplified expression used with singular success by Hengsten- 
berg and Mark in determining the actual size and shape of the 
colloidal micelles of rubber and cellulose is 

Rrj = 0.088 b cos * - U V> 2 cos 3 | , 

where b = BR is the direct linear breadth of the interference. 
The necessary conditions for the Laue equation are for absorption 
in the crystal powder which is negligibly small, for completely 
random orientation, for particles of the same form and size, for 
undistorted lattices, and for known crystal structures. Patterson 
extended the theory to the case where the particles have different 
sizes and showed that the sizes must have a Maxwellian distribu- 
tion, while Mark favored a symmetrical distribution of the Gauss 
type. Without information concerning the distribution func- 
tion, the average particle size cannot be determined. Brill 
extended the theory to the case of substances opaque to x-rays 
and derived corrections for absorption and for the overlapping of 
the a-doublet interferences. The writer has extended these 
calculations and derived the following general and rigorous 



INTERPRETATION OF DIFFRACTION PATTERNS 339 

formula for ma t the extension (or size) of the crystal particle in the 
direction a, : 



4d( B + ?rr sin x sin )( 73 irr sin % sin ) 

where B = b ^ (b measured width of interferences at 

points of half-maximum intensity, d = separation of the a-dou- 
blet; d = lattice constant from known crystal structure; and the 
other symbols have the same significance as noted before. 

The latest and most ingenious advance in particle-size measure- 
ment has been made by Brill and Pelzer. The previous methods 
have all been subject to uncertainties concerning the relation 
between blackening of the photographic film and the intensity of 
incident x-rays, and the determination of positions of half- 
maximum intensity of diffraction interferences by means of the 
photometer. If the specimen under examination is in the form of 
a hollow cylinder (and thus is transparent to x-rays and obeys the 
Laue equations), then over a certain range of particle size each 
interference will be split into two maxima, the separation of which 
is a measure of particle size. Instead of measuring breadth at 
points of half-maximum intensity, the much more direct measure- 
ment of the distance between two lines is involved. For such a 
case the particle size (for the cubic system) must have a value 

D > 



For both large particles yielding sharp interferences, and for very 
small particles for which these two maxima become broad and 
overlap, single lines are observed. The simpler equations 
derived for the particle size involved in the split lines are as 
follows : 






where e is the linear separation of the two maxima. 



340 



APPLIED X-RAYS 



The equation for the case of very small particles for which the 
pairs of lines fuse is 



' 



9 K 

where B' = -- and B is the breadth of half-maximum 
cos 




10 20 30 40 50 60 70 80 90 100 HO 120 130140150 
Diff rcic-Hon Angle in Deg. 

FIG. 150. Graphical method of determining grain size in the colloidal range. 

(Brill.) 

intensity. Rigorous comparative tests have been made for the 
new equations derived for hollow cylindrical specimens, with 
complete agreement for magnesium oxide (Brill and Pelzer) and 



INTERPRETATION OF DIFFRACTION PATTERNS 341 



even for preparations of colloidal gold, silver, and carbon (Clark 
and Zimmer). 

Brill has performed a useful service in presenting a graphical 
method for the determina- 
tion of particle size. The 
standard curves (shown in 
Fig. 150) derived from the 
foregoing formulas show the 

r> 

values of r? as they depend 



upon- and x- The values 6, 

the interference width, r, the 
specimen radius, and x> the 
diffraction angle, are all deter- 
mined and the point on the 

chart for- against x is located. 

r & A 




_, 1C1 __. 

FIG. 151. Diffraction patterns for 
cadmium hydroxide, showing smaller 



The VfllllP of n PnrrP Particle size (broader lines) the lower the 
me value OI q ^ COrre- temperature of precipitation. 

spending is found by interpolation between the curves of definite 
value, from which 77 and then the particle size and shape are 
calculated. 

3. Examples of X-ray Determination of Submicroscopic Grain 
Size. Some examples of diffraction photographs of colloidal 




FIG. 152. Patterns for colloidal metals. A, Silver, particle size 21 X 10~ 7 
cm.; B, gold, particle size 13 X 10~ 7 cm.; C, gold, particle size 2.1 X 1(T 7 
cm. 

materials are shown in Figs. 151, 152, and 153. In Fig. 151 pat- 
terns for cadmium hydroxide precipitated at 25, 40, and 100 
show clearly that the lower the temperature, the smaller the 



342 



APPLIED X-RAYS 




I 



p 



O 

CO 



Cu 

a 



O 

a 

~u 

8. 



Q 



INTERPRETATION OF DIFFRACTION PATTERNS 343 



particle size and the broader the interferences. In Fig. 152 are 
presented standard patterns for colloidal gold and silver with the 
following grain sizes: A, silver sol. 21 X 10~ 7 cm; B y gold sol. 
13 X 10- 7 cm;- C, gold sol. 2.1 X 10~ 7 cm. Figure 153 gives a 
comparison of grain size of three commercial varieties of tin 
dioxide used as opacifying agent in enamels. 

Brill has compared the Scherrer and Laue equations for several 
samples of iron as follows: 



Sample 


Scherrer 


Laue 


Fe from Fc 3 O 4 


2 3 X 10~ 6 


2 X 10- 6 


Heated 10 hr. at 1000 


4 2 X 10~ 6 


00 


Fe from carbonyl I (300) .... 


7.7 X 10~ 7 


1 X 10~ 


II 


6 X 10~ 7 


9 X 10~ 7 


III 


1 X 10~ 6 


1.1 X 10-* 


IV 


1.2 X KT 6 


1.0 X 10- 


(1000) . 


3 X 10- 6 


00 


Electrolytic iron 


2 3 X 10~ 6 


2 3 X 10~ 6 



There is thus general agreement except for large sizes where the 
Scherrer equation fails. It is adapted only for small particles 
in the range and for heavily absorbing substances. Brill has 
employed lead glass tubes for substances of small absorbing 
power in order to meet the condition of nearly complete absorp- 
tion, the diffraction taking place only superficially. 

The particle size of martensite has been determined several 
times, Westgren finding 10~ 7 , Wever 10~ 6 ,and Selkjakov 2 X 10~ 6 
cm. Clark and Brugrnann in studying the structure of case- 
hardened steel, which is martensite and troostite very largely, 
estimated a particle size of 10~ 7 . 

One of the most important and interesting applications is 
that of particle size of metal catalysts. Clark, Asbury, and 
Wick 1 were the first to make a study of particle size as related 
to the activity of finely divided catalysts. They measured 
photometrically the line breadths of diffraction spectra from 
a number of nickel catalysts with identical crystal lattice type 
and dimensions, prepared in various ways and differing widely 
in catalytic activity in hydrogenation and dehydrogenation 
processes. Most of these catalysts consisted of particles larger 
than 10~ 6 cm. so that the Scherrer equation did not apply. 

1 J. Am. Chem. Soc. 9 47, 2661 (1925). 



344 APPLIED X-RAYS 

In general, increase in activity and decrease in particle size did 
not run parallel as might be expected. There is a more definite 
relationship for platinized-asbestos catalysts used in the contact 
sulfuric acid process. Levi 1 has made several measurements of 
particle size of the platinum family of metals from the photo- 
metered x-ray diffraction spectra, with the result that granules 
of platinum were twelve to twenty-nine times as large on the side 
as the unit crystal cell; palladium thirteen to twenty-nine, 
rhodium six, iridium four, ruthenium seven to eight, osmium six 
(latter two hexagonal). 

Some of the most interesting particle-size measurements have 
been made on such non-metallic substances as carbon-black, 
pigments, colloidal suspensions, rubber, cellulose, etc. The 
question is raised as to where the discontinuity between crystal- 
line and amorphous appears, and whether there is any evidence 
of amorphous metal at grain boundaries, etc. It is reasonable 
to suppose that diffraction lines may become so broad that they 
will coalesce and produce the effect of general fogging of the film 
just as an amorphous material would be expected to do. From 
the evidence of carbon black an amorphous state may show 
transition to crystalline as judged by changes in physical or 
chemical properties, while the x-ray pattern is unchanged at first, 
simply because the crystalline planes are still too few and too 
distorted to enable sharp interference. It must be realized 
that temperature oscillations of atoms in a lattice and also dis- 
tortion both have the effect upon diffraction lines of broadening 
them just as small grain size. These factors must be known, 
therefore, before adequate interpretation is possible. There is 
no positive x-ray proof of the amorphous cement theory of metal 
aggregates in spite of numerous attempts. Nor can it be said 
that the theory has been disproved though it seems unlikely. 
It has been possible to show that many glasses, always considered 
"amorphous," do consist of extremelysm all crystals. For 
example, vitreous silica consists of cristobalite crystallites of size 
about 1.5 to 2.0 X 10 " 7 cm. 2 

4. The Shape of Colloidal Particles. An important extension 
of this method is in the determination of the shape of colloidal 

1 Atli accad. Lincei (6), 3, 91 (1926). 

2 RANDALL, KOOKSBY, and COOPER, Trans. Soc. Glass. Tech., 14, 219 
(1930). 

CLARK and AMBERG, ibid., 13, 290 (1929). 



INTERPRETATION OF DIFFRACTION PATTERNS 345 



particles. If all points for all interferences lie smoothly on the 

r> 

same r/ curve, then a regular shape, e.g., cubic, is immediately 

indicated. In studies of colloidal nickel prepared elect rolytically 
in the presence of varying sulfur contents Brill found that 
the b/r values for the (200) plane interferences were all too 
high. The cause of the discrepancy could be determined by 
assuming various particle shapes and comparing the breadths for 
(200) interferences with the standard constant (111) interference 
breadths in the equation for the cubic system 

X 

i? = 



where hi, & 2 , AS are the usual hkl indices. Perfect agreement is 
obtained when calculations are made for a particle built on the 
octahedral planes and greatly elongated perpendicular to these 
planes. For the nickel with 5.8 per cent sulfur the following 
results are obtained by assigning the values mi = m% = 9 and 
w 3 = 27, or the edge lengths actually 45 and 165 A.U.: 



Indices 


Half value 
breadth found 


Calculated 


111 


66 


64 


200 


96 


92 


220 


I 07 


I 10 



For the preparation with smallest particle size only the (111) 
interference appears, simply because only these planes are present 
in sufficient number in the tenuous elongated particle to produce 
visible diffraction effects. 

The relative variations in intensities and in breadths of inter- 
ferences for the interferences appearing on a pattern of carbon 
black, as a series of specimens from different sources is compared, 
is a means of evaluating the carbon black not only in terms of 
average particle size but also in shape. In the experience of the 
author with scores of carbon-black samples, some appear to have 
nearly cubical or spherical shape and others to have extremely 
tenuous almost unidimensional shape. The properties of these 
blacks when incorporated in rubber, for example, are greatly 
different, the shape of the primary particle being even more 
important than minimum size. 



346 



APPLIED X-RAYS 



5. Particle Size Measurement in the Microscopic Range. 
A method of evaluating grain size to supplement and check 
microscopic measurement of grains of the order of 10~ 3 to 




7 8 9 10 

FIG. 154a. Grain-size standards (A S.T.M ) for the estimation of the diameter 
of average grain o f annealed materials, particularly non-ferrous alloys such as 
brass, bronze, and nickel-silver. X 75. Average grain diameter as follows: 



010 
015 
025 



4. 035 

5. 045 



nm 
n m . 
nm. 



6 065 mm. 

7 090 mm 

8 120 mm. 

9 150 mm. 
10. 200 mm. 



10~ 2 cm. in diameter has long been needed, particularly if some 
information can be obtained about grains below the surface of a 
polished specimen. X-ray patterns are now filling this require- 



INTERPRETATION OF DIFFRACTION PATTERNS 347 

ment. It has been demonstrated already that with grain sizes of 
10~ 3 cm. or larger, the diffraction interferences are no longer 
uniform and continuous circles or lines. These interferences 
show individual spots and as the size increases the Debye-Scherrer 




789 

FIG. 1546. Standard x-ray diffraction patterns for increasing grain size in the 
microscopic range (compare Fig. 154a). 



1 009 mm. 

2 012 mm. 
3. 020 mm. 



4 033 mm 

5 037 mm 

6 045 mm. 



7. 065 mm. 

8. 085 mm. 

9. 0.095 mm. 



rings disappear and a uniform "peppering appears." The size 
of the spots depends upon the divergence of the primary x-ray 
beam, the size and shape of the focal spot on the target of 
the x-ray tube, and the extent of the crystal in the plane 
of the reflecting face. Consequently, the size of the interference 



348 



APPLIED X-RAYS 



spot on the photographic film from a grain increases with increas- 
ing grain size as long as the cross section of the crystal perpendic- 
ular to the ray to be reflected is smaller than the cross section of 
the impinging bundle of rays. Mark and Boss have shown a 
linear relationship between the size of interference spots for 
particles between 10 and lOOju (10~ 3 to 10~ 2 cm.) and the grain 
size measured microscopically. The slope of the straight lines 
depends upon the experimental conditions and apparatus but, 



0060 


C5 

^ 0.060 

S 

o 

< Q040 

2 
S 

0.020 


























*/ 


X 
























7\ 


r 
























\/ 
























.x; 


i^ffx 
























/ 


' 

























-n 


3 






















^ 


,Xx 

V 
























X 


o 






















& 


























X 


^v 


























020 040 060 060 1.10 1.20 14 



Series A a Brass 
Small camera 
x Large camera 



M M Image Length 

Series B a, Brass 
o Small camera 
v Large camera 



* Series C a Brass 
o Steel 



Fiu. 155. Graphical correlation between image lengths of x-ray diffraction 
interferences and average grain diameters in microscopic range. (Clark and 
Zimmer.) 

once known, grain sizes may be directly read off for any specimen 
from a measurement of the interference spots. 

Clark and Zimmer have greatly extended these results, using 
the brass samples from which standard A.S.T.M. grain-size 
photomicrographs were prepared (Fig. 154a). The corresponding 
standard x-ray patterns photographed in most carefully con- 
structed cylindrical cameras are shown in Fig. 1546. When the 
microscopic measurements are plotted against the lengths of the 
x-ray diffraction images, the straight-line plot of Fig. 155 is 
obtained. The results with two other series of brass samples, 
steel, carborundum, silica, etc., all lie on this same curve, so 



INTERPRETATION OF DIFFRACTION PATTERNS 349 

that it undoubtedly represents a universal relationship. It is 
essential, however, that the annealed metal sample shall not show 
residual preferred orientation or fibering. It is essential that the 
grains should have uniform size, since otherwise the x-ray meas- 
urement will give the average only of the largest particles, the 
small particles producing no individual sharp interferences. The 
effect of size distribution is very clearly demonstrated in Fig. 156. 
Two specimens of silica with the same average particle 
size as prepared and measured by Drinker and Hatch at the 




FIG. 156. Diffraction patterns for two samples of silica with the same average 
particle size but differing widely in the distribution of sizes. Left, average size 
4.4ju, distribution (standard deviation) 1.341; right, 4.5/z and 2.166, respectively. 

Harvard School of Public Health were subjected to x-ray analysis 
by Aborn and Davidson. The difference is remarkable. In a 
the deviation from the average was very small, while in b it was 
large. Without a knowledge of the fact that the average particle 
sizes were the same, and of the distribution, the mistake would be 
made of assigning a considerably larger particle size to b in which 
the large grains producing individual interferences are balanced 
by grains too small to produce distinguishable spots. Micropho- 
tometric curves are reproduced in Fig. 157 for grain sizes of 4.4/*, 
standard deviation 1.34 (Fig. 154a); and 36^, standard devia- 
tion 1.28. These were made by turning the film around an axis 
so that one of the diffraction circles was continuously registered. 
It is obvious that there are no equations comparable to those for 
colloidal particles for calculating particle size of large grains from 



350 APPLIED X-RAYS 

a measured quantity such as diffraction interference breadth. 
Hence the microphotometric curves were measured, including 
number of peaks per unit length, average height of peaks, area 
per peak, and the total area under peaks per unit length. 
When for specimens with nearly the same size distribution the 
last-named quantities are plotted on log paper against average 
particle size, the points lie on a straight line. For specimens 
with widely different distribution but the same average size, 
the points do not lie on this line. This work on silica is of great 





FIG. 157. Microphotometer curves for diffraction rings of silica samples. Left, 
average size 4.4/u; right, average size 36.0/.1. 

importance in laying the foundation for further work on metal 
grain sizes. It is evident that considerable care and skill are 
required in accurately deducing grain size for the region in 
question. 

6. Examples of Measurement of Size of Microscopic Particles. 
It is needless to point out the very great importance of grain 
size in terms of practical behavior of commercial materials. 
Practically all annealing operations following mechanical work 
involve grain growth. Magnetic permeability and hysteresis 
loss in electric steels are certainly dependent upon grain size. 



INTERPRETATION OF DIFFRACTION PATTERNS 351 

The life of electrical contact points is a function of optimum 
grain size. Even the enameling of steel, corrosion, electrodeposi- 
tion, and numerous other phenomena depend upon grain size. 
Many of these will be illustrated in the next chapter, devoted to 
heat treatment and to practical applications of x-ray methods to 
commercial metals. The control of grain size in metallurgical 
products is one of the great achievements of the science. Another 
typical application has been research on the re-use of plaster of 
paris molds. These deteriorate very rapidly on re-use, the tensile 
strength becoming much less on each successive recalcination. 
X-ray photographs show that the gypsum particles grow larger as 
strength decreases. The addition of J^ per cent A1 2 O 3 increases 
strength by decreasing grain size. 

Orientation of Grains. Many research and practical problems 
arise in which a knowledge of orientation of crystal planes in a 
single metal crystal or of single grains in an aggregate are highly 
desirable. It has been demonstrated previously that the x-ray 
goniometer is a powerful method of ascertaining orientation. 
One especially excellent instrument has been devised by Weissen- 
berg for such problems. Single metal crystals are made fre- 
quently by cooling a melt in a quartz tube by extremely slow and 
careful cooling, as first devised by Professor Bridgman. 
Obviously, no planar faces are developed and recourse must be 
taken to goniometric establishment of orientation of planes with 
respect to one direction or another before physical data may be 
properly interpreted. There are frequent references in the litera- 
ture to x-ray goniometry of this kind, especially with respect to 
to the presence or absence of twinning. Again, a strip or sheet of 
metal may be poly crystalline and yet have certain properties 
dependent upon just how the individual grains (of course, large) 
are oriented with respect to the surface. This is especially true 
of electric or magnetic properties, which may differ widely for two 
specimens, say of silicon steel, with the same apparent grain size 
and general structure. In this case the Laue method of crystal 
analysis may be employed. A great service has been performed 
by M. Majima and S. Togino in making Laue photographs for 
body-centered and face-centered cubic metals in every possible 
and known orientation with respect to the x-ray beams. It 
is necessary, therefore, only to compare a Laue pattern for a grain 
in a sheet, to the surface of which the x-ray beam is perpendicular, 
with the standard patterns in order to establish easily the orienta- 



352 APPLIED X-RAYX 

tion of the lattice planes of the grain in question with respect to 
the surface. 

Sir William Bragg has indicated another field in which knowl- 
edge of orientation is of practical importance. Depending on 
how jewel bearings for watch movements are cut from original 
sapphires are the wearing properties. Figure 158 shows Laue 
patterns for two such bearings with different crystallographic 
orientations and different resistance to wear. 



tt&t^ : :v ':'"' ^^s 




FIG. 158. Patterns for artificial sapphires used in jewel pivots of watch 
movements with same structure but different orientations and different wearing 
properties. (Sir William Bragg,} 

Internal Strain. Many metal structures fail because of gross 
defects which may be detected readily by radiographic examina- 
tion (Part I). But many metal objects may appear radio- 
graphically perfectly sound and still fail. The cause here is far 
more deep-seated and is concerned with residual internal strain or 
lattice plane distortion. Strain in transparent objects is readily 
ascertained by interference colors when examined in polarized 
light. In this manner glass apparatus is tested. Dirigible 
models of transparent celluloid have been studied under all 
conditions of stress. The writer has even detected strain in 
linseed oil and patent leather films in this way. But for opaque 



INTERPRETATION OF DIFFRACTION PATTERNS 353 

objects such as metals the method is precluded. The use of 
gage marks for detecting strain in metals is well-known. For 
example, the diameter of a cylinder of metal is very carefully 
measured. Successive layers from the inside of the cylinder are 
then removed on a lathe and the changes in the outside diameter 
with the relief of strain observed. There are many modifications 
of this technique which have been widely employed but there are 
serious objections and limitations. In the first place, the dimen- 
sional changes may be too small to measure accurately. Again, 
the direction of the strain may be such as to be missed entirely 




FIG. 169. Laue patterns of a normal and of a bent crystal of gypsum, illustrating 
asterism. (Czochralski.) 

by the gage-mark method. In all of metallurgy there has been no 
problem which has so urgently required an adequate method. To 
the detection and even quantitative estimation of internal strain 
x-ray diffraction science has made a great contribution, although 
the application still requires much fundamental research and 
standardization. 

Figure 159 shows what happens to the Laue diffraction pattern 
of a single crystal (gypsum) when it is bent. The spots are 
elongated to radial streaks or "asterism striations. " Any pat- 
tern, even for a polycrystalline material which shows these radial 
streaks, is an indication of internal strain. The crystal planes 
are distorted so that reflection takes place as though cylindrical 
mirrors had replaced plane mirrors. Figure 160 shows how a 
strain pattern can be synthesized by loading successively a strip 
of iron while the exposure is made. Even under the elastic limit 
there is clear evidence of strain ; at higher loads slipping on planes 
occurs and rupture accompanied by fibering of the metal in many 
cases. Figure 161 shows the strained condition of a block of cast 



354 



APPLIED X-RAYS 




FIG. 160. Effects upon the pattern of successive loadings of specimen of silicon 
steel, illustrating asterism striations as evidence of internal strain. 




FIG. 161. Pattern for chilled cast steel showing internal strain. 



Iso-Strainal Lines 

(Numbers Represent Relative 
Intensity of Strain) 




FIG. 162. Distribution of internal strains in cross section of large steel casting, 
determined solely from x-ray diffraction patterns. 



INTERPRETATION OF DIFFRACTION PATTERNS 355 

steel which has been rapidly chilled. The distribution of strains 
of a large casting determined solely by x-ray patterns is shown in 
Fig. 162. The world-wide interest in this figure, since its original 
publication several years ago, is an interesting sidelight upon the 





FIG. 1G3. Effect of strain in broadening diffraction interferences. Left, 
strained; right, unstrained. 



value of this method in affording information heretofore 
impossible. 

Internal strain also manifests itself by a broadening of the 
diffraction lines for powder patterns (see Fig. 163). In other 




Change of intensity of 6,0,0 diffraction interference 

ioio',0 

Fio. 164. Changes in intensity of high-order reflections with deforming force. 

(Hcngsteriberg.} 



words, interference is less sharp for distorted or bent planes just 
as is true for a very few planes (colloidal particles). This same 
phenomenon occurs also at higher temperatures where the 
thermal vibrations of the atoms cause a departure from planes. 



356 APPLIED X-RAYS 

Finally, the newest and most nearly quantitative method of 
measuring internal strain is concerned with the diminution in 
intensity of lines particularly at large angles (high orders). 
Hengstenberg 1 has made an investigation of KC1 crystals, with 
the interesting results shown in Fig. 164 for intensity changes for 
6,0,0, 8,0,0, and 10,0,0 reflections. Such relationships have been 
observed qualitatively also for cold-worked and annealed metals, 
the ratio /2oo//4oo, for example, being much greater for the cold- 
worked specimens. 

The exact mechanism involved in strain is still not well 
understood. It is to be distinguished clearly from the effect of a 
uniform deforming force which produces slipping on lattice 
planes. Hengstenberg has calculated for the condition of strain 
that, for a certain degree of deformation of 4 per cent change in 
length of an edge parallel to the direction of compression, 3 per 
cent of the atoms are displaced from their normal positions to a 
maximum of one-eighth the distance between atoms. Strain 
must represent a condition of localized failure on the glide planes. 
In contrast to this irregularly distributed strain, plastic deforming 
forces on the surfaces of whole glide blocks do not change the 
lattice constants. The high-order lines remain perfectly sharp, 
so that the Koi-doublet is perfectly resolved. Consequently, 
whole blocks of the crystal at least 600 A.U. in dimensions must 
slip relative to each other, since deviations of the lattice constant 
of only 0.5 per cent or the formation of glide blocks smaller than 
600 A.U. would cause inevitably an increase in breadth of the 
diffraction lines. 

Brill and others have demonstrated also that the intensity of 
scattered radiation is markedly greater for strained specimens. 
It is the function of heat treatment, of course, to eliminate 
such a condition. Strain is usually accompanied by an increase 
in tensile strength for reasons which are not clear. Strain 
as it precedes fatigue and failure will be illustrated together with 
other important examples in Chap. XVIII for metals. The same 
considerations apply to ceramic materials, glass, bakelite, and 
similar materials. 

Lattice distortion can be produced not only by mechanical 
deformation but also by the introduction of foreign atoms which 
form solid solutions. These effects may be expressed quantita- 
tively by the intensity changes as has been done by Hengsten- 

1 "Fortschritte der Rontgenforschung," p. 139, 1931. 



INTERPRETATION OF DIFFRACTION PATTERNS 357 




vina t. 

