SOLID STATE SPECTROSCOPY: INFRARED ABSORPTION 0F DECABORANE Thesis {or “as Degree 0‘ M. S. MICHIGAN STATE UNIVERSITY David T. Somerville 1963 IIIIIIIIIIIIIIIIII IIIIII IIIIII IIIIIII ° 293 01743 0160 LIBRARY Michigan State University ABSTRACT SOLID STATE SPECTROSCOPY: INFRARED ABSORPTION OF DECABORANE by David T. Somerville The infrared absorption spectrum of decaborane (B10H14) is studied in the sodium-chloride range (4000 - 667 cm'l) in the vapor, in solution, and in the solid, as an ancillary study in a program on the interaction of electromagnetic radiation with lattice vibrations. Particular attention is paid to the changes in the absorption Spectrum 1, the region of absorption corresponding to the stretch- near 2600 cm- ing mode of singly-bonded hydrogen atoms in the decaborane molecule, because it is a mode likely to be affected by being built into the lattice. The spectra in the vapor and in solution were obtained by standard techniques. For the solid, various methods were tried; pel- leting and evaporation gave suitable spectra. The detailed molecular and crystal structure of decaborane is described in order to provide a basis for interpreting the changes in the spectrum in going from one phase to another. The rise in trans- mission just before an absorption maxima is interpreted in terms of the Christiansen Filter effect. Tentative explanations are given for l the appearance of a shoulder on the 2600 cm" absorption band, and for the doubling of this absorption band upon condensation of the molecules into the solid. Identification of the two minima of the doublet is based on the atomic environment of the terminal hydrogens of the molecule. Analysis of the line shape on the basis of a damped harmonic oscillator is promising for the dilute-phase spectra, but impracticable for the solid-state spectra because of the splitting of the line. SOLID STATE SPECTROSCOPY: INFRARED ABSSRPIION OF DECABORANE By David T. Somerville Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Physics and Astronomy 1963 ACKNOWLEDGMENTS During the time the author was involved in the several phases of his research, he was ever conscious of the many people assisting him in the work. Now that the thesis is completed, he faces an arduous task to express his appreciation without appearing to be overly sac- charine. Nevertheless, some individuals have provided such major contributions toward the completion of the problem that their efforts cannot be left unrecorded. The author is indebted to Dr. Donald J. Montgomery for ini- tially suggesting the problem and for his guidance and encouragement as the work progressed. Thanks go to Dr. R. D. Spence and Mr. David Arnold who constructed the decaborane molecular and crystal lattice models; to Dr. R. H. Schwendeman, of the Michigan State University Chemistry Department, whonmflkeavailable a Perkin-Elmer Model 21 recording spectrOphotometer during the early part of the studies; to Misters Charles Randall, Sita- ram Singh Jaswal, and Kwok Fai Yeung, who as members of the solid-state Spectroscopy group provided assistance during several stages of the work; to Mr. Jack Carmichael who supplied the solvents for various experimental considerations; to Mr. C. Earl McKinney who assisted in the running of spectra; to Mr. Jerry J. Tomecek who prepared the ii figures; and to Mr. Frank Radovich, Market Development Department, American Potash and Chemical Corporation, who supplied the decaborane used in the experimental considerations. The author also wishes to express his gratitude to the United States Air Force for supporting the solid-state-spectroscopy program, in particular, The Solid State Science Division Air Force Office of Scientific Research Office of Aerospace Research United States Air Force Contract No. AF 49(638)-622 Grant No. AFOSR 62-37 Some of the work was facilitated by the availability of certain sup- plies and equipment from a related project sponsored by the Metallurgy and Materials Branch, Division of Research, United States Atomic Energy Commission. Finally, he should like to acknowledge, though in a very inade- quate manner, the constant help furnished by his wife, Joyce, who typed and proofread the entire manuscript. Her faith and understand- ing has been a constant source of inspiration. iii TABLE OF CONTENTS Chapter Page I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . 1 II. MATERIALS . . . . . . . . . . . . . . . . . . . . . . . 5 A. Decaborane 5 1. Chemical properties 5 2. Physical properties 8 3. Toxicity 8 B. Procurement and Analysis of Sample 9 C. Spectrophotometer 10 III. PREVIOUS CONSIDERATIONS . . . . . . . . . . . . . . . . 11 IV. EXPERIMENTAL CONSIDERATIONS . . . . . . . . . . . . . . 12 A. Safety Precautions for Decaborane 12 B. 'Sublimation 13 C. Evaporation 15 D. Pelleting 20 E. Mull 24 F. Solution 30 G. Vapor 34 V. RESULTS . . . . . . . . . . . . . . . . . . . . . . . . 38 iv A. General Decaborane Absorption B. Specific Decaborane Absorption C. Christiansen Filter Effect VI. INTERPRETATION OF RESULTS . A. Crystal Structure B. Origin of Spectra Variations C. Analysis of Line Shape 1. Absorption by Thin Films 2. Absorption by Vapor and by Solution D. Suggestions for Future Studies BIBLIOGRAPHY. . . . . . . . 38 39 47 53 53 64 69 71 72 76 77 LIST OF TABLES Table Page I. INFRARED ABSORPTION FREQUENCIES OF DECABORANE (cm'l). . . . . . . . . . . . . . . . 40 II. B-H TERMINAL STRETCHING FREQUENCIES OF DECABORANE (cm‘l). . . . . . . . . . . . . . . . 47 vi Figure, 10. 11. LIST OF FIGURES The decaborane molecule. The five boron atoms of the asymmetric unit of structure, which constitutes one- half of the molecule, are labeled with primed numerals. The remaining boron atoms are labeled with unprimed numerals. . . . . . . . . . . . . . . . . . A thin sheet of air separating two semi-infinite KBr crystals. The interference pattern resulting from the small spacing between the substrate and the lens cover. This particular pattern was observed upon operating the spec- trophotometer double-beam with a pair of KBr discs in each beam . . . . . . . . . . . . . . . . . . . Absorption spectrum of a KBr pellet (blank) . Decaborane pellet absorption spectrum . Absorption spectrum of Nujol film (blank) . Decaborane solution (Nujol) absorption spectrum. The increase in transmission at 2800, 2650, and 1400 cm"1 is due to the lack of balance between the absorption of the Nujol in the reference beam and in the sample beam. Decaborane solution (benzene) absorption spectrum. Only the absorption attributed to B-H terminal stretch- ing is shown. . . Decaborane vapor absorption spectrum. Decaborane film absorption spectrum . Absorption spectrum of benzene (blank). vii Page 17 18 21 23 25 26 27 28 29 32 12. 13. 14. 15. 16. l7. 18. 19. 20. 21. 22. The absorption spectrum of decaborane dissolved in benzene. Most of the characteristic decaborane absorp- tion bands are masked by strong benzene absorption. Greater amounts of benzene in the reference beam than in the sample beam cause the relative transmission to be greater than 100% in certain regions Skewed absorption pattern observed in decaborane vapor spectrum when the gas cell is being raised to tempera- ture during the scanning period . . . . . . . . Comparison between the decaborane vapor absorption spectrum when the gas cell is at equilibrium (broken line), and the spectrum (solid line) when the gas cell is cooling. Schematic diagram of decaborane absorption spectrum . B-H terminal stretching band in decaborane vapor ab- sorption spectrum . . . . . . . . . . . . . . . . . B-H terminal stretching band in decaborane solution (Nujol) absorption spectrum. The increase in trans- mission on the high-frequency side of the absorption is a result of the lack of balance between the absorp- tion of the Nujol in the reference beam and in the sample beam . . . . . . . . . . . . . . . . . B-H terminal stretching band in decaborane solution (benzene) absorption spectrum . . . . . . . . . . B-H terminal stretching band in decaborane pellet absorption spectrum. The large amount of transmission on the high-frequency side of the absorption is due to a Christiansen peak (See Section V, C - Christiansen Filter Effect). . . . . . . . . . . . . . . . . . . B-H terminal stretching band in decaborane film absorp- tion spectrum . B-H terminal stretching band in vappr, solution, and pellet absorption spectra . . . . . . . . . . . . . . . The dispersion curves for (a) a crystal in the neighbor- hood of characteristic absorption, and (b) a transparent medium. . . . . . . . . . . . . . . . . . . . . . . viii 33 35 37 38 42 43 44 45 46 48 49 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. Decaborane pellet and decaborane vapor absorption spec- tra (B-H terminal stretching band). A Christiansen peak appears on the high-frequency side of the absorp- tion in the pellet spectrum; no similar transmission peak is observed in the vapor spectrum. (a) Disordered crystal structure, (b) Ordered crystal structure. Model showing one of the two possible molecular orien- tations in the decaborane crystal lattice. This parti- cular orientation is specified by a plus in Fig. 24 . Model showing one of the two possible molecular orien- tations in the decaborane crystal lattice. This parti- cular orientation is specified by a minus in Fig. 24. Three hydrogen atoms are not observable from this view, but appear in Fig. 27 . Model shown in Fig. 26, except that all 14 hydrogen atoms and all 10 boron atoms can be seen. . . Decaborane ordered crystal structure--twin A, Decaborane ordered crystal structure--twin B. View of twin A showing the relative distance between the base plane molecules and the molecules in the plane translated a distance co/2 from the base plane (also observed in twin B) . . . . . . . . . . . . . . . Schematic diagram illustrating the arrangement of xz- layers for twin A . (a) Diborane, (B2H6); (b) Pentaborane, (B5H9); (c) Decaborane, (ENNN4)° The four sets of B-H pairs are labeled a,b,c,d . . Plot of )j_)j+ vs transmission T for decaborane vapor . ix 51 54 56 57 58 6O 61 62 63 65 75 I. INTRODUCTION The study of the interaction of electromagnetic radiation with atomic and molecular systems has proved valuable to the chemist and the atomic physicist because of the information it has furnished on both the structure and the energy levels of these systems. It is the hope of the solid-state physicist that spectroscopy will play a role in his field similar to that which it has played in atomic and molec- ular studies. Experimental difficulties have slowed the development of spectro- sc0py in advancing the understanding of phenomena in solids, in par- ticular, of lattice vibrations. The characteristic frequencies of lattice vibrations extend far into the infrared; consequently, ade- quate experimental techniques could not be developed until infrared instruments of wide range and high sensitivity became available. Two probes for the study of lattice vibrations are atomic mass and atomic force field. The dependence of lattice vibrational fre- quencies on the force field is complicated; in contrast, the depend- ence on atomic mass is simple, in the first approximation being proportional to the square root of the atomic mass.1 Therefore, iso- topic mass may be chosen as the probe to give results readily tested against theory. The natural procedure would be to study isotopically impure substances by varying the isotopic composition, and to study isotopically-pure compounds by varying the isotopic mass. Such work has been in progress in this laboratory.2’3’4’5 The samples are prepared in the form of thin films evaporated on appro- priate substrates. Thick single crystals would be desirable to study, but their production at varying isotopic compositions would be pro- hibitive in money and time. Tonic crystals are desirable because of their strong interaction with electrcmagnetic radiation. Light ele- ments and/or tightly-bound elements are studied, to keep the antici- pated spectral response within the range of cur instruments. Lithium fluoride and lithium hydride satisfy the above conditions, and at the same time decrease the complexity of interpretation because of their simple lattice structures. The initial work consequently consisted of obtaining the far-infrared absorption spectrum of lithium fluoride (Li6F19, Li7F19) and lithium hydride (L16H1, Li6H2, Li7H1, Li7H2). Extending the general study of solid-state Spectroscopy leads one to consider more complicated molecules. The stable isotopes of boron (B10, B11) are available in bulk quantities, and have a large relative mass difference. The boron hydrides, then, are natural to 11 as well as H1 and study, with the possibility of varying BIO and B H2. Since decaborane (B10H14) is the only boron hydride in the form of a solid at rocm temperature, it was chosen to be studied first. Unfortunately, isotopically-enriched decaborane proved difficult and expensive to obtain. The weak molecular bonding in the crystal sug- gested, moreover, that the lattice vibrations lie too far in the in~ frared to be detected by our instruments. These disadvantages, along with the high toxicity of the substance, caused the immediate direction of this work to be changed. Instead of seeing how the vibrational frequencies are altered by changing the mass cf the particles of the vibrating system, we see to what extent, if any, the frequencies vary as we change the environment of the particles; that is, we investi- gate how the infrared absorption changes in going from the moderately- disordered surroundings in the liquid or in solution, to the highly- ordered structure in the solid, or to the completelyodisordered environment in the vapor. By observing any changes in the spectrum we may gain information concerning: (a) the effect of inter- and intra—molecular bonding on the formation of the lattice. (b) the nature of the inter-molecular forces which hold the individual molecules together in the crystal lattice. (c) the isomeric configurations which might be associated with different crystalline modifications. (d) the influence of the crystal lattice on the molecular motions. (e) the interaction of the more or less localized vibrations of the molecules with the lattice vibrations. The problem becomes, therefore, to obtain the infrared absorpo tion spectra of B10H14 in various states, and to interpret any changes observed in the spectrum accompanying the changes in state. Inter- pretation will involve consideration of the absorption effects of molecular environment in the crystal lattice, a suitable comparison of the stretching vibrations to a damped harmonic-oscillator, and an analysis of transmission behavior of the solid in the regions of strong absorption in terms of the Christiansenofilter effect. To simplify interpretation, we concentrate our efforts on the absorption due to a Single vibration, the B-H terminal stretching mode° II. MATERIALS A. Decaborane Since the end of World War II, the boron hydrides have become something more than merely an academic pastime to the inquisitive chemist. Because of their high heat of combustion and their low molecular weight, the boron hydrides and their derivatives are of interest in the propulsion field. That the boron hydrides are be- coming of major interest in the missiles program is evident from the forthcoming construction of several highnenergy fuel plants proposed by boron-hydride distributors. Gallery Chemical Company is building a $38 million plant for the Navy at Muskogee, Oklahoma, and a smaller privately-financed plant at Lawrence, Kansas. Olin Mathieson Chemi- cal Corporation has completed a companynowned $5.5 million plant at Niagara Falls, and is building a $4.5 million plant for the Navy and a $36 million plant for the Air Force at Model City, New York.6 Decaborane itself is also useful as a catalyst, a vulcanizer, and a mild reducing agent.7 1. Chemical properties: One of the most Stable of the hydrides, decaborane can be kept in air or oxygen at 500~6OOC for days without change. At 250°C in the absence of air, only 93% of the B10H14 is decomposed after 24 hours. In general, it is soluble without reaction in hydrocarbons such as hexane, benzene, and toluene. On the other hand, it may form Shock-sensitive solutions in oxygenated or halogen- ated solvents, or