EFFECTS OF CRYSTALLOGRAPHIC TRANSFORMATIONS
ON THE PHOTOELECTRIC EMISSION FROM URANIUM
RICHARD KENT FRY
B. S., Kansas State College
of Agriculture and Applied Science, 1956
submitted in partial fulfillment of the
requirements for the degree
MASTER OF SCIENCE
Department of Physics
KANSAS STATE COLLEGE
OF AGRICULTURE AND APPLIED SCIENCE
TABLE OP CONTl^NTS
EXPERIMENTAL APPARATUS .
Experimental Tube .
High Vacuum System
Radiation Source . .
EXPERIMENTAL PROCEDURE .
EXPERIMENTAL RESULTS ...
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
(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
(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 v.as 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
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
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
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.
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.
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
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
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.
^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.
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-
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
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(17) Rauh, E.
Work function, ionization potential and emissivity
of uranium. Argonne Nat'l Laboratory, ANL-5554.
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IFFEOTS OF CEYETALLOGRAPnIC TRAN6P0RMATI0NB
ON THE PHOTOELECTRIC FJIISSION FROM URANIUM
RICHARD KENT FRT
B. s., Kansas State Collega
of Agricultiire and Applied Eclence, 1956
AN ABSTRACT OF A THESIS
snbrnitted in partial fulfillment of the
requirements for the degree
MASTER OF SCIENCE
Departaient of rhysios
KANSAS STATE COLLEGE
OF AGRICULTURE AND APPLIED SCIENCE
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-
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.