APPLBCABILiTY OF THE LOREN?Z-OSC§LLATOR MODEL T0 ENFRARED ABSORPTION EN UTHEUM FLUORWE The-sis far flue Degree of Ph. D. MICHEGAN STATE UNIVERSITY Chasrfles M. Randail 19’é4 -" IMIIUHWWHWIIWWIWififlfllflflfli um” 3 1293 01743 0178 Michigan State University This is to certify that the ; thesis entitled APPLICABILITY OF THE LORENTZ—OSCILLATOR MODEL TO INFRARED ABSORPTION IN LITHIUM FLUORIDE presented by CHARLES M. RANDALL i has been accepted towards fulfillment of the requirements for Ph. D. degree in PHYSICS DJMJTM Major prgfessor) Date November 19, 1961+ 0-169 ABSTRACT APPLICABILITY OF THE LORENTZuOSCILLATOR MODEL TO INFRARED ABSORPTION IN LITHIUM FLUORIDE by Charles M. Randall The Lorentz model of a dispersion oscillator with a constant damping factor has long been used to describe the absorption of electromagnetic radiation by a crystal lattice. Modern theoretical investigations indicate that the damping constant should actually vary with frequency. Nevertheless, if the damping factor does not vary too rapidly in the region of the principal absorption, the model remains useful. We have devised a method to obtain the dispersion frequency QJO and damping factor (y from the experimental data by a least-squares fitting technique. We have compared the experimental results obtained from thin-film transmission measurements on lithium fluoride with the predictions of theory when isotoPic mass, film thickness, and temperature are changed. The agreement is satisfactory for isotopically pure films, and suggests that the method may be useful in characterizing the behavior of isotopically mixed films. N, ‘ APPLICABILITY OF THE LORENTZ-OSCILLATOR MODEL TO INFRARED ABSORPTION IN LITHIUM FLUORIDE \ . B , A . y \- R' \V Charles M? Randall A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR.0F PHILOSOPHY Department of Physics and Astronomy 1964 ACKNOWLEDGMENTS Worthwhile accomplishments are seldom made without the help of many peOple. It is my privilege to acknowledge those who have made this work possible: Professor D. J. Montgomery not only suggested and directed the work but has been a constant source of encouragement and counsel. The breadth and depth of his knowledge has been of great help and will always challenge me, while his example in human relations will ever serve as a model. Dr. John R. Hardy gave several ideas valuable in the interpretation of the data. The Physics Department sh0p under the direction of Mr. Richard Hoskins has furnished several pieces of apparatus and much helpful technical advice. In particular Mr. Robert Cochrane carefully con- structed several important pieces of equipment. Richard Fuller and Sitaram Jaswal, fellow graduate students, made many helpful suggestions, provided a sounding board for many ideas, assisted in carrying out the details of many experiments, and helped in many other ways to make this project a success. The drawings were done carefully and skillfully by Dipak Bazaj. Several undergraduates have also been active with the work: Kwok Fai Yeung, who spent hours polishing crystals and helped deve10p a method of analyzing spectra; Gene Gardner, who has spent many tedious hours transferring spectra from film to cards; and Karl Zetterholm, who took over much of the computer programing and organization of data for analysis. The MSU Computer Laboratory gave valuable assistance in programing. The high-energy nuclear-physics group under the leadership of Mr. Ronald Beery made the Hydel machine available, and gave several suggestions on computer programing. The research has been supported by the Air Force Office of Scientific Research and All University Research Grants. I am very grateful to the National Science Foundation for support through a Cooperative Graduate Fellowship. Last but most important my wife, Bernadette, has been understanding and a source of encouragement during the course of the work, and has given invaluable assistance in the preparation of this thesis, including typing several rough drafts before typing the final form. To all these people, and to many others who have helped in one way or another, it is my privilege to express my appreciation. *fiW*‘k‘i¢t&fifl%§c ii TABLE OF CONTENTS CHAPTER I 0 INT RODUCT ION O O O O O O O O O O O O‘ O 0 II. APPARATUS AND EXPERIMENTAL TECHNIQUE . . Sample Preparation . . . . . Temperature Measurement and Control Thermometer Fabrication . . . Thermometer Calibration . . Dewar and Temperature Control . Transmission Measurements . . . . . Spectral Analysis . . . . . . . . . III. RESULTS AND DISCUSSION . . . . . . . . . Infrared Dispersion Frequency‘410 . Dependence on Thickness . . . Dependence on IsotOpic Mass . Dependence on Temperature . Apparent Thickness d . . . . . . . Dependence on Temperature . . Dependence on Actual Thickness and IsotOpic Mass . . . . . Reduced Damping Constant {/wo . Dependence on Actual Thickness Dependence on IsotOpic Mass . Dependence on Temperature . Effect of IsotOpic Mixing . . . . . REFERENCES . . . . . . . . . . . . . . . . . . . . APPENDIXES . . . . . . . . . . . . . . . . . . . . iii 36 38 38 42 42 44 44 44 47 47 50 54 56 TABLE I. II. LIST OF TABLES Page Supplier's isotopic and chemical analysis of lithium samples 0 0 O O O O O O I O O O O O O O O O O O O O O 6 Expected dependence of single dispersion-oscillator parameters on experimental variables . . . . . . . . . 39 III. Contributions to the temperature dependence of the dispersion frequency of lithium fluoride . . . . . . . 45 iv 10. ll. 12. 13. 14. 15. 16. 17. 18. 19. '20. 21. LIST OF FIGURES Horizontal evaporation arrangement for LiF . . . Resistance thermometer and evaporation jig . . . Vertical evaporation arrangement for indium Indium resistance-thermometer calibration curve Low-temperature dewar . . . . . . . . . . Detail view of dewar tail . . . . . . . . sample hOIder O O O O O O O O O O O O O O Resistance-thermometer measuring circuit . Optical path of spectroPhotometer . . . . StraY']. ight Curve 0 o o o o o o o o o o o 7 Corrected Li F spectrum ._ . . . . . . . . Original Li7F spectr0photometer trace . . Spectr0photometer 100% line . . . . . . . Corrected and calculated L16F spectrum . Dependence Dependence Dependence Dependence for LiF . Dependence Dependence 0f wmin 0n thiCkness o o o o o o o of uuo on thickness for L17F films of “U5 on temperature for LiF . . . of apparent thickness on temperature of XYIAJO on thickness for Li7F films of K/wo on temperature for LiF . . Theoretical phonon distribution function for LiF . Page 10 13 14 16 18 19 23 26 27 28 29 37 40 41 43 46 48 49 51 LIST OF APPENDIXES APPENDIX Page A. Infrared parameters of a Li6F film at various temperatures 0 O O O O O O O O O O O O O O O O O O O 5 7 B. Infrared parameters of isotOpically-mixed LiF film at various temperatures . . . . . . . . . . . . 58 C. Infrared parameters of a Li7F film at various tempe rature 8 O O O O O O O O O O O O O O O O O O O O 5 9 D. Infrared parameters of a series of Li7F films of various thickness at room temperature . . . . . . . . 