in solvents containing reactive carbonyl groups.8’9 Although BlOHl4 does not react with oxygen under atmospheric pressure at 60°C, it explodes when heated with oxygen in a closed system at 100°C. Hydrolysis at moderate temperatures is slight; deca- borane is hydrolyzed less than 10% in 10 days at room temperature. Hydrolysis proceeds quantitatively and rapidly enough for analysis at 200°C with the following reaction: B10H14 + 30 Hzo—slo lamb + 22 H2 (8) The boron framework of the B10H14 molecule can be described by saying that the boron atoms occupy ten of the twelve vertices of a distorted icosahedron. (Fig. l) Boron atoms, I, IV, I', IV', form a perfect rectangle. The symmetry of the molecule is such that boron atoms V and V' lie exactly in one of the mirror planes of the molec- ule, and II, III, II', III', in the other mirror plane. The surface of the molecule consists entirely of hydrogen atoms. Ten "terminal” hydrogen atoms are each joined singly to a boron atom in directions roughly corresponding to fivefold axes of the distorted icosahedral figure suggested by the boron atoms. Each of the remain- ing four "bridge" hydrogen atoms serves as a connection between two boron atoms. The bridging hydrogen atoms complete the surface of the Fig. l. ~ The decaborane molecule. The five boron atoms of the asymmetric unit of structure, which constitutes one-half of the molecule, are labeled with primed numerals. The remaining boron atoms are labeled with unprimed numerals. molecule outlined by the other hydrogen atoms and also make the co- ordination number of each boron Six.10 2. Physical properties: Decaborane, the only boron hydride solid at ordinary temperatures, is the heaviest of the volatile hy- drides. It is a colorless, well-crystallized solid with a density at room temperature of 0.94 g/cm3. Melting at 99.60-99.700, B10H14 boils under atmospheric pressure at 213°C. The substance slowly vaporizes at room temperature, its vapor pressure being 0.05 cm Hg at 25°C. When the vapor is rapidly condensed, it crystallizes in compact aggre- gates. If crystallized slowly, it forms clear, transparent, needle- like crystals that may attain a length of several centimeters.8’9 3. Toxicity: Decaborane is acutely toxic, significant hazards existing by all practical routes of administration. Its toxicity is comparable to phosgene, hydrogen cyanide, and hydrogen sulfide. The inhalation hazard offered by the vapors of B10H14 is such that maxi- mum allowable atmospheric concentration for a human being in an eight- hour day is 0.3 mg/m3.7 The odor is detectable at subtoxic levels, but it is not a reliable index. The hazards from skin absorption is also appreciable.11 The primary effect or action of B10H14 is on the central nervous system. In addition, there is evidence of damage to the liver and kidneys; moreover changes in nucleic-acid metabolism indicate that it is an active metabolic poison. Studies Show that during periods of exposure, the effects of the poison are cumulative. The recovery of animals receiving repeated doses was markedly delayed, compared to those receiving a single dose.12 To eliminate serious health hazards when working with BlOHl4, adequate control measures must be applied. B. ngcurement and Analysis of Sample IsotOpically-enriched decaborane is inordinately expensive. The only estimate offered to us was for 100 grams of enriched deca- borane at $6,000, exclusive of the cost of the enriched KBF4 starting material.* Decaborane of natural isotopic composition was supplied by the American Potash and Chemical Corporation. Their analysis is as follows: Melting Point 97.1 - 98.2o Decaborane (assay) minimum 99.0% Non-volatile impurities (at 50° and 1 mm Hg) less than 2.0% Metals: Aluminum 0.01% Iron 0.02% Nickel 0.05% Silicon 0.06% Magnesium 0.01% Manganese 0.06% Copper 0.01% *Personal correspondence with Mr. Frank Radovich of American Potash and Chemical Corporation. 10 C. Spectrophotometer The major part of the work was performed with a Perkin-Elmer Model 21 double-beam recording spectrOphotometer with interchangeable monochromator prisms. Initially, the 666 - 286 cm‘1 (15.0 - 35.0“) range was studied with the use of cesium-bromide Optics. Sodium-chlo- chloride optics, which allowed investigation in the 4000-666 cm.1 (2.5 - 15.0") region, were later introduced for the main part of the absorption studies. The Model 21 instrument permits manual or auto- matic programing of slit width, and variation of the recording speed and pen speed over a wide range. The scale of the recorded spectrum 1 1 can be varied from a minimum of 1 cm/lOO cm' to a maximum of 50 cm/lOO cm‘ . To reduce atmospheric absorption, the sample area is enclosed in a metal housing, and the case is purged with dry air. A.Model 137 Perkin-Elmer KBr double-beam Spectrophotometer ("Infra- cord") was used for work in the potassium-bromide region, 800 - 400 cm'l, _(12.5 - 25.0“). A Beckman IR-7 Spectrophotometer with cesium-iodide optics was made available to us by the Chemistry Department of Michi- gan State University for the range 700 - 200 cm'1 (14.3 - 50.0“). III. PREVIOUS CONSIDERATIONS The earliest studies on infrared absorption of B10H14 were made 13 by Keller and Johnston in 1952. Decaborane was melted between AgCl plates, and allowed to cool. Between 446 cm":1 and 2624 cm'l, 75 ab- sorption bands in solid B10H14 were reported. In 1954, Bellamy14 worked extensively with BlOH14 dissolved in various solvents, and found that the absorption pattern varied with the solvent. Miller and Hawthorne15 observed absorption in solution and in the vapor. For B10H14 in C82, they reported a broad band at 2565 cm‘l; for the vapor, only the lines at 1885 cm'1 and 1510 cm"1 are mentioned. Decaborane in solution and in pellets was studied in the LiF region (0.1 - 6.0“) by Beachell16 in 1960. In solution he found a single broad band for B10H14 at 3.858“, but in pellets found the band Split into four components at 3.813“, 3.833p, 3.863”, and 3.938p. Kletz and Price17 did some work concerning the change in the ab- sorption Spectrum accompanying the change of state of alkyl phenols. The formation of doublets on crystallization was reported, and was interpreted as due to association involving hydrogen bonds. A de- crease in band width and an increase in absorption frequencies were observed in going from the liquid to the solid. 11 IV. EXPERIMENTAL CONSIDERATIONS A. Safety Precautions for Decaborane The extreme toxicity reported for decaborane demanded that elab- orate precautions be taken in handling it. Methods were deveIOped that controlled the harmful decaborane fumes present under normal temperature and atmospheric conditions. Samples were prepared in a dry box equipped with an exhaust pump and filteracovered openings to allow air intake (Kewaunee Scientific Equipment, Basic Laboratory Model Dry Box). The contaminated dry-box atmosphere was exhausted directly to the outside through flexible ducting. During the prepara» tion of decaborane samples, contact with the skin was avoided by work- ing in the dry box with externallymaccessible rubber gloves sealed to the frame of the box. The working area was kept well ventilated to decrease the con- centration of fumes in case of leakage from the dry box or the sample holders. Additional precautions were taken by wearing an air-line respirator when transferring the samples from the dry box to the Spectrophotometer, and when making preparations that necessitated exposure to the fumes. A KBr cover lens was used over the evaporated- film and the mull samples* in order to prevent sublimation and reaction *Recommended in a personal communication with Harold C. Beachell, Professor of Chemistry, University of Delaware, Newark, Delaware. 