EFFECT OF ISGTQPIC COMPOSITIQN GM INFRARED ABSORPTION OF THIN FELMS OF LITHIUM FLUOMDE AND LITHIUM HYDRIDE Thosis éor Fm Dogma asf Fix. 5). MECHlGAN STATE UNIVERSETY Ramzzi Hanna Misha E95? '— lllflllifllllWQHWIIIWTUHW 3123 01743 0376 This is to certify that the thesis entitled Effect of Isotopic Composition on Infrared Absorption of Thin Films of Lithium Fluoride and Lithium Hydride presented by Ramzi Hanna Misho has been accepted towards fulfillment of the requirements for Elan—degree tum OJ Mm Major pvolesso D. J. Montgomery 1);.th 1 0-169 LIBRARY Michigan State University ABSTRACT EFFECT OF ISOTOPIC COMPOSITION ON INFRARED ABSORPTION OF THIN FILMS OF LITHIUM FLUORIDE AND LITHIUM HYDRIDE by Ramzi Hanna Misho The interaction of electromagnetic radiation with crystalline latticesis studied by observing the absorption of far-infrared radiation in thin films of certain simple substances evaporated on various sub- strates. To elucidate the nature of lattice vibrations, the isotopic composition of the absorbing substance is varied. The substances studied are lithium fluoride made from varying proportions of Li . . . . . l9 . . . and L1 in combination Wlth F , and lithium hydride made from . . .6 .7 . . . . 1 varying proportions of L1 and L1 in comblnation w1th H and H . The substrates are polyethylene, potassium bromide, and cesium bromide. Observations are made in the wavelength region 10-40 . . o o 0 microns, and at film temperatures of 300 K, 200 K, and 120 K. Each resulting spectrum is inspected for a principal absorption line and for subsidiary lines. The shape of the principal line is examined, and the variation of the parameters characterizing it, are studied with respect to isotopic composition, temperature, and nature of the substrate. Ramzi Hanna Misho So far as dependence on isotopic mass is concerned, the position of maximum absorption for isotopically-pure LiF and LiH follows quantitatively the predictions of the elementary portion of the Born theory, namely, that the dispersion wavelength is pro- portional to the square root of the reduced mass. The positions of . . . . . . 19 . the absorption max1ma for isotopically-1mpure L1F are 1nter- . .6 l9 .7 19 . med1ate between those for pure L1 F and L1 F , and are 1n agreement with the elementary Born theory if the average isotopic masses are used. The positions of the absorption maxima for iso- topically-impure LiH do not follow any simple law. So far as dependence on temperature is concerned, the dispersion wavelengths . . . . . .6 1 for pure and 1mpure L1F and L1H--w1th the except1on of L1 H and .7 1 . . . L1 H --decrease shghtly w1th decreas1ng temperature, as would be expected theoretically. The absorption bands of all the pure and impure LiF and LiH become deeper and narrower with decreasing temperature, in qualitative agreement with theory. The effect of substrate, though not pronounced, is complicated and difficult to understand. We may conclude generally that although the main features of the interaction of electromagnetic radiation with crystal- line lattices are understood, most of the details cannot be predicted quantitatively, and great improvement in the theory is needed. EFFECT OF ISOTOPIC COMPOSITION ON INFRARED ABSORPTION OF THIN FILMS OF LITHIUM FLUORIDE AND LITHIUM HYDRIDE BY RA MZI HANNA MISHO A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOC TOR OF PHILOSOPHY Department of Physics and Astronomy 1961 I. "\ ‘v ‘5‘ N ii ACKNOW LEDG MEN TS I would like to express my deep appreciation to Professor D. J. Montgomery for suggesting the problem investigated in this thesis and for his constant counsel and guidance during the four years I spent on the campus of Michigan State University. His insight, broad perspective, understanding, and patience have always been a source of encouragement. My sincere appreciation and thanks go to: Mr. Kwok Fai Yeung who did most of the calculations and helped in the experimental work; Mr. Charles Kingston and his technical staff for building the low- temperature cells and rebuilding the evaporator; Dr. Harry Eick of the Department of Chemistry for the use of a dry box and other equipment; Miss Suzan Langham for weighing and mixing the various composi- tions used in the experiment. Major financial support for this work was provided by the U. 5. Air Force Office of Scientific Research. The project was initiated with the help of an All-University Research Grant from Michigan State University and was continued through support from the U. S. Atomic Energy Commission. This help is gratefully acknowledged. Chapter II. III. IV. REFERENCES CITED TABLE OF CONTENTS INTRODUCTION ............................ Statement of Pr oblem THEORETICAL OBSERVATIONS ............. EXPERIMENTAL TECHNIQUE ............... A. Apparatus B. Film Preparation C. Temperature Measurement EXPERIMENTAL RESULTS ................. A. Lithium Fluoride B. Lithium Hydride DISCUSSION OF EXPERIMENTAL RESULTS ........ A. Dispersion Wavelength x0 = ch/wo B. Damping Constant y/wo iii Page 10 2.3 23 29 35 37 37 63 81 81 85 93 iv LIST OF TABLES Table Page . . . l9 . 1. Composuions of LiF and their reduced masses . . . . 52 . . 19 . . 2. Value of v/wo for the various L1F composuions . . . . 62 3. Compositions of LiH, their average reduced masses and their dispersion wavelengths .................. 69 4. Effect of isotopic mass on infrared dispersion wavelength ...................................... 82 5. Effect of isotopic composition on dispersion wave- 6+XF19 ............................... length for Li 84 Figure 18-19. 20-21. 22. 23. 24. LIST OF FIGURES Schematic version of infrared spectrum for a thin absorbing film .................................... General View of apparatus ......................... Cut-away view of the low-temperature sample holder . . Detailed sectional view of the sample holder ......... Stray-radiation run ............................... Atmospheric-absorption run ....................... . . . . 19 Infrared absorption spectra of thin films of LiF containing varying proportions of LiéF19 and Li7F19 as indicated on individual figures. Temperature, 300° K; substrate, polyethylene sheet ............... . . . . 19 Infrared absorption spectra of thin films of LiF containing 30% L16F - 70% Li7F (Figure 18) and 70% L16F - 30% Li7F (Figure 19). Temperatures, 300% and 2000K; substrate, polyethylene ................. Infrared absorption spectra of thin films of LiF19 containing 30% Li6F - 70% MM“ (Figure 20) and 70% Li6F — 30% Li7F (Figure 21). Temperatures, 3000K and 1200K; substrate, polyethylene ................. . . . 1 . Infrared disper51on wavelength for L1F 9 films evaporated onto sesium-bromide substrate, as a function of isotopic composition x. Temperature: 300° K and 1200K ................................ Infrared dispersion wavelength for LiF19 films evaporated onto polyethylene substrate, as a function of isotopic composition x. Temperatures: 3000K, 2000K, and 120°K ................................ Separation of main absorption peak from minor ones, for spectrum of Li6F19 film deposited onto polyethylene substrate. Temperature: 2000K ................... Page 16 25 26 27 38 39 40-50 53-54 55-56 58 59 61 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. Lines of equal reduced mass for lithium hydride made of varying proportions of L16, L17 and H1, HZ . ........ 7 1 Infrared absorption spectrum of Li H film evaporated onto KBr substrate. Temperatures: 3009K, 1200K . . . . 7 2 Infrared absorption spectrum of Li H film evaporated onto KBr substrate. Temperatures: 3000K, 1200K . . Infrared absorption spectrum of Li7Hl film, on which is superimposed the spectrum of Li7H2 with abscissa multiplied by square root of reduced masses. Sub- strate: KBr; temperature, 300°K .................. Infrared absorption spectrum of Li7H1 film on which is superimposed the spectrum of Li7H‘2 with abscissa multiplied by square root of reduced masses. Sub- strate: KBr; temperature, 1200K . ............... 7 1 Infrared absorption spectrum of Li H evaporated onto KBr substrate. Temperatures: 1250K, 1770K, 2349K, and 3180K ......................................... 7 Infrared absorption spectra of Li H1 evaporated onto KBr substrate. Temperatures: 3100K, 3570K, 4000K, and 4400K ..................................... . . . 1 Infrared absorption spectrum of Li6H film evaporated onto polyethylene substrate, after reaction with atmos- phere. Temperatures: 3009K, 120°K ............... 