60 vi CHAPTER I INTRODUCTION In 1665 Sir Isaac Newton decomposed white light from the sun into the visible spectrum; in 1800 Sir William Herschel found that the greatest heating power of the spectrum lay outside the visible, just below the red end of the spectrum. Interest in this "infrared radiation" has continually grown as it has been realized that the electromagnetic interactions of the more massive constituents of matter are characterized by it. Every material body emits, absorbs, transmits, and reflects infrared radiation in a characteristic manner. The physicist can and indeed has employed the analysis of this radiation to increase his understanding of both the radiation field and the pr0perties of matter. Technological applications of the radiation and commercial instruments for its study, however, have appeared for the most part only during the last two decades or so. Our understanding of the interaction of electromagnetic radiation with solids is far from satisfactory. For even the simplest types of solid there has been no theoretical treatment of any rigor, and there has been no experimental study of any completeness. Even with the theoretical models available, until the recent widespread availability of high-speed electronic computers, investigators in this field were forced by the sheer magnitude of the computations involved to make drastic simplifying assumptions. In our laboratory we undertook a program of experimental and theoretical investigation that we hOped could contribute to advancing the understanding of the interaction between the radiation and the vibrations of the crystal lattice in the region where photon energies are comparable with phonon energies, and in materials where the interaction is strong. Thus we were led-~as 1 and his school in their pioneering work begun 30 years were Czerny ago--to infrared studies of ionic crystals. We chose substances as simple and familiar as possible, namely the alkali halides, or certain other substances with NaCl structure, and we chose as parameters the 1 temperature, and wherever it was feasible and worth while, isotOpic composition. We chose to study the photonuphonon interaction by means of transmission measurgments, since certain parameters describing the phonons are nearly directly evident from this type of data, and since samples are frequently easy to prepare. As is common in scientific work, the apparent simplicity of the infrared response of these materials disappeared upon closer examination. It has become clear that successful quantitative descritpion of the photonuphonon interaction will require extensive data on a full set of materials over a wide range of carefully controlled parameters. We wish to begin with a substance which is tractable and familiar, and which lets us vary isotOpic mass significantly. Lithium fluoride, 6 or Li7 in prOportions as desired in combination readily available with Li with the isotOpically pure F19, forms stable and durable films. The binding forces are large enough and the reduced mass of LiF small enough, moreover, to cause the lattice vibration frequencies to be sufficiently great that most of the phenomena of interest lie in regions of the spectrum that are easily investigated with modern commercial infrared spectrOphotometers. Techniques for obtaining suitable samples for infrared transmission measurements by evaporation in high vacuum have been developed in our laboratory as well as in others. Largely ignored in other thin-film investigations, however, is careful attention to the problem of temperature measurement and control, which has been in part the object of the present study. Thin-film measurements can give only part of the information about the photon-phonon interaction, but they give that information in fairly convenient form. In this study we begin the investigation of the limits of the accuracy and the meaning of parameters (infrared dispersion frequency, damping constant, apparent film thickness) as obtained in our thin-film studies. We find that these parameters can be used meaningfully to characterize the observed phenomena in the case of isotOpically-pure substances. We then attempt to apply this simple characterization to absorption in isotopicallynnixed substances. a much more complicated phenomenon for which experimental results are sorely needed to guide the theory. CHAPTER II APPARATUS AND EXPERIMENTAL TECHNIQUE For convenience we discuss the experimental work involved in this study in four sections; 1) sample preparation, 2) temperature measurement and control, 3) transmission measurements, and 4) spectral analysis. Sample Preparation Because of the strong absorption of the alkali halides near their infrared dispersion frequency, transmission measurements in this region must be made on very thin samples, which are conveniently obtained by high-vacuum evaporation onto suitable substrates. The commercial evaporation system used in this study is equipped with a nickel-plated steel base plate through which pass feed-throughs for high currents and for mechanical motion. The pumping system consists of a 4" oil diffusion pump rated at 750 liters per second at 0.1 micron, backed by a lS-cfm mechanical pump. Between the diffusion pump and the base plate is a chevron-type liquid- nitrogen baffle and a 4" gate valve. An ionization gauge is connected to the pumping line just below the base plate. Thermocouple gauges in the high-vacuum line and the forepump line indicate the pressure during roughing Operations. The Pyrex bell jar is 14" in diameter and 15 3/8" in height. Usually the system will pump down to the 10 “Torr region in 4 or 5 minutes, and to less than 5 pTorr within 30 minutes. Currents up to 250 amps are supplied from a low-voltage transformer connected to the llO-volt lines through a lS-amp variable autotransformer. One of the high-current leads passes through an instrument transformer for monitoring the current through the boat. The LiF films were evaporated over indium resistance-thermometer elements (to be described later) that had been previously evaporated on the 0.040"-thick high-density polyethylene (HDP) substrates. The horizontal evaporation apparatus used for the LiF films is shown in figure 1. The molybdenum boat was packed with the desired sample material and placed in the evaporator. When the pressure was below 5 pTorr, the current through the boat was increased over a period of three or four Figure l. BELL JAR ‘ BASE PLATE / SUBSTRATE SHUTTER Arrangement for horizontal evaporation of LiF films. 5 minutes until the boat appeared dull red at typically 200 amperes. The pressure was observed to rise rapidly by several “Torr and then to fall, probably due to the release Of water vapor trapped in the powdered LiF. After the pressure fell to nearly its former value the boat was rapidly heated to bright red and the shutter Opened. Experience had shown that a film of suitable thickness appeared green by interference when viewed at nearly grazing incidence in white light reflected from the baseplate. After such a film was produced in from 30 to 50 seconds by a boat about 95 mm from the substrate, the shutter was closed, and the current turned Off. The film was then removed from the evaporator and placed in the sample holder prior to insertion in the dewar. Early runs were made with commercial LiF, for which analysis is unavailable. Later runs were made with isotopically enriched LiF from Oak Ridge National Laboratories. The supplier's isotOpic and chemical analyses Of the lithium in the three ORNL samples are given in Table I. The samples from which the isotopically mixed films were evaporated were weighed from the ORNL LiF samples on a single-pan balance sensitive to 0.1 mg. Typically 400 mg Of a mixture were prepared. Different boats were used for evaporation Of films with different isotOpic composition. Temperature Measurement and Control Inasmuch as the thin films which are under study are deposited on thick