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Full text of "Effects of crystallographic transformations on the photoelectric emission from uranium"

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B. S., Kansas State College 
of Agriculture and Applied Science, 1956 


submitted in partial fulfillment of the 

requirements for the degree 


Department of Physics 







Experimental Tube . 

High Vacuum System 

Radiation Source . . 

Current Measurement 








In 1905, (W) and 1906, (15) Einstein applied the quantum 
theory to photoelectricity, obtaining his famous equation, 

E " h-r- ^ , 

where E « kinetic energy of emitted electron, 
h « Plank's constant, 

tTb frequency of radiation incident upon surface, and 
^= work function of the emitting surface. 
Einstein's equation supplied a direct connection between the 
photoelectric effect and the quantum theory of radiation. 

However, Einstein's equation neglects the energy of the 
electrons within the metal. A more accurate equation would be 

B - hv + Eg - ^ , 
where E^ is the surface directed kinetic energy of the electron 
within the metal before its excitation by a photon. Thus, 
classically, an electron would be emitted photoelectrically if 

hv + Eg - ^ > 0. 

In 1928, Sommerfeld (18) derived, by use of quantum sta- 
tistics, an expression for the energy distribution of unbound 
electrons in metals by assuming the electrons behaved as a 
highly degenerate Fermi gas. These unbound electrons were 
assumed to be free of the crystal lattice (except for the poten- 
tial barrier at the surface of the metal) and exchanged energy 
with each other by elastic collision. Sommerfeld' s theory has 
been highly successful in explaining various physical properties 
of metals associated with the unbound electrons. 

Fowler (16), using Sommerf eld' s theory as a basis, de- 
veloped a graphical method by which the work function of a 
metal can be determined from photoelectric data. Fowler 
assumed : 

(1) Unboxind electrons in metals have an energy distri- 
bution given by the theory of Sommerf eld. 

(2) The transmission coefficient of the potential bar- 
rier at the surface of the metal is unity for elec- 
trons with energy greater than the barrier height 
and zero for electrons with energy less than the 
barrier height. 

(5) The probability that an electron with energy E 7!±X1 
interact with a photon of frequency -y is constant 
for all electron energies and radiation frequencies 
near the threshold for emission. 

With these asstimptions the photoelectric current per unit 

light intensity is given by: 

where i = photocurrent per unit light intensity, 

P(E ) » Sommerfeld's distribution function for the num- 

i » o^P(Eg) dE 
hVp -h V 


ber of electrons with surface directed energy 
between E^ and E^ + dE , 

e e e 

cx = constant of proportionality, 
h-V;=4= work function of the metal, 
h = Plank's constant, and 

V « frequency of the incident radiation. 

By in-fcegration of the preceding equation, Fowler obtained 
log(i/T^) » B + P(x), where 

X «■ hV"" h]4 t k "being Boltzman's constant, 

i ■ photocurrent per unit light intensity, 

T « absolute temperature in degrees Kelvin, 

B = a constant which depends upon the density of unbound 
electrons within the metal and upon the probability 
of interaction between photons and electrons, and 

P(x) » a certain transcendental function. 

With this result Fowler suggested a graphical method for 
obtaining the work fuaction of a metal from experimental data 
of emission per -unit light intensity at various wave lengths 
near the threshold frequency taken at Ecme constant temperature. 
His suggestion was this: If log(i/T^) is plotted versus hV, 
the result should be a curve of the same shape as the theoret- 
ical curve of F(x) versus x. If the ordinate of the experi- 
mental curve is raised by an amount B, and its abcissa shifted 

^V^i the experimental curve should coincide with the theo- 
retical curve. The amount by which the abcissa of the exper- 
imental curve is shifted to bring it into coincidence with the 
theoretical curve would then be the photoelectric work function 
of the metal divided by the product of Boltzman's constant and 
the absolute temperature . 

However, Cardwell (6), (7), (8), (9), (10), (11), (12), 
and others, using the method of Fowler to analyze data taken on 


carefully outgassed metals which undergo allotropic crystal- 
lographic transformations have found that the photoelectric 
properties of these metals change significantly at crystal- 
lographic and/or magnetic transformation temperatures. 

Uranium is a metal that undergoes allotropic crystallo- 
graphic changes at about 665°C and 770°C. Below 665°C the 
crystal lattice is orthorhombic ; between 66$°C and 770°C, te- 
tragonal; and above 770°C» body centered cubic (Duwez, 15) • 
This thesis is primarily concerned with the changes, if any, 
in the photoelectric emission from uranium with change in crys- 
tal structure at the two transformation temperatures. 