12 13 with moisture when in the spectrophotometer. An object coming in contact with decaborane was thoroughly cleaned with benzene or hexane. In particular, the KBr plates used as substrates were cleaned in this way before being re-polished for subsequent use. B. Sublimation To obtain a film by sublimation, we heated a volatile substance and allowed it to deposit on a cool substrate. Sublimation in 33323 is advantageous because of the relatively free path to the substrate, which allows easier film deposition and less contamination. The toxicity of decaborane, however, required sublimation in a removable atmosphere. The use of a vacuum system allowing controlled removal of the fumes or permitting the deposited film to be removed from the system in the dry box was first considered. A vacuum system satisfying the requirements imposed by the toxicity of decaborane was not practical because of the cost and time necessary to build such a device. The existing vacuum equipment was being used for other thinwfilm work and, therefore, could not be converted to the desired system. Conse- quently, a technique involving deposition in the dry box was attempted. Two electrodes were attached to an insulating base upon which was placed a metal stand to hold a potassium-bromide disc acting as 14 a substrate; the discs were l/8winch thick and l l/8minch in diameter. A high-resistance wire, fastened between the electrodes, cradled a molybdenum boat into which the decaborane was placed. A thin insulam ting strip of mica was placed between the boat and the wire to pre» vent both current flow through the molybdenum and localized heating of the boat° In this way the decaborane could be heated, and was expected to deposit on the Ktr disc held ab ut three inches above the molybdenum boat. To screen the substrate from any highly—volatile impurities in the decaborane powder, a movable aluminum wedge was interposed between the boat and the disc during the early part of the evaporation. All attempts to obtain a film by this method resulted in the combustion of decaborane before deposition was complete. It became obvious that gentler heating was needed. Decaborane was placed in a weighing bottle underneath a KBr substrate held on the bottle cover by a metal spring. With the cover on the bottle, the device was a closed system that could be placed in a hot-water bath to cause the decaborane to sublime and deposit cn the substrate without escape of the harmful vapors to the atmosphere. A beaker of ice was kept on top of the weighing glass to cool the substrate and minimize the reevaporization of the deposited decaborane. The water bath consisted of a large beaker containing about one inch of water; the beaker was heated by a hot plate. The samples were removed in 15 the dry box and covered with a similar KBr disc when scanned in the spectrOphotometer. A shortcoming of this method was the inability to shield the substrate during the early stages of sublimation. All samples prepared in this manner failed to produce an absorp- tion spectrum. What formed on the substrate was in fact not a film, but an agglomeration of long, needle-like crystals. The same sort of deposit resulted whether the substance was heated slowly or quickly, or if it was first dissolved in benzene and then sublimed. Removal of the beaker of ice during sublimation did not alter the result. A layer of crystals such as that formed during the sublimation of decaborane will cause scattering as well as absorption. Scatter- ing effects may dominatermder certain conditions. But scattering may result in lower transmission than is observed. Decaborane appears to condense following sublimation in the form of long, thin crystals. Such a deposition may not absorb because of the thickness of the aggregate. Previous work by Zimmerman2 with thin films of LiH may be interpreted as indicating that too thick a film will result in the failure of the material to absorb. C. Evaporation When attempts to prepare a film by sublimation failed, evapora- tion of decaborane from solution was tried. Thiophene-free benzene, l6 dried over sodium, was found to be a satisfactory solvent. In the dry box, approximately 0.5 to 0.7 mg BlOHl4 was dissolved in two or three drops of C6H6 on a KBr disc. The benzene was allowed to evaporate from the sclution, while the substrate was moved in a circular path to increase the rate of evaporation and to distribute the solution evenly across the disc. Another KBr disc was placed over the film to act as a lens cover and to keep the BlOHl4 from evaporating in the radiation of the Spec» trophotometer. The small spacing between the substrate and lens cover produces an interference pattern superimposed on the absorption spec~ trum (Fig. 3). To understand this pattern, we study a thin, non- absorbing dielectric sheet separating two semininfinite non-absorbing dielectric media, as indicated in Fig. 2. By standard boundary-value techniques applied in electro- magnetic theory, the reflection coefficient R is given by (r12 + r23)2 - 4r12r23 sinzdzd (1 + r1‘2r23)2 " 4r12r23 Sinzazd with «'2 s at a 211/A, where A is the wavelength within the sheet; and r12 E.( JE.1 - {5’2 ) / ( fg'l +'JE'2 ) a r2,a(«€2-¢e—3)/. But, erl ==Jif3 = n, the refractive index of the plates, and Jirz = l, the refractive index of air. Then r12 = - r23 s.r = (n u l)/(n +,l) We have R = (Arzsinaxd)/[(l » r2)2 + 4rzsinaad] l7 KBr Fig. 2. - A thin sheet of air separating two semi-infinite KBr crystals. was auouumo amazowunma mask .awon sumo ow muwwv “mm «0 “Hum w Sues amonuoansov umuoEOuonoouuooow wnu wawuwnmoo noon vo>uomno .um>oo mama onu com mumuumnam onu ooosuon wcwummm HHmEm msu scum maHu~5mou anouuwm mucoummumuaa oak u .m .wwm 18 000. Don. OOON “7&3 mmm232m> oonN Goon Donn 80¢ — J _ C) O) s é NOISSst'Nvui °/. l9 and l - R = (1 - r2)3/[(l - r2)a + 4r2 sinazd] {(1 - r2)2/(l + r4)]/[1 - (2r2 cos de)/(1 + r‘)] With double-beam techniques, the recorded transmission is actually a ratio of the sample transmission to the reference transmission. We therefore are interested in the ratio of the transmission for two films differing in thickness by‘. We write the thickness d of the thicker film as (10 + k6, that of the thinner film as do - £8, where do is the average thickness. I-_-] III Define D 52u(do+%8), 2‘*( do ‘ 5‘5) , 2r2 / (].+ r4 ) . Then the ratio of the transmission T for the thicker film to the transmission T_ for the thinner film is Ii 3 1 - B cos 0_ T__ 1 - B cos D+ u: U "I III = (l - B cos D_)(1 + B cos D+ + BacoszD+ +... g l + B(l + B cos D+)(cos D to terms in BB. For KBr, r3 = (1.53 - 1)3/(1.53 + 1)2 = 0.044 and r+ = 0.0019. Hence we may approximate B as B g 2r2 = 2(n - l)3/(n + l)2. Upon substituting the definition of D+, D_, B, and d s ZflVA and replacing wavelength A by wavenumber 17 .=. l/A, we find T+/T_ “=’ 4U“ ' 1)/(n + 1)]2 Sin(41rdo17) sin(21'rSi7)- {l + 2[(n - l)/(n + 1)]3cos[41'r(do + $951} that is, the transmission ratio as a function of wavenumber 57 fluctuates above and below 100% by a maximum amount 4[(n - 1)/(n + 1)]9~17.67. for the air-KBr system, upon neglecting the second-term within the braces* The form of the fulctuation is that of a sinusoid inf? with short period Xdo, amplitude-modulated by a sinusoid in‘Dwith long period 1/8. + - cos D_) *The seemd-mrkr term introduces a minor second-order short- period modulation with amplitude not exceeding 8.8% of l7.6%“‘1.5%. 20 By varying the amount of decaborane dissolved in the benzene, films of different thicknesses could be produced. The thickness was found to have no effect on the position of the absorption maxima, if indeed the film showed selective absorption at all. Hexane was also used as a solvent in the evaporation of decaborane, but the position of the absorption maxima was not affected significantly by the choice of solvent. D. Pelleting A well-known method of sample preparation in near-infrared spectroscopy of powdered substances is pelleting. In the present study, a Perkin—Elmer evacuable die was used to press a mixture of KBr and B10H14 into a thin transparent disc, 13 mm in diameter and 0.7 to 1.0 mm in thickness. The composition of the mixture for the pellets was 0.5 mg B10H14 mixed with 200 ~ 300 mg KBr. The KBr pow~ der was of 325 mesh and 250 mesh, corresponding to screen openings of 0.0017 inch and 0.0024 inch, respectively. Because KBr is highly hygroscopic, the elimination of moisture from a pellet is difficult. The Ktr was kept above room temperature by heating the powder on a hot plate before placing it in the die. As shown in Fig. 4, water absorption is present in the pellet, but not in a region that will distort the decaborane absorption spectrum. 