ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN ANN ARBOR FINAL REPORT ON INFRA-RED STUDIES OF CRYSTALS (Period: 15 May 1951 to 15 May 1954) BY G. B. B. M. SUTHERLAND Principal Investigator and C. Y. PAN LIANG Project 1957 SIGNAL CORPS, DEPARTMENT OF THE ARMY CONTRACT DA 36-039 sc-5581 SC PROJECT 152B-10, DA PROJECT 3-99-15-022 SQUIER SIGNAL LABORATORY, FORT MONMOUTHE N. J. October 1954

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - TABLE OF CONTENTS PagG I. PURPOSE OF THE INVESTIGATION 1 II. ABSTRACT 2 III, PUBLICATIONS AND REPORTS 3 IV, FACTUAL DATA 4 A. Barium Titanate 4 B. Diamond 10 C. Brucite 26 D. Micas 26 V. MAJOR CONCLUSIONS 59 A. Barium Titanate B, Diamond C. Brucite D. Micas VI. FUTURE PROGRAM 60 A. Barium Titanate B. Diamond C. Brucite D. Micas VII. PERSONNEL 61 VIII. APPENDIX 61 ii

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - FINAL REPORT ON INFRARED STUDIES OF CRYSTALS I. PURPOSE OF THE INVESTIGATION The general purpose of this investigation was to use infrared analysis as a means of exploring the structure of certain crystals. In particular it was originally hoped that light could be thrown on: (a) the nature of the changes in structure which accompany the changes in the ferro-electric properties of barium titanate and possibly throw further light on the cause of the ferroelectric effect- (b) the nature of the structural differences between Type I and Type II diamonds; (c) the nature of the differences between various micas in so far as these are due to the positions of the hydrogen atoms. As the work progressed, it seemed advisable (before tackling (c) in detail) that a simpler crystal containing OH ions should first be investigated. For this reason, a separate research was made on the infrared spectrum of bruoite (Mg(OH)2). In fact it turned out that the spectrum of brucite proved much harder to interpret than those of certain micas, Nevertheless, the results obtained on brucite are of considerable interest in the general field of infrared analysis of crystal structure, since these indicate that the positions of the hydrogen atoms deduced from X-ray analysis may be wrong. Alternatively, a new effect has been found in the infrared spectra of crystals which cannot be accounted for on current...: —---------— 1

1- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - theories II. ABSTRACT This report gives an overall survey of research carried out between 15 May 1951 and 15 May 1954 at the University of Michigan on the infrared spectra of various crystals. There were four separate investigations which ran concurrently, the emphasis on each varying from time to time, depending on the supply of suitable personnel and other local circumstances, The first investigation was on Barium Titanate and associated with it, some work was done on other titanates and on titanium dioxideo The second investigation was on Diamond* associated with this were investigations on Silicon and Germanium, especially on the theoretical side, The third investigation was on Brucite (i.eo magnesium hydroxide)0 The fourth investigation was on Micas, especially muscovite, biotite and phlogopite. This report will deal with the investigations in the above order instead of following the chronological order, although the latter corresponds to the former in a general way. Since a good deal of the detail of this work has already been reported either in quarterly or technical reports or in publications, we shall not repeat more of the detail than is considered necessary. Instead, references will -1 2

7- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - be given to earlier accounts of details and here the general results and conclusions will be emphasised, However, important details which have not been reported earlier will be given in the appropriate place. III. PUBLICATIONS AND REPORTS Publications "The Infrared Spectrum of Brucite" by Ro T. Mara and G. BB.Mo Sutherland, Jo Opt. Soc. Amero 43, 1100 (1953)o "The Rule of Mutual Exclusion" by T, Venkatarayudu, J. Chem. Phys, 22, 1269 (1954), "The Infrared Spectrum of Barium Titanate" by R. T. Mara, G.BBoMo Sutherland and Ho V. Tyrell, submitted to the Physical Review, September, 1954 and will appear in November, 19540 "The Problem of the Two Types of Diamond" by Go.B.B.M Sutherland, D. E, Blackwell, and W. G, Simeral, submitted to "Nature" September 1954 and accepted for early publication. Talks "Interpretation of the Infrared Spectrum of Diamond" by W. G, Simeral and GoBB.M. Sutherland Ohio State Symposium in Molecular Spectra at Columbus, Ohio, June 159 1953, "The Location of the Hydrogen Atoms in Muscovite and Biotite" by C, yo Pan Liang and G Be B.M. Sutherland Ohio State Symposium on Molecular Spectra at Columbus, Ohio, June 17, 1954. am3

F- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - "Relation between X-ray Results and the Infrared Spectra of Large Molecules" by Go Bo B M, Sutherland Gordon Conference on Infrared Spectra at Meriden, N, Ho, August 5, 1954o IVo FACTUAL DATA IV A. Barium Titanate The general situation reached on barium titanate by 15th May 1954 is given in the following inset paragraphs which are a copy of a letter recently submitted for publication to the "Physics Review." The Infrared Spectrum of Barium Titanate The infrared absorption of barium titanate (BaTi03) has been studied between 2p and 335. The spectrum obtained (Fig0 A) consists of two broad bands, one centered near 550 cm"1, the other starting near 450 eml- and reaching a maximum beyond 300 cmul. The low transmission in the high frequency end of the spectrum is due to scattering since the barium titanate was examined as a fine powder deposited on a KBr (or NalG) plate from a suspension in isopropyl alcoholo Several specimens of barium titanate were examined, The majority showed additional bands at 6.95, 9.45, and ll65p~, which were proved to be due to carbonate ion impuritiesO Other impurity bands were noted at 7.1, 10o.3, 11.05,. —-----------— M.A —-------------

-ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN % TRANSMISSION O I ______\ ~~~~~~~~~~~I I'\ 0 -0 ^CO ^ // o ~i 41 - 6 FIG. A -5

-- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - 11.4, 11.85, and 12o85i, but the impurities were not identified. The spectrum of a very pure specimen of powdered strontium titanate (SrTiO3) was observed between 2p and 15o. (Figo B) It is identical with that of barium titanate obtained under similar conditions over that region of the spectrum, Nolandl has recently reported the spectrum of a single crystal of strontium titanate between 1l and 10o5p at which wavelength the extinction coefficient is greater than 100 cm-l and is still increasing. He finds two weak bands near 5.5i and 7.5,o These could easily have been missed by us since our effective thickness was much less than the thickness he used. We might add that the spectrum of a single crystal of barium titanate just run in this laboratory by M. Haas shows a weak band at 8L and a "cut off" near 1122,o The spectrum of ilmenite (FeTiO3) has been recorded by Hunt and others2, With the exception of a weak band at 100 cmi1, it is also very similar to that of barium titanateo Apart from impurity bands, there appears to be no difference between the spectrum of barium titanate in the hexagonal and in the tetragonal form over the range 2j to 15po No change was observed in the spectrum of barium titanate m-6

[ ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN % TRANSMISSION' -\S~~~ 0 o 0 0 0 0 II o......... i ii iiii iiil0 ________________^______________0 ----- ^ —----- &~~~~~~~~ FIG. B -7

7- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - (ceramic) when heated to 150~ Co The foregoing observations may be considered in the light of recent theories about the ferroelectric character of barium titanateo Jaynes3 has predicted from an electronic theory that there should be an infrared absorption at 1000 cm'l. There is definitely no strong absorption band in the neighborhood of 1000 cm'o1 Although a few specimens have shown a very weak absorption near 1000 cm, this is most probably due to BaO impurityo Megaw4 has proposed that the change from the cubic form (above the Curie point of 120~ Co) to the tetragonal form corresponds to a change in the character of the bonds round the Ti and 0 atomsa If this were so, one might expect a change in the spectrum on heating to 150~ Co and also differences between the spectra of the tetragonal and hexagonal forms of BaTiO3 since the latter is not ferroelectrice This change should be very marked in the strong band near 600 em"1 since this band (which is common to all titanates and is found also in rutile (TiO2) is undoubtedly connected with a vibration of the TiO6 tetrahedrao No such change was observed, It is possible, of course,, that changes may have occurred at lower frequencies beyond the range of detection. This work was sponsored by the Uo S. Army Signal Corps under Contract DA 36-039 sc-5581 from the 8-0

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Squier Signal Laboratory, Ro T, Mara Go Be B, Me Sutherland H, Vo Tyrell Randall Physics Laboratory University of Michigan Ann Arbor, Michigan References 1 2 J. A. Noland, Phys. Rev. 94: 724 (1954) J. M. Hunt, M. P. Wisherd, and L, C, Bonham. Anal. Chem, 22- 1478 (1950) E. T, Jaynes. "Ferroelectricity." Princeton Univ. Press- 69 (1953) H. Do Megaw. Acta Crystallographica 5: 739 (1952) 4 f-9