The Fowler theory and method of analyzing photoelectric 
emission from metals, based on Sommerf eld's theory, does not 
accoiint for this effect; However, the Sommerf eld model as- 
sumes that the \inbound electrons in metals do not interact 
with the crystal lattice. It is indicated that, because of 
the above mentioned anomolous behavior, the Sommerf eld theory 
is only approximately correct and that a more accurate model 
which includes the interaction of electrons with the crystal 
lattice is needed to describe electronic behavior in metals. 

A second purpose of this thesis is to report on the high- 
vacuum techniques utilized in this ex]:eriment. High-vacuum 
technique is a valuable experimental tool and especially so in 
photoelectricity, as results are highly dependent upon whether 
the metallic surface is free of occluded gas. The techniques 
recently developed by Alpert and others (1), (2), (3), (4), will 

enable the author and other investigators to make subsequent 
photoelectric studies on uranium and other metals at pressures 
on the order of 10''''"^mm of mercury and perhaps lower. 


The measurements of photoelectric emission from uranium 
were made on an integrated system of apparatus, the components 
of which were mounted under and upon a metal and transite vac- 
uum table which was specially constructed for this purpose. 
The fore pump and oil diffusion pump were under the table as 
were the transformers to supply the current to heat the ura- 
nium specimen. Upon the table that part of the vacuum 
system which was baked out by means of ovens placed over the 
system. This part included the experimental tube, the ion 
gauge, the Alpert-type high-vacuum valve and the copper foil 
trap. Also on the table were the soiirce of monochromatic 
light and the various meters. A description of some of these 
components follows. 

Experimental Tube 

The glass experimental tube contained the urani;im spec- 
imen, which was a ribbon of normal urani\im metal approximately 
0.03 nim thick, 4 mm wide, and 12 cm long, suspended in a loop 
from the Kovar-tiingsten leads to which the specimen was spot 

welded. The several specimens used were supplied by the Atomic 
Energy Commission. 

A molybdenum collecting cylinder surrounded the uranium 
strip to catch the photoelectrons Twhich were accelerated from 
the uranium by a potential difference between the collector and 
epecinen of -155 volts. After being collected by the cylinder, 
the photoelectrons passed through a current measuring device to 

Radiation from the monochromator was focused upon the spec- 
imen through a quartz window in the experimental tube and an 
opening in the collecting cylinder. A. pyrex window was located 
on the opposite side of the eacperimental tube for observing the 
specimen with an optical pyrometer through another opening in 
the collecting cylinder, rhe cylinder could be rotated by 
msans of an external magnet so that the openings in the cylin- 
der were out of allignment with the windows in order to prevsat 
evaporation of the uranium onto the windows while heating the 
specimen to high temperatures during outgassing. 

A guard ring was placed above the collecting cylinder so 
that only those electrons emitted by the lower part of the spec- 
imen were collected by the cylinder. The tube was enclosed la 
a metal box for electrostatic shielding. 

High Vacuum System 

Using techniques recently developed by Alpert, et^ al. , 
pressures on the order of 10"*^^ mm of mercury were obtained. 


An oil diffusion pump of the type GF-25W, manufactured by Dis- 
tilation Products, Inc., was backed by a Welch Duo-seal mech- 
anical pump. Dow-Corning 705 pumping oil was used. Pressures 

of 2 X 10 mm of mercury were consistently attained, after 
thorough bake-out of the vacuum system by use of the diffusion 
pump only. 

A copper foil trap developed by Alpert (2) was used between 
the oil diffusion pump and the system to be evacuated to prevent 
contamination of the system by the diffusion p\imp oil. 

An Alpert-type metal high-vacuum valve (1), (2) manufactured 
by the Granville-Phillips Company, but of lower minimum conduc- 
tance than the Alpert valve (Bills and Allen, 4), was used to 
seal the system off from the diffusion pump in order to allow 
the ion gauge to further reduce the pressure within the system 
after the diffusion pump had reached its equilibrixim pressure. 

An Alpert ion gauge was used to measure the low pressures 
and also, as mentioned above, to evacuate the system beyond the 
range of the diffusion pump (1), (3). Previous ion gauges had a 
lower limit to the pressure which they could messure due to a 
residual cxirrent produced by the release of photo-electrons from 
the ion collector by the soft x-rays which were produced by the 
•Ifctron bombardment of the grid. The Alpert gauge extended the 
lower limit of ion gauges by using a fine wire for the collector 
and enclosing it within the grid, thereby reducing the solid 
angle subtended by the collector at the grid for the interception 
of x-rays produced at the grid. 