21 000. .Axawanv uoHHom umM m we abuuoomm nequHOmA< u .q .mHm arr—.3 mwm232u><3 009 OOON oonN 000» Down 000¢ om _ _ _ _ [om om NOISSIWSNVHJ. % 22 The powders were mixed and placed into the die while they were in the dry box. The mixture was pressed into a pellet ig_y§ggg with a Wabash Model lZulO-S hydraulic press, under pressures of approxim mately 6,000 lb/inz for five minutes or more. The main disadvantage of the pellet method in the far-infrared region is lack of reprcducibility in the spectra. This variability is due to the differences in particle size, and possibly to the changes resulting from the very high local temperatures and pressures deve10ped during the formation of the pellet.18 In the present inves- tigation, however, reproducibility was ntt a problem when temperature and humidity were kept constant and the same mesh KBr powder was used. Chemical reactions between the substance under study and the materials in the alkalimhalide matrix must also be considered. Since high local temperatures and pressures may cause the water in the matrix to react with the decabrrane, the pellet spectra were checked for boric- acid characteristic absorption bands, as recorded by Miller and Wilkens.19 The strong H3803 band at 3270 cm”1 does not appear in the pellet spec- tra as shown in Fig. 5. The very strong absorption at 1450 cm"1 might be present, but it would be obscured by the strong BlOHl4 absorption in this region. Since the strong band at 1195 cm"1 is missing, or so weak that it cannct be distinguished from the noise of the spec" trophotometer, the amount of boric acid present must be slight. 23 com .asuuuomw :OquHOmnm uoHHom mamuonmoon u .m .wwm A763 mwm232w><3 COO. 00m. OOON comm 000m 00mm _ _ _ a _ _ 08¢ ON on O¢ Om am Oh Om NOISSIWSNVHJ. °lo E. Mull In comparing mulling and pelleting as methods of sample prepara~ tion, Baker20 concluded that in combination they will yield signifi- cantly more information than will either separately. A mulling liquid must satisfy certain general requirements. It should be free from absorption bands in the spectral region of interest; it should have approximately the same refractive index as the powder outside the ab- sorption bands, so that the amount of scattering by the powder will be small; it should have a moderate viscosity, and should mix well with the powder.18 Nujol, a highly-refined mineral oil, is often satis- factory in mull preparations. Its absorption spectrum is shown in Fig. 6. Approximately 1 mg of decaborane was mixed into a drop of Nujol on a KBr disc. The layer of the mineral oil had to be thin to minimize liquid absorption. To prepare the sample for the spectrophotometer, another KBr disc was placed on top of the mull to confine the mixture and keep the decaborane from evaporating while in the infrared radia- tion. A pair of KBr discs with a drop of Nujol between them was in- serted in the reference beam of the spectrophotometer as compensation. The resulting spectrum (Fig. 7) shows a single absorption band in the 2600 - 2500 cm'1 region, which is also found in solution and vapor spectra (Fig.3 8, 9). In the same region, on the other hand, pellet and film samples (Fig.5 5, 10) have two absorption bands. In 25 com 000. .Axoman EHHM acnsz mo souuooom aofiumHOmn¢ . .e .wwh $-63 mum Eazu><3 00m. OOON 00mm 000» 00mm 80¢ on . _ _ _ Co. NOISSI WSNVHJ. ’/o 26 can .aoon mamaaw osu GA was Boon monouomou «nu ca Hanoz oSu mo coauQHOmnm onu comsuon moowamn mo xumH oSu on mac ma uao ooqa can .omom .oowm um scammfiamcmuu a“ omoouuaw ona .aouuommw $.58 mwmzazw><3 coauQHOmnm AHoflszv aowuoaow ocmuoamuon u .n .wwm 000. com. OOON coma 80m 000» 08¢ 4 4 T . _ . o. 1 ON I on I o¢ Km 8 1 cm 1 Oh : Om Om NOISSIWSNVUL °/o 27 -9() ' 8C) ‘ '70 - (50 ‘ 5Cbr 40- TRANSMISSION 3C>- °lo o I l l l l 2800 2600 2400 WAVE NUMBER" (cm“) Fig. 8. - Decaborane solution (benzene) absorption spectrum. Only the absorption attributed to B-H terminal stretching is shown. 28 000 000. .souuoomm aoHuQHOmnm Homm> ocmuonwuon n .m .wwm .753 mmm232u><3 000. 000m 000m 000m 00mm 000¢ 0 _ _ — _ . I (D N l C) '0 1 C) fi' l C) IO J (D (D 1 C) p. “lo NOISSIWSNVHJ. 29 00m 000. .Eouuoomm coauQHOmam anm mcmuonmoon I .OH .7600 mwm222m><3 000. 000m 000m .mE 000m _ _ 4 8 6 <5 F- (D K) NOIssmsuvui l C) m 30 View of the solubility of decaborane in hydrocarbons, it was feared that Nujol, a mixture of long-chain hydrocarbons, dissolved the B10H14. To study the possibility that the absorption is due to dissolved rather than suspended materials, some powder was allowed to stand in Nujol in a test tube for 64 hours. The Nujol solution was found clear, with no decaborane particles observable. A drop of the liquid was scanned, and the characteristic solution absorption was observed. Petroleum jelly, also a mixture of longmchain hydrocarbons, gave similar results when used as a mulling substance with decaborane. For future work, we recommend that mulling agents other than long-chain hydrocarbons such as silicones be considered. The dearth of special chemical facilities for handling decaborane made such studies uneconomi- cal«in our laboratory. F. Solution Absorption studies of decaborane in solution were made with two KBr cavity-cells manufactured by the Connecticut Instrument Corporation. Thin cavities are necessary to keep the solvent absorption small. The KBr cells have 1.0 mm pathlengths and 0.068 ml volumes. For solution spectroscopy, the solvent must not react with the solute and must not absorb in the region of interest. Carbon tetra- chloride and carbon disulfide satisfy these requirements almost ideally. 31 But these solvents produce decaborane solutions that are reported to be shock sensitive, and whose handling requires elaborate facilities. Benzene and hexane dissolve decaborane to form stable solutions, but the solvents themselves show some absorption close to the region of interest (2600 cm"1). Whether this absorption interferes seriously with the decaborane spectrum depends on the amount of solvent in the beam. With the KBr liquid-cell, the relatively great thickness (1 mm = 1000p) results in a prohibitively great absorption with hexane. With benzene, the absorption is significant near 2600 cm-1 (Fig. 11), but compensation by an identical benzene-filled cell in the reference beam allows its use in the study of the principal deca- borane band. Most of the other bands were masked, however, by the benzene absorptions. (Fig. 12) In the controlled atmosphere of the dry box, approximately 0.3 mg decaborane was dissolved in 2 ml benzene. The solution was put into the liquid cell with a No. 23 needle and syringe. The sample was scanned with use of double-beam techniques. Other solution methods are suggested by the solubility of deca- borane in highly viscous substances, such as long-chain hydrocarbons [Section IV, E - Mull]. ‘With such materials, liquid cells need not be used; instead the solution is merely spread between KBr discs which are then mounted in the spectrophotometer. In this way the pathlength 32 000. .AxGmHnV mamuomn mo Esuuommm cofluQHOmp¢ u .HH .me $-88 OOON mwm232m><3 Doom 000m Down ooo¢ oom- _ 6 <5 c': c3 c3 ‘0 If) fl" '0 N NOISSIWSNVHJ. °/. 1 C) p. 33 .maonou samuumu ca NooH swan Houmouw on cu cosmmfiamsmuu o>fiumawu can momsmo Soon onEmm mzu ca smnu Econ mucouommu msu as mooncon mo munsosw Houmouw .oOHuQHOmnm maouaon mcouum ma poxmma mum moans soHuQHOmnm componmoww owumfiuouompmso msu mo umoz .moonoon a“ vm>H0mmHv momuonmomw mo asuuomam :oHuQHOmnm mna $.53 mmmzazm><3 000. 009 OOON 00mm Coon _ _ a . a _ _ . s q _ _ q A _ _ _ a D l l 8 s: s a NOISSIWSNVHJ. °/. C) (O (D p. Om 100. 