substrates, care must be taken to determine the temperature Of the -film, rather than that Of the substrate. Because we are concerned with the average temperature over the area Of the film illuminated by the beam of the spectrOphotometer, we chose a wide-area resistance thermometer. Very pure indium, whose resistivity changes significantly with temperature down to its superconducting transition at 3.40K, makes a suitable elementz. Thermometer fabrication: - The resistance thermometer is an evaporated U-shaped film of indium in a fouruterminal resistor configuration, as shown in the upper part Of figure 2. Four small wire Stationers staples were punched through the HDP substrate and clinched before the film was evaporated. With ordinary tin-lead radio solder, No. 34 formvarninsulated c0pper leads were soldered to one end Of each staple on the side Opposite the side which was tO receive the film. With a small soldering iron at about 1700C, a groove was formed in the film side of the HDP from each staple to the anticipated location of its connection with the indium film. Table I. Supplier's IsotOpic and Chemical Analyses Of the Lithium from Oak Ridge National Laboratories in the Form Of LiF. The chemical analyses are semi-quantitative results and should not be interpreted or construed to be precise quantitative determinations. Batch number SSS(hy) Isotopic Analysis (Atomic Percent) Li6 95.72 i 0.17. Li7 4.38 1 0.17. Semi-quantitative Chemical Analysis in Parts per Million Ag < 1 Cs <40 Pb 15 Al 20 Cu 10 Rb <10 Au <1 Fe 1,000 Si 75 B 10 Hg <10 Sn 20 Ba 1 K <10 Sr 2 Bi <2 Mg 12 . Ti <1 Ca 550 Mn <10 v <1 Cd <2 Mo <1 w <40 CO <2 Na 25 Zn <100 Cr 3 Ni 10 Batch number SSS(b) IsotOpic Analysis (Atomic Percent) Li6 99.3 i 0.27. Li7 0.7 i 0.17. Semi-quantitative Chemical Analysis in Percent A1 <. 01 Fe .05 Pb <. 01 Ba . 01 K <. 01 Sn <.‘ 01 Be <. 001 Mg . 01 Sr . 01 Ca . 25 Mn <. 01 v <. 01 Cr <. 01 Na . 02 Zn <. 25 Cu . 02 Ni <. 01 Table I (continued) Batch number SS7(c) IsotOpic Analysis (Atomic Percent) Li6 less than 0.01% Li7 99.9924z Semi-quantitative Chemical Analysis in Percent Ca <;004 Fe .006 Total Metals -<;15 K <004 A1 (.001 Carbonate .06 Na <004 Hg .00938 Total Anions <.08 8 In-Ag SOLDE I . Cu LEADS {A /}0u LEADS STAPLES STAPLES O \— SUBSTRATE O , I A [In FILM THERMOMETER SUBSTRATE_—\ MASK / p.11.-- \\\\\‘xv P { MONlTOR p SUDE LEADS “Hug”--. rung"-.. fir MONITOR Stunts—J EVAPORATION JIG Figure 2. (Upper) Indium resistance thermometer deposited on a high- density polyethylene (HDP) substrate, showing method of making connections to the film. Not shown is the conducting paint added after the film is evaporated. (Lower) Jig for evaporation of indium film for indium resistance thermometer. 9 This groove was filled with an indium~si1Ver alloy (95% In~SZ Ag) which melts at 1650C, has a wetting ability as high as indium, and greater strength3. The surface Of the alloy was made flush with the surface Of the HDP by machining and grinding. The resulting substrate was then placed in the evaporation jig shown schematically in the lower part of figure 2. (The HDP has a smooth side and a rough side; it has been found the thermometers are much more reliable if they are deposited on the rough face, possibly because this side seems harder, and has fewer deep scratches that lead tO thin spots in the film where early failure may occur.) The thickness Of the thermometer element was estimated during evaporation by noting the resistance Of the indium deposited on the fixed geometry Of two monitor slides placed beside the mask which controlled the dimensions Of the thermometer. .These monitor slides were made by using a diamond saw to cut a slot about 1 3/4" long 1/16" away from and parallel to the long side Of an ordinary 1" x 3" microsc0pe slide. The central 1 1/8" portion Of the 1/16" strip thus formed was temporarily masked with plastic tape, and the ends were covered with a mixture of gold salts in an organic carriera. When the tape was removed and the glass heated to nearly its softening point, the carrier oxidized and left on the glass a conducting gold film, which was then connected to wire leads by pressure contact. The cover which held the slides in place masked them in such a way that the only electrical path between the gold lands was the 1/16" glass strip. The two blank monitor resistors, 1 1/8" x 1/16", were connected in series and their resistance was measured during the evaporation with a laboratory Ohmmeter. The evaporation apparatus is shown schematically in figure 3. Indium of 99.999% purity supplied by the Indium Corporation of America was placed in the molybdenum boat, and the vacuum system was closed and pumped down. Since the presence of oxygen and water vapor in the residual atmosphere Of the evaporator will affect the electrical prOperties of 5, the ratio Of water molecules to indium molecules evaporated films striking the substrate per unit time was lowered by keeping the chevron baffle at liquidnnitrogen temperatures throughout the pumping cycle. The ratio Of oxygen atoms to indium atoms was lowered by evaporating indium as a getter over the interior of the bell jar prior to opening 10 SUBSTRATE\ J'G‘\ _r— 1 ] MOVABLE SHUTTER —\ I] L /-SUPPORT BOAT [1 J \f L BASE PLATE ‘ J EVAPORATOR Figure 3. Arrangement for vertical evaporation of indium films. 11 the shutter between the boat and the evaporation jig to allow the indium film to be deposited on the substrate. The shutter was kept Open for 10 to 15 seconds, until the resistance on the monitor slides fell to 8 to 10 Ohms, resulting in a thermometer element with a nominal room- temperature resistance of about 20 Ohms. When the thermometer was removed from the evaporator, conducting paint was applied between the film and the lands to insure good electrical contact. Thermometer calibration: - Two thermometers were calibrated by enclosing them in a brass-and-cOpper container with an electrical heater on the outside. The container was surrounded with sponge-rubber insulation and put inside a brass can about 4" in diameter and 9" long. A copper-constantan thermocouple compared the temperature at the surface Of the thermometer with that of the inside surface of the outside brass can. Leads from the thermometer and from the thermocouple were brought out through an 18" length Of %"-diameter stainless-steel tubing. This tube supported the can and served as a duct for evacuating it with a mechanical forepump, or filling it with helium gas by means Of suitable valving. The current source for calibration consisted of a 1.3-volt mercury battery in series with a 50-Ohm precision resistor for measuring the current, and apprOpriate variable resistors to adjust the current to values not greater than about lmA. The voltage drop across the resistance thermometer and across the precision resistor, as well as the thermocouple voltage, were measured with a Leeds and Northrup K~3 potentiometer. The thermocouple was also the sensing element for the heaterucurrent controller consisting of a Leeds and Northrup Type—G Speedomax recorder with Double» action Proportional-controller attachment. ‘All the voltages of interest were also continuously monitored with a Daystrom-Weston multipoint recorder. When the thermometer had been mounted in the can, the system was closed and flushed several times before it was filled to approximately atmospheric pressure with helium as an exchange gas. The can was placed in a stainless-steel dewar, which was then filled with liquid nitrogen. When the system had come to equilibrium as indicated on the recorders, measurements of the various voltages were made with the typenK potentiometer. The resistance R was determined and normalized by dividing by R0, the resistance at 0°C. The helium was then pumped out of the can and the '12 controller set to some temperature and turned on. The measurements were then repeated, after thCh the controller was set to a new temperature. This cycbe was repeated to obtain a complete calibration curve Of normalized resistance vs temperature. The curve in figure 4 shows the results of measurements on two films. 