7 Infrared absorption spectrum of Li H1 film evaporated onto polyethylene substrate, after reaction with atmos— phere. Temperatures: 3000K, 1200K ................ 1 2 Plot of (X+>\_) / as a function of transmission T for a spectrum of Li7H1 evaporated onto KBr substrate. Temperature: 1200K .............................. Separation of main absorption peak from minor ones, for spectrum of Li7H film deposited on KBr substrate. Temperature: 1200K. .............................. )‘o X 2 Plot of (T - T) as a function of l T-T ' T - T . o 0 min spectrum of Li-IH1 evaporated onto KBr substrate. Temperature: 1200 K. .............................. vi 64 66 67 68 71 72 73 75 76 78 79 80 37. 38. 39. 40. Dependence of infrared dispersion wavelength on absolute temperature for LiF1 films of various isotopic compositions evaporated onto CsBr and onto polyethylene ................................. Dependence of infrared dispersion wavelength on absolute temperature for LiH and LiD films eva- porated onto KBr ................................. Plot of y/wo against isotopic compositions for Lil“19 evaporated onto polyethylene and recorded at 3000K . . . Variation of y with absolute temperature for Li7F19 film evaporated onto polyethylene substrate ........... 86 87 90 91 I. INTRODUCTION This thesis deals with the interaction of electromagnetic radiation with the solid crystalline phase. Every substance has its own characteristic spectrum, possessing selective absorption at certain frequencies in the spectrum. The spectral characteristics are determined by the atomic masses, the configuration in space, and the binding forces present. Around 1950, relatively large amounts of stable isotopes became available, and it became possible to utilize these substances in the study of bulk properties of matter. By use of isotopes of the same element, the atomic mass can be changed while the atomic force field is kept the same. The depen- dence of physical properties on the mass is usually simple, whereas the dependence of force field is very complicated. Hence, one may sometimes make comparisons between isotopes of the same element when it is not practical between different elements. The character- istic energy of the far infrared radiation matches that of the lattice vibrations, and therefore depends in the first order on isotopic mass. A program using the isotopic mass as a probe for the study of the physical properties of matter was started a few years ago in our laboratory. The work described in this paper constitutes an exten- sion and refinement of this program. Besides using the isotopic mass as the only variable under consideration, one may also use the isotopic composition as another variable. A new type of phenomenon may be expected to appear if one uses a mixture of various propor- tions of the stable isotopes. Specific heat, electrical resistivity, infrared absorption spectrum and other phenomena depending on lattice vibration spectrum may all be expected to show modified behavior. In the experiments discussed in this paper, the isotopic mass is used as a probe to study the infrared absorption spectra of ionic and partially ionic crystals. The spectrophotometers available to us cover the region of the spectrum from 2 to nearly 40 microns. To get the frequency of vibrations high enough to bring the infrared absorption bands for lattice vibrations into accessible wave lengths, one has to use elements as light as possible, with binding forces as strong as possible. The alkali halides are excellent materials for study, because of their simple structure and high electric moment. One chooses lithium because it is light and because its isotopes Li and Li7 are readily obtainable and give large relative mass difference. The lightest halogen is fluorine; it has only one stable isotope, F19. Lithium fluoride, LiF, is a well known substance, and is easy to handle; but its characteristic absorption bands are beyond 30 microns, an inconvenient region of the spectrum. One then expects easy pre- paration and handling, but difficult observation. Lithium fluoride, like the other alkali halides, possesses ionic crystal structure. The optical properties of many of these alkali halides have been studied previously. These properties are governed, in the infrared region of the spectrum, primarily by the vibrations of the crystal lattice. In the literature the experimental results are compared with theories of lattice vibrations, and in many cases an explanation that is more or less plausible can be given. In an ionic crystal, ions may be assumed as being charged mass points intercon- nected by approximately harmonic forces. The fundamental optical mode of vibration of such a system has a simple dependence on the masses of the constituent ions. Besides the fundamental optical mode, the other secondary modes may exist which cannot be explained on the simple model described above. Several suggestions have been given in attempted explanation of the existence of these secondary modes. Lax and Burstein (1) suggested a possible deformation of the electron cloud about the atoms during lattice vibrations, leading to a second-order electric moment, and in turn to the appearance of auxiliary bands in the infrared absorption and reflection spectra of the ionic crystals. Barnes, Brattain, and Seitz (2) suggested that the secondary structure is due to the anharmonicity in the lattice vibrations. Szigeti (3) has combined both effects in a systematic general treatment of this model. Wallis and Maradudin (4) in a paper discussing the impurity-induced infrared absorption suggested that the presence of isotopic impurities in the crystal lattice leads to a broad absorption on the low-frequency side of the main maximum even when the harmonic approximation is made. Barnes (5) was the first to study experimentally the far-infrared absorption spectrum of natural LiF. He found that the absorption maximum is at a wave length of 32. 6 '1’ 0. 3 microns, with one side band in the 25 to 28 microns region and another in the 18 to 20 microns region. Stevenson and Nettley (6) studied the infrared transmission 6 7 limits and reflectivity of Li F19 and Li F19, and found that the 619 reflection measurements give peaks at 16. 7 microns for Li F , and at 15. 8 microns for Li7F19. The ratio of these wave lengths agrees with the simple theory. Other work has also been carried on by various investigators on the optical properties of natural and isotopically-enriched lithium fluoride at various temperatures and under different circumstances. For example, Heilman (7) measured the optical constants n and k for LiF in the region of the infrared reststrahlen band. Hohls (8) studied the dispersion and the absorp- tion of LiF in the infrared. Klier (9) studied the temperature depen- dence of the optical constants of LiF in the infrared. Hass and Ketelaar (10) measured the width of the infrared reflection bands of LiF and gave values for its dielectric constant, normal index of refraction, and dispersion wave length. Gottleib (11) studied the 6 19 optical properties of crystals of natural LiF, and of Li F and . 9 . L1 F at various temperatures. Montgomery and Misho reported briefly some results on the dispersion wave length for isotopically- mixed lithium fluoride. As mentioned earlier in this chapter, the characteristic absorption of lithium fluoride lies beyond 30 microns, a region where experiment is difficult. To bring the region of characteristic absorptions to more convenient wave lengths, one must either decrease the mass of the ions, or increase the binding force. One should restrict his choice to monovalent elements in order to keep simple structures. The Group-I elements have in their outer shell a single _s_-electron that can be easily removed. The Group-VII elements have two _s_-e1ectrons and five p-electrons that can easily take on an additional electron to form a closed shell. From this point of view, hydrogen may be considered to be either the lightest alkali metal or the lightest halogen, since its single _s_-electron may either be removed, or may take on another electron to form a closed shell consisting of a pair of l_s_-electrons. Thus we are led to con- sider the use of hydrogen fluoride or of lithium hydride as light "alkali halides. " Hydrogen fluoride does not crystallize as an ionic crystal but instead as a molecular crystal. Infrared spectroscopy will then yield information only about its intramolecular vibrations, rather than its lattice vibrations, the topic of interest in the present work. Therefore, we are left with lithium hydride, which forms a partially- ionic sodium-chloride structure. The isotopic proportions of both cation and anion can be varied. We use only Li6 and L17, and H and H2. But one could also use H3, despite its radioactivity, if there were really need for it. For the lightest lithium hydride (Li H1), the characteristic absorption band is around 17 microns, a region quite easy to work in. For the heaviest (nonradioactive) lithium hydride (Li7H2), the characteristic absorption is around 22. 