34 in the solution may be made very small, since it is determined by the thickness of the layer rather than by the fixed dimension of the cavity cell. G. Vapor Experiments on the vapor were made with the aid of a Perkin-Elmer lO-cm gas cell having KBr end-windows. Approximately 15 mg B10H14 powder was placed in the cell. Three feet of Electrothermal "Heat by the Yard" thermal tape was placed around the gas cell to heat it and thereby vaporize the BlOHl4' The behavior of the vapor absorption pattern during various stages of heating and cooling of the cell warrants comment. If the cell and its contents were at equilibrium, there would be no transient phenomena. It is impractical, however, to work always at equilibrium; therefore, it is necessary to understand the behavior of the material in the cell as it warms or cools. The heating causes evaporation of the solid BIOH14 at the bottom of the cell; the vapor redeposits in part on the KBr end-windows as the cell cools at the conclusion of a run. At the beginning of the following run, as the cell comes up to temperature, the deposited crystals re-evaporate, and the transmission increases as time goes on and lower wavenumbers are reached (Fig. 13). If this interpretation is correct, then in the steady state of true equilibrium, 35 .powuom mcwocmom osu mawusw musumumanu Ou powwow mcwwn ma Haoo wow osu Cogs Enuuoomm uommN mcmuonmump as pm>uomno cumuuma nOHuQHOmnm vamxm n .mH .mwm FE: muggy/<3 com. . coca comu. coon . . . _ , . _ a _ _ a: _ _ _ _ 14 a _ . _ AV. 3 - ow L - on ./. I; 1 Nu Hv m - o... w m 1 m. nu mu - on 1 4 cm - 2. 36 there should be no general rise. Such behavior is indeed observed (Fig. 9). During the cooling of the cell, there occurs a loss of structure in the BlOH14 spectrum, as well as a decrease in transmis- sion. The loss of structure could be due to both the crystal forma- tion on the cell windows and the smaller amount of B10H14 vapor in the cell. The lesser degree of selective absorption resulting from crystallized decaborane is consistent with the failure to observe absorption in a thin film of B10H14 deposited by sublimation tech- niques [See Section IV, B - Sublimation]. Fig. 14 compares the ab- sorption spectrum of the gas in the heated cell with the absorption pattern after the cell has cooled. 37 .mcwaooo ma Hamo mow ox“ cogs Amowa pwfiomv Eduuommm may pom .mmcwa :mxonnv Esfipnflfiwswm um ma HHmo mom can smc3 Esuuummm oOwumHOmnm pommw momuonmomp mcu :mmBumn camfiumano a .¢H .wflm ATE“: mwm232w> momuonmomo CH pawn mowLoumuuw HmcwEuou mum 1 .0H .wflm ATE": mmmfiszw><>> OOmN OmmN OOwN Comm 0— . _ . . _ _ _ . a _ _ _ _ q .1 _ _ Oh NOI SSIWSNVHJ. °/o 43 .Emmn ofiaamw msu cw pom Emma mosmummou ozu :H HOMDZ msu mo coauQHOmnm mcu oom3uon mocmamn mo xomH onu mo uadmmu m m« :oHuQHOmam ocu mo spam uocmnvmumssmwn wnu no cowmmwemcmuu :H mmmmuoofi 0:9 .Esuuomam cofluauomnm AaOmszv sowu5HOm ocmuonmomp :H pawn.mowsououum Hmcwahou mum 1 .NH .me ATE: mwmzszmi; comm OmmN comm Ommw o. . _ . 41 q . —\ _ _ _ _ _ . . . _ _ ON Om Ge. 00 cm °/o NOISSIWSNVHI 44 .Esuuooam ooHuQHOmnm Amommconv oowuofiow mcmnonmomw CH pawn mowsououum HmowEhmu mum a .wH .wwm $.53 mumsazmi; 00 mm on mm 88 8mm 83 . _ a _ . _ _ _ a _ 1 ON on o o o to ‘0 d' NOISSHWSNVHI % C) r. O 60 cm 00. 45 .Auoommm Houfiwm ammomwumfluso n U .> oofiuomm ommv xmom ommamfiumwuso m Ou out ma cowumHOwnm osu mo mvflm hoomsvoHMumez osu co scammwemcmuu mo unsoam owuma 05H .asuuoomw coauQHOmam umHHmm mamuonmoov a“ pawn wofisoumuum Hmowahou mnm 1 .aa .wwm .753 592353; on». u 88 on ma coma . onmu Ob % NOISSIWSNVUI 46 oncu .Esuuooam oowuaHOmam EHHM momuonmoop GH.UCmp wowsoumuum Hmoweuou mum u . .720. mmmzazu> ow vows moflnououum HmGHEnou Elm a .Hm .wfim runs mmmzazmi; On¢~ OOoN Ommm OOON Omom . . . . _ . . _ . . a _ - O. Put-4mm (\fitfl/ 1 nsslnu 1.435 \\\ a ll ON \ \ I I III. I moa<> s /.. . I \s\ \s / la. 4 \\ xx a/ . I on \\\ \ / l \ \ x \s\ \ a ll|| \\ \ l , .......-3......:.-.... \ z .. \ l on \ 1.1.... \ 1 \ Oh NOISSIWSNVHJ. "lo 49 '9 A . ‘i l ' i a )NChr )K’ WAVELENGTH REFRACTIVE INDEX l“-fl 1 L—L .1 Fig. 22. - The dispersion curves for (a) a crystal in the neighborhood of characteristic absorption, and (p) a transparent medium. medium whose dispersion curve is represented by curve Q'should show a maximum of transmission at the wavelengthJAChr corresponding to the point of intersection of a and 2. At this wavelength the sample is optically homogeneous, and light of this wavelength will be preferen- tially transmitted by the mixture, since it will not be scattered by the multiple refractions and reflections occurring at other wave- lengths. The strong absorption in the region of,ko masks another Christiansen peak which would otherwise occur at the second inter- section of the two dispersion curves. The increase in transmission may also be observed at wavelengths far removed from the absorption band, as a result of the gradual crossing of the dispersion curves. The high transmission at'XChr is known as the Christiansen-filter effect, first observed by C. Christiansen24 with visible light, and 50 25 in the infrared. later by Barnes and Bonner Abnormally high transmission peaks on the high-frequency side of the absorption bands appear in the BlOH14 pellet, vapor, and film spectra (Fig.s 5, 9, and 10). The most pronounced effect is in the pellet spectrum, as is to be expected, since the effect is greatest for particles of linear dimension slightly larger than.AChr.25 The vapor spectrum shows an increase in transmission near the 1509 cm'1 and 860 cm'1 absorptions as well as at 1200 cm'l. Christiansen trans- mission should not appear in vapor spectra, since vapor particles are too small to act as refracting centers. The fact that the effect does appear in Fig. 9 indicates that crystals have deposited on the gas- cell windows during the scanning of the vapor (see Section IV, G - 2222;)~ The B-H terminal-stretching absorption in the pellet and the vapor samples of B10H14 are compared in Fig. 23 in order to show the difference in the transmission due to the Christiansen effect. The increase in transmission on the high-frequency side of the B-H stretching band is believed to be due to the equality of the refractive index of B10H14 and KBr at 2650 em'l. As an absorption band is ap- proached from the low-frequency side, the refractive index increases until it reaches a maximum. This increase causes lower transmission owing to high reflectivity. The characteristic absorption only serves 51 I,n.~..1. ..i|l 1|. F.‘..l!.i \ ‘1! An. - .Esuuommm uomm> msu a“ vm>nomno mg xmom :OOmmemomuu umHHEMm on masuuooam uoHme onu ow sofluauOmnm msu no spam zoomsvmumugmwz ago :0 mammamm xmom ommomwumwusu < .Avamn mowsoumuum Hmowauou mlmv muuoomm GOquSOmnm pomm> ocmponmomp was uoHHom oomuonmomm c .mm .mwm .753 mmmzazmis q .u a. u _ - u a Q o— om % 2...- moa<> m l 5ij 9M N .3 m no cc m 0 nu Ion om cilll\llloislll\n\r)sc.l|‘|§ no» 52 to enhance the loss by multiple reflection and thereby further depress the transmission. This combined effect accounts for the slow decrease 1 in transmission as the pellet absorption at 2528 cm' is approached from lower frequencies. VI. INTERPRETATION OF RESULTS A. Crystal Structure The crystal structure of decaborane was determined by Kasper, Lucht and Harker10 in 1950. They described the structure as a par- tially-ordered system with a highly-twinned* crystalline edifice at room temperature. To understand the partially-ordered lattice, we first consider the disordered structure and then the twinned, ordered structure. Fig. 24a is a schematic diagram of the disordered structure projected on the (001) face. According to the notation of Kasper gp‘gl.1 , a circle represents one-half the B10H14 molecule, such as the half-molecule made-up of the primed borons and their bonded hydro- gens shown in Fig. 1. Two circles and their connection represent one molecule; the direction of the connector between the circles is perpendicular to the BV’BV' bond. In the disordered structure**, the *A twin may be defined as a crystal built up of two or more in- dividuals of the same crystal species in intimate contact with each other over part of their bounding surfaces and oriented with respect to each other in certain well-defined ways. The components of a twin may be re- flections of each other in a plane called the twinning plane. When there are two individuals, in contact along the twin symmetry plane, the crys- tal is called a contact twin. If individuals related in this way occur alternately and in large numbers,one has polysynthetic twinning. A high degree of polysynthetic twinning is found in the BlOH14 crystal structure. For a rather extensive treatment of twinning, the reader is referred to R. W. Cahn, Advances in Physics 3, 363 (1954). **This crystal system is orthorhombic and the space group is Pnnm (Dig) with parameters a0 = 7.225A, b0 = 10.44A, co = 5.68A. 53 54 .