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN -- The above letter contains all of the important fundamental results on barium titanate. The details have already been given in Quarterly Reports 1, 2, 3 and 4 or in the First Annual Report (August 1952 ) With regard to TiO2, there is nothing to add to the work reported in the First Annual Report (August 1952)o IV, B, Diamond, Silicon and Germanium All of the factual data on diamond, silicon and germanium have been given in Technical Report N o, 1 (June, 1953) with -one exception. In the summer of 1953, Dr. Harmon Craig of the Institute for Nuclear Studies in Chicago University kindly agreed to make an analysis of diamonds of various types to determine the C13/C12 ratio as we thought this might throw light on the cause of anomalous absorption in Type I diamondsWe sent him three diamond chips; one was a strong Type I, one a weak Type I and one a Type IIo We have now received the report of his analysis. It turned out that the strong Type I had the lowest C13/C12 ratio, while the Type II had an intermediate value of this ratio. This proves that the C13 content of diamond is quite unconnected with differences between Type I and Type II diamonds, Our general conclusions on Diamond at present are contained in the following inset paragraphs which are a copy of an article recently submitted for publication to "Nature"t

-. ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - The Problem of the Tw s of Diamond Introduc tion Exactly twenty years ago, Robertson, Fox and Martin1 reported the existence of two types of diamond having marked differences in infrared and ultraviolet absorption, in photoconductivity and 2 birefringence. Somewhat later, Raman and Nikalantan reported that many diamonds had extra spots or streaks in their X-ray diffraction patterns. This observation was confirmed by Lonsdale and Smith3, who reported that extra streaks were characteristic of Type I diamonds and also that in general Type II diamonds appear to be much more mosaici in structure than Type I diamonds. The principal characteristics of the two types of diamond as determined from these early investigations are summarized in Table I. TABLE I Characteristic Features of the Two Types of Diamond Physical Property Type I - Type II Infrared Bands at 4 to 5p Bands at 4 to 5u Absorption. Absorption 8 to 1@0 None between 8 and 1 Ultraviolet Complete beyond Absorption 3000 Ao.Transparent to 2250 A. X-ray Shows extra spots diffraction and streaks Normal Photoconduct Biringen Poore s ent AbGood _ Birefringence Present Absent Subsequently Sutherland and Willis4 and also Ramanathan showed that Type I diamonds are not uniform _____ -11- ___11_

r' Ik I AM I lk A 9-' %M Ik I Af t m A A% US I~ I9 I do IM ~ ~ L Ias A laiI 1 A iU AA * eII A Alk - tNIINItt UINi KLt.AKHI IN1I:IlUl I * UNIVtKbII Y UV MIIM1AIAN in their infreared absorption, since the extinction coefficient of the 8-101 band varies very widely from diamond to diamond. Thus the Type II diamond may be regarded as a limiting case in which the value of the extinction coefficient of the 8 - 10p band has become vanishingly smalls A similar gradation has been found in the position of the ultraviolet cut-off and in the intensity of the extra spots in the X-ray diffraction patterns. Thus diamonds may be more satisfactorily classed as extreme Type I, medium Type I, weak Type I and Type IIo It should be added that Blackwell and Sutherland6 have reported two types of Type II diamond, neither of which exhibited any absorption in the 8 - 10 region but which showed differences in the 3 - 5L regiono No explanation for these anomalies in the physical properties of diamonds has been yet put forward which has received general acceptanceo In an attempt to seek a satisfactory solution of this puzzling phenomenon, we have made an extensive investigation of the infrared and ultraviolet spectra of a selection of diamondso In a short paper giving an account of some of the early results6, we suggested that the Type II diamond was a normal pure diamond while all Type I diamonds had some impurity or imperfection in their structure which would account for the anomalies. The purpose of the present note is to present briefly the _________________ -12- _____________________________

r~ir IkEII* irr~M~& friII i rriIuIT urr iir hAI,"' i#M A k.- Tl NiNEE 1MIINU isccKtAIL ii I IuI * u Iv cIiV u l'r MiiLnIMAN -I main results of our investigations with particular reference to the imperfection theoryo Type I and Type II Diamonds First, however, it is necessary to consider a little more carefully the distinguishing features of Type I and Type II diamonds0 Although any one of the properties listed in Table I has been generally accepted as a reliable guide in distinguishing Type II from Type I diamonds, the parallelism of all the physical properties is not at all satisfactory in classifying Type I as "extreme", "medium", or "weak"t and occasionally a diamond classed as Type II on the basis of one physical property would be classified as Type I, if one of the other properties were used. In a paper primarily concerned with possible correlations between the counting properties of diamonds and their crystal texture (as shown by divergent beam X-ray photographs) Grenville-Wells7 has listed various physical properties of 38 diamonds0 Four of these diamonds had a cut-off in the ultraviolet below 2400 A., yet exhibited anomalous extra strong X-ray streaks, i.e. by ultraviolet examination these four diamonds would have been classed as weak Type I but by X-ray streaks as medium or strong Type Io Similarly three diamonds which showed no extra streaks (and would therefore have been classified as Type II) had their ultraviolet cut-off at wavelengths longer than 2830 A. ------------- -13- -...

r...~nffir ij. Iiiltlllll LIP _. I Ikl*lr ^- " AI/ lO "I lem AR! H ^ I r- Ci I.N WI'N I:KIN iI AK KLM IN.I Ii U C * UNvii T I r IVIC I Ir MIIAN (indicating that they were medium or strong Type I). Through the courtesy of Dr. Grenville-Wells, we have been able to examine the infrared spectra of 13 of these 38 diamonds. We have found that in every case there is excellent correlation between the infrared and ultraviolet method of classifying diamonds, but very poor correlation between the infrared and X-ray method. In this connection it should also be added that the observations of Grenville-Wells has shown that mosaic character cannot be reliably correlated with Type II diamonds as originally suggested by Lonsdale3, There is, therefore, strong evidence that the same cause operates in producing the extra absorption found in the infrared and ultraviolet spectra of all Type I diamonds but that additional factors may be the cause of the extra streaks and of the mosaic character found in the X-ray photographs of certain diamonds. In view of this, we propose to use a modified nomenclature in the future for the description of Type I and Type II diamonds. A diamond which is found to be Type I (or Type II) by spectroscopic means will be denoted by IS (or IIS) while a diamond classified by X-ray methods will be denoted by IX (or IIX). The spectroscopic symbol can be elaborated to read Sir or Suv depending on whether infrared or ultraviolet radiation was used in making the classi fication; similarly, the X-ray symbol should be V- -14-

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - 1 modified to read X1 or Xd to indicate whether the diamond was classified by extra streaks on a Laue photograph or mosaic character as shown by a divergent beam technique. Possible extensions of this notation by using combinations of the X and S symbols together with e, m and w to denote extreme, medium and weak are sufficiently obvious and need not be discussed hereo The distinctions just drawn between the various Type I and Type II diamonds are important in what follows, because in this communication we shall restrict our discussion to IS and IIS diamonds. It appears to us that at least some of the confusion in the diamond problem can be eliminated in this way. In other words, there are several Type I and Type II diamond problems and we propose to start with the IS and IIS types, since the classification by infrared and ultraviolet absorption has been found (by the examination of several hundred stones) to give very consistent results. We may begin by considering what would be predicted for the ultraviolet and infrared spectra of diamond assuming the Bragg structure and the current theories of molecular spectrao Ultraviolet Absorption of an Ideal Diamond From the examination of the ultraviolet spectra of large numbers of hydrocarbons, it has been found -15..... J

r Cklid21XISUrrILIY rt'r AfliI mirvii rir! - mmiuirnerru ^r &LA1i IIa A CI I L -- I.lII.Crc:M;IMWI KC.IM.iA^1.Un Il-U i'CU *- U- N-VCK)I rT Ur M1IIMIAN -- that only those hydrocarbons which contain a double or triple carbon-carbon bond exhibit absorption at wavelengths longer than 2000 Ao Since diamond presumably contains only single bonds, its ultraviolet cut-off might be expected to be below 2000 Ao Since no IIS diamonds have been found with a cut-off below 2200 A,, it appears at first sight as if all diamonds are anomalous in their u, vo absorption with IIS less anomalous than ISo However, EICevens and Platt8 in an investigation of the ultraviolet spectra of branched saturated hydrocarbons have shown that as the degree of branching increases, the edge of the ultraviolet cut-off moves to longer wavelengths, e.go from 1715 Ao in n-pentane, to 1795 A. in 2,2,,33Stetrzaethylpentane. One might, therefore, anticipate that diamond (which from this point of view resembles an extremely highly branched large hydrocarbon moulcule) would have its ultraviolet cut-off in the neighborhood of 2000 Ao In order to test this hypothesis, we have examined the ultraviolet spectrum of adamantane (GC10H1) which consists of four "fused" cyclohexane rings and which would yield diamond if it ever could be "polymerisedo" The ultraviolet cut-off of adamantane5, while not as sharp as that of a IIS diamond, is indeed very close to 2200 A. We should add that Herman9 has recently made a theoretical calculation of the separation between the filled and unfilled electronic energy...... 16