In conjiiaction with the ion gaiige an ion gauge power supply, 
constructed from instructions and a circiut diagram developed and 
furnished to the author by P. Malmberg and A. McCouhrey of the 
W«8tinghou8e Kesearch Laboratories , was used to regulate the 
emission current of the ion gauge and to furnish power for out* 
gajBsing the ionization gauge electrodes by electron bombardment. 

Hadiatlon Source 

The source of ultraviolet light was a high-pressure mercury 
arc. Light from the arc was focused by a quartss lens onto ths 
entrance slit of the Bausch and Lomb grating monochromator. A 
second quartz len*:- focused the emergent beam upon the uranium 
saatple through the quartz window in the experimental tube. The 
wave lengths used were chosen from characteristic lines produced 
by a mercury arc. 

Current Measureraent 

Collector current of the ion gauge was of the order of 10"*^^ 

amperes and the photoelectric emission current was of the order 
of lO""^^ amperss. To measiire these small ciirrents a Keithley 
model 410 ^JiBmrneter was used. This instrument is a high imped- 
ance vacuum tube voltmeter that measures the voltage across self- 
contained standard resistors. The scale reads current directly 
and the instrument is accurate bo within three percent. Teflon 


insulation and electrostatic shielding was used for all circuits 
carrying these minute currents. 


The system was baked out at 420°C by means of ovens placed 
over that part of system to be evacuated to ultra-high vacuum. 
This process was necesaary in order to remove the gases from "blie 
inner surface of the glass parts of the system. 

The uranium filament was outgassed with a conduction current 
which was slowly increased to seven amperes, at which current 
the specimen was at an extreme red heat. It has been found that 
excessive evaporation is prevented by outgassing for long periods 
of time at the lower temperatures aad increasing the temperature 

The collecting cylinder was outgassed by heating it to high 
temperatures with a high-frequency induction heater. 


After the high vacuum had been attained and outgassing of 
the filament and the collecting cylinder of the experimental tube 
achieved, monochromatic light of a p;iven wave length was focused 
upon the specimen. The emission current was then measured at 
various values of the uranium filament conduction cuxrent. These 
measurements were taken while increasing and decreasing the fil- 
ament cxirrent to check on the reproducibility of the data. The 


current due to photoelectric emission was obtained by subtracting 
the thermionic emission current from the total emission current 
readings. A graph was then m .de of photoemission versus fila- 
ment current at constant wave length. 


Measurements were made using half a dozen wave lengths, but 
those made first were prior to the achievement of desirable out- 
gassing conditions and these measarements were not reproducible, 
although the curves obtained from such measurements had the same 
general shape, i. e. , changes in emission occured at the saaw 
heating currents, as those taken during the latter stages of ths 
experiment . 

Figure 1 is a graph of photoemission versus filament current 
for the 2552 A° and the 2302 A° lines of the mercury spectrum. 
It will be noted that; 

(1) The data is reproducible. 

(2) There is a hysteresis in the curves.^ 

(3) Sharp changes in photoemission occur at two 

places in the emission current versus heater 


current curves. 


i?i J f®^ explained as being due to both the time 

its iLl'^flT^l'^ ""S^® ^^^^^"^ filament current chan^^e, and 
chL^e? crystallographic change behind the temperature 


The specimen temperatures at these two filament currents are 
indicated on the graph. t-uirem^s are 
































Th«Be measurements strongly Indicate that the photoelectric 
•alSBion from uranivun changes markedly at the two transformation 
temperatures. The change in photocurrent with crystal stracture 
could be due to a change in the work-function, a change in the 
reflectivity of the uranium, or a variation of the quantum effi- 
ciency with crystal structure, or some combination of all three. 

Further experiment is needed to determine which of the three 
possibilities accounts for the phenomenon: Measurement of the 
reflectivity of uranium at various temperatures could be madej 
analysis of photoelectric data by the method of ?owler would 
ascertain whether the work function changes or whether there is 
a change in quantum efficiency with crystal structure, or both. 

It was pointed out in the introduction to this thesis that 
taking into account the interaction of the electrons with the 
crystal lattice may be needed to explain this phenomenon. How- 
ever, Callen (5) has indicated th it electrostatic conditions at 
crystal surfaces is quite complicated due to tha dependence on 
the crystal plane involved, exchange and correlation effects 
between the electrons, and impurities within the crystal lattice. 
How these affect photoemission is not well understood quantita- 
tively. Further investigation is needed to resolve the problem. 



Appreciation Is expressed to Dr. A. fi, Cardwell, iiead, 
Department of Phyeice, for his experienced advice and helpful 
criticisms during the progress of this experiment and his help 
in the preparation of this paper. 

Acknowledgment is also made to the national i;^^cience Foun-> 
dation for supplying the funds needed to carry out this work, 
to the Atomic 'energy Commission for supplying the uranium spec- 
imens, and to ?. R, Malmberg and A. 0. UcCoubrey of the 'Nesting- 
house Research Laboratories for supplying the circuit diagram, 
instruction and photographs from which the ion gauge power 
supply was constructed. Appreciation is expressed to Dr. Robert 
Katz of the Department of Physics for his helpful advice. 


(1) Alport, 0. 

iTew developments in the production and measurement 
of ultra-high vacuum. J. Appl. Phye., 24: 860-876. 
July, 1953. 


^erimentB at very low presauras. Science 122 1 
729-755. Oct., 1955. 

(5) Bayard, P. and D. Alpert 

Extension of the low pressure range of the ionization 
gauge. Rev. £ci. Inst., 21: 571-572. June, 1950. 

W Bills, D. and F. Allen 

Ultra-high vacuum valve. Rev. Sci. Inst., 26: 654- 
656. July, 1955. 

(5) Callen, E. 

Electrostatic potential in crystals. Am. J. Phys.. 
25: 158-149. March, 1957. 

(6) Cardwell, A. B. 

The photoelectric and thermionic properties of iron. 
Natl. Acad Sci. Proc, 14: 459-445. June, 1928. 

(7) ^ 

Effects of a crystal lographic transformation on the 
photoelectric and thermionic emission from cobalt. 
Natl, Acad. £ci. rtoc, 15: 544-551, July, 1929. 



oelectric and thermionic omission from cobalt. 
Hjys. Rev., 58 : 2055-2040. Dec, I95I. 

TF^Sff^'J^^*^ properties of tantalum. Fhya, Rev,, 
38: 2041-2048. Dec., 1951. ' 

"TEer^onic properties of tantalum, ^hys Rev., 47: 
628-630. April, 1955. 

The photoelectric and thermionic properties of 
nickel. Phys. Rev., 76: 125-127. July, 1949. 


(15) Duwez, P. 

The effect of the rate of cooling on the allotropic 
transformation temperatures of uranium. J. Appl. 
Phys., 24: 152-156. Pehr. , 1955- 

(14) Mnstein, A. 

Generation and transformation of light. Ann. der 
Phys. (Leipzig), 1?: 152-148. June, 1905- 

(15) _ 

Li.p;ht generation and absorption. Ann. der Phys. 
(Leipzig), 20: 199-206. May, 1906. 

(16) Fowler, R. H, 

The analysis of photoelectric sensitivity curves for 
clean metals at various temperatures. Phys. Rev., 
58: 45-56. July, 1951. 

(17) Rauh, E. 

Work function, ionization potential and emissivity 
of uranium. Argonne Nat'l Laboratory, ANL-5554. 
21p. May, 1956. 

(18) Sommerfeld, A. 

Zur Elektronentheorie der Metalle auf Grund der Permis- 
chen Statistik. Ztschr. f. Phys., 47: 1-60. Feb., 1928. 



B. s., Kansas State Collega 
of Agricultiire and Applied Eclence, 1956 

snbrnitted in partial fulfillment of the 
requirements for the degree 

Departaient of rhysios 



The theory of photoelectric emiBsion from a metallic sur- 
face is reviewed. It is pointed out that the theory due to 
Einstein, Fommerfeld, Fowler, et. al. , accounts for a smoothly 
varying dependence upon temperature of photoemission from metals 
and does not account for abrupt changes in photoemission exhib- 
ited by various metals at crystallographic transformation temp- 

A description is given in some detail of the experimental 
apparatus and the high-vacuum techniques employed. 

Mtoasureoents were made of photoemission from uranium at 
various temperatures at constant wave lengths. It was found 
that photoemission changed markedly at approximately the two 
tenrperatxires at which uranium undergoes allotropic cry&tallo- 
graphic transformations. 

Possible effects causing the phenomenon are listed with 
an indication of the subsequent experiments necessary to deter- 
mizM which effect is responsible. It is noted that taking into 
account the interaction of the electrons with the crystal lat- 
tice may be needed to explain changes in photoelectric emission 
with crystallographic transformations.