— . r P“ .I‘IFInIlI-W‘i . OHDU Oahu m. ..o as. .mHSuUSHum Hmumzuo vmumcHOmHo 1, /~N~u+u: +-. // NA: .. «: a- . if Hmumzuo wmumwuo.- .nqm .wwm .7 X . II +/ 7 - .nsN .mam .s-_ u: u a: + 2. 55 molecule occupies with equal probability either one set of orienta- tions, or another set related to the first by a mirror plane parallel to the plane of the diagram. A plus or a minus next to a "half molec- ule" distinguishes between the two possible orientations; as it turns out in the actual structure, the two halves of every molecule are oriented in the same direction. Molecular models of the two orienta- -‘ (m‘ n..”" tions are shown in Fig.3 25 - 27. We arbitrarily assign a plus to l the molecular orientation shown in Fig. 25, and assign a minus to the b molecular orientation shown in Fig. 26. A plus and a minus appear with each circle in Fig. 24a because each orientation of the molecule is equally likely in the disordered state. The fraction % denotes that the plane of the half molecule is translated a distance co/2 (2.84A) in the 3* direction from the plane of the other molecules. We choose to call the plane of the other molecules the pap; plppg. Fig. 24b is a schematic of the two ordered twins; that is, both twin A and twin B have ordered structures.** The orientation of a *The vector E'is one of the three fundamental translation vec- tors (or primitive translation vectors) with the formal property that in the lattice, the atomic arrangement looks the same in every respect when viewed fromaany point F as when viewed from the point ?’= f + n13 + nzb + n33 where n1, n2, n3 are arbitrary integers.26 In the case of the ordered structure due to the orthorhombic system, c is perpendicular to the plane of the diagram. **In both twins the crystal would be monoclinic and a monoclinic axes is indicated in the figure. The orthorhombic cell is used because of its relation to the small cell of the disorderedacrystal (a0' = 2ao, b?' = 2bo). The ordered space group is P2/c (CZh) with parameters a0 = 14245A, bo'= 20.88A, co = co'= 5.68A. 56 O '3‘-f{.1:\0 “ I J - ./ . ’q“. . v V Fig. 25. - Model showing one of the two possible molecular orientations in the decaborane crystal lattice. This particular orientation is specified by a plus in Fig. 24. 57 Fig. 26. - Model showing one of the two possible molecular orientations in the decaborane crystal lattice. This particular orientation is specified by a minus in Fig. 24. Three hydrogen atoms are not observable from this view, but appear in Fig. 27. 58 Fig. 27. - Model shown in Fig. 26, except that all 14 hydrogen atoms and all 10 boron atoms can be seen. 59 molecule is denoted by the plus-minus notation applied to the dis- ordered structure. In the ordered system, however, each molecule may be in either one orientation or the other, but not in both. Twin A and twin B differ only in the orientation of the four molecules in the plane translated a distance co/2 from the pa§QDp1§p23 Fig.3 28 - 30 show models of the twinned structures. Twin A is shown in Fig. 28 and TE! ’3 twin B is shown in Fig. 29. At room temperature there exists a variation in the periodicity “c; . . of the molecular orientation along the b direction of the lattice. This periodic structure is the partially-ordered state of the BlOH14 crystal lattice. Suppose we consider twin A and assign the letters a, p, g,'d to the xz-layers of the structure, as shown in Fig. 31. For the partially-ordered state, there is a mixing of the two twins subject to the condition that an‘g or 2 layer is always followed by only a p.0r a g_layer. It was assumed by Kasper that the four layers (g, p, g, g) occur with equal frequency, and that correlation exists between neighboring layers only by the condition that §.or p_is always followed only by p.or g, A possible grouping of xz-layers in the partially—ordered structure is as follows: ---acbdacbd--~acbdadbcadbc---adbcbcad--~ The probability that a specific layer has the same kind of layer as a second neighbor was found10 to be 1/20. 60 Fig. 28. - Decaborane ordered crystal structure--twin A. 61 twin B. - Decaborane ordered crystal structure-- Fig. 29. 62 Fig. 30. - View of twin A showing the relative distance between the base plane molecules and the molecules in the plane translated in distance co/Z from the base plane (also observed in twin B). 63 How mummmfiuux mo acoEowcmuHm A, onu mawumuumSHHH .< aw3u Emuwmflv UfiumEmsom 1 .HM .me re +~:n\ u-2QW \V+~: Myra: ‘Mu-~= -Ne.n\ \MV+N~. +-.n\ an. an. on Ac. 64 B. Origin of Spectra Variations We are now in a position to describe accurately what are considered to be the origins of the observed bands. Let us first consider the spectrum of the molecule alone as it appears in the vapor. The band that has been the center of our interest, near 2600 cm'l, is attri- buted to the 10 terminal hydrogens, each stretching the single bond connecting it to a single boron atom. The basis of this assignment is that in general a hydrogen atom bonded to a heavier atom vibrates with a high frequency (cf. C-H, 3000 cm'l; N-H, 3300 cm'l; O-H, 3600 cm-l), and specifically that B-H stretching vibrations in diborane (Fig. 32a) and pentaborane (Fig. 32b) have frequencies in the region 2500 - 2600 cm'l. Moreover, the large change in dipole moment occurring in this mode, and the large number of terminal atoms, point to a strong absorption, as is indeed observed. The 10 terminal hydrogen atoms are not all equivalent, however, so some structure might be expected in the band. We believe that the shoulder at 2600—2601 cm'1 reflects this non-equivalence. As shown in Fig. 32c, the hydrogen atoms attached to boron atoms V and V' form a set of equivalent atoms (labeled a), those attached to II and 11' another set of equivalent atoms (labeled p), those attached to I, IV, I', IV' another set of equivalent atoms (labeled 2), and those attached to III and III' still another (labeled d). We ascribe, for reasons discussed later, the shoulder to the group of equivalent B-H atoms 65 (a) diborane B H, o 2 (b) pentaborane B539 {he C)‘ Q (c) decaborane " B10H14 I @\ @fig , (The four sets of B-H pairs are C Q - labeled a,b,c,d.) Fig. 32. - (From L. Pauling, The Nature of the Chemical Bond) . 66 labeled a, Strictly speaking, of course, we should talk only about normal vibrations, in which all atoms participate. But the high fre- quency of this band results in almost no coupling with the lower fre- quencies of other vibrational modes of the molecule. Hence it makes sense to speak about stretching vibrations of hydrogen atoms alone. The next mode to be considered is that of the stretching of the four bridged hydrogen atoms. Because of the bridged nature of the bond, stronger bonds might be expected; the inter-atomic distances, however, are 1.34 - 1.40 A compared to 1.25 - 1.29 A for the terminal-hydrogen bonds indicating a weaker bridged-hydrogen bond. Hence §_priori, it is difficult to say where the absorption should lie. In early studies with pentaborane Hrostowski and Pimentel21 ascribed bands in the 1800 - 2140 cm"1 region to B-H bridge stretching vibrations. But Shapiro, Wilson, and Lehman23 found that bands in this region for diborane (B2H6) disappeared when one terminal hydrogen was replaced by an alkyl group (CH3 or CZHS)’ but reappeared when two terminal hydrogens were replaced by alkyl groups. Hence absorption in this region appears to be con- nected with vibrations of terminal rather than bridged hydrogens. l to the bridge- Shapiro pp 31. definitely assign a band at 1500 cm’ stretching mode in the alkyl diboranes, but warn that the frequency of this mode is dependent upon the parent boron hydride. amuthfl _ . . . .