Refractive index of alkali halides and its wavelength and temperature derivatives
Cite as: Journal of Physical and Chemical Reference Data 5, 329 (1976); https://doi.org/10.1063/1.555536 Published Online: 15 October 2009
H. H. Li
ARTICLES YOU MAY BE INTERESTED IN
Refractive index of alkaline earth halides and its wavelength and temperature derivatives Journal of Physical and Chemical Reference Data 9, 161 (1980); https://doi.org/10.1063/1.555616
Refractive index of silicon and germanium and its wavelength and temperature derivatives Journal of Physical and Chemical Reference Data 9, 561 (1980); https:// doi.org/10.1063/1.555624
Optical constants of graphene measured by spectroscopic ellipsometry Applied Physics Letters 97, 091904 (2010); https://doi.org/10.1063/1.3475393
Journal of Physical and Chemical Reference Data 5, 329 (1976); https://doi.org/10.1063/1.555536 5, 329
© 1976 American Institute of Physics for the National Institute of Standards and Technology. Refractive Index of Alkali Halides and Its Wavelength and Temperature Derivatives
H. H. Li
Center for Information and Numerical Data Analysis and Synthesis, Purdue University, West Lafayette, Indiana 47906
Refractive index data for 20 alkali halide" are l>yhRII<:tiv,.ly "Ilrvpyprl, p.ompil,.rl. !mel !malyzNi. The most probable values at 293 K for the transparent ref"ion are generated for the materials for which experimental data are sufficiently abundant and reli\lble. Provisional values are also provided for the wavelen~th regions where available data are insufficient or missing. Rea!;Oonable estimations of refrac tive index for the very scantily measured materials were made by incorporatinl! the dielectric constants and wavelengths of absorption peaks into a simplified dispersion equation. Temperature derivatives of refractive index for most of the alkali halides were unavailable. However, using the existing data for the five most commonly used alkali halides, novel empirical facts were discovered and dn/dT for mllIR" w~rp p.on"trtl('tprl for !-Ill of the alkali halides. The calculated dnldT values agree remarkably well with the existing experimental data.
Key words: Alkali halides: optical constants: refractive index: temperature coefficient of refractive index. Contents
List of Tables ...... '" ... _... , .... '" .... __ " _..... " .... . 329 3.8. Sodium Iodide. NaI._ ...... -... . 408 List of Figures ...... 33] 3.9. Potassium Fluoride, KF ...... 414 List of Symbols ...... _...... _...... 332 3.10. Potassium Chloride, KCl...... 421 1. Introduction ...... 332 3.11. Potassium Bromide, KBr...... 436 2. Theoretical Background and Empirical 3.12. Potassium Iodide, 1\.1...... 449 Formulas. __ ... '" ...... _. 336 3.13. Rubidium Fluoride, RbF ...... 460 2.1. Refractive Index ...... 337 3.14. Rubidium Chloride, RhCJ ...... 466 2.2. Temperature Derivative of Refractive In- 3.15. Rubidium Bromide, RbBr ...... 474 dex, dn/dT ...... 339 3.16. Rubidium Iodide, RbI...... , '" .. , 481 3. Numerical Data ... _...... _.. _...... 341 3.17. Cesium Fluoride, CsF .. , ...... 488 3.1. Lithium Fluoride, LiF '" ...... 341 3.18. Cesium Chloride, CsC1...... '" ...... 494 3.2. Lithium Chloride, LiCl...... 361 3.19. Cesium Bromide, CsBr ...... 502 3.3. Lithium Bromide, LiBr. .. '" ., ... _...... 366 3.20. Cesium Iodide, Csl. .... , ...... 512 3.4. Lithium Iodide, Lil ...... 371 4. Conclusions and Recommendations ...... 522 3.5. Sodium Fluoririp., NaF.._._ ...... 376 s. Acknowlerlgment~._ .. __ ..... _. __ . ____ ._. _... ______526 3.6. Sodium Chloride, NaCl...... 385 6. References ... _...... 526 3.7. Sodium Bromide, NaBr. .. _...... _...... _. 402 List of Tables
Page 1. Available Experimental Data Sets on the 5. Parameters for the dn/dT Formulas of Alkali Refractive Index and Its Temperature Halides at Room Temperature ...... 342 Derivative ...... _...... _...... 333 6. Recommended V alueson the Refractive In 2. Some Physical Properties of Alkali Halides dex and Its Wavelength and Temperature at Room Temperature ...... -.... _...... - 835 Derivatives for LiF at 293 K ...... 347 3. Available Parameters for Dispersion Equa 7. Source and Technical Information on the Re tions of Alkali Halides at Room T empera- fractive Index and dn/ dT measurements of tures ...... _...... _" _., 338 LiF ...... 352 4. Some Useful Parameters for Dispersion Equa 8. Experimental Data on the Refractive Index tions of Alkali Halides at Liquid Helium of LiF ...... _...... 355 Temperature ...... _...... 339 9. Experimental Data on dn/dT of LiF ...... 359 10_ Comparison of Dispersion Equations Pro- posed for LiF ...... _...... , .... _.. 360 11. Recommended Values on the Refractive In- C0l>yril!ht CD 1976 by thp U.S. Secretary of Cnmm .. rce on l.ehalf of tl](' United States. Thi, ("oPFi:rht will h~ as"i~ned to the American In~titut .. of Physics and the American Chemical dex and Its Wavelength and Temperature 50("iety. til whom all requests rc!!ardin!! reproduction should he addre"s("d. Derivatives for LiCI at 293 K ...... _ 362
329 J. Phys_ Chern. Ref. Data, Yol. 5, No.2, ] 976 330 H. H. U
i,ist of l' abies - Continued
Pa~e 12. Source and Technical Information on the Re 34. Source and Technical Information on the Re fractive Index and dn/dT measurements of fractive Index and dn/dT Measurements LiCl ... '" ...... 365 of NaI ..... , '" ...... 413 13. Experimental Data on the Refractive Index 35. Experimental Data on the Refractive Index of LiCl...... 365 of NaI ..... , ...... 413 14. Recommended Values on the Refractive In- 36. Recommended Values on the Refractive In dex and Its Wavelenglh ami TellljJelalule dex and Its WaveleIlglb allU TellljJeraluIe Derivatives for LiBr at 293 K...... 367 Derivatives for KF at 293 K...... 415 15. Source and Technical Information on the Re 37. Source and Technical Information on the Re fractive Index and dn/dT measurements of fractive Index and dn/dT Measurements LiBr...... 370 of KF...... 419 16. Experimental Data on the Refractive Index 38. Experimental Data on the Refractive Index of LiBr ... '" ...... 370 of KF...... 419 17. Recommended Values on the Refractive In 39. Comparison of Dispersion Equations Pro- dex and Its Wavelength and Temperature posed for KI'...... 420 Derivatives for Lil at 293 K...... 372 40. Recommended Values on the Refractive In- 18. Sourcc and Tcchnical Information on the Re dex lind Its Wavelength and Temperature fractive Index and dnl dT Measurements of Derivatives for KCl at 293 K...... 423 Lil...... 375 41. Source and Technical Information on the Re 19. Experimental Data on the Refractive Index fractive Index and dn/dT Measurements of Lil ..... , '" ...... 375 of KCI...... 428 20. Recommended Values on the Refractive In 42. Experimental Data on the Refractive Index dex and Its Wavelength and Temperature of K(~l...... 43] Derivatives for NaF at 293 K...... 377 43. Experimental Data on dn/dT of KCI...... 434 21. Source and Technical Information on the Re 44. Comparison of Dispersion Equations Pro- fractive Index and dn/dT Measurements of posed for KCl...... 435 NaF...... 381 45. Recommended Values on the Refractive In- 22. Experimental Data on the Refractive Index dex and Its Wavelength and Temperature of NaF...... 382 Derivatives for KBr at 293 K...... 438 23. Experimental Data on dn/dT of NaF ...... 383 46. Source and Technical Information on ihe Re 24. Comparison of DIspersIOn Equations Pro- fractive index and dn/dT Measurements posed for NaF...... 384 of KBr...... 443 25. Recommended Values on the Refractive In- 47. Experimental Data on the Refractive Index dex and Its Wavelength and Temper. J. Phys. Chern. Ref. Data, Vol. 5, Nc. 2, i 976 ...... VE INDEX OF ALKALI HALIDES 331 List of Tables - Continued Pa~t.' 57. Experimental Data on the Refractive Index Refractive Index and dn/dT Measure- of RbF...... 465 ments of CsF...... 493 58. Recommended Values on the Refractive 73. Experimental Data on the Refractive Index Index and Its Wavelength and Tempera- of CsF...... 493 ture Derivatives for RbCl at 293 K...... 467 74. Recommended Values on the Refractive 59. Source and Technical Information on the Index and Its Wavelength and Tempera- Refractive Index and dn/dT Measurements ture Derivatives for CsCI at 293 K...... 495 of RbCl...... 47] 75. Source and Technical Information on the 60. Experimental Data on the Refractive Index Refractive Index and rln/ dT Measure- of RbCl ...... '" ...... 472 ments of CsCl...... 499 61. Experimental Data on dn/dT of RbCl...... 472 76. Experimental Data on the Refractive Index 62. Comparison of Dispersion Equations Pro· of esCl ...... '" ...... 500 posed for RbCl...... 473 77. Comparison of Dispersion Equations Pro- 63. Recommended Values on the Refractive posed for CsCl...... 501 Index and Its Wavelength and Tempera- 18. Recommended Values on the Refractive ture Derivatives for RbBr at 293 K...... 475 Index and Its Wavelength and Tempera- 64. Source and Technical Information on the ture Derivatives for CsBr at 293 K...... 504 Refractive Index and dn/dT Measurements 79. Source and Technical Information on the of RbBr ...... ,. '" ...... 479 Refractive Index and dn/dT Measure- 65. Experimental Data on the Refractive Index ments of CsBr ." ...... 508 of RbBr...... 479 80. Experimental Data on the Refractive Index 66. Comparison of Dispersion Equations Pro- of CsBr .. , ...... 509 posed for RbBr...... 480 81. Experimental Data on rln/dt of CsBr...... 510 67. Recommended Values on the Refractive 82. Comparison of Dispersion equations Pro- Index and Its Wavelength and Tempera- posed for CsBR...... 511 ture Derivaiives for RbI at 293 K...... 482 83. Recommended Values on the Refractive 68. Source and Technical Information on the Index and Its Waveleng:th and Tempera- Refractive Index and dnldT Measurements ture Derivatives for Cs1 at 293 K...... 514 of RbI...... 486 84. Source and Technical Information on the 69. Experimental Data on the Refractive Index Refractive Index and dn/ dT Measure- of RbI...... 486 ments of CsI...... 518 70. Comparison of Dispersion Equations Pro- 85. Experimental Data on the Refractive Index posed for RbI...... 487 of Cs1...... 519 71. Recommended Values on the Refractive 86. Experimental Data on dnl dT of CsI...... 520 Inrle"x ::mrl Tt~ W ::Ivpl.pngt h ano Tp.mpp.ratI1Tp. 87. Comparison of Dispersion Eql1::1tions Pro- Derivatives for CsF at 293 K...... 489 posed for Cs1...... 521 72. Source and Technical Information on the List of Figures 1. Absorption Spectrum of a Typical Alkali- 13. dn/dT of LiBr...... 369 Halide Crysta1...... 334 14. Refractive Index of Li1...... 373 2. OJ t..1J (d~lIldT) vs. Atomic Number of Alkali 15. dn/dt.. of Lil...... 374 Ion of Alkali-Halide Crystals...... 341 16. dn/dT of til...... 374 3. 0:'/0: vs. Atomic Number of Alkali Ion of 17. Refractive Index of NaF...... 379 Alkali-Halide Crystals...... 342 18. dn/d'A of NaF...... 380 4. Refractive Index of LiF (transparent region)... 349 19. dn/dT of NaF...... 380 5. Refractive Index of LiF ...... 350 20. Refracti ve I ndex of N aCl (trans parent 6. dn/d'A of LiF...... 351 region)...... 389 7. dn/dT of LiF...... 351 21. Refractive Index of N aCL...... 390 8. Refractive Index of LiCl...... 363 22. dn/d'A of NaCl...... 391 9. dn/d'A of LiC1...... 2,64 23. dn/ dT of N aCl ______... 391 10. dn/dT of LiCl...... 364 24. Refractive Index of NaBr...... 405 11. Refractive Index of LiBr...... 368 25. dn/d'A of NaBr ...... 405 12. dn/d'A of LiBr...... 369 26. rln/ dT of N aBr ...... 406 J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 H. H. U List of Figures - Continued Pagr 27. Refractive Index of NaI...... ·411 49. a Constant p Electrical polarizability: also code for A, Ao, A J. A:!. Constants of dispersion equations Pulfrich or Abbe refractometer b Constant R Code for reflection method B Constant; oxygen line of wavelell~t h 0.687 T Temperature; code for transmission f.Lm method c Constant: velocity of light V Phase velocity of light in medium 1/ c Constant: hydrogen line of W<:lvcjcllgi h Volume 0.656 J.Lm Linear thermal expansion coefficient D Code for deviation method: aj~o sodiulll Damping factor D doublet A ~ 0.5893 J.Lm E Complex dielectric constant F Code for focal length method: al:-;o hydro- Real part of E Imaginary part of E gen line of wavelength 0.486 J.Lm Static dielectric constant Code for interference method €o , High-frequency dielecirie constant L Code for multilayer method ll I( Extinction coefficient: oscillator strength 1\1 Code for immersion method Wavelength of light n Refractive index Wavelength of the ith absorption band no Refractive index of short (uv) waveiengths Wavelength of infrared absorption band lV Complex refractive index: also density of Effective wavelength of ultraviolet absorp- harmonic oscillator tion band 1. Introduction The purpose of this work is to present and review for the most probable values of the refractive index, its the available data and information on the refractive wavelength derivative dnld'A, and temperature deriva index of alkali halides, to critically evaluate, analyze, tive lin/dT. and synthesize 1 the data, and to make recommendations The recommended and provisional values generated cover the widest possible transparent wavelength ranges I Tb(' I<,rlll is u,;"d I., eonnol<, Iilp preciirtion. dPrivu!ion. or {'stimation oi data ha!'('d un ,;ound and are for the purest form of alkali halide for which J. Phys. Chern. Ref. Data, Vol. 5, No.2, 197'6 REFRACTIVE INDEX Of AlKAU HAliDES measuremellts have been made. However, for the and dn/dT are grouped for visual comparisoll. 'I'll<' :li materials which have been very ~canti]y measured or complishments in this 'work are discussed and iht' lll'(''] have not been measured at all, reasonable estimations for further measurement~ is suggested. are made for wide wav~}ength ranges. The last section consists of the source references used The introductory text descrihes the general pro in the extraction of data and/or information. Onlyorig cedures and methods for the evaluation and synthesis inal sources of data have been used in the analysis. The uf lIte availa.ble Jala. auJ fUl the generation of recom e[[ecti ve cut-off date for literature re:5earch wa5 March mended values. It also discusses the present status of 1975, while the earliest referenced source was dated the experimenta1 data and other considerations con 1874. With such a comprehensive compilation of infor cerning the body of data. mation and presentation of results, the author believes 1n the theoretical background seclion, the general that any scientist or optical engineer will find this report theory of the refractive index and its temperature a great help in regard to refractive index and its temperp. derivative is discussed. Correlations of the dielectric ture derivative. constants and the refractive index are described. An For a transparent material, the refractive index, n, important result in this work is the discovery of empir is defined as the ratio of the velocity, c, of electromag ical relationships which enable us to calculate dn/ dT netic radiation in vacuum to the phase velocity, v, of the data at 293 K for some materials on which no data are same radiation in the material, i.e., available. In the data presentation section we treat each material n = cjv. 0) separate]y, review the individual pieces of available data and information, and describe the considerations Since the index of refraction of air is only about 1.0003, involved in arriving at the finaI" assessment and recom n is conventionally measured with respect to air jnstead mendation and the theoretical guidelines or semi of vacuum and no correction is made. emjJl1ical CUl1elalluu::, UIl which the data analysis and In non-absorbing media, the refracrive index is a real synthesis are based. Figures and tables following the quantity, while in absorbing media a complex index of discussions present the recommended values, in addi refraction, N, is used. The complex index is defined as tion to the original data, specimen characterization, and measurement information for the 283 sets of the N=n+iK, (2) data extracted from 100 documents in the primary liter ature. Distributioll of the available data sets is shown in where K is the extinction coefficient or absorption iT)(lex. table 1. Both nand K are frequency dependent. The real and In the conclusion, figures are presented in which all imaginary parts of the square of the complex refractive the recommended curves on the refractive index, dn/d'A index are the real and imaginary parts of the complex dielectric constant of the material, i.e .. TABLE 1. AVAILABLE EXPERIMENTAL REFRAC11VE INDEX DATA AND lTS TEMPERATURE DERIVATIVE (3) dn/dT Transparent Region The dispersion in an optical material is intimately re IJata Wavelength Quality Data Tl'a~~:~~~;~gion Quality Sets of Data Coverage Sets coverage' of Data lated to the microscopic structure of the material. On LiF 47 wide range good fair range poor the short wavelength side, transmission is restricted by LiCI two wavelengths poor electronic excitation, and for long wavelengths by molec LiBr two wavelengths poor Lil single waveiength poor ular vibrations and rotations. The width of the trans parent spectral range increases as the energy for elec NaF 15 wide range good fair range poor tronic excitalioll is increased and that for molecular NaCI 49 wide range good 10 fai r range fair NaBr limited to 0.2-0.67 wn fair vibrations decreased. Theoretical and experimental Na! single wavelength poor ~.tudics on the ionic crystals indicate that crystals having sm~n jon~ with strong bonding have a wide ultraviolet KF limited to 0.21-0.59 wn fair KCI 38 wide range good fair range fai r transparency: this is true for alkali halides. KBr 27 wide range good limited to < 1 jPI'. poor The alkali halides are typical ionic compounds and KI 21 wide range fair limited to < 1 wn poor their physical properties are in general well under RbF single wavelength poor ShH)d. The majority of the alkali halides crystallize RbCI limited to 0.19-0. 