1 Between 0 and 3000K the temperature was determined from the thermocouple voltage by means Of preliminary NBS Cryogenic Engineering Laboratory tables which for all temperatures concerned differ by less than a degree from published values6. Calibration above 300°K was made with other tables7 which for temperatures between 250 and 3000K agree with the cryogenic tables to within % degree. A thermocouple, made Of wire from the same reel as that for the thermocouple measuring the difference between the can and the thermometer, had one junction attached to the outside Of the can and the other immersed in an ice bath. The voltage from this thermocouple was usually from 5.517 to 5.525 vawhen the can was submerged in liquid nitrogen. .From the tables, this voltage corresponds to a temperature Of about 78.50K, slightly over a degree above the liquid-nitrogen boiling point Of 77.40K. The difference may be due to heat leaks into the can, oxygen dissolved in the liquid nitrogen, or differences between the thermocouples in the present experiment and those used to construct the tables. -In any case the temperature is known to within 1 deg~C or about 2% on an absolute basis at liquid-nitrogen temperature, and more accurately at higher tempera" tures. Dewar and Temperature control. - The dewar for the Optical studies, which was Obtained commercially, is shown in figure 5, with details Of its lower part shown in figure 6. It is constructed Of stainless steel, with the exception Of the bottom Of the inner tail, and the radiation shields, and the lower part Of the outer vacuum container, which are all made Of copper or brass. All interior vacuum surfaces are gold plated. The lower mounting ring holds the dewar on an aluminum plate forming the cover of the sample compartment Of the spectrOphotometer during measurements. The rotating seal allows the substrate to be lined up with either of two pairs of perpendicular Openings in the outer vacuum container. Over one pair of Openings 0.040"~thick HDP windows are sealed with O-rings. The other pair of Openings, which are somewhat larger, will 13 .seoao nooaooeao osu pow mum o3o£m museum .mumu Ensemou moomumammn Edwpqw How w>yoo :OHumpowamc .4 muowwm (l) . AOMV enououomEoH 00m OON oo. _ . _ . _ a L . _ loo.— 14 Figure 5. Dewar used for low-temperature infrared-transmission studies. Not shown are the electrical feedthroughs just above the rotary assembly or in the pressure-relief head. _ £01.53 £68: <>_.m< Dwm. < _ .. Emcmh Imbo . \b _u_\~.. _m a}... aqua“. mo...>m< 4):: Om<<>m 16 HEATER SPACER S HOLDER INNER TION SHIELD OUTER RADIATION SHIELD OUTER VACUUM CONTAINER BLANK COVERS Figure 6. Detail view of the lower portion of the dewar. The two HDP windows in the outer vacuum container through which the infrared radiation passes into the dewar are not shown; they are parallel to the plane of the picture, one in front of, the other behind, the sample holder shown. l7 eventually be used to evaporate reactive materials within the dewar. They are at present closed with brass plates against O-ring seals. The bottom of the outer radiation shield is attached by a threaded joint in order to facilitate access to the inner tail. The inner radiation shield below the bottom of the inner tail also is screwed on to permit its removal for changing samples. The sample holder is shown in figure 7. In use the flat copper plate is loaded against the COpper block forming the bottom of the inner tail. The leads from the thermocouples, the resistance thermometer, and the heater are brought through holes in the side of the inner radia— tion shield, and are wrapped around the inner shield for thermal grounding. They are then brought to the outside of the outer shield through holes just above the threaded joint for the bottom part of the outer radiation shield, where they are attached to permanently installed leads which leave the dewar either through feedthroughs just above the rotable seal, or through a feedthrough installed in the pressure-relief valve. The heater, which consists of two windings of 35 turns of resistance wire connected in parallel, has a resistance of about 45 ohms. The substrate with the indium resistance thermometer carrying the film to be studied is held in place with the film side towards the heavy c0pper plate by a small plate on the back of the substrate and by four 6-32 machine screws. Two COpper-constdntan thermocouples are fastened between the smart plate and the substrate at the tOp and bottom of the holder. The junction of one couple is Placed at the bottom, and is referred to a junction at the top to give the difference in temperature across the holder. One junction of the other thermocouple is placed at the tOp of the holder, and is referred to a junction in an ice bath, to give the absolute temperature of the top of the holder. The K-3 potentiometer can be switched to measure any of the thermocouple voltages. In addition these voltages are continuously monitored with the multi-point self-balancing recording potentiometer. Since the potentials of some of the thermocouples may change polarity during the course of a run, the recorder zero is displaced with a simple voltage divider powered by a 1.35-V mercury battery. The current supply for the resistance thermometer is shown in figure 8. Coarse adjustment of the thermometer current is made by THERMOCOUPLE POSITIONS Figure 7. l8 HEAT ER SAMPLE HOLDER ' COpper sample holder. The heater consists of several turns of resistance wire wrapped around the vertical coPper block and insulated from it by Teflon tape. The thermocouples are clamped between the HDP substrate and the brass backing plate (not shown). l9 .uwoouwo mogu3mooa Houososuosuaooamuwflmon onu mo amnwmww JOOHm .w ounmwm .5264 m04h40> v. mN >0: Sodom Egon 8248mm «womoumm _m «wkméofizyroa O... «05.3”. o$ 555.02%...» mozflmomm zomommn LIL . c on 20 switching various fixed dropping resistors into the circuit with the adjustable resistor. Fine adjustment is made by means of a lOuturn potentiometer which varies the output voltage of the Zener-diode- stabilized regulated power supply between 100 and 250 volts. Since the resistance of the thermometer represents only a very small fraction of the total resistance of the load on the power supply, this supply is essentially a constant-current source. The voltage across the thermomew ter potential terminals is therefore directly proportional to the ‘thermometer resistance. This voltage, as well as the voltage drOp across the 20-ohm precision resistor in the current supply, can be connected by a switch to the K-3 potentiometer to permit the resistance of the thermometer to be determined. The voltage across the thermometer is also continuously monitored by the multipoint recorder. The thermometers under the LiF films were not individually calibrated. They were normalized by assuming that the film and