Atoms of dissolved substance 

FIG. 165. Distortion of lattice 

introduction of foreign atoms. 



by 



berg. The intensity of a mixed crystal reflection according to 
Laue is fy*~ (pi^i + pz&z) 2 (pure crystal ^ 2 ~ ^i 2 ) where p is the 
atomic per cent of each component and ^ is the scattering power 
of the atoms which is proportional to the atomic number at reflec- 
tion angle 0. This expression 
has been experimentally veri- 
fied for silver-gold alloys. 
The fact that all the diffrac- 
tion interferences varied in 
intensity in the same way as 
compared with pure silver 
proved conclusively that the 
gold atoms with about the same 
size as silver atoms had negligi- 
ble distorting effect in the silver 
lattice. An opposite effect is 
characteristic of mixed crystals 
with lattice distortion, such as 
duralumin. The intensity 
data are as follows : 
Quenched: (p^ + p 2 * 2 ) 2 = (0.02 X 29 + 0.98 X 13) 2 = 177.7 
(copper 2 atomic per cent) 

Tempered: (p^i) 2 = (0.949 X 13) 2 = 161.0 

(CuAl 2 separated) 

The 111 and 200 reflections for the quenched duralumin are 
actually more intense in the above proportion but with increasing 
diffraction angle the ratio diminishes and for (420) reflections the 
intensity is 10 per cent smaller. The explanation is to be found 
in lattice distortion, as exemplified in Fig. 165, caused by the 
presence of copper atoms in the aluminum lattice. 1 

THE X-RAY ANALYSIS OF FIBER DIAGRAMS AS RELATED TO THE 
FABRICATION OF METALS AND ALLOYS 

1. Fiber Diagrams. It is now a familiar fact that metal pow- 
ders or random aggregates yield pinhole diffraction patterns on 
flat photographic films consisting of concentric uniformly intense 
rings. Whenever a piece of drawn wire or thin rolled foil is 
used as a specimen, perpendicular to the primary beam, the 
diffraction rings are very intense in localized intensity maxima 

1 The copper atoms are smaller than aluminum; hence Fig. 165 actually 
represents an opposite case. 



358 APPLIED X-RAYS 

as though more crystal grains are contributing reflection effects in 
certain directions, while in other positions few, if any, crystal 
grains are available for reflection, and there is little or no blacken- 
ing on the film. Thus the rings observed for random arrangement 
of grains become series of symmetrical segments in the case of 
directed or preferred orientation. This type of pattern for 
worked metals, generally designated fiber diagrams, has been 
illustrated in Fig. 121, for aluminum wire, and Fig. 166 for alumi- 
num sheet. 

Drawn wires and rolled sheets represent different types of 
preferred orientation. In wires the same pattern is obtained 

with any orientation as long 
\ as the x-ray beam passes 

perpendicular to the wire 
* \ axis, while in rolled sheets 

differently appearing fiber 
%*''*''. '. %*. patterns are obtained with 

""" ' P ** ^ ie beam Perpendicular or 

Kf , parallel to the rolling plane. 

% These are fiber structures 

in the same sense that 
cellulose, stretched rubber, 

FIG. 166. Diffraction pattern for cold- and as best OS are fibers, 
rolled aluminum foil showing libering 

or preferred orientation. Left, x-ray None of these materials is 

beam perpendicular to rolling direction; ft gi Je crygtal; a jl are built 
right, beam parallel to rolling direction. " ^ 7 

up of many crystal grains, 

but these are arranged so that a definite crystallographic axis is 
parallel to the nxis of the fiber. In an aluminum wire which has 
not been annealed after drawing, the x-ray pattern demonstrates 
that the body diagonals, or [111] direction, in all the grains, each 
of which is a single crystal built up from unit face-centered cubes, 
lie parallel to the wire axis. Evidently, therefore, this common 
orientation has been induced in the process of mechanical work- 
ing; the particular position is evidently that which will present 
maximum resistance to further deformation. It will be noted 
that no other limitation has been put on preferred orientation in 
an aluminum wire, for example, than that the [111] direction is 
parallel to the wire axis, or direction of drawing. Hence any 
grain may be turned anywhere through 360 deg. around a body 
diagonal as an axis and still fulfill conditions, and thus the outer 
form of grains in the wire may appear perfectly irregular with any 



INTERPRETATION OF DIFFRACTION PATTERNS 359 



kind of a face in the surface. Herein lies the difference in the 
orientation of grains in a rolled sheet or foil, for in this case a 
definite crystallographic direction lies parallel to the direction 
of rolling and, also, a definite crystallographic plane in all the 
crystal grains lies parallel to the plane of rolling. For example, 
in strongly rolled iron or steel a face diagonal [110] direction lies 
parallel to the direction of rolling, and a cube face parallel to the 
plane of rolling. On account of this added limitation in rolled 
structure which does not apply in drawn wires or complete fiber 
structure, this is called limited fiber structure. 

In the foregoing discussion ideal cases of exact arrangements 
have been implied. In practice these cases are never realized, 
since the orientations are never perfect, though the greater the 
deforming force, the more nearly do the grain positions approach 
the ideal. As will become apparent, it is possible to determine 
from the x-ray patterns the departures from limiting ideal 
orientations. 

As previously explained, the Laue or monochromatic pin- 
hole method is almost exclusively used in the study of worked 
metals, since it affords a pattern 360 dog. in azimuth. It is 
necessary only to mount a wire or sheet specimen over the outer 
pinhole so that the beam will pass perpendicular to the wire 
axis or rolling direction. The pattern is registered on a flat 
photographic film. 

2. The Interpretation of Complete Fiber Patterns (Drawn 
Wires). Of first concern is the pattern of the Debye-Scherrer 
rings which defines the particular metal. All the lattice planes 
with the same lattice spacing d reflect rays on the same diffraction 
ring, which is continuous in the case of random orientation or 
segmented into spots or arcs for fibered materials. It is useful 



Body-centered cubic 


Face-centered cubic 


Indices 




Indices 




ao/dA = Vh* + /c 2 + I 2 


a*/dku = Vh 2 + k* + / 2 


(110) 


1 41 


(111) 


1 23 


(200) 


2 00 


(200) 


2 00 


(112) 


2 45 


(220) 


2 83 


(220) 


2 83 


(113) 


3 32 


(130) 


3.16 


(222) 


3 46 


(222) 


3.46 


(400) 


4 00 



360 



APPLIED X-RAYS 



to list for the body-centered and face-centered cubic lattices the 
planar indices corresponding to the rings which appear, passing 
from the innermost outward. 

In this fashion it is possible to determine the planar indices 
for each ring. 

Next to be found are the positions of the intensity maxima 
upon the rings. One of the sets of parallel reflecting planes 
may be imagined rotated 360 deg. around an axis perpendicular 
to the primary x-ray beam. In the course of this rotation 
it will pass four times through the proper angle for reflection 
in accordance with Bragg's law and produce upon a photo- 
graphic plate placed behind the specimen a four-point pattern 



X- Fibre Axis 




X-Pays 



Fiu. 167. -Analysis of the ideal 
four-point fiber diagram, with x-ray and nine O Clock). 



which is symmetrical with respect 
to a vertical line on the plate par- 
allel to the rotation or fiber axis, 
and also with respect to a horizon- 
tal line. In other words, these 
maxima are, for example, at the 
clock hour-hand positions of 1 :30, 
4:30, 7:30, and 10:30 (see Fig. 167). 
If this particular reflecting plane 
in a special case is parallel to the 
axis of rotation (or fiber axis) , then 
only two spots are produced on the 
ring on the horizontal line (three 
No reflection 



beam perpendicular to the fiber axis. O CCUrs, of Course, if this plane is 

exactly perpendicular to the rotation axis. Two spots occur on 
the vertical line (twelve and six o'clock) if the angle of the reflect- 
ing plane with respect to the rotation (fiber) axis is equal to the 
angle of incidence of the x-ray beam. It is at once clear, there- 
fore, that the positions of intensity maxima on a given ring on the 
photographic plate may be measured and used directly to deduce 
the positions of lattice planes in the wire in a very simple manner. 
If a is the angle between the normal to the set of reflecting planes 
and the rotation (fiber) axis, and 5 is the angle measured on the 
film between a radius drawn through a particular intensity maxi- 
mum and the vertical line (which is known to be parallel to the 
rotation or fiber axis), then 

cos a 



cos 5 = 



- - 
cos 9 



INTERPRETATION OF DIFFRACTION PATTERNS 361 

where 9 is the angle of incidence. At small reflection angles, 
such as are true for the most important diffraction circles for 
metals, cos 6 is approximately 1. Hence 5 = a. Thus a 
simple angle measurement on the film is also the value for the 
angle between the normal to a set of reflecting planes and the 
fiber axis. 

In any cubic lattice the angle between the fiber axis with 
indices uvw and a lattice plane hkl is given by 



cos a = 



uh + vk + wl 



+ v 2 + w 2 



+ k 2 + 



In aluminum wire the [111] direction is the fiber axis. The 
innermost ring registers the reflection from all the octahedral 




FIG. 168. Theoretical fiber diagram for aluminum wire with [111] parallel to 

wire axis. 

planes, (111), (Til), (ill), (111), and the other four parallel 
to these. Hence a, and consequently 5, on the film will be deg. 
for (111), which means that the (111) planes are perpendicular 
to the fiber axis [111] (as by definition), and cannot reflect. 
For the others a = 71 = 5 (see Fig. 168). 

Further data for aluminum wire calculated in this way are 
shown in the table at top of p. 362. 

Since there is agreement between the calculated positions and 
those found experimentally for drawn aluminum (Fig. 121), the 
assumption of the [111] fiber axis is correct and the wire structure 
may be represented as shown in Fig. 169, with the unit crystal 



362 



APPLIED X-RAYS 



King number 


Planes 


Number 
cooperating 


, degrees 


(1(111) 


(Til) 


6 


71 


}5(222) 


(ill) 








(Hi) 






(2(200) 


(100) 


6 


55 


(6(400) 


(010) 








(001) 






3(220) 


(110) 


6 


35 




(101) 








(on) 








(HO) 


6 


90 




(101) 








(OH) 






4(113) 


113, etc. 


6 


30 




113, etc. 


12 


59 




113, etc. 


(> 


80 



cubes oriented with cube diagonals parallel to the wire axis, but 
at random around these diagonals as axes. 

For body-centered cubic wires like iron (Fig. 170) the assump- 
tion may be made that the [110] direction is parallel to the wire 
axis and this is then tested. 



King 


Planes 


Number 
cooperating 


a, degrees 


(1(110) 


(101) 


8 


60 


}4(220) 


(101) 








(Oil) 








(Oil) 






2(200) 


(100) 


4 


45 




(010) 








(001) 


2 


90 


3(112) 


(211), (121), etc. 


8 


30 




(112), (112), etc. 


4 


55 




(211), (121), etc. 


8 


73 




(112), (112), etc. 


4 


90 


5(130) 


(130), (310), etc. 


4 


27 




(301), (031), etc. 


4 


48 




(130), (310), etc. 


4 


63 




(103), (013), etc. 


12 


77 


6(222) 


(Ill), (111) 


4 


35 




(HI), (111) 


4 


90 



INTERPRETATION OF DIFFRACTION PATTERNS 363 



As a matter of fact, the intensity maxima lying on the Debye- 
Scherrer rings are not sharp spots but are really arcs of 10 deg. in 
cases of extreme cold work, or more (Fig. 171). This means, 
of course, that all the crystal grains are not perfectly oriented 
and that there is a "scattering" in a cone around an average or 



r\ 



\j 




FIG. 169. Diagram showing unit crystal cubes in aluminum wire with 
cube diagonals parallel to the axis of the wire, but oriented at random around this 
axis. 

ideal position which is the wire axis itself. The scattering 
angle or apex of this cone is obviously half of the arc length 
of the intensity maxima. Every possible gradation of pre- 
ferred orientation may be practically observed in metal specimens 
from sharp spots to continuous rings for random arrangement. 

X- Fibre Axis 



X-PayS 





FIG. 170. Fiber pattern for hard-drawn FIG. 171. Analysis of true fiber dia- 
steel wire. grams. 

The arc lengths of the maxima are, therefore, a measure of the 
amount of cold work and preferred orientation or fibering in a 
given specimen, either directly produced or residual after heat 
treatment. 

In many cases of examination of fabricated metals it may be 
impossible or undesirable to orient the specimen with the fiber 



364 



APPLIED X-RAYS 



axis perpendicular to the primary x-ray beam. If, then, the 
specimen is placed at an oblique angle, a pattern is obtained with 
exactly the same Debye-Scherrer rings as before but the four- 
point diagram is changed when two of the points move apart on a 
ring and the other two together, still retaining symmetry with 
respect to vertical and horizontal lines on the film. Instead of 
one angle 6 to be measured for the four spots, there are now two 
angles, 61 and 6 2 , evaluated by 



cos 6 2 = - 



cos a. cos ft sin 9 



sin ft cos 6 



and 



_ cos a - cos (180 - ft) sin 9 

COS Oo ; /""., r>f\o n\ r\ * 

sm (180 ft) cos 9 



where a is the same as before, ft is the angle between the fiber 
v _c,'^ A AV,<* axis and the direction of the 

primary beam, and 9 is the 

^4CZ T. 

MA 




-X-Rays 



FIG. 172. Effect upon diffraction 



angle of incidence (Fig. 172). 

For evaluation of the indices 
of the fiber axis in a drawn 
metal, two or three methods are 
available : 

a. Trial and failure method 
by assuming indices, calculating 
the intensity maxima to be 
expected on the various rings, 
as above illustrated for 
aluminum and iron, and com- 
paring with experimental film. 

b. Use of patterns for ob- 



pattern of tilting fiber axis at angle ft. l ique l y oriented fiber axis with 

a series of values for the angle ft. If the crystal lattice plane 
perpendicular to the fiber axis (Polanyi's diatropic planes) 
reflect a beam of wave length X incident at the angle 9, then when 
ft = 90 9, an intensity maximum will appear at the twelve 
o'clock position on one of the Debye-Scherrer rings due to (hkl) 
planes. For cubic crystals the evaluation of the (hkl) indices 
for the ring upon which the intensity maximum appears gives at 
once [hkl] the fiber axis, since the normal to these planes is the 
same as the axis. 



INTERPRETATION OF DIFFRACTION PATTERNS 365 

c. Sometimes only two or three intensity maxima are necessary 
to evaluate the fiber axis. Glocker and Kaupp 1 give the example 
of electrodeposited copper with maxima on the (111) and (200) 
(or (100), second order) rings. Since 

uh + vk + lw 

cos a = 7- . 

VV + v 2 + w 2 Vh 2 + k 2 + I 2 

where [uvw] is the fiber axis and (hkl) a set of planes, then for the 
(111) and (100) planes, respectively, 

u + v + w 

cos ai = p / = 

\/3 Vu 2 + v 2 + w 2 

u 

COS 2 = , __ 



Intensity maxima appear on both rings at 90 deg.; hence 61 = 
= 5< 2 = a 2 ; furthermore, substituting the values of cos 




FIG. 173. Pinhole spectrograms of FIG. 174. Same as Fig. 173 with 

commercial rolled copper sheet, with rolling direction parallel to x-ray beam, 
rolling direction perpendicular to x-ray 
beam. 

and cos 2 , = u + v + w and = u, or v w. The fiber 
axis is therefore [Oil]. 

X-ray patterns taken with the beam parallel to the fiber 
axis are characterized by uniform Debye-Scherrer rings indicative 
of random orientation (Figs. 173, 174, 175, and 176). 

3. Multiple Fiber Structures in Drawn Wires. Sometimes 
more than one preferred orientation is observed as a multiple 
fiber structure. This is true of face-centered cubic metals in 

1 Z. Physik., 24, 121 (1924). 



366 



APPLIED X-RAYS 




FIG. 175. FIG. 176. 

FIG. 175. Surface reflection spectrogram of duralumin sheet, with beam 
impinging on specimen in direction of rolling. 

FIG. 176. Same as Fig. 175 with specimen turned through 90. 




Silver Gold Copper Aluminum 

FIG. 177. Debye-Scherrer patterns for hard-drawn wires. (Schmid and 

Wassermann.) 



INTERPRETATION OF DIFFRACTION PATTERNS 367 

which both [111] and [100] directions serve as fiber axes. The 
distribution of grain orientations between these two varies 
depending on the metal. This has been studied quantitatively 
by Schmid and Wassermann. 1 Diffraction patterns shown in 
Fig. 177 were registered on a cylindrical film instead of the usual 
flat film, so that the layer line diagrams characteristic for fibers 
are more prominently shown. The data obtained for the per- 
centage of crystals in the [100] and [111] orientations and for the 
half length of interferences on the (200) ring as a measure of the 
exactness of fibering are as follows : 



Metal wire 


Per cent crystals with 


Half length of interferences 
on (200) ring 


[100] 


[HI] 


Parallel to direction of 
drawing 


[100] 


[HI] 


Aluminum 



40 
50 
75 


100 
60 
50 
25 




3 30' 
3 
4 30' 
3 


Copper 
Gold. 
Silver 


7 
8 30' 
7 30' 



The scattering around the [100] preferred orientation is evi- 
dently twice as great as around the [111] axis. The presence of a 
double fiber structure with varying proportions of each and 
variations in scattering around a fixed position have great 
practical significance in differentiating drawing, annealing, 
and physical properties of aluminum, copper, gold, and silver. 

4. The Zonal Structures of Hard-drawn Wires. An interesting 
structural phenomenon in hard-drawn wires is illustrated in 
Figs. 178a and 178& for copper wire. A beam of monochromatic 
x-rays defined by a slit was reflected from the surface of a cold- 
drawn copper wire about 0.5 mm. in diameter. The pattern in 
a shows a nearly random arrangement of grains in spite of the 
prediction concerning fibering. The wire was then etched down 
in successive steps and an x-ray examination made. The struc- 
ture of the innermost core of the wire in b is characterized by 
extreme fibering. Hence, wires drawn through dies have 



1 Z. Physik., 42,779 (1927). 



368 APPLIED X-RAYS 

distinctly zonal structures with the grains becoming more 
perfectly oriented the nearer to the wire axis considered as a 
line at the exact center. In other words, in the passage through 
the die, the flow of metal exactly in the direction of drawing 
occurs only in the middle of the wire, whereas in the walls the 




(a) (fc) 

FIG. 178. Patterns illustrating zonal structure in copper wire. Left, surface; 
right, innermost core. 

metal is flowing inward as well as along the length of the wire and 
the crystal grains are thus disposed at an angle to the core. 

Ordinary powder diffraction spectra (Hull method) also show 
the zonal structure. Figure 179 (upper) shows the pattern of the 



FIG. 179. Hull diffraction patterns showing zonal structure of copper wire. 
Upper, outer mantle; lower, core. 

original copper wire, which is really the structure of the outer 
mantle of the wire. The intensities of the various diffraction lines 
are just about those to be expected from a somewhat random 
orientation. Figure 179 (lower) is the pattern for the core of this 
wire after etching down to a diameter of about 0.13 mm. A sur- 
prising change has occurred since the (111) line has entirely 



INTERPRETATION OF DIFFRACTION PATTERNS 369 

disappeared, the (200) line is about the same, the (220) line is 
about doubled in relative intensity, the (311) line is about half 
as intense, etc. This illustrates the error which might be made 
in the interpretation of such patterns if the facts were not known. 
The phenomena here observed agree with a [100] direction for the 
fiber axis but not so well with the [111]. 



1.75 



1,30 



i.uu mm. u.4 mm. 

FIG. 180. Patterns for copper wire showing zonal structure with decreasing 
diameter, (ftchmid and Wanticrmann.) 

This condition of a central linear zone and a conical mantle, 
of course, is of primary importance in affecting the texture of 
the wire, and in the proper interpretation of diffraction patterns. 
The zonal structure of wires has also been studied by Schmid and 
Wassermann. 1 In Fig. 180 are reproduced patterns from their 
work on copper wire with the diameters 1.75, 1.3, 1.0, and 0.4 
mm. Not only does the sharpness of fibering shown by the 
shorter interference maxima increase as layers are removed, but 
there is also evidence of unsymmetrical interferences. From 
these the inclination of the fiber axis [111] to the wire axis in 
different zones is determined as follows: 

1 Z. Physik., 42, 779 (1927). 



370 



APPLIED X-RAYS 



Distance of Layer from 
Center, Millimeters 
1 75 (outer skin) 
1.6 
1 3 
0.9 
4 



Inclination Angle, 
Degrees 
<2 
9 
6 
4 




This indicates that, in the outermost skin of the wire, the effect 

of the die has been to keep the 
grains which are oriented 
nearly parallel to the direc- 
tion of drawing, but slightly 
below this the conical flow is 
evident. The texture of a 
hard-drawn wire, therefore, 
181. Schmid and Wassermann 
kilograms per square 




FIG. 181.- 



-Diagram of zonal texture of 
hard-drawn wires. 



may be represented in Fig. 
report tests of tensile strengths in 
millimeter corresponding to zones for two specimens of hard- 
drawn copper wire, as follows: 



1. Original diameter 4.85 mm 
Etched to 3.20 mm 
Drawn to 3.20 mm 

2. Original diameter 1.75 mm 
Etched to 1.00 mm 
Drawn to 1.00 mm 



Tensile Strength 

... . 38 3 

41 3 

45 2 

46.1 

. . 52 8 

. 51 



It is evident that the core zone of a wire has the highest tensile 
strength in keeping with its parallel preferred orientation. 
This anisotropic or zonal structure is an inherent property and 
improvement in the superficial zones is not gained by increasing 
the amount of cold work. 

5. Summary of X-ray Results on Deformation Structures of 
Drawn Wires. All body-centered cubic metals when drawn are 
characterized by a [110] direction parallel to the direction of 
drawing; all face-centered cubic metals have a [111] direction in 
the wire axis, with a second orientation of [100], the proportion 
of crystal grains in the various metals varying as explained above. 
An exception in the case of copper wire recrystallized at 1000 C. 
has been noted. Only the core of these wires and perhaps the 
outermost skin approximate these orientations, since in the mantle 
zones the fiber axis is inclined to the wire axis. In answering 



INTERPRETATION OF DIFFRACTION PATTERNS 371 

the question why a particular crystallographic direction becomes 
parallel to the direction of deformation it may be noted that the 
most thickly populated atomic planes in the body-centered cubic 
lattice are the (111) planes, with the (100) planes next most densely 
populated. It is a general drawing phenomenon, therefore, that 




FIG. 182. Pinhole pattern for rolled sheet metal showing nearly random crystal 

grains. 

the most densely populated planes take up positions perpendic- 
ular to the wire axis, and that these orientations are such as to 
present maximum resistance to further deformation. 

6. Interpretation of Fiber Patterns for Rolled Sheets (Limited 
Fiber Structure). It is possible for cold-rolled sheet metal to 




FIG. 183. Structure of sheet metal with randomly oriented grains. 

produce a diffraction pattern indicating nearly random orienta- 
tion of grains, as in Fig. 182. The structure of the sheet could 
then be diagrammatically drawn as Fig. 183. But in general, 
as explained above, crystal grains in a rolled sheet not only take 
up positions with a certain crystallographic direction parallel 



372 



APPLIED X-RAYS 



to the direction of rolling but are further limited by having 
certain crystallographic planes parallel to the plane of rolling 
and to the transverse direction. Thus the diffraction pattern 
for rolled sheet steel in Fig. 184 indicates clearly the structure 




FIG. 184. Pinhole pattern for rolled sheet steel showing preferred orientation of 
grains (for complete analysis, see text). 

of the sheet with preferred orientation of grains as pictured in 
Fig. 185. The diffraction patterns enable the evaluation of the 
indices of these three characteristic directions (i.e., rolling direc- 
tion, the normal to the rolling plane, and the transverse direction 




Fiu. 185.- 



- Structure of rolled sheet metal (steel) with preferred orientation of 
grains. 



lying in the rolling plane at right angles to the rolling direction), 
and also with remarkable accuracy the departure or scattering 
from the theoretically ideal orientation as is always observed in 
practical cases. The rolling direction may be readily ascertained 
by the methods outlined under drawing, although all of the 



INTERPRETATION OF DIFFRACTION PATTERNS 373 



diffraction interferences will not be present on account of the 
further limitation in rolling. For the determination of the crys- 
tallographic indices of the transverse direction and the normal to 
the plane of rolling, a further step must be taken. The best 
method is that of Glocker, explained in detail in his book: 1 a 
single metal crystal is considered to rotate through 360 deg. 
around the known fiber axis, and the reflection angle 9 of the 
x-ray beam, impinging at right angles to the axis of rotation, 
on the different lattice planes of the crystal is plotted as a func- 
tion of the angle of rotation. The result is a series of rotation 
curves which are extremely useful in interpreting results on 
rolled sheets or foils. Glocker gives curves for fiber axes [112], 
[001], and [111], with octahedral (111), cubic (100), dodecahedral 
(110), and (113) planes for each. He considers in detail the 
case of rolled silver in which [112] is parallel to the rolling direc- 
tion and (110) planes are parallel to the rolling plane. 

7. Detailed Analysis of Pattern for Rolled Steel. To show in 
detail how a diffraction pattern of commercial rolled sheet may be 
completely interpreted, the example of low-carbon sheet steel is 
selected. The following analysis of a pattern similar to Fig. 184 
is carried through in three parts: 

a. Identification of the diffraction rings. 

b. Identification of the type of fiber orientation. 

c. Determination of the type and degree of perfection of 
further limits of orientation. 

The method consists essentially in assuming certain origins, 
orientations, and limitations and in checking theoretically desired 
patterns against those experimentally obtained. 

a. Identification of Diffraction Rings. 

If 9 = angle of incidence of x-rays with atomic planes, 

D = diameter of ring on film, 
5 cm. = distance from specimen to film, 
then 9 = ^ tan- 1 (1/5 X fl/2). 