66 ~ fair single wavelength bad in the rock salt sturcture in which each cation (alkali RbBr limited to 0.21-0.66 wn fair RbI limited to 0.18-0.66 IJm fair metal ion) is surrounded by six nearest-neighbor anions (ha]ogen ions), and each anion by six nearest-neighbor CsF single wavelength poor cations. The cations and anions are each situated on CsCl limited to 0.22-0.67 IJm fair CsBr 8 wide range good wide range average value the points of separate face-centered cubic lattices, and CsI 13 wide range good wide range fair these two lattices are interleaved with each other. J. Phys. Chern. Ref. Data, Vol. 5, No.2, 1976 334 H_ H. U This type of' crystal i~ callt'd the p-form_ A few of the Although alkali halides are, in principle, good optical alkali halides 110fillaliv ('rv~taJlize in a slightly dif. materials, only five of them {LiF, NaCl, KCl, KBr and fnc-nt dIrdllr;emcnt, typified by the room-tcmperature C8I) arc commonly u5cd bCCtlU8e thc others lack me structure of cesium chloride. In this structure~ each chanical strength or are ehemically or thermally cation is surrounded by ~ight nearest-neighbor anions unstable. and conversely. The cations and anions in this structure The applications of high-power jilfrared lasers, which may be considered to occupy respectively the points are now being developed at a rapid rate, are partly hm of two interpenetrating simple cubic lattices. This type hed by the lack of suitable transparent optical materials. of crystal is called the a-form. A few physical properties As a result, much of the high-power laser research is of alkali-halide crystals are listed in table 2. directed toward finding adequate high-temperature win In order to utilize any dispersive medium, spectro dow and dome materials in the wavelength region of scopists must have a knowledge of the index of refrac 2 f.Lm to 6 f.Lm and near 10.6 f.Lill. The alkali halides have tion and dn/d'A for all wavelengths transmitted by the large transmission ranges spreading from the ultra medium. Such data are also useful to physicists for violet to the infrared and are available in large sizes and evaluating theoretical dispersion equations and for high purity. They are excellent materials for photo studying the forces between the constituents of the chemists who are interested in ultraviolet transparency ~rystal. The alkalme halIdes, havmg the CUbIC structure, and for laser scientists who are concerned with infrared are favorable subjects for such studies. lranSillission. In spite of their intrinsic weaknesses, they In figure 1, we show a schematic view of the absorp are considered good window materials and are recom tion spectrum of a typica1 alkali-halide crysta1. At the mended by the National Materials Advisory Board [1J2_ right (~ 40 f.Lm) are seen the absorption peaks associated Efforts are being made to improve their mechanical with optical phonons while nearer to the left (~ 0.15 strength and thermal endurance without altering their ,.tm) are seen the absorption peaks associated with optical properties, particularly the refractive index. excitons. In the transparent region between these The refractive index ot alkali halides and its tem extremes the crystal absorbs little light and has a dis perature derivative have been surveyed and studied persion which can be characterized by a high-freque11cy from time to time by a number of investigators, in dielectric constant E,,, = nJ, where no is the refractive cluding Smulmla [2], Ballard [3], Coblentz [1,], and index at short wavelength. In absorbing regions of the Winchell [5J, to name just a few. Refractive index data spectrum, the imagjnary part of E is non-zero. Both are compiled in a number of handbooks such as those the real and imaginary parts of E can be obtained from sponsored by Landolt-B()rnstein [6], AlP [7]~ and eRe the experimental reflectivity (preferably over a wide [8], etc. However, their main concern is to provide a range of wavelengths) and the use of the Kramers general picture through a few particular sets of data. The Kronig relation or the Lorentz oscillator model. In purpose of the present work is quite different from that optical technology, the refractive index is needed only of the above-mentioJ1f~cI works_ It hRS two major aims: (1) for the transparent region of the material. One does to exhaustively search the open literature so that a com not have to carry out a complicated analysis and plete compbehensive bibliographic reference js com calculation to obtain the refractive index. Direct pjled, and (2) to generate recommended values based on methods are available for high precision measure t he t'xistin~ experimental data on the refractive index ments. The minimum deviation method iE' usually used to obtain the refractive index to the fourth decimal place, and the interference method to the third. 'l:j;':'\JII'~ in bliJC'h.c't:-. indinuc' Ht<'I.HUft' I"t'fen:'IH.'(:"S al HIP ~nc1 of {hl~ paper. I r J~l---0 r\~ ~I ~ I i i \ Ir1 I I I I I . I \ 1 : I \ )~ 0.1 10 100 WAVELENGTH, >.., f-Lm FIGURE L A.hsorption Spectrum of i:l Typi{'aI Alkali-Halide Crysta; J. Phys. Chem. Ref_ Data, Vo!' 5, No.2, ! 976 H. H. U ""I II "I")II"I,lill;" df'III',:II\{" lill/(tf', SO t.hat critically indices at low temperatures is also given in a 1atter ,'\ ,dILI\1'.\ \11111lt'ril'a\ data an' available for scientific and section. ,'Jl"llltTt'lll" \l~i' Inherent in the character of this work is the fact ;Cdll)]ill~ tl'](~' open literature one finds that in most that we have drawn most heavily upon the scientific cases the measurements of refractive index were carried literature and feel a debt of gratitude to the authors nnl at various tp.mpp.raturp.s and rp.duced to a rp.fp.rp.nce whose rCBultB havc bccn uscd. temperature chosen according to the investigators' preference. Unfortunately, the temperature derivatives 2. Theoretieal Background and Empiricai of refractive index for alkali halides are in general either Relations only partially measured or not available. Therefore, it The study of the propagation of light through matter, is highly desirable to reduce the existing refractive particularly solids, comprises one of the important and index data and present them ata uniform reference interesting branches of optics. The many and varied temperature. It is aJso important that the temperature optical phenomena exhibited by solids include selective derivative of refractive index be made available in absorption, dispersion, double refraction, polarization the form of a function of wavelength constructed from effects, and electro-optical and magneto-optical effects. existing dn/dT data and theory, so that the users can Many uf tilt:: u!-,ljcal plUpta tie~ of ~o1id~ can be under easily calculate the required values over a limited range stood on the basis of classical electromagnetic theory. of temperature. The first task in generating recommended values The macroscopic electromagnetic state of matter at was to analyze the data on. the temperature derivative a given point is described by four quantities: of refractive index. With the analyzed values of dnl ll) The volume density of electric charge dT, all the refractive index data were then reduced (2) The volume density of electric dipoles, called the to the reference temperature of 293 K chosen for the polarization present work. The corrected data were then subjected (3) The volume density of magnetic dipoles, called to evaluation and critical selection. Least-squares the magnetization fitting of the selected data to a given equation was then (4) The electric current per unit area, called the cur- carried out. r~nt d~nsity Recommended values for refractive index and the All of these quantities are considered to be macro corresponding wavelength and temperature derivatives, scopically averaged in order to smooth out the micro dn/ dA. and dnl dT, are calc:ulated from the correlating scopic variations due to the atomic makeup of matter. equations where sufficient experimental values are avail· They are related to the macroscopically averaged elec able. However, for the region where experimental tric and magnetic fields by the well-known Maxwell evidence is either insufficient or poor, only provisional equations [114]. or typical values are provided. Data are presented at Detailed discussion of Maxwell's equations is beyond integral wavelengths with small increments for the the scope of the present work. What we should bear in transparent region. Intermediate values can be obtained mind is that the general solution of Maxwel1's equations by the following linear interpolations: is a wave function for electric or magnetic field. In the treatment of the interaction of light and matter, the light is considered as an oscillating electric field that engulfs the component molecules of matter. Each of the mole n A' = n" + ( ~~ ) d AI - A ), cules may iJe considered to be a charged simple har (4) monic oscillator. When these component oscillators are driven by the engulfing electric field of light they be come excited by that field and emit Huygens-like spheri cal wavelets. In the early development of the theory of The second expression in eq (4) is based on the fact propagation of light in matter, there was no practical that dn/dT is relatively independent of temperature alternative to treating the matter as a collection of Oyer a faidy \"t'iJe lal1ge of temperarures. However, charged harmonic oscillators subject, perhaps, to damp the application of this expression should be limited to ing forces. Fortunately, the modern developments in the the temperature range 293 ± 50 K. theory of matter and its interaction with radiation have No attempt was made to analyze the refractive index shown that this simple model has broad utility, and that data obtained at temperatues other than near room it can be employed in the discussion of refractive indices. temperature, since the required data are generally In this section, only a brief review of the theoretical inadequate. However, information and results belonging background on the refractive index and its temperature to this category are listed along with those at room derivative is given. A two-oscillator model is used to temperature for the purpose of comparison and com estimate the refractive index for those materials on pleteness. Moreover, some of the important physical which the index is available only at a single wavelength. parameters p.ssp.ntl~l for the calculation of refractive Effort was largely concentrated in finding means for es- J. Phys. Chern. Ref. Data, Vol. 5, No.2, 1976 REFRACTIVE INDEX OF ALKALI HALIDES 331 timating the dn/dT data for the materials without avai1- Real crystals are neither perfectly linear dielectrical1y, able data. Empirical evidence was found and formulas nor are they perfectly harmonic. The effect of non were constructed and used to make reasonable estimate linearity and anharmonicity is to introduce a damping for dn/dT. term [13]. Equation (8) is extended to become 2.1. Refractive Index . "b/A2 E = El + ~E2 = Euv + ,£.,; A2 A2 . 'A' (9) j - j -L'Yj Maxwell's theory gives the relationship Equation (9) is widely used in investigating the infrared (5) optical properties of ionic crystals [14-16]. In the transparent wavelength region, the effects contributed where n is the refractive index, E the dielectric constant, from absorption bands are negligibly small. In such and P the polarizability. If one treats the material as cases the damping terms can be omitted and eq (9) is equivalent to a collection of harmonic oscillators reduced to the Sellmeier formula. resonant to radiation of various wavelengths l\.i, one In an ideal application of eq (7), one would need to ean derive [114J the equation know thp wavplpngth of all of the absorption peaks. This is very difficult in practice because of the large number of absorption peaks. In fact, only a few absorption peaks (6) are accessible for experimental observation. In order to include the effects due to unobserved absorption bands where A is the wavelength of the incident radiation, on the refractive index in the transparent region, an equation similar to eq (7) is used to interpret the and Ci is a constant which depends on the number of oscillators per UnIt volume and t.he "oscillator experimental data: strength" of the oscillators resonant at wavelength Ai. Equation (6) is generally called the SeHmeier formula, I t can be derived by modern quantum theory from (10) more sophisticated models of the solid, with Ai denoting the wavelengths of the various absorption bands of the material. where At'S and A/S are the observed wavelength of For the transparent region, it was tradit.ionally be- absorption bands. A is a constant which equals the lieved that the dispersion formula of the SeHmeier quantity 1+ tal,' where al,' 's are the coefficients of the type best fits t.he alkali halides. The consequence of ultraviolet terms "faJ.;A2/(A2-A7,.) with At..'S much smaller this was that most of the early experimental workers than the wavelengths in the transparent region. In the adopted eq (6) with t.he A; sand c; s as adjustable infrared region, the dominant contribution to the re empirical constants chosen only to fit the data, with no fractive index in the transparent region comes from the other experimental and theoretical basis. Nevertheless, fundampntal ahsorption hand whilp othpr ahsorption this equation, if used correctly, gives a good deal of bands contribute little effect on the refractive index in information concerning the position of absorption band, the transparent region. As a result, in most cases, only oscillator strength and the dielectric const.ant for static one term due to the predominant contribution is in field, Es. cluded in eq (10): The relationships between the dielec For the transparent region, eq (6) can be written as tric constants and the coefficients in the dispersion equation remain with no change: (7) Euv= A + !,ai, (11) and Terms in the first summation are contributions from (12) the ultraviolet absorption bands and those in the seGond from the infrared absorption bands. In the infrared Fortunately, a wealth of experimental data on Euv, region, however, the At s of UV absorption peaks are Es, Ai. and Aj is available for alkali halide crystals. In much less than A and eq (7) is reduced to some cases, good values of a and b are also available to initiate a least-squares calculation. Table 3 displays all the selected values of available parameters. The (2) available values of o/}u) (dAIJdT) are also listed for calculation of the temperature derivative of the refrac tive index. In addition, the available values of damping where Euz: = 1 + 2: aj = Es - 2: bj is the high-frequency factors, 'Yj in eq (9), are also included for the purpose dielectric constant. of completeness. J. Phys. Chem. Ref. Data, Vol. 5, NO.2, 1976 REfRACTIVE INDEX OF ALKALI HALIDES 339 For some materials, experimental data on n are TABLE 4. SOME USEFUL PARAMETERS FOR DISPERSION EQUATIONS OF ALKALI HALIDES AT LIQmD HELIUM TEMPERATURE (T=4.2 K) insufficient to perform the least-squares fitting. Ex amples are LiCl, LiBr, CsF, for which n has been meas a b • b AI Cum} a ured at only a single wavelength, the mean of sodium { s 'uv ~ D lines. For such cases a means should be developed to LiF 8.50 1. 93 31. 45 0.0724 Liel 10.83 2.79 45.25 obtain reasonable estimates by use of the available data LiBr 11. 95 3.22 53.48 for other properties which are intimately related to n. LiI 3.89 66.01 The following simplified equation (two-oscillator model) of the Sellmeier type is proposed for this purpose: NaF 4.73 1.75 36.17 0.0808 NaCl 5.43 2.35 56.18 0.1169 NaBr 5.78 2.64 68.49 Nal 6.60 3.08 80.65 KF 5.11 1. 86 49.63 KCl 4.49 2.20 66.23 O.llOl KBr 4.52 2.39 81. 30 0.1305 where A is an adjustable parameter, Au the unweighted KI 4.68 2.68 91. 32 0.1598 averaged value of the wavelengths of the ultraviolet absorption peaks, and Al the wavelength of the funda RbF 5.99 1. 94 61. 35 RbCl 4.58 2.20 mental infrared absorption peak. The adjustable param 79.37 RbBr 4.51 2.36 105.82 eter A in eq (13) can be determined even if only one RbI 4.55 2.61 122.70 lllea::SUlell1elll u[ n i::s available I,ecau:,e Llle lluaulitie:, Es, Eli!', Au, and Al are available (see table 3). CsF 7.27 2.17 74.6:> Note that in the present work no attempt was made to CsCI 6.68 2.67 93. £10 CsBr 6.38 2.83 127.39 analyze the refractive index data other than those ob Cs] 6.32 3.09 152.67 tained at temperatures near room temperature, because of insufficiency of data. However, information and data a Static dielectric constants and the wavelengths of transverse belonging to this category are listed along with those for phonon are taken from Ref. [21j. b High-f""p.l']l,pn~y nipjp(>h"';(> (>onc:t~ntc; And \1 ?TP tn\..--pn f.,.."m room temperature (see section 0). 1n the far infrared Ref. [13J. region, the refractive indices at low temperatures are usually derived from the analysis on the reflection spectra. The static and high-frequency dielectric con regions, especially in tbe inirared, are very often un stants and the wavelengths of absorption peaks at low available - a very discouraging fact to workers in laser temperatures are either found by these analytic calcu research. It is, t,herefore, highly desirable to obtain a lations or by direct measurements. In order to facilitate theoretical prescription which allows prediction of the calculation of the refractive indices at low tempera dn/dT over a wide range of wavelengths, based on at tures. we have listed in table 4 the up-to-date values most a small number of known measurements. of important physical parameters which are essential Ramachandran [l7] presented a semiempirical in constructing the dispersion equation a1 low theory of thermo-optical effects in crystals, in which the temperatures. dispersion was fitted to experimental data~ employing a series of oscillator frequencies and strengths as adjust 2.2. Temperature Derivative of Refractive Index, able parameters. A close correlation was found between cin/dT temperature shifts of various parameters and those of the fundamental oscillator frequencies. Unfortunately, F or users of the refractive index, information on the the parameters chosen were rather numerous and often temperature d.erivative, dn/dT, is indispensable. The physically obscure or not unique: no general prescrip temperature dependence of the refractive index of tion was presented for deter~ining their temperature crystals is of considerable interest in connection with a variations, which are necessary for calculating dn/dT: wide v3rie'.y of optics applications. In the area of high· Tsay, Bendow, and :Mitra D8] introduced a two power Jasers, dn/dT plays an important role in thermal oscillator model which accounts for the variation with lensing problems. A great deal of research effort is temperature of the energy gap (electronic contribution ::;peuL ill fimling lbe magnitude of dn/dT and its fre Lu dfl/dT) and lhe fundamental phonun frequency quency dePf~ndence in the laser wavelength regions. (lattice contribution to dn/dT). Although this model is With regard to the thermo-optical behavior of the alkali useful in predicting valuable information, it fits the halides in general, the existing data are not so useful as existing data rather poorly and is inadequate for generat might be expected. Although a sizable body of experi ing recOJ'nmended data. A somewhat modified approach mental work on dn/dT exists, much of the data is con is to formulate a semiempirical equation which serves centrated in limited spectral regions, usually in the the dual purpose of giving a good fit to existing data and visible and near ultraviolet. Useful data outside these a reasonable prediction of missing information. J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 340 H. H. U For the transparent region where absorption can be on replacing C, 2 KlI(l/AII) (dAllldT), and A~I by A(), AI, ignored, lhe dispersion equaliun, ell (10), t.:an be rc dud A 2 , le~pectivdy, wc have written as 2n dn = -3a(n2 -1) +Ao (14) dT where B = A -1. If one differentiates eq (14) with (19) respect to temperature, one can arrive at the equation dn dB (1 dN) K i AY' Since the quantIt1es K I, 1../, and 0/1../)· (dAd dT) are 2n dT= dT+ F!' dT +AZ -A7 experimentally available, this leaves in eq (19) only three adjustable parameters, A 0, A 1, and A z. Although the adjustable parameters in eq (19) can be determined by a small number of experimental data, a wide wavelength range of the input data is required. Unfortunately, this condition is not satisfied by the since Ki may be written as where Nis the number 1 dN 1 dV LiF 0.21-1.08 J.tm and at 3.5 ILm -F! dT=V dT=3ex., (16) NaF 0.21-1.08 J.tm and at 3.5 J.tm and 8.5 ILm NaC1 0.21-8.85 }Lm and at 10.6 }Lill where ex. is the linear thermal expansion coefficient. KCl 0.21-8.85 J.tm and at 10.6 }Lill and 21.0 J.tm eq (15) may be written: KBr 0.26-1.08 }Lm K1 0.25-1.00 /-tIll CsI 0.30-46.24 p..m dn f' (') ) ...L ~ F( ) dAi) 'In -=L -~fY n--l 1 2.. ,A, A;. (1---: dT ' (7) dT i AI ' It is dear that meaningful least-squares calculations can only be carried out for the five materials (LiF, NaF, where C is effectively a constant over a limited tempera NaCl, KCl, and Csl) for which the available data cover ture range and a sizeable wavelength range. In the process of calcula tion we have found two empirical facts which gave clues to further reduce the unknown parameters in eq (19). The fin;t is that the parameter Az in eq (19) turns out to he very close to the square of the wavelength of the To this point, we have followed Ramachandran [I7J uv absorption peak nearest the transparent region. closely. The second term on the right side of eq (17) The second relates to the quantity (1/.