5 microns, a region still much easier to work with than the 30- micron region characteristic of lithium fluoride. Therefore, use of the hydride gave us the great advantage of working in a much more accessible region of the spectrum. On the other hand, the use of the hydride presents several liabilities: theoretically, the hydride is not ionic; it seems to have high deformability of the charge clouds; its chemical behavior is in general more complicated than that of the true alkali halides; it is extremely reactive with water vapor; and thus in thin-film form, can react with the least amount of water vapor (and perhaps other substances) to produce a strong chemical transformation resulting in profound changes in the spectrum. Spectral bands due to the contamination by lithium hydroxide are then separated with difficulty from possible side bands occurring in the pure substance alone. It is possible, how- ever, by appropriate evaporating techniques and by variation of temperature to identify the various bands. The visible spectrum of gaseous lithium hydride was studied as early as 1925 (13) by Watson. The absorption and band spectra of gaseous LiH were studied by Nakamura (14) in 1929, and its molecular constants were calculated. The first work on the iso- topic shift of the band spectra of LiH and LiD was reported by F. H. Crawford and T. Jorgensen (15) in 1934. The infrared spec- trum of gaseous LiH was studied by Klemperer (16) in 1955, and the near-ultraviolet absorption spectrum of LiH and LiD was studied by Velasco (17) in 1957. Filler and Burstein (18) studied the infrared lattice vibration spectrum of natural lithium hydride. Their reflection spectra from single crystals in the range 2-50 microns showed strong peak in the region from 9 to about 18 microns with a minimum around 8 microns. The first infrared absorption spectrum of solid lithium hydride was obtained by Zimmerman (19), who worked with solid thin films of isotopically-pure LiH and LiD at room temperature. The characteristic absorption wave lengths were in agreement with the simple theory. Zimmerman also determined the infrared absorption spectra of thin films of L16H made up of different isotopic compositions with respect to hydrogen. No simple theoretical interpretation was possible. Besides LiF and LiH, there are of course other substances that could be used. Studies on compounds composing Group-II elements 24 in combination with Group-VI elements appear promising; Mg 0 2 and Mg 6O, for example, is a useful case. One of course can also 16 17 18 . . . get 0 , O and O , but their rare isotopes are much too expenswe in high purity. Other combinations of groups that would be of in- terest are Group-III, Group-V compounds. Here the isotopic pro- portion of the B+++ in combination with the anions N- , p and perhaps As--- could be varied. Elemental semi-conductors of Group-IV - Si, Ge, and perhaps C and Sn - could be studied also. However, sample preparation would be -more complicated and observations more difficult. Certain ternary compounds, for example, LiBH , CaCO 4 3, and certain other elements - for example, S or Se - and some organic compounds could also be considered. The study of crystalline acids and amides, where hydrogen bands are of great importance in determining the crystal structure, would be of particular interest. Moreover, certain hydrides of more complicated structures, for example, decaborane, B10Ml4 would seem to constitute extremely interesting subjects for further study. Statement of Problem 19 The infrared absorption spectra of thin films of Li6F and 7 1 Li F 9, and of films made up of different isotopic compositions of 19 7 l9 6 the Li F and Li F , and evaporated on two different substrates (polyethylene and cesium bromide), are obtained at three different temperatures (approximately 3000K, 2000K, 1200K). The infrared 6 l 6 2 7 l 7 2 absorption of Li H , Li H , Li H and Li H , and of films made up . . . . . .6 1 .6 Z .7 1 of different isotopic compOSitions of Li H and Li H and of Li H and .7 Z . Li H , and evaporated on three different substances (polyethylene, potassium bromide and cesium bromide), are obtained at two dif- ferent temperatures (approximately 3000K and 1200K). The measurements at low temperatures are made with the hope of identifying certain bands which may be due to contamination, or which may represent genuine side bands occurring in the original compounds. The resulting spectra are analyzed to see how isotopic mass affects the presence, shape, and position of absorption bands, and to see what light can be shed on the general mechanism of inter- action of electromagnetic radiation with lattice vibrations. 10 II. THEORETICAL OBSERVATIONS In this chapter, the derivation of the dispersion formula for a simple ionic crystal is reviewed, the transmission coefficient for a thin film is quoted, and a few of the theoretical results derived in Born and Huang (20) are analyzed and rewritten in a form suitable for the experimental results to be discussed subsequently. To derive the dispersion formula for an ionic crystal, we assume that the macroscopic theory is fully contained in the follow- ing pair of phenomenological equations: 1/2 6-6 .. _ o oo 2 ° V_V _( 411' ) (DO—E— - (00 W - YE .1 600- 1 60 - 600 2 E : 411 E. + 4-" (DOE Here W is the displacement of a positive ion relative to a negative one, multiplied by the square root of the reduced mass per unit volume; E, and E are the dielectric polarization and electric field as defined in Maxwell's equations; 60 is the low-frequency dielectric constant; 600 is the high-frequency dielectric constant; 000 is the circular infrared dispersion frequency. 11 To get the dispersion formula, one substitutes the following periodic solutions into the above equations: ) E: — —o -iwt P: > — —o W: - -o ’ 1 Weget: — 6-6 2 _ o oo 2 . -wW—(T) (JOE-(coo +1wY)W 6.0-1 .0400; E:( 411’ LE3” 4“) “0V1 Eliminating W from these two equations, (606 1) (60- 600) (002 E = 411' + 2 E ’ and comparing this result with Maxwell's equation, 2=§ + 4.3: 69 we obtain the dispersion formula: (6 -6) 6:6 + 20° .................... (1) 1431-) «(f—H311 O O O In the experiment described in the following chapters, the trans- mission of the infrared light through thin films of LiF and LiH is studied. An expression for the transmission of light of a given frequency is incident normally on a plate of thickness d is given by: 1 T : ...................... s. (2) 1 +1... (51;) (5*2 - 52) 12 where n2 is equal to E, the complex dielectric constant. From this expression one may show easily that for very thin films suspended in air, the minimum transmission occurs exactly at the dispersion frequency. The films studied in the experiment described in this paper are actually deposited on thick substrates. The reflectivity at the film-substrate surface is given by 12 , where n is the refractive index of the substrate and [(n-nll/(nml) 111 that of the film. A further loss by reflection occurs at the substrate-air boundary, where the reflectivity p is [(n-l)/(n+l)]2. The loss in transmitted intensity through reflection is approximately the sum of the losses at the two interfaces. For example the re- fractive index of LiF in the infrared is about 1. 4, for CsBr about 1. 6; here the losses by reflection amount to about 6%. The refractive index of LiH is about 1. 6, that of KBr is about 1. 5; if KBr is used as substrate for LiH film, about 4% of light intensity is lost. From equation (1) one can write: (e -e) ”00+ .3. °° , 00 1-(—) +1(——)(—3—) (L) (s) (A) O O O a d . 00 “ -21(——)(1-) 00 (0 .v. 0 0 er - c =(e -e) o oo 2 The expression for T can now be written as Z [1- (ii-)2] +(—‘i)2(—"—)‘Z (L) (.0 (O T = O 0 O 2 [1451?] + 6—?qu +‘-"§(§) (3)-L) (60- em) 0 O O O 0 We now make the following substitutions: k x 2 (5134—92 0 a .