the thermocouple were at the same temperature just after the film was installed in the dewar and before liquid nitrogen had been added. From the normalized resistance expected at this temperature according to the calibration curve (figure 4) and from the measured resistance, a value for the resistance at 0°C, R0, was estimated, and used to normalize the resistance values measured subsequently. Because all temperature measurements depend on the first one, temperatures measured with the resistance thermometer are probably not better than about 5%. As a rough check on the temperature-measuring_devices, after measurements were completed on the substrate and thermometer used to Obtain 100% lines from the spectrophotometer, the outside vacuum cover and the outer radiation shield were removed from the dewar. Then the inner tail with the sample cell attached was surrounded first by liquid nitrogen and later by ice water. With calibration as described above, the indium film when surrounded by nitrogen (boiling point 77.40K) indicated a temperature of 76.5°K. The thermocouple first indicated a temperature of 79.8OK, but then slowly drifted up to 840K. This shift is probably due to thermal gradients across the soldered connections in the thermocouple leads to the sample cell. When the tail was surrounded by ice water, the signal from the thermocouple was zero, indicating the thermal-gradient problems are significant only for large temperature 21 differences, where they may limit the accuracy of such measurements to about 10%. The potential from the thermocouple showing the temperature difference between the sample holder and the ice bath, after passing through an RC filter with a time constant of about 4 seconds, forms the sensing signal for the heater controller. The difference between this potential and that from another mercury-batteryupowered voltage divider set to deliver a voltage corresponding to the desired temperature, is applied to the input of a Leeds and Northrup DC microvolt amplifier. The output of this amplifier, after further amplification by a Mandrel DC amplifier, becomes the error signal applied to a CD current regulator controlling the heater current8. For most measurements the sample holder was spring loaded against two ring-shaped spacers of 0.040"-thick HDP on the bottom of the inner tail. After evacuation of the dewar, the inner and outer tails were filled with liquid nitrogen. Since the spacers thermally insulate the sample holder, the equilibrium temperature reached in this way was still considerably above liquid-nitrogen temperatures. To decrease the temperature further, the vacuum space of the dewar was filled with helium gas as a heat exchanger. When the temperature had nearly reached its new equilibrium value, the helium was pumped out and measurements were begun. When higher temperatures were desired the heater input power was first adjusted for the maximum that the heater could stand. When the desired temperature was reached, the power was reduced to approximately that needed to maintain the temperature, and the amplified error signal from the thermocouple was fed into the regulator.to provide continuous control. With this system it was possible to change to a new temperature and attain equilibrium within an hour. After equilibration the thermocouple potential usually re» mained constant to within.: 30 “V, corresponding to temperature variations less than i l.5°K. Transmission‘Measurements The transmission spectra Of the LiF films were obtained with a commercial double~beam far-infrared spectrOphotometer, the PerkinuElmer Model 301. A diagram of the Optical path of this instrument is shown 22 in figure 9. Between the source at I and the Golay detector, several of the reflection elements, the transmission filters at F3 and the crystal chOppers, may be changed to isolate a narrow band of the electromagnetic spectrum for dispersion by the grating 01. The mechanical linkage between the grating and its synchronous~drive motor is designed so that the frequency passed by the monochromator is directly proportional to the number of drivewshaft turns, which is presented on an arbitrary scale of 100 "drum turns" per revolution. Calibration of the drum turns in terms of frequency for any grating is made by operat- ing the instrument in the single-beam mode and observing the positions of the atmospheric-absorption bands (mostly due to water vapor). The 9, and a straight frequency of these bands is taken from the literature line is fitted to the data by the method of least squares.* The ratio of the signals in the two beams is presented on a visual-readout indicator and on a strip-chart recorder driven by a synchronous motor. The position of a point on the strip chart is correlated with the position of the wavenumber drive by a microswitch Operated by a cam on the wavenumber drive. The microswitch actuates a device which marks pips along the edge of the recorder chart or on the pen trace itself. A pip appears for every drum turn number ending in zero, and an extra pip appears for numbers ending in 95. To keep the instrument from having widely varying sensitivity as it scans through atmospheric-absorption bands, the instrument maintains a constant signal level in the reference beam by adjusting After our calibrations were completed a paper10 appeared which gave a list of more precise values for the atmospheric~absorption lines as found with a Perkin-Elmer 301 instrument. These new values are estimated to be correct to within 0.1 cm'l. The differences between the fre~ quencies assigned in this recent paper and those taken by us for the calibration lines of the 30-line/mm grating used in the study are, with 1, the new assignments tending to one exception, all less than 0.35 cm“ be about 0.1 cm"1 lower than the older ones. The difference is unimport" ant in studying the rather broad latticeuvibration bands, which have half-widths of about 35 em'l. Figure 9. 23 Optical path of the Perkin-Elmer 301 faruinfrared spectro~ photometer. Reflection elements on F1, Fl', and F2 may be changed from outside the instrument. Mirrors M4, M4', and M12 (along with the choppers) may also be changed to isolate a band of the electromagnetic spectrum for dispersion by the grating Gl before detection by the Golay cell near M22. 24 mmEEOhOImOEUmmw 0m~.<~.u.z_ - max". << oowmmwemomeu o>eumwmz .Homz mo Hmumxuo xoesu 851mm m we nowmeEmomuu uncommon moo waepuooou mo pocemuoo o>uso unweaammuum .oH munmwm AaIEOV accosvoum 0mm II ooe one can — _ I — _ _ T _ _ _ — _ — _ _ _ — _ — . . . ooHum«EmaouH unsouom . on God 27 .muwaw can no some? oueon How ooHuoouuoo Hooowueppm o . . so oudoepdw mommouo one no pouuoHo mo .mooHH No new NooH mnemamso Mom pouoouuou xowHH um EHHM m AauaoV hoooavoum .smuoasoo man man m mo asuuoomm use .HH ouowem So one . oom one . . . . . . . _. . o I on _ _ . r _ . . . . o3 coeuugeucsua uncouom 28 .o>flup nonesco>o3 one we wOHOOOm so» on coeuwmoo uumso oou ouoHou momma unmoo sou mo mambo Eouuon one new sou wooas moan Homospww may .poaamuno mos HH ousmwm songs scum oomuu novuooou HouoEouonmonuOOOm Homemwuo may _t A t ’ -.._,. .. a I . A .. 0 1 . .-....--—’.... . I o ...-...'i... . l 1 I r .,. I O .NH shaman 29 coo 0mm .HouomEoo osu an pouuoHoou mo mafia NooH < .MH ouzwwm AatEOV honosvoum omN 8m . . . . _ . cowomfifimcoua unmouom on OOH 3O D‘" ' A “(Fwd/c [flood/c 0” n e where h is the complex index of refraction related to the complex dielectric constant €( cu ) and the permeability It by 5( w) = ( 6" /y,)25 = E I for p = 1. There exists no theories at present which indicate in any detail the form and the temperature dependence of é?