Sin 9 


D 


D/2 


Tan 20 


2B 


e 


(observed) 


3 76 


1 88 


0.376 


20 36' 


10 18' 


179 


5 66 


2.84 


566 


29 30' 


14 45' 


255 


7.28 


3 64 


0.728 


36 2' 


18 1' 


0.309 



1 " Materialpriif ung mit Rontgenstrahlen," pp. 312-324, Berlin, 1927. 



374 



APPLIED X-RAYS 



Calculation of the theoretical values of sin assuming these 
plane families to be the (110), (200), (211): 

d = interplanar distances. 

a = length of unit cell cube of Fe = 2.87 A.U. 
(hkl) = (100), (200), (211). 

X = 2 d sin 9, sin 9 = ^ 
X for Mo Ka = 0.710 A.U. 



Hence sin 9 = 



and d = 



+ k 2 + 



hkl 


d 


Sin 6 (calculated) 


Siri 6 (observed) 


110 


2 03 


175 


179 


200 


1.435 


247 


255 


211 


1 171 


303 


309 



This is close enough agreement from these rough measurements 
definitely to establish the identity of these rings. 

The inner broad band is caused by the polychromatic or white 
radiation reflected by the planes of greatest spacing (110). The 
inner edge is determined by the short wave length of the white 
radiation, which is determined by the peak voltage across the 
x-ray tube. The outer edge is caused by an absorption edge due 
to the silver of the film emulsion, which occurs at a wave length of 
0.485 A.U. 

To check this outer absorption edge, the following calculation 
is made : 



X - MM. -.O- -,,- 0.1* 

Diameter of outer edge of ring = 2.50 cm. 

sin 9 = sin }$ tan- 1 (1/5 X D/2). 



D 


D/2 


Tan 29 


20 


O 


Sin B 
(observed) 


SinB 
(calculated) 


2.50 


1.25 


0.25 


14 2 f 


7 1' 


122 


120 



This agreement is also quite close. 



INTERPRETATION OF DIFFRACTION PATTERNS 375 

The determination of minimum wave length from the diam- 
eter of the inside edge of the white radiation band is as follows: 
Diameter of inner ring edge = 1.60 cm. 

M- = 0.16 = tan 29 
o 

9 = 4.75. 
sin 9 = 0.083. 
X = 2dsin9 = 2X 2.03 X 0.083 = 0.336 A.U. 

Peak voltage = V = hc/\e = 12354/X = 36,768 volts. 

b. Identification of Fiber Orientation. Since the reflection of an 
x-ray beam from an atomic plane must always lie on a plane 
determined by the beam and a perpendicular to the atomic plane 
at the point of reflection, the azimuth of the spots appearing on 
the various rings can be determined by calculating the angle 
between the perpendicular of the atomic planes being considered 
and the fiber axis, which is placed perpendicular to the beam. 
The following notation may be adopted : 

a = angle between perpendicular to atomic planes under con- 
sideration and fiber axis. 

5 = azimuth angle of spot on film (starting with zero at the 
twelve o'clock position on the film). 

9 = angle of incidence of the x-ray beam upon atomic plane. 

Polanyi gives the relation between these angles as cos 5 = 

^> but as such small values of 9 as appear in these diagrams 

cos 9 vv & 

the cosine of 9 so nearly equals one that it is within limits of 
accuracy to simplify to cos 5 = cos a or <5 = a. 

Thus the azimuth of an intensity maximum on any ring is 
directly the angle between the perpendicular to the plane 
family causing the ring and the fiber axis. This angle between 
a perpendicular to any family of planes (hkl) and any fiber 
axis (uvw) can be given by solid analytical geometry to be : 

uh + vk + Iw 
cos a = p 



w 



Since Glocker gives the fiber axis direction in a sheet of iron 
as [110], this orientation will be assumed and the theoretically 
determined positions of the spots on each ring will be compared 



376 APPLIED X-RAYS 

with the actual diagrams. With (uvw) as (110), the equation 
simplifies to 

h + k 

COS a = -pz = r=z' 

<\/2 Vh 2 + k 2 + I 2 

Using this equation the theoretical azimuth of spots on the 
various rings is as follows: 

Pianos Azimuth, Degrees 

no o 

TlO 90 

101 60 

100 45 

001 90 

112 55 

112 90 

121 30 

121 73 

These diagrams should be symmetrical along both a vertical and 
a horizontal axis, for every spot at angle 5 on the right there is one 
at 5 on the left, and one on the right and left at (180 5). 

In comparing this theoretical complete fiber diagram with 
the actual diffraction patterns the fiber axis is assumed to be 
perpendicular to the x-ray beam which practically may not be 
exactly true. This will tend in some cases to shift the positions 
towards one pole or the other and cause fiber spots which originate 
from planes at high angles from the fiber axis to appear with less 
rotation than would be expected, as will be discussed in the next 
section. 

In Fig. 184 the following experimental interferences are 
observed : 

INNERMOST SHARP KING (110) 

Present 

60 Missing 

90 Present 

SECOND SHARP RING (100) 
45 Present 

90 Missing 

THIRD SHARP RING (211) 

30 Present 

55 Missing 

73 Present 

90 Missing 



INTERPRETATION OF DIFFRACTION PATTERNS 377 

The broad band can have the same intensity maxima as the 
sharp (110) ring: 

Present 

60 Missing 

90 Present 

Since this orientation takes care of all the spots appearing on 
the diffraction pattern but calls for spots which do not appear, 
it is evident that the assumption of a [110] axis is correct, but that 
there is a further limitation of orientation in a rolled sheet. 

c. Type and Degree of Perfection of Further Limitation. It 
has just been shown that, as was expected, a cube face diagonal 
lies parallel to the surface of the sheet or nearly so and in the 
direction of rolling. The other condition of a cube face lying 
parallel to the surface of a sheet which is usually given will be 
taken as the zero position and angular rotation about the face 
diagonal fiber axis necessary to cause the appearance of various 
spots will be calculated. Then, by the presence or absence of 
certain spots, the degree of perfection of the fulfillment of this 
condition can be determined on each film. If this orientation 
were perfect, only a very few spots would appear on any ring, and 
the ring itself would be missing. 

The calculation of this angle of lateral rocking to one side and 
the other about the zero position necessary to cause the appear- 
ance of each spot is very involved in most cases, and a complete 
solution of this problem of a cubic lattice rotating about a [110] 
axis has been worked into the series of rotation curves by R. 
Glocker, mentioned above. These curves were used in investi- 
gating how great an angle of rotation of the cube about the [110] 
fiber axis from the zero position of the (100) face in the sheet is 
necessary in order that a diffraction spot may occur by having 
fulfilled the law specifying the angle of diffraction. 

It will be seen that in the special case of any planes containing 
the x-ray beam the necessary angle of rotation about any axis 
perpendicular to the beam will directly equal the angle B given 
in the diffraction equation. 

The presence of spots on the two (110) rings at the twelve and 
six o'clock positions can be explained only by another type of 
imperfection in orientation. This is a tipping of planes which in 
a perfect orientation would contain the x-ray beam and be per- 
pendicular to the fiber axis, about an axis perpendicular to both 



378 



APPLIED X-RAYS 



the beam and the fiber axis. This is actually an inclination of the 
fiber axis to the surface of the sheet, and its calculation falls in 
the special case mentioned in the last paragraph. The angles 
of rotation necessary for the appearance of the various spots on 
the several rings arranged in the order of their appearance with 
increasing rotation were found to be as follows: 



Necessary angle 
of rotation 


Ring 


Radiation 


Azimuth, degrees 


4 


no 


White 


90 


9 


112 


Ka 


73 


10 


110 


Ka 


90 


18 


112 


Ka 


30 


18 


110 


Ka 


60 


20 


100 


Ka 


45 


22 


110 


White 


60 


45 


112 


Ka 


90 


70 


112 


Ka 


55 



The angle of inclination of the fiber axis to the sheet necessary 
to cause the appearance of spots at the six and twelve o'clock 
positions on the rings will be calculated. These reflections can 
only originate from (110) planes, and the inclination is directly 
equal to the angle of incidence given by the Bragg equation for 
this set of planes. 



Ring 


Radiation 


Wave length 


Inclination angle 


(HO) 
(HO) 


Mo Ka 

White 


710 A. U. 
336 


10 18 

4 45' 



Inclination of the fiber axis to the surface of the sheet in both 
directions with respect to the direction of the last pass will have 
the effect of causing the spots to extend over a wider angle on 
the circles and will cause spots to appear at slightly smaller 
rotation angles than those calculated to be necessary. If more 
grains are inclined in one direction than in the other,* which in 
general seems to be the case, the intensity maxima will be dis- 
placed in one direction of azimuth and there arises a possibility 
of the appearance of spots on one side of the equator which have 
no corresponding spots on the other side. 



INTERPRETATION OF DIFFRACTION PATTERNS 379 



d. Experimental Check. For the particular specimen con- 
sidered here the necessary rotation or the degree of imperfection 
of limitation of the complete fiber diagram caused by rotation 
around the fiber axis is 35 deg. ; the inclination of the fiber axis to 
the sheet estimated from the relative intensities of the two polar 
spots to each other and to other interference maxima is small; 
and the majority of the inclinations of the fiber axes are greater 
in one direction than in the other with respect to the direction of 
last pass through the rolls. 

8. Summary of Experimental Results on Structures of Rolled 
Foils. 





I attice 






Metal 


J 


Treatment 


Fiber axis [FA], rolling plane (RP) 




type 






Aluminum 


F. C C. 


Rolled 


I [355] or [112] || FA, (135) or (110) || RP 








(four positions possible) 








II [100] || FA, (001) || RP (average reduc- 








tion) 


Silver 


F. C. C. 


Rolled 


[112] || FA, (110) || RP (two mirror image 








orientations) 






Recrystallized 


[112] |1 FA, (113) || RP 






250 to 800 C 




Gold... 


F. C. C 


Rolled 


I [112] || FA, (110) || RP 








IT. [100| 1| FA, (001) || RP 


Copper 


F. C C. 


Rolled 


[112] || FA, (110) || RP 






Recrystallized 
250 to 1050 C 


[100] || FA, (001) || RP 


a-brass 


F. C. C 


Rolled 


[112] || FA, (110) || RP 






Recrystallized 
300 to 702 C 


[112] || FA, (113) || RP 


Platinum 


F. C. C. 


Rolled 


I. [112] || FA, (110) 11 RP 








II. [100] || FA, (001) || RP 


Iron 


B. C. C. 


Rolled 


[110] || FA, (100) 11 RP 






Rerrystallized 


[350] || FA, (100) || RP 






600 




Tantalum 
Tungsten 


B. C. C. 
B. C C. 


Rolled 
Rolled 


Same as rolled iron 



9. Differences in Preferred Orientation in Surfaces of Thicker 
Sheets of Rolled Face-centered Cubic Metals. Although there 
are numerous statements in the literature to the effect that the 
preferred orientation assumed upon cold rolling metals having 
the same crystal structure are identical for the case of very thin 
foils, recent work has shown that this is not true for face-centered 
metals at least in the surface layers of fairly thick sheets. Holla- 
baugh and Davey 1 have investigated the preferred ranges of 

1 Metals and Alloys, 2, No. 4, 256; No. 5, 302 (1931). 



380 APPLIED X-RAYS 

the crystal fragments in the surfaces of sheets of aluminum, 
nickel, copper, and silver for a series of samples of each metal, 
with consecutively increasing number of passes through the 
rolls. Instead of the usual transmission method, they used a 
special reflection method and investigated only the surfaces of 
comparatively thick sheets. The orientations found for the 
four metals were similar only in that for each of them one face 
diagonal of the cube always lies in a plane which is parallel to 
the direction of rolling and perpendicular to the rolling surface. 

Nickel and copper were found to behave identically in that 
there was one symmetrical preferred range of positions about 
the across axis with symmetrical limits about the along axis. 
Silver was found to differ from nickel and copper in that there 
are two symmetrical preferred ranges about the across axis 
with no limitation about the along axis. The behavior of 
aluminum was found to be different from that of the three other 
metals in almost every respect. The limits of the preferred 
positions were found to vary on rolling instead of remaining 
unchanged as in the others. Like silver, aluminum shows two 
ranges of positions about the across axis, but unlike silver these 
ranges are unsymmetrical. Aluminum also shows variable 
limits around the along axis. 

Although these metals investigated have the same crystal 
structure and approximately the same atomic size and lattice 
parameters, they differ in valence. The authors believe that 
these differences in the preferred orientation in the surfaces 
of cold-rolled face-centered metals may be accounted for in 
terms of the number of valence electrons of the atoms of these 
metals. They assume that valence electrons in the atoms 
control the lattice forces and that these differences cause the 
difference in behavior noted for the four metals discussed. 

10. Plastic Deformation of Zinc and Magnesium. Unusual 
interest has been attached to the x-ray study of the deformation 
of zinc both as single crystals and as polycrystalline aggregates. 
The following resume of earlier investigations is quoted from " The 
Science of Metals" by Jeffries and Archer. 

Mark, Polanyi, and Schmid in Germany studied the deformation 
of single crystals by means of x-ray crystal analysis. They found 
change of orientation at slip planes produced during the ordinary tensile 
test in single crystals of zinc. Conditions for maximum elongation of 
single crystals of zinc were determined. Zinc crystallizes with a 



INTERPRETATION OF DIFFRACTION PATTERNS 381 

hexagonal space lattice. The plane of easiest slip is the base of the 
unit hexagonal prism. When this plane makes an angle of approxi- 
mately 45 deg. with the wire axis, the crystals are very ductile. Single 
crystal wires broken in tension at room temperature have shown as 
much as 600 per cent elongation; broken at 205 C., elongations up to 
1700 per cent have been obtained. Although zinc is not regarded as 
very ductile, these values for elongation are the highest of any known 
metal. Unless the plane of easiest slip is at an opportune angle with 
respect to the wire axis, the crystal is relatively brittle. Single crystal 
wires of bismuth were tested at 200 C. and showed up to 300 per cent 
elongation. In this case also the plane of easiest slip must make an 
angle with the wire axis of about 45 deg. or the crystal will be brittle 
when broken in tension. During the process of elongation of the zinc 
single crystals, the round wire changed into a flat ribbon. The width 
of the ribbon was at first slightly wider than the original diameter of 
the wire. Slip occurred in a plane about 45 deg. from the wire axis 
and extended across the whole cross section of the wire in such a manner 
that the intersection of each slip plane with the wire surface formed an 
ellipse. The slight widening of the ribbon was due to the rotation of 
the elliptical sections. As the elongation increased, the general orienta- 
tion of the crystal changed, so that the angles of the easiest planes of 
slip became more nearly parallel with the direction of extension. 

The elongation is accompanied by a continued strengthening of 
the crystal and Polanyi believes that this is due to a bending of slip 
planes, so that the resistance to slip is increased. The exact mechanism 
of this strengthening is rather uncertain, but Polanyi assumes that the 
crystal units themselves undergo inner changes which lead to this result. 
As a matter of fact, Geiss and von Liempt have concluded from their 
investigations on single crystals of tungsten that the atoms themselves 
are deformed by tension, but the only evidence adduced by them for this 
conclusion is the change in temperature coefficient of resistance. 

Mathewson and Phillips have described a new mechanism 
of deformation of zinc based on the study of large rectangular 
crystals. One of their conclusions was that deformation pro- 
duced twinning with a rotation of some of the basal planes into 
positions 94 deg. removed from their original position, or about 
the same as that of the prismatic planes before twinning. A 
second conclusion was that fracture occurred along the basal 
planes in their new position, and therefore that fractures pre- 
viously regarded as prismatic were in reality basal. Wilson 
and Hoyt showed then that cold rolling of polycrystalline zinc 
strip causes rearrangement of the zinc crystals not by twinning 
but in accordance with the classical theory of plastic deformation. 



382 



APPLIED X-RAYS 




FIG. 186. Pattern for forged Dowmetal (magnesium alloy). 




FIG. 187. Theoretical fiber diagram for [001] parallel to fiber axis in hexagonal 
crystals, with which pattern in Fig. 180 agrees. 



INTERPRETATION OF DIFFRACTION PATTERNS 383 




FIG. 188. Pattern for Dowmetal extruded at ordinary temperatures. 




FIG. 189. Theoretical fiber diagram for [210] parallel to fiber axis, hexagonal 
system, with which pattern in Fig. 188 agrees. 



384 



APPLIED X-RA YS 




FIG. 190. Pattern for Dowmetal extruded at high temperatures (compare 
with Fig. 188 for different orientation and much larger grain size). 




FIG. 191. Theoretical fiber diagram for [110] parallel to fiber axis, hexagonal 
system, with which pattern in Fig. 190 agrees. 



INTERPRETATION OF DIFFRACTION PATTERNS 385 

Extension of slender zinc single-crystal specimens causes rear- 
rangement of the basal planes in accordance with the classical 
theory, the single crystal structure being preserved. The 
formation of the after-elongation thread is accompanied by 
severe lattice deformation which promotes twinning and frag- 
mentation, though the single-crystal structure seems very per- 
manent. The fracture of a thick zinc crystal occurs as depicted 
above with twinning present. The fracture of slender zinc 
crystals under simple tension is prismatic with twinning absent. 

The growing industrial importance of magnesium and its 
alloys also lends particular interest to the mechanism of its 
deformation. Figures 186 to 191 show diffraction patterns 1 and 
theoretically calculated diagrams, respectively, for forged and 
extruded Dowmetal (nearly pure magnesium alloy). The 
analysis of the patterns proves that the forged magnesium alloy 
possesses a fiber axis parallel to the [001] direction while the 
extruded alloy shows a [210] fiber axis in the direction of extru- 
sion at low temperatures and a [110] direction at high tempera- 
tures, a curious change in glide direction with temperature. 
Schmid working with single crystals found translation on the 
basal planes with the diagonal axis of the first kind as glide 
direction. Above 225 translation on the pyramid faces occurs 
with the same glide direction. In many important respects 
therefore magnesium differs in behavior from zinc and cadmium. 

11. Preferred Orientations, in Electrodeposited Metal Sheets. 
In the preceding sections the production of a directed crystal 
orientation by means of mechanical work has been considered 
in detail. The question naturally arises as to whether crystals 
may actually grow in such a way as to have a common crystallo- 
graphic direction parallel to the axis of growth. Experiment 
proves that electrodeposited metal films show a fiber structure 
similar to drawn metals, and that the grains grow out parallel 
to the stream lines of the current or perpendicular to the surface 
of the electrode. The interpretation of the fiber patterns leading 
to an evaluation of the indices of the fiber axes proceeds exactly 
as outlined above. Of course, the fiber axis is parallel to the 
cross section or thinnest dimension of the deposited sheet. If, 
then, an x-ray beam impinged at right angles upon the surface 
of such a sheet, it would pass parallel to the fiber axis. As 
demonstrated for wires, the pattern is always indicative of 

1 Kindly furnished by Dr. L. G. Morell, Dow Chemical Co. 



386 



APPLIED X-RAYS 



random orientation, since the crystal units may be oriented 
anywhere through 360 deg. around the fiber axis. It is neces- 
sary, therefore, to have films thick enough to pass the beam 
perpendicular to the fiber axis or to use the method of inclining 
the fiber axis at an oblique angle to the primary beam. Bozorth 1 
has published curves for graphical analysis of patterns so obtained 
with the formula 

cos a cos /3 sin G 

cos 8 = : --- r . 

sin ft cos 9 

Many excellent papers have been published on detail studies 



Element 


Lattice 


Solution 


Current 
density, 
amperes 
per 
square 
centi- 
meter 


Fiber axis 


Observer 


Silver 


F. C C. 


Cyanide 


007 


Random 


G locker and 












Kaupp 


Silver . 


F. C. C 


1 N AgNO 3 


010 


[HI], [001] 


docker and 












Kaupp 


Silver 


F. C. C 


1 N AgNOs 


022 


Random 


docker and 












Kaupp 


Copper 


F. C C. 


1 TV CuS()4 


03 


[Oil] 


docker and 












Kaupp 


Nickel 


F. C. C. 


{Ni(NH4)4S0 4 or 
1 TV NiCl 2 + 
9 N NiS() 4 


005 


[001] 


Bozorth 


Nickel 


F. C. C. 


N1SO4 -f boric acid 


10 


[001] 


Clark and 










[Oil] 


Frohc.h 










(on under- 












lying cop- 












per) 




Nickel 


F. C. C. 


9 N NiCl 2 -f- 1 N 


005 


[211] 


Bozorth 






NiSG-4 








Lead 


FCC 


Pb (C1O4)2 or fluosilieatc 


1 


[211] 


Clark, Fro- 












lich and 












Aborn 


Chromium 


B. C. C. 


Grube 




[HI] 


docker and 












Kaupp 


Iron 


B. C. C 


10 per cent Fe(NIT4>4S()4 


001 


[111] 


docker and 












Kaupp 


Iron. 


B C C. 


10 per cent Fe(NII.i) 4>SO4 


015 


Random 


Glocker and 












Kaupp 


Iron 


B. C. C. 


50 per cent FeCl? 


001 


[HI] 


^docker and 












Kaupp 


Iron 


B C C 


50 per cent FcCla at 100 


0.1 


Random 


Glocker and 






C. 






Kaupp 


Iron 


B. C. C. 


Same -\- CaCl-2 


1 


[112] 


docker and 












Kaupp 



l Phy*. Rev., 26, 310 (1925). 



INTERPRETATION OF DIFFRACTION PATTERNS 387 

involving effects of electrolytes, current density, temperature, 
concentration, stirring, orientation as a function of thickness, 
effect of base electrode metal, recrystallization, presence of 
small amounts of addition agents, pH, electrode potential, etc. 
Glocker summarizes the results as shown on page 386. 

12. Deposition of a Metal from Solution by Displacement. 
Metallic silver deposited from a solution of silver nitrate by 
introducing a small piece of copper has a fibrous structure with 
the axis [110] which makes an angle of 30 deg. with the direction 
of growth. The microcrystals show a rotation around this 
axis with an angle of 11 deg. As the (111) planes of the 
silver crystals lie parallel to the flat surfaces of the deposited 
metal, the direction of growth of the deposited silver lies nearly 
parallel to the [112] axis. 1 

13. Properties of Mirrors and Sputtered Films. Very thin 
films of metals have been frequently studied. Foils of platinum, 
nickel and copper 7 to 18 microns thick produced by cathodic 
sputtering and thermal evaporation show a structure. The 
support upon which the film is deposited and the presence of 
gas have a profound effect upon the crystal arrangement. 

14. Growth of Texture of Castings. Superficial observation 
alone discloses the regularity of grain orientations and directions 
of growth in castings. In both body-centered and face-centered 
cubic metals the orientation is such that (100) planes lie parallel 
to the long axis of the crystal grain. In white tin (110), in the 
hexagonal close-packed metals (Mg, Zn, Cd) (1010), with (0001) 
perpendicular, and in bismuth (111) planes lie parallel to this 
direction. It is obvious that these preferred arrangements in 
commercial metal castings are of great significance in determining 
the possibility of machining operations and the tensile strength. 
For example, a zinc casting with radially arranged dendritic crys- 
tal grains has a modulus of elasticity of 800 kg. mm. 2 and a 
coefficient of expansion of 38 X 10~ 6 ; if the crystallization is con- 
trolled so that the orientation is parallel to the long dimension of 
the casting, the modulus of elasticity is 12,000 kg. /mm. 2 and the 
coefficient of expansion is 14 X 10~ 6 . It is possible therefore by 
means of x-ray analysis of structures of specimens cut in a certain 
way from castings prepared by a given technique to ascertain 
what crystallographic directions correspond to the dimensions of 
the unit. 

1 Tsuboi, Kyoto Coll. Sci. Memoirs, 11, 271 (1928). 



CHAPTER XVIII 

PRACTICAL APPLICATIONS OF X-RAYS TO PROBLEMS 
OF METALLURGICAL INDUSTRY 

In preceding chapters the fundamentals of x-ray metallography 
have been outlined. The interpretation of diffraction patterns 
has been presented in terms of the characteristic crystal struc- 
tures of pure metals and alloys, and in terms of important tech- 
nical properties such as grain size, internal strain, and effects of 
mechanical deformation. The immediate practical industrial 
significance of these fundamental facts has been pointed out in 
part and other applications are obvious to anyone acquainted 
with metallurgical problems. It is now the purpose to enumerate 
briefly some of the actual problems of practical metallurgy, 
aside from the structure and constitution of alloys, and to illus- 
trate some of the results of approach to these problems by the 
x-ray method. This list is merely one selected somewhat at 
random and is in no sense a complete record of achievement. 
Most of the examples have been selected from among the investi- 
gations in the writer's own laboratory. 

In general, the x-ray method has been called upon to decide 
upon the proper method of manufacturing technique, to assure 
constant properties, and to make a fundamental distinction 
between metal or alloy commodities with satisfactory and 
unsatisfactory behavior. For commercial metals the scientific 
methods of interpretation derived for pure materials as pre- 
sented in preceding chapters are applied, although every new 
metal specimen is a new subject for research in itself. Gradually, 
metallurgical industry is coming to the realization, on the one 
hand, that there is nothing mysterious in x-rays or magic in the 
searchings of ultimate structures and, on the other harnd, that 
these rays are not a panacea for all troubles unsolvable by other 
methods even though a brilliant record of achievement is already 
written. X-rays enable the observation of the interior of solid 
objects for gross inhomogeneities, and they extend the scope of 
fine-structure analysis far beyond the microscope down to the 

388 



PRACTICAL APPLICATIONS OF X-RAYS 389 

ultimate architectural pattern of atoms in space. Without 
undue enthusiasm it may be stated as a fact that the contributions 
of x-ray research to metallurgical science over so few years surpass 
the record of all other experimental methods. The growing 
interest and confidence in a great research tool are demonstrated 
by the number of experimental installations in the research 
laboratories of metallurgical manufacturers and universities. 