= (1&2 O 1r = (9H6 -e) a C 0 00 Y _ z = 5 (1 2+ L+x-(2-a) ThenT= ”’9 “X = X (l-x)2+ax+Bx %+X-(Z-a-B) We make the further substitutions: _ 1, Y - x X A =5 2 - a B = (3 and 1 - C = T ( -A) Then: 1 - C =—X——- y-(A-B) or: y = E + (B-A) l3 14 Equation (4) represents a straight line when y is plotted against 21?- , with slope m :3 419m - e) c o co and intercept 2 b=B_A:(-YE§)(€O-€OO)-2+(::(—) . 0 From these equations one can solve for the damping constant v: Y :onb-m-l-Z. .............................. (5) where 000 is determined from inspection of the absorption spectrum. Then b and m can be read directly from the plot of y vs. E. Rewriting equation 4, we find 2 __l__ _ (l-x) +ax+fix — 2. T (l-X) +ax 21+ ‘3 (—1-+x-Z+a) x XE _1+(c )(6 -€) w 0002 Y 2 (—-—w—)+(:— o o (igHeo-EOO) ‘l+ A 2 yx 2 x o o (T-T)+(21rc) 15 . 1 . . . . For max1mum -- T equals T , and minimum transmisSion I . . T minimum occurs at X = X0. Moreover, as denoted in Figure l, a schematic illustration of the course of the absorption, there are two wavelengths X+ and X for which the transmission has a given value T > T . . For - min each pair XX =X . ....................... . ..... (6) Equation 6 shows the symmetry of the absorption spectrum around X0, a fact which is of much help in the separation of the superimposed peaks. We once more rewrite equation (4) in the following form: 1 _ F3 T "1 + M + a where w 0 00 2 M = (-- - —) . w to o 1 T It is necessary to replace 71-,- by 1%?- where Too is defined as shown in figure 1, since there is other absorption besides the main one.( for an ideal case, where only the main absorption peak is T =1. present, 00 ) :o_o_ _[M+a+8] T — M+a and .uxou 05 5 Swim mw mHonflam .385 m5. mo mandamus o 33. . A fiwnoaoafima’ nommuommwp 05. um mazooo GofimmfiEmnmfl Edging .ox fiwcgofiw? $5de @93on ma .H. Cowmmwgmcmnu ofi whom .Efim mGBHOmnm 55 m 90m fish—00mm ponds?“ mo Commnoty oflmgmaom H szOHm u\.s‘ +K 0K 1‘ u\.K 00 1 W «All . . . _ _ lrll . _ _ . . . .Iu' _ — .h"ls'lulu'lllu4s' . . . _ _ {FIIIIIIIII Isl... ulllillllllulili _ _ _ _ _ illlliliiinluiliullinll Illl _ _ 4 l7 T 0013 T- 00 M=-(a+8)+ T 1 2'1‘000(T _T)-(a+s) .............................. (7) (1) Equation (7) represents a straight line plotted in the M, ————(T 1T) 00 plane with a slope T009 and an intercept (a+13). Here Too can be found directly from the spectrum. T008 and (a + )3) can be read directly from the plot of equation (7). The thickness d of the film can now be calculated, since _ vd _ .r— 8-(—-—)(€.-€)andv—w a. c o oo 0 Therefore (310 Y(€ - 6) o a) ZTTV—a-(60-6m) Of course this procedure provides in addition a means for calculating the damping constant )1. It is possible also to derive expressions for a and {3, and thus for y and d, using Tl/2 and Ml/Z as defined in figure 1, corresponding to A.“ Tl/2 = (1/2) (TOO + Tmin), OI‘ T1/2 :_1_ (1+ (1 ) T 2 (1+8 00 also +. T00 Ml/Z a Therefore X _ _ >\1/2 o 2 M1/2"1+f"(i 'T) 0 1/2 and Tmin ___ Ml/Z - 5 Too Ml/Z from which __ min fi— Ml/z (1" T )3 00 and T in 00 so that c8 : 6 .. d wova( 0 Eco) )‘o M1/2 (1' Tmin/ Too) T . 211 M .3119 - fl/Z '1‘00 (60 €00) l9 or : >\o (kl/2 >‘o ) (\( Too _ min (8) 217 (60- 600) X xl/Z Tmin T00 and X _ ZTTC 1/2 Y __{_ ( x - ................ . ....... (9) o o Here the quantities X0, )‘1/2’ Tmin and T00 can all be read directly from the spectrum; 60 and 600 are given in the literature. The preceding analysis provides a method for the measurement of the damping constant v and the film thickness d. In principle, it provides a method for separation of the main absorption peak from the minor side peaks. To get reasonable results, it is desirable that the spectrum be clean, and free from extraneous atmospheric absorption bands. Now all the spectra of lithium fluoride are recorded in the region 15 to 40 microns. The region from 24 to 40 microns is full of water absorption bands that interfere with the LiF spectrum and introduce inaccuracy in the true position of the minimum absorption. On the other hand, the spectra of lithium hydride are recorded in the region 10 to 28 microns. This region is relatively free of atmospheric absorption, but there is much trouble from spurious peaks due to lithium hydroxide and other compounds contaminating the film itself. Nevertheless, the above method of analysis is useful. 20 To study the behavior of the damping constant near the dispersion wavelength, we consider the equation: d 1 15(6’6) —T—:l+wo “2 Y2 (7.7-7.7) +1.".— 0 O The minimum value T , occurs at w = (.0 min 0 1 ——(€-€) T =1+ C o 2 min (1- CL) 0 (02 1 -1--2—-(-i-(€-€) T. y c 00 min and —(€-€oo) (ZTTC)2 V“ 1 1 >10 T. ' min If the spectra of the same film are recorded at two different tempera- tures (primed and unprimed) the ratio of v at these two temperatures will then be: 1 1' 2 TI , ' 1 l : 0 min Y' X 2 1 1 .............................. (10) o T , min To make comparisons with other measureable quantities, say the damping constant at the dispersion wavelength, and the product of the index of refraction n by the extinction coefficient k observed in other experiments, we use the dispersion formula equation (1) and the definition of the dielectric constant to get: to 2 2 2 (EO— €00)[1-(:’;) 1 n(1-k':€oo+ (022 w2 [1- (:7) 1 HF) (51) O O O 2 (e -e )(—Y)<——“’) 0 oo (0 (i) O O 2 2nk= 2 2 [1 - ($21 + (f—Fiwi) O O 0 If we write nk = k and put 00 = 000, we get 2 2 n -K =6 00 and (€-€)00 t an= =— Y where (60- 600) wo has been written as t for short. Solving these two 2 equations for k we get: 262 YCD 2 t i— 1+ 27 + N ngm Expanding the square root and neglecting higher order terms we get: 6 2 00 t 2 2v E (I) 2 + l t 1511—! The dominating term is we have 2 t k. as ZY or 2)( ; upon neglect of the other two terms, 22 23 III. EXPERIMENTAL TECHNIQUE A. Apparatus l. Spectrophotometers: Two infrared spectrophotometers are used in the experiment. The first is a Perkin-Elmer double-beam recording spectrophotometer, model 137 (”Infracord”) with potassium bromide optics covering the range 12. 5 to 25 microns. The second is a Perkin-Elmer double-beam spectrophotometer, model 21 with sodium chloride or cesium-bromide optics, covering the range of 2 to 40 microns. Both spectrophotometers have Nerst glowers as sources, and vacuum thermocouples as detectors. The model 137 is always used under the same settings, with fixed range, fixed recording speed, and fixed source intensity. There is only one automatic slit-width program; the slit can be controlled manually, however, if desired. The model 21 is a much more elaborate instrument. Prisms may be interchanged; a sodium- chloride prism is used for the region 2 to 15 microns, and a cesium- bromide prism for the region 15 to 38 microns. For the work reported in this thesis, only the cesium-bromide prism is used. The slit can be controlled manually, or operated with variable automatic programming. The recording speed and the pen speed can be changed over a wide range. The source intensity and the amplifier gain and damping can be varied to give the desired 24 sensitivity. The wave length scale of the spectrum can be adjusted by changing the gear ratio. The case can be purged with dry nitrogen gas to minimize the effect of atmospheric absorption. 2. Evaporator: The evaporator consists of three major parts: A diffusion oil pump, a cylindrical glass bell jar 12 inches in diameter and 18 inches long, and a cylindrical cold trap 14 inches in diameter and 7 inches long. The tube connecting the oil pump to the bell jar is 13/4 inches in diameter. The bell jar sits on a steel circular disc, 16 inches in diameter and 1 inch thick. Eight Kovar-seal leads pass through the plate. A rod that can be rotated from the outside, along with four other fixed rods used to hold the low-temperature cell, passes through the plate into the bell jar. The jar can be evacuated through the fore pump directly, with the diffusion pump shut off from the circuit. When the vacuum is around 25 microns, the bell jar is evacuated through the already hot oil, by the use of three vacuum valves. This procedure brings the pressure down to its lowest value in the shortest time. The vacuum in the evaporator is about 10"5 mm Hg. Figure 2 shows a general view of the evaporator and the apparatus. 