(t4J). Hence we chose a basically phenomenological model suggested initially by Lorentz, namely, a single dispersion oscillator of frequency “Jo and damping constant 3’. This model gives the following expression of €(uJ):11 aw): 6.. + €°“‘€~ - ‘ (.2) / —— (w/w.)‘ — z (imam/w.) where Eco , the dielectric constant in the visible region of the spectrum, summarizes the effects near Lijo of vibrations (other than those of the lattice) whose characteristic frequencies are much higher than (*Jo’ e.g., polarization of the electron clouds in the atoms; the quantity 6 o, the dielectric constant at frequencies much less than we, represents the. effects of polarization of the entire crystal, including distortion of the ionic cores. The result of inserting this expression for the dielectric constant in equation (1) is too complicated to yield directly much information about the parameters in equation (2). For thin films equation (1) may be expanded in a series Of powers of qu/c. A suitable approxima« tion is provided by including powers through the second. When equation (2) is used to give a, simple expressions for the parameters in equation (2) may be obtained12 based on data for Lt) within.: 10% of avg: V2 X/w. = {E I/( 0.0— D...) - l/Da] S} ) ca) 31 Va _ 2 c ' __ v. _ A __ W, 2:. (“L May/Z. (3c) where w_ and 60+ are the frequencies on either side of the trans- mission minimum which have equal values of transmission, S is the lepe of the graph of ( "U/UUO - “Jo/u) )2 as a function of [l/(Doo - D) - 1/(0,o - Dump], 0min is the minimum value of the transmission, and D00 is the transmission outside the absorption band and differs from unity as a result of scattering and absorption by other mechanisms.. The expressions for d and XVLLIO require a tedious plotting to find S. If one picks two special points, however, on the Spectrum, one at wo where D = Dmin’ and the other at Cat/g5 where D = Pao3 gem ecumHFHOmoucoemeonmeu woumaooHMO won me mama weaom use .o>Lao smengeamaMm we mafia pmqup mcH .moma Ednuooomv MONHH um Eaew hoe; n no ammonium ooeuuoomnm AHIEOV honedvoum .qH roswom ooe one com on . . . _ . . _ _ _ . . . . o scammwemomua I I on unoopom . _ _ . . . . _ . _ . _ . OOH 38 material was controlled to have nearly pure Li6F, nearly a half-and-half mixture of Li6F and Li7F, and nearly pure Li7F, corresponding respectively and precisely to the fractions x = 0.007, 0.514, and 0.9999 in the expression [(1 - x) Li6 . x Li7 ]F19. For Li7F, films of various thick» nesses were studied, to permit examination of the validity of the assumptions made in applying electromagnetic theory in equation (2). The parameters determined by the least-squares fit outlined above to the portion of these spectra within': 10% of (4)0 are listed in Appendixes A, B, C, and D respectively. A direct investigation of whether the dispersion-oscillator formula fits the data better than some other kind of expression is sterile until the formula has been proved inadequate, or until a physical basis has been put forward for another expression. .Instead we vary the experimental conditions of temperature, film thickness, and isotOpic mass, and see whether the behavior of the parameters (4)0, X/w o’ and d is consistent with expectation. Table II summarizes the relations to be considered. They will now be discussed in some detail. Infrared dispersion frequency Lug 2gp§ndence on thicknegg. - The parameter ago is closely related to cabin, the frequency of minimum transmission, and is commonly taken as that frequency. Actually, on the dispersion-oscillator model, ‘x/min varies slightly with thickness d for fixed (2)0, as seen in figure 15, showing values of LL’min cilculated from equations (1) and (2) for LiF with (4)0 taken as 304 cm and ‘o’lw o as 0.082. Thus, although 6L)min may vary slightly with thickness, there is no reason for the parameter (4)0 as obtained in our analysis to vary with thickness, since it is characteristic of the material only. At present we do not have facilities for direct measurement of the thickness, and we can determine only the apparent thickness; (4)0 should of course be just as independent of the apparent thickness d as the real thickness. Figure 16, a plot of ¢2Jo against d, shows that bog is indeed constant at 306.0 cm-l. To see whether this value is reasonable in view of our knowledge of other properties of the crystal, we make 39 Table II Expected dependence of single dispersion-oscillator parameters on experimental variables. Experimental IsotOpic Actual Reduced Temperature Thickness mass T t H parameter Dispersion frequency t0 1? -35 l - QT (4J0 Apparent thickness t1 iP T0 d Reduced damping to Weakly Increasing constant Increasing Wu) 0 40 .Nwo.o n o 3\\p ...qu 0.13m. u 03 “madame? Hmuwfimnmm . TEE .HoumZHomcccowmummmwp of you «.3 pam :v maoflmsvm Eoum pmumasoamo mm c mmmcquu do £53 we mocmpcmmcn .2 3:me 3 v 38.329 o.~ OH.o Ho.o Hoo.o n . J . q _ d . II «on 03 EU ATV :8 «3 I II mom _ . p _. I _ p p 41 .mmmmmcxoflsu msoHHm> mo wEHam m\«A we mmwumw m you w mmmcxowsu ucmummmm so QC . m mmcxuwfi. I a . I.\ _nxu so wuamwsmmmm .oa msawsm cud 9.6 o 1 . _ a- — _ . 1 J .0 II II God is l... .|.. cow 03 ”..l I i . I XIII”... con i > Aoav .w>o x . _ I; P _ _\ L» b _ 42 . . . 1 use of Szrgeti's relation w: =-— [ (e..+ 2%, r 2)](e a/MPL <7) where a is the lattice constant, 171- is the reduced mass, and (3 is the compressibility. With room-temperature values of lattice constant a = 1.98 x 10"8 cm, compressibilitylg (3 = 1.35 x 10"12 cmz/dyne, dielectric constants as given before, and with reduced mass 1; = 8.50 x 10.724gm, we find a calculated we of 319 cm-1, in what is undoubtedly fortuitously close agreement with our room-temperature value of 306.0 cm'l. Dependence on isotOpic mags. - A change in isotOpic mass for a: monatomic isotopically pure substance is equivalent to a change in the time scale for the motion in both classical and quantum mechanics, as follows directly from the equations of motion. That is, frequency may be traded for square root of reciprocal of mass, provided comparison is made at temperatures equivalent in the statistical-mechanics sense. For diatomic substances the relations are more complicated, but semi" quantitatively we should expect the same kind of behavior. We should perhaps then examine the ratio of (4)0(Li—6)/CAJOCLi~7) at equal Debye temperatures; but, as will be seen, L‘Q varies only slightly with temperature, and it may seem less arbitrary to compare the values for different isotOpic mass at the same temperature. ‘At 3000K we find the observed ratio to be 324.7/306.0 = 1.0611, in good agreement with the reciprocal of the square root of the ratio of the reduced masses, 1.0590. This result is in good agreement with work done earlier by -different methods by others in our laboratoryzo. If we had compared the dispersion frequencies at equal Debye temperatures, that is, 300°K/l.059 = 283°K for Li7F corresponding to 300°K for ‘Li6F, we would have found ~LUO (Li-6)/€AJO(Li-7) = 1.0654 (see figure 17). The difference is not important. Dependence on temperature. - The effect of temperature T on (AJO may be roughly estimated by the Szigeti relation (7), which should reflect the predictions of a more accurate theory. We compute from equation (7) the relation: 43 .ccfiuwmoaezo uaaocOmw accurwwflc mo me.ww How ; resumcuo61c 4.1c1> .Hoocc1roicc :.Iw.nampc .I" \ijwa Aomv mHSumHoQEmH oom CON OOH a . _ _ _ _ o I: mom... 4 11 03 u: ~30\oOmojo\oOmu 0 a»... X A753 III II. CON 03 I. moooDVoum cofimummuan IIIVHHmWHHHH II. com I X it o a .Olll . XI I... .1 . ....I o ...firl. -T ‘9 IIARU. _ _ _ _ LIL 44 Jon. _ I _LDa. [98 l )5. l 93 (a) $3 9? — (604.2”? (5&sz __L __ “1.9"!