0- L 110M L W M.Mf MILI IM 0 w rr A r% loo a a L I des, r q NW~ I I A E I llg A sqr i Al% 1 a 1^2 II^ A Iko!,- ENGINEERING KIt5AKCH IN.SILUIIU * UNIVt:KbllY V1 MImHIAN levels of diamond and obtained a value of approximately 6 electron-voltso This corresponds to an absorption edge of about 2050 Ao We therefore conclude that the IIS diamonds have perfectly normal ultraviolet absorption and that only the IS diamonds are anomalouso Infrared Absorption of an Ideal Diamond From investigations on the infrared absorption spectra of hydrocarbons, the force constants involving carbon-carbon bonds are sufficiently accurately known to make it certain that the fundamental frequency spectrum of the diamond lattice must extend from about 1400 cm"1 (7.lP1) to about 300 cm"1l (3355)o The exact distribution of the normal modes over this range is a much more difficult problem but calculations have been made by Smith 1 which give reasonable agreement with the observed second order Raman spectrums and her results can be regarded as a very good first approximation to the true distributiono It is necessary to consider next to what extent these frequencies may be expected to be active in absorption0' Using the results of Teller11 and Lifshitz12 it can be shown that none of the fundamental frequencies should be active in absorption but that combinations of fundae mentals may give rise to absorptiono Now IIS diamonds exhibit no absorption between 1800 cm'1 and 100 cm"1 (ieoo the fundamental region) but do have bands between 350 m and 0 m1 and 1800 m __________________ 17- _

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - I (i.e. the region of combination frequencies)o Thus IIS diamonds are completely normal in their infrared as well as their ultraviolet absorption. Problem of the IS Diamonds The conclusion that IIS diamonds are perfectly normal in their optical absorption properties is an important one, The problem of the IS and IIS types of diamond is now reduced to the problem of why IS diamonds show anomalous absorptiono A few years ago, two of us suggested6 that the extra absorption found in IS diamonds might be due to impurity centres in diamondO The exact nature of these was not specifiedo Impurity centres may consist of 1) foreign atoms9 2) missing carbon atoms, or 3) carbon atoms which are not in the same electronic state as the majority of carbon atoms in the diamond lattice. We may now consider what the effects of such impurity centres would be on the absorption spectrum of diamondo aa) Ultraviolet Spectrum It is now well established that chemical impurities in silicon and germanium cause the edge of the main absorption band in these elements to move to longer wavelengths13o Thus the shift of the absorption edge from 2250 A. in IIS diamonds to 3000 A6 (or even further) in IS diamonds could be due to chemical impuritieso The effect of missing carbon atoms on the ultraviolet spectrum is not so easy to predict, 1P85 J

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN - but, in general, lattice defects of this type may be expected to decrease the gap between the ground state and the lower edge of the first band of energy levels, Thus the observations are probably also consistent with this second type of impurity centre. The third type of impurity centre might also be expected to cause a shift of the absorption edge to longer wave-lengths, but in addition might be expected to give rise to discrete lines superimposed on the continuous absorption, Such discrete lines are observed and we have been able to prove that certain of these lines are closely correlated with certain infrared absorption bands in the range below 1800 cm"l (cf. (2) below). We may conclude that the extra absorption shown by IS diamonds in the ultraviolet can be readily accounted for in a qualitative manner by an impurity theory and that, of the three types of impurity centre considered, that arising from carbon atoms in an abnormal state seems most probable, b) Infrared Spectrum Anything which destroys the centre of symmetry midway between each neighboring pair of carbon atoms in the ideal diamond lattice can cause absorption to occur in the region of fundamental frequencies. Thus any of the three varieties of impurity centre considered could conceivably account for absorption by IS diamonds in the region below 1800 cml. Before.,... -19

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - discussing which seems most probable, we shall summarise the most important results of our investigations on the infrared spectra of IS diamonds. (1) Absorption maxima of variable intensity have been found in IS diamonds at the following frequencies below 1800 cm-1: 1540, 1520, 1426, 1372, 1332, 1282, 1203, 1171, 1093, 1003, 780, 480 and 328 cm'l, No absorption was found between 300 cm'l and 100 cm-1 All but two of these bands appear to fall into two groups (as shown in Table II) in the sense that the bands in each group always occur together and have the same relative intensity but there is no correlation between the bands in the separate groups. The two maxima near 1530 cm-1 have not so far been correlated with either group, but this may be due to the difficulty of making accurate intensity measurements on these weak bands. Many of the Group B bands (e.g. at 1426, 1372, 1332 and 328 cm"1) are very sharp. All the Group A bands are broad. TABLE II Distribution of the Absorption Bands of IS Diamonds Group A Group B cmn- L em~l 1282 1426 1203 1372 1093 1332 480 1171 1003 780 328

AIlk I iII INW U rA IL I A A r t A ~ IA III L IAl I I* rc I AIIklr I NFl al Ior A % I - LtINIINttKI IN KtLtAKHM INb I U I I UNIVtKbI I Y Vt MII1IIAN - (2) It has been found that as the intensity of the Group A bands increases, the cut-off wavelength in the ultraviolet moves to longer wavelengths and the intensity of an ultraviolet line at 3157 Ao increases, However, in IS diamonds containing Group B bands, the intensity of this group of bands is independent of the position of the ultraviolet cut-off, but is correlated with the intensity of an ultraviolet absorption line at 4155 A. (3) Following the methods of Smith10, we have calculated the branches of the vibration spectrum of the diamond lattice and have been able to explain the high frequency (>1800 cmnl) bands of IS and IIS diamonds in terms of allowed combinations The Group A bands in the low frequency (<1800 cm l) spectrum of IS diamonds can also be accounted for in this way, but most of the Group B bands cannot be associated with calculated maxima for the ideal diamond lattice, (4) When IS diamonds are heated to 400~ Co, the only detectable change in the infrared spectrum (between 4000 and 700 cmr1)' is a decrease of about 30% in the intensity of the 1372 cm"l bando This band also moves to lower frequencies as the temperature increases, the temperature coefficient being 1 cm"l/500 Co Diamonds (IS and IIS), which had been heated to 1700~ Co and were re-examined at room temperature, showed no change in infrared spectrum. 21- _____

riIirrIrIlIIl, nrrC A nIDU ILITITI ITC rr II III/CDEITV ^Cl AlI/LUII_ A kI r EN I rN t I I NU KstWcm^tf n mINI-1uIc0 uNIV iC IT vr m I.niw - N (5) The infrared absorption bands of IS diamonds show no dichroic effects in regions where optical birefringence is observed. (6) Irradiation of IIS diamonds by neutrons, deuterons and x-rays has so far failed entirely to produce any of the absorption bands characteristic of IS diamonds, Neutron irradiation appears to give rise to the formation of graphite. Deuteron irradiation caused color changes in the surface layers (green for a IIS and brown for a IS diamond). (7) There is no correlation between variations in the C13/C12 ratio in diamonds and the intensity of the characteristic IS bands, It is clear from the foregoing results that there is probably more than one cause for the appearance of anomalous absorption in IS diamonds, since the absorption bands fall into at least two classes which exhibit different propertieso Moreover, part of the absorption can be confidently assigned to the activation of normally forbidden frequencies of the ideal diamond lattice but some of the bands appear to be due either to chemical impurities or to carbon atoms in an abnormal state. Isotopic effects cannot account for the anomalous absorption. Since deuteron irradiation fails to convert a IIS into a IS diamond, it seems unlikely that vacant sites are the cause of the IS anomalies, -22___....