3. Low-temperature cell: As shown in Figures 3 and 4, the low-temperature cell consists of an outside cylindrical brass tube 8 1/2 inches long and 4 inches in diameter. A vacuum valve is connected near its top. An inside cylindrical brass tube 4 inches Figure 2. General view of apparatus, showing the eva- porator at the center, the Model 137 spectrophotometer to the right, and the Model 21 spectrophotometer to the left. Figure 3. Cut-away view of the low-temperature sample holder. The inner portion has been raised to clarify details of the cover construction. Figure 4. Detailed sectional view of the sample holder. FIGURE 2 OOOOOOOOO PLE ENTRANCE HEATER-INLETs—x \ m ”(16) m L 11.1 .1. VGA UM VALVE MW f—rga‘n GA 8| IGN ._ LIQUI DA AIR NITA INER———_/ WI INDOW /E> ELL) 28 long and 3 inches in diameter is connected to a stainless steel tube 6 inches long and 1 1/2 inches in diameter. The openings of the windows on the outside cylinder are 1 1/2 inches in diameter and 1 1/4 inch in diameter, respectively. A brass tube 1 5/8 inches in diameter forms part of the sample holder, being soldered across the inner tube parallel to its base, to be surrounded by the cooling agent from all sides. This tube is threaded across half its length. A second tube threaded along its outer surface fits inside the sample tube, and presses a flat brass ring tight against a shoulder in the middle part of the sample tube. The outside surface of the ring is threaded. In the center is a hole 7/8 inches in diameter with a shoulder where the sample sits, in a pocket containing a heater wire. A cap threaded across its inside surface fits on the disc. To insure good thermal contact between the sample and the sample holder, a Small circular copper spring is placed above the sample and is pressed on by the cap. The leads of the thermocouple for meas- uring the temperatures of the sample and its surroundings are extended inside the cell through a tube on the top plate plugged by a Clipped rubber hose which is filled with vacuum grease to prevent air leakage. Two Kovar seals are soldered to the top plate of the Cell to provide electrical connections for the heater around the sam- ple, The window holders are designed to permit the use of different kinds of substrate (potassium bromide, polyethylene or cesium 29 bromide). The window sits on rubber O-rings and is held in place by a brass holder. The cell is designed to operate from liquid-air temperatures to temperatures as high as 400°C. A duplicate cell was built to provide compensation for the reference beam of the spectrophotometers. B. Film Preparation l. LiF. LiF is a stable compound with cubic NaCl structure, melting at 842°C and boiling at 1676°c. Its solubility in water at 18°C is 0.27 gram per 100 grams of water, and at 35°C is 0.135 grams per 100 grams of water. Separated isotopes of lithium in metallic form were supplied by the Oak Ridge National Laboratory. The metal was converted to fluoride by treating it with hydrofluoric acid. Small quantities of powdered fluoride were placed on a boat inside the bell jar of the evaporator. Each boat is made of a molybdenum sheet 3/8 inch wide, 2 inches long, and O. 003 inch thick. The boat is connected to the power supply through two of the Kovar leads. The substrate is placed 4 inches above the boat. Plates of cesium bromide 1 inch in diameter and 1/8 inch thick, and sheets of polyethylene 1 inch in diameter and O. 040 inch thick are used as substrates. As the powder is set for evaporation, air is pumped out of the bell jar through the fore pumps directly. When the pressure is around 25 microns, the bell jar is evacuated by means 30 of a diffusion pump. The pressure drops to around 10-4 mm in about 5 minutes. The boat is heated slightly for a few minutes, allowing it along with the powder to outgas. The current is now raised until the powder melts and evaporates. If an attempt is made to evaporate it without outgassing, it hops off the boat. During the early part of the evaporation, an aluminum shutter screens the substrate to prevent deposition of readily volatile impurities. The evaporation is continued until the films are of the order of O. 01 to 0. 10 microns thick. Films containing varying compositions of Li6F 9 and Li F19 are also evaporated. Samples of the different compositions were prepared using a precision balance and processed just like the iso- topically-pure specimens. 2. LiH: LiH is a reactive compound with cubic NaCl structure, melting at 6800C. It has a density of 0. 780 'f 0. 007 gm/cm3 at 20°C. It reacts vigorously if it comes in contact with water, liberating hydrogen gas and leaving lithium hydroxide as residue. It also reacts with humid air to form a coating of lithium hydroxide and lithium carbonate. At 2000C, LiH reacts even with dry air. Lil-I and LiD samples were obtained in powder form from the Foote lVlineral Company and from Metal Hydrides, Incorporated, 31 respectively. The approximate analysis by weight as supplied by the manufacturers is as follows: Lié Li7 _H_1. if ,7 1 L1 H 3% 97% 100% 0% 7 Li H2 3% 97% 2% 98% l 2 Li6H and Liél-I were obtained in lump form from the Stable Isotopes Research and Production Division of Oak Ridge National Laboratory. The manufacturer reports the following analysis for the samples: 6 1 Li H Grams lithium per gram material: Experimental Calculated 0. 8470 0. 8574 Spectrographic analysis 1‘“ Element Weight percent Na '0. 28 Ca ** <0. 004 K <0. 004 Ag 0. 0004 Cu 0. 001 Mg 0. 002 Mn 0. 004 Mo <0. 0004 *The spectrographic results reported herein are semi-quantitave estimates and should not be interpreted or construed to be precise quantitative determinations. **No spectrum line visible; probably absent; definitely less than value given. Element Weight percent Al 0. 003 B <0. 002 Ba 0.004 Be <0. 0002 Cd <0. 0006 C0 <0. 002 Cr <0. 0001 Ni 0. 006 Pb 0. 001 Si 0. 004 Sn <0. 0002 Sr <0. 001 V <0. 001 Zn <0.1 Nb <0.1 .6 2 . . . Li H Grams lithium per gram material: Experimental Calculated 0. 7473 0. 7527 Spectrographic analysis: Element Weight percent Na <0. 004 Ca <0. 004 K 0. 004 Ag 0. 001 Al 0. 002 B <0. 002 Ba 0. 002 Be <0. 0002 Pb 0. 0008 Si 0. 002 Sn <0. 002 Sr <0. 001 Cd <0. 0006 C0 <0. 002 Cr 0. 0001 33 Element Weight percent Cu 0. 0015 Mg 0. 002 Mn 0. 0002 Mo <0. 004 Ni 0. 006 V <0. 001 Zn <>> on On 1 mm 18 :6 - il‘ B? (X 3ONV11INSNVUL m magnum ow omgh s. 3: Eozud>§ 0..., as ’ mm 14F 0% > T § t (7.) annulmsuvui M if“ Figures 7—17. Infrared absorption spectra of thin films of . 19 7 l L1F containing varying proportions of Li6F19 and Li F 9 as indi- cated on individual figures. Temperature, 3000K; substrate, P01Y' ethylene sheet. 0v saga m 0H CH.— 3: on J1 Ikozm4m><3 s ON y T if ‘s 81. m BDNVLLINSNV 3: pm ‘ * a gm h l 3 53 «3 3&3 s8 Ibozw4m><3 MN rd m lgvulmuval {/2 06. on on 3: 1523?; mm Cu h 4 OEM bud RON tanned.” 80m 4 3‘ m aonvumsu T E. O¢ Ihozw4w><3 on 3: .1 bsm mm ow OH gm . . . EON mam—ha Ron lambda RON. em 16 v N s m I. l V N s... 3 m 13 .o. 2.: zEzud>§ st st s... ‘H A." MMBHN 3...... s. -22... s. - 15—— N ,o m gullmsuzi 1 pp 3: zSzudZi lmwr «Hugh 3J3- non nausea «on H . N . V m 3DNV llIHSNVUl f T n8. a." ~53 too In .3 BBB.- .nhuwd $00 1 c .1556); owl 3 . l W T f m DDMLLIISNVUL f . if (/'7 o¢ mm 3: Eozmnui m {A 959nm . .. . .Bn manna «2.. 3&3 T NVLLIN'IVNL .3; 9/3 3: 155.62; mm on 3 cm ,0. 3 gm o .fiHhhHHfls COthfiH “ON . o l. N V N s . m I. u o . 3 ohm ONW fin. Aivom Ihozquzfis bur 0.— fig.- .Hhhfld $00 OOHMQHA $0." m 3 uuimsuv. rm ’17 3 II) I u inns-Mu . 51 evaporated on polyethylene and recorded at 3000K. For these spectra, the sample compartment of the spectraphotometer was tightly covered with aluminum foil, the recorder pen was set at its lowest speed, the amplifier gain set at its highest value, and the spectra were recorded at slow speed. The various compositions and their reduced masses are listed in Table I. The results at room temperature are in agree- ment with the results found earlier in reference (12). 3. Effect of temperature: At low temperature, the dispersion wavelengths of the pure Lit/3F19 and Li7F19 films, and of the films made from their various compositions, shift towards shorter wave- lengths. Their absorption spectrum becomes deeper and narrower. The average amount of the shift in the dispersion wavelength of films evaporated on the polyethylene substrate at 1200K and 2000K is l. 3 and 0. 5 microns respectively. The average shift for films evaporated on CsBr substrates is l. 2 microns. Typical spectra of films evaporated on polyethylene sheets, as recorded at 3000K, 2000K and 1200K, are shown in Figures 18 through 21. 