“ ’ 2. a3?“ and list the contributions of the various terms, in Table III. By far the largest contribution is that due to the effect of thermal expansion on the static dielectric constant 6- o' The overall effect is that (1/ WC) 9000/ a T = -142 x 10'6/deg-K. The values observed for Li6F and Li7F in units of 10-6/deg-K are respectively 255 and 239. This agreement is reasonable, considering the fact that all the temperature coefficients are room-temperature values. Apparent thickness d In contrast to we and K/uJo, the parameter d is supposed to be characteristic of the particular films,.and not of the material. In conjunction with the reduced damping constant X/CA’Oa it determines the depth of the minimum. Dependence on temperature. - Since thermal expansion‘causes a negligible change in actual film thickness (of the order of 2000 x 50 x 10-6/deg = 1%), we should expect the apparent film thick" ness d to be nearly independent of temperature T. Figure 18, a plot of d against T, agrees with this prediction. “ Dependence on actual thickness and isotopic mass. - We should of course expect the apparent thickness to equal the actual thickness as determined independently. As yet we have not develOped techniques to measure the thickness directly. Until such measurements are made, we cannot verify that the apparent thickness is independent of actual thickness and isotOpic mass, as the dispersion-oscillator model predicts. Reduced damping constant J/wo Dependence on actual thickness. - Like 600, the parameter 3’/ wo is supposed to characterize the material only, and therefore be independent of thickness. In conjunction with the apparent thickness d, it determines the width of the absorption band. As explained before, we do not know 45 Table III Contribution of various terms to the dependence of the infrared dispersion frequency of LiF on temperature. Source Contribution x 106/Kp Reference 1 aa + 18 21 a 31E _1_ Qé - 12 19 (9 9 T 1 Q6. +306 15 -— + (:0 2 ,9 T 1 96:0 - 9 16 éw+2 a '1' 46 AH ampocnudemu mcrqomcm momuo> mcwcwmmoEoo owmouomw camcmwmwp mo msgew imcrc mm c wmmcxswru ccmtrmq< .rm mermem Aomv musumuoaama com com 00H _ a m _ o . to... < “_c._.\00m._._.\.ofl o “...: x .....I II 0.79 x x x x . 3 l x I A3 moocxoasa [1% O 0.. q . ”€9.8an oo 0 II ..I 0N6 « o o Ilall 4 < 4 1| IL h . . _ _L 47 the actual thickness t, and instead use the apparent thickness d as its measure. Figure 19, a plot of 67a) 0 against d for the series of L17F films observed at room temperature, though it shows an unwelcome scattering, exhibits no trend. The agreement is probably acceptable. .Dependence on isotOpic mass. - Here the theory is complicated, but isotOpic mass can have only a slight effect. As an example, let us I, consider an expression derived by Born and Huang‘z, 3 z . 7. X: 2C h ‘3" V MLM + :17? {6[ WM?) .+[Zc‘$l/"(n‘)+39’"m‘Z/},(9) q we where ‘+’(r02) is the overlap energy function as a function of nearest- neighbor distance r0, V' is the cell volume, C is a constant of the order of unity, M is the mass of the positive ion, and m is the mass of the negative ion. We compare damping at the same temperature, although perhaps we should choose equal Debye temperatures. Onlylm and (4)0 should change appreciably with isotOpic mass. Hence we find the ratio of reduced damping constants should be XV“): =( M')Vz M + M 3’1~ . ...... ...—_______ ; (10) X/Wo M m+M' where the prime refers to Li7F. .For isotOpically-pure lithium fluoride we find the value 1.018. Experimentally we observe too much scatter in ‘X/Lb’o to pick up a difference this small. We must content ourselves with noting that the reduced damping constants for both Li6F and Li7F lie in the same band on a plot of {/u.) 0 against T, as shown in figure 20 now to be discussed. Dependence on temperature. - Although there exists no complete detailed theory of the broadening of absorption bands, the basic mechanism seems to be understood. In the harmonic approximation the absorption lines would be infinitely sharp; only mechanical anharmonicity and higher-order electric-dipole moments allow a broadening. At least two phonons must be involved, and these phonons can come from widely separated regions of the vibration spectrum. In any event, it seems 48 .mEHHw m m HA Hmuo>mm 9.5 you w mmoaxowzu ucmummmm $6.15 0 3\b uamumooo waHQEmp twosomm .mH muowfim 3v «mono—3:9 0N.o o~.o o T q] — u — _ _ C III III! oo~.o X xv . . o 1. . Aoa\k v . w>u 1 3\k 1 I .H _ _ P _ _ _ _ . oo~.o 49 .coHoqmomaoo caucuowfl tomumwmwp to mEHHw now H musumumaEmu m1m~¢> rare?» oom Aomv oHSumuomEmH ctmunccc mmmemp Emphomm CON OCH 4 _ q _ _ mo: 4 u.._._.\.omo_._.\.oe o “:3 x II III AW“ IIMVIIIIIIII I; x 1%.... x 4 \q / < \ II |HH\~mfiw Av nu .111 I11 AU [thy Au .1111111hV1 .IIIIIIIIIIII 11. Au 0 \\ . \O\\ :1 Au .. .1 _ n r I»! _ .QN Twflmnm no.0 935B o~.o 50 clear that at temperatures quite low in comparison with lattice charac- teristic temperatures, where virtually no phonons are present, the reduced damping 370;)0 should be nearly independent of temperature. As the temperature reaches values sufficient to excite appreciably the various peaks in the lattice-vibration spectrum, new absorption mechanisms enter, and the damping should increase. Examination of the data exhibited in figure 20, plots of X/uJ 0 against T for films of various isotOpic compositions, does little to confirm or refute this picture. The temperature where the reduced damping constant should start to rise can be estimated from the phonon spectrum. Figure 21,:fiupspectrum calculated by Karo and Hardy23, shows that few phonons will be excited thermally below about 2000K. Hence the damping should be constant below this temperature, and start to rise above it. Although a slight tendency for the curve to rise with increasing temperature may be read into the curve, it would be gratuitous to claim any real meaning until the low-temperature behavior can be explained. Apparently the damping starts to increase as the temperature falls below 1209K or so; there seems to be no way to understand this behavior theoretically, and it is likely that it is an artifact of the experimental technique or the analytical method. Until this point is resolved, we must keep in mind the limitations on the use of Kl“) o as a parameter to characterize the absorption. Effect of Iggtopic Mixing We have deliberately excluded the dependence of the parameters on isotOpic composition, because the theory is extraordinarily difficult. Rather our motivation is to use the parameters to characterize the effect of isotOpic composition. Naively one might expect an isotOpicallyn mixed crystal to behave like an isotOpically-pure crystal of reduced mass equal to the average reduced mass Of the mixture. ,For many prOperties this description is reasonable and correct. Let us test it for our parameters we, d, and ‘(lw o’ basing our comparison on our results for the SOZ-SOZ mixture of Li6F and Li7F. For the dispersion frequency, examination of figure 17 shows that (A) o for the isotOpically-mixed film is indeed intermediate between the values for the isotOpically-pure films. At room temperature the 51 .. mpnmm paw oumM ma poumadoamo mm mag mom mowuoaow cowusnfluumwp modern .HN mpnmam «N Tm n...O_ x 3 E N. O. m m V. N O q/ I .. I _ _ _LVLWJO ... 