1. The X-ray Analysis and Control of Heat Treatment and 
Recrystallization of Cold-worked Metals, a. The Province of 
Heat Treatment. When metals are worked by rolling or drawing, 
they become fibered. In other words, aggregates in which the 
crystal grains have random orientation assume in the process 
of mechanical deformation a structure in which the grains 
assume a definite orientation with respect to a common direction 
that of rolling or drawing. The analysis of the mechanism 
from x-ray patterns is given in the preceding chapter. These 
sheets or wires are now characterized by strongly directional 
properties and it is the province of heat treatment in general to 
cause a recrystallization of the grains while retaining the form 
of the sheet or wire, so that a random, non-directional orientation 
is again obtained as is absolutely required, for example, in forming 
steels. Again internal strains introduced by rapid chilling in 
castings, etc., are relieved by heat treatment. The x-ray 
method finds powerful practical use in discovering just how 
completely the fiber structure or the internal strain has been 
removed. In its sensitiveness as such a control method it far 
transcends the microscopic or other physical tests. 

It is the purpose of the present section to consider in a more 
quantitative manner the mechanism of recrystallization during 
heat treatment of single relatively pure metals, principally 
aluminum, silver, and copper. The information which has been 
derived from x-ray researches, chiefly by Glocker, Kaupp, and 
Widmann, 1 on these metals is astonishing in its scope. 

b. Heat Treatment of Cold-rolled Foils. There are three 
possible effects of heat treatment of cold-rolled foils: (1) the 
directed orientation of grains is completely lost and the new 
grains are in random arrangement from the outset of recrystalliza- 
tion; (2) between the states of fiber structure and final random 
arrangement there is an intermediate step consisting of a directed 

'Z. Physik., 45, 200 (1927); Z. Metallkunde, 17, 354 (1924); GLOCKER, 
"Materialprufung mit Rontgenstrahlen," p. 332, Berlin, 1927. 



390 



APPLIED X-RAYS 



arrangement different from that produced in rolling, which goes 
over into the random type of temperatures in the neighborhood 
of the melting point ; (3) the new recrystallization or intermediate 
directed orientation persists to the melting point. 

(1) Recrystallization of Aluminum Sheet. At all degrees of 
rolling, even up to 98 per cent reduction, aluminum recrystal- 
lizes with a random orientation of grains. Heating for 15 min. 
at 265 C. does not destroy the fiber pattern of the rolled sheet 
(Fig. 166) but at 275 C., or above, this is lost. The pattern 
consists now of concentric rings with a spotted appearance 
indicative of a random arrangement of larger grains (Fig. 192). 




f 



FIG. 192. -Pattern for cold- 
rolled aluminum foil after anneal- 
ing, showing recrystallization in 
random arrangement. 



FIG. 193. -Pattern for cold- 
rolled silver foil after annealing at 
225-750C., showing recrystalliza- 
tion in new preferred orientation. 



This is the type of structure which might be generally expected, 
and for all the metals with degrees of rolling below 90 per cent 
reduction, including silver and copper, this is observed. Alumi- 
num thus represents the first of the above alternatives. 

(2) The Recrystallization of Silver. Glocker was the first to 
observe that with strongly rolled silver (97 per cent) the recrystal- 
lization did not take place with chaotic arrangement of grains, but 
with a new crystallographic orientation (Fig. 193) with the (113) 
planes in the plane of rolling instead of the (110) planes as in the 
original rolled structure. This structure is maintained even 
after 10 days or more of heating at 300 C., but at higher tempera- 
tures (rapidly at 850 to 900) the random orientation results, 
together with a considerable increase in grain size. These 
facts illustrate the very important fact that long annealing at 
low temperatures does not necessarily produce the same effect 



PRACTICAL APPLICATIONS OF X-RAYS 



391 



as annealing for a short time at high temperatures, as is so often 
believed and practiced in metallurgical circles. 

The sequence of events during recrystallization as interpreted 
from the x-ray patterns may also be tested and compared with 
the results of technological tests on tensile strength, elasticity, 
and grain size. Widmann's data as plotted in Fig. 194 show 




200 ..400 600 800 1,000 1,200 1,400 
Anneoil IMOJ Temperorrure >" Degrees Ceyrriojroiole 

FIG. 194. Tensile strength, elongation, and grain size of rolled silver sheet as 
functions of annealing temperature. (Glocker and Widmann.) 

distinctly the breaks occurring with the appearance of the new 
directed position at 200 and with random orientation at 800. 

The very curious fact also was found that if the silver is reduced 
only partially in one rolling operation, is heated at 700 C., and 
again rolled down to final thickness, then the properties are 
distinctly different from those of the silver reduced in one roll- 
ing only. In the former case the x-ray patterns indicated that 



392 



APPLIED X-RA YK 



the sheet begins to recrystallize at room temperature. Con- 
sequently annealing produces abnormally large grains and loss 
of tensile strength, the metal is characterized by mixed, very 
large and very small grains, and is difficult to handle practically. 
(3) Impurities Change Recry stabilization Temperature. The 
effects of small amounts of impurities on the recrystallization 
temperature of silver may be determined far more accurately 
from the x-ray patterns than from microscopic analysis. Wid- 
mann's studies of this subject have been fully substantiated 
by the present writer. In the following table are listed the data 
on the effects of impurities. 



Element 


Impurity 


Recrystalliz.Mtion 
temperature, 
degrees 
Centigrade 


Weight, 
per cent 


Atomic, 
per cent 


Pure silver 






150 


Copper . . . 
Copper 
Copper 
Aluminum 


303 
12 
073 
2 


51 
20 
123 
93 


230 
200 
175 
190 


Zinc- 


119 


195 


145 


Lead 


059 


03 


145 


Niekel . 


1 


15 


137 


Gold 


1 


054 


112 


Gold 


2 


11 


110 


Palladium 


1 


10 


112 


Iron 


035 


068 


110 


Iron 


055 


107 


20 


Iron ... 


065 


126 


20 



It is clear that copper and aluminum raise the temperature, 
while all other elements, particularly iron, lower it. Five 
hundredths of 1 per cent of iron is sufficient to lower the tem- 
perature of recrystallization of silver to room temperature. 
Ancient as is the metallurgy of silver, this fact has been discovered 
only recently by means of x-rays. It is safe to conclude that 
silver, except of the highest purity, always has contained at 
least this trace of iron. Why then has not recrystallization 
served to ruin, practically speaking, cold-rolled silver articles? 
The answer is that copper also is universally present and in 
amounts of 0.1 per cent or less completely compensates for the 



PRACTICAL APPLICATIONS OF X-RAYS 



393 



powerful effect of 0.05 per cent iron. In the same way aluminum 
compensates for gold which also lowers the recrystallization 
temperature of silver. It is interesting to note, however, that 




(b) (c) 

FIG. 195. Recrystallization of low carbon steel shim stock, (a) Original 
rolled structure; (6) recrystallized in new preferred orientation; (c) heated above 
upper critical point to produce random arrangement of grains. 

the temperature of 150 for pure silver does not hold for the very 
purest silver (considerably less than 0.0005 per cent iron and 
0.00002 per cent lead) possible to prepare. Very pure silver 
recrystallizes at room temperature. Copper has little effect on 



394 



APPLIED X-RAYS 



grain size and on the appearance of the intermediate directed 
orientations of silver; iron, nickel, and especially lead, increase 
grain size, and zinc decreases it. The recrystallization positions 
of grains are not so perfectly directed in the presence of the 
metals. Thus, for the first time is it possible to have a quantita- 
tive idea of the metallurgical importance of very small amounts 
of impurities. In every case addition of larger amounts has 
little or no effect as compared with the introduction of the 
first traces. 

(4) The Recrystallization of Iron. Both brass and iron (body- 
centered cubic) behave somewhat similar to silver when rolled 

and annealed. For iron 
rolled 97 per cent and heated 
above 600 there is an orien- 
tation so that the [350] direc- 
tion is parallel to the rolling 
plane, while the cold-rolled 
metal is characterized by a 
[110] direction. Figure 195 
shows a series of patterns for 
low-carbon steel subjected to 
various heat treatments; of 
particular interest are the 
new recrystallization orien- 
tation and the fact that ran- 
dom orientation is obtained 
only after heating above the 
upper critical point. Silver, brass, and iron, therefore, represent 
the second of the three recrystallization mechanisms. 

(5) The Recrystallization of Copper. When strongly rolled 
copper (99 per cent) is annealed, a new phenomenon is observed. 
The recrystallization structure shows a new orientation of 
grains with the cube faces parallel to the rolling plane. Copper 
of ordinary purity, after complete reduction by cold rolling, 
tends to recrystallize with a chaotic arrangement of grains; 
but if a first reduction of 50 per cent is made with tiot rolls 
at 600 C., followed by cold rolling, the cubic recrystallization 
arrangement is so nearly perfect that the x-ray diffraction pattern 
indicates practically a single crystal (Fig. 196). The further 
remarkable fact is that this structure persists clear to the melting 
point. Not only does copper differ from silver (dependent, of 




FIG. 196. Pattern showing very high 
degree of preferred orientation in 
recrystallized copper sheet. 



PRACTICAL APPLICATIONS OF X-RAYS 



395 



course, on the method of rolling) in an entirely different recrystal- 
lization orientation, but also in the fact that this never goes over 
to the random structure. It follows, therefore, that such a sheet 
has greatly different properties from one in which the grains 
are in disordered arrangement. 

A comparison of the tensile strength, elasticities, and grain 
sizes of the two kinds of copper sheet is given in Fig. 197. Both 
the strength and elasticity of the sheet with cube-face (oriented) 
grains are smaller than those of the random sheet. Czochralski 
has found that these properties are minimum in the direction 
of the cube edge, as is true here, while physical properties of 
the ordinary sheet are an average (higher) of all directions. 
The oriented sheet, however, is more resistant to corrosion than 
the random. 

The effects of impurities as ascertained by Widmann from x-ray 
patterns are as shown in accompanying table. 



Element 


Impurity 


Recrystallization 
temperature, 
degrees 
Centigrade 


Weight, 
per cent 


Atomic, 
per cent 


Electrolytic copper, unmolten. 
Electrolytic copper, melted 
Tin 


24 


129 


205 
250 
375 


Silver 


24 


14 


340 


Lead . 


15 


046 


325 


Manganese 
Phosphorus 
Cadmium 


23 
36 
19 


267 
73 
108 


320 
325 
300 


Antimony 
Sulphur 


06 
21 
14 
28 
20 


032 
0.42 
119 
302 
065 


280 
275 
250 
250 
250 


Arsenic 
Nickel 


Gold . 


Silicon 


06 


13 


245 


Zinc . 


33 


32 


220 


Bismuth ... . 
Iron. ... .... 


027 
21 
12 

18 


008 
24 
0.28 
8 33 


200 
190 
150 
150 


Aluminum 
Cuprous oxide 





(6) The Recrystallization of Silver-copper Alloy. In light of 
the foregoing results with pure silver and copper, it is interesting 



396 



APPLIED X-RAYS 



to compare the x-ray results on sheets of an 80:20 silver-copper 
alloy. 1 

For a strip rolled down to 98 per cent, the tensile strength is 
90 kg. /mm. 2 as compared with 40 for silver and 50 for copper. 
After annealing at 800 the strength is only 30. The elongation 
of the alloy becomes noticeable only above 300 but approaches 



60 

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260 
240 
220 

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100 5 

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80 c 
60 
40 
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200 400 600 800 1,000 1,700 1,400 
Annealing Temperature in Degrees Centigrade 



Fio. 197. Tensile strength, elongation, and grain size of cold-rolled copper 
sheet (full lines) and of a sheet reduced 50 per cent by hot rolling and 50 per cent 
by cold rolling (dotted lines) as functions of annealing temperature. (Cf locker 
and Widmann.) 

that of silver (20 per cent) after treatment at 800. While the 
softening and recrystallization lie in a range of only about 20, 
the range in the alloy lies between 200 and 700 C. Mixed 
crystals, embedded in the eutectic and richer in copper, are 
brought out when the specimen is heated nearly to the melting 
point. Even heating for hours at 780 shows only a few of these 



1 GLOCKER and WIDMANN, Z. Metallkunde, 20, 129 (1928). 



PRACTICAL APPLICATIONS OF X-RAYS 397 

crystals because the grains are smaller than 2ju; at 800 the grains 
are five times larger but show no preferred orientation. The 
first evidence of recrystallization in the x-ray photographs 
appears at 400, when some diffuse lines become sharply resolved 
into doublets. Unless the specimen is heated for hours above 
780, x-rays give the typical diagram of rolled silver. 

c. The Recrystallization of Wires. The drawing of metals 
into wires represents also a fibering of the grains but with a differ- 
ent mechanism which is somewhat simpler as previously explained. 
For all face-centered cubic metals (silver, copper, aluminum, gold, 
lead, etc.) a [111] direction, or cube-body diagonal, is parallel 
to the wire axis with every possible orientation of the cubes (360 
deg.) around the diagonal; for body-centered cubic metals (a-iron, 
molybdenum, tungsten, etc.) a [110] or cube-face diagonal is 
parallel to this axis. In general, there are no intermediate new 
orientations of grains during recrystallization by heat treatment. 
Instead, the sharply localized intensity maxima in the diffraction 
patterns for the wires gradually become more indistinct with 
increasing temperature. The last traces of fibering are remark- 
ably persistent and an entirely random arrangement is attained 
only after annealing near the melting point. 

Sachs and Schiebold 1 have compared the x-ray diagrams and 
the tensile strength of a cold-drawn aluminum wire (1.18 mm.) 
after various annealing treatments. The treatments and tensile 
strengths are as follows: 

Kilograms per 
Square Millimeter 

Original . 24 4 

150, Khr 18.7 

200, M hr 14 3 

250) 

350M hr .... 11 

550) 

The x-ray diagrams show a gradual increase in particle size 
with dots appearing on a continuous background of the diffraction 
rings at 250 and 300 ; at 550 there appear large spots, far fewer 
in number but still lying on rings. At 150 the interference 
maxima broaden, indicating a departure of the oriented particles 
from perfect alignment, but even after annealing at 550 strong 
evidences of fiber structure remain. 

1 Z. Metallkunde, 17, 400 (1925). 



398 



APPLIED X-RAYS 



An exception to the general effect of annealing, however, is 
observed with very pure aluminum wire. 1 It was been found 
that on heating hard aluminum wire (0.35 or 0.8 mm. diameter, 
99.95 per cent pure) at 600 for 3 hr., recrystallization occurs 
with perfect undirectional orientation of the grains with a [111] 
direction parallel to the wire axis. This orientation is the same 
as in the original cold-drawn wire, so that aluminum differs 
from copper in this respect, and, of course, from aluminum of 
lesser purity. The texture of the wire seems very nearly un- 
changed by the treatment, but the tensile strength has decreased 
from 20.6 kg. /mm. 2 to 3.5, and the elongation has changed from 
1 to 5 per cent (single crystal wires 20 per cent). Here it is 
clear that the grain orientation is not the only factor governing 
elastic properties. 

For aluminum-silicon alloy wires, the strength decreases 
from 26.5 to 15.6 kg./mm. 2 after heat treatment, the elongation 
increases from 2 to 17 per cent, but the grain orientation and 
texture indicated by the x-ray pattern are unchanged. 

The single case of intermediate recrystallization preferred 
orientation is with deeply drawn copper wire annealed above 
1000 C. 2 

The new orientation is with a [112] direction, instead of 
[111] parallel to the wire axis. This observation is further sub- 
stantiated by Tammann and Meyer who counted in a cross 
section the following orientations of faces: (111) 27 per cent, 
(101) 12 per cent, (100) 61 per cent; whereas theoretically for 
chaotic arrangement the proportions are respectively 38, 40, 
and 22 per cent. Such a wire acts as a single crystal as com- 
pared with ordinary wires with random orientation. Following 
are the comparative data: 



Treatment 


Tensile strength, 
kilograms per 
square millimeter 


Elasticity, 
per cent 


Original 
300 


49 3 
24 4 


* 1 
30 


800 


23.9 


23 


1000 (3 hr., oriented) 


21 3 


17 



1 SCHMID and WASSERMANN, Z. tech. Physik., 9, 106 (1928). 

2 SCHMID and WASSERMANN, Z. Physik., 40, 451 (1926) 



PRACTICAL APPLICATIONS OF X-RAYS 



399 



a) 




FIG. 198. Diffraction and microscopic studies of annealing of cast steel, 
(a) Original structure, as cast, showing internal strain; (6) commercial anneal, 
showing incomplete removal of detrimental structure; (c) ideal annealed structure 
of same steel. 



400 APPLIED X-RAYS 

In general the x-ray study of wire annealing is not quite so 
satisfactory as that of rolled foils. Studies on crystalline wires 
of zinc and tin by Polanyi and his associates prove that often 
the change in mechanical properties and recrystallization evi- 
dence in x-ray patterns do not run parallel, since under certain 
conditions of original cold working and annealing these crystals 
may soften without evidence of recrystallization. 

2. Annealing of Cast Steel. Figure 198 shows the structures 
of cast steel as cast with large internal strain, of this steel annealed 
according to commercial practice, and of the same steel with an 
ideal structure obtained by the selection of correct temperature 
and time of heat treatment through the agency of x-ray diffrac- 
tion patterns. One of the great manufacturers of castings was 
annealing large steel pieces for 6 hr. at a somewhat indefinite 
temperature. A short x-ray investigation proved beyond 
question that the correct temperature of annealing could be 
determined within 10, and that under these conditions a 
greatly improved structure was obtained not in 6 hr. but in } hr. 
The economic value of such a single discovery is at once evident 
in speeding production twelvefold without additional expense. 
Such examples in this general field of heat treatment for the 
removal of strains and directional properties might be multiplied 
many times. 

3. Magnetic Properties as a Function of the Structure of Sili- 
con Electric Steels. Figures 199 to 204 reproduce again the first 
series of pinhole diffraction patterns ever made for silicon steel 
strips with varying magnetic hysteresis loss as noted. If the 
grain boundaries have not been unduly thickened by overheating 
in the annealing furnace, the magnetic loss may be calculated 
empirically from the number and size of diffraction spots on a 
given area of the various patterns. Occasionally some strips 
may be unusually brittle and have unaccountably high loss. 
In every case an x-ray examination proves that the large single 
grains have an extraordinary orientation of crystallographic 
planes with respect to the surface of the sheet due to an uncon- 
trolled factor in the rolling or annealing operation". In the 
ordinary case it will be remembered that iron grains in a rolled 
sheet are oriented with a [110] direction parallel to the direction 
of rolling and (100) planes in the surface of the sheet. The 
Epstein test for measuring magnetic loss usually employs one 
hundred or more strips and an average value is, of course, meas- 



PRACTICAL APPLICATIONS OF X-RAYS 401 




FIG. 199. Transformer, steel, hys- FIG. 200. Transformer steel, hyster- 
teresis loss 0.8636 watt/lb. esis loss 0.8181 watt/lb. 




FIG. 201. Transformer steel, hyster- FIG. 202. Transformer steel, hys- 
esis loss 0.8068 watt/lb. teresis loss 0.7727 watt/lb. 




FIG. 203. Transformer steel, hysteresis loss 0.6J31 watt/lb. 



402 APPLIED X-RAYS 

ured. On several occasions in the writer 's laboratory it has 
been possible by single patterns to separate a bundle into at 




FIG. 204. Transformer steel, hysteresis loss 5535 watt/lb. 




() 

FIG. 205. Comparison of grain perfection in silicon electric steel, (a) 
Supposedly superior grade as now produced commercially showing imperfect 
grains; (6) specimen free from strain produced by simple technique. 

least five groups, two with a lower loss, two with a higher, and 
one with the same average loss of the whole original bundle. 



PRACTICAL APPLICATIONS OF X-RAYS 403 

More important from the standpoint of magnetic properties 
than grain size is grain perfection, i.e., freedom from all strain. 
This has been amply demonstrated in recent extensive experi- 
ments in the writer's laboratory. The x-ray pattern is the only 
guide to establishment of the correct rolling and heat treatment 
which will insure grain perfection. Figure 205a shows the 
pattern of supposedly highest quality silicon steel commercially 
produced in 1932, while Fig. 2056 shows the result of remarkably 
simple technique, derived with the help of x-ray control, from 
the same raw material. The magnetic properties of the latter 
as well as ductility are markedly superior and scientific control 
of production is easily possible by regulation of the silicon con- 
tent, percentage cold reduction, without intermediate anneal, 
time and temperature of annealing, extent of a further pinch pass, 
and final heat treatment. New mills with small rolls enable 
cold rolling of the silicon steel successfully for the first time. 
Since silicon steels represent large-grained aggregates, the x-ray 
diffraction patterns are characterized by a random peppering of 
spots rather than definite rings. Hence it would appear to be 
impossible to discover by ordinary diffraction methods whether 
there is any tendency toward preferred orientation of these large 
grains throughout a sheet. Recourse is then taken to the simple 
device of slowly moving the specimen in its own plane across the 
pinhole by a suitable mechanical device during the exposure. 
The resultant pattern is an integration over a large number of 
grains instead of the few contained in only a certain area tra- 
versed by the x-ray beam in the stationary sample. If there is a 
preponderance of orientations in any one direction, a definite 
concentration of spots will appear, just as localized intensity 
maxima indicated preferred orientation on the interference rings 
for small-grained specimens. The indications are that some 
such preferred orientation may actually be beneficial for certain 
magnetic properties. 

Further studies will lead undoubtedly to the production and 
selection of steel for electrical purposes with such lowered mag- 
netic loss and superior permeability that the size of electrical 
machinery for a given load may be reduced appreciably. 

4. The Stages of Reduction and the Effects of Variables in 
Commercial Cold Rolling of Sheet Metals. The fundamental 
investigations of the types and degrees of preferred orientation 
produced in metal sheets by cold rolling have been considered 



404 



APPLIED X-RAYS 



in the preceding chapter. However, the course of changes in 
crystal fragmentation and orientation during successive stages 
in the rolling process and the effect of variables in the raw material 
and in the technique of rolling upon the establishment of the 




(a) 



(c) 




W) () (/) (0) 

FIG. 206. Changes in structure with steps in rolling of low-carbon sheet 
steel, (a) Hot-rolled strip; (6) one pass, 7 per cent reduction; (c) 9 passes, 47 
per cent reduction; (d) 14 passes, 71 per cent reduction; (e) 19 passes, 85.5 
per cent reduction; (/) 21 passes, 90 per cent reduction; (g) 30 passes, 97 per cent 
reduction. 

ultimately attained preferred orientation are of greater com- 
mercial significance. Clark and Sisson have made a long series of 
studies of these problems for various metals as follows: 

A. Percentage reduction and its relation to various factors. 

1. Structure. 

2. Power requirements. 

3. Hardness. 

4. Amount of distortion as disclosed by the resolution of the x-ray 



5. Type and degree of orientation. 



PRACTICAL APPLICATIONS OF X-RAYS 



405 



B. Effect of variables in original material on structures. 

1. Grain size. 

2. Thickness. 

3. Carbon content. 

C. Effect of rolling variables upon structure. 

1. Roll diameter. 

2. Speed of deformation. 

3. Reversal of strip. 

4. Percentage reduction per pass. 

D. Effect of deformation due to combined tension and compression. 

1. Applied tension during rolling. 

2. Effect of stretching followed by rolling. 

3. Drawing of flat sheets. 

4. Rolling of drawn wires. 

5. Rolling at various angles. 

The scope of these data is obviously far too extensive to permit 
presentation of results here except for a few points of especial 
interest. 

A. Structural Changes with Successive Reductions. The change 
in x-ray patterns with successive reductions is best represented 
by Fig. 206a to g for low-carbon steel, selected from a series of 84 
samples. Here the x-ray beam passed perpendicular to the 
rolling direction and to the surface of the sheet. 



Figure 


Pass 


Gage, inches 


Percentage 
reduction 


Pattern 


175a 





0.158 





Large random grains 






(hot-rolled strip) 






1756 . 


1 


1475 


7 


Fragmentation below 










35/x and appearance of 










rings 


175c . . 


9 


084 


47 


Nearly complete frag- 










mentation, random 


17 5d. 


14 


046 


71 


Appearance of six-point 










fiber pattern character- 










istic of drawing 


175e 


19 


023 


85 5 


Passing from six- to four- 










point pattern 


175/ 


21 


0.0165 


90 


Typical rolling pattern 


1750 .... 


30 


005 


97 


Perfected orientation 



From a whole series of steel samples the following average 
results were obtained: 



406 APPLIED X-RAYS 

Per Cent 
Appearance of Reduction 

Continuous rings (fragmentation) 27 

Sharp rings. . . 38 

Six-point fiber pattern . 54 

Four-point fiber pattern 76 

Such values, of course, are greatly dependent on type of mills, 
chemical composition, thickness, grain size, and orientation in the 
original material. 

These results confirm those of Tammann who found that in 
rolling two clearly defined changes in crystal orientation can be 
distinguished; the first in which the force due to rotation of the 
rolls acts as a stretching force (six-point x-ray pattern), and the 
second in which the action of the rolls is similar to that of simple 
compression arid exerts the greatest influence on the final orien- 
tation in cases of large reductions. 

B. Effect of Initial Grain Size. Grain size has considerable 
influence upon the structure of cold-rolled steel during early 
stages of reduction but after large reductions the effect is lost. 
The smaller the initial grain size, the less cold work is required 
to produce fibering (see also topic 16, page 418). 

C. Effect of Initial Strip Thickness. The degree of fibering 
depends not only on the percentage reduction but also on the 
initial strip thickness. A sample reduced from 0.08 to 0.01 in. 
does not show the same degree of preferred orientation as one 
reduced from 0.04 to 0.005 in., although both have received 
87.5 per cent reduction. 