kItIklllCDIkI DICr A DC lDU IICTITIT. I I3LII%/DrCITV /C" Irl/UlLI/T A Kl I — C IJ Im IC NI WAcM^n l I I mUIC' UruIVK uI3 I 1 vr IvminiMi -NConclusions Our present conclusion is that carbon atoms in an abnormal state and chemical impurities probably both contribute in varying degrees to produce IS diamondso If some carbon atoms exist in a state which enables them to form double bonds in IS diamonds, then the bands near 1530 cml1 could be due to the vibration of carbon-carbon double bonds in an unsymmetrical environment, and the movement of the ultraviolet absorption edge towards 3000 Ao is consistent with the introduction of a few conjugated double bonds into the structure, Since graphite is a more stable form of carbon than diamond, it is tempting to consider that in IS diamonds some parts of the structure have gone part way towards graphite, However, the neutron irradiation experiments seem to produce graphite without giving the typical IS features as an intermediate stage. With regard to chemical impurities, it should be realised that there is very good spectroscopic evidence14 for the presence of many impurities in the average diamond and some evidence14 (although much weaker) that IIS diamonds are less impure than IS diamonds. This is a point on which we hope to conduct further investigationso The appearance of some very narrow absorption bands in Group B (which do not seem to belong to the diamond lattice) is most easily explained by. -23

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN attributing them to the presence of chemical impurities, What does seem certain from these investigations is that Type I diamonds (specifically IS diamonds) are imperfect. This is an unexpected result, since in our experience all large diamonds of gem stone quality are always Type I diamonds, While some very small Type II diamonds are perfect octahedra, all the large Type II diamonds which we have examined are very far from any of the ideal crystalline forms of diamond (octahedron, cube, etco) and in fact, usually exhibit a layered structure with highly irregular faces and fractured edges, It would almost appear as though a large single crystal having the ideal Bragg structure is unstable and requires certain impurity centres to be incorporated to give stability, The beneficial effect of impurities in the growing of large single crystals is well known to workers in that field15l A full account of this work is now being prepared for publication in a more appropriate journal. Acknowle dgements We are most grateful for the loan of diamonds from Industrial Distributors Ltd.o Messrs Triefus and Co., Lazare Kaplan and Sons Inc.. the late Professor W. T. Gordon, Dr. K. Lonsdale, Professor.____._ -24- ____

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - C. B. Slawson, Dr. W. C. Parkinson and Dr. GrenvilleWells. We are very much indebted to Dr. Harmon Craig for making the C13/C12 analysis for uso Some of the later phases of this work received valuable financial aid from the U.S. Army Signal Corps under Contract DA 36-039 sc-5581o G. B B, M. Sutherland D. E. Blackwell a Wo G. Simeral b Randall Physics Laboratory University of Michigan Ann Arbor References 1) Robertson, R., Fox. J, J. and Martin, A. E. Phil. Trans. Roy. Soc., A, 232:463 (1934) 2) Raman, C. V. and Nikalantan, P. ProCo Ind. Acad. Sci., 11:379 (1940) 3) Lonsdale, K. and Smith, H. Nature, 148:112 (1941) 4) Sutherland,'G.B.B.M. and Willis, Ho Ao Trans. Faraday Soc., 41:289 (1945) 5) Ramanathan, K. Go Proc. Ind, Acado Sci., 24:137 1946 6) Blackwell, D. E. and Sutherland, GBB, Mo J. Chim Phys. 46:9 (1949) 7) Grenville-Wells, H. J. Proc. Phys. Soc., 65:313 (1952) 8) Klevens, H. B. and Platt, J. R. J. Am. Chem. Soc. 69:3055 (1947) 9) Herman, F. Phys. Rev., 88:1210 (1952) 10) Smith, H. M. F. Phil. Trans. Roy. Soc., A, 241:105 (1948) 11) Teller, E. Hand. und Jahrbuch der Chem. Physik, 9, II:161 (1934) a. Now at the Solar Physics Observatory, Cambridge University. b. Now with E. I, duPont de Nemours Co., Wilmington, Delaware. ~ -25

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - 12) Lifshitz, I. M, J. of Physics (U.S.S.*R), 7:215 & 249 (1943); ibid, 8:89 (1944) 13) Fan, H. Y. and Becker, M, in "Semi-Conducting Materials", Butterworth Ltdo, London (1951), pp. 132 14) Chesley, F. G. Amer. Min., 27:20 (1942) 15) Buckley, H. E. "Crystal Growth", John Wiley (1951) A suitable condensation and revision of the full account of the work on diamond, silicon and germanium given in Technical Report No. 1 (June 1953) is gradually being prepared for publication, One other piece of work related to diamond may be mentioned at this point. Dr. Venkatarayudu has shown that in the case of crystals which possess a centre of symmetry (diamond is such a crystal) the rule of mutual exclusion breaks down for combination frequencies although it is still true for fundamentals. This work has been published in the Journal of Chemical Physics and a copy is given in Appendix I of this report. IV. C. Brucite A full account of all the experimental work on Brucite done in the period covered by this report has already been given in Technical Report No. 2 (October 1954). Part of this work has already been published in the Journal of the Optical Society. This is attached to this report as Appendix II. IV. D. Micas After making a general survey of the spectra of muscovite, -2-...

-- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - r i biotite, phlogopite (natural and synthetic), lepidolite, and zinnwaldite (which has been described in the first Annual Report of August 1952), attention was directed to the identification of bands characteristic of the OH group other than the well-known 3,( absorption. The results of this work were rather inconclusive and were reviewed in the second Annual Report (June 1953). We therefore concentrated our efforts on a thorough investigation of the 35 absorption in muscovite and biotite using polarised radiation. Brief reports of this work have been given in Quarterly Reports 9 (December 1953) and 10 (March 1954) and in this section of the report we shall describe the detailed investigations made on the 35 bands of muscovite and biotite and the resulting conclusions reached regarding the location of the hydrogen atoms in these micaso The Location of the Hydrogen Atoms in Muscovite and Biotite from Investigations on the Dichroism of Absorption Bands in the 3u_ Region Tsuboil has recently reported a similar investigation on muscovite, but his theoretical treatment of the problem is incomplete, and our experimental data are considerably superior. Vergnoux, Theron and Pouzol2 have also attempted to locate the hydrogens in muscovite from studies on its birefringenceo The results of this earlier work will be discussed later when comparison can be made with our results, It is convenient to start by describing briefly the results of X-ray studies on the structure of the micas in order to understand clearly the atomic framework into which the hydrogen atoms have to fit, -27 II

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - The first application of X-ray analysis to the structure of mica was made by Mauguin3. Some years later Pauling4 described the general structural scheme, but the only complete X-ray analysis of a mica structure appears to be that of Jackson and West5 on muscovite. From a study of powder photographs of several micas, Nagelschmidt6 concluded that there are two general classes into which all micas fall, viz. (a) the muscovite type and (b) the phlogopite-biotite type. Following Brindley7, these two types may be described in terms of two structural units which we shall call T units and 0 units. The T unit (or tetrahedral layer) is composed of linked SiO4 tetrahedra (Figo 1) in which approximately one-fourth of the Si++++ ions are replaced by Al+++ ions. The 0 unit (or octahedral layer) consists of two plane sheets of 0" and OH" ions arranged in hexagons of 0" around each OH'. (Fig, 2) Between these sheets is a plane of ions which are located at the centers of octahedra formed by joining the vertices of two triangles such as A B C and A'B'C, one of which belongs to each sheet. However, only two-thirds of the available centers are occupied by Al+++ in the case of muscovite (Fig. 3A), whereas, in phlogopite Mg++ ions occupy all of the available centers (Fig. 3B), while in biotite, some of the Mg++ ions in the phlogopite structure are replaced by Fe++ ions (Fig. 3C). The way in which these two units are combined to give a typical mica is illustrated in Fig. 4, which according to Bragg8, gives three views of the conventional crystallographic unit cell. Four T units are arranged as shown, i.e. in two ___ -28-. _____~_._.