00m 3 z I 009 52 observed ratios are: 1.033: 1.026: 1, those calculated as the reciprocals of the square root of the average reduced masses are 1.031: 1.027: 1. The agreement is satisfactory, and indeed continues to be so over the entire range of temperature given. For the apparent thickness, there is little to add to the previous discussion for isotOpically pure films; figure 18 shows the same kind of constancy of d with T. For the reduced damping constant, we must surely give up our naive picture. The parameter X/wo is nearly independent of isotOpic mass, on both theoretical and experimental grounds, as discussed above. Hence, for a given film thickness, the width of the absorption peak would be nearly independent of isotopic mass. Yet on another naive picture one might suspect the actual absorption in a mixed film might be something like a superposition of two separate absorption peaks, the components behaving more or less independently; the resultant peak would widen, and might even exhibit structure. In reality, of course, the lattice-vibration spectrum must be extremely complex in the case of mixed films, and the absorption peak must be something intermediate between the two naive models described. Examination of figure 20 shows the reduced damping constant to be significantly greater for the mixed film than for the pure film. In sum, it appears that representation of the infrared dispersion peak by a LorenEzlln oscillator permits a useful characterization of the Optical behavior of films of ionic crystals in terms of two material parameters, (1)0 and Zf/L4Jo, determined from absorption spectra of thin films, and two other material parameters éo, and 6 0, determined by other means. The behavior of these parameters with respect to temperature, isotopic composition, and (presumably) chemical composition should afford a valuable means of increasing our understanding of the interaction of electromagnetic radiation with crystals. Obviously other techniques, particularly reflection from thick single crystals, and Raman and Rayleigh scattering, are required to provide a basis for fuller understanding. But far studies of materials that are reactive, that are difficult to crystallize, or that are available only in small amounts, the study of absorption in thin films offers great promise. 53 The present work has demonstrated that it is practical to use a large portion of the absorption peak to determine the parameters, that the values thus obtained have considerable validity, and that the parameters behave about as reasonably as present theory is capable of predicting. Further experimental work must be carried out to increase the accuracy of the temperature measurements, and to deve10p methods of determining actual film thickness. Further work on the method of analysis must be carried out to establish the Optimum portion of the spectrum to take for analysis, and to deve10p criteria of goodness of fit. Systematic investigation, then, of the effect of temperature and chemical composition in chemically and isotOpically pure substances should lead to the elucidation of familiar phenomena; and investigation of the effect of chemical and isotOpic composition in mixed crystals should lead to discovery of new phenomena. 2. 3. 4'. 5. 6. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 54 REFERENCES R. Bowling Barnes and.M. Czerny, z. Phyzik _z_2_, 447 (1931); R. Bowling Barnes, Z. Phyzik 153 723 (1932).; G. R. White and s. B. Woods, Rev. Sci. Inst. g_8_, 63b (1957). R. B. Belser, Rev. Sci. Inst. 25, 180 (1954). Hanovia Liquid Bright Gold 261, Engelhard Industries, Inc. H. J. Caswell, J. App. Phys. 32, 2641 (1961). R, L. Powell, M. D. Bunch, and L. P. Caywood, Advances in Cryogenic Engineering g, 537 (1960). Henry Shenker, John I. Lauritzen, Robert J. Corruccini, and S. T. Lonberger, Reference Tables for Thermocouples, National Bureau of Standards Circular #561 (1955). T. M. Dauphinee and S. B. Woods, Rev. Sci. Inst. 26, 693 (1955). H. M. Randall, D. M. Dennison, Nathan Ginsburg, and Louis Rs Weber, Phys. Rev. 5;, 160 (1937). ' K. N. Rao, R. V. deVore, E. K. Plyler, J. Research National Bureau of Standards 67A, 351 (1963). M. Born and K. Huang, Dynamic Theory of Crystal Lattices (Clarendon Press, Oxford, England, 1956), p. 83. D. J. Montgomery and K. F. Yeung, J. Chem. Phys. 31, 1056 (1962). M. H. Lietzke, "A Generalized Least Squares Pragram for the IBM 7090 Computer" ORNL-3259, available from the Office of Technical Services, Department of Commerce, Washington 25, D. C. (50c). 'M. Born and K. Huang,‘gp. cit., p. 85. J. S. Bosman and E. E- Havinga, Phys. Rev. 129, 1593 (1963). R. S. Krishnan, Progress in Crystal Physics 1, 153 (1958). B. Szigeti, Proc. Roy. Soc. A204, 51 (1950). ‘M. Born and K. Huang, op, cit., p. 52. International Critical Tables GMcGraw Hill, New York, 1928), Volume III, pp. 47, 48. D. J. Montgomery and R. H. Misho, Nature 183, 103 (1959); R. H. Misho, Ph.D. disertation, Michigan Statute University, 1961. 55 21. values of the coefficient of thermal expansion are taken from American Institute of Physics Handbook, Dwight E. Gray, editor (McGraw~Hi11, New York, 1963), second edition, p. 4773. 22. M. Born and K. Huang, op. cit., p. 362. 23. A. M. Karo and J. R. Hardy, Phys. Rev. 129, 2024 (1963). APPENDIXES 56 57 Appendix A Infrared parameters of a Li6F19 film at various temperatures as determined by nonlinear least-squares analysis of that portion of the spectrum within: 107. of WC. Spectrum Temperature Thickness d Dispersion Reduced Damping number (KO) (microns) Frequency wo Factor {/6120 . (cm ) 168 297.0 0.216 323.6 0.102 169 298.0 0.231 1 323.8 0.100 170 96.8 0.236 341.4 0.087 171 148.4 0.247 337.6 0.082 172 220.6 0.241 ' 332.1 0.081 173 296.3 0.230 325.7 0.102 174 117.0 0.245 339.8 0.091 175 160.6 ‘ 0.215 334.6 0.076 176 188.4 0.219 .332.3 0.078 177 222.8 0.225 329.5 0.081 178 250.6 0.241 328.3 0.089 179 275.6 0.222 "326.5 0.091 180 298.6 0.225 A 325.6 0.096 \" ‘ 58 Appendix B Infrared parameters of a [(51.37%) L17.(48.63%) Li61Li6F19 film at various temperatures, as determined by nonlinear least-squares analysis of that portion of the spectrum Within 1' 10% of’ mo. Spectrum Temperature Thickness d Dispersion. Reduced Damping number (K9) (microms) Frequency 000 Factor x/u) 0 (cm ) 194 296 0.167 314.3 0.110 195 123 0.174 330.0 0.104 196 155 0.174 326.1 0.105 198 186 0.178 323.4 0.112 199 218 0.176 320.5 0.104 200 243 0.171 317.9 ‘ 0.109 ' 201 270 0.182 315.8 0.107 202 295 0.188 314.6 0.115 203 298 0.171 - 315.1 0.120 204 298 0.183 315.3 0.124 59 Appendix C Infrared parameters of a Li7F19 film at various temperatures as determined by nonlinear least-squares analysis of that portion of the spectrum within 1 10% of uJO. Spectrum Temperature Thickness d Dispersion Reduced Damping number (K9) (microns) Frequency to! Factor K/uu (cm'l) o o 184 118 0.149 321.7 0.095 185 155 0.141 317.8 0.085 186 187 0.139 315.1 0.081 188 244 0.139 309.9 0.081 189 255 0.139 307.8 0.085 190 296 0.138 306.2 0.090 191 297 0.150 305.4 0.998 Appendix D Room-temperature infrared parameters for a series of Li F Spectrum number 220 219 222 223 60 7 19 films as determined by nonlinear 1east¥squares analysis of the spectrum within: 107. of Lao. Thickness’d (microns) 0.031 0.059 0.139 0.222 Dispersion Frequency a) (cm'1) 0 304.5 _ 305.3 306. 7 306.9 Reduced Damping Factor K/UJ o 0.111 0.111 0.125 0.108 "111111111111