D. Effect of Carbon Content. Most of the previous work on 
preferred orientation in cold-rolled sheets has been carried out 
on pure metals. In steels the pearlite is hard and more brittle 
than ferrite and concentrates at the junctions of the ferrite 
grains with the result that when pearlitic steel is cold rolled 
gliding takes place only in the ferrite. During the rolling process 
the pearlite is dispersed while the soft ductile ferrite forms a 
plastic bond which is not oriented, so as to form a straight fiber 
structure but is curved around the pearlite particles. The x-ray 
pattern, therefore, gives the appearance of random arrangement 
for high-carbon steels. 

E. Effect of Rolling Variables. (1) The roll diameter has less 
effect on final structure than the total percentage reduction. 
The smaller the rolls, the greater is the angular divergence of 



PRACTICAL APPLICATIONS OF X-RAYS 



407 



the grains laterally in the rolling plane from the ideal preferred 
direction, while large rolls tend to produce more divergence 




(c) (d) 

FIG. 207. Patterns for sheet steel, made with x-ray beam perpendicular to 
rolling direction and parallel to rolling plane, from which amount of cold work 
may be calculated. Percentage reductions: (a) 16; (6) 36.5; (c) 53; (d) 85. 

normal to the rolling pkne. Numerous other small differences 
may also be quantitatively ascertained, particularly for early and 
intermediate stages of reduction. 



408 APPLIED X-RAYS 

(2) With small rolls the same structure is obtained at speeds 
from 70 to 800 ft. per minute, and with unidirectional or reversed 
passes through the rolls. 

(3) Various combinations of tension and compression of the 
sheets have been studied in detail, both experimentally and with 
vector theory. Fiber structures are ultimately obtained but 
the appearance of the four-point pattern characteristic of com- 
pression can be greatly delayed by application of tension. 

(4) Interesting results are obtained by rolling metals in all 
directions (random), at 90 deg. (very perfect fibering), 60 deg. 
(six-point instead of four-point patterns), etc. 

(5) An x-ray method of determining the amount of cold 
rolling to which a sheet has been subjected. In the usual method 
of taking x-ray diffraction patterns of cold-rolled sheets, the 
x-ray beam passes perpendicular to both the rolling direction 
and the plane of rolling. Preferred orientation may appear 
only after 60 to 70 per cent reduction, depending on the type of 
mill and original material variables. If the beam is made to 
pass through the material perpendicular to the rolling direction 
and parallel to the rolling plane (edge-on of the sheet), evidence 
of preferred orientation is obtained after 15 to 30 per cent reduc- 
tion, depending upon the above mentioned variables. This 
orientation gives a six-point fiber pattern similar to that for cold- 
drawn wires. Instead of the pattern changing to a fourfold 
pattern upon further reduction as is the case when the beam is 
normal to the rolling plane, the type of pattern remains the 
same. However, as the percentage reduction increases, the 
intensity maxima become sharper, as illustrated in Fig. 207 
for 16, 36.5, 53, and 85 per cent reduction. If the percentage 
reduction is plotted against the sine of the angle of arc formed 
by the intensity maxima on the broad inner band of the pattern, 
a straight line is obtained. For a large number of specimens 
this relationship has been found accurate within a maximum of 
10 per cent. 

In certain cases it has been possible even to determine very 
small amounts of cold work such as roller leveling after annealing, 
by careful examination of the x-ray patterns (elongation and 
splitting of interference spots). 

5. Structure of Welds. Figure 208 shows the comparison 
of a weld of the same steel made by the ordinary arc method and 
by the hydrogen-atmosphere method. The former is char- 



PRACTICAL APPLICATIONS OF X-RAYS 



409 




FIG. 208. Comparison of structures of steel welds. Left, ordinary arc method; 
right, hydrogen-atmosphere method. 




FIG. 209. Diffraction patterns and photomicrographs for satisfactory 
(above) and unsatisfactory (below) forming steels. Note residual rolling 
structure in the latter. 



410 APPLIED X-RAYS 

acterized by very small, highly distorted grains (radial striations), 
and the latter by much larger, random unstrained grains with 
requisite strength and ductility. 

6. Forming Steels. One of the great contributions has been 
to define specifications in terms of structure for forming steels, 
especially since unstrained and random properties are essential. 
Patterns and photomicrographs for supposedly four grades of 
forming steel, soft, quarter hard, half hard, and hard, demon- 
strate that there are only two grades essentially. Satisfactory 
and unsatisfactory forming steels are easily differentiated by 
the patterns in Fig. 209. The latter retains a residual preferred 
orientation of grains introduced in the original rolling; hence 
the annealing has been entirely inadequate and failure in the 
forming operation can be predicted definitely from such a pattern. 
Figure 210 demonstrates the structure of a sheet after successful 
forming and explains why another sheet failed. 

7. Forming Copper. Phillips and Edmunds have demon- 
strated that hard-rolled copper has a pronounced fiber structure 
with [353] as the fiber axis, instead of [112] as found by others, 
and (110) planes in the surface. A preferred orientation is 
found in the annealed sheet which forms ears on cupping, while 
that which forms without ears has random orientation. The 
formation of ears in drawn copper is avoided by the limitation 
of rolling reduction to 65 per cent and annealing at 500 to 
600 C. 

In general, all sheet metals which fail in forming operations 
show evidences, by the extremely sensitive diffraction method, of 
residual fibering which the annealing treatment has not removed, 
or a new recrystallization orientation, such as is commonly 
found for copper shown in Fig. 196. 

8. Neumann Bands in Ferrite. Mathewson and Edmunds 
in a remarkable x-ray study by the Laue method have definitely 
settled the long controversy over the origin of these bands by 
proof of twinning along planes of the form [211]. 

9. Passive Metals. An interesting application has been 
the attempt to investigate passive metals upon the assumption 
that a very thin layer of oxide is the cause. Krliger and Nahring, 
for example, give results of the x-ray examination of finely pow- 
dered passive iron, nickel, and chromium by the Debye-Scherrer 
and Bohlin-Seemann methods. In no case does the photograph 
show lines corresponding with a known or unknown oxide of the 



PRACTICAL APPLICATIONS OF X-RAYS 



411 





FIG. 210.-Structures of forming steels after forming. Above, satisfactory; 
below, unsatisfactory. 



412 



APPLIED X-RAYS 



metal, although these should be apparent if the oxide layer 10~* 7 
cm. in thickness were present. These results are not in agree- 
ment with the view that solid layers of oxide are present on these 
metals in the passive state. The existence of a molecular layer 




(&) (c) 

FIG. 211. Patterns for molybdenum ribbon used in electric resistance fur- 
naces, (a) Cold rolled in the United States; (b) cold rolled, German process; (c) 
ribbon after use in furnace, showing marked grain growth. 

of oxygen, which Tammann suggests may cause passivity the 
free valencies of the metal at its surface being saturated by oxygen 
atoms, while the metal lattice remains unchanged would not 
be detectable by x-ray examination. 



PRACTICAL APPLICATIONS OF X-RAYS 413 

10. Changes in Electric Furnace Resistor Ribbon. Figure 211 
shows the patterns of two types of cold-rolled molybdenum 
ribbon used in resistance furnaces, and another which demon- 
strates what happens after short usage a very large growth of 
grains. 

11. Crystal Structure of White -fractured and Reclaimed 
Malleable Iron. It is well-known that malleable iron suffers 
embrittlement when quenched from the blue-heat zone, but 
that this is prevented by quenching from just under the A\ 
point. This might be explained as due to changes in structure 
of the ferrite grains or to grain boundaries. The x-ray diffraction 
pattern of normal black-fractured malleable shows spotted 
rings indicating random orientation of fairly large grains, and 
considerable strain as shown by the radial asterism streaks. 
Malleable iron embrittled by quenching from 460, that quenched 
from 650 to 700, that embrittled by quenching from 450 and 
reclaimed by quenching from 700, the same plus an additional 
quench from 450 which produced no embrittlement, all gave 
nearly identical diffraction patterns. The explanation of 
observed properties is evidently related to the grain boundaries 
which under the experimental conditions were not registered. 

12. Comparison of Effects of Twisting and Bending Steel 
Wires. (0.60 per cent carbon, annealed at 1200 F.). The origi- 
nal structure of the wire is shown in Fig. 212 together with the 
patterns, respectively, after 38 twists and 10 bends. Grain 
fragmentation begins with the first twist and reaches a maximum 
between 3 and 5 twists, followed by a much more gradual effect. 
After 13 twists the beginning of fibering or preferred orientation 
is evident, and this is quite marked for the case of 38 twists. 

For the bending tests the wire was bent through an angle 
of 90 deg. and returned to its original position. The next bend 
was made in the opposite direction, the third like the first, etc. 
Severe grain fragmentation begins with 1 bend, since the pattern 
is more diffuse. Two bends were equivalent to 13 twists in this 
respect ; 3 bends introduces preferred orientation which becomes 
more perfect up to the breaking point. The bending test, there- 
fore, is much more severe. 

13. The Effect of Constitution on the Structure of Wires 
Drafted and Annealed (Basic Open-hearth and Acid Bessemer 
Steel). Two series of steel wires of the same analysis essentially 
(carbon 0.10 per cent), except for phosphorus (0.018 (A) and 



414 



APPLIED X-RAYS 



0. 102 (5)), were studied. Among many interesting differences in 
behavior are the following: under identical conditions after 
drafting 10 per cent and annealing at 1300 F. for 1 hr., reerys- 
tallization has begun in A, but not at all in B; with 15 per cent 




FIG. 212. Patterns showing effects of twisting and bending on steel wire, 
(a) Original; (6) after 38 twists; (c) after 10 bends. 

drafting and annealing at 1100 F. for 1 hr. ; recrystallization in A 
is nearly complete with very large grains but not perfectly 
random, while in B a very much smaller grain size and larger 
residual fibering is shown. Both produce random recrystalliza- 



PRACTICAL APPLICATIONS OF X-RAYS 



415 




Fio. 213. Comparison of effects of drawing reduction on steel with small 
and large initial grains, (a) Original (small grains) ; (?>) after 5 per cent reduction; 
(c) after 15 per cent reduction; (d) original (large grains); (c) after 5 per cent 
reduction; (/) after 15 per cent reduction. Compare (a) and (d), (6) and (e), 
(c) and (/). 



416 APPLIED X-RAYS 

tion for 15 per cent drafting and annealing at 1200 F. for 1 hr., 
but the grain size of A is still appreciably greater than that of B. 
After annealing temperatures of 1600 F. complete recrystalliza- 
tion occurs in both with random distribution and freedom from 
distortion. The impurities in Bessemer wire clearly tend to 




FIG. 214. Patterns from specimens in same lot of 0.10 per cent carbon Bessemer 
continuous mill rod, showing non-uniformity of structure. 

retard grain growth and to retain directional properties intro- 
duced in cold working. 

14. Effect of Carbon Content on Annealing. X-ray studies of 
0.06, 0.19, and 0.34 per cent carbon steel wires drafted similarly 
and annealed at the same temperatures for the same length 
of time prove that increasing carbon increases sluggishness in 
recrystallization, causes smaller but less distorted grains. In 



PRACTICAL APPLICATIONS OF X-RAYS 



417 




418 APPLIED X-RAYS 

a similar way it has been possible to define in every case the 
temperature at which recrystallization begins after a given 
drafting or reduction in area by cold work, the temperature 
at which good annealing occurs, with removal of strain and 
directional properties due to original cold work, the grain size 
resulting from a given treatment, etc. 

16. Effect of Grain Size on Plastic Deformation. With 
ordinary low-carbon basic open-hearth steel wire, a large-grained 
sample may be drawn as much as 15 per cent without suffering 
complete grain fragmentation or noticeable preferred orientation, 
whereas the fine-grained sample will show on its diffraction 
pattern definite fibering with only 5 per cent reduction. These 
facts are shown in Fig. 213. 

16. Non-uniformity of Production. Many examples of this 
might be presented. In Fig. 214 are shown the patterns for four 
samples of Bessemer steel and from the same continuous mill, 
selected from various coils. The differences require no comment. 

17. The Relation between Reduction, Temperature of Anneal- 
ing, and Structure. Two beautiful series of patterns are repro- 
duced. Figure 215 is for a constant annealing temperature of 
1200 F. with successive reduction of low-carbon sheet of 2, 5, 
10, 15, 20, 40, 60, and 80 per cent. Figure 216 is for 1500 F. 
temperature of annealing for the same specimens. These 
patterns constitute a splendid standard. The most marked 
effect is the difference between the temperatures of 1200 and 
1500 on the specimen reduced in cross-sectional area by 2 per 
cent. At the lower temperature no recrystallization occurs, 
while at the higher so great is the change that only a single grain 
of iron is in the beam. 

Relationships between these three variables can best be shown 
by a three-dimensional diagram such as represented in Fig. 217 
which shows readily how research on a given metal can lead 
to a thorough scientific method of heat treatment rather than 
an entirely empirical one. In this figure, the variable which 
may be determined from x-ray data in this case is grain size, 
though any other property might also serve. It proves that 
the final annealed structure of a sheet which has been cold- 
rolled to 90 per cent reduction without intermediate anneals 
must be different from that of the sheet which has been rolled 
down in steps with intermediate anneals. Each of these in effect 
places the specimen back at per cent reduction. The diagram 



PRACTICAL APPLICATIONS OF X-RAYS 



419 



J* 

s 



2 
'o 



8 



^ 



^ t 
g 

w 



CO 
rH 
<N 

O 





420 



APPLIED X-RAYS 



shows also that if very large grains are desired following a com- 
plete cold reduction, the specimen is annealed, giving the size 
characteristic for the reduction at the right of the diagram, 
then given a pinch pass or very small cold reduction so that 
the conditions on the left of the diagram are realized, and then 
again heat-treated. 

18. Quench and Temper Structures of Carbon Spring Steels. 
Goss 1 has shown by x-ray patterns that these structures are quite 
independent of each other and that ill effects of distortion due 
to improper quenching cannot be removed by tempering, which 




10 20 30 40 50 60 70 80 90 

Per Cen+ Reduction 

FIG. 217. Three-dimensional diagram illustrating scientific control of recrystal- 
lization of cold-worked metals. 

merely facilitates the precipitation of Fe 3 C out of solid solution 
but does not change the as-quenched structure of the a-iron 
matrix. 

19. Differentiation between Mechanical and Galvanic Gold 
Plating. The designation of gold-filled and plated objects such 
as jewelry is often subject to governmental regulation, particu- 
larly as to whether the gold layer is rolled or electrolytically 
deposited. Dehlinger and Glocker 2 have shown that these 
may be easily distinguished by x-ray diffraction analysis when 
other tests fail. The rolled filling or plating shows a fiber pattern 
and the electrolytic deposit a random arrangement of grains. 
Distinction can be made even after polishing or otherwise 
working an electrolytic gold layer, or after heat treatment and 
recrystallization. 

20. Problems of Fatigue of Metals. Comprehensive work 
in combining x-ray research with fatigue tests has not yet been 

1 Trans. Am. Hoc. Steel Treating, 19, 182 (1931). 
2 . MetaUkunde, 21, 325 (1929). 



PRACTICAL APPLICATIONS OF X-RAYS 



421 



completed, although progress has been made and more should 
be expected. The chief difficulty has been in providing speci- 
mens sufficiently thin for x-ray analysis. As an example of 
such research some preliminary results are presented in Fig. 
218 for steel rails, the diagram in Fig. 219 showing the location 
of samples. The ideal structure shown by No. 14 may be con- 
trasted with No. 26 for example, which shows strain and actual 




14 25 26 

FIG. 218. X-ray study of structure of steel rails, with numbers referring to 
location in rail in Fig. 219. 

preferred orientation of grains. In such an area fissures usually 
occur, largely as a result of the varied structure in contiguous 
portions of the rail. 

21. The Examination of Very Large Specimens by the Back- 
reflection Method. In practically all of the examples cited in this 
entire book, the x-ray diffraction patterns have been made by 
transmission through the specimens carefully prepared by etching 
so as to introduce no spurious effects. But in industrial practice 
it is frequently desired to know the ultimate crystalline condition 
of a finished product or of a large specimen which cannot be cut 
up. For example, in steel rails, in aluminum alloy airplane pro- 



422 



APPLIED X-RAYS 



pellers, and in very large steel structures such as oil stills where 
sound structure and freedom from strain are so essential for safety 
at high temperatures and pressures, such an examination of a fin- 




Fio. 219. Diagram showing location of specimens subjected to x-ray exami- 
nation for fine structure, some of which are presented in Fig. 218. 

ished unit before installation would be invaluable. One method 
would, of course, consist in making hollow borings, with subse- 




FIG. 220. Experimental arrangement on General Electric diffraction apparatus 
for back-reflection method. 

quent welding of the holes. However, the writer has deemed it 
advisable to try and develop a method in which the x-ray beam 
may be reflected from the surface. The method involving a graz- 



PRACTICAL APPLICATIONS OF X-RAYS 



423 




FIG. 221. Back-reflection pattern from steel rail. 




FIG. 222. Diagram explaining diffraction interferences on film at ABC in back 

reflection. 



424 



APPLIED X-RAYS 



ing angle of incidence as in Fig. 99, with such an apparatus as that 
shown in Fig. 87, is well-known and has been frequently used for 
fairly small specimens. Utilizing the usual equipment, however, 
it is necessary to reflect straight back from the surface of very 
large specimens as shown in Fig. 220. In this case, therefore, 
the photographic film is mounted around the pinhole and registers 
the patterns of rays diffracted directly back from the surface. 
A typical pattern from a steel-rail specimen is shown in Fig. 
221. The concentric pairs of rings seem at first sight to be very 
familiar until it is noticed that the less intense line is inside 
of the stronger line of each pair. If these pairs represent resolu- 
tion of the Ka-doublet of molybdenum, then in ordinary powder 
diffraction films, of course, the stronger Kai line comes inside 
the weaker Ka^. This apparent reversal is, of course, readily 
explained by a consideration of Fig. 222. The photographic 
plate is at ACE. If a cylindrical film, as in the Debye-Scherrer 
method, were placed coaxial with the specimen, the primary 
beam passing through the specimen would strike the film 
at the top of the circle and the diffraction lines would appear 
as shown. The pattern in Fig. 221 is, therefore, to be read 
from the outside in towards the center, rather than from 
the center, as would be the case if the film were placed 
on the opposite side of the circle. These diffraction circles 
correspond, therefore, to lines appearing at the very end of 
usual spectra and hence to planes of relatively high indices. 
The analysis is as follows, the distance from sample to film 
being 3.5 cm.: 



Radius of 


</> 





Sin 6 


h 2 + & 2 


Indices 


dhki 


ring 








+ Z 2 






1 475 


22 50' 


78 35' 


98021 


62 


(372 

<5 6 1 


363 A.U. 


3 25 


42 52' 


68 34' 


0.9308 


56 


642 


0.383 


3 90 


48 6' 


65 57' 


0.9132 


54 


(363 
/5 5 2 


0.391 



The method has the disadvantage, of course, that long exposure 
is required to develop sufficient intensity for these diffraction 
effects from sparsely populated but closely spaced planes. 



PRACTICAL APPLICATIONS OF X-RAYS 425 

However, large specimens of Armco iron with grains large enough 
to produce a spotted pattern by direct transmission also gave 
back-reflection patterns with large spots. On account of the 
large resolutions of the Ka-doublet the method should be useful 
for evaluating spacings very accurately and for following small 
changes due to solid solution. 



CHAPTER XIX 

THE STRUCTURE OF COLLOIDAL AND AMORPHOUS 
MATERIALS AND OF LIQUIDS 

X-ray Diffraction by Crystalline and Amorphous Substances. 

It is now evident that crystals act as three-dimensional diffrac- 
tion gratings for x-rays by virtue of the arrangement of the lattice 
units (atoms, ions, molecules, or groups of these) on sets of 
equidistant parallel planes. With a beam of monochromatic 
rays passing through a specimen, a pattern on a photographic 
plate is obtained, which is absolutely characteristic of the 
material whether it is crystalline or amorphous, what are its 
crystallographic system and space-group defining coordinates 
in space, and the interplanar spacings, whether it is a single 
crystal or an aggregate, whether the aggregate has random or 
preferred orientation of grains, whether it is a single pure sub- 
stance or is a mixture of two or more individuals or a solid solu- 
tion, how large the grains or particles are or how thick a film, 
and whether there is distortion or strain. It follows that an 
amorphous substance would merely scatter x-rays in all directions 
and produce a general fogging of the photographic plate without 
evidence of diffraction interference maxima, whereas any kind 
of arrangement of ultimate units, even though very imperfect, 
would produce a diffraction pattern characterized by interference 
maxima. Even a single diffuse broad diffraction ring indicates 
at least an elementary tendency toward organization. One 
of the most remarkable facts from x-ray science is the extreme 
rarity of the true amorphous state. Repeatedly it has been 
found that a specimen, which by all ordinary methods of examina- 
tion appears to be amorphous, produces unmistakable evidence 
of an organized ultimate structure under the searching scrutiny 
of radiation with wave lengths only 1/10,000 as long as ordinary 
light, by means of which microscopic examination is made. 
Even liquids produce diffraction halos indicative of transient 
arrangement of molecules governed by distances of nearest 
approach in their thermal agitation and designated by Stewart 

426 



STRUCTURE OF MATERIALS AND LIQUIDS 427 

as "cybotaxis." And just now results on diffraction halos from 
gases have given evidence of the true structure of atoms in the 
sense of the distribution of diffuse wave like negative electricity 
according to Heisenberg and Compton, instead of sharply 
corpuscular electrons moving in orbits as depicted by the Bohr 
theory. 

Diffraction by Colloids. A single crystal subjected to analysis 
by the pinhole method produces a Laue diffraction pattern 
characterized by a symmetrical array of spots, lying on a series 
of ellipses. As the size decreases and more individuals lie in the 
path of the beam, this symmetrical pattern gives way to a random 
11 peppering " of spots. As the size decreases and the number 
increases still further, these small spots begin to assemble on a 
series of concentric rings. Finally the spots become so small 
and numerous that they merge into uniformly intense con- 
centric rings, the so-called "powder" pattern. The maximum 
range of grain diameter over which these sharp rings are registered 
is from 10~ 3 to 10~ 5 cm. It is clearly evident that a sharp 
interference effect can take place only with a certain minimum 
number of parallel diffracting planes in each particle. As 
this number falls below the minimum, or, in other words, as the 
particle size decreases below about 10~ 5 cm., it follows that 
interference is less perfect and that the diffraction rings (or lines 
by the Hull-Debyc-Scherrer method) will become broader in 
proportion to decreasing size until in the neighborhood of 10~ 8 
cm. atomic dimensions are reached. These will merge and the 
pattern would be classed as amorphous. A measurement of 
line breadth in the colloidal range will therefore enable calcula- 
tion of particle size as was illustrated fully in Chap. XVII. The 
question arises as to how small a particle can be and still produce 
a diffraction pattern upon which maxima may be detected. 
Levi in his study of metallic catalysts reports that particles 
only about five times as large as the unit crystal cell (in other 
words 10 or 15 parallel planes) will produce resolved diffraction 
maxima, even though these are very diffuse. 

Now it must be noted that diffuse diffraction maxima must be 
the consequence of any crystal grating which is imperfect in 
the sense of having too few parallel planes, or of having these 
planes, ordinarily sufficient in number, distorted, bent, or imper- 
fectly aligned. In other words, it is conceivable that an assem- 
blage of fairly large colloidal particles might yield very diffuse 



428 APPLIED X-RAYS 

patterns simply because molecules which may themselves be very 
large are not oriented in regular fashion. This condition is 
observed in the colloidal gels and is particularly interesting in 
the light of the prediction that simple mechanical stretching 
might tend to pull these diffracting units into parallel position 
and thus permit them to act as a diffraction grating. 

The question which naturally arises next is whether there is a 
continuous transition between crystalline and amorphous state. 
From what has been said concerning continuous broadening of 
lines till these merge and spread over the entire film, such a 
process would be indicated. Sir William Bragg quotes the 
experiment by the present writer on carbon. An activated 
charcoal producing an essential amorphous pattern had certain 
characteristic chemical and physical properties which changed 
over to those of graphite upon brief heating at 1100 C. The 
x-ray pattern, however, was unchanged since no lines appeared. 
The great activity of the original charcoal was ascribed to the free 
valences of disorganized carbon atoms. Upon heating, the solid 
phase being retained throughout, these began mutually to attach 
themselves to satisfy these bonds and to form crystal planes of 
graphite, which were still too few and bent to permit interference 
of rays, though the properties were typical of graphite. This 
stage of elementary organization was designated paracrystalline. 
Upon further heating the grains grew in size, and the planes in 
number and rigidity, so that broad diffraction lines for colloidal 
dimensions finally sharpened to the typical graphite spectrum. 

Another state of affairs, however, is observed with those sub- 
stances so masterfully studied by Friedel, which display meso- 
morphic states of matter or liquid crystal phases. Here there 
are sharp discontinuities between the liquid or so-called amor- 
phous phase (though this yields liquid rings), the nematic (in 
which the long molecules point in one direction but are not 
constrained in parallel planes and hence produce no crystal 
patterns), the smectic (in which the molecules are arranged in 
parallel planes in one direction, thus giving a crystal interference 
for one dimension only), and finally the crystalline in which the 
molecules take up regular marshalling in three dimensions. 
Undoubtedly, then, transition phenomena must occur in all cases 
of solidification of a molten substance, but only in the case of 
certain long organic molecules is the temperature range of each 
state sufficiently extended to permit detection and examination. 