4. Effect of substrate, polyethylene, CsBr: It is found that the position of the dispersion wavelength varies to some extent with the different substrates. As mentioned earlier, polyethylene discs 1 inch in diameter and 0. 040 inch thick, and CsBr plates 1 inch in diameter and 0.125 inch thick, were used as substrates for the thin films of LiF. There appears to be about 0. 2 micron difference TABLE (1). Reduced masses %Li6F19 070L17F19 lix px/us 100 0 4.570 0.941 90 0 4. 633 0. 951 80 20 4.695 0.957 70 30 4.755 0.963 60 40 4. 813 0. 969 50 50 4.869 0.975 40 60 4.924 0.980 30 70 4.976 0.985 20 80 4.027 0.990 10 90 4.077 0.995 0 100 5.125 1.000 HS==5.125 Figures 18-19. Infrared absorption spectra of thin films of . l9 . . .6 .7 . .6 LiF containing 30% Li F - 70% Li F (Figure 18) and 70% Li F - 30% Li7F (Figure 19). Temperatures, 3000K and 2000K; substrate, polyethylene. Figures 20-21. Infrared absorption spectra of thin films of . 19 . . .6 .7 . .6 LiF containing 30% Li F - 70% Li F (Figure 20) and 30% Li F - 7 70% Li F (Figure 21). Temperatures, 3000K and 1200K; substrate, polyethylene. Ce. 3: 502334; on ow mH gm Sum—H «on iguana Ron 4 xoOON xooom 4r suvlll g m BONVIIM g f 3: x5233; lel lunarlll om lllmwll. pw GH "ugh odhhflu flan Iadhofln $2.. x.oo~ x.oom 3 5.473% on insulin L .3 50232,; Ami 104ml lmwl on . .‘ . u Susi a2. sauna." 3n x.o~_ XoOOm 1"" “I 3:11:va 3: 7.52335, .5 gm 2.? Ms. M s... w r 3&3 so». .3on s2. I 3 VALIICNVNA I‘D 57 between the dispersion wavelength of films evaporated on polyethylene and those of the same compositions evaporated on CsBr substrates. Films evaporated on CsBr plates have the longer dispersion wave- length. This effect is shown in Figures 22 and 23. Figure 22 shows the variations of the dispersion wavelength with the various composi- . .6 19 .7 l9 tions of Li F and Li F evaporated on polyethylene and recorded 0 o o . . . at 300 K, 200 K and 120 K. Figure 23 shows the variations of the various compositions evaporated on CsBr and recorded at 3000K and 1200K. 5. Evaluation of X0: As mentioned earlier in this chapter, the spectrum due to the atmospheric absorption interferes with the LiF spectrum. To obtain the net spectra the atmospheric effects are subtracted from the original LiF spectra. The stray radiation that starts to become relatively important at 35 microns and higher owing to the drop in the absolute spectral intensity of the source is also subtracted in part from the original LiF spectra. Two auxiliary minima appear on the short wavelength side of the LiF spectrum. The first peak is around 18 microns, the second is around 25 microns. These minima are shallow and hard to distinguish, but they may be separated from the main absorption peak as follows: The whole spectrum is first corrected for the atmos— pheric effects and stray radiation. Then, with the help of the equation 2 >.+>._ 2 k0 , where )lo can be estimated to within ‘1' 0.1 or better, the 1 Figure 22. Infrared dispersion wavelength for LiF 9 films evaporated onto sesium-bromide substrate, as a function of isotopic composition x. Temperature: 3000 K and 1200K. 19 Figure 23. Infrared dispersion wavelength for LiF films evaporated onto polyethylene substrate, as a function of isotopic composition x. Temperatures: 3000K, 2000K, and 120°K. ..u0_|_ O 2...»: o. .8 gm :zmu mug zo_:moaiou Dip—.09 ON on O¢ on Go on 0080”. *0. IO M 3 8.0. i H-VUdNI AV 0 MN ugh :qu 5.: 20:68:00 2.882 «Lo: 0 o. 8 on 2. on .8 cs 8 oo oo. ujoo.ooo.om~8ooo.¢bmiow.o.. o a. s . q 1. m u m m‘ H m m H 53;». w m H m .3 m m H m m . x68“ m m m m 1N0 x.oomi Em . 'VUrJNI BJWM .IU .33 N0 10 HS )d 3 Wu 9 NOIS 60 short wavelength side of the main absorption peak is constructed from the long wavelength side of the main absorption peak. The constructed short-wavelength side is then subtracted from the main portion of the spectrum at the corresponding wavelengths. The result is the separation of the auxiliary minimum near the main peak. The second auxiliary minimum is separated by the same procedure. Figure 24 shows the . . . 19 . separation procedure as applied to a spectrum of Li F film evaporated on polyethylene, and recorded at 2000K. 6. Evaluation of v/woz Equation (9) is used to calculate v/ too at 3000K. Table 2 lists these values for the spectra shown in Figures 7 through 17. Equation (10) is used to find y/y' and y/y" for the spectra shown in Figures 18 through 21, where v is the damping con- 0 o o stant at 300 K, y' at 120 K and y" at 200 K. These values are shown below: v/v' v/v” 30% LiéFlg, 70% Li7F19 4.1 2. 3 70% 1461719, 30% 117149 4.1 2. 4 Unfortunately the parameter v/wo is highly sensitive to inter- ference by atmospheric absorption and instrumental noise, and it can be determined with meaning only by great expenditure of time and care. Consequently this parameter was determined on one substrate (poly- ethylene) for all compositions at room temperature only and for selected compositions at low temperature and on the same substrate. Figure 24. Separation of main absorption peak from minor .6 19 . . ones , for spectrum of Li F film depOSited onto polyethylene sub- strate. Temperature: 2000K. 6 CW on 2: :Ezmdiz Om 0N ON «.N flan-OHM iJli i? f“ N m ziuuimsufi T TABLE(2L yfifi) 0]. L16F19 % Li7F19 y/tso 100 0 0.089 90 10 0.099 80 20 0.098 70 30 0.104 60 40 0. 106 50 50 0.107 40 60 0.107 30 70 0.103 20 80 0.106 10 90 O. 096 0 100 0. 099 63 B. Lithium Hydride Part of the work on LiH was carried out with the Model 137 Perkin- Elmer spectrophotometer in the region 12. 5 to 25 microns. The rest of the work was carried out with the Model 21 over the range 10 to 35 microns when it became available. The spectral region of interest for the study of LiH is nearly free of atmospheric interference. Unlike the work on LiF, where the isotopic mass of only the cation was varied, both the lithium isotopic mass and the hydrogen isotopic mass were varied. Figure 25 gives the average reduced mass of all the compo- . . .6 .7 1 2 , Sitions of Li and Li , H and H . We notice that the greatest change 1 2 in the reduced mass comes from replacing H by H , of course. The . . .6 . .7 change in the reduced mass is small when L1 is replaced by Li . In the work done with LiH, KBr windows were used most of the time, polyethylene windows being used only occasionally. 7 2 1. Effect of isotopic mass--Li6H1, LiéHz, Li7I-Il, Li H : The position of the dispersion wavelength of thin films of each of the four isotopically-pure compounds is listed below: LiéH1 LiéH2 Li-IH1 Li7HZ )t (microns) 16. 97 22. 30 17. 05 22. 45 These films were evaporated in an atmosphere of hydrogen on KBr Plates 1 inch in diameter and 1/8 inch thick. The thickness of these fi1rns is of the order of 0. 01 to 0.1 microns. Replacing Lib by Li7 REDUCED MASS OF L i H I.509350I2 LSGSSGGG . H2 P, I00 * ’ R + L5 +~ \ + L4 I L3 0.5 . l.2 LI LU HI T 0-9 O ' 0.5 IOO'I. Us ~ 1.17 0.86347I6 0.88I5I 796 FIGURE 25 Lines of equal reduced mass for lithium hydride made of varying proportions of Li6, Li7, and H1, H2. 65 shifts the dispersion wavelength by a small amount, of the order of 0.2 micron, whereas replacing H1 by H2 shifts the dispersion wavelength by about 5. 5 microns. These results are in agreement with those obtained by Zimmerman. Figures 26 and 27 show typical spectra as obtained with the spectrophotometer model 137. Spectra of LiH films show an auxiliary minimum around 20 microns. Figure 28 shows a spectrum of Li7H1 film at 3000K superimposed on spectrum of Li7H film when the abscissa has been multiplied by the reduced mass, again at 3000K. The close agreement between the theoretical pre- diction to be discussed later and the experimental results can be observed in this figure. . . . . .6 l .6 2 2. Effect of isotopic composuion [xLi H , (l-x) Li H ], 7 1 7 Z [xLi H , (l-x) Li H ]: Films of varying isotopic compositions of both 2 2 LiéHl, Li6H , and of Li7H1, Li7H were evaporated on KBr substrates and their spectra were studied. The results agree with those ob- tained by Zimmerman. Table 3 gives the reduced mass, and the wavelength of the absorption peaks from the various compositions used. 3. Effect of temperature: The spectra of thin films of 6 1 6 7 7 2 Li H , Li H , Li H , and Li H and their various mixtures were obtained at 1200K and at 3000K. At 1200K, the spectra of the LiéH2 7 2 and Li H become deeper and narrower. The dispersion wavelength shifts toward shorter wavelengths by about 0. 