\u) (d.\uldT) = expresses the change in refracIive index resulting from A !l2KI/' In the case of NaF and NaCI this does not de a change in density, while the remaining terms give the pend on the halide involved: a result that will be assumed change due to the shifting of the absorption bands with to hold for the other alkali halides. This idea is also temperature. supported by the fact that a log-log plot of 01 AuHdAu/dT) In the following development, we will modify eq (7) against the atomic number Z of the four alkali ions for to an empirical form which resembles Tsay's [18], but which data are available, is a straight line despite the with adjustable parameters. As in arriving at eq (13), variety of halide ions involved (see fig. 2). This figure we replace the sum in eq (17) by two terms, one repre shows that (l/Au) (dAu/dT) and Z are connected by a senting the effects of the bands in the ultraviolet region, power law, and thus a reasonable value for the former associated with a mean wavelength Au, and the other quantity can be predicted for Rb (a dot in the figure), arising from the fundamental infrared absorption band [or which u more direct determination is not presently AI. of wavelength Thus eq (17) is simplified to available. Only one unknown parameter, A 0, in eq (19), then remains to be found in order to make a meaningful 2n dT·=C-3ex.(ndn 2 -1) +F(A, Au) (~dAu)dT estimation for those materials on which no experimental Au data are available. This problem is solved and discussed in the next paragraph. (18) At an intermediate wavelength, A, in the transparent region, the contribution from the infrared is negligible J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 REFRACTIVE INDEX OF ALKALI HAUDES 341 (1/AUHdAU/dT)vs. ATOMIC NUMBER OF ALKALI ION OF ALKALI - HALIDE CRYSTAL Z (l/Au){dAu/dT) LI 3 6.~ No \I Z.3 K 19 1.45 Rb 37 (0.85) PREDICTED Ca 55 0.61 Z (ATOMIC NUMBER) FIGURE 2. (l/Au) (dAu/dT) vs Atomic Number of Alkali Ion of Alkali-Halide Crystals and A 2 is much smaller than A2. Equation (18) can then calculated by the formulas constructed in this way be reduced to agree remarkably well with the available data, as one (20) can see in the next section. The prediction made fOl dn . ( 1 dAU) an unmeasured material can be considered as reasona 2n dT = - 3a (n2 - 1) + Ao + 2 (Eur - 1) Au dT . ble estimation. Here it should be emphasized that the dn/dT formulas developed in this work are only valid By treating the variation in index as due entirely to the at 293 K. However, it seems reasonable to apply them change in density except at the extremes of the trans in the range 293 ± 50 K. mitting range, we define an effective linear thermal expansion coefficient a' such that 3. Numerical Data dn , 2 ) 2n dT=-3a (n -1. (21) Reference data are generated through critical evalu ation, analysis, and synthesis of the available experi mental data. The procedure involves critical evaluation The values of a' for LiF, NaCl, KCI, and CsI were eval of the validity and accuracy of available data and in uated at wavelength 1 J,tm. It is interesting to find that formation, resolution and reconciliation of disagree the ratio, a '/ a, is linearly related to the atomic number ments in conflicting data, correlation of data in terms of the positive ion of alkali halides, as shown in figure of various controlling parameters, curve fitting with 3. The prediction for Rb is indicated by a dot. The con theoretical or empirical equations, comparison of re stant A 0 in eq (20) can be calculated by combining eqs sulting values with theoretical predictions or with (20) and (21): results derived from semi-theoretical relationships or from generalized empirical correlations, etc. Physical 2 uVLi<;al vrindple!; and semi-empirical techniques are A 0 = 3 (a - a') (n - 1) - 2 (Ell!' - 1) ( ~? ).(22) :u employed to fill gaps and to extrapolate existing data so that the resulting recommended values are internally With these empirical findings we are in a pOSItIOn to consist~nt ::lncl cov~r ::lS wicl~ R r::lne;~ of ~::lr.h of th~ construct formulas of the form of eq (19) to calculate controlling parameters as possible. dn/dT for all alkali halides over a wide range of A. No attempt was made to analyze the thin film data For convenience, we display in table 5 all the neces and the reststrahlen region results because of scantiness sary parameter values for constructing dn/dT formulas, of reliable information. However, experimental data of although some of the parameters are already listed in this sort are also presented in data tables along with tables 2 and 3. those for the transparent region. In view of the scantiness of dn/dT data and the non The compilation CUl1Laim:i a l1UmLt;l uf 1l~Ul t;:, and unique temperature for observation, the dn/dT values tables of refractive index and its derivatives as a func- J. Phys. Chern. Ref. Data, Vol. 5, No.2, 1976 342. K. H. U 1.3 .----,----a---;--'j-a-v-s-.--rAT-O-M-,c---rN-U-M-S-E-R'---O-F-A-L'K-A-L-' -'-O-:N,----,----,---.-----,----,~ OF ALKALI - HALIDE CRYSTAL J.I Rb~ tf ~ 0.9 tf a'/a Li 0.57 No II 0.65 K 19 0.7:3 0.7 Rb 37 (0.911 PREDICTED No' Cs 55 1.10 O.50~----L-----:,~O-----L-----:2~0--:--~----3fo~-~--~~--~-~5~0---L---~6'0 Z (ATOMIC NUMBER) FIGURE 3. a' fa vs Atomic Number of Alkali Ion of Alkali·Halide Crystals TABLE 5. PARAMETERS FOR THE dn/dT FORMULAS OF ALKALI HALIDES AT ROOM TEMPERATURE d 1 d~a 1 dA b c 1 _ld d Ad e g Ah a'/a a n A/ A1 0 ~ dT. ~dT Euv ES-~v I LiF 6.5 0.57 3.32 13.0 0.93 7.11 32.79 1. 387 (0.0738)2 12.09 -8.13 LiCl 6.5 0.57 4.38 21. 0 1. 75 9.11 49.26 1.659 (0.143)2 22.75 -12.85 LiBr 6.5 0.57 4.98 25.0 2.16 10.07 57.80 1.779 (0.173)2 28.08 -14.18 LiI 6.5 0.57 5.94 22.0 2.80 7.23 70.42 1.951 (0.212)2 36.40 -14.90 NaF 2.3 0.65 3.17 12.5 0.74 3.332 40.57 1.322 (0.1l7)2 3.404 -0.92 NaCl 2.3 0.65 3.97 28.0 1.33 3.56 60.98 1.532 (0.158)2 6.ll8 -0.50 NaBr 2.3 . 0.65 4.23 32.0 1. 60 3.796 74.63 1. 622 (0.188)2 7.360 -0.12 Nal 2. ::J 0.65 4.55 2:1.0 2.U1 4.27 tjti.21 l.'(4tl \V. l:l:ts) 2 l:I.24ti U.57 KF 1. 45 0.73 3.48 23.0 0.85 3.65 51. 55 1.358 (0.126)2 2.465 -0.08 KCI 1.45 0.73 3.71 27.0 1.17 2.64 70.42 1.480 (0.162)2 3.393 0.19 KBr 1.45 0.73 3.87 36.0 1. 36 2.54 87.72 1. 544 (0.187)2 3.944 0.39 KI 1. 45 O. '73 4.08 34.0 1. 65 2.44 98.04 1.840 (0.219)2 4.785 0.80 RbF 0.85 0.91 2.75 25.0 0.93 4.55 63.29 1. 392 (0.132)2 1. 581 -0.89 RbCl 0.85 0.91 3.60 34.0 1.18 2.74 85.84 1.483 (0.166)2 2.006 -0.84 RbBr 0.85 0.91 3.75 38.0 1. 34 2.52 ll4.2'9 1. 540 (0.191)2 2.278 -0.89 RbI 0.85 0.91 4.15 36.0 1. 58 2.36 132.45 1. 623 (0.223)2 2.686 -0.85 CsF 0.61 1.10 3.20 25.0 1.16 5.92 78.74 1.472 (0.136)2 1. 415 -2.54 CsCl 0.61 1.10 4.63 32.0 1. 63 4.32 100.50 1. 625 (0.162)2 1. 989 -4.27 CsBr 0.61 1.10 4.74 40.0 1. 78 3.88 136.05 1.678 (0.187)2 2.172 -4.75 Csl 0.61 1.10 4.90 34.0 2.02 3.57 161. 29 1.757 (0.218}2 2.464 -5.53 a - From Figure 2. l..J - Frum FIgure 3. c - From Table 2. d - From Table 3. e - n is evaluated at wavelength of 1 IJID. f - A2 equals the square of the wavelength of the uv absorption peak (listed in Table 3) nearest the transparent region. g - AI = 2 (€uv-1) l/Au(dAu/dT}. h - obtained according to Eq. (22). tion of wavelength. The conventions used in this presen In all figures containing experimental data, a data set tation and special comments on the interpretation and is denoted by a ringed number. These numbers corre use of the data are given below. spond to those given in the accompanying tables on The refractive index of alkali halides and its wave source and technical information and experimental length and temperature derivatives are presented data. When several sets of data are too close together according to the material order listed in table 1. Original to be distinguishable, some of the data sets, though data are tabulated as they appear in the literature. listed in the table, are omitted from the figure for the However, energy expressed in units of wave number or sake of clarity. For each of those omitted data, an electron volt was converted in all cases into wavelength asterisk is placed after the value in the experimental in units of Mm. data table. The much heavier curves drawn in the J. Phys. Chem. Ref. Data, Vol. 5, No.2, i976 REFRACTIVE INDEX OF ALKALI HALIDES 343 figures represent the proposed values of the property. In the tables of recommended (including provisional) These heavy curves may be continuous or dashed. values, the values are presented with step-wise increas Heavy continuous (solid) curves represent recommended ing increments in wavelength. The magnitudes of the reference values. Accompanying sections of heavy increments vary with the slope and curvature of the dashed curves are used to represent the provisional curve to facilitate linear interpolations. The following values. scheme is uniformly adopted for this presentation. For the index nand dn/dT figures, the wavelength is plotted on a logarithmic scale in order to cover a wide Wavelength range Increment wavelength range in a single plot. For the dn/dA figure, < 0.30 /-Lm 0.002/-Lm both dn/dA and A are logarithmically plotted. For the 0.30- 0.40 /-Lm 0.005/-Lm four materials LiF, NaCl, KCI, and KBr, the refractive 0.40- 0.60 /-Lm O.Ol/-Lm index data for the transparent region are replotted on 0.60- 1.00/-Lm 0.02/-Lm an enlarged scale in order to show the details in the 1.00- 5.00/-Lm 0.05/-Lm variation of the property. 5.00-10.00 /-Lm O.lO/-Lm The tables on source and technical information give 10.00-20.00 /-Lm 0.20/-Lm for each set of data the following information: the refer > 20.00 /-Lm 0.50/-Lm ence number, author's name (or names), year of publi cation, experimental method used for the measurement, In the tables, values for each property are given to the wavelength range covered by the data, temperature of same number of decimal places in order to show the observation, and description and charactcrization of variation of thc propcrty and for tabular smoothncss; the specimen and information on measurement condi this should not be interpreted as indicative of the ac tions that are contained in the original paper. In these curacy of the values. The uncertainties of the tabulated tables the code designations used for the experimental values on the refractive index and dn/dT for each ma methods for refractive index determinations are as terial in different wavelength ranges is given in the follows: discussion pertaining to the material. In connection with this, the tabulated values are classified as "recom D Deviation method (prism method) mended values" or "provisional values." The criteria P Pulfrich or Abbe refractometer of the classification depend upon the level of confidence I Interference method of the values as given below: T Transmission method R Reflection method Uncertainty range Classification M Immersion method For refractive index: L Multilayer method ~ 0.005 recommended F Focal length method > 0.005 provisional The methods listed above are arranged in the order of For dn/dT (in units of 10-5 K -1): the inherent accuracy and the popularity of their ~ 0.3 recommended usages. The deviation method is the most popular and > 0.3 provisional accurate means of determining the refractive indices to the fifth decimal place or better. The Pulfrich re It !';honld be noted that recommendations arc made fractometer and interference technique can be used only for the bulk material at 293 K in the transparent up to the fourth decimal place. Transmission, reflection, wavelength region. and immersion methods yield results good to the third In general, refractive indices obtained by the deviation place, while the multIlayer and focal length results method are reported to the fifth or sixth decimal place. are no better than two or three places. For a compre However, detailed composition and characterization of hensive yet concise review of all these methods, the the specimens are usually not clearly given by the re reader is referred to the text in [3] and [1..]. searchers and impulitie::; ill tlIe ::;ample and conditions For some materials, dispersion equations have been of the surfaces are decisive factors affecting the ob proposed in a number of earlier works. In such cases, served results. Therefore such highly accurate data can a table listing a few typical proposed equations is not be applied to a sample chosen at random. For this given. All equations are converted to the form of eq reason we do not attempt to recommend any particular (10) whenever possible so as to facilitate a visual com set of data with the reported high accuracy, but to gen parison. This table is by no means an exhaustive collec erate the most probable values for the pure crystals. As tion; however, it gives the reader a general picture on a result, the estimated uncertainties for the recom the evolution of the dispersion formula used in the mended values on the refractive index are higher than calculation of the refractive index. those of the reported data obtained by high-precision J. Phys. Chern. Ref. Data, Vol. 5, No.2, 1976 H. H. U 11l(';I~IIIT!lWnts. in this work, the highest estimated ac from these unknown terms is included in the adjustable curaey of refractive index is to the fourth decimal place. constant A of eq (0) of section 2 with the restriction that In each of the next twenty subsections, data and in eqs (11) and (12) have to be satisfied. This was the formation on an alkali halide are presented in this order: standard procedure used in determining the number of a brief text discussing the available data, terms in the dispersion equation of the materials NaF, a table of recommended (including provisional) NaCl, NaBr, KF, KCl, KBr, KI, RbCI, RbBr, and RbI values on n, dn/dA, and dn/dT, for which available data were adequate. In the case of a figure of n (sometimes two figures for clarity), each of the four cesium halides, except CsF, only one a figure of dn/ dA, of the two infrared absorption peaks was included in a figure of dn/ dT, the calculation because the other contributed insignifi a table of source and technical information, cantly to the refractive index. For each of the six ma a table of cxpcrimcntul dutu on n, terials, namely LiCl, LiBr, LiI, NaI, RbF, and CsF, the a table of experimental data on dn/ dT (if any), refractive index was measured for only a single wave a table for comparison of proposed dispersion equa length, the means of the sodium D line. Therefore, in tions (if any). this case the dispersion equation was constructed based In constructing the dispersion equation for a given on the two oscillator model in which the effective ultra material, the number of terms in the equation depends violet absorption peak was derived from the linear upon the available information on the wavelengths of average of the observed peaks. The weighted average aL~urpLiuH peak::;. Nu CtLLempt WCt::; utC1Je Lu eyuCtliz.e the was not used becau::;e Lite revurleJ iI1lel1::;.ilje~ wele Hot number of terms for all the materials by introducing reliable. The ultraviolet absorption peak of the remain terms with unknown absorption peak positions. Although ing material, LiF, was not available; the effective uv there exist many absorption bands which have not been peaks were therefore treated as an adjustable param observed, their effects on the transparent region are eter. The result obtained in this case is in close agree likely to be negligible. The overall effective contribution ment with that obtained by Tilton and Plyler [32]. J. Phys. Chern. Ref. Dcta, Vol. 5, No.2, 1976 REFRACTIVE INDEX OF ALKALI HALIDES 345 3.1. Lithium Fluoride, Lif these works give a spectrum of the refractive index of LiF from 0.00236 J-tm to 2000 J-tm. Lithium fluoride is transparent from 0,12 to 9.0 J-tm. Data obtained by deviation and interference methods In the region 0.25-4.5 /-tm the dispersion is low and are chosen for our data analysis and evaluation. Among transmission is high. Less transmission and higher the chosen sets, those measured by Tilton and Plyler dispersion are found in the low ultraviolet and the [32] and Harting [30] are reliable, and heavy weights are infrared. In the low ultraviolet, optical components must therefore assigned to them. The accuracy of the values be made very thin in order to obtain maximum trans reported by Gyulai [27] is one unit in the third decimal mission. Selected specimens of lithium fluoride, in place, altho~gh his values are given to the fourth place moderately thin pieces, may be expected to transmit for the purpos'e of tabular smoothness. Hohls' data in several percent of the light down to wavelengths as the region 5.48-11.62 p,m are for thin films, resulting short as 0.11 /-tm. Impurities in the crystal, poor polish, in large uncertainties because the properties of thin and layers of foreign material on the surface may re films are not unique, but vary widely with surface con duce the transmission in the Schumann region down ditions, the process of preparation and the aging of the to a negligible quantity. In the infrared, transmission film specimens. Schneider's data [28] are extracted begins to fall off rapidly at 7 /-tm, and a prism is useful from a figure, with uncertainties depending on the to 5 J-tm. operator's judgment, and resulting values that may be Optically speaking, lithium fluoride closely resembles either consistently high or low. Data sets with large un calcium fluoride. However, lithium fluoride is prefera certainties are assigned low weights. ble to calcium fluoride for use in prismatic form because Since the selected data sets were measured at various of its much greater dispersion in the infrared and greater temperatures, corrections should be made to reduce all transparency in the extreme ultraviolet. of the data to 293 K. Not much dn/dT data are available: Unlike the other alkali halides, lithium fluoride is however, the results of the least squares fitting of the practically insoluble, and advantage is taken of this dn/dT data to eq (19), together with the results obtained fact in the purification of the salt. High purity single for NaF, NaCl, KCl, and Cs1, lead to the parameter crystals of lithium fluoride up to 4 kg in weight are values listed in table 5. This enabled us to construct commercially available and are suitable for making the following expression for dn/dT in units of 10-5 K-l, optical components in various sizes. valid in the temperature range 293 ±50K: Measurements of the refractive index of lithium fluoride date back to 1927. The existing data cover a dn .) 12.09 ",4 spectral range from 0.00236 to 600 p,m and at 2000 p,m. 2n dy=-9.96 (n--: 1) -8.13+ (",2-0.00544)2 Based on the optical behavior of the material and the experimental techniqueB, theBe data fall quite naturally 184.86 ",4 into two categories: the transparent region (~O.ll to (23) + (",2 -1075.18) 2 ' ~ 9.0 J-tm) and the absorption regions (<: 0.11 and '> 9.0 /.Lm). whprp A is in units of JLm. Close agreement of the values For the transparent region, since large sizes of LiF calculated by this equation and the experimental data are easily obtained, the deviation method is commonly can be seen in the dn/ dT figure. By use of this equation, used with the sample in prismatic form. This method the refractive index data obtained at temperatures other was adopted by a number of researchers: Gyulai [27] than 293 K were reduced to 293 K, allowing construction in 1927, Schneider [28J in 1935, Hohls [29] in 1937, of a dispersion equation for LiF. Harting [30J in 1943, Durie [31] in 1950, and Tilton and Dispersion equations for LiF were proposed from time Plyler [32] in 1951. The deviation method, though the to time by a number of authors and appeared in different oldest, is often considered as the most accurate; less forms. Table 10 lists the dispersion equations in chron accurate data can be obtained by the interference ological order, to facilitate a close comparison and reveal method. clues for choosing initial parameter values for iterative Due to the high absorption in the low uv and far IR fitting' calculations. The other necessary input param regions, the deviation method and interferometry cannot eters can be found in table 3. With the aid of the avail be used. Refractive indices are obtained either by able information, least-squares fitting of the reduced measuring transmission of thin films or by theoretical data to the form of eq (10) was readily carried out and analysis of the reflection spectra from the bulk material. resulted in a dispersion equation of LiF at 293 K in the Rough data may be due to difficulties in thin film prep wavelength region 0.10-11.0 J-tm. aration and inaccuracy in the reflectivity measurement",_ While numerous publications are available for the 0.92549 ",2 6.96747 ",2' 2 (24) refractive index in the IR regions, only three sets of n = 1 + ",2 _ (0.07376)2 + ",2 - (32.79)2 data exist in the low uv regions, for 0.00236-0.0113 J-tm, 0.0496-0.1771 p,m, and 0.0898-0.1240 J-tm. Collectively, where", is in units of /-Lm. J_ Phy"_ Ch",",. R... l Ooto, Vol. 5, No_ 2. 1976 H. H. U Lqll;tlinns (2~n and (24j were used to generate the For refractive index: rcl"cn'IW(' data given in the table of recommended \'(dllc~. The values of dn/d'A were simply evaluated by Wavelength range Meaningful Estimated 1he iirst derivative of eq (24). Although the values of (,urn) decimal place uncertainty, ± n are given to the fifth decimal place and dn/dT to the second, they do not reflect the degree of accuracy and 0.10- 0.15 2 0.01 the extent of reliability. They are so given simply for 0.15- 0.25 3 0.001 smoothness of tabulation. For the proper use of the tab 0.25- 0.35 4 0.0005 ulated values the reader should follow the criteria 0.35- 3.00 4 0.0002 given below. 3.00- 5.00 4 0.0005 5.00- 7.00 3 0.001 7.00-11.0 3 0.006 For dn/dT: 0.10- 0.15 0.9 0.15- 2.00 2 0.2 2.00-10.00 2 0.3 10.0 -11.00 0.9 J. Phys. Chern. Ref. Dato, Vol. 5, No.2, 1976 REFRACTIVE INDEX OF ALKALI HALIDES 361 3.2. Lithium Chloride, liCI used to construct a formula for estimating dn/dT in the transparent region: The only available measurement on the refractive i Ildex of solid Liel was made for one spectral line, the ~odium D line. by Spangenberg [45] in 1923 using the 2n dTdn = - 13.14 (n-'))- 1 - 12. 85 (26) immersion method. For molten Liel, Zarzyski and Naudin [44] determined the index for the Hg green line 22.75 A4 382.62 A4 (It a temperature of 888 K. + (A 2 - 0.02045)2 + (A 2 - 2426.55)2' The reasons for the scantiness of the data are the difficulties in crystal growing and sample preparation. where dn/dT is in units of 10- 5 K-l and A in fLm. i\ number of other physical properties of Liel were Equations (25) and (26) were used to generate the investigated: values are given in tables 2 and 3. Although reference data given in the table of recommended there is only one value of n available, a dispersion equa· values. As noted, these equations are based totally I ion can be based on the knowledge of the dielectric on the available data on the thermal linear expansion, constants and the characteristic absorption peaks. Using the values of known parameters from table 3 dielectric constants, the wavelengths of absorption and The value of Spangenuerg, we uUlaiu peaks, and the empirical parameters. Consequently, the accuracies of the estimated values are governed by the uncertainties of the above mentioned parameters. Es = 11.86, The following criteria are indicated by careful studies f=UI'= 2.7S, of the parameters. All = 0.137 fLm (averaged value of two peaks), For refractive index: Al = 49.26 J1,m, Wavelength range Meaningful Estimated n = 1.662 for A = 0.5893 fLm. (fLm) decimal place uncertainty, ± The adjustable parameter A of eq (13) was found to be 0.17- 0.30 2 0.05 2.51. This leads to a dispersion equation of LiCl which 0.30- 1.00 3 0.005 is valid at 293 K in the transparent region, 0.17 to 16.0 1.00- 5.00 3 0.008 fLm: 5.00- 9.00 2 0.01 9.00-16.00 2 0.02 2-251 0.24'11.2 9.11A2 n -. + A2 _ (0.137)2 + A2 _ (49.26)2' (25) For dn/dT: where A is in units of fLm. 0.17- 0.32 0.9 No experimental data on dn/dT are available. How· 0.32-12.0 0.4 ever, our empirical parameter values in table 5 were 12.0 -16.0 0.9 J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 366 H. H. l! 3.3. lithium Bromide, LiBr No experimental data on dn/dT are available. How ever, our empirical findings in table 5 were used to The only available measurement on the refractive assemble a formula of LiBr for the transparent region: index of crystalline LiBr was made for one spectra] line, the sodium D line, by Spangenberg [45] using the dn immersion method.· For molten LiBr, Zarzyski and 2n dT = - 14.94 (n 2 - 1) -14.18 (28) Naudin [44] determined the index for the Hg green line at a temperature of 843 K. 28.08 A4 -t- 503.50}. 4 The reasons for the scanlincl:;l:; uf the data al e LIlt:: + {}. 2 - 0.02993)2 (I\. 2 - 3340.84)2' difficulties in crystal growing and sample preparation. A number of other physical properties of LiBr were where dn/dT is in units of 10 -5 K -1 and A in /-Lm. investigated; values are given in tables 2 and 3. Although Equations (27) and (28) were used to generate the there is only one value of n available, a dispersion equa reference data given in the table of recommended tion can be constructed by incorporating the available values. Since these equation are based totally on the data on the dielectric constants, the wavelengths of absorption peaks, etc., into a two-oscillawf dispersion data on the thermal linear expansion. the dielectric constants, the wavelengths of absorption peaks, and equation. Using the values of known parameters listed the empirical parameters, the accuracies of the calcu in table 3 and the available refractive index, we obtain lated values are controlled by the uncertainties in these quantities. The following criteria were eSTablished ailer Es = 13.23, these correlated parameters were carefully studied. ElIl' = 3.16, For refractive iridex: Au = 0.164 fJ-m (averaged value of three peaks), Wavelength range Meaningful Estimated (/Lm) decimal place uncertainty, ± Ar - 57.80 fLm, 0.21- 0.30 2 0.01 n = 1.784 for A = 0.5893 ,urn. 0.30- 1.00 3 0.005 1.00- 6.00 3 0.008 The constant A of eq (13) is found to be 2.88. This leads 6.00-11.00 2 0.01 to a dispersion equation for LiBr valid at 293 K in the 11.00-20.00 2 0.05 transparent region, 0.21-20 ,urn: For dn/dT: n'2 = 2.88 + 0.28 }.2 + 10.07 }.2 (27) }. 2 - {0.164)2 A2 - (57.80)'2' 0.21- 0.40 0.9 0.40-13.0 0.4 where A is in units of }Lm. 13.00-20.0 0.9 J. Phys. Chem. Ref. Data, Vol. 5, hlo. 2, 1976 REFRACTIVE INDEX ·OF· ALKALI HALIDES 371 ~ 4. I itl,ium Iodide, liJ dn 2n = - 17.82 (n 2 - 1) - 14.90 dT (30) Only one value of the refractive index of LiI is availa ble, measured by SpangenbergI45] in 1923. Such scanti 36.40 A4 318.12 )..4 ness of data is probably due to difficulties in· crystal + (A 2 - 0.04494)2 + ()..2 - 4958.98)2' growing and sample preparation. A number of other physical properties of LiI are known; some values are given in tables 2- and 3. With this single value of n, the !\There dn/ dT is in units of 10 - 5 K - 1 and A in p.,m. dispersion equation can still be constructed· by utilizing Equations (29) and (30) were used· to generate the the available information on the dielectric constants lecommended values. Since the construction of these and the wavelengths of absorption peaks. equations is based totally on the available data on the U sing the values of known parameters listed'in table 3 thermal linear expansion, the dielectric constants, the and the available value of n, we find wavelengths of absorption peaks, and the empirical parameters, the reliability of the calculated valuesis Es 11.0o, ~ governed by the uncertainties of these quantities. The following accuracies were estimated after carefully t:uv = 3.00, studying· the correlated properties: Au = 0.171 p.,m (averaged value of 7 peaks) For refractive index: A/= 70.42 p.,m, Wavelength range Meaningful Estimated n = 1.955 for A= 0.5893 p.,m. (p.,m) decimal place uncertainty,± The value of the parameter A of eq (13) was found to be 0.25- 0.30 2 0.01 3.55. This leads. to a dispersion equation for Lilwhich 0.30- 1.00 3 0.005 is· valid at 293 K in the transparent region, 0.25:-25 /.Lm: 1.00- 8.00 3 0.008 8;00-13.00 2 0.01 0.25 )..2 7.23 )..2 2 13.00'-25.00 2 0.03 n = 3.55 + A2 _ (0.171)2+)..2 _ (70.42)2;' (29) For dn/dT: where).. isjn units of p.,m. No experimental data on dn/dTare available. How 0.25- 0.55 1 0.9 ever, our empirical parameters in table 5 lead to a 0.55-20.00 1 O.~ formula for dn/dT in, the transparent region: 20.00-25.00 1 0.9 376 H. H. 1I 3.5. Sodium Fluoride, NaF dn 2n dT= -9.5l{n2 -l) -0.92 Sodium fluoride is less. hygroscopic than the other alkali halides, with the exception of lithium fluoride. 3.404A4 83.30A4 It is transparent over the same range as calcium fluoride, + (1..2 -0.01369)2+ (A2-1645.92)2' (31) a wider range than that of lithium fluoride. -It is not satisfactory mechanically, but it has some uses in cases for estimating dn/dTof NaF in units of 10-5K-l. Value!" where a particularly low refractive index is needed. calculated by this equation agree very well with the It can be easily evaporated as a thin film and can be available data as shown in figure 19. u:sed for reflection-reducing coatingtl, tlincc it has one Radhakriehnan [48] worked out a formula to correlate of the simple crystal structures. A number of the the dispersion and the characteristic absorption peaks. characteristic physical properties have been measured~ His formula gives values of 6.00, 0.114 J.Lm and 45 /-Lm those related to the dispersion of NaF are listed in for the static dielectric constant, and the wavelengths of table 3_ ultraviolet absorption and infrared absorption peaks, Available data on the refractive index of NaF are not respectively, in considerable disagreement with the abundant, mainly because of its mechanical weakness. values now available (see table 3). The uluavioler absorption region was investigated by After making temperature currectiuml to the chu~en Sano [49J, the transparent region by Hohls [29J, data on n, the resulting values were least-squares fitted Harting [30], Kublitzky [50J, and Spangenberg [45J, to eq (10) with the aid of appropriate parameters from and the infrared region by Randall [51]. Zarzyski and table 3. We get as the dispersion equation of NaF at N audin [44] obtained n for molten N aF at the Hg green 293 K in the transparent region, 0.15-17.00 /-Lm, line at a temperature of 1273 K. After carefully reviewing of all of these investigations, we selected the data re .) _ 0.32785 A2 3.18248 A2 ported by Hohls [29], Harting [30J, KubliIZky [50J, and n--lA1572+ A~- (0.117)2+ A2- (40.57)2' (32) Spangenberg [45] as the basis for the generation of reference data. Among the selected data, those of where A is in units of /-Lm. Harting [30] and Hohls [29] (curve 3 in fig. 17) are Equations (31) and (32) were used to generate the ref reliable and receive heavy weight in the analysis. The erence data given in table 17; dn/dA values were evalu accuracy of Kublitzky's value is one unit of the third ated by taking the first derivative of eq (32). The genera decimal place, although his values are reported to the ted values are given to extra decimal places for the fourth place. Three sets (curves 4, 5, and 6) of Hohls' purpose of tabular smoothness. The uncertainties in the measurements are for thin films and therefore are not values are as follows: consistent with those of bulk materials. Values reported by Spangenberg are inaccurate. Low weights were For refractive index: given to the data sets with low accuracies. It appears that all the 'chosen data were obtained at Wavelength range Meaningful Estimated temperatures close to 293 K and that the dn/dT values (J.Lm) decimal place uncertainty, ± are small (less than -1.5 X 10-5K-l), so that correc tions to the chosen data are not significant. However, 0.15- 0.20 3 0.006 knowledge of dn/dT is indispensable for reducing the 0.20-11.00 4 0.0005 n values to other temperatures. Limited experimental 11.00-17.00 3 0.006 data on dnldT were reported by Hohls and Harting. The results of the least squares fitting of the dn/dT Fordn/dT: data to eq (19), together with the results obtained for 0.15- 0.18 0.9 LiF, NaCl, KCl and CsI, lead to the empirical parameter 0.18- 3.00 0.1 values listed in table 5. These enable us to construct a 3.00-13.00 0.4 formula 13.00-17_00 0.9 J. Phys. Chern. Ref. Data, Vol. 5, No.2, 1976 REFRACTIVE INDEX OF ALKALI HALIDES 385 3.6. Sodium Chloride, NoCI (19) was made. The results, together with those obtained for LiF, N aF, KCI and Csl, provided clues that led to the Rock salt is uniformly transparent from 0.2 !-Lm in parameters listed in table 5. With the aid of these param t lie ultraviolet to 12 /-tm in the infrared. In the region of eters we were able to construct a formula for calculating l~) I-lm the absorption increases rapidly. Rock salt in dn/dTfor NaCl: moderately thin pieces may be expected to transmit s(~veral percent of the light up to wavelengths as long dn 2 liS 26.0 /1-m. However, a plate 1 cm in thickness is com 2n dT=-11.91 (n -1) -0.50 pletely opaque to radiation of wavelengths greater than :W/Lm. 6.118 A4 199.36 A4 Rock salt has long been a favorite material for in + (A2-0.02496)2+ (A2-3718.56)2' (33) frared spectroscopy. It polishes easily and, although hygroscopic, can be protected by evaporated plastic 5 coatings. It shows excellent dispersion over its entire where dn/dT is in units of 10- K -1 and A in /Lm. transmission range. It has been difficult. however. to In figure 23, values calculated by eq (33) are compared obtain natural rock salt crystals of sufficient size and with the experimental data. It appears that for wave pmity for making optical components. As crystal lengths less than 2 microns the calculated values are growing techniques advanced, synthetic sodium chloride higher than experimental data, while for longer wave crystals have been grown up to 11.3 kg in weight com lengths the reverse is true. After a careful review of the mercially, making this material readily available for data on dn/dT and the table of source and technical Jarge optical parts and stimulating the design and con information, we find that data sets 34,42,43 and 45 were struction of infrared instruments. obtained at mean temperatures of about 330 K, which is Measurement of the refractive index of sodium about 40 degrees higher than 293 K, while data set 44 chloride "dates back to 1871, when Stefan [53] deter was obtained at temperatures about 20 degrees lower mined the refractive indices of a rock salt prism for lines than 293 K. Although we stated in connection with eq B, D, and F. Since then, a large amount of data in the (4) that dn/dT is found to be relatively independent of transparent region has been contributed by a number of temperature over a" fairly wide range of tempera jnvestigators, among them are Martens [54J, Paschen tures, it has been in fact observed in halide crystals that f.5.5]. and Langlpy [S()l They llsed either the deviation the absolute value of dnJdT lncrpaRPR Rompwh::lt with method or interferometry in their experiments. It was increasing temperature. This fact is demonstrated not until 1929 that measurements were carried out be clearly by eq (33), as can be seen in figure 23 in the wave yond the transparent region. Kellner [57] determined length region below 2 /-tm. In the higher wavelength refractive indices of NaCI in 23..;..35 /-tm region, based region, the existing data are insufficient to test the dn/dT on information on transmission and reflection of thin formula, but the correctness of this formula can be specimens. Data in the infrared region are now available substantiated by two facts. The first is that the calcu up to 300 /-tm and at 2000 /-tm. Most of the IR data were lated curve is approximately parallel to curve 44, which determined from the analysis of the reflection spectra. is consistent with the observed dn/dT behaviors. The After a careful review of the available" data, six data second is that the empirically constructed formula sets measured by Martens [54], Paschen [55], Hohls for Csl predicts correct values for Csl in the long 129j, Harting [30], Rubens and Nichols [58], and Rubens wavelength region, as is discussed in subsection 3.20 and Trowbridge [59], were selected as the basis for refer and is assumed to be generally the case here. ence data generation because of the consistency of their Equation (33) was used to make temperature correc results. Data sets which are not selected were either tions to the selected data sets which were obtained at reported as poor values or were determined by inade temperatures other than the selected reference tempera quate methods. Data for the absorption regions were ture, 293 K. not included in the analysis but are given here for Various dispersion formulas have been reported by completeness of data presentation. Note that the a number of authors, in different forms. Table 29 con selected data, except those of Harting, were obtained at tains a number of typical formulae. They have all been a temperature of 291 K. A temperature correction should reduced, wherever possible, to standard forms so that be l11ad~ Lv r~duce them to 293 K. d c1U5e L:umpali::;vJl cau L~ ~a~ily made. From the in The temperature coefficient dn/dT is available over formation in tables 29 and 3, input parameters for least a large part of the transmission region of NaCl. Based squares fitting were obtained. The calculation yielded on the existing data on dn/ dT and the parameters from the following dispersion equation for NaCl at 293 K in tables 2 and 3, a least-squares fitting of the data to eq the transparent region, 0.20-30.00 /-tm, J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 386 H. H. U 2 _ --L 0.19800",2 0.48398",2 For refractive index: n -1.00055 I ",2 _ (0.050)2 + ",2 __ (0.100)2 Wavelength range Meaningful Estimated 0.38696"-2 0.25998,,-2 0.08796,,-2 (JJ-m) decimal place uncertainty, ± + ,,-2- (0.128)2 + "-2- (0.158)2+ "-2- (40.50)2 0.20- 0.25 3 0.006 + 3.17064,,-2 0.30038"-2 3 0.25- 0.35 4 0.0005 ',,-2-(60.98)2+,\2-(120.34)2' (4) 0.35-10.00 4 0.0001 10.00-15.00 4 0.0003 15.00-25.00 3 -0.006 where "- is in units of JJ-m. 25.00-30.00 3 0.02 Equations (33) and (34) were used to generate the reference _data given in the table of recommended For dn/dT: values; dn/d,,- values were evaluated from the first derivative of eq (34). The numbers in the table of recom 0.20- 0.24 0.8 mended values do not reflect the degree of accuracy 0.24- 4.00 0.2 and extent of reliability; extra decimal places are given 4.00-15.00 0.4 for tabular smoothness. Actual uncertainites are as 15.00-20.00 0.6 follows. 20.00-30.00 0.9 J. Phys. Chem. Ref. Data, Vol. 5, ... 402 H. H. LI 3.7. Sodium Bromide, NaBr where dn/dT is in units of 10-5K -] and A is J-tm. dn/dT values in the visible region given by eq (35) are about Sodium bromide is very hygroscopic and highly solu -4.0 X 10-5K -1, close to those proposed by Tsay [IB]. ble in water and is therefore not a useful material for By use of eq (35), data reported by Gyulai and Wulff making optical components despite its transparency and Schaller were reduced to 293 K, ready for the least over a wide wavelength region from about 0.25 to more squares calculations. The other necessary input param than 30 J-tm. While NaBr is not useful for ordinary eters were taken from table 3. The result of the curve applications, it is an interesting material for scientific fitting calculations is a dispersion equation for N aBr research. The wavelength of ultraviolet absorption peaks at 293 K in the transparent region, 0.21-34.0 J-tm. has been measured by Hilsch and Pohl [23] and by Schneider and O'Bryan [24] and that in the infrared was reported by Lowndes and Martin [13], who also 2 2 investigated the dielectric constants. The results 2 _ 1.10463A 0.IBBI6A n -1.0672B+ A2- (0.125)2+ A2- (0.145)2 obtained by these investigators are shown in table 3. Experimental work ~n the refractive index of N aBr 2 2 2 is very scanty and is limited in the near ultraviolet and 0.00243A 0.24454A 3. 7960A + AZ- (0.176)2+ A2- (0.188)2+ A2- (74.63)2' (36) visible regions. Only five documents could be found in the open literature. By a careful review of the avail able data sets one finds that only two sets of data, those of Gyulai [27] and Wulff and Schaller [05], can be w;eJ where A is in units of (.LID. to carry out analysis: the others are either inaccurate Equations (35) and (36) were used to generate the or otherwise unsuitable. The accuracy of the data of recommended values on the refractive index and its Gyulai is one unit of the third decimal place. though the wavelength and temperature derivatives. Note that in the values in his paper are given to the fourth for the purpose table of recommended values the values are given to of tabular smoothness. The uncertainty of the single more decimal places than their accuracies, for the value of Wulff and Schaller is 0.0001. Bauer's film data purpose of tabular smoothness and visual continuity. appears too low in comparison with the bulk material In order to use the values properly, the readers should data and Spangenberg's values [45] are clearly inac follow the criteria given below. curate, probably because of the hygroscopic character of N aBr and the use of an inadequate method. The For refractive index: single measurement of Zarzyski and Naudin [44] is for molten NaBr. Wavelength range Meaningful Estimated Gyulai's data were obtained at a temperature of 339 (J-tm) decimal place uncertainty, ± K, 46 degrees higher than the temperature chosen for reference data generation. Since the temperature deriva 0.21- 0.24 2 0.02 tive of refractive index of N aBr in the visible region is 0.24- 0.40 3 0.002 5 of the order of - 4.0 X 10- K -] [IB], temperature cor 0.40- 0.70 3 0.001 rections to Gyulai's values are significant, about two 0.70- 8.00 3 0.002 units in the third decimal place. Information on dn/ dT B.00-20.00 3 0.006 is needed to carry out these corrections. but it isnn· 20.00-25.00 3 0.008 available. Reasonable estimation of dn/dTcan be made 25.00-34.00 2 0.02 by the following formula, constructed from the param eters listed in table 5. For dnldT: dn 2 2n dT=-12.69(n -1) '-0.12 0.21- 0.28 1 0.9 0.28-22.00 0.4 + 7.36A4 242.94A2 (35) 22.00-34.00 0.9 (A 2 - 0.03534) 2 + (A 2 - 5569.64) 2' J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 408 H. H. LI 3.8. Sodium Iodide, Nol dn 2ndT =-13.65 (n 2 -l) +0.57 Refractive index data of NaI are available only for a single line, mean of sodium D lines, reported by Spang 4 4 enberg [45] in 1923. The reasons for such scantiness of 9 .246A 247 .66A + (A 2 - 0.05198) 2 + (11. 2 -7432.16)2 , (38) data are probably the difficulries in crYlSla1 gwwiug and sample preparation. It is fortunate that the essential 5 parameters for constructing a dispersion equation of where dn/dTis in units of 10- K-l and A in /-tm. NaI are available through the literature, as listed in Equations (37) and (38) were used to generate the rec table 3. Using the values from table 3 and the available ommended values. Since these equations were derived value of n: from the available data on the thermal1inear expansion, the dielectric constants, the wavelengths of absorption peaks, and the empirical parameters,. the accuracies E<~=7.28, of the generated values are controlled by the un certainties of these component properties. In order to Euv=3.01, properly use the recommended data table, we have carefully reviewed each of the correlated properties Au = 0.170 /Lm (averaged value of 5 peaks), and set up the following criteria that the readers should follow. A./ - 86.21 p.m, n= 1.7745 for A=0.5893/Lm, For refractive index: the adjustable parameter A of eq (13) is computed to be Wavelength range Meaningful Estimated 1.478. This leads to the dispersion equation for NaI at (/-tm) decimal place uncertainty, ± 293 K in the transparent region, 0.25-40.00 /Lm. 0.25- 0.40 2 0.02 2 _ . 1.53211. 2 4.2711. 2 0.40- 1.00 3 0.005 n -1.478+ IV- (0.170)2+ "-2- (86.21)2' (37) 1.00-20.00 2 0.01 20.00-40.00 2 0.02 where n is in units of p,m. For dn/dT: No experimental data on dn/dTfor Na1 are available, but, with our empirical findings, reasonable estimations 0.25- 0.35 0 >1 on dn/dT can be made by a formula constructed by 0.35-30.00 1 0.8 using the predicted parameters of table 5, 30.00-40.00 0 >1 J. Phys. Chem. Ref. Data, Vol. !>, No.2, 1976 414 H. H. LI 3.9. Potassium Fluoride/ KF about 0.8 X 10-5 K -1 too large, but there is no direct experimental evidence to substantiate either one of the Potassium fluoride is not a suitable material for optical predictions. However, since the dnJdT formulas con components beacuse of its hygroscopic character and structed by our empirical parameters lead to predictions the difficulty of growing crystals. However, it is an in for the material in agreement with experimental data, teresting subject for basic research and scientific we have reason to believe that eq (39) gives reasonable studies because of its simple crystal structure and its dnldTvalue for KF. By use of this equation, Kublitzky's transparency in the ultraviolet region. The wavelengths values were reduced to 293 K. of the characteristic absorption peaks and the electrical A dispersion equation of KF at 330 K was proposed properties have been studied by many investigators. by Radhakrishnan [481 on the basis of Kublitzky's Listed in table 3 are a few important results which were measurements. Since the wavelength of the fundamental used in out analysis of data. phonon was not known then, the adjustable constants The refractive index of KF has not been extensively in his equation were chosen to fit the data without measured. Among the five sets of refractive index data reference to the infrared absorption peak, as shown in found in the literature, three were measured for a single table 39. With the available information in table 2>, spectral line, the sOdm'm D line, one for the melt, and the least-squares fitting of the reduced data to eq (10) one for a limited spectral range from 0.21 to 0.58 /-tm. led to our dispersion equation for KF at 293 K in the Upon careful examination of the available data, transparent region, 0.15-22.0 J.Lm- WP. found the following: (l) Kublitzky's values f501 are reported to the fourth decimal place, although the ac curacy is one unit in the third decimal place. We have used his reported values as the basis of our work. (2) Results of SpangelllH:~q~, (45] dud uf Wulff [07] ale in consistent, although the same experimental method was where A is in units of ,urn. used. The discrepancy cannot be accounted for by the Equations (39) and (40) are used to generate the recom temperature difference, because dn/dT (about -1.2 X mended values. Since more decimal places than needed 10-5 K -1 [18]) is too small to account for such a big are given to the property values for the purpose of tabular deviation, about 0.0019~ in n nor can the discrepancies smoothness, the readers are advised to follow the criteria between the results of Kublitzky and those of Wulff given below in order to use the recommended values be accQuntcd in this way. (3) There are no dn}dT data propedy. available. Since the data of Kublitzky were obtained at a tempera F or refractive jndex: ture of 330 K, they had to be reduced to 293 K. Since no dn/dT data was available, the empirical parameters Wavelength range Meaningful Estimated in tabJe 5 were used to construct the following expression (/-tm) decimal place uncertainty, ± for dnJdT in units of 10-5 K-t, valid in the temperature range 293 :t: 50 K: 0.15- 0.18 2 0.05 0.18- 0.21 3 0 ..005 dn 2n dy=-10.44 (n 2 -1) -0.08 0.21- 1.00 3 0.002 1.00- 6.00 3 0.004 6.00-14.00 3 0.008 4 2.465A 167.90A 4 14.00-22.00 2 0.05 + (A2-0.01588)2+ (A2-2657.40)2' (39) For dn/dT: where A is in units of /-tm. The dn/dT values calculated by eq (39) for the visible region are about - 2.0 X 0.15-17.00 1 0.5 10-5 K-l. Compared with Tsay's [181 value, our value is 17.00-22.00 1 0.9 J: Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 REfRACTIVE INDEX OF ALKALI HALIDES 1121 3.10. Potassium Chloride, KC! dn .) . 3.393A4 2n dy=-11.13 (w-1) +0.19+ (A2-0.02624)2 Potassium chloride is widely used in' spectroscopy, since its optical properties make it a convenient window + 142.56A4 (41) and prism material from the ultraviolet to the infrared (A2- 4958.98) 2 regions. The transmission range is about 0.21 to 30 /Lm. A plate 1 cm in thickness transmits radiation up to. 24 where dn/dTis in units of 10-5K -1 and 'A is in /Lm. /Lm. Since strong absorption occurs near the trans In figure 36, the results calculated by eq (41) are limits, the 11<;f"f111 mis~ion tnm~mi~sion range of KCl compared with the experimental datu. It appears that is about 0.38 to 21 J-tm. Of all the substances which for wavelengths longer than five microns the calculated are otherwise suitable for optical parts, KCl is trans values are in general lower than the observed values, parent over a wide range of the infrared spectrum. and that in the short wavelength region, 0.25-0.50 J.Lm, KCI is grown in the same way as NaCl, but sometImes the curve is higher than experiment. By a review of the multiple crystals instead of single-crystal ingots result. sources. one can find that data sets 32, 34, and 36 (32 Therefore, large prisms are somewhat rare and ex and 36' not shown in fig. 36) were obtained at about pensive. Crystals 30 cm in diameter are available. 330 K, some 40 degrees higher than 293 K, while data Measurement of the refractive index of potassium set 35 was obtained at a mean temperature about 15 chloride dates back to 1871, when Stefan [53] deter 'degrees lower than 293 K. The trend of these data mined the refractive index of a sylvite prism for the B, indicates that the absolute value of dn/ dT increases D and F of Fraunhofer lines. Later work, represented with increasing temperature. Although dn/dT data of b; Rubens [72], Martens l54], Paschen [55], and Gyulai curve 9 were obtained at a mean temperature of 293, [271 provided a large amount of data in the transparent they appeared to be randomly scattered and not con region. l\1:easurements beyond the transparent region sistent with the trend demonstrated by curves 34 and 35. were not made until 1934 when Cartwright, et a1. [61J It can be safely said that eq (41) predicts correct analyzed the reflection and transmission spectra of KC1 dn/dT values for wavelengths smaller than five microns. thin films in the infrared region, 126 to 232 /Lm. In the For wavelengths larger than five microns, experimental low ultraviolet region, Tomiki [89] published values ob evidence is not sufficient to substantiate the predictions tained by analyzing the reflection spectra. Refractive made by eq (41). However, the fact that the empirically index data are now available for a wide wavelength range constructed dn/dT formula for CsI predicts correct from 0.106 to 232 /Lm. values for CsI in the long wavelength region, as dis By a careful examination of the available data and in cussed in subsection 3.20, gives strong evidence that formation, five data sets provided by Martens [54), eq (41) can be used to calculate the dn/dT data fOT Paschen [55], Hohls [29], Harting [30], and Rubens and KC] in the long wavelength region. Nichols [58J~ were selected as the basis for reference Equation (41) was used to make temperature correc data generation. The values of Hohls were obtained for tions on the selected data sets which were obtained at a very thin plate specimen, and are slightly lower than temperatures other than the reference temperature, those for bulk material. Data sets which are not 8eleeLed 293 K. were either reported with unreliable values or were mea Dispersion formulas of KCI have been proposed from sured under iriadequate conditions. Data in the ab time to time by a number of authors, and have appeared sorption regions were not analyzed, but are included in different forms. Table 44 contains a number of typical here for completeness of presentation. Since the selected formulas. They have all been i-educed, wherever data were obtained at various temperatures, the tempera possible, to standard forms so that a visual comparison ture derivative, dnldT~ was needed to reduce the data can be easily made. From tables 3 and 44, preliminary to 293 K. parameters for a least-squares fitting were obtained. Measurements of the temperature coefficient of the The calculation yielded the following dispersion equation refractive index, dn/dT, made avajJabJe in the wavelength for KCl at 293 K in the transparent region, 0.18-35.0 /Lm. region from 0.21 to 21-0 /-Lm by a number of jnvestigators" were sufficient to carry out a least-squares fitting calcu 0.30523A2 0.41620A2 lation. Potassium chloride IS among the five materials 11,'2= 1.26486+ A2- (0.100)2 + A2- (0.131)2 which provided the empirical results that led to the 0.18870'A2 2.6200'A2 (42) parameters in table 5. With the aid of these parameters + A'2- (0.162)2 + )..2- (70.42)2' we constructed a formula for estimating dn/dT over a broader range of 'A: where A is in units of /Lm. J. Phys. Chern. Ref. Data, Vol. 5, No.2, 1976 422 H. H. LI Equations (41) and (42) were used to generate the For refractive index: recommended values. The values appearing in the table of recommended values do not reflect the degree of Wavelength range Meaningful. Estimated accuracy: extra decimal places are given simply for (J.Lm) decimal place uncertainty, ± tabular smoothness. In order to use the table properly, the reader should follow the criteria given below. 0.18- 0.20 2 0.01 0.20- 0.24 3 0.005 0.24- 0.35 4 0.0005 0.35-10.00 4 0.0001 10.00-15.00 4 0.0002 15.00-21.00 4 0.0005 21.00-30.00 3 0.006 30.00-35.00 3 0.008 For dn/dT: 0.18- 0.20 I 0.9 0.20- 4.0 1 0.3 4.00-}5.00 0.5 15.00-35.00 0.9 J. Phys. Chern. Ref. Data, Vol. 5, No.2, 1976 436 H. H. LI 3.11. Potassium Bromide, KBr evident the effects due to the thermal shifts of absorption peaks. However, by use of our novel findings, reasonable Potassium bromide has optical characteristics similar estimation of dn/dTfor a wide wavelength range is not a to those of rock salt, but, having a higher molecular problem. The empirical parameter values in table 5 were weight, it transmits further into the infrared. Crystals used to construct the dn/dTfor a wide wavelength range up to 11 kg are available from Harshaw Chemical Com is not a problem. The empirical parameter values in pany. Very pure samples have been obtained and they table 5 were used to construct the dn/dT formula of can be cleaved easily. KEr is of interest to designers of KEr for the whole transparent region: optical instruments because of its transparency in the infrared region. Although KEr is transparent from 0.20 to 42 /-tm, the useful region is from 0.3 to 30 Mm because dn __ ( 2_) 0 9 3.944A4 strong absorption occurs near the transparency limits. 2n dT- 11.61 n 1 + .3 + (A2-0.03497)2 Measurements of the refractive index of KEr date back to 1874. For the transparent region experimental 182.88A4 values were obtained mainly by the deviation method. + (A2-7694.80)2' (43) For low ultraviolet and far infrared wavelengths there were no measurements until 1967, when Vishnevskii, where dn/dTis in units of 10-::;K-l and A in /-tm. et al. [90] reported their results for the region from A comparison of the values calculated by eq (43) and 0.170 to 0.197 /-tmand Handi, et al. [16] reported re the existing data is shown in figure 40. It appears that sults for the region 35 to 770 /-lm. the calculated values are in general higher thl'ln the After carefully reviewing this work, we have selected experimental values, but we have reason to believe that the data sets reported by Spindler and Rodney [96], eq (43) predicts correct dn/dT values for the whole Stephens, et al. [97], Forrest [98], Harting [30], and transparent region. Gundelach [99] as the basis of the generation of ref 1. It has been observed in halide crystals that the erence data. Data sets which were not selected either absolute value of dn/dT increases with increasing reported poor values or were determined by inadequate temperature. Spindler and Rodney obtained dn/dT at methods. Data for thin films are not consistent with 295 K; our dn/dT~ for 293 K, should be located above those for the bulk material. The properties of the thin their values. This is clearly shown in figure 40, where film vary widely with the surface conditions,the treat the calculated curve is above and roughly parallel to ment of the sample and the thickness and aging of the curve 5. Although the separation of these two curves film. As a consequence, the thin film data are useless seems too large to account for only two degrees in unless a protecting coating was deposited to preserve its temperature difference, it is within the uncertainties in characteristics. Data for the absorption regions were not our calculation and the experiment. included in the analysis, but are presented here for 2. In the case of CsI, the empirically constructed completeness. Note that the selected data were obtained formula predicts correct dn/dT values in the long wave at different temperatures: the effect of temperature vari length region, as discussed in subsection 3.20. One can ations should be corrected before they were used for expect this is to be the case here. data analysis. Spindler and Rodney derived an empirical relation Data on the temperature coefficient of refractive (given in table 49) between dn/dTand wavelength, based index, dn/ dT~ of KEr are very scanty and limited. Only on their experimental results. This expression indicated five sets were found, covering the wavelength range from that dn/dT increases with increasing wavelength in the 0.26 to 1.1 Mm. Amongthe available data, those of Spind visible region 0.4 to 0.71 Mm, but no attempt was made ler and Rodney [96] are reasonably good, and those of to derive dn/dT beyond the visible region. Hartmg [11] show a wide scatter and are not internally Equation (43) was used to make temperature correc consistent. The single value of Stephen, et al. [97] is a tions to the selected data sets which were obtained at rough averaged value of dn/dTin a wavelength range of temperatures other than 293 K. 0.1.01. to 25.11· fLm at 295 K, and is consistent with the re Quite a few dispersion equations have been proposed sults of Spindler and Rodney. The single value reported from time to time by a number of authors, and in various by Forrest [98] is the average value of dn/dTin a wave forms. Table 49 displays a few of typical formulas. They length range of 0.40 to 0.77 Mm at a mean temperature of have all been reduced, wherever possible, to standard 301 K and is consistent with the other data sets. The forms so as to facilitate a visual comparison. From the single measurement of Korth [100] is not accurate. The information in tables 3 and 49, preliminary parameters available data on dn/dT are not suitable for a curve for least-squares fitting were obtained. The calculation fitting calculation, because the wavelength coverage yielded the following dispersion equation for KEr at of the acceptable data is not wide enough. to make 293 K in the transparent region, 0.20 to 42.0 /-tm. J. Phys. Chern. Ref. Data, Vol. 5, No.2, 1976 REFRACTIVE INDEX QF ALKAI.I HALIDES 437 For refractive index: W' avelength range Meaningful Estimated 0.15587r.. 2 0.17673r..2 2.06217/-..2 (/Lm) decimal place uncertainty, ± + /-..2- (0.187)2 + /-..2- (60.61)2 + r..2- (87.72)2' (44) 0.20- 0.25 3 0.006 0.25- 0.35 4 0.0005 where /-.. is in units of /Lm. 0.35- 0.40 4 0.0002 Equa.tions (43) and (44) were used to generate the 0.40-20.00 4 0.000] recommended values. The property values are given to 20.00-26.00 4 0.0005 more decimal places than needed simply for the purpose 26.00-35.00 3 0.006 of tabular smoothness. In order to use the table of recom 35.00-42.00 3 0.008 mended values properly, the readers should follow the following criteria: For dn/dT: 0.20- 0.25 0.9 0.25- 4.0 0.3 4.0U-;)0.UU 0.5 30.00-42.00 0.9 J. Phys. Chern. Ref. Data, Vol. 5, No.2, 1976 REFRACTIVE INDEX OF ALKALI HALlUt) 449 3.12. Potassium Iodide, KI discoveries by which the unknown parameters of eq (19) for each of the alkali halides were predicted. This Potassium iodide is valuable as prism material, but enabled us to construct a dn/dTformula forKI at 293 K it is too hygroscopic {being about twice as soluble in in the transparent region: water as potassium bromide) and too soft for field use. It is also soluble in alcohol and in ammoriia. Ingots 19 em dn·__ ( 2_) 08 4.785,,-4 in diameter are available. Although KI is one of the 2n dT- 12.24 n 1 + . 0+ ("-2-0.04796)2 softest rocksalt-structure alkali halides, not a suitable optical material, its wide transparency, 0.25 to 50 f.Lm, 165.92,,-4 draws attention in crystal structure research. Funda +cV -9611.84)2' (45) mental absorptions in the ultraviolet and infrared regions, static and high-frequency dielectric constants where dn/dTis in units of 10-5 K- 1 and A in f.Lm. have been measured by a number of investigators, and In figure 43, the values calculated by eq (45) are' the results are listed in table 3. compared with the experimental data. It appears that Reasonable amounts of data on the refractive index our calculated values do not agree with those reported of K1 are available in the open literature. By careful by Harting. However, we have reasons to believe that examination of the aVl'!lbhle rbtl'! WP finrl thRt for thp. eq (4:;) prprllr.tl"; l";;ltll";fRp.tory rln./rlT val11p.~r for KI. transparent wavelength region the results of Gyulai [27] 1. The figure shows that the curve of eq (45) is the and Ha:rting [30] are consistent (with temperature lower envelope of Harting's data. If the uncertainties of effects considered) to the fourth decimal place in spite .Harting's measurements are the deviations of the points of the fact that Gyulai quoted an accuracy of one unit from the averaged position, our predictions are con at the third decimal place. Korth's values [100], although sidered to be in acceptable agreement with the Harting's being reported to the fourth decimal place, are good values. only to thc third place. Bauer'B valucB appear too low 2. Although it hM been obBerved in halide crystals to be· considered as useful data because of his use of that the absolute value of dn/dT·increases with increas thin films, and the unfavorable surface conditions of the ing temperature, the variation is small in a fairly wide samples. Data reported by Sprockhoff [95] and Topsoe range of temperatures. This is the basis of the second and Christiansen [101] appear slightly too high at the expression of eq (4). It is clearly shown in figure 43 that assumed temperature; they either observed at a con our predictions are located at a reasonable distance from siderably lower temperature or used inadequate samples. Korth's data point, in view of the difference in In the infrared region, 40 /-tm and up, data were temperatures. leduced by analyzing the information on reflection and 3. The predictions of the dn/dTformula for CsI based .ransmission sp~ctra. Data are available from the on the empirical parameters of table 5 agree closely figures of Badni, et al. [16], Edlridge, et al. [103], and with the data in the long wavelength region· as discussed Berg, et al. [104]. They are not included in the data in subsection 3.20. We assume that this is also the case analysis but are presented here for completeness. for Kl. Data measured by Gyulai, Harting, and Korth were . Based on the above discussions, eq (45) was confidently Idopted for our analysis. The selected data sets were used to reduce the selected refractive index data to )btained at different temperatures: Gyulai's measured 293 K. at 339 K, Harting's at 293 K, and Korth's. at 311 K. Ramachandran [17] attempted to construct dispersion Information on dn/dTis needed to carry out temperature equations to fit the data provided by Gyulai and Korth, corrections on the selected data sets, but little is respectively, and found two equations,. one for wave..: available. lengths from 0.206 to 0.615 f.Lm at 339 K, and the other Data on dn/dTweregiven by Harting [30] and Korth for wavelengths from 4 to 29 p,m at 311 K, as shown in [l00]. The values reported by Harting are for a wave table 54. Note that these equations do not include the ength region from 0.248 to 1.083 /-tm and a temperature contributions of absorption bands located at the other )f 293 K. Although this data set covers a sufficient wave end of the transparent region. This will lead to improper length range for a curve fitting calculation, its un extrapolations. It is our goal to· work out a formula favorable scatter led to unreasonable values of the which includes the effects due to the absorption bands adjustable parameters in eq (19). A single but reliable at both ends of the transparent region, and yields the value was given by Korth for the Hg green line at a mean refractive indices for the whole transparent region at a temperature of 337 K. As a consequence of the lack of chosen reference temperature, 293 K.· Based on the reasonable data, temperature effect corrections to the information in tables 3 and 54, input parameters for available data on refractive index were never considered least-squares fitting were obtained. The result of the in early survey works or in handbooks. In the present fitting is a dispersion equation for KI at 293 K in the work, however, this problem was solved by our empirical transparent region, 0.25-50 f.Lm. J. Phys. Chern. Ref. Data, Vol. 5, No. 2, 197E 450 H. H. LI n 2 = 1.47285 For refractive index: 0.165121\2 0.412221\2 0.441631\2 + 1\2- (0.129)2+ 1\2- (0.175)2+ 1\2- (0.187)2 Wavelength range Meaningful Estimated 0.160761\2 0.335711\2 1.924741\2 (J.tm) decimal place uncertainty, ± + 1\2- (0.219)2+ 1\2- (69.44)2+ 1\2- (98.04)2' 0.25- 0.35 3 0.008 0.35-10.00 3 0.002 (46) 10.00-25.00 3 0.003 25.00-40.00 3 0.006 40. DO-SO. 00 :3 0.009 w here A il:5 in units of p.JIl. Equations (45) and (46) were used to generate the recommended values for n, dn/dl\, and dn/dT. More For dn/dT: decimal places are given than are needed, for tabular smoothness. Readers are advised to use the· criteria 0.25- 0.27 0.9 given below in order to insure the proper usage of the 0.27- 2.00 0.3 table of recommended values. 2.00-30.00 1 0.4 30.00-40.00 1 0.5 40.00-50.00 0.9 J. Phys. Chern. Ref. Data, Vol. 5, No.2, 1976 460 H. H. LI 3.13. Rubidium Fluoride, RbF 4 2n ddTn=- 8.25 (n 2 -1) - 0.89 + 1.58111. (11.2 - 0.01742) 2 The refractive index of RbF is available only for a single spectral line, the sodium D line, measured by 227.5011.4 Spangenberg [45] in 1923 using the immersion method. + (11.2 _ 4005.62) 2' (48) One of the reasons for the· scantiness of the data is di1lic.::ulLy 111 c;ry~lal growing. Tlwugh little attention was 5 paid to the refractive index measurement, a number of where dn/dT is in units of 10- K-l and A in j.tm. other physical properties of RbF were investigated. Equations (47) and (48) were used to generate the Values of a few of them arf~ giVf~n in tahlp.~ 2 ancJ .~ recommended values of refractive index and its wave Although' there is only a single value of n available, a length and temperature derivatives. In the table of dispersion equation can be formed by correlating the recommended values, more decimal places than needed dielectric constants and the wavelengths of absorption are given, for tabular smoothness and internal com peaks to the refractive index by the two-oscillator parison. The readers are advised to follow the criteria model. Using the values of known parameters from given below in order to find meaningful values from the table 3 and the available value of n: table. For refractive index: Es= 6.48, Eu\'= 1.93, Wavelength range Meaningful Estimated Au=0.12'1. p.m (average of two peaks), (~m) decimal place uncertainty, ± 11.)=63.29 j.tm, 0.15- 0.21 2 0.02 n= 1.398 for 11.=0.5893 j.tm 0.21- 0.30 3 0.008 0.30- 0.1.0 3 0.006 the value of the adjustable parameter A of eq (13) is 0.40-.1.50 3 0.005 found to be 1.395. This leads to a dispersion equation 1.50- 8.00 3 0.006 for RbF at 293 K in the transparent region from 0.15- 8.00-11.00 3 0.008 25.0 j.tm. 11.00-15.00 3 0.02 15.00-25.00 2 0.03 (47) For dn/dT: where A is in units of j.tm. 0.15- 1.00 1 0.8 No experimental data on dn/dT are available. Our 1.00-10.00 1 0.0 empirical parameter values in table 5 were used to 10.00-20.00 1 0.8 construct a dn/dTformula for the transparent region: 20.00-25.00 0 ~1 J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 466 H. H. U 3.14. Rubidium Chloride, RbCI RbCl in terms of its characteristic absorption peaks, l1,"in~ (~Yll1::li'", chlta. Thp- wavp-Iengths of 11ltraviolet Rubidium chloride is hygroscopic and must be care absorption peaks, indicated by his equation, agree with fully handled to preserve the surface polish. The trans the measured values listed in table 3. However, no in mission region of RbCl is approximately from 0.18 to formation concerning the infrared absorption peak and 40 f.Lm. The gradual decrease in transmittance at dielectric constants was gIVen. This leads to large un shorter wavelengths is due to surface scattering that certainties in the long wavelength region. Since the is caused by the roughness of the surface, and not to wavelength of the fundamental infrared absorption peak absorption or scattering within the material itself (105]. and the dielectric constants for high and low frequencies The available data on the refractive index of RbCI are now available (see table 3), a better formula of the are very limited; only.three reports were found. Sprock Sellmeier type can be constructed, and the extrapola hoff [951, in 1904, was probably the first to measure tion into the infrared can be carried out with less un the refractive index of RbCl for three spectral lines certainty. By using the known parameters with eq (10), (the C, D, and F lines), by the minimum deviation the least-squares fitting of Gyulai's data (reduced to method. These three values remained unchecked until 293 K) yielded a dispersion equation for RbCI at 293 K Gyulai [27], in 1927, performed experiments for an in the transparpot region, O_lR-400 fJ.m- extended wavelength region from 0.19 to 0.58 I-'-m by the deviation method at an elevated temperature, 321 K. The accuracy of his measurements is one unit of the thil·d decim9.1 place, but the reported values are given + 0.5660011.') O.14493A'? 2.74000A" to the fourth place for tabular smoothness. The refrac }..z_ (0.138)2+ )..2- (0.166)2+ ,V- (85.84)2' tive index for sodium D line was remeasured using the immersion method at room temperature by Wulff and (50) Heigl [87] in 1928, and the result deviated from that of Sprockhoff only in the fourth decimal place. In addition, where).. is in units of fJ-m. the temperature derivative, dn/dT. for sodium D line Equations (49) and (50) are used to generate the in the temperature range from 296 to 298 K was deter reference data given in the table of recommended values mined, and a value of -1.0 X 10-4K-l was reported. on refract-ive index, dn/dA and dn/dT. In this table, This value is obviously inaccurate. more decimal places than needed are given for the pur The values reported by Gyulai f27] were adopted in pose of tabular smoothness. In order to use this table the· present work to generate reference data on· the properly, the readers should follow the criteria given refractive index of RbCl. Since the data was obtained below. at a temperaure of 321 K, dn/dT is needed to reduce thi" !,;p1 of dflt::l to ?9;i K No p)'cpprlmpntAl cI::ltfi on rlnJrlT For refractive index: are available to carry out the corrections, but our em pirical findings permit reasonable estima60n of dn/dT Wavelength range Meaningful Estimated for a wide wavelength range. Using the predicted (J,Lm) decimal place uncertainty, ± parameiers in table 5, the following dn/ dT formula 0.18- 0.20 2 0.02 was constructed for RbCl: 0.20- 0.25 3 0.005 0.25- 0.35 3 0.004 0.35- 1.50 3 0.002 dn 2 2n dT=-10.80(n -1) -0.84+ 1.50-10.00 3 0.004 10.00-21.00 3 0.008 2.006)..4 186.32)..4 21.00-40.00 2 0.02 (.\2-0.02756)2+ (A 2 -7368.51)2' (49) For dn/dT: where dn/dT is in units of 10-5 K-l and).. in fJ-m. This equation was used to reduce Gyulai's data to 293 K. 0.18-- 0.20 o ~l Radharkrishnan l48] worked out a dispersion formula 0.20-30.00 I 0.5 (shown in table 62) expressing the refractive indices of 30.00-40.00 o ~1 J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 474 H. H. LI 3.15. Rubidium Bromide, RbBr those obtained by direct measurements (see table 3) but Rubidium bromide is hygroscopic and must be gives no information concerning the infrared absorption handled with great care to protect the surface polish. peak. As a consequence, extrapolation using this equa A plate of moderate thickness with properly polished tion will be uncertain. We have constructed a bette~ surfaces is transparent from 0.25 to 40 J.un. Roughness formula of the Sellmeier type, which gives the refrac· of the surfaces causes a considerable decrease in tive index at wavelengths beyond Kublitzky's work with transmittance. It is found that the gradual decrease in less uncertainty. Using the information in tables 3 and transmittance at shorter wavelengths is caused by im 66, the input parameters for the least-squares fitting perfection of the surface and not by absorption or were obtained, the result is a dispersion equation for scattering within the material itself [105]. RbBr at 293 K in the transparent region: Only two sets of measurements were found in the open literature. In 1904, Sprackhoff [95J measured 0.16301A.2 0.29841A.2 refractive indices of RbBr for three spectral lines, 2 n = 1.4S931 + 'A,2 _ (0.123)2 + "'-2 - (0.146)2 namely the C, D, and F lines, by the minimum deviation method. Thirty years later, Kublitzky [50J used the 0.17198A.2 0.12186A. 2 same technique in measurements for m{)rp linps in ::; + ),2- (O.lSS)2+ >.2- (O.17R)2 region from 0.219 to 0.58 /-Lm at a temperature of 308 K. 0.13039A.2 2.520A.2 The accuracy of his measurements is one unit in the + 'A2- (0.191)2+ A. 2- (1l4.29)2' (S2) third decimal place, but his reported values are given to the fourth place for the purpose of tabular smoothness. Scantiness of available data leaves us no choice but to where A. is in units of j.J..m. use Kublitzky's measurements as the basis for generat Equations (S1) and (52) are used to generate the ing reference datu. Information on dn/dT is needed to recommended values of refractive index, dn/d'A' and reduce Kublitzky's values from 308 to 293 K, but it is dn/dT. In this table, more decimal places than needed not available. This is not a problem, because we have are given for the purpose of tabular smoothness. In found empirical parameters which are used to construct order to obtain meaningful' values from the table, readers dn/dT formulas, and have proved to give correct predic are advised to follow the criteria given below. . tions, as is discussed in subsections 3.11 and 3.12. Using the parameter values in table 5, we are led to the For refractive index: following equation for dn/dT for RbBr at 293 K ill lhe transparent region: Wavelength range Meaningful Estimated (/-Lm) decimal place uncertainty, ± dn 2n dT= -11.25(n2 -l) -0.89 0.21- 0.22 2 0.02 0.22- 0.30 3 0.005 0.30- 0.40 3 0.003 2.278A.4 191.S2A.4 (51) 0.40- 1.50 3 0.002 + (A.2~0.03648)2+ (A.2-13062.20)2' 1.S0-1S.00 3 0.004 1S.00-30.00 3 0.006 where dn/dT is in units of 10-5K-l and A in j.J..m. This 30.00-40.00 3 0.008 equation was used to make temperature corrections to 40. OO-SO. 00 2 0.02· the selected data. Radhakrishnan [48J attempted to correlate the dis For dn/dT: persion and absorption bands by means of a dispersion formula and obtained an equation valid at 308 K, as 0.21- 0.22 o ~1 shown in table 66. His equation yields wavelengths of 0.22-40.00 I 0.5 ultraviolet absorption peaks which agree closely with 40.00-50.00 o ~1 J. Phys. Chern. Ref. Dato, Vol. 5, No.2, 1976 REFRACTIVE INDEX OF ALKALI HALIDES 481 3.16. Rubidium Iodide, Rb! Hilsch and Pohl [23J and Schneider andO'Bryan [24J (see table 3), but it gives no information concerning the Rubidium iodide is the most hygroscopic of the infrared absorption peak and the dielectric constants. rubidium halides and care must be exercised in handling Naturally, extrapolated values for the long wavelengths it to preserve the surface condition, which plays an as given by this equation have large uncertainties. It is important role in its transparency. A plate of RbI a few mm thick wIth well-polished surface is rransparem therefore not an adequate formula for a wide wavelength range. Using the information in tables 3 and 70, the input from 0.25 to more than 50 /-Lm. The gradual decrease parameters for the least-square fitting of the data to eq in transmittance at shorter wavelengths is due to surface (10) were obtained. The calculation yielded a dispersion scattering that is caused by the roughness of the equation for RbI at 293 K in the transparent region, 0.24 surface and not by absorption or scattering within the material itself [lOS]. . to 64.0 /-tm. As with the other rubidium halides there are few data available; only two sets of data were found for the n 2 = 1.60563 transparent region, those of Sprockhoff [95J (for C, D, 0.00947,\2 0.01073,\:1 0.00136,\2 and F lines) and Kublitzky [50J (for the region 0.25- + ,\2- (0.120)2+ ,\2- (0.134)2+ ,\2- (0.156p 0.58 fLm). In the ultraviolet, Baldini amI Rigaltli [106J investigated a narrow spectral region, 0.18 to 0.25 /-Lm, + 0.41864,\2 0.4177111.2 0.13707,\2 deriving the optical constants of thin films of RbI from ,\2- (0.179)2+ ,\2- (0.187P+ 'A2- (0.223)2 the reflection spectra The wRvp]pngths of thp- ultraviolet 2.360YIA~ absorption peaks derived from this work are inconsistent (54) + ,\2 - (132.45)2 with those observed for the bulk material. Because of the lack of data, we had to rely on Kublitz ky's data as the basis for generating the reference data. where 'A is in units of !-tm. The accuracy of this set of data is one unit in the third Equations (53) and (54) were used to generate the decimal place, hut the reported values are given to the recommended values of refractive index, dn/d'\ and fuUl til place. However, we used the reported values in . dn/dT for RbI. Since more decimal places than needed the data analysis. Since this data set was obtained at a are given for the purpose of tabular smoothness, readers temperature of 309 K, the temperature coefficient of the are advised to follow the criteria given below in order to refractive index is needed to reduce the data to 293 K. use the recommended values correctly. Experimental values are not available. In the present work, values of dn/dT can be estimated for a wide For refractive index: wavelength range, using our empirical findings discussed in subsection 2.2. Using the parameters values from Wavelength range Meaningful Estimated table 5, a dn/dT formula was constructed for RbI in the (/Lm) decimal place uncertainty, ± transparent region: 0.24- 0.25 2 0.02 0.25- 0.30 3 0.004 dn 0.30- 0.40 3 0.003 2n· = -12.45 (n2 -1) -0.85 dT 0.40- 1.50 3 0.002 1.50-20.00 3 0.003 + 2.606)..4 169.92)..4 20.00-30.00 .3 0.006 (,\2-0.04973)2+ (,\2-17543.00p' (53) 30.00-50.00 3 0.009 50.00-64.00 :2 0.02 where dn/dT is in unitS of 10-5 K -1 and ,\ in /Lm. This equation was m:ed to reduce Kublitzky's data to 293 K. For dn/dT: Radhakrishnan [48J obtained a dispersion formula (shown in table 70) based on Kublitzky's data. This 0.24- 0.27 0 ;:,1 formula gives the wavelengths of three ultraviolet 0.27-45.00 U.5 absorption peaks, which agree with tho~e !"tudied by 45.00-64.00 0 ;:,1 J. Phys. Chern. Ref. Data, Vol. 5, No.2, 1976 H. H. 1.1 3.17. Cesium Fluoride, CsF empirical parameter values in table 5 were used to construct a dn/dT formula for the transparent region: The refractive index of CsF for a single spectral line, the sodium D line, was obtained by Spangenberg [45] dn using the immersion method. He gave two values for n, 2n dT= --9.60 (n 2 -1) - 2.54 one for a-CsF, and the other for ,B-CsF. The fact that there is one measured value of n only for one wavelength 1.42A4 296.00A4 does not prevent us from making a reasonable estimate + (A 2 - 0.01850) 2 + (A 2 - 6199.99) 2 ' (56 ) of the refractive indices for a wide transparent region 5 bee{lu~e there exist known property parametcra in where dn/dT is in units of 10- K -1 and A in !Lm. timately related to the refractive index, enabling us to Equations (55) and (56) were used to generate the make the necessary calculations. Using the values from recommended values of the refractive index, dn/dA table 3 and the available n: and dn/dT for CsF. As noted, these equations are based totally on the available data on the thermal linear expan Es=8.08, sion, dielectric constants, the wavelengths of absorption peaks, and our empirical parameters. As a conse-quence, Euv=2.16, the accuracies of the estimated values are governed by the uncertainties in the above mentioned parameters. Au = 0.121 /-Lm (averaged value of 3 peaks), The following criteria are recommended. For refractive index: Wavelength range Meaningful Estimated n = 1.478 (of a-CsF), for A= 0.5893 p.m, (!Lm) decimal place uncertainty, ± 0.15- 0.19 2 0.02 the adjustable constant A of eq (13) is found to be 1.60. 0.19- 0.30 3 0.008 This leads to a dispersion equation for a-CsF at 293 K 0.30- 1.50 in the transparent region, 0.15-30.0 !Lm. 3 0.003 1.50-10.00 3 0.006 10.00-16.00 3 0.008 (55) 16.00-30.00 2 0.03 For dn/dT: where A is in units of /-Lm. If we used the refractive index of ,B-CsF, the value of 0.15- 0.16 o ~1 A would be negative, which is not an acceptable solution. 0.16-22.00 1 0.5 No experimental data on dn/dT are available, but our 22.00-30.00 o ~l J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 494 H. H. LI 3.18. Cesium Chloride, CsCI dn 2n dT=-13.89 (n 2 -1)-4.27 Cesium chloride is very hygroscopic and highly 4 4 soluble in water. It is, therefore, an unsatisfactory 1.989A 276.48A + (A2 - 0.02624)2 +(A2-10100.25)2 , (57) material for making optical parts, despite its optical transparency over a fairly wide wavelength region. where dn/dT is in units of10-5 K -1 and A in jLin. Equa While CsC} is not suitable for ordinary applications, it tion (57) was used to calculate dn/dT values for reducing is an interesting object for scientific studies. The wave Wulff's data to 293 K. lengths of absorption bands in the ultraviolet region With the information available from table 3, a least have been measured by Hilsch and Pohl [23] and by squares fitting of the reduced data to eq (10) was carried Schneider and O'Bryan [24]. Lowndes and Martin [13] out. It resulted in a dispersion equation for esCI at measured the infrared absorption band and the dielec 293 K in the transparent region, 0.18-40.0 jLm. tric constant. In table 3, t.he results of the above work are listed. n 2 = 1.33013 + 0.98369 A2 0.00009 A2 Because it is an unfavorable material for optical use, A2 - (0.119)2 + A2 - (0.137)2 (58) there have been few measurements of the refractive 0.00018 A2 0.30914 A2 4.320 A2 index. For the transparent region, only four data sets + ,\2 - (0.11.5)2 + ,,-2 - (0.162)2 + 'A? (100.50)2' covering a limited wavelength range were found in the literature. Upon careful examination, one finds that the where A is in units of jLm. works, of Wulff, et al. (the first three listed in table 75) In practical use, the contributions of the third and ploJuct:d I diaLlt: rt:~ulL~ which can be used as the basis fourth tt:11H art: ~IIlall and can be neglected; they are for the reference data generation. Results reported by given here for completeness. Equations (57) and (58) Sprockhoff appear to be unreliable, as the given values were used to generate recommended values of refractive seem too high for the assumed temperature. The large index dnldA and dnldT. In the tahle~, the property discrepancies may be attributed either to the measure values are given to more decimal places than needed, ments being made at a lower temperature than was for tabular smoothness. In order to use the recom reported, or to the measurements being made on im mended values correctly, readers should follow the pure specimens. In the infrared region, Vergnat, et al. criteria given below. [26] obtained refractive indices. for powdered CsC] by For refractive index: analyzing the reflection spectrum. This set of data is presented here for completeness, but it was not used for Wavelength range Meaningful Estimated data analysis. (~m) decimal place uncertainty, ± Data reported by Wulff, et al. were obtained at a 0.18- 0.20 2 0.01 temperature of 298 K, five degrees higher than our 0.20- 0.30 3 0.005 chosen reference temperature. Since the value of 0.30- 0.40 3 0.003 dn/dT of CsCl is about 6.0 X 10-5 K-1 in the visible 0.40- 1.50 3 0.001 region [18], a temperature correction of about 3 units 1.50-20.00 3 0.003 in the fourth decimal place needs to be made. 20.00-30.00 3 0.006 Ahhough there is not a single experimental value of 30.00-40.00 3 0.008 dn/dT available in the literature, we can make reason For dn/dT: able estimates of dnldT over a wiele w:welength range, using our empirical discoveries. Using the parameter 0.18- 0.19 o ~l values in table 5, the following dn/dT formula was 0.19-30.00 1 0.4 constructed for CsCI: 30.00-40.00 1 0.9 J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 502 H. H. LI 3.19. Cesium Bromide, CsBr pletes the record of activities in determining the refractive index of CsBr. Early measurements of the refractive index of CsBr In view of the available information discussed above, were made by Sprockhoff [95] in ]904. He used the we used the two data sets by Rodney and Spindler [107, minimum deviation method to determine the refractive ] 08] as the basis for generation of recommended values. indices for three visible spectral lines, 0.4.86, 0.589, and Since the data sets were reported at temperatures of 0.656 Mm. Although his values were presented to 4 300 and 297 K respectively, temperature corrections decimal places, the temperatures at which the data were needed to reduce the selected data to 293 K. were obtained were not specified; the significance of However, there was little data on which to base such the data is thus uncertain. corrections. Rodney and Spindler [J 07] reported an In the following 50 years, no other measurement of averaged dn/dT value of - 7.9 X 10 -5 K -1 for the the refractive index of CsBr was reported. The main wavelength range 0.36-39 Mm, but no detailed variation reasons for this long blank period were the difficulties of dn/ dT was given. in crystal growing. Large crystals suitable for optical In the present research this obstacle was removed components were not available. It was not until 1953 by our empirical methods, as discussed in subsection that large crystals of CsBr of reasonably good optical 2.2. With the aid of the predicted parameters in table 5, quality welE 5ucce::,::,fully grown, ploviding a Hew we constructed a formula for dn/dT values for CsBr material for infrared· studies in the range beyond the over the entire transparent region: 25Mm limit of KBr, out to about 40 Mm. A mixed crystal of thallium bromide-iodide. known as KRS-5. was pre viously the only material available for use in this region. 2n -dn = -14.22 (n 2 -1) - 4.7 5 The dispersion of CsBr compares favorably with that dT (59) of KRS-5 beyond 20 microns, and when the effects of inhomogeneity and retlection losses are considered the 2.172 ,\ 4 310.40 ,\ 4 resolving power of a CsBr prism is much better. + (,\2 - 0.03497)2 + (,\2 - 18509.60)2' The refractive index in the transparent region of CsBr was extensively and precisely measured by where dn/dT is in units of 10-5 K-l and ,\ in Mm. Rodney and Spindler [107, 108] in ]952 and J953. The The results of this process and encouraging. In figure minimum deviation method was used fOl a wide wave 64, it is evident that our averaged value of dn/dT in the length range from 0.365 to 39.22 Mm. Rodney and transparent region is about - 8.2 X 10-5 K-l,while the Spindler [107] worked out a dispersion equation of value of Rodney and Spindler is - 7.9 X 10 -5 K -1. In CsBr as shown in· table 82. They pointed out that five the better set of the selected data, Rodney and Spindler of the seven constants in that equation were determined [107J obtained refractive indices at temperatures ranging by means of a simultaneous solution. The constants from 297 to 304 K, and then reduced to 300 K with appearing in the denominators of two terms represent accuracies within ± 1 or 2 X 10 - 5. If the errors are the infrared and ultraviolet absorption bands. The ultra totally due to the uncertainties of dn/dT, which is very violet term was determined by taking a weighted mean likely, the uncertainty in dn/ dT is about 0.3 X ] 0 - 5 K -1 of several measured bands. The infrared term is an or higher. The accuracy of the other set is perhaps less estimate based on information on CsCI, and is probably than 0.0001. Therefore, it can be safely said that the too low. predictions of eq (59) are reasonable. The selected dato Hefractive indices of CsBr in the infrared absorption were reduced to 293 K using this equation. region, 30-275Mm, were derived by Geick [109] in ] 961, From the information in tables 3 and 82, input paramo. based on the analysis of transmission and nearly-normal eters for a least-squares fitting were obtained. The reflection spectra. He concluded that an absorption peak calculation resulted in a dispersion equation for CsBr was located at 136.7 Mm. The infrared region up to 200 at 293 K in the transparent region, 0.21-55.0 Mm. Mm was reinvestigated by Vergnat, et a1. [26] in 1969. The Lorentz damped-oscillator model was used to analyze the normal reflection spectra. Two absorption peaks were found at 97.09 and ]33.33 Mm, with the one of longer wavelength predominating. These results indicated that the wavelength in the infrared term used 0.00975 ,\2 0.00672 ,\2 by Rodney and Spindler was low. + ,\2 - (0.160)2 + ,\2 _ (0.173)2 (60) In the millimeter-wavelength region, the refractive index at 2000 Mm was determined by Dianov and 0.34557,\2 3.76339,\2 lrisova [47] in 1967. The result, n 2 = 6.55 at room tem + ,\2- (0.187)2 + },2_ (136.05)2' perature, agrees closely with the value of static dielec tric constant given by Vergnat, et a1. [26]. This com- where ,\ is in units of Mm. J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 REFRACTIVE INDEX OF ALKALI HAI.IDES 503 Equations (59) and (60) are used to generate the For refractive index: recommended values of refractive index, and its wave Wavelength range Meaningful Estimated length and temperature derivatives. The property values (/Lm) decimal place uncertainty, ± are given to more decimal places than needed to assure 0.21- 0.25 2 0.01 tabular smoothness. In using values from the table, 0.25- 0.35 4 0.0003 readers should follow the criteria given below. 0.35-30.00 4 0.0001 30.00-40.00 4 0.0005 40.00-55.00 3 0.006 For dn/dT: 0.21- 0.22 o ~ ] 0.22-40.00 0.4 40.00-55.00 0.9 J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 512 H. H. LI 3.20. Cesium Iodide, Csi temperature derivative of the refractive index quite thoroughly in his paper; however, an equation for Early measurements on the refractive index of CsI calculating dn/ dT in general was not given. were made by Sprockhoff [95] in 1904, using a minimum The temperature coefficient of the refractive index deviation method for three visible spectral lines, 0.486, of Cs1 unlike that of other alkali halides, has been 0.589, and 0.656 }-tm. Although his values were pre measured over the whole transparent region. Using the sented to four decimal places, the temperature at which existing data on dn/ dT and the parameters in tables 2 the data were taken was not specified. These three and 3, a least-squares fitting of the data to eq (19) was values were the only available data for about 50 years. carried out. The results. together with those obtained fOT The main reason for such a long period of inactivity LiF, NaF, NaCI, and KCl, provided the basis for the was the difficulty in growing adequate crystals. Large procedure discussed in subsection 2.2; see also figures and good quality crystals suitable for optical com 2 and 3. These results were used to predict the unknown ponents were not available; also, the need for infrared parameters of eq (19) for all the twenty alkali halides, transparency was not generally felt. as given in table 5. With these parameters we can It was not until 1955 that the refractive index for the construct a formula for calculating dn/dT for CsI. wide range of transmission (0.29 to 53 }-tm) was measured by Rodney [110] on several cesium iodide samples dn grown by the Harshaw Chemical Company. The re 2n dT = - 14.70 (n 2 -1) - 5.53 fractive indices were measured at temperatures near 15, 24, and 34°C by the deviation method. The tempera + 2.464 A4 242.76 A4 ture derivatives of refractive index were determined (A 2 - 0.04752)2 + (A 2 - 26014.46)2' for each wavelength and all data were reduced to 24 °C. (61) He adopted a dispersion equation of the Sellmeier type. simplified to five terms, to fit the reduced data. Although where dn/dT is in units of 10 -5 K -:-1 and A in p.,m. his dispersion equation fitted his data quite well, more terms could have been included to advantage, since Comparison of the predictions of eq (61) and the information on more than five absorption bands was then experimental data shown in figure 67 shows excellent available. agreement except at two points, at about 0.30 and 0.35 /-tm. From the fact that the constructed formulas In the ultraviolet region, 0.20-0.25 /-Lm, Lamatsch, dn/dT Rossel, ann Saller [111J clerlvecl the refractive indices always agree with experimental data at low wavelengths, from information on the transmission and reflection as shown in dn/dT figures of LiF, NaF, NaCI, and KCI, spectra. Sinc€; they used vacuum-evaporated thin film we believe that eq (61) gives reasonable estimates in the samples, the wavelengths of the two absorption bands low wavelength region. Equation (61) is confidently used obtained are higher than that of the bulk material. Large to reduce the selected data to 293 K. discrepancies between this set of data and that calcu As listed in table 3, the ultraviolet absorption spec lated from Rodney's work are to be e"xpected. trum of CsJ between 0.10 and 0.24 J.tm consists of seven Va1ues of the refractive index beyond the tran:sparent absorption peaks. The infrared speetrnm comprises region in the infrared were obtained by Vergnat, et a1. two fundamental absorption peaks, but the dominant 126] in 1969, by analyzing the reflection spectrum. They effect on the refractive index is due to the peak at found that the wavelengths of infrared absorption bands 161.29 }-tm. In the present work, the effects of all the are 117.65 and 161.29 /-Lm at room temperature. One of absorption peaks on the refractive index in the trans the two values is in close agreement with that of Rodney, parent region are taken into consideration, and the as shown in table 87. As a matter of fact, the pre best fit equation is used to calculate the refractive index dominant contribution to the absorption is due to the of CsI at 293 K in the transparent region, 0.25-67.0 }-tm. one band that Rodney used. 2 2 In the millimeter wavelength region, the refractive n 2 = 1.27587 + 0.68689 A + 0.26090 A index ::It 2000 JIm W::l~ obtained by Dianov and Jrisova A2 - (0.1 ~O)2 >..2 - (0.147)2 [47] in 1966. Their result, n 2 = 6.452 at room tempera ture, agree to the first decimal place with the static + 0.06256 A2 0.06527 A2 0.14991 A2 dielectric constant given by Vergnat, et a!. [26]. This A2 - (0.163)2 + A2 - (0.177)2 + A2 - (0.185)2 completes the record of the published activities in determining the refractive index of CsI. + 0.51818 A2 + 0.01918 A2 3.38229 A2 From the available information, the data of Rodney A2 - (0.206)2 A2 - (0.218)2 + A2 - (161.29)2' were adopted CI.::I the ba::li~ for t.he gCHClat.jUIJ uf let.:Ul1l mended values. Since this set of data was measured at (62) a temperature of 297 K, corrections had to be made to reduce the data to 293 K. Rodney [110] discussed the where" A is in units of }-tm. J. Phys. Chern. Ref. Data, Vol. 5, No.2, 1976 REFRACTIVE INDEX OF ALKALI HALIDES 513 Equations (61) and (62) were used to generate the For refractive index: recommended values of refractive index and its wave Wavelength range Meaningful Estimated length and temperature derivatives. In the table of (/-Lm) decimal place uncertainty, ± recommended values, more decimal places than needed 0.25- 0.35 4 0.0002 are given, for tabular smoothness and internal compari 0.35-20.00 4 0.0001 :;Ul1. IJl u~ing values from the table, readers sho1Jlci 20.00-40.00 4 0.0002 fol1ow the criteria given below. 40.00-50.00 4 0.0005 50.00-67.00 3 0.001 For dn/dT: 0.25- 0.35 0.8 0.35- 1.00 1 0.5 1.00-50.00 1 0.3 50.00-67.00 o 1 J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 522 H. H. II 4. Conclusions and Recommendations The purpose of the present work is to generate recom Experimental data on the refractive index of alkali mended values on the refractive index and its tempera halides and its temperature coefficient are exhaustively ture coefficient for all of the twenty alkali halides. This surveyed and reviewed. In addition, a number of objective is now achieved. Equations (23) to (62) were physical properties which are related to the dispersion constructed by either least-squares fitting of the selected IJh~IlUIIJ~IJa aI~ selecLed frum the upen literature. avallaule data 10 eq (10) Of. by correlating the related The distribution of the refractive index data among properties and empirical parameters. the twenty alkali halides is not even. LiF, NaCI~ KCI, Based on the dn/ dT data of the five materials, LiF, and KBr were extensively measured; NaF. KI. CsRr. NaF. NaCl. KCl. and {:sl. two interesting fa~ts werp and CsJ received reasonable care; NaBr, KF, RbCI, discovered (as discussed in section 2.2) and used to RbBr, Rb( and CsCI were scantily and limitedly ob predict the unknown parameters of eq (19) for all the served; while LiCI, LiBr, Lil, NaI, RbF, and CsF were alkali halides. The results calculated by the constructed practically total1y ignored, except at a single wavelength. dn/dT formulas agree very well with the available data. The situation is even worse in the case of the tempera Equations (23) to (62) were used to generate recom ture coefficient of refractive index. LiF, NaF, NaCI, mended values of n, dn/d'A and dn/dT for bulk materials KCI, and Csl were scantily investigated over a sizable at 293 K; these are summarized in figures 68, 69, and wavelength range; KBr and KI were measured only 70. It should be noted that the formulas based on scanty over a limited wavelength region. No observation was or null data are subject to further modification and made for the remaining 13 alkali halides. expansion when experimental data are available. J. Phys. Chem. Ref. Data, Val. S, No.2, 1976 526 H. H. LI The technology related to high·power infrared lasers Standard Lens and Prism Material with Special Reference to is progressing rapidly and, consequently, there is Infrared Spectroradiometry," J~ Opt. Soc. Amer., 4, 432- 47, 1920. an increasing need for determining the effects thattex [5] Winchell, A. N., and Winchell, H., The Microscopical Charac posures to high·power laser beams have on materials. ters of Artificial Inorganic Solid Substances, 3d Edition, Among other things, the refractive index of alkali halides Academic Press, New York and London, 1964. at elevated temperatures are needed. Unfortunately, [6] Landolt·Bornstein, Physikalisch-Chemische Tabellen, 5th an exhaustive survey of the literature, as in the present Edition, Vol. 2, 911-22, 1923: Vol. 3, 1467-72, 1935: 6th Edition, Vol. 2, No.8, 2-405-2-432, 1962. work, shows that refractive indices are only available [7] Gray, D. E. (Editor), American Institute of Physics Handbook, at about room temperature and at a few specified tem 3d Edition, McGraw-Hill Book Co., New York, 2342 pp., 1972. peratures such as that of liquid nitrogen, liquid helium, [8] Weast, R. C. (Editor), Handbook of Chemistry and Physics, The etc. In a limited number of cases, the temperature Chemical Rubber Co., Ohio, 1969. coefficient of refractive index has also been measured [9] Stull, D. R., and Prophet, H., "JANAF Thermochemical Tables," National Standard Reference Data Series - National Bureau in the vicinity of room temperature. Because of this of Standards NSRDS-NBS 37, 1141 pp., 1971. lack in high-temperature data, some of the recent effort [10] Wolfe, W. L., Handbook of Military Infrared Technology, U.s. has been devoted to obtaining refractive indices at Government Printing Office, Washington, D.C., 906 pp., 1%5. elevated temperatures_ However, these activities are [II] Tro<;t, K. F., "Thermal Expansion of Alk~li Halides of thc focused only on measurements at a few spectral lines Na-CI Type at High and Low Temperatures," Z. Naturforsch., B 18(8), 662-4, 1963. characterizing the lasers of interest. Consequently, our [12] Kirchner, H. P., Scheetz, H. A., Brown, W. R., and Smyth, H. T., basic knowledge of the refractive index at high tempera· "Investigation of Theoretical and Practical Aspects of the tures is still scanty. For the purpose of providing useful Thermal Expansion of Ceramic Materials," Cornell Aero data to modern science and technology, as well as for nautical Lab. Rept., 101 pp., 1962. [AD296188] the future development of optical devices, a well-planned [13] Lowndes, R. P., and Martin, D. H., "Dielectric Dispersion and the Structures of Ionic 1.Hlli ... ",<;," Prot:' Roy. Soc., .<\30B, and 5Y5tClTIatic progralTl of 111ea5Ulell1ellt of the re 473-96, 1969. fractive index for selected materials, including alkali r14] Jasperse, J. R., Kahan, A., and Plendl, J. N., "Temperature halides, over a wide range of temperatures and wave Dependence of Infrared Dispersion in Ionic Crystals LiF and lengths is highly recommended. MgO," Phys. Rev., 146(2), 526~42, 1966. [15] Genzel, H. H., and Weber, R., "Dispersion Measurement on NaCl, KCI, and KBr Between 0.3 and 3 mm Wavelength," Z. 5. Acknowledgments Phys. 154, 13-8, 1959_ [16] Handi, A., Claudel, J., Chanal, D., Strimer, P., and Vergnat, P., This work is jointly supported by the Office of Stand "Optical Constants of Potassium Bromide in the Far Infrared," ard Reference Data (OSRD) of the National .Bureau of Phys. Rev., 163(3),836-43, 1967. Standards (NBS), U.S. Department of Commerce and [17] Ramachandran, G. N., "Thermo-optic Behavior of Solids, v_ by the Defense Supply Agency (DSA), U.S. Department Alkali Halides," Proc_ Indian Acad. Sci., 25A, 481-97, 1947. of Defense (DOD). The part of work supported by DSA [18] Tsay, Y. F., Bendow, B., and Mitra, S. So, "Theory oft he Temper ature Derivative of the' Refractive Index in Transparent was under the auspices of the Thermophysical and Crystals," Phys. Rev., 88(6), 2688-%, 1973_ Electronic Properties Information Analysis. Center [19] Lowndes, R. P., "The Temperature Dependence of the Static (TEPIAC), a DOD Information Analysis Center. Dielectric Constant of Alkali, Silver, and Thallium Halides," The author is grateful to 1. H. Malitson of NBS and Phys. Lett., 21(1), 26-7, 1966. L. A. Harris of the Research Materials Information [20] Andeen, C., Fontanella, .I., and Donald, S., "Low-Frequency Center, Oak Ridge National Laboratory (RMIC/ORNL), Dielectric Constant of LiF, NaF, NaCl. NaBr. KCl. and KBr by the Method of Substitution," Phys. Rev., 82 (12), for their valuable suggestions and helpful discussions. 5068-73, 1970. The author wishes to thank T. Connolly of RMIC/ORNL [21] Kartheuser, E., "Polarons in Ionic Crystals and Polar Semi for his assistance in review of the completeness of conductors," iDevreese, J. T., Editor), North-Holland} bibliographic coverage. C~ntributions of.J. B. Lee during American Elsevier, 717-33,1972. the early stages of this work are also acknowledged. [22] Hodby, J. W., Borders, J. A., and Brown, F. c., "Cyclotron Resonance of the Polaron in KCI, KBr, KI, RbCl, AgCl, . AgBr, and TICI," Phys. Rev. Lett., 19(7). 952-5.1967. 6. References (23] Hilsch, R., and Pohl, R. W., "Dispersion Frequencies of Alkali Halides in the Schumann Region," Z. Phys., 59,812-9,1930. [II National Materials Advisory Board, "High-Power Infrared-Laser [24] Schneider, E. G., and O'Bryan, H. M., "The Absorption of Ionic Windows," National Academy of Sciences-National Academy Crystals in the Ultraviolet," Phys. Rev., 51(5),293-8,1937. of Engineering, Washington, D.C., Publication NMAB-292, [25] Handi, A., Claudel, J., Morlot, G., and Strimer, P., "Trans 168 pp., 1972. mission and Reflection Spectra of Pure and Doped Potassium [2] Smakula, A., "Physical Properties of Optical Crystals with Iodide at Low Temperatures," AppJ. Opt., 7(1), 161-5, 1%8. Special Reference to Infrared," Office of Technical Services, [26] Vergnat, P., Claudel, J., Handi, A., Strimer, P., and Vermillard, U.S. Dept. of Commerce Document No.1l1,052, 286 pp_, 1952. F., "Far Infrared Optical Constants of Cesium Halides at [3] Ballard, S. S., McCarthy, K. A., and Wolfe, W. L., "Optical Low Temperatures," J. Phys., 30(8-9), 723-35, 1969. Materials for Infrared Instrumentation," Michigan Univ., [27] Gyulai, Z., "The Dispersion of Some Alkali Halides in Ultraviolet Willow Run Lab., Rept. No. 2389-1I-5, 115 pp., 1959. Region," Z. Phys., 46,80-7, 1927. [AD 217367] r28] Schneider, E. G., "Optical Properties of Lithium Fluoride in the (4] Coblentz, W. W., "Transmission and Refraction Data on Extreme Ultraviolet," Phys. Rev., 49(9),341-5, 1936. J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976 REFRACTIVE INDEX OF· ALKALI HALIDES 527 [29] Hohls,H.W~, "Dispersion and Absorption of Lithium Fluoride [53] Stefan, J. M., "The Influence of Heat on the Light Refractionoi and Sodium Fluoride in the Infrared," Ann. Phys., 29, Solids," Sitzungsber. Akad. Wiss. Wien, 2, 63,223-45,1871:. 433-48; 1937. [54] Martens, F. F., "The Dispersion of Ultraviolet Radiation," Ann~ [30] Harting, H., "The Optical Aspect of Some Crystals and Their Phys., 6, 603-40, 1901. Representation by the Hartmann Equation," Z. Instrum., 63, [55] Paschen, F., "The Dispersion of Rocksalt and Sylvite in . 125-31, 1943. Infrared," Ann. Phys., 26, 120-38, 1908. [31] Durie, D. S. L., "The Refractive Indices of Lithium Fluoride," [56] Langley, S. P., "The Dispersion of Rock Salt and Fluorite," J. Opt. Soc. Amer., 40(12), 878-9, 1950. Ann. Astrophys. Obs. Smithsonian Inst., 1,219-37,1900. [32] Tilton, W. L., and Plyler, K K., "Refractivity of Lithium Fluoride [57]· Kellner, L., "Investigations in the Spectral Region Between2Q With A pplication to the Calibration of Infrared Spectrometers," and 40 Microns," Z. Phys., 56,215-34, 1929. . J. Res. Nat. Bur; Stand., 47(1), 2S-:-30, 195t. [58] Rubens, H., and Nichols, E. F., "Experiments With Heat [33] Bispinck, H., "Optical Determination of the Thickness and Radiations of Long Wavelengths," Ann. Phys. Chern., 60, Refractive Index of Non·Absorbing Thin Films on the Metallic 418-62, 1897. or Glass Substrates," Optik, 25(3), 237-48, 1967. [59] Rubens, H., and Trowbridge, A., "Contribution to the K.nowledge [34] Roessler, D. M., and Walker, W. c., "Optical Constants of on the Refractive Index and Absorption of Infrared Radiation. Magnesium Oxide and Lithium Fluoride in the Far Ultra for Rocksalt and Sylvite," Ann. Phys. Chern., 60, 724~39; violet," J. Opt. Soc. Ame·r., 57,835-6,1967. ·1897. . [35] Kato, R., "Optical Properties of LiF in the Extreme Ultraviolet," [60] Borel, G. A., "The Refraction and Dispersion of Ultraviolet J. Phys. Soc. Jap., 16~ 2525-33,1961. Radiation in Some Crystallized Substances,'" Compt. Rend,., [36] Frohlich, D., "The Optical Constants of LiF in the Region of 120, 1404-6, 1895. Infrared Characteristic Frequencies," Z. Phys., 169,114-25, [61] Cartwright, C. H., and Czerny, M., "Dispersion Measurements 1962. on NaCI and KCI in the Far Infrared Region. II.," Z. Phys~, [37] Frohlich, D., "Temperature Dependence of the Optical Con 90,457-67, 1934. . stants ofLiFin Region ofInfrared Characteristic Frequencies," [62] Geick, R., "Dispersion of NaCl in the Region of Infrared Char Z. Phys., 177, 126-37; 1964. acteristic Frequencies," Z. Phys., 166,122-47, 1962. (38] Genzel, L., and. Klier, M., "Spectral Investigations in the [63] Vinogradov, E. A., Dianov, E. M., and lrisova, N. A., "Michelson Region Around I mm Wavelength. III. Dispersion Measure Interferometer Used in Measuring the· Refractive Index of ments on LiF," Z. Phys., 144,25-30, 1956. Dielectrical Materials in the Region of the 2 mm Wavelength," . [39] Heilmann, G., "The Temperature Dependence on the Optical -Radiotekh. Elektron., 10, 1804-8, 1965. Constants of LiF in the Region of Infrared Characteristic [64] Czerny, M., "Measurements on the Refractive Index of NaCI Frequencies," Z.Phys., 152,368-83, 1958. in the Infrared to Prove the Dispersion Theory,"· Z; Phys., [40] Gottlieb, M., "Optical Properties of Lithium Fluoride in the 65,600-31, 1930. Infrared," J. Opt. Soc. Amer., 50(4),343-9, 1960. [65] Barbaron, M., "Refraction of Solids Measured at Low Tempeia~ [41] Shklyarevskii, LN., EI-Shazli, A. F. A., and Govorushchenko, hire," Ann. Phys., 6, 899-959, 1951. A.. I., "Dispersion of the Refractive Index in Magnesium [66] Roessler, D. M., and W alk~r, W. C., "Optical Constants·· of Fluoride, Lithium Fluoride, and Cryolite Films," Opt. Sodium Chloride and Potassium Chloride iIi the Far Ultra Spektrosk., 32~4), 769-71, 1971. violet," J. Opt. Soc. Amer., 58,279-81, 1968. [42] Lukirskii, A. P., Savinov, E. P., Ershov, O. A., and Shepelev, [67] Marcoux, J., "Measurement of the Index of Refraction of Some Yu. F., "Reflection Coefficients of Radiation in the Wavelength Molted Ionic Salts," Rev. Sci. Instrum., 42(5). 600-2,1971. Range from 23.6 to 113 A for a Number of Elements and [68] Dianov, E. M., and- lrisova, N. A., "Determination of the Absorp~ Substances and the Determination of Refractive Index and tion Coefficient of Solids in the Short-Wave Region of the Absorption Coefficients," Opt. Spectros. (USSR), 16(2), Millimeter Band," J. Appl. Spectros. (USSR), 5(2}, 187~9, 168-72, 1964. 1966. [43] Ramaseshan, S., _"Faraday Effect in Some Cubic Crystals," [69] Mitskevich, V. V., "Dynamical Theory of NaCl-Type Ionic Ind. Acad. Sci., Proc., A25, 459-66, 1947. Crystals. II. Dielectric and Optical Properties," Sov. Phys; [44] Zarzyski, J., and Naudin, F., "Index of Refraction and Re Solid State, 3(10), 2211-7, 1962. fractivity of Molten Salts," Compt. Rend., 256, 1282-5, 1963. [70] Rubens, H., "The Dispersion of Infrared Radiation," Wied: [45] Spangenberg, K., "Density and Refraction of Alkali Halides," Ann., 45, 238-61, 1092. Z. Kristallogr.; 57, 494-534, 1923. [71] Ruberis, H., and Snow, B. W., "Refraction of Long WaveJength ,[46] Abeles, F., "The Determination of the Refractive Index and Radiation in Rocksalt, Sylvite, and Fluorite," Wied. Ann:, Thickness of Transparent Thin Films," J. Phys. Radium, 46,529-41, 1892. 11(7),310-14,1950. [72] Ruben~, R., "The Kettclel--IIclmhQlt~ Di~per~ion f'ormula:," [47] Dianov, E. M., and lrisova, N. A-., "Measu;ement of the R~. Wied. Ann., 54, 476-85, 1895. . fractive Index of Crystals Having NaCl- and· CsCI-Type [73] Rubens, H., "The Dispersion of Infrared Radiation in Fluorite," Structures," Sov. Phys. Solid State, 8(7), 1807-8, 1967. . - Wied. Ann., 51,381-95, 1894. . .. [48] Radhakrishnan, T., "The· Dispersion Formulae of the Alkali [74] Martens, F. F., "The Di.~per~ion of Fluorite, Sylvite,Roeksalt,. Halides," Proc. Indian Acad. Sci., 27A, 165-70, 1948. Quartz, and Calcite, as Well as the Dispersion of Diamorid," Ann. Phys.,·8, 459-65,1902. [49] Sano, R., "Optical Properties of NaF Single Crystals in VUV Region," J. Phys. Soc. Jap., 27(3), 695-705, J969. [75] Cartwright, C. H., and Czerny, M., "Dispersion Measurements on NaCl in the Far Infrared,"-Z. Phys., 85,269-77,1933. [50] Kublitzky, A., "Some Optical Constants of Alkali·Halide [76] Pulfrich, c., "The Influence of the Temperature ontheRe.~ Crystals," Ann. Phys., 5, 20,793-808, 1934. fraction of Glasses," Ann. Phys. Chem" 45(4), 609-65, 1892; [51] Randall, C. M., "Interft:rometric Measurements of the Far II{ r77] Miyata, T., and Tomiki, T., "Optical Studies of NaCl Single. Refractive Index of NaF at Low Temperature," U.S. Air Crystals in 10 e V Region. II. The Spectra of Conductivity Force Rept. SAMSO-TR-70-304, 1970. [AD7110641 at Low Temperatures, Absorption Constant and Energy Loss,"· [52] Randall, C. M.,· "Interferometric Measurements of the Far J. Phys. Soc. Jap., 24(6), 1286-302, 1968.' Infrared Refractive Index of NaFat Low Temperature," [78] Miyata, T., and Tomiki, T., "The Urbach Tails and ReHection Aspen International Conference· on Fourier Spectroscopy Spectra of NaCl Single Crystals," J. Phys. Soc. Jap., 22U); (I970},371-6, 1971. 209-18, 1967. J. Phys. Chem. Ret Data, Vol. 5,.No.2,1916 528 H. H. LI [79} Joubin, P:, "The Rotary Magnetic Dispersion." Ann. Chim. [98) Forrest,J. W., "Refractive Index Values for Potassium Bromide," Phys., 6, 16,78-144,1889. ./. Op!. Soc. Amer.. 32,382, 1942. [80j Dufel, M. H., "Comparative Measurements of the Refractive [99] Gundelach, E., "The Dispersion of KBr Crystal in the Infrared," Indices Measured by the Prism and the Total Reflection," Z. Phys., 66, 775-83, 1930. Soc. Francaise Min. Cristallo. Bull., 14, 130-48, 1891. [100) Korth, K., "Dispersion Measurements on Potassium Bromide [8I} Micheli, F. J., "The Influence of the Temperature on the Ultra· and Potassium Iodide in the Infrared Region," Z. Phys., 84, violet Radiation Dispersion in Fluorite, Rocksalt, Quartz, and 677-85, ] 933. Calcite," Ann. Phys., 4, 7,772-89, 1902. [101] Topsoe, H., and Christiansen, C., "Optical Researches on Some [82] Liebreich, E., "The Change of the Refractive Index With the Series of Isomorphous Substances," Ann. Chern., Phys., 1, Temperature in the Infrared Region for Rocksah, Sylvite, and 5-99, 1874. FluoriLe," Veil •. DeuL. Phy ",. Ge"'., 13(]), 1 13,1911. [102] Bdl, E. E., ;'Tlle U",e of A",ymmctrie Interferograma in Trans t83] Liebreich, E., "The Optical Temperature Coefficient for Rock mittance Measurements," .1. Phys., 28(3-4), C2-18-25, 1967. salt, Sylvite. and Fluorite in the Region of Lower Tempera [l03] Eldridge, J. E., and Kembry, K. A., "Further Measurements tures." Verh. Deut. Phys. Ges., 13(18-19),700-12,19] L and Calculations of the Far·Infrared Anharmonic Optical [84] Langley, S. P., "The Invisible Spectra," Ann. Chern. Phys., 6, Properties of KI Between 12 and 300 K," Phys. Rev., B8(2), 9,433-506, 1886. 746-55, 1973. [85] Wulff, P., and Schaller, D., "Refractometric Measurements on [104] Berg, .J. I., and Bell, E. E., "Far-Infrared Optical Constants Crystals and Comparison of Isomorphic Salts With Noble of KI," Phys. Rev., B4(10), 3572-80, 1971. Gd" ne"embling and Non-Resembling Cationo. 8. Com [lOGJ McCa,·thy , D. E., "Transmittance of Six Optical Matcrialo from munication About Refraction and Dispersion of Crystals," 0.2 Mm to 3.0 Mm," App!. Opt., 7(6), 1243, 1968. Z. Kristallogr., 87,43-71, 1934. [106] Baldini, G., and Rigaldi, L., "Ultraviolet Optical Constants of [86} Bauer, G., "Absolute Values of the Optical Absorption Con Thin Films Determined by Reflectance Measurements," j. stants of Alkali-Halide Crystals in the Region of Their Opt. Soc. Amer., 60(4), 495-8, 1970. Ultraviolet Characteristic Frequencies," Ann. Phys., 5, 19, [107] Rodney, W. S., and Spindler, R . .I., "Refractive Index of Cesium 434-64, 1934. Bromide for Ultraviolet, Visible, and Infrared Wavelengths," [87] Wulff, P., and Heigl, A., "Refractometric Measurements on .I. Res. Nat. Bur. Stand., 51 (3), 123-6, 1953. Crystals," Z. Kri,.tallogr., 77> M-l?l, lQ~l [lOR] Roclney_ W. S~; and Spincller. R . .T .• "Refnlr.ti".~ Jnclir.f'~ of [88] Wulff, P., "An Interferometric Method to Determine the Re Cesium Bromide," J. Opt. Soc. Amer., 42(6),431, ]952. fraction in Crystals," Z. Elektrochem., 34, 611-6, 1928. [J 09] Geick, R .. "Dispersion Measurements on CsBr in the Region [89] Tomiki, T., "Optical Constants and Exciton States in KCl of Its Infrared Characteristic Frequencies," Z. Phys., 163, Single Crystals. 1. The Low Temperature Properties," .J. 499-522, 1961. Phys. Soc. Jap., 22(2),463-87,1967. 1110] Rodney. W. S., "Optical Properties of Cesium Iodide," J. Opt. [90] Vishnevskii, V. !'l., Kulik, L. N., an'd Romanyuk, N. A., "On Soc. Amer., 45(11), 987-92, 1955. the Refractive Properties of Alkali-Halide Single Crystals in [111] Lamatsch, H., Rossel, j., and Saurer, E., "The Optical Constants the Vacuum Ultraviolet Region," OPt. Spectros. (USSR), of Csl in the Excitonic Region," Phys. Status Solidi. B49m . 22(4).317-8, 1967. .311-6, 1972. [91] .1ohnson, K. W., and Bell, E. E., "Far-Infrared Optical Properties [lJ 2] Fedyukina, G. N., and Zlenko, V. Ya., "Determination of the of KCI and KBr," Phys. Rev., 187(3), 1044-52, 1969. Refractive Index of Transparent Bodies using a Scratch and [92) Durou, c.,. Giraudou, ]., and Moutou, c.. "Refractive Indices Immersion Liquids," Zap. Vses. Mineral. Obshchest., 101 (3), of Aqueous Solutions of CUS04, ZnSO~, AgNO.h KCl, and 374-5, 1972. H~SO~ for He-Ne Laser Light at 8=25 C," .1. Chern. Eng. [113] Kolosovskii, O. A., and Ustimenko, L. N., "Measurement of Data, 18(3),289-90,1973. the Temperature Coefficient of the Refractive Index oflnfrared [93] Trowbridge, A., "The Dispersion of Sylvite and the Reflectivity Materials Using a CO 2 Laser," Opt. Spectros. USSR., 33(4), of Metals," Ann. Phys., 3. 65,595-620, 1898. 430-1, 1972_ [94) Wulff, P., and Anderson, T. F., "A New Rotating Prism Method [114] Fowles. G. R., Introduction to Modern Optics, Holt, Rinehart to Photographic Determination of the Dispersion. II. Report and Winston, Inc., New York, 304 pp., 1968_ on Refraction and Dispersion of Crystals," Z. Phys., 94, [115] Herzberger, M., and Salzberg, C. D., "Refractive Indices of 28-37, 1935. Infrared Optical Materials and Color Correction ofIR Levels," [95J Sprockhoff, M., "Contributions to the Relationships Between .I. Opt. Soc. Amer., 52,420-3, 1962. the Crystal and Its Chemical Stability," Neues Jahrb. Mineral., D16] june, K. R., "Error in the KBr Dispersion Equation," App!. Geol. Palaeont.. Beilage, 18, 117-54, 1904. Opt., 11(7), 1655, 1972. [96] Spindler, R . .I., and Rodney, W. S., "Refractivity of Potassium (117) Strehlow, W. H., and Cook, E. L., "Compilation of Energy Band Bromide for Visible Wavelengths," J. Res. Nat. Bur. Stand., Gaps in Elemental and Binary Compound Semiconductors 49(4),253-62, 1952. and Insulators," 2(l), 163-99, 1973. [97] Stephens, R." E., Plyler, E. K., Rodney, W. S., and Spindler, [118] Young, K. F., and Frederikse, H. P. R., "Compilation of the R. J., "Refractive Index of Potassium Bromide for infrared Static Dielectric Constant of Inorganic Solids," 2(2),313-409, Radiant Energy," .1. Opt. Soc. Amer., 43(2),110-2,1953. 1973. J. Phys. Chem. Ref. Data, Vol. 5, No.2, 1976