- I 67 Modes representing deformation of the skeleton would be expected to lie farther out in the infrared; indeed, the complex absorption 1 pattern appearing around 1000 cm' is attributed to B-B skeletal 1 to skeletal bending.13 Important stretching, and that around 300 cm' as these bands are, they are so complex that their study is best left as a separate study. In the dilute solutions studied, the band near 2600 cm'1 appeared to broaden somewhat. Such an effect is expected. In substances where a strong rotational broadening of the vibrational lines occurs in the vapor phase, the quenching of the rotation in solution will tend to narrow the lines. But the difference in environment from one decaborane molecule to another in the solution will widen the vibrational lines.27 In decaborane, rotational broadening should be slight because of its symmetrical structure, but environmental broadening should be appreciable. In the solid, the effect of interaction of the terminal hydrogens with neighbors on adjacent molecules appears strong. The line does not merely broaden, but actually appears as a doublet, the shoulder on the high-wavenumber side persisting. There is a slight decrease in the frequency of the minima of the doublet as compared with that of the minimum of the single band of the vapor and solution. The decrease in frequency may be made plausible in the following way. If molecules in the condensed phase attract each other, the electronic configuration 68 of the molecule is so modified as to give weaker bonding within the individual molecule than exists between the atoms of the molecule in the condensed phase.27 In other words, by building the molecules into a crystal lattice, associative bonds are formed between atoms of neigh- boring molecules; the original valency bonds within the molecule are subsequently weakened so that the frequency of the intra—molecular vibrations are decreased.17 We attribute the origin of the doublet to different sets of terminal hydrogen atoms as they are positioned with respect to their neighbors in the lattice. That is, since a shoulder and single ab- sorption band appear in the vapor and solution spectra, we explain the shoulder plus the doublet in the solid spectrum in terms of the inter-molecular environment in the decaborane crystal. Consideration of the crystal structure (Fig.s 28 - 30) shows that the set of terminal hydrogen atoms labeled g_in Fig. 32c, has essentially the same atomic environment as the set of hydrogen atoms labeled p,* We consequently assign the minimum of the doublet appearing near 2525 cm'1 to the bond stretching of the B-H pairs indicated by the set of hydrogen atoms labeled 2 and by the set labeled g, The hydrogen atoms of set §_have a nearest-neighbor environment consisting of a single atom of the g *An atom of the g set has a nearest-neighbor environment consisting of two atoms of the 3 set and an atom of the p set; an atom of the h set has an environment of two atoms of the g_set and an atom of the Q’set. 69 set. We assume that the condensed environment of the lattice has a negligible effect on the B-H stretching vibrations involving the hydrogen atoms of set Q, We assign the shoulder exhibited in all 1 spectra near 2600 cm' to this set. The minimum of the doublet 1 is attributed to the stretching vibrations appearing near 2565 cm” of the hydrogen atoms of set 2, Obviously, this set has a nearest- neighbor environment consisting of hydrogen atoms of the g_set or of the p and of the 3 sets.* C. Analysis of Line Shape No rigorous theoretical expression has been derived for the line shape in an absorption spectrum. For many purposes, a linear damped harmonic oscillator is taken as the basis of an §g_hpg representa- 1 28 and for ionic solids, tion. This analysis, both for isolated molecules leads to the following expression for the complex dielectric constant E: as a function of angular frequency a): 8(0) 4 C(ce) = 1 8(0) - as») 1 - (ca/om - ice/momma.) Here 8(0) 5 80, the static dielectric constant, is the limiting value of 8 as (Japproaches zero; C(09) 5 Sb , the high-frequency dielectric constant, is the limiting value at frequencies high enough that ion-core *All of the discussions concerning the environment of the hydro- gen atoms are independent of both molecular orientation and the plane of the molecule in the unit cell. 70 motion has ceased, but not so high that electronic transitions occur. The parameter 030: the infrared-dispersion frequency, is a kind of resonance frequency; the parameter 3‘, the damping constant, is related to the half-width of the absorption peak. For optical studies, we need the complex refractive index E} defined as fis(gu)lésn+ik where u, the magnetic permeability may be taken as unity for nonmag- netic substances. Here n is the ordinary (real) refractive index, and k is an absorption coefficient. It is easy to show that 3 - k2 = + (£30 '€-)1:11;1(9/Uo)2] = A2 n E" E1 - («J/wow? + (w/SOVW/wofi’ and a (e - )(f/wa/w) = 2 2n. [1 - (Wowo>?lz~£—+ (w/UOWWI s)” " B ' Standard electromagnetic theory is then applied as is appropriate to the specific experimental situation. Each component of a plane electromagnetic wave, traveling in the direction of the positive z-axis, is proportional to (gamma-yr) = ezwlulzz/c e—amlyt- = e11r£y(flilc)e-3Tfkv2/c e—z'rrLyt where 27= l/A =U/c, A being the wavelength 1.}; vacuo, and c the speed of light. The intensity I is proportional to the square of the absolute value of the amplitude, that is, 71 e-‘irrkuz/c = e-acokz/c = e-lk-era/A 1. Absorption by Thin Films. By standard theory, the transmis- sion coefficient T = I/I0 for electromagnetic radiation of wavelength )\= 2wcfia incident normally on a plane parallel plate of thickness d is given by 1/1' = '[(l + fi)2 e-i-fllTrd/A _ (1 _ 3);, ei-h'ZTIJ/A When the value for fi'==e% is substituted in this equation, the result- ing equation is awkward to solve for 930 and 3‘. As shown in Montgomery and Yeung,29 a good approximation is provided by 1/1: 2’ 1 + (2nk)(21rd/,\) + {[(n2 + k2)2 - 2(n2 - k2) + l]/4(2nk)2]}(2nk)3(21rd/A)2 a 2 2 3 + {1/3 [1 - (n - k )J/(znk) )(2nkf (21rd/A) + For transmission from 100% to about 25%, the terms in d3 and higher may be neglected; and in the neighborhood of the absorption peak, as explained in Montgomery and Yeung, the coefficient of the term in d2 simplifies, and we may write 1 s ifs - Sacra/Mu + was -€s)/(f/wa)1<2«d/Aa)} (ca/coo - coo/cm + (Moo)3 1 - T We see that T’1 - 1, and hence T, is symmetric in “/00 =2-J/270 =/)'/A and its reciprocal. Hence there are two values of 29(labeled2'y+ andfl_) for a given value of T. It follows immediately that 370 = (22,21) % A plot of (j:#22_)% against T should give a horizontal line at ordinate 72 270 over the domain of the abscissa Tminé T5 T6 . The success of this technique has been discussed by Montgomery and Yeung, 123, ElE° for their work with lithium fluoride and lithium hydride, where con- siderable success has been achieved. In the present work, however, the principle absorption peak splits into a doublet. Hence this analysis cannot be applied directly. Modifications of it are possible, but we have not yet been able to demonstrate their utility. 2. Absorption by Vapor and by Solution. By standard theory, the transmission coefficient T of electromagnetic radiation of wavelength .A= 2flcfiv passing through a cell of thickness L containing a concen- tration x of material having a complex refractive index fi'= n + ik as condensed material, has the following form: T = exp (-2kx - 2nLAA) Upon taking logarithms and expressing A in terms of the angular frequency 2Ncfio ,‘we have - 1n T = 2ka6J/c = 2xL (Do/c)(O/Qo)k . To evaluate the adequacy of the theoretical expression for on), we need to calculate avkqo)k for comparison with - 1n T. First we calculate k by eliminating n between the expressions for n8 - k2 s A2 and 2nk a B3. The result is k2 = as? /1 + (Ag/Be)? - A2/33 , a result too complicated to be visualized easily when the full expressions 73 for A? and B2 as functions ofluJare inserted. But experiment shows typically that in the neighborhood of the absorption maximum, n2 - k3 = 5;, is about 2, where as 2nk = (£0 - “NU/(Jo) is about 100. Hence the term in braces in the expression for k3 is very nearly equal to unity. In this approximation k‘g l/(E B, and win =S ,1. WW flea -ié7a.‘:i oomuonmooo How H scammflemcmuu m> +.mlwn mo uon 1 .mm .me zo.wm.2mz