STRUCTURE OF MATERIALS AND LIQUIDS 429 

Results on Colloidal Metals and Inorganic Compounds. 

Numerous references are to be found in the literature to experi- 
mental measurement of particle size for colloids as well as 
identification of crystallographic system. It is convenient to 
determine these properties as functions of various methods of 
preparation of industrial materials. Citation of only a few 
examples must suffice here. 

1. First of all, the identification of the colloidal state as differ- 
entiated from the molecular or supercolloid states (not limited to 
solutions as is the Tyndall cone) . 

2. Relation in grain size and structure in extremely thin electro- 
deposited films and colloidal sols, such as those prepared by the 
Bredig arc method. 

3. Catalytic activity, as for nickel hydrogenation and dehydro- 
genation catalysts, as a function of lattice structure and grain size 
(work in the writer's laboratory indicating an optimum rather 
than minimum grain size associated with greatest activity). 

4. Structure and grain size of colloidal lead as a function of 
therapeutic value when injected into tissues subsequently irradi- 
ated with x-rays. 1 

5. Structure and grain size as functions of spreading, wetting, 
obscuring power, stability, gloss, etc., and of method of prepara- 
tion in pigments (zinc, lead, tin, aluminum, and other oxides). 

6. The discovery of the presence of colloidal crystallites in 
glass, entirely apart from coloring agents added. 2 

7. Grain-size measurements in tungsten for electrical contact 
points and other rnetals where grain boundaries are not satis- 
factorily developed for microscopic counting even for large grains. 

8. Studies of possible allotropic forms of colloids produced 
at various conditions of pH (in all ranges the sphalerite lattice 
and not the wurtzite is found for colloidal zinc sulfide, contrary 
to various contentions). 

9. Numerous cases of identification of colloidally dispersed 
phases in natural and artificial minerals, alloys, including marten- 
site and troostite, etc., uniformly mixed or at grain boundaries; 
clear differentiation between solid solution and physical mixtures. 

10. Test for presence of invisible colloidal particles, such as 

1 CLARK and PICKETT, /. Am. Chem. Soc., 62, 465 (1930) 

2 PARMELEE, CLARK, and BADGER, J. Glass Tech. 13, 285 (1929); CLARK 

and AMBARY, ibid., 13, 290 (1929); RANDALL, ROOKSBY, and COOPER, ibid., 

14, 219 (1930). 



430 APPLIED X-RAYS 

brass or copper in parchment; completeness of filtration and 
dialysis. 

11. Grain size and uniformity (particularly barium), in metal 
mirrors, in radio tubes, photoelectric cells, etc. 

12. Identification of adsorbent films and chemical changes (e.g., 
mercuric chloride solution adsorbed on charcoal gives the crystal 
diffraction pattern for colloidal rnercurous chloride). 

13. Studies of the phenomena involved in dyeing of textiles 
utilizing metallic sols adsorbed on fibers (sometimes fibered 
layer, sometimes random). 

14. Estimation of crystallinity, dispersion and grain size of 
excess sulfur in vulcanized rubber. 

15. Classification of amorphous carbon, coal, and resins. 
Recently a series of papers have appeared from the laboratory 

of Sir C. V. Rarnan, which have advanced to a remarkable degree 
the knowledge of the structure of materials usually classed simply 
as amorphous. This has been made possible by the observation 
of an entirely new phenomenon appearing at small angles to the 
primary beam in the diffraction patterns of all varieties of 
amorphous carbon, namely, a strong scattering extending to 
about 7 deg. This corona was first observed in solutions of 
cane sugar and was definitely attributable to the molecules of 
the dissolved substance which are distributed at random in the 
solvent, much in the same way as gaseous molecules. 

Krishnamurti 1 has found for samples of sugar, benzene, and 
naphthalene charcoals and carbon obtained by charring ash-free 
gelatin with molten sodium, together with colloidal graphite 
prepared by exploding graphite acid in a vacuum, that all showed 
the small angle scattering in a marked manner. The patterns 
displayed two rings in addition to the central scattering, the first 
and prominent ring corresponding to the (002) reflection of 
graphite, having a spacing of about 3.8 A.U. as compared to 
3.4 A.U. of graphite. The outer ring was fainter and broader 
and showed a spacing of 2.12 A.U. comparable to the (111) spacing 
of graphite (2.06 A.U.). The observations accord with the idea 
that in the amorphous state the carbon atoms join together in 
clusters, forming highly anisotropic units, essentially two dimen- 
sional, the thickness being about one-third the length or breadth. 
Assuming that the central scattering is due to the dimensions 
in the plane of the particle, and the first ring to its thickness, a 
1 Indian J. Physics, 6, 473 (1930). 



STRUCTURE OF MATERIALS AND LIQUIDS 431 

rough calculation gives about sixty atoms of carbon per unit. 
This picture of the carbon particle agrees with chemical evidence, 
mainly its oxidation to mellitic acid, and adsorptive properties. 

Mahadevan 1 has made an extensive x-ray study of the various 
varieties of coal, principally vitrain and durain. Vitrain, for 
example, gives two halos in the position of the two most promi- 
nent graphite carbon rings. They are wide and diffuse, suggest- 
ing the colloidal nature of the diffracting particles. The halos 
are due to the complex carbon molecule present in vitrain. The 
increase of moisture content seems to be accompanied by a finer 
division of the particles as evidenced by broadening of the rings. 
The results on durain indicate that it belongs to a colloidal 
system of the suspensoid type, where vitrain acts as a dispersion 
medium and the ash and vegetable detritus (with free carbon as 
end product) as disperse phases. In a study of vitrains of 
different geological ages, the intensity of the general scattering is 
seen in the case of the older coals to be approximately propor- 
tional to the sum of moisture content and volatile matter. In 
all cases the sizes of the diffracting particles are found to be of 
colloidal dimensions. The mineral matter in the ash is also 
present in a colloidal state. These and related investigations 
have opened up a whole new series of applications of the x-ray 
diffraction method by amorphous solids. There has been a 
further extension to the case of natural and fossil resins 2 and 
to the changes during heating of ordinary rosin, shellac, and 
synthetic resins. 3 The importance of these studies can scarcely 
be overestimated, on account of the much greater amount of 
information obtained on seemingly hopeless materials and on 
account of the possibility of solving many difficult problems, 
particularly in chemistry and geology. 

The Nature of Colloidal Solutions as Revealed by X-ray 
Diffraction. Following the discovery of Krishnamurti 4 that 
diffraction pattern of aqueous solutions of cane sugar, levulose, 
and glucose were distinguished by intense scattering at small 
angles due to the dissolved molecules, it was then possible to 
undertake the study of colloidal solutions for which the state of 
molecular aggregation has been the subject of much speculation. 

l lbid., 4, 457; 5, 525 (1930). 
2 Ibid., 6, 345 (1930). 

* Ibid., 4, 99 (1930). 

* Ibid., 3, 209; 307 (1928); 5, 489 (1930). 



432 



APPLIED X-RAYS 



The molecular weight of dextrin calculated from the extent of 
" amorphous" scattering by means of the Bragg formula n\ = 2d 
sin comes out 600 and for gelatin, 3000, which are not improb- 
able values. The solution of sodium oleate produced a ring 
due to the presence of big groups or micelles of sodium oleate 
in the solution. The extent of the gaseous scattering gave the 
dimension for the sodium oleate molecule, agreeing with that 
calculated from molecular weight and density. An excess of 
scattering directly adjoining the central spot is due to big groups 
of ionic micelles described by McBain. Aqueous solutions of 

starch, tannic acid, and gurn 
arabic showed a further 
scattering at small angles to 
the primary beam, due to the 
dissolved molecules or 
micelles. The molecular 
weights calculated from the 
extents of the coronas were 
6200, 3134, and 2810, respec- 
tively. Thus, a starch 
molecule contains about 10 
dextrin molecules united to- 
gether, and a tannin micelle 
contains 10 simple molecules 
of the formula CuHioOg. 
The greater importance of 
these studies is at once apparent, when it is considered that 
extremely valuable information should be obtained from biological 
fluids including blood, filterable virus, etc. In all these cases of 
amorphous solids, liquids, and solutions, the x-ray patterns are 
characteristic in showing the presence of one or more diffraction 
bands, even though these may be ill-defined. The purely amor- 
phous scattering where no maxima are present evidently can 
exist only in the case of ideal gases. All of these newer investiga- 
tions are in agreement with the contention by the writer that such 
a material as amorphous carbon represents an intermediate 
state, designated as paracrystalline, through which the atoms of 
carbon have to pass before obtaining the orderly arrangement 
underlying the graphite structure. 

Diffraction by Liquids. It has been known definitely since 
1916 that liquids through which x-rays are passed produce 




FIG. 223. Typical pattern for "amor- 
phous" material such as liquids. 



STRUCTURE OF MATERIALS AND LIQUIDS 433 

diffraction patterns characterized by one or more halos or inter- 
ference rings, usually somewhat diffuse (Fig. 223). Approxi- 
mately eighty papers dealing with this subject theoretically or 
experimentally have now appeared. It is not possible here to 
present the historical development but rather to give the status 
of experimental results as it now stands. An excellent survey 
of researches up to 1928 is given in a paper by Drucker. 1 

The preponderance of opinion now is that the diffraction effects 
with liquids indicate orderly spacial arrangements of molecules. 
The phenomenon is understood qualitatively in the same sense 
that crystal diffraction is understood. In spite of numerous 
theoretical attempts to evaluate the phenomena exactly, these 
have not been so successful as the conception of what Stewart 
calls "cybotaxis" a regularity of molecules grouping in liquids. 
Interference effects might be due to periodicities within the atom 
(electron distribution), within the molecule (atomic distribution), 
or between molecules. The first must be true for monatomic 
substances which were investigated by Debye and Scherrer in 
1916. Certain halos for other compounds may be due to atomic 
distribution, but certainly the third cause is predominating in 
complex molecules, since the chief diffraction maxima are 
accounted for by a periodicity in the distribution of molecules. 
This would be particularly true for asymmetrical molecules. 
In liquids these would have a certain distance of nearest approach 
side by side or end to end. According to Stewart, 2 

... if x-rays give evidence of periodic molecular grouping it must 
not be supposed that these groups are large or that the molecules in 
any one well defined group remain permanently members of that group. 
At any one instant these small orderly molecular groups might exist 
at numerous points in the liquid, the regions between them being not 
so orderly. 

This orderly arrangement in groups is called " cybotaxis." There 
is every evidence, therefore, that the Bragg law n\ = 2d sin 9 
can be applied to liquid diffraction interferences just as truly 
as to crystalline solids. Scattering centers at random (that is 
amorphous material) would produce a large scattering near 0, 
but such is not the case for liquids any more than it is for crystals. 
Furthermore, the integrated intensity in the region of the chief 

1 Phyxik. Z., 29, 273 (1928). 

2 Rev. Modern Physics, 2, 116 (1930). 



434 APPLIED X-RAYS 

diffraction maximum for equal masses per unit area for a solid 
and liquid show the same values, again indicating distinct 
coherence. 

The principal work on liquid diffraction has been carried out 
by Stewart and associates at the University of Iowa, who have 
used the ionization spectrometer, and by Raman and associates 
at Calcutta, who have used the photographic method. A brief 
summary of some experimental conclusions must suffice. 

1. In diffraction rings of chain molecules such as n-alcohols, 
n-fatty acids, n-paraffms, etc., there is always a major intensity 
maximum corresponding to a spacing of 4.6 A.U. which is evi- 
dently the effective diameter of the molecule. 

2. Branched-chain isomers invariably increase the effective 
diameters of the chains in characteristic manner. 

3. In polar compounds such as n-alcohols, etc., a second 
maximum, whose position depends upon the number of carbon 
atoms, indicates values of d which are twice, or less than twice, 
the molecular length, indicating a grouping of two polar molecules 
by attraction of the polar OH, COOH, etc., groups. Spacing 
less than twice molecular length could be accounted for by a 
tilt with respect to planes, entirely in accord with observations on 
solid films (see page 319). For isomers in which the polar group 
is not attached to the end or next to the end carbon atom, 
doubling does not occur. 

4. The carbon atom in these chains occupies a distance of about 
1.24 A.U. per atom, indicating probably a zigzag arrangement. 

5. Stewart has accomplished simultaneous measurement of 
more than one diameter in a chain in such compounds as 2- 
methyl hexane (5.25 and 4.84 A.U.) and cfo'-n-propyl car- 
binol (4.85 and 4.5). A third maximum gives the length. 
This is a powerful support in indicating the actual molecular 
arrangement. 

6. Benzene and cyclohexane give sharp rings, indicating a 
ring structure with thickness of 4.7 and 5.1 A.U. (Stewart), 
greater than observed for flat rings in crystals. Para derivatives 
give least thickness. 

7. The effect of temperature on diffraction patterns is precisely 
that which might be predicted upon the basis of crystal data. 
The intensity maximum is displaced (expansion), and the maxi- 
mum is diminished in intensity and increased in width (greater 
disorder due to thermal agitation). 



STRUCTURE OF MATERIALS AND LIQUIDS 435 

8. Impurities, particularly containing heavy atoms, have a 
large effect sometimes upon results. The distinction of purity 
and isomerism constitutes a very useful application. 

9. Some apparent discrepancies among experimenters have 
been found recently to be due to the fact that, with an x-ray 
beam which has not been filtered with greatest care in order to 
render it monochromatic, halos are produced as an interference 
effect of general radiation. With copper radiation and liquid 
fatty acids this secondary ring is obtained with specimens thicker 
than 2 mm., according to Thibeau and Trillat, 1 who further reach 
the conclusion that inner halos, frequently observed by Stewart 
and attributed to molecular length, are always due to diffraction 
of general radiation supposedly by the same spacing as that of the 
principal halo (cross section). Clark and Still well 2 have proved 
that with molybdenum radiation at a tube voltage of 33 kv. or 
more the inner ring is produced by diffraction and filtration of 
general radiation and bears no relation to molecular length 
while at voltage below 27 kv. the inner ring is characteristic of 
the liquid under examination. 

10. Several interesting researches have shown that in many 
instances the liquid halos correspond approximately in their 
positions to the principal diffraction maxima for the same sub- 
stance as a solid. 3 

11. For totally miscible pairs of organic liquids the pattern 
exhibits a single major maximum which has an angular position 
between the maxima for the pure constituents and shifts directly 
with the concentration. 4 On the other hand, an emulsion or 
phenol in water produces the interferences for both constituents. 
Hence in a solution there exists a single type of cybotactic group 
to which molecules of both constituents contribute, whereas 
in the emulsion two types of cybotactic groups exist. This 
constitutes a fundamental differentiation between solutions and 
non-solutions. 

12. Stewart and Edwards 5 have ingeniously shown for a 
series of 22 octyl alcohols that there is a definite correlation 
between the coefficient of viscosity and the perfection of grouping 

1 Z. Physik., 61, 816 (1930). 

2 Radiology, 15, 66 (1930). 

3 KRISHNAMURTI, Ind. J. Phys., 3, Part II, 225 (1928). 

4 MEYER, Phys. Rev., 38, 1083 (1931). 
6 Phys. Rev., 38, 1575 (1931). 



436 APPLIED X-RAYS 

in the direction of chain lengths as measured by relative halo 
intensities. This corresponds with the view that the viscosity 
within liquid groups is caused by longitudinal slippage. The 
temperature coefficient of viscosity is negative because the size 
of groups decreases. 

13. An exceptionally careful investigation of water over a 
range of temperatures has been made both by Meyer, 1 who used 
a strictly monochromatic x-ray beam obtained by crystal reflec- 
tion and the photographic method, and by Stewart 2 with his 
usual ionization method. There is general agreement in finding 
three interference maxima corresponding to distances 3.13, 2.11, 
and 1.34 (Meyer), 3.24, 2.11, 1.13 (Stewart). The distance 
between molecules as scattering centers represented by the most 
prominent halo decreases with temperature, while the breadth 
of the halo increases, whereas the distance corresponding to the 
next most important halo increases. This halo tends to disappear 
with increasing temperature. There is a quantitative similarity 
between the periodicities found in the liquid and the three most 
important periodicities in powdered ice. These results are 
particularly interesting in the light of theories of molecular 
association in water. The water diffraction results seem to 
indicate periodicities of only one kind of molecular grouping, 
just as the results on ice indicate one kind of crystal structure 
only. Hence it would appear that the simple explanation of 
molecular association is the association in cybotactic groups 
of a relatively large number of molecules and not in complexes 
such as di- or tri-hydrol. This is different from the type of 
association found in isomeric alcohols for example. When the 
polar OH group is on the end or next to the end carbon atom, 
the association arranges molecules end to end in the same line 
with two polar groups adjoining, whereas in the case that the 
OH is elsewhere the associated molecules lie side by side. 

14. A comparison of diffraction effects of isotropic liquids and 
liquid crystals 3 proves that generally these are similar (unless 
the mesomorphic smectic state, described by Friedel, is observed). 
Stewart 4 has observed that the intensity of the principal maxi- 

1 Ann. Phyxik, 6, 701 (1930). 
*Phys. Rev., 37, 9 (1931). 

3 For a complete modern survey of the entire subject see Z. Krist. y 79, 
Heft 1-4 (1931). 

4 Phys. Rev., 38, 931 (1931). 



STRUCTURE OF MATERIALS AND LIQUIDS 437 

mum for the anisotropic liquid (117.4 to 134 C.) para-azoxy- 
anisol is 10 per cent greater than that for the transparent 
liquid (143 C.). If cybotactic groups exist in the liquids, 
these " companies" might group together into a large " regiment " 
responsible for the liquid crystalline phenomena. A marked 
optical but small x-ray difference is thus to be expected. Ordi- 
nary liquids appear perfectly isotropic optically, but, using dis- 
tances small compared to an optical wave length, the liquid is 
never isotropic but consists of cybotactic groups oriented in all 
positions and disclosed by x-rays. When these groups enlarge 
they finally become evident by optical examination. 

A logical extension of such researches is the effect of a magnetic 
field. There has been cited some evidence of orienting effects 
on liquid molecules of magnetic fields as disclosed by diffraction 
patterns, but Stewart found none, a result which he ascribed 
to the smallness of the cybotactic groups. A marked effect, 
however, is obtained for the liquid crystalline state, explained 
better by an anisotropic polarization than by a permanent 
magnetic moment. 

In a magnetic field the directed orientation is indicated on 
the diffraction rings by localized intensity maxima (fiber pattern). 
The pattern is markedly sharper in passing from the nernatic 
to the smectic phase in the magnetic field as observed by Herr- 
mann and Krummacher. These workers have also proved 
that, when a melt of a substance which displays mesomorphic 
phases solidifies in a magnetic field, the crystalline powder 
is fibered in a direction parallel to the field ; the intensity maxima 
for the pattern correspond in position to those for the liquid 
crystals in the magnetic field. 

Further researches on structural effects in magnetic and 
electric fields will be awaited with greatest interest. 

15. Molecular orientation of chain compounds in surface films 
has been considered in Chap. XVI (page 332). Upon the basis 
of the Harkins-Langmuir theories, it would be expected that even 
in liquid films such orientation should be observed. Trillat 
has obtained evidence of this orientation in diffraction patterns 
for liquid lead oleate film on mercury drops. This orientation 
has also been observed repeatedly in the writer's laboratory, 
although far sharper effects are obtained if these films are cooled 
to the point of solidification, even of the very thinnest layer on an 
underlying molten liquid. 



CHAPTER XX 

THE STRUCTURE OF HIGHLY POLYMERIZED ORGANIC 
SUBSTANCES FOUND IN NATURE 

Only a short time ago, very little could have been said upon 
this subject, not only from the x-ray diffraction point of view 
but even from that of chemical investigation. The new appear- 
ance of a book of more than 250 pages by Meyer and Mail:, 1 
bearing the title of this chapter, is in itself sufficient evidence 
of the amazing progress in the study of some of the most familiar 
natural materials. Impetus to these investigations was given 
to a large extent by the x-ray analysis of polymerized for- 
maldehyde in the laboratory of Staudinger. The polyoxy- 
methylenes O CH 2 O CH 2 O CH 2 are linear and 
easily produce characteristic x-ray diffraction patterns. Such 
compounds as these are the basis of the synthetic resins of 
commerce, of which the best known is bakelite, made by con- 
densing formaldehyde with phenol or its derivatives. In these 
cases the reaction is complicated by the fact that the linear 
polymers are themselves linked together into a molecular jumble 
to give a structure of which the textile counterpart is neither yarn 
nor velvet pile, but a mass of "felted" fibers. These synthetic 
resins, therefore, yield very diffuse patterns. 

The most illuminating work in the field of synthetic polymers 
in which x-ray diffraction methods have served as a valuable 
aid is that of Carothers and his associates. 2 A long series of 
linear superpolymers (with molecular weights above 10,000) has 
been prepared by condensation reactions as follows: 

- O R CO O R CO O R CO O R CO 

O R CO - 
Polyester (from hydroxy acid) 

1 "Der Aufbau der hochpolymeren organischen Naturstoffe," Leipzig, 
1930. 

*J. Am. Ghent. Soc. y 51, 2548, 2560 (1929); 52, 314, 711, 3292; 54, 1559, 
1566, 1569, 1579 (1932). 

438 



STRUCTURE OF POLYMERIZED ORGANIC SUBSTANCES 439 

- - OR0 CO R' CO 0RO CO R' CO- 

Polyester (from dibasic acid and glycol) 

O R CO NH R' CO NH R' CO R 

CO 
Mixed polyester polyamide 

O CO R CO O CO R CO CO R CO 

Polyanhydride 

With these are to be compared: 



NH R CO NH R' CO NH R CO NH 

Rt r*(\ . . . 
v^vv 

Silk (polyamide) 




_0- 

Cellulose (polyacetal) 

It was found possible to spin and cold-draw the synthetic super- 
polymers into beautifully oriented crystalline fibers, as shown by 
x-ray patterns. A useful degree of strength and pliability in 
these fibers requires a molecular weight of at least 12,000 and a 
molecular length not less than 1000 A.U. These results give 
great support to the interpretation of the structures of natural 
polymerized materials now generally accepted. 

X-ray results on the colloidal polymerized natural products 
indicate clearly that a common structural plan is utilized for 
such widely different substances as cellulose, proteins of all kinds, 
chitin, rubber, gutta percha, balata, and chicle. Long primary 
valence chains or macromolecules are built up from a relatively 
simple molecular group (e.g., dehydrated glucose residues in 
cellulose and isoprene in rubber). A bundle of these chains, 
which may be 500 A.U. long, is held in position by secondary 
valence forces and constitutes the colloidal micelle familiar in 
diffusion and molecular weight experiments. 

From usual diffraction patterns, however, very much smaller 
periodicities and simpler constitution are directly measured. 
The explanation is found in the fact that the long macromoleculea 
are spiral in character, and one turn in the screw axis is sufficient 
for a diffraction periodicity, since all other turns are exactly the 



440 APPLIED X-RAY8 

same. Within the unit crystal cell, therefore, only a small 
number of the molecules of the parent monomer are found, instead 
of one or more of the actual long macrornolecules. The infor- 
mation obtainable from diffraction patterns of the crystalline 
part of these natural products is as follows: 

1. Crystallographic system. 

2. Dimensions of the unit crystal cell and the number of 
monomeric molecules in each, from a known density value. 

3. Coordinates of atoms within the unit cell which demonstrate 
molecular shape of simplest chemical unit, and the bonding of 
these through primary valence bridges into polymerized chains 
with small periodicities due to screw axis of symmetry. Thr^e 
chains are further indicated by optical anisotropy and by -lie 
remarkable persistence during all kinds of chemical treatment, 
such as oxidation, rnercerization, xanthogenation, nitration, 
acetylation of cellulose, vulcanization of rubber. 

4. The length of the macromolecules or in other words of the 
colloidal micelle, and of the cross section, which is determined 
by the number of chains in a bundle. These magnitudes are 
ordinarily calculated from the breadths of the intensity maxima 
as explained in a previous section. It has been possible, however, 
in the writer's laboratory to measure these large spacings from 
direct diffraction interferences when sufficiently long x-ray wave 
lengths are employed, so that angles of diffraction will be in turn 
sufficiently large to permit resolution from the undiffracted 
x-ray beam. 

5. The arrangement of the micelles within the substance, 
whether random or with a preferred orientation with respect 
to one direction, as in a fiber axis. In the former case a pinhole 
diffraction pattern shows uniformly intense continuous concentric 
rings. As definite positions are taken up, intensity increases in 
certain places and decreases in others. Rings become arcs and 
then symmetrically arranged spots as the orientation is increas- 
ingly more perfect. 

6. In terms of all the foregoing types of information, the effects 
of chemical change, swelling, and mechanical deformation, such 
as tension, can be followed and, of course, observed properties 
rationally accounted for. 

It is not possible in this chapter to present in detail for this 
great class of colloids the x-ray data and the steps in interpreta- 
tion. Rather, these results will be briefly tabulated and particu- 



STRUCTURE OF POLYMERIZED ORGANIC SUBSTANCES 441 



lar attention paid to the practical consequences and predictions 
from structural models constructed from x-ray data. 

TYPICAL X-RAY DATA FOR FOUR IMPORTANT POLYMERIZED ORGANIC 
NATURAL MATERIALS 



Product 


System 


Unit 
cell 


Dimen- 
sions, 
A U 


Number 
of groups 


Space- 
groups 


Micelle size 


Cellulose* 


Moriochnie 


a 


8 3 


4O\Hio(> 6 


Cr 


50 A U cross 






b 


10 22 






600 A 1 1 length 






c 


7 9 








CeMilose hy- 
jf ato 


Monoclinic 




a 


84 
8 14 


4C(,H 1 o()o 


cv 


Doubtful, chains 


(mercerized) 




b 


10 30 






less parallel 






c 


9 14 












ft 


62 




9 




Hubber 


Orthorhornbic 


a 


12 3 


8C 6 ll8 


F4 


150 X 500 X > 


(stretched) 




b 


9 3 






600 






c 


8 1 








Silk fibroin . 


Monoclinic 


a 


9 68 












b 


7 00 












c 


8 80 












ft 


7,5 51' 


4 alanylglycyl 







* The data given are those of Meyer and Mark Sponsler prefers the following, a = 10 7 
A U ; 6 = 12 2 A U ; c = 10 3 A U Angles within 2 or 3 of right angles, 8Cr,IIi<)(K groups 
per unit cell The two unit cells are actually very closely related and are merely differently 
oriented in the same fundamental lattice Sponsler's c dimension is the same as b in the 
table, representing the periodicity along the fiber axis 

Direct Measurement of Colloidal Particle Sizes. The methods 
of particle-size measurement presented in Chap. XVII obviously 
involve assumptions and independent methods of evaluation are 
necessary for their test. The best possible method would, of 
course, depend upon actual diffraction interference corresponding 
not to the small unit crystalline cells but to the length and cross 
section of colloidal particles, for each of which d may be cal- 
culated by the simple Bragg equation. This necessitates a 
regular arrangement and uniform size of these colloidal particles 
with respect to each other, so that specimens are limited to 
organic micellar systems consisting of small elongated particles 
regularly oriented in a fiber, such as in natural cellulose and in 
stretched rubber. Another difficulty naturally is that the 
diffraction interferences corresponding to colloidal dimensions 
of one or two hundred A.U. will appear at such small angles, that 
resolution from the primary undiffracted beam will be extremely 



442 APPLIED X-RAYS 

difficult or impossible. There are two experimental possi- 
bilities: define the beam by extremely fine pinholes or slits, 
or else utilize x-radiation with a wave length much greater than 
that usually employed (molybdenum Ka-doublet 0.71 A.U.; 
copper 1.54 A.U.). By the first method with copper radiation 
Mark 1 was able to distinguish a broad interference spot very 
near the primary beam for bamboo and wood cellulose, corre- 
sponding to a spacing of between 50 and 100 A.U. and evidently 
due to reflection from the surfaces of particles of this breadth. 
Clark and Corrigan 2 have utilized the second method with 
interesting preliminary results. A combined x-ray tube, pinhole 
system, and camera was constructed with the target of the tu'je 
magnesium (Ka wave length 9.86 A.U.) (Fig. 21, page 38). -)n 
account of great absorption of radiation, the entire apparatus was 
operated at the x-ray tube vacuum, and extremely thin specimens 
of rubber and cellulose employed. Upon the films appeared a 
ring for unstretched rubber corresponding to 99.3 A.U. and for 
cellulose fibers the spacings 85.0 (evidently corresponding to 
Mark's value for breadth and verified by Thiessen in optical 
examination with the Spierer lens), 274.1, 168.0, and 156.0 A.U. 
The micellar sizes, deduced from measurement of interference 
breadths and calculation by the Laue equation, are approximately 
50 X 50 X 600 A.U. for cellulose and 150 X 500 X > 600 A.U. 
for stretched rubber. Further researches by this important 
direct diffraction method will permit a careful comparison of 
values and establish the validity of the equations deduced from 
theoretical considerations, which may then in turn be used with 
confidence for those colloidal substances in which there is no 
organized micellar structure. 

The Crystal Structure of Insulin. Since the discovery of this 
important substance for the treatment of diabetes there has been 
great interest in its composition and structure. It has been 
known for some time that insulin exhibited certain optical prop- 
erties of a true crystal. Although numerous attempts have been 
made by Freudenberg and others, no x-ray diffraction pattern 
could be obtained beyond the usual ring due to the 3.5 A.U. 
spacing common to proteins. Work of this kind employing the 
usual copper T^a-radiation has been carried on in the writer's 
laboratory for more than two years. In the belief that absence 

1 Faraday Soc. Hon., p. 387 (March, 1929). 

2 Radiology, 16, 117 (1930); Ind. Eng. Chem., 23, 815 (1931). 



STRUCTURE OF POLYMERIZED ORGANIC SUBSTANCES 443 




Fia. 224. Typical pattern for cellulose pattern (ramie). 




FIG. 225. The unit crystal cell of cellulose. (Meyer and Mark.) The 
CeHioOs groups (hexagons) are represented as held together by oxygen bridges, 
each pair forming a cellobiose unit. The dimensions of the monoclinic cell con- 
taining four dehydrated glucose groups are a = 8.3 A.U. (horizontal) ; b 
10.22 A.tT. (vertical); c = 7.9 A.U. (perpendicular to plane of paper). 



444 



APPLIED X-RAYS 



of interference might be due to very large spacings in crystalline 
insulin, Clark and Corrigan 1 investigated the structure with 
the long magnesium Ka-radiation by means of the apparatus 
already described. A crystal pattern was obtained and the unit 
cell dimensions deduced were 130 X 100 X 80 A.U., giving an 
axial ratio of ^:1:^. With the aid of microscopic data the 
crystal form was found to be monoclinic, with one angle between 
88 and 90, the crystals frequently assuming a pseudo-hexagonal 
form. The crystals were positive. On the basis of the approxi- 
mate molecular weight of 35,000 generally accepted, and the 
density of 1.315, the number of molecules of this highly poly- 
merized complex substance per unit cell is 24. An entirely nr V 
field of investigation of very complex natural and synthesi;- xl 
materials is opened up by this application of very soft x-rays. 
Resume of X-ray Results on Natural Polymerized Materials. 
1. Cellulose.' 2 ' a. Proof of identity of crystalline part of natural 




FIG. 220. Model of structure of cellulose fiber, showing colloidal micelles 
built up from bundles of long chains of CeiiioOs groups. Three kinds of binding 
forces are involved, a, primary valence linkage along molecular chain; b, second- 
ary valence forces holding chains in bundle; c, tertiary forces between micelles. 
The principal variation in celluloses from different sources is in the arrangement 
of the micelles parallel in nearly perfect fiber as shown here, spiral, random, 
or brush heap as in cellophane, etc. The miccllar dimensions are of the order 
of 500 A.U. long (also the length of the long-chain molecules) and 50 by 50 A.U. 
in cross section. The micelle therefore may contain 6,000 to 12,000 glucose 
groups, or 1,500 to 3,000 unit cells. 

varieties of ramie, sisal, jute, hemp, flax, cotton, wood, tunicin 
(animal cellulose) ventricosa B cellulose (bacterial), valonia, etc. 
(Fig. 224, typical pattern; Fig. 225, unit cell; Fig. 226, model 
of fiber). 

b. Rational explanation of properties such as tensile strength 
and elasticity from arrangement of micelles: the more perfectly 
parallel to the fiber axis the greater the tensile strength (Fig. 
227). 

1 Pht/s. Rev., 40, 639 (1932). 

2 See, CLARK, Ind. Eng. Chem., 22, 474 (1930), fora complete presentation. 



STRUCTURE OF POLYMERIZED ORGANIC SUBSTANCES 445 



c. Differentiation of cellulose fibers in terms of micellar 
arrangement (parallel to fiber axis in ramie, spiral layers in 
cotton) and of other substances present. 

d. Surest method of identification of true cellulose, which 
involves both constitution and spacial coordinates: esterify 
unknown, dissolve in proper solvent, spin and regenerate fiber 
under tension to orient micelles, saponify in solid phase, and 




(a) 



(b) 




(a) (b) 

FIG. 227. Effect of arrangement of colloidal micelles on diffraction patterns 
of cellulose, (a) Fiber (improved rayon) ; (6) cellophane sheet. 

examine diffraction pattern of fiber suspected to be cellulose. 
This is the method employed for testing cellulose synthesized 
from sugars by Hibbert. 

e. A remarkable improvement in the quality of rayon from the 
prediction that tension on plastic fiber during regeneration should 
pull micelles parallel (x-ray fiber pattern) and greatly increase 
tensile strength; a structural test of every step in the process to 
yield optimum structure and properties; assurance that the 



446 APPLIED X-RAYS 

manufacturing process has not been so severe as to break primary 
valence chains in original raw material (wood pulp or cotton 
linters), as was the case before x-ray research with micellar 
lengths only half as great as in starting material (Fig. 228). 

/. Improvements in cellophane manufacture to eliminate 
directional properties due to slight fibering in sheet when com- 
pletely random arrangement is desirable. (See Fig. 227.) 

g. Classification of raw cotton from degree of fibering since 
ultimate structure is conditioned by growth environment; proof 
that ancient cottons had a superior fibrous structure not now 
existent in any cultivated variety (Fig. 229). 




Fia. 228. Patterns for old (left) and new (right) varieties of rayon, showing 
great increase in preferred orientation in latter, introduced by tension during 
coagulation. 



h. Study of growth of cotton daily from the root hair to mature 
50-day fiber; diffraction patterns characterized by gradual 
increase in organization, decrease in lattice dimensions and 
hence intermicellar swelling and the sudden appearance of fibering 
with wall thickening. 

i. Classification of kind of wood, angle of fibrils, differentiation 
of spring and summer wood, and of normal and compression wood 
(upper and lower side of bough) (Fig. 230). 

j. A method of proving whether swelling is reversible and inter- 
or intramicellar; e.g., wood and cotton swell when water pene- 
trates between micelles; other solutions penetrate between chains 
and produce change in lattice dimensions; new processes for 
impregnation of wood to avoid swelling arid water penetration. 



STRUCTURE OF POLYMERIZED ORGANIC SUBSTANCES 447 




(a) 



(6) (c) 

FIG. 229. Comparison of structures for cotton, (a) Good grade of modern 
cotton ; (b) ancient cotton with much more perfect alignment of micelles parallel 
to fiber axis; (c) ordinary cotton subjected to chemical swelling and mechanical 
tension. 




FIG. 230. Typical patterns for wood, showing variations. Left, high density 
yellow poplar; right, compression structure on leaning side of tree trunks. 



448 APPLIED X-RAYS 

k. A new process successfully predicted from cellulose model 
that cotton may be suitably swollen, maintaining solid form, 
stretched, and greatly strengthened by virtue of improved 
orientation of micelles (see Fig. 229c). 

I. A proof that only the triacetate and trinitrate form definite 
crystalline substances, since esters of intermediate composition 
show x-ray interferences for unchanged cellulose and for the tri- 
ester only; for parts in which all of hydroxyl groups have not 
reacted, the distortion of the lattice results in no observable sharp 
interferences. On this account none of the commercial nitrate 
or acetate films yields more than a very diffuse amorphous 
pattern, so that variations in manufacturing steps cannot ' o 
followed; by plastic stretching of the films molecules are pul' H! 
more nearly into alignment, but only a pseudo-crystalline pat- 
tern and structure are gained before breakage on account of the 
interference of amorphous material with completely parallel 
orientation. 

m. Discovery of the only method of obtaining native cellulose 
back from mercerized: two trinitrates are found from x-ray 
patterns, both produced from either native or mercerized cellulose 
under controlled conditions. Upon denitration trinitrate I 
yields native, and II hydrated cellulose only. 

n. Identifications of various compounds such as Knecht's 
(with nitric acid) Norrnann's (copper-alkali-cellulose), copper- 
amino-cellulose; a rational explanation of observed chemical 
properties and reactions, oxidation splitting, etc. 

o. Conditioning of fiber structure to problems of dyeing, to 
various types of paper and a control of paper manufacture. 

p. The proof that celluloid is a double compound of nitro- 
cellulose and camphor. In a remarkably convincing series of 
papers, 1 Katz and associates have utilized x-ray patterns corre- 
lated with optical anisotropy to show that with small camphor 
contents (to 10 per cent) unchanged long nitrocellulose micelles 
and long micelles of the camphor-nitrocellulose compound lie 
side by side. The first possess strongly positive birefringence 
with respect to the longest axis, the latter weakly negative. 
The changes in diffraction patterns clearly indicate such a reac- 
tion with camphor, other cyclic ketones, acid amides and esters, 
aldehydes, and nitriles (all predicted and verified from the 

1 Z. physik. Chrm., 149, 371; 151, 145, 163, 173 (1930). 



STRUCTURE OF POLYMERIZED ORGANIC SUBSTANCES 449 

observation of C=0 combination with nitrocellulose chain) 
as swelling and gelatinizing agents. 

2. Rubber. a. Unique proof of micellar structure and parallel 
orientation of long-chain molecules of C & H 8 when stretched 
(Fig. 231). Unit cell shown in Fig. 232. 




(a) (6) (c) 

FIG. 231. Diffraction patterns for rubber, (a) Unstretched; (&) stretched 
crepe or smoked sheet; (c) stretched vulcanized rubber. 

b. A fundamental mechanism of elasticity based upon the 
mutual effects of double bonds in the unsaturated hydrocarbon 
in coiling up springlike molecules. 




^rV I { ^ i n 
f <*./2.3A ^ 



FIG. 232. Unit crystal cell of stretched rubber. 

c. A method of racking rubber 10,000 per cent or more, devel- 
oped largely in the course of x-ray work. 

d. Discovery that rubber after long standing at cool tempera- 
tures " freezes" and produces diffraction interferences for random 
crystal grains. 



450 APPLIED X-RAYS 

e. A " melting curve " for natural rubber determined by von 
Susich 1 from x-ray patterns. In frozen samples interferences 
disappear above 35 C., while with increasing degree of stretching 
the temperatures at which crystalline patterns became amorphous 
increase up to 90 C. for great elongation. 

/. The only exact method of distinguishing natural and 
synthetic rubbers so far produced, and the criterion of successful 
synthesis in the future another indication that the terms 
rubber, cellulose, etc. ; imply not only constitution but also 
spacial structure. Duprene or polymerized chloroprene, obtained 
by the addition of HC1 to vinyl acetylene, is the first synthetic 
rubber to give a rubber-like fiber pattern upon stretching. 2 
That the new product is not identical with natural rubber, h^w- 
ever, is shown by a comparison of the b spacings (along the frew 
axis) of the stretched specimens: 

Rubber .. 8 39 15 A.U. 

Chloropreno ... 4 81 03 

a-Gutta percha. . ' . 8 78 12 

0-Gutta percha . 4 87 07 

g. Sharpening of interferences on vulcanization, indicating 
sulfur bridge formation between chains though the unit crystal 
cell is the same; with increasing sulfur content, loss of elasticity 
as a result of net formation of molecules in hard rubber. 

h. Cooling of racked rubber with liquid air results in patterns 
with the appearance of Laue single-crystal diagrams for metals, 
indicating larger organized lattice units than the usual micelle. 

L Rational explanation of greater tensile strength of stretched 
samples with greater van der Waals' forces; e.g., unstretched 
raw rubber (liquid air) 5.4 kg. mm. 2 , stretched 35.1; vulcanized 
unstretched 5.3, stretched 44.4. 

3. Gutta Percha, Batata , and Chicle. There has been a very 
considerable disagreement concerning the structures of gutta 
percha and balata which are, like rubber, polymers of isoprene. 
The discrepancies have at last been explained in the work of 
Hopff and von Susich 3 and of Still well and Clark. 4 These two 
substances produce diffraction patterns different from rubber, 

1 Naturwissenschaften, 44, 915 (1930). 

2 CAROTHERS, WILLIAMS, COLLINS, and KIRBY, /. Am. Chem. 8oc., 63, 
4203 (1931). 

3 Kautsehuk, 11, 234 (1930). 

4 Ind. Eng. Chem., 23, 706 (1931); Kautsehuk, 6, 86 (1931) 



STRUCTURE OF POLYMERIZED ORGANIC SUBSTANCES 451 

but probably like each other. There are two modifications, 
the a which is stable below 60 C. and ft produced by heating 
above 60 C., giving different patterns in the unstretched as well 
as the stretched state. Stillwell and Clark have found balata 
in ordinary commercial form to differ from ordinary gutta percha, 
in the same way that von Susich's a-modification differs from 
0-gutta percha (Fig. 233). 

Chicle has been studied by Stillwell and Clark. The hydro- 
carbon constituent here is identical with gutta percha. 
The resins, calcium oxalate, and other substances constitute the 




FIG. 233. Patterns for unstretched and stretched a-gutta percha (left) and 
/3-gutta percha (right). 

remainder of this product. This gutta hydrocarbon may be the 
explanation of frozen rubber crystals and crystals isolated from 
rubber by Pummerer and Koch, Bureau of Standards, and others. 

Rubber, gutta percha, balata, and chicle all are built from 
hydrocarbon chains of the same constitution. The difference 
comes in a cis configuration for rubber where the identity period 
is 8.4 A.U. and a trans form in the gutta percha, or zigzag chains 
with an identity period of 8.8 A.U. 

4. Proteins. a. Silk fibroin, one of the constituents of natural 
silk, shows a distinctly crystalline structure (Fig. 234), the 
analysis of which is given in the table. The chains of ammo 
acid r^idues are bound in peptide linkage to form long spiral 



452 



APPLIED X-RAYS 



macromolecules, with four alanylglycyl residues per unit cell. 
The micelles are embedded in a matrix and are perhaps here 




FIG. 234. Fiber structure of natural silk. 




(a) (b) 

FIG. 235. Fiber structures of wool and air. (a) a-form, unstretched; (b) 

0-form, stretched. 

and there chemically bound together. The amorphous part 
. of the silk consists of irregular chains, which may even b', bound 



STRUCTURE OF POLYMERIZED ORGANIC SUBSTANCES 453 

into micelles, but without lattice arrangement. Such micelles 
are termed by Meyer and Mark " mixed micelles" by analogy 
with " mixed crystals." The great strength of the peptide chains 
and the bonds holding the micelles together are explained by the 
high molar cohesion of CONH (10,600), demonstrated by high 
heat of vaporization, high boiling point, and high dielectric 
constant. A chain of 100 peptide residues (350 A.U.), as in 
fibroin, possesses a molar cohesion of over 1,000,000, very nearly 
the same as in a cellulose chain. 

The micelles are resistant like cellulose to swelling media, in 
the sense of change of lattice dimensions. Swelling is, therefore, 
in;^rmicellar a proof that within the micelle no free amido 
an< carboxyl groups exist. Only concentrated acids such as 
formic and some salt solutions swell the protein to the point of 
solution. The cobweb spun by the spider gives a pattern prac- 
tically identical with that of fibroin. 

b. Wool and Hair. (1) All untreated wool samples give an 
x-ray fiber diffraction pattern which is substantially the same 
for the various varieties of wool as well as for animal hair, human 
hair, porcupine quills, etc. The most prominent features of this 
fiber pattern shown in Fig. 235a are as follows: 

Two sharp spots on either side of the center of the photograph 
appear on the equator. It is these spots, particularly charac- 
teristic of a large interplanar spacing or identity period, which 
give the marked fiber pattern. 

The next most prominent feature is an outer, somewhat 
diffuse ring which is really a composite of several overlapping 
reflections. This ring is characterized in most of the wool 
samples by a sharper arc on the meridian or at the twelve and 
six o'clock positions. These parts of the pattern are unquestion- 
ably due to a crystalline constituent of the wool fiber. There 
is also present at very small angles, z.e., around the central O 
spot, a diffuse haze which may be superposed on the sharp spots 
above noted. This haze is due to the disorganized or non-crys- 
tallized material in the fiber. Careful analysis of the best pat- 
terns show that there is a spacing of 5.15 A.U. along the axis 
of the fiber, and dimensions of 27 A.U. and 10.3 A.U. in directions 
parallel to the fiber axis. 

The x-ray pattern is what would be expected from an imperfect 
crystalline system in which the only sharply defined transition 
or identity period is that parallel to the fiber axis, suggesting 



454 APPLIED X-RAYS 

long, filament-like molecules which cling together sidewise with 
varying degrees of perfection. The diffuse nature of the pattern, 
and the possibility of overlapping of several sharp crystalline 
interferences, prove the existence of very imperfect junctions 
and mixed crystallization effects. The halo around the center 
corresponding to disorganized matter is most prominent always 
in cases where scales are present. This is particularly true in 
the case of merino wool. 

The slight variations in the pattern from one wool to another 
are concerned with the prominence of this halo, the sharpness 
of the inner spots, the diffuseness of the outer ring, and the 
definition of the meridian arc on this ring. These latter prop- 
erties determine how perfectly lined up the crystalline protein 
units are with respect to the axis of the fiber. In general the 
fibers with highest tensile strength and straightest properties 
are characterized by the highest degree of parallel arrangement. 

(2) Effect of Tension. The change in the x-ray diffraction 
pattern when the wool fibers are stretched 30 per cent or more 
has been noted independently by Astbury and Street and in 
the writer's laboratory. The diffraction pattern changes in 
appearance and measurement show that the dimensions also 
change (Fig. 2356). A sharp arc noted on the meridian for 
the unstretched or alpha wool disappears and new strong spots 
appear on the equator of the outer ring. The spacing for this 
stretched or beta wool along the axis of the fiber is 6.64 A.U., 
an increase of 29 per cent over that for unstretched wool. Two 
other dimensions at right angles are 9.3 and 9.8 A.U. 

It has been possible to assure this change more readily for 
samples stretched wet. It has been impossible to stretch dry 
wool much beyond 30 per cent without rupture. The definite 
change, of course, means an actual change in the molecules 
aligned parallel with the axis of the fiber of which these smaller 
dimensions represent some repetitional part (Fig. 236). The 
complete passage from the alpha to the beta form must take place 
in three stages in view of the fact that wool in cold water may be 
stretched twice as far and in steam three times as far as perfectly 
dry wool. The percentage elongation required to bring out the 
beta pattern varies from one kind of wool to another within a 
small range and the fact that some of the alpha form remains 
while the beta form is developing makes it difficult to classify 
wool on this basis. 



STRUCTURE OF POLYMERIZED ORGANIC SUBSTANCES 455 

Stretching in cold water is reversible under ideal conditions, 
although in steam a permanent set is obtained upon stretching, 
this being in accordance with the 29 per cent extension of the 
change above noted. With constant length maintained stretched 
wool gradually loses tension and its original power of recovery 
of its original length is removed. X-ray photographs support 




FIG. 236. Molecular models for fibrous proteins. Left, unstretched or a- wool; 
right, stretched or /3-wool. (Astbury.) 

the idea that in order to repeat a load extension curve up 
to 30 per cent it is necessary to stretch the fiber quickly 
and to allow it to rest unstretched in water between succes- 
sive extensions. This rest period is highly necessary in order 
that there may be a reversion from the beta to the alpha 
form. If the loading curve is slow, greater extensions are 
obtained than with rapid loading. It follows, of course, that 
the properties of wool in the beta form, however produced 
and especially if a permanent set has been obtained, must 
be vastly different from the alpha wool and must be asso- 
ciated with a loss in resilience. Astbury expresses the opinion 



456 APPLIED X-RAYS 

that this transformation is the explanation of the " permanent 
wave." 

(3) Effect of Reagents. The alkali sulfides are among the 
most powerful solvents of wool and it has been established for 
some time that the change is accompanied by both free S S 
and free SH linkages. The exact nature of the reaction is 
not known. Stretched wool is far more susceptible to sulfide 
than unstretched. In the latter case there is a continuous 
destruction of the protein, while for stretched wool there is an 
immediate non-solvent reaction followed by a continuous solvent 
action. Astbury has observed that the most intense x-ray reflec- 
tion given by stretched wool has the same spacing as the most 
intense reflection given by cystine. This spacing is at right 
angles to the sheath axis and may be the half length of the 
cystine molecule and the full length of the cysteine molecule. 

The scale sheath of the fiber remains unaffected by all sodium 
or potassium sulfides but a very considerable swelling takes 
place in the cortex, such that the scale sheath is split from end 
to end. The fact seems fairly well substantiated that in the 
beta or stretched form of the wool there are molecular chains 
linked side by side with molecules of cystine or cysteine. These 
molecular chains are ruptured by treatment with sulfide and the 
beta structure relieved of tension reverts to the alpha structure. 
On account of the destruction of protein in the fiber, however, 
the original orientation is lost. The principal molecular group- 
ing in the unstretched wool repeating itself along the fiber axis is 
5.15 A.U., which is the same period as that observed in cellulose. 

This seems to suggest that in wool there are long filament- 
like molecules which are built up by continuous repetition of 
hexagonal ring systems connected by bridge atoms. Other 
relationships are also observed which confirm this general idea. 
A chain of 100 amino acid residues in a protein would possess a 
length of 350 A.U. and have a molar cohesion of over 1,000,000, 
a value very similar to that of a cellulose chain. 

c. Tendons, Collagen, Gelatin, and Tissues. The protein 
materials in natural fibrous form also produce fiber diffraction 
patterns. Stretched gelatin films approach the same structure, 
though never so perfectly crystalline, evidently because the 
ends of the micelles are ragged. The identity period for tendon 
is 8.4 A.U. (Fig. 237), distinctly different from the value 7.0 in 
silk. A different arrangement of the chains is indicate^, as is 



STRUCTURE OF POLYMERIZED ORGANIC SUBSTANCES 457 

found for rubber and gutta percha. All properties indicate 
that a tendon is constructed similarly to racked rubber; heating 
causes contraction and disappearance of the fiber patterns. 
Hence here again are long-chain molecules in parallel orientation 
in bundles, a structure further verified by lengthwise splitting 
when frozen in liquid air. 

Strength is obtained by such structure as shown by the fact 
that fresh tendon had a tensile strength of 11 kg./mm. 2 ; after 
contraction at 80 C., 3.0 kg./mm. 2 ; and after stretching back 
to the original length 10.6. 




FIG. 237. Typical diffraction patterns for human tendon. Left, unstretched : 
right, stretched, showing effect of tension in pulling long protein molecules into 
parallel orientation. 