Fig. I. Tetrahedral Layer, Composed of Linked SiO4 Tetrahedra. The circles Represent Oxygen Atomsr the Silicon Atoms at the Centers of Tetrahedra are not shown Fig.2. Octahedral Layer. Composed of Two Plane Sheets of 0 — and OH- ions. The Red Circles Represent One Sheet, Black Circles Represent Another Sheet. Circles in Full Line Represent 0 —, in Dotted Line Represent OH7 * Represents Center of One of the Octahedra 29

Fig. 3A. Octahedra of Muscovite, A AL+++ Fig.3B. Octahedra of Phlogopite, x Mg Fig. 3 C. Octahedra of Biotite, ~ Fe ++ x Mg++ 30

7- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - - $.18I -- b = 9.o0 A Al (A) KI1< k o r -- - -- - - -0 H I oH OHi I ) o I o oAl Ao oA Alo o 1 0 R fM? F ft K (;- --- 0) —-. K.9 T 0 I oA/1' I I I OH [ J oH I 0 o 0 0 o 0 0I A1 I oAl Alo oAt Al oI I I 0 I ~ 0 OH I OH oH I'- I — — J K K K ) (C) (B) OH o / Fig. 4 The Crystal Structure of Muscovite. (A) Projected on a plane normal to a-axis. (B) Projected on a plane normal to b-axis. (C) Projected on cleavage plane. -31

7- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - pairs with the vertices of the tetrahedra pointing inwards towards one another; the two pairs are separated from one another by a plane of K+ ions (Fig. 4A). The 0 units consist of the 0 — ions of the vertices of the Si04 tetrahedra together with OH' ions at the center of each hexagon of 0 — ions and the intervening layer of metallic ions (Figs. 4A and 4C) The muscovite structure, in which only two-thirds of the octahedral centers are occupied is known as dioctahedral, while biotite and phlogopite in which all of the octahedral positions are occupied are referred to as trioctahedral, It should be noted that the crystallographic unit cell illustrated in Fig. 4 contains 8 OH" ions although it should be remembered that some of these OH" ions may be replaced by Fions in natural phlogopite. In synthetic phlogopite, all of the OH~ ions have been replaced by F" ions. S ymetry Properties and Selection Rules for OH Vibrations in Muscovite Let us now restrict our attention to these 8 OH" ions and consider a somewhat different view of the crystallographic unit cell (Fig. 5) in which the c axis is horizontal, and only the oxygens of the OH- ions are shown. The space group of muscovite has been determined by X-ray analysis5 to be C6 The symmetry elements are:- (Fig. 5): (1) A twofold (C2) axis parallel to the b axis through the center of the unit cell (2) Two centers of symmetry (i) located symmetrically with -32

I CA I IK m z z m m 70 z m m -t C -I m C) 73 z z — I m I m -4 0 "n mm FIGURE 5. A B C D E F G H ----- Crystallogrsphic Unit Cell of Muscovite A'B'C'D'E'F'GtH' ----- Bravais Unit Cell of rMuscovite 1,2,3,4,5,6,7,8 ---—.Eight OH groups in one Crystallographic Unit Cell C2 ----------— Two Fold Axis -g (B'IDIFIH) ------— Glide Plane i ----------— Center of Symmetry a, b, c -— Crystallographic Axes J

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN respect to the two groups of 0 atoms in each half of the unit cell (3) A glide plane (o-h) bisecting the unit cell horizontally i.e. BIDIFIH,. For the space group C6h, the Bravais unit cell (whiCh determines the infrared selection rules) is smaller than the conventional crystallographic unit cell we have been discussing. The Bravais unit cell is given by AtBtC'D'EtF'G1Ht and contains only 4 OH' ions. X-ray analysis has located the oxygen nuclei and our problem is to consider possible positions of the hydroge nuclei consistent with this space group. It is, of course, only necessary to determine the location of any one of the four hydrogens since the positions of the other three are then determined by the symmetry operations of the space group. Since the mass of the hydrogen is so much less than that of the oxygen and the binding forces between these two atoms are much greater than those between either of them and any other atom in the lattice, we may consider the vibrations of the OH- ions as falling into three classes: a) Stretching vibrations of the OH" ions in which the hydrogens move along the lines of the OH bonds b) Deformation vibrations of the OH ions in which the hydrogens move at right angles to the OH bonds c) Motions of the OH' ions in which the OH' ions move as rigid units. Using the methods of group theory9, the 24 fundamental modes of vibration of the four OH- ions can be put into 4 -534-..

7- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN symmetry species as shown in Table I, in which n is the number of stretching vibrations, D of deformation vibrations (pseudo rotations of the OH' ions) and T of translational motions. These last are essentially lattice vibrations involving the other heavy atoms in the structure and need not be considered in what follows. We shall also ignore the deformation vibrations in this section of the report and concentrate on the stretching vibrations which are responsible for the absorption band common to all micas (except synthetic phlogopite) near 2.8p. TABLE I Cjh E C2 i o-r n D T IR R Ag 1 1 1 1 1 2 3 f P B 1 -1 1. -1 1 2 3 Au 1 1 -1 - 1 1 2 3 P f B I -1 1 o-l 1 2 3 f p Bu I -1 aI 1 1 2 3 p f U..... _ _ _, _ _ _ _ _I_ _ __ p = permitted, f. forbidden, IR - Infrared, R = Raman According to Table I there are 4 OH stretching modes, two of which (Au, Bu) are permitted in infrared absorption, the other two (Ag, Bg) being permitted only in Raman spectra. The physical character of the Au and Bu modes is illustrated in Fig. 6, which shows projections of the unit cell perpendicular bz and az planes. The z axis is perpendicular to the a and b axes and thus makes an angle of 5~ with the c axis. It will be observed that the change of electric moment for the Au mode is......___.______________ -55-.....___________________

02 7 Ca I I I I Iz I I b - a I - - I I N~~~~~~~J 7 a.7 7 & I 0) b b a IE 4100 Z14 - 17 N I%- - z m z (A) z m m z G) 70 m m 70 rb -4 m~ B aB z m v0 C, =t 0 Cn z z Figo 60 MODES of OH Stretching Vibrations of Electric Moment Changeo Muscovite and the Corresponding I A

rmloirrlnal r rI rA AI I Ie s IAs ml l r Ir I II&III I O a l I* A Ia t- INUIIN ttKIN KttAKL.M IN III U I t * UNIVtKbI I Y VU MItKlIUAN parallel to the b axis, whereas that for the Bu mode has one component parallel to the z axis and another component parallel to the a axis. It will be observed that these two modes of vibration can be regarded as motions in which the modes for the two ions in the right and left hand halves of the unit cell are identical.but are combined in phase and out of phase with one another. Since the distance between the two oxygens in either half of the unit cell is much less than the distance between any two oxygens in opposite halves of the unit cells, we shall assume that Au and Bu give rise to a single absorption band, i.e. the separation between the Au and Bu frequencies is too small to be observed experimentally. This assumption is justified by the observation that muscovite only exhibits one OH stretching frequency at 2.75k even when examined with a prism of LiF. The position of any one of the four hydrogen atoms can be defined by 3 parameters, viz. ao, bo, and zo its coordinates with reference to the associated oxygen atom measured respectively along the a, b and z axes. We have assumed in Fig. 6 that the hydrogen atoms point away from one another but these directions could all be reversed and there will be a corresponding ambiguity in our final results. It is now possible to write down an expression for the absorption coefficient of the 2.75p, absorption band as a function of a, b, z (the corresponding displacement coordinates) and the angle of refraction r which the refracted ray makes with the z axis. Two orientations of the crystal should be -37-

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - considered (Fig. 7):'A) The electric vector of the incident radiation is kept perpendicular to the b axis and the crystal is tilted through a range of angles about the b axis. In this case the absorption coefficient b should be proportional to (4a cos r + 4z sin r)2 This absorption is due solely to the Bu species. (B) The electric vector of the incident radiation is kept perpendicular to the a axis and the crystal is tilted through a range of angles about the a axis. In this case the absorption coefficient a should be proportional to (4b cos r)2 + (4z sin r)2. This absorption is partly due to the Au and partly to the Bu specieso Experimental Results on Muscovite The results described below were obtained on a sheet of mica about 3L thick using a Model 21 Perkin-Elmer Infrared Spectrometer with a rock salt prism. The directions of the a and b axes were determined by the optical method10. Using a silver chloride polariser, the absorption of plane polarised radiation by the muscovite was investigated between 2 and 3,58 (1) with the b axis vertical for various angles of tilt about the b axis, (2) with the a axis vertical for a similar range of angles of tilt about the a axis, A typical series of spectra thus obtained is shown in Fig. 8. The results are summarized in Table II in which the first column -38

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN z (Yl (BO) Z 4- - r 4 b(Asu 1b 1 ( e O+z, ] (A) (B) Fi-g 7 Orientations of Muscovite and Electric Moment Change of OH Stretching Vibrations (A) b Axis perpendicular to plane of paper, crystal tilted about b Axis, Incident E Vector perpendicular to b Axis, (B) a Axis perpendicular to plane of paper, crystal tilted about a Axis, Incident E Vector perpendicular to a Axis. -39

