EFFECTS OF CRYSTALLOGRAPHIC TRANSFORMATIONS ON THE PHOTOELECTRIC EMISSION FROM URANIUM by RICHARD KENT FRY B. S., Kansas State College of Agriculture and Applied Science, 1956 A THESIS submitted in partial fulfillment of the requirements for the degree MASTER OF SCIENCE Department of Physics KANSAS STATE COLLEGE OF AGRICULTURE AND APPLIED SCIENCE 1958 LP TABLE OP CONTl^NTS INTRODUCTION EXPERIMENTAL APPARATUS . Experimental Tube . High Vacuum System Radiation Source . . Current Measurement OUTGASSING PROCESS EXPERIMENTAL PROCEDURE . EXPERIMENTAL RESULTS ... CONCLUSION ACKNOWLEDGEMENT LITERATURE CITED INTRODUCTION V 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 e 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 4 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. EXPSRIIJENTAL APPARATUS 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 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 ground. 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. 7 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 —8 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. 8 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 9 insulation and electrostatic shielding was used for all circuits carrying these minute currents. OUTGASSING PROCESS 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 slowly. The collecting cylinder was outgassed by heating it to high temperatures with a high-frequency induction heater. EXPERIMKNTAL PROCEDURE 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 10 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. SXPSfillQDnBiL &SSULT& 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 2 current curves. 1 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 2 The specimen temperatures at these two filament currents are indicated on the graph. t-uirem^s are !! }} II O U O its o o g 4* (« o I 1 2 V4 o a o ti 4* O a 3 S 1 (« O II 4* i 12 CONCLUSION 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. 15 ACKNOWLBDGMFOT? 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. LITERATUEE CITT^D (1) Alport, 0. iTew developments in the production and measurement of ultra-high vacuum. J. Appl. Phye., 24: 860-876. July, 1953. (2) ^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. (8) (9) (10) (11) (12) 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 (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. 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 1958 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- eratures. 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.