Botanical tissues are webs spun from long primary valence 
carbohydrate chains, held by molecular cohesion of unsolvated 
groups or by chemical bridges. The chains may carry solvated 
shells on the polar or ionizable groups to account for the familiar 
freshness. Similarly, animal tissues are webs of protein chains 
forming cell walls and accounting for combination with water. 
The most important difference between tissues, animal and plant, 
lies in the comparative non-elasticity of carbohydrate chains as 
compared with the pliable protein chain. Seifriz has stated 
positively, as a result of the study of elasticity, that the last 
molecular entity of a living substance must possess an elongated 
form. Fibrous tissues, such as muscles and tendons, have prin- 
cipal valence chains parallel to the fiber axes. Tissue sheets, 
such P.S the fascia, have the chains in one plane. 



458 APPLIED X-RAYS 

The presence of distinctive larger, regularly arranged bundles of 
these long chains as micelles seems clearly proved in cellulose, 
stretched rubber, silk fibroin, etc. In other cases as in 
unstretched rubber and in tissues, the matter is not altogether 
settled. Studies of birefringence, of course, prove parallel orienta- 
tion and these larger complexes can be demonstrated if the 
dependence of birefringence on imbibition of liquids with differ- 
ent indices of refraction shows a distinct minimum. The 
separation of birefringence due to the form of rodlike particles, 
as distinguished from that of single parallel long molecules (or 
characteristic birefringence), has actually been accomplished. 
It is not essential to give the name of crystalline to these con- 
ceptions of oriented long chains which actually diffract x-rays. 
A much higher degree of arrangement is implied by the term 
crystalline, since these long molecular chains still possess a rota- 
tional degree of freedom and hence are mesocrystalline or meso- 
morphic. For the first time, however, it is possible to attack the 
complex problems of chemical structures of chains, their positions 
in organs, the changes of their forms and position, the relation 
to each other and to the tissue fluidity. These have already 
been solved for the simpler fiber sections. 

One problem to account for is the fact that many tissues which 
are insoluble in water still yield considerable quantities of pro- 
tein to the solvent a fact which demonstrates that the protein 
could not have been bound in a chemical network. 

Przibram 1 has lately demonstrated by biological methods that 
the chrornatin threads and even genes can be measured in length 
as 10~ 4 to 10~ 6 . The protein molecule is only one power of ten 
under the size of these powerful biological units. 

Coming then to the behavior of living tissues, it has been 
demonstrated from mechanical and x-ray investigations that 
in the extended muscle the principal valence chains are in parallel 
orientation; in the contracted muscle, not. A muscle stretched 
and dried produces a fiber diffraction pattern, while a dried 
contracted muscle is amorphous, in keeping with the fact that the 
stretched muscle frozen with liquid air splits into shreds parallel 
with the fiber axis, while the contracted frozen muscle breaks 
into small clumps. Von Htirthle 2 has shown that the biref ringent 

1 PRZIBRAM, p. 238, "Der Aufbau der Hochpolymeron Organisohen 
Naturstoffe," Leipzig. 

2 VON HURTHLE, p. 239, "Der Aufbau der Hochpolymeren Organischen 
Naturstoffe," Leipzig. 



STRUCTURE OF POLYMERIZED ORGANIC SUBSTANCES 459 



(a) 





part of the muscle fibrils is the actual contractile substance. 
This birefringence decreases with contraction; consequently 
the chains in the contracting fibril lose their parallel orientation. 
Until recently it has been impossible to prove whether or not 
this mechanism is operative in truly living muscle. Experiments 
by Boehm and Schotzky 1 and by Clark and Corrigan, 2 utilizing 
the new high-powered x-ray tubes which 
permit very rapid exposures, have thrown 
clear light upon this uncertainty. Dif- 
fraction patterns of living, electrically con- 
tracted frog muscle (excited by an applied 
voltage to tetanus contractions), have 
previously been procurable at a great 
sacrifice. As each muscle after killing the 
frog remains sufficiently fresh for only 1 4 
mm. in the path of an intense x-ray beam, 
several hundred muscles have been 
necessary. Diffraction patterns may 
now be obtained in 2 min. with only six 
muscles. With the exception that the 
diffraction ring for water is present, the 
patterns are the same as for dried muscle. 
Contracted living muscles show a great 
decrease in fibering as compared with the 
muscle at rest (Fig. 238). 

A plausible mechanism for muscular 
action can be deduced in terms of inner 
molecular forces. 3 Rubber contracts 
because of double bonds in the long 
hydrocarbon chains which cause a spring- 
like coiling. In muscle protein there are 
many free basic and acid groups in the chains, since glutaminic 
acid and arginine and lysine may be derived. At the isoelectric 
point COO~ and NH 3 + ions may attract and pull the chain into 
a close spiral. 

In acid or alkaline media, however, COO" or NH 3 + ions repel 
each other and straighten out the chain. In confirmation of 
different chain configurations, casein and hemoglobin form the 

1 Nalurwissenschaften, 18, 282 (1930). 

2 CLARK and CORRIGAN, Ind. Eng. Chem., 23 (1931). 

3 MEYER and MARK, loc. tit., p. 238. 




(c) 



FIG. 238. Diffraction 
patterns for frog muscles. 
(a) Dried muscle; (6) 
living muscle at rest; (c) 
living muscle excited to 
tetanus contraction. 
(Boehm and Schotzky.) 



460 APPLIED X-RAYS 

homogeneous layers in acid or alkaline aqueous solutions 7 or 8 
A.U. thick, while globules form only on a neutral surface. 

Hence contraction or expansion resides in the ultimate long- 
chain molecule. Since these are bound together by molecular 
cohesion or bridges throughout the whole length of the muscle, 
an inner molecular change with changing pH value produces a 
contraction or expansion on the macroscopic scale. The physio- 
logical and chemical changes relating to production and destruc- 
tion of acid in the muscle, therefore, lead to direct action on the 




FIG. 239. Patterns for two specimens of surgical catgut (sheep intestines) 
ligatures, showing difference in fibering and tensile properties (right, greatly 
superior) . 

protein chains and account for the mechanical work. The 
important conception of change in form of the protein chain as a 
function of the medium may, therefore, be extended to the 
behavior of protoplasm and to many physiological problems. 
The foregoing account of the new knowledge of natural colloidal 
protein materials is sufficient to indicate the practical value of 
such methods of study. The changes in tissues shown by x-ray 
diffraction throw great light not only on physiological processes 
but also on pathological developments. A detailed paper from 
the writers' laboratory shows how cancerous tissue (uterus, 
breast, bones, etc.) produces characteristically different effects 
from the normal specimens, which may result in valuable diag- 
nostic progress. 1 A technological application is in the production 
of improved surgical catgut for ligatures and sutures. Here 
the process of swelling and tension, referred to so frequently, 
is highly effective in improving micellar orientation followed 

1 CLARK, BUCHER, and LORENZ, Radiology, 17, 482 (1931). 



STRUCTURE OF POLYMERIZED ORGANIC SUBSTANCES 461 

by the x-ray patterns (Fig. 239), and tensile strength. The 
dispersion and respinning both of silk and of animal tissues are 
an accomplished procedure, and any desired properties can be 
obtained in terms of regulation of the variables. In other words, 
catgut of an inferior quality can be vastly improved by these 
steps, just as cotton or rayon can be structurally changed and 
improved by swelling or dispersion and tension. 



INDEX 



Absorption, 91 

coefficients, 91 

edges, 66 

mechanism of, 95 

practical applications of, 106 

spectra, 56 

Acceleration law in Bohr theory, 72 
Acids, aliphatic, 326 

dicarboxylic, 329 
Age-hardening, 302 
Aircraft parts, testing of, 123 
Aliphatic chains, 316 
Allotropic modifications, 152 
Alloy steels, 303 
Alloys, 279 

analogies from, 292 

classification of systems, 283, 294 

compound formation in, 280 

eutectics, 280 

interstitial arrangement in, 280 

iron, 295 

substitutional arrangement in, 279 

superstructure, 281 
Aluminum, deformation structures 
of, 358, 361, 380 

recrystallization of, 390 
Amorphous matter, 426 
Arnphiboles, structure of, 274 
Analysis, chemical, by x-rays, 82, 

332 
Annealing, of cast steel, 400 

effect of carbon content on, 416 

temperature of, 418 
Anthracene, crystal structure of, 309 
Aromatic compounds, 310 
Asbestos, 254 
Asterism, 353 
Atomic radii, 234, 265 



Atomic structure, Bohr theory of, 71 
from intensities of scattering by 

gases, 100 
modern theory of, 79 

Atoms, arrangement of, 211 
sizes and shapes of, 265 

Austenite, 297 

Autoelectronic effect, 23 

Automotive parts, testing of, 123 



B 



Back-reflection diffraction method, 

421 

Bacteria, effect of x-rays on, 154 
Bakclite, structure of, 438 
Balata, 450 
Balmer series, 68, 72 
Barium carbide, 253 
Battery, high-voltage storage, 40 
Benzene ring, 309 
0-iron, 299 
0-rays, 98 

Biological effects of x-rays, 140, 153 
Bohr orbit, 259 
Bohr theory, 71, 80 
Bone, structure and constitution of, 

255 

Bragg and Peirce, law of, 93 
Bragg diffraction law, 180 
Bragg spectrometer method, 190 
Bragg spectrum, 222 
Brass, structures of, 282 
Bucky diaphragm, 112 
Bunsen law, 143 



Calcite, as standard crystal grating, 

50 
Camera, Seemann-Bohlin, 203, 285 



463 



464 



APPLIED X-RAYS 



Cancer, 153, 154, 158, 159 
Carbon, crystalline structures of, 307 
Carbon blacks, 344, 428, 430 
Cast steel, 400 
Castings, growth texture of, 387 

rudiographic examination of, 119 
Catalysts, 150, 343 
Catgut, surgical, 460 
Cellophane, 446 
Celluloid, 448 
Cellulose, 444 
Cellulose esters, 448 
Cement, 256 
Ccmentito, 298 
Ceramic materials, 257 
Chemical analysis by x-rays, 139, 

144 

Chemical effects of x-rays, 139, 144 
Chemical reaction mechanism, 142 
Chicle, 450 

Circuits for x-ray machines, 44 
Coal, radiography of, 125 

structure of, 431 

Cold-rolling, effect on texture of 
metals, 358, 371, 405 

effects of variables in, 403 

stages in reduction by, 403 
Collagen, 456 
Colloidal metals, 429 
Colloidal particles, shape of, 344 

size of, 336, 441 
Colloids, diffraction by, 427 

flocculation of, 149 

nature of, 431 
Coloration by x-rays of glass and 

minerals, 151 

Combination principle, 70, 78 
Complex formation, 252 
Compounds, of carbon, 246 

inorganic, 231 

long-chain, 319 

organic, 246 

results of analysis of inorganic, 245 

of organic, 314 
Compton effect, 96, 131, 132, 134, 

162 

Conductivity, effects of x-rays on, 
134 



Coolidge tube, 18, 25, 32, 104 

for quantitative analysis, 88 
Cooling, 19 
Coordination, 264 
Copper, forming, 410 

recrystallization of, 394 

wire structure, 367 
Corrosion of alloys, 304 
Cotton, 446 
Counterfeit coins, 107 
Crystal analysis, Bragg method of, 
188-190* 

Hull-Debye-Scherrer, 188, 189, 
199 

Laue, 185, 188, 189 

monochromatic pinhole, 188, 189 

powder method of, 188-190 

rotation method of, 188, 189, 195 

Schiebold-Polanyi, 188, 189, 195 
Crystallography, fundamentals of, 

172 
Crystals, classification of, 260, 262 

spectra from, 49 

submicroscopic, 336 

types of, 259 

and x-ray diffraction, 171, 180 
Cybotaxis, 433 

D 

Debye factor, 215 
Debye-Scherrer method, 201 

rings, 236 
Deformation, effect of grain size 

on, 418 
Deformation structures, in drawn 

wires, 370 
Diamond, 307 

Diffraction, by amorphous sub- 
stances, 426 

apparatus, 185 

by colloids, 427 

by crystalline substances, 426 

of electrons, 7 

by fibers, 357 

of hydrogen atoms, 7 

interferences, 208 

by liquids, 432 

methods, 188 



INDEX 



465 



Diffraction, patterns, 208, 335 

by powders, 199 

tubes for, 31 

of x-rays by crystals, 4 
Diopside, 274 
Diphenyl, 310, 313 
Dosage, measurement of, 160 
Doublets, 70 

Duane and Hunt, law of, 53, 54 
Duane ionization chamber, 164 
Duprenc, 450 
Durain, 431 
Dyeing of textiles, 430 

E 

Eder's solution, 165 
Effective wave length, 104 
Einstein equivalence law, 147 
Electric steel, 400 
Electrical conductivity, 134 
Electrical precautions, 47 
Elect rodeposition of metals, 385 
Electromagnetic waves, 4, 6 
Electrons, back diffusion of, 23 

dual nature of, 7, 79 

in x-ray tube, 78 

Elements, crystalline structures of, 
231 

discovery of, 69 
Emulsions, diffraction by, 435 
Enamels, 257 
Energy-level diagram, 76 
Erythema, 38, 166 
Esters, 330 
Exposure charts, 113 
Extinction, 216 

F 

F curves and values, 214, 311 
Fatigue of metals, 420 
Ferrite, 299 
Fiber diagrams, 357 

for drawn wires, 359 

for rolled sheets, 371 
Fiber structure, 365 
Fibers, orientation in, 375 
Filament, line focus, 28 

spiral, 18 



Films, formation of, 331 

metal, 387 
Filters, 67 
Filtration, 101 
Fluorescence, 136, 138 
Fluorescent characteristic x-rays, 

95 

Fluorescent screen, 36 
Fluoroscopy, 112 
Focal spot, 19 
Foils, rolled, 379 

heat treatment of, 389 
Formaldehyde, polymerized, 438 
Fourier series anah'sis of structure 

factor, 216 
Frequency law in Bohr theory, 73 

G 

Gage, uniformity of, 106 

7-rays, 6, 129 

Gases, scattering by, 100 

Gelatin, 456 

Gems, 256 

Genetics, and x-rays, 154 

Glass, coloration of, 151 

structure of, 344, 429 
Goldschmidt law for ionic crystals, 

268 

Gnomonic projections, 220 
Grains, orientation of, 351 

size of, 336, 346 
Graphite, 308 
Gratings, 49, 50 
Gutta percha, 450 

H 

Hafnium, 69 

Hair, 453 

Hardness, of alloys, 300 

of crystals, 272 

of x-rays, 14 
Heat treatment, x-ray analysis of, 

389 

Hcteropolar combination, 262 
Heusler alloys, 304 
Hexamethylbenzene, 311 
Hexamethylenetetramine, 317 
Homopolar combination, 263 



466 



APPLIED X-RAYS 



Hydrates, identification of, 253 
Hydrogen atom, diffraction of, 7 
Hydrogen peroxide, decomposition 
of, 142 



I 



Illinium, 69 

Indices of lattice planes, 173 

Industrial diagnosis, 111 

Inhomogeneity, examination for, 107 

Inorganic compounds, structures of, 
245 

Insulin, 442 

Intensifying screens, 116, 138 

Intensity, measurement of, 160 
biological method, 166 
chemical method, 165 
coloration method, 166 
fluorescent method, 166 
heat method, 160 
ionization method, 161 
photographic method, 165 
selenium-cell method, 166 

Interfaces, molecular orientation at, 
332 

Interplanar spacirigs, calculation of, 
209 

Ion radii, 265 

Ionic combination, 262 

Ionic crystals, law of formation, 268 

Ionization by x-rays, 131, 161 

Ionization chambers, 164, 167, 190 

Ions, sizes and shapes, 265 

Iron, polymorphism of, 238 
reclaimed malleable, 413 
recrystaUization of, 394 
systematization of alloys of, 295 
white-fractured, 413 

Isomerism, 331 

Isomorphism, 271 



Jewel bearings, orientation of, 352 
K 

K series, 56, 59 
Kenotron, 42 
Ketones, 330 



L series, 56, 62 
Lattices, crystal, 52 

layer, 271 

space, 176 
Layer lines, 224 
Laue method, 185 
Laue patterns, 138 

gnomonic projection of, 220 

interpretation of, 218 

stereographic projection of, 219 
Laue spots, 336 
Lead, colloidal, 429 

as protection against x-rays, 104 
Liquid crystals, 436 
Liquids, diffraction by, 432 

effect of magnetic fields on, 437 
Lime, plasticity of, 257 
Lindemann glass, 34 
Lorcntz factor, 216 
Lubrication, 332 
Luminescence, excitation of, 136 
Lyman series, 68, 72 

M 

M series, 63 

Magnesium, plastic deformation of, 

380 

Magnetic field, molecular orienta- 
tion in, 437 
Magnetism, crystal structure and, 

^304 

Martensite, 299 
Masurium, 69 
Medical diagnosis, 108 
Mesomorphic states, 428 
Metal castings, radiographic diagno- 
sis of, 108 

Metal radiography, 119 
applications of, 124 
tubes for, 26 

Metallic combination, 264, 276, 277 
Metallurgy, applications of x-rays 

in, 388 

Metals, cold working of, 389 
colloidal, 429 
control of heat treatment of, 389 



Metals, deposition from solution, 387 

clectrodeposited, 385 

fatigue of, 420 

passive, 410 

structure and properties of, 275 
Metastability, effect of x-rays upon, 

152 

Methane derivatives, 315, 316 
Mica, 275 
Micelles, 444 
Microphotometer, 116 
Microscope, ultraviolet, 5 
Miller indices, 173 
Mineralogy, applications in, 254 
Minerals, coloration of, by x-rays, 

151 

Mixtures, determination of com- 
position, 106 
Molecular form, 330 
Molecular orientation, 332 
Molecular weight, 331 
Molecules, arrangement of, 211 
Momentum law in Bohr theory, 72 
Monochromatic pinholc method, 228 
Monochromatic x-rays, 66 
Morphotropism, 271 
Moseley law, 67, 69, 78 
Multiple-diffraction apparatus, 207 
Muscle, 459 



N 



N series, 63 

Naphthalene, crystal structure of, 

309, 313 

Nematic state, 428 
Neumann bands in ferrite, 410 



O 



Orbits, electron, 73 
Organic compounds, crystal analy- 
sis of, 314 

highly polymerized, 438 

substituted radicals in, 314 
Orientation, of fibers, 375 

of grains, 351 

molecular, 332 

preferred, in sheets, 379, 385 



Orientation, surface film, 332, 437 
Oscillation patterns, 222 



Paintings, radiographic examination 

of, 127 

Paracrystalline state, 428 
Paraffin hydrocarbons, 37, 321 
Paraffin wax, 324 
Particle size, in colloids, 336, 441 

in microscopic, range, 346 
Paschen series, 72 
Pearlite, 298 
Pearls, 256 

Penetrometcr, Benoist, 103 
Pentaerythritol, 315 
Permutites, 255 
Phosphate rock, 255 
Photochemistry, 1 40 
Photographic effect of x-rays, 143 
Photolysis of KNO 3 , 147 
Photon, 7 

Physical effects of x-rays, 131 
Pigments, 429 

Planck action constant, 7, 73 
Planck-Einstein quantum equation, 

53 

Plating, gold, 420 
Point groups, 179 
Polarization, 263 
Polymerized materials, 438 

results of x-ray investigations on, 

444 

Polymorphism, 271, 327, 331 
Porosity, 107 

Potassium nitrate, photolysis of, 147 
Potassium persulfate, decomposition 

of, 142 

Potentials, critical excitation, 76 
Powder spectra, interpretation of, 

226 

Powders, diffraction by, 199 
Properties, prediction of, 272 

of x-rays, 10 

Protection from x-rays, 104 
Proteins, 451 

effect of reagents on, 456 

of tension on, 454 
Purple of Cassius, 253 



468 



APPLIED X-RAYS 



Q 

(Qualitative analysis, 86 
Quality, measurement of, 103 
Quantitative analysis, 86 
Quantum theory, 7, 79 

R 

r unit, 163 

Radii, atomic, 234 

ionic, 266 
Radiography, 108 

applications of, 125 

cost of, 128 

industrial diagnosis by, 111 

medical diagnosis by, 108 

tubes for, 26 

use of x-rays in, 129 
Railroad equipment for x-ray test- 
ing, 122 

Rails, diffraction research on, 421 
Rayon, 445 
Rays, 0, 98 

cathode, 3, 9 

cosmic, 4, 6 

electric, 6 

7, 6, 129 

grenz, 38 

Hertzian, 6 

radio, 6 

Roentgen, 3 

ultraviolet, 6 

visible, 6 

Reactions, chemical, 38, 253, 332 
Reerystallizat ion, of aluminum 
sheet, 390 

change of temperature of, with im- 
purities, 392 

of copper, 394 

of iron, 394 

of silver, 390 

of silver-copper alloy, 395 

of wires, 397 
Rectifiers, 41, 42, 43 
Refractories, 257 
Regulator, gas pressure for gas 

tubes, 17 
Resistor ribbon, 413 



Rhenium, 69 

Richardson equation, 19 

Roentgen rays, 3 

Rolling, effect on texture, 403 

Rotation method, 195 

Rotation pattern, 222 

Rubber, 449 

Rydberg constant, 68, 70, 75 

8 

Scattering of x-rays, 91 

Shock-proof equipment, 48 

Silicates, structure of, 273 

Silk fibroin, 451 

Silver, recrystalli/ation of, 390 

Silver-copper alloy, recrystalliza- 

tion of, 395 
Smectie state, 428 
Soaps, 330 
Solid solution, 289 
Solid state of matter, 171 
Solutions, colloidal, 431 
Sorbite, 298 
Space groups, 179 
Space lattices, 176 
Spacmgs, calculation of, 209 
Spectra, absorption, 56, 57 

chemical analysis from, 82 

continuous, 52 

crystals for, 49, 50 

emission, 55, 57, 59 
K series, 59 
L series, (52 
M and N series, 63 

powder, 226 

ruled grating, 51 
Spectrograph, 82 

Seemann, 84 

Siegbahn, 87 

slit less, 197 

wedge, 197 
Spectrometer, double, 66 

ionization, 190 

Spectroscopy, of soft x-rays, 332 
Spinels, 254 
Starch, 432 
Steel, 296 

alloy, 303 



INDEX 



469 



Steel, bending of, 413 

forming of, 410 

quench structure of, 420 

rolled, 373 

silicon, 400 

temper structure of, 420 

twisting of, 413 
Stereographic project ion, 219 
Storage buttery, high voltage, 40 

structure of plates of, 253 
Strain internal, 352 
Structural formula, testing of, 331 
Structure factor, 100, 211 
Sugar crystal, change of, with heat, 

37 

Sugars, 318 

Sulfur, conductivity of, 134 
Sulfur trioxide, transformations of, 

152 

Superstructure alloys, 281 
Surfaces, molecular orientation at, 

332, 437 
Symmetry, elements of, 100, 211 



Tangent drop method, 320 
Tannin, 432 
Targets, cone, 29 

magnesium, 38 
Tartaric acids, 317 
Tendons, 456 
Textiles, 444, 451, 453 
Therapy, deep, 157 

superficial, 38 

Thickness, determination of, 106 
Thiourea, 316 
Tin, single crystal of, 175 
Tissues, 38, 456, 459 

effect of x-rays on, 155 
Tolerance dose, 105 
Transformers, 41 
Troostite, 298 
Tubes, autofocus, 29 

Coolidge, 18,32, 111, 204 

cross-focus, 33 

demountable, 34 

diagnostic, 26 

diffraction, 31 



Tubes, deep therapy, 20 

dofok, 27 

electron, 12, 18 

gas, 12 

Hadding-Siegbahn, 14 

helium filled, 30 

high intensity, 35 

ion, 12 

Lange and Braseh, 25, 53 

Lauritsen, 25 

Leiss, 15 

life of, 21, 23 

line filament, 28, 33 

long wave, 38 

manufacturers of, 13, 20 

metal radiograph ic, 26 

Metalix, 22, 29, 42, 111, 204 

Mtiller, 21, 30, 33 

neon filled, 30 

Ott-Selmayr, 34 

Philips, 21 

rotating anode, 29 

self-shielding, 29 

Seernann, 15, 36 

Shearer, 16 

Siemens-Pantix, 24 

special, for very high voltages, 23 

Tuve, 25 

Westinghousc gun-typo, 31 

Wyckoff-Lagsdin, 16 

XP, 29, 30 
Tungsten, contact points, 429 

filaments, 19 

U 

Ultramarines, 255 
Urea, 316 



Vacuum, Coolidge, 18 

Valence, and x-ray spectra, 64 

Valence electrons in alloys, 292, 294 

Valence forces, 264 

Vegard law of additivity, 280 

Vitrain, 431 

Voltage, measurement of, 46 



470 



APPLIED X-RAYS 



W 

Water, association of, 436 

diffraction by, 436 
Wave lengthy measurements of, 58, 

63 

Weissenberg goniometer, 198, 225 
Welds, soundness of, 122 

structure of, 408 

Wires, deformation structures in, 
370 

effect of constitution on behavior 
of, 413 

fiber structure in, 365 

reerystallization of, 397 

zonal structure of, 367 
Wood, 446 
Wool, 37, 453 



X-rays, biological effects of, 153 

chemical effects of, 139 

effect on tissues, 155 

generation of, 10 

and genetics, 154 

ionization by, 131 

monochromatic, 66 

photographic effect of, 143 

physical effects of, 131 

properties of, 3, 10 

protection from, 104 
X-unit, 6 

Z 

Zeolites, 255 

Zinc, plastic deformation of, 380 

Zonal structure in wires, 3(57