'NOISSIWISNVIt %'NOISSIIWSNVti % 40

I - ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN TABLE II Tilted about b axis T zL h 1- II b fb |b || b b i r T (Obs.) (Cal. ) T (Obs.) (Cal.) -40~ - 23055 81.3.189.182 38.6.870.889 -30~ -18 ~23 78.9.225.225 40*7.853.889 -20~ -12028 75.6.273.272 41.6.856.889 -10~ - 6~17t 72.2.324.318 41.0.887.889 0~ 0 68.9.372.360 41.0.892.889 +10~ + 6017t 67.4.392.396 41,4.877.889 +20~ +12028t 64.5.428.423 41.5.859.889 +300 +18023t 62.3.449.441 39.2.889.889 +40~ +23055t 60.3.462.449 37.2.904.889 Tilted about a axis E a a aE I a i r T (Obs.) (Cal ) T (Obs.) (Cal.) -40~ -23055t 43.1.769.758 68.0.352.360 -30~ -18~23t 42.5.812.810 70.6,330.360 -200 -12~28' 42.1.844.852 71.2.332.360 -10~ - 6~17' 42.0.862.879 71.0.340.360 00 0 41.2.887.889 70.4.351.360 +10~ + 6017t 42.3.855.879 70.0.354.360 +20~ +12028t 42.9.826.852 71.2.332.360 +300 +18023t 42.9.803.810 70.8.328.360 +40~ +23055t 42.3.786.758 69.6.331.360 L -41

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN gives the angle of incidence (i), the second gives the angle of refraction (r), the third gives the percent transmission (T), and the fourth gives the absorption coefficient (4) computed from T by the equation o( loge 100 cos r T The refractive index was assumed to be 1.585 since it can be shown that for these angles of incidence, the effects of double refraction can be ignored. It will be observed that the absorption coefficients oa and o(b are very nearly constant for all angles. We define ~a and c~ as the absorption coefficients corresponding to da and ab when the electric vector is parallel to the axis of tilt. It can be readily shown that ~l should be proportional to (4b)2 and oa should be proportional to (4a)2. This is a test of our experimental error, since the coefficient should be constant for such a series of observations. However, when the electric vector is perpendicular to the axis of tilt, Ovaries with i. Using all the data from normal incidence, we have (according to the expressions above) (4a)2 = 0.36 and (4b)2 = 0.89 giving 4a 0.6 and 4b _ 0.943. Using next the data with i =-30~, r -18023' for tilt about b and E perpendicular to b we get (4a cos 18~ 23. - 4z sin 18~ 231)2 0.225 giving 4z: 0.3. If now these values of a, b and z are substituted in the above -42

r- ENG-INEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN expressions for a andocb we obtain predicted values for ~(a and b for all other angles. These values are given in the fifth columns of Table II. It will be seen that the agreement is very satisfactory. It will be noticed that in the above computations z was assumed positive. This is equivalent to saying that the two hydrogens in one half of the unit cell cannot point towards one another. This seems a reasonable assumption because if they point towards one another, then internuclear distance 0 becomes about 1.9A. Secondly it is necessary to take a positive in order to get agreement with the observed values of c( b' The sign of b is still undetermined. If, however, we choose b to be negative (according to the conventional orientation of the axes) the hydrogen assumes a much more likely position in the unit cell than for b positive. The resulting orientation of the OH group in the first layer of the Bravais cell is shown in Figure 9. Our result may now be compared with that given by Tsuboi. Corresponding to the values we find of 15~ and 58~ respectively for the angles HOB and BOA (Fig. 9), Tsuboi obtained values of 20~ and 51~. He discarded these values as improbable on symmetry considerations and replaced them with the figures 16.5~ and 60~ attributing the difference to "the vibration of the H atoms about their equilibrium positions". It is clear from our work that this last assumption is unnecessary. We can only conclude that Tsuboits measurements of the absorption coefficients are in error for some unknown reason. -43- ____

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN b _A 9 The Orientaton o Ogroup (No 1 in Fi Fig The Orientation of OH gro (No 15 in Fig A in Muscovite..HOB = 15~, ZBOA = 58~ -44

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN The work of Vergnoux, Theron and Pouzol2 enabled them to determine only the angle BOA (Fig. 9) for which they obtained a value of 59~0 Our value for this angle is 58,~ Thus our results agree with those obtained by an entirely independent method viz. birefringence measurements, Symmetry Properties and Selection Rules for OH Vibrations in Biotite The space group of biotite does not appear to have been determined by X-ray methods. We assumed at first that it was the same as muscovite (i e C6 ) but this would not account 2h for the fact that biotite shows two well resolved OH stretching frequencies near 3,u where muscovite has only one. If, however, the Bravais cell for biotite is twice as large as that for muscovite, then this doubling becomes understandableo We were led in this way to the conclusion that the space group for biotite must'be C instead of C6 but initially we assumed 2h 2h9 that this distinction only applied when the positicon:s of the hydrogen atoms were taken into account. Subsequent examination of a model of biotite in which only the positio:ns oftf the atoms heavier than hydrogen are considered has shown that biotite can belong to the CG space group. The proof will be outlined, 2h although it is hard to follow without a spatial modelo The necessary and sufficient conditions for a lattice to have a C2h space group can be described in the following way1. Take the origin of coordinates at a center of symmetry (i) and the x, y and z axes parallel to the crystallographic axes a,

-- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - b and c respectively (Fig, 5), For any arbitrary position (x, y, z) the following coordinates must be equivalent: (1) x ~ a/2, y ~ b/2, z. (2) s, y, z. (3) x y, c/2- z. (4) x, r, c/2 + z. This means that if (x, y, z) represent the coordinates of any of the atoms in the unit cell, then an equivalent atom will be found at the position given by these four transformations. It may readily be verified from a model that these- conditions are fulfilled by all the atoms in muscovite. However, condition (1) cannot be fulfilled by the Fe and Mg atoms in biotite. Since the necessary and sufficient conditions for a C4h space group are just (2), (3) and (4), (which correspond respectively to the symmetry elements i, C2 and c-g), and can be fulfilled by all of the atoms in biotite, we conclude that the space group for biotite should be Ch instead of C62h It should be remarked that the partial replacement (i.e. one quarter) of the Si atoms by Al atoms in the Si04 tetrahedra means that strictly speaking the conditions for C6 h and C 2h 2h space groups are exactly fulfilled by none of the micas. However, the conditions are fulfilled by the 0 atoms of the OH' groups and the selection rules are essentially determined by this fact. The Bravais cell for the C2h space group is exactly twice as large as that for the Ch space group. It coincides with -46

-- ENGINEERING RESEARCH INSTITUTE - UNIVERSITY OF MICHIGAN the conventional crystallographic unit cell of Fig. 5 and thus contains 8 OH- groups. The resulting 48 fundamental modes of vibration fall into 4 symmetry species as shown in Table III. Thus there are now 4 OH- stretching modes active in infrared absorption. The physical character of these four modes is illustrated in Figs. 10 and 11 together with the resulting changes of electric moment. The pair of modes shown in Fig. 10 may be expected to have the same frequency value for the same reason that the two active modes in muscovite had the same numerical value, i.e. negligible interaction across the plane of the K+ ions. The same is true for the other pair of Fig. ll. TABLE III 4,...........,.....,,. 4 b E~ 2i ~ g n *p __ _^ _ IR BR'2h E C2 4 6i h Ag 1 1 1 1 2 4 6 f p Au 1 1 1 - 1 2 4 6 p f Bg 1 -1 1 -1 2 4 6 f P Bu 1 -1 -1 1 2 4 6 p f.......~~~~~~~~~~~~~~~~~~~~~~.....,~,.;:..,,:.,, _ In order to construct Figs. 10 and 11 it was necessary to assume a direction for one of the 4 OH" groups which are inside the Bravais cell for muscovite and another direction for one of the 4 OHl groups which are outside of this cell. The orientations of all of the 8 OH- groups in the Bravais cell of the Ch space group are then fixed by symmetry. Using the same notation as for muscovite, we may now write down expressions for the absorption coefficients of the two absorption bands as functions of al, bl, Z, a2, b2, z2 (the -47-

I b C e \ b \~~L~ I ^ A, -z-' —-M —-.a Mment Chan (27 c- nd b IIA_ a I m z (a) z m m 70 z m m m 70 x z C) m 0 I z m 70 V) -- 0 "M=;c x

b C z ZA,~ z~z Ia I a z,, FIGURE 11. MODES of OH Stretching Vibrations of Biotite and the Corresponding Electric oment Change (83 band \, % Moment Change (2o835 band) I m'Z z m m z m rn -4 m 0 C) z m 0 <l> -, 0 n C( z I i