4 micron. The effect 7 Figure 26. Infrared absorption spectrum of Li H1 film evaporated onto KBr substrate. Temperatures: 3000K, 1200K. Figure 27. Infrared absorption spectrum of Li H film 0 eVaporated onto KBr substrate. Temperatures: 300 K, 1200K. 0N Nun—OHM ‘n‘ Amzomnzzv IPGZNl—mzqg ¢N NN ON m_ 0. ¢_ 4 q _ a q IJIIJO mON Cmvs 101'. I _... {\‘E I 1 L00 7 ("L00 .vN 5N gm $2010.}. Ibuzu4w><3 ON a. w. v. o_.._ d1 4 q « .90 .Mooom .ougmnomfiou 3mm ”manuumndm .mommme poodpou mo noon oumfivm >3 60333.95 mmmmomnm £33 NEWJ mo Eunuoomm ofi pomomamuomdm mm #033 no .Efim Hmnflq mo 8.9.30on non—AHOmnm @9835 ON magnum Amzomog: Ihozm4w><3 ¢N NN. ON 9 m. S e n 7 s d 4 13.: H N # /// \ .- 1a....» / \ t... 1.. 10¢ // \\ Aug..- d #3.... I \/ he i . I 4 \- \\\\ x A can. in M 1.5.0 t \\\\ //I om x coon l l 1 i}; 2 NE: -8 x .2, .11.. II .1 TABLE (3). Reduced masses and dispersion wavelengths % Liél-i1 %Li‘1-11 Average reduced Dispersion mass wavelength 100 O O. 864 16. 97 99 1 0. 871 17. 00 98 2 0. 876 17. 00 95 5 0. 896 22. 20 90 10 O. 928 21. 13 80 20 O. 973 21. 15 70 3O 1. 057 21. 15 60 40 1. 123 21. 05 50 50 1. 188 21. 4O 4O 60 1. 253 21. 6 3O 70 1. 319 21. 17 20 80 1. 386 21. 9 10 9O 1. 449 22. 25 0 100 1. 550 22. 30 70 is seen in Figures 26 and 27. A similar effect is observed in the spectra of the isotopically-impure films. At 1200K, the spectra of the LiéH1 and Li7H1 films become narrower and deeper as expected, but the dispersion wavelength shifts by about 0.1 micron toward longer wavelengths. Figure 29 shows a spectrum of a Li7H1 film at 1200K superimposed on a spectrum of Li7H film for which the abscissa for the latter at 1200K has been multiplied by the square root of the ratio of the reduced masses. Contrary to theory--to be discussed later--the two peaks do not coincide. Some of the spectra of Li7H1 film were taken at temperatures intermediate between 1200K and 3000K, and at temperatures higher than 3000K. Figure 30 shows the spectra of Li7H1 at four different temperatures between 1200K and 3000K. These spectra were recorded as the liquid air in the chamber around the sample was evaporating, and the temperature of the sample was slowly rising. Figure 31 shows spectra of Li7H1 film at temperatures higher than 3000K. Higher temperatures were obtained using a chromel resistance wire wrapped around the sample holder as a heater. 4. Effect of substrate-~potasium bromide, cesium bromide: One-inch diameter and l/8-inch thick plates of CsBr and KBr were 6 used as substrates for the evaporation of Li H1, Li6H2, LiVH1 and Li7H2 thin films; moreover, one-inch diameter and 0. 04-inch thick poly- ethylene sheets were sometimes used. As was found for LiF, the 7 .MOONH 699390950» mnmm "oumuumndm .mommmE poo9pon no 9009 oumswm >9 “6039338 ammfiomnm £93 mmwwd mo 59.30on mg» pomomnfinomdm mg 3033 90 ea Hm 91H mo 59.30on 90398QO «Banana N. GN Eda—OHM Amzomgzv Ihozmqm><>> L vN mm ow m. m. e. . 37 a a q a 1.1.: _ 9 O .1?! [ON 193 .. 10¢ "Illl'lllllllull‘fllllll llllll (III... I l 1...... 1 cod .. low I X CON. 2. 1 4a1\£ 0) NIB..._ 1" 10m . 4 Q) _I N ml— nllll .- rill-ll ill-Ila c8. Figure 30. Infrared absorption spectrum of Li7Hl o evaporated onto KBr substrate. Temperatures: 1250K, 177 o 0 K, 234 K, and 318 K. 7 1 Figure 31. Infrared absorption spectra of Li H evaporated onto KBr substrate. Temperatures: 3100K, 3570 K, 4000K, and 4400K. 7a .N On guru 32010.2. rhozm4m>4’ a. h. n. fi 4 q 4 fi 2.3. /.... nu Hm mmDOHh szomoiv Ihozm4w><3 mm . _N m. h. n. n. A . q q a + 3 2 1 x. o_n m 74 position of the dispersion wavelengths of the thin LiH films seemed to depend to some extent on the substrate. Between 0. l and 0. 2 micron difference appears between the dispersion wavelengths of films evaporated on KBr and those evaporated on CsBr. Those evaporated on CsBr have the longer wavelength. 5. Effect of the atmosphere: As was mentioned in an earlier chapter, LiH reacts quickly with humid air. It was there- fore necessary to store the LiH powder in a desiccator at all times. Films were evaporated in a vacuum, and kept in it during the entire experiment. The shape of the spectrum begins to change as more andmore LiH is changing to its oxide or hydroxide form. The rate of inter— action depends of course on the vacuum and on the thickness of the film. When air is allowed to enter the cell, LiH changes completely to other forms, probably LiOH, H O. The spectra of the reacted 2 films are completely different from the LiH spectra. Figure 32 ,6 1 , 0 0 shows the spectrum of a reacted Li H film at 300 K, and at 120 K. 7 1 Figure 33 shows the spectrum of a reacted Li H film at 3000K and at 1200K. The spectra of reacted LiD have the same shape as those of reacted LiH spectra. Those of reacted composed films have the same shape as reacted LiH and LiD also. 6. Evaluation of k0: Primarily we had arrived at the equation k4}. = X02. This equation provides a means of calculating Figure 32. Infrared absorption spectrum of LiéH film evaporated onto polyethylene substrate, after reaction with atmosphere. Temperatures: 3000K, 1200K. Figure 33. Infrared absorption spectrum of Li7H1 film evaporated onto polyethylene substrate, after reaction with atmosphere. Temperature: 3000K, 1200K. Amzomozzv Iewzmqm><>> mm om - . MN om an museum mummmuazn< may maaa_ .:nvmw mundane acm.aH mmam< .mzmnnmamwnom . zo.mna<>> J _:-.. u ON m .ON 10m (°/e)' BONVIIIWSNVHI 77 the dispersion wavelength accurately to within f O. 01 micron, since the spectra of the LiH and LiD films are uniform and are not affected much by atmospheric absorptions. Figure 34 demonstrates the pre- cision of this method of measuring k0; from this figure we notice that X_)\+ is fairly constant in the region around k0. As an extension of procedure we may separate the peaks in the LiH and LiD spectra and in the reacted LiH and LiD films. Figure 35 demonstrates this technique as applied to a spectrum of Li7H1 film at 1200K. 7. Evaluation of y/woz Equation (9) and equation (10) are used to calculate y/wo and y/y' for the films of LiH and LiD, shown in Figures 26 and 27. The results are listed below: Y/wo £1: LiH 0. 1195 2. 487 LiD O. 1877 2. 060 y/y' is the ratio of damping constant at 3000K to that at 1200K. K >. 2 1 Figure 36 shows a plot of #:0- - T) vs. Tl-T - T _ T for o o 0 min aLi7H1 film evaporated on KBr and recorded at 1250K. The curve is nearly a straight line indicating the accuracy of measuring y/w . o Hmvm 0990 bondhommcwo m 94 mo 59.30on m 90m .H. nonmgcumcmuu mo dofiugm .m mm .MOONH "09998923969. .oumnumobm -+ Ouo Qt A A: E a N. . en 58: . at L. 00 0' On ON C. O . . . q . q . . . . 1 . on... _ 1‘5...- I‘Il'nuuu-I-unnuuauuml'F- 1 V\ . tutu-nu _ 4.1.0.0“ Iffifi— v .. ... _ . ‘e _ r e . .fl xeou. «i u .I~.4 not: mm "559E Amzomozzv Ihozmqm><>> _ VN NN ON m. m. ¢. . . r . . . o 3...; 3.0.0 2 '01 I I I I I I I I _ T-‘M'h A i ‘ N 2n. 0 " A ‘ o v‘ ‘ s I. ‘ I 0‘ o 4'4 . v ‘ .20» , - .IO- - Li’H' ~ l25°K - . "0.04 FILM .0' " - 0‘ d 7'24“: 1 l 1 1 1 .0: .02 .05 .no .20 .50 LG 2.0 5.0 I0. I I 0.1. - To- T k . x o 2 l 1 Figure 36. Plot of (— - __ f - - x0 x ) as a unction of T _ T T _ T . o 0 min 7 l for a spectrum of Li H evaporated onto KBr substrate. Temperature: 1200K. 81 V. DISCUSSION OF EXPERIMENTAL RESULTS Comparison of present theory with experimental results requires knowledge of reflection data as well as transmission data; even then the theory contains parameters too difficult to be calculated. Hence we content ourselves with testing the predictions that follow from general arguments only. A. Dispersion Wavelength x0 = ch/wo 1. Effect of isotopic mass on x0: Ordinarily the simple theory of lattice vibration is said to show that any characteristic frequency, for example, the infrared dispersion frequency, depends inversely on the square root of isotopic mass. Actually some general arguments, to be detailed shortly, show that this statement is not quite exact. It is however a very good approximation, and we shall accordingly test it directly. In Table 4 are summarized the infrared dispersion wave- lengths and the reduced masses for all the isotopically pure substances at all the temperatures and substrates that we have used; in addition are listed the ratios of the dispersion wavelengths to the ratio of the reduced masses, in each case the heaviest substance being used as a reference. 2. Effect of isotopic composition on A0: Although it is not clear what effect isotopic composition has on the position of the dis- persion wavelength, it is natural to try to correlate the position with TABLE (4). Effect of isotopic mass on infrared dispersion wavelength “/65 Polyethylene CsBr KBr “J 300°K 120°K 3000K 1200K 300°K 1200K x/xs i/xs x/is x7xs x7is x7xs .6 19 L1 F 0.941 0.947 0.951 0.948 0.945 - - .7 19 L1 F 1.000 1.000 1.000 1.000 1.000 - - ,6 1 L1 H 0.746 - - 0.758 0.773 0.756 0.769 .6 2 L1 H 0.987 - - 0.996 0.995 0.993 0. 993 7 1 Li H 0.754 — — 0.760 0.773 0.759 0.774 ,7 2 Li H 1.000 - - 1.000 1.000 1.000 1.000 83 the average reduced mass of the substance under study. Even then, it is not clear whether the arithmetic mean is superior to the harmonic mean. The difference between these two means, however, is slight, and hence we test only the arithmetic mean. Table 5 lists the compo— . . . l9 Sitions of LiF used, evaporated onto CsBr and polyethylene substrates 0 0 . and recorded at 300 K, and 120 K. Here the ratios )‘OX/XOO /2 “’l‘zt / )1 P5X p~S which should equal unity according to the simple assumption just . . . . . . . 19 mentioned, 18 given for the varying compOSItions of L1F . The departure from unity is slight, amounting on the average to only a few parts per thousand. The values for CsBr substrate are a little more regular than those for polyethylene. For LiH, the shift of A0 with isotopic composition is so irregular it is not worth-while to tabulate the results here. 3. Effect of temperature on X0: Lithium fluoride: A cross plot prepared from Figures 22 and 23 is shown in Figure 37, a plot of dispersion wavelength against temperature for selected compositions of LiF”. The average shift(1. 250/180 K-deg)/3l. 511 ‘V 2 x 10-4/K-deg. In the absence of strong interaction with the substrate, this coefficient should roughly equal that of the temperature coefficient of the elastic modulus of LiF, namely, 3. 5 x 15—4/K-deg. The argument is probably satisfactory. 84 TABLE (5). Effect of isotopic composition on dispersion wavelength for Lib?19 CsBr substrate P. E. - substrate 300°K 1200K 300°K 1200K x k 00 X (0 )t 00 X (.0 ox x 0x x ox x 0x x 0. 0 31. Opt 1. 004 29. 90 . 005 30. 80 l. 004 29. 50 1. 008 0 1 30. 9 0. 994 29.8 . 995 30. 9 l. 000 29. 3 0. 994 0 2 31.3 1.001 30.1 .999 31.2 1.004 29.3 0.985 0 3 31.5 1.000 30.4 .002 31.3 1.000 30.1 1.008 0.4 31.7 1.001 30.5 .999 31.4 0.997 30.2 1.006 0.5 31.8 0.998 30.7 .000 31.5 0.995 30.5 1.010 0. 6 32.0 0.998 30.7 .994 31. 6 0.992 30. 6 1.009 0 7 32. 2 1. 000 30. 9 . 995 31. 7 0.990 30. 5 0. 999 0.8 32.3 0.997 31.0 .994 31.4 0.992 30.8 1.003 0 9 32.4 0.995 31.3 .998 32.1 0.993 30.9 1.001 1 0 32.7 1.000 31.5 .000 32.5 1.000 31.0 1.000 85 Lithium hydride: Figure 38 shows the variation of k0 with temperature for LiH and LiD. The behavior for LiH is indeed anomalous, and we are hesitant to consider the increase in RC real without additional study. 4. Effect of substrate on AC: From Table 5 one observes that the dispersion wavelength for LiF on polyethylene is a few tenths of a micron smaller than that on CsBr. Since there is negligible absorption by either substrate in this region of the spectrum, and since the elastic modulus for LiF is much higher than that of either polyethylene or CsBr, we are at a loss to give a plausible explanation for this shift. Although epitaxy is more likely to be encountered with Cs Br substance, we cannot at this stage ascribe the shift to this effect. B. Damping Constant y/tpo 1.. Theoretical considerations: The general arguments that we wish to make are the following: a. The equation of motion for isotopically-pure substances in the Newtonian formulation contains mass and time on one side only of the equation of motion, in the form of mass times a second order time derivative of spatial coordinates. The other side of the equation contains only spatial coordinates and atomic parameters other than mass. Figure 37. Dependence of infrared dispersion wavelength . 19 . . . . on absolute temperature for LiF films of various isotopic compo- sitions evaporated onto CsBr and onto polyethylene. Figure 38. Dependence of infrared dispersion wavelength on absolute temperature for LiH and LiD films evaporated onto KBr. '86 kn EN 3... h OOn OON 00. N 41 1 d a 4 L3 .6» W I. r .n H m a m .35 lfin mzu4>zhu>qoa an no llll ifn LiD LiH # 300 260 160 -‘- W—t 23" N N :- '- SNOUGM (1) Y 17* TV“ FIGURE 38 88 Therefore the solutions can contain time and mass only in the combination: time/square root of mass, and hence all frequencies must be related by the condition 1/2 . . wOM = constant; or if equivalent temperatures are introduced in place of frequencies through the relation 1/2 . . -hw = k9, then 9M = constant. SpeCifically we may conclude that the lattice-vibrational frequency distribution can differ between isotopes only by a scale factor equal to the ratio of the square root of the masses. General dimensional considerations show that the temper- ature must enter only in the ratio of KT, the average thermal energy, to hwc’ where wc = k GC/‘H in some . . . . 1/2 characteristic frequency inversely proportional to M . Therefore comparisons between various phenomena dependent on lattice-vibration interactions should be made at equal reduced temperature T/e. In the case of isotopically-impure substances, part ”a" of the above argument breaks down; nevertheless calcu- lations on the change of lattice-vibrational spectrum by introduction of lattice impurities, suggest that the effect of isotopic substitution can be taken into account by averaging the isotopic mass in some way. This view cannot be completely correct, although for many phenomena, 89 it would appear to have validity. Thus we have seen that for a position of absorption maximum, i. e. , the dispersion wavelength, the shift with isotopic composition was accounted for by use of an average isotopic mass; but now we shall see that for the width of absorption band, which is proportional to y/wo, the solution is not quite so simple. 2. Consideration of experimental results: To illustrate these ideas, we look at the solid curve in Figure 39, a plot of v/wo against 1 isotopic composition for LiF 9 evaporated on polyethylene and observed at 3000K. One notices that the absorption coefficient increases as the 7 proportion of Li is increased, falling slightly as isotopically pure .7 19. . . Li F is reached. The last value is somewhat higher than that for . . .6 19 . isotopically pure Li F , but according to paragraph "c" above, com- parison should not be made at the same absolute temperature, but at the same reduced temperature. Theory does not give adequate guides as to the dependence of y/wo on the absolute temperature T, hence we make use of our experi- mental data as shown in Figure 40. The absolute temperature for .7 19 . .6 19 Li F corresponding to the reduced temperature for Li F at room . 0 0 temperature is 300 /l. 059 = 282 K. From the graph we can estimate . .7 19 . . then the value for damping constant for Li F to be 0. 086, in compari- 6 1 son with 0. 088 for Li F 9. The values do not agree perfectly, but Figure 39. Plot of v/wo against isotopic compositions for l LiF 9 evaporated onto polyethylene and recorded at 3000K. Figure 40. Variation of v with absolute temperature for 7 Li F19 film evaporated onto polyethylene substrate. an mgr” x m2.6... c on 00. _ 2...»... own. 4 r . 0% r . mood O.m x+0...._ 100.0 .3 N. illlll / .l l- \ t I'll-III! I _IIIII|.|.IIIIIII‘I‘ .do (:2 l 3 magnum EL .r .m .n a." EA to 75x 2.: they are close enough to indicate the pow er of this argument. For isotopically impure lithium fluoride, we note that this procedure does not reduce y/wo to a constant value, but rather that there seems to be an increase due to the mixing. Hence it is clear from the solid line that mere scaling alone will not bring absorption spectra for iso- topically-impure substances into coincidence; and from the dashed curve, it is clear that although use of a scaling factor in conjunction with comparison at equal reduced temperature suffices to account for isotopic-mass effect in isotopically pure compounds, it does not account for it in isotopically-impure compounds. The effect of substrate is slight and we have not yet been able to deduce much information from it. 92 LiH has proved to be less tractable than LiF. This circumstance is undoubtedly due both to imperfections in experimental technique and to the rather complicated chemical bonding in this substance. 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