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN respective displacement coordinates of any one of the inner 4 hydrogen atoms and any one of the outer 4 hydrogen atoms) and r. Thus we obtain: For Modes of Vibration of Figure 10 (2.72k absorption band) b C[4(al - a2)cos r + 4(zl + z2) sin r]2, o b C[4 (bl - b2)]2 a C[4(bl - b2)cos r] +[4(z + z2) sin r2, and Ca 44(al- a)] 2 For Modes of Vibration of Figure 11 (2.835 absorption band) b(F[4(al + a2)os r + 4(Zl + Z2) sin r] 2, b [4(bl + b2)] a C[4(bl + bg)cos r2+[4( + z2) sin r]2, and da [4(al + a2)]2 The orientations of the crystal which should be considered for these vibrations are illustrated in Fig. 12 and 13. It should be noted that the orientations of the OH' groups here are assumed in an arbitrary way. The true values (relative) of al, bl, zl, etc. have to be determined by experimental results. We may now discuss the experimental data on biotite. Experimental Results on Biotite The same techniques were used here as for muscovite and the results are summarized in Table IV and V. The crystal section was much thicker ( 225p) than for muscovite. A typical series of spectra is illustrated in Fig. 14, while Fig. 15 illustrates the variation in the absorption coefficients of each band as the crystal is tilted about either the a or the b axis. It will be noticed in Fig. 14 that the high frequency band (2.72p) increases greatly in intensity for tilting about either the a or the b axis. Thus the change of moment for this -50

I I - ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN z z E -+r r__ (8u) tr (A<i) 4(bi-bI a -r -r 4(z,+z; (Bu) (B,() (A) (B) Fig 12. Orientations of Biotite and Electric Moment Change of OH Stretching viDrai-ons u./ u'Uu TB) similar to.Fig. 7. \JA) <atAil I J z z +r rl (8L+.).(3,4+I a,). +r1 (A )'4-(b,+ i, 4(z,-ZZ) -r (B') I, -r 4(z,-z) (Bu) (A) (B) Fig. 13. Orientation of Biotite and Electric Moment Change..'-a-".. - - ='"::-:" -. I -,A I.JAJ I of OH Stretching vp ratlons;- oo0 ua:in u. of. tchi VI.-, r~ \Jh aiu> (B) similar to Fig. 7* -51

i- ENGINEERING RESEARCH. INSTITUTE * UNIVERSITY OF MICHIGAN TABLE IV Absorption Coefficients of 2.72p Band Tilted about b axis Tilted about a axis E L b i r T-<Ur. |T ( Obs.)'b (Cal. ) a (Ob*)Iia (al. i -40~ -23o55-t 1. 053 1. 280 1. 061 1. 280 -30.-18023'.750.774.772.774 -20~0 12028'.391.362.439.362 -10~ 6~017t.079.093.109.093 0 0 0 0 0. 0 +10~ + 6017t.115.093.103.093 +20~ +12028.442.362.443.362 +300 +18~23t.779.774.795.774 +40~ +23055 1 1.097 1.280 1.109 1.280 TABLE V Absorption Coefficients of 2.83P Band ___E-Lb I-L a.i r..b (Obs.),Ob (Cal.), a (Obs.) a (Cal.) -400 -23055t.541.490.437.406 -30 -18023t.564.528.457.437.200.12028.582.559.470.463 -10~ 6017t.583.580.485.480 0. 587. 587.486.486 +10~ + 6017t.562.580.485.480 +20~ +12028t.535.559.479.463 +300 +18 23.517 *528.458.437 +400 +23055t.475.490.424.406. _.............,............. _,.......,......., -... ~.........,,,,...:.. Tilted about b axis Tilted about a axis -52

80 70 60 cn fn 50 40 1- 30 S BIOTITE. TILT ABOUT b-AXIS. 70 BIOTITE. TILT ABOUT &-AXIS. Fig. 14. Spectra of Biotite

I (A) m z m m 70 z 6) 70 m rn )Ip 70 nn crr z m, 0 +20 +40 I cn I E I a, Tilt about a E 1 b, Tilt about b cb -0.6 -0.4+ -0.4 (B) -0o2. -0.2 I I c z m -I, z z0 I I I I I I I I lb -40 -20 0 t20 +40 -40 -20 0 +2o0 +40 E 1 a, Tilt about a E ~ b, Tilt about b FIGURE 15. Variation of Absorption Coefficients (A) 2.72Y band, (B) 2.83A band.

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN mode of vibration must be almost entirely along z (or c) axis. This corresponds to the behavior predicted for the mode of vibration of Fig. 10 if al and bI are respectively nearly equal to a2 and b2. We therefore assign the 2.72p band to Fig. 10 mode. Similarly the 2.83p band is assigned to Fig. 11 mode. If there were no absorption at 2.72p for normal incidence, the change of moment should be exactly along the z axis. Investigation of the behavior of this band at low and high temperature made it appear that this residual absorption for normal incidence was due to other causes (c.f. Quarterly Report I of September 1954) and in this report we shall ignore this absorption. That means we assume al - a2 and b - b2, and we shall call them just a and b. In Table IV we shall assume it is zero as a first approximation. According to Fig. 13(A), if the difference between l, and Z2 is large, we should observe an asymmetric variation in the absorption coefficient of the 2.83p band as the crystal is tilted about the b axis to the positive (+r) or negative (-r) side of its original position. The variation of ob in Table V shows very little asymmetry indicating that zI and z2 are nearly equal. Therefore we shall also assume zI a z2 = z as a first approximation. In computing o, the refractive index was assumed to be 1.585. We may now compute a, b and z from the experimental data as follows: -55

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Using the data from the 2.83p band with normal incidence, we have (8a)2 = (.587) and (8b)2 = (.486) giving 8a - +.766 and 8b = +.697 Using next the data from the 2.72k band with i =1i30~, r: + 18023t, for tilt about b or a and r perpendicular to b or a we get (8z sin r)2 = (8z sin 18023')2. 0.774 (average value) giving 8z + 2.79. If now these values of a, b and z are substituted in the above expressions for a and o b for each band, we obtain predicted values for 0a and b for all other angles. These values are given in the fourth and sixth columns of Table IV and V. The resulting orientation of the OH group in the first layer of the unit cell is shown in Fig. 16. The sign of z can be reasonably assumed as positive because if the hydrogen atoms point towards one another the internuclear H-H distance O will be less than 1A. The signs of a and b cannot be determined by computation. These are under investigation now, and a full discussion will be given in a subsequent report. -56

-ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - z Fig. 16. The Orientation of OH Group (No. 1 in Fig. 5) in Biotite. /-HOB = 70", ZBOA X 42". -57

[ -- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - REFERENCES 1 M. Tsuboi, Bull. Chem. Soc., Japan 23, 83 (1950) 2 A. M. Vergnoux, Comptes Rendus. 238, 467 (1954) 3 C. H. Mauguin, Bull. Soc. Franc. Min 51, 285 (1928) 4 L. Pauling, "The Nature of the Chemical Band", Cornell University Press, (1942) 5 W. W. Jackson and J. West, Zeit. f. Krist 76, 211 (1930) and 85, 160 (1933) 6 G. Nagelschmidt, Zeit. f. Krist, 97, 514 (1937) 7 C. W. Brindley, "X-ray Identification and Crystal Structure of Clay Minerals", Mineralogical Society of London, (1951) 8 W. L. Bragg, "Atomic Structure of Minerals" Cornell University Press, (1937) 9 S. Bhagavantam and T. Venkatarayudu, "Theory of Groups and its Application to Physical Problems", Andhra University, Waltair, India, (1951) 10 T. R. P. Gibb Jr., "Optical Methods of Chemical Analysis", McGraw-Hill Book Company, Inc., (1942) 11 International Tables for X-ray Crystallography, Volume I, Kynoch Press, Bermingham, England, (1952) -58

-- ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN V. MAJOR CONCLUSIONS A. Barium Titanate The experimental work done on barium titanate does not support the theory of Jaynes. At present, it also does not support that of Ilegaw, but observations at longer wavelengths are required to verify this tentative conclusion. B. Diamond The work on diamond gives strong support to the idea that Type I diamonds are imperfect but does not yet establish the source of imperfection. There are probably several sources of imperfection, foreign atoms or carbon atoms in anomalous states being most strongly indicated. C. Brucite Our investigations on brucite lead to the conclusion that either the unit cell is much larger than that determined by X-ray methods which have not placed the hydrogen atoms correctly or some new effect has been found in the infra-red spectra of crystals which cannot be explained in current theories of the vibration spectra of crystals. D. Micas The work on the micas has shown that the orientation of the OH groups in muscovite and biotite are very different. There is a strong indication that biotite belongs to the C4h space group in contrast to muscovite which belongs to the C h space group. The orientations of the OH groups in muscovite and biotite have -59

-- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN not yet been absolutely determined, but it has been possible to reduce the choice of these orientations to a very limited number of possibilities. VI. FUTURE PROGRAM A. Barium Titanate Work will continue on the differences between the infra-red spectra of the various forms of barium titanate and also the spectrum of strontium titanate. Once real differences have been established, it is hoped that these will throw light on the origin of ferroelectricity in barium titanate. B. Diamond An attempt will be made to determine the nature of chemical impurities in various diamonds (Type I and Type II) by means of spectrographic (emission) analysis. C. Brucite If time and personnel are available, an attempt will be made to resolve the disagreement found here between X-ray and infrared methods of analysis of the structure of brucite, D. Micas Work will continue on the determination of the absolute orientation of the OH groups in muscovite and biotite. The over-all interpretation of the spectra of all micas will also be studied. -I -60

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - VII. PERSONNEL The following people have been engaged in the work described in this report. Prof. G. B. B. M. Sutherland, Principal Investigator Dr. R. T. Mara (November 1951 - August 1953) Dr. W. G. Simeral (June 1951 - June 1953 Part Time) Dr. C. Y. Pan Liang (March 1953 - May 1954 Half Time) Dr. T. Venkatarayudu (February - May 1954) Dr. S. Krimm ( May 15 - August 15, 1951 Part Time) Mr. H. J. V. Tyrell (September 1 - October 31, 1951) Mr. G. Allen (October - December 1953 Part Time) Mr. A. Dockrill (May 1951 - May 1954 Part Time as Laboratory Technician) VIII. Appendix I (This is a more complete version of the note published in Jour. of Chem. Physics 22:1269 (1954) SELECTION RULES FOR SOME COMBINATION AND OVERTONE LINES IN DIAMOND by T. Venkatarayudu, M.A., Ph.D., FASc. Structure of Diamond:- Diamond may be regarded as having been made up of two interpenetrating cubic face-centered simple structure of carbon atoms. Each atom of one structure is at the center of the tetrahedron formed by its four nearest neighbours of the other structure. The positions of the carbon atoms in the crystal are usually described with reference to the -61

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN crystallographic axes, which are the edges of a cube. Accordingly, the co-ordinates of the eight atoms in the unit cube are given by (0,0,0), (11/2,/2,1/2), (1/2,0,1/2), (0,1/2,1/2;, (1/4,1/4,1/4), (3/4,3/4,1/4), (3/4,1/4,3/4), (1/4,3/4,3/4). The above description is convenient for enumerating the symmetry elements of the crystal. But for a study of the frequency spectrum of diamond, it is advantageous to describe the co-ordinates of the atoms in the Bravais cell. The Bravais cell, in this case, is the parellelopiped formed by the edges 12, 13 and 14 and contains only two non-equivalent atoms (1 and 5 in the figure). (Two atoms are said to be equivalent, if one of them can be obtained from the other by means of a lattice translation. Factor Group Analysis:- It is well known that all modes of oscillation, other than those in which equivalent atoms have identical motion, are forbidden in their fundamentals both in Raman effect and in the Infra-red absorption. Normal modes in which equivalent atoms have identical motion may be studied by considering the crystallographic point group of the crystal. The effect of a translational operation of symmetry on such modes is the same as that of identity. The symmetry operations of the point group 0h7, the appropriate character table and the selection rules for the fundamental modes etc, are tabulated below with the usual notation. Symmetry modes coming under Alg, Eg and F2u are Infra-red active. We thus see that diamond has only one normal mode of oscillation which is active in its fundamental in Raman effect and forbidden in the Infra-Red _ -62-

-- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - absorption. Oh7 E 803 32 6 6S4 i 8S6 3 6C2 6C4 ki 1 1 1 1 1 1 1 1 1 o Raman Active 2g I I 1 -1 -1 1 1 1 - -1 g 2 -1 2 o o 2 -1 2 o o o Raman Active lg 3 o - -1 l 1 3 o -1 -l 1 o 2g 3 o -l 1 -1 3 o -l 1 i - 1 Raan Active lu 1 1 1 1 1 -1 - 1 -1 -1 o 2u 1 1 1 - -1l 1- -1 l 1 1 o 2 -1 2 o o -2 1 -2 o o a lu 3 0 -l1- 1 -3 0 1 1 -l o F2u 3 o - 1 -1 -3 o 1 -1 1 Translation(M) R 2 2 2 2 2 o o o o o 6 0 -6 12 -12 0 0 0 0 0 Finite Space Group Analysis:- A detailed study of the Finite Space Group Analysis is under investigation. In the following discussion, we restrict ourselves to the case where the motions of atoms separated by twice the primitive translations are identical. The repeating unit' cell is then formed by taking eight times the Bravais cell. This cell contains 16 nonequivalent atoms. (Two atoms are now called equivalent if one can be obtained from the other by twice a primitive translation,) In the figure is shown a portion of the diamond structure, The dark tircles denote atoms belonging to one simple structure whereas the white circles denote the atoms belonging to the other. 63

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN'3 I& I- - I I+ If i- ---- ir —-; \I f 11 t 1 1-' 1 I I J I I: I IIII I t FIGURE -64

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN The Bravais cell is a rhcmbohedron formed by the primitive translations T1, T2, T3 respectively obtained by joining the atoms 1,2; 1,3; 1,4;. This rhombohedron contains only two nonequivalent atoms which are numbered 1 and 5. The unit cell which we now choose is the rhombohedron formed by the primitive translations which are twice 1,2; 1,3; and 1,4;. This rhombohedron contains 16 non-equivalent atoms which are numbered 1 to 16 in the figure. The co-ordinates of the atoms referred to cubic axes are given below. 1,2,3,4: 0,0,0; 0,1/2,1/2; 1/2,1/2,0; 1/2,0,1/2, 5,6,7,8: 1/4,1/4,1/4; 1/4,3/4,3/4; 3/4,3/4,1/4; 3/4,1/4,3/4. 9,10,11,12: 1,1,1; 1,1/2,1/2; 1/2,1/2,1; 1/2,1,1/2. 13,14,15,16: 5/4,5/4,5/4; 5/4,3/4,3/4; 3/4,3/4,5/4 3/4,5/4,3/4, The group of symmetry elements now is of order 384 and they are obtained by combining the eight translations with the 48 elements of symmetry which form the crystallographic point group Oh7. The elements of this group fall into 20 conjugate classes and the appropriate character table, ymmnctry modes coming under each type are given below. The representations designated A1, A2, A3, A4 El, E2, Fl F2, F3, 4 correspond to the factor group representations Alg, A2g, Alu, A2u, Eg, Eu, Flg, F2g, Flu, F2u respectively. Al E1 F2 may be called the activity representations for Raman effect and the representation F4 may similarly be called the activity representation for the infra-red. We further give below the reduction of the product representations -65-.

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - and also the reduction of the symmetric square representations from which we can directly read the selection rules for the simple combination lines and the first overtones.

I - I z LL. 0 0 0 - | I o o o0 0 0 0o 0 0 0 0 0 0 0 0o 96" 96 9-~ 0 8o 0 0 0 0 0 0 0 0 0 0 0 O 0 ~ 9 t 91 ft ~~~~~~~~~~~~~~~~~~~~~~~~1 0 -1~~~~~~~~~~~~~~~~~~~~~~~~~~~~ L x I = IF - I I 0 i i I I I qi 4 I I a I 4 4 * d L t L I L L L U; 0 LU Z I |- T L L::3 I,,_o I I O Z 0 =w 0,~ 0 Z 0 9 0 1 t o 0 1 0 0 0 0 0 0 0 I 0~ 9 9~ 0 I ij- 0 0 0 0 0 0 0 0 o 0 0 0 1 9.~ z I z o z l:~ o o O o o o O 1 O o r I ^ - I a 0 I 0 0 e 0 0 0 T a 0 0 1 I+f~ 2 1 2O 0 T 000 0 0 T 2 0 0 I t ~t - ~ V~ 1 0- T 0 0 - o0 0 0 1o o o Z 0 1 -9 0 0 o 0 0 o o 0 0 0 0 0 0 9 9 0 0 O' - 0- 0 0 0 0 0 0 0 0 Z 0 9 9 0Z 0 0 0 - 0 0 0 0 0 0 z 0 9 C o - -0 T O I 0 T- T I 1- 1 0 -T I - 0 ~ ~- 0 I0 +- C I V 1+ 0 + i - 0 C C I 0 C - I 0 1 I II- t I 0 C T I 1~ 0 ~ C Vo~o 0 C - I- 0 Clow T T I -- 0 C I T - I 0 C Z 0 I a 0 T - 0 a 0 0 O0 IT a~ 0 0 a V-2 Z 0 a 0 V c 0 0 0 0 a T Z2 0 0 V TI t I- V I V- I VI- I' I I T- V - IV V - T- I I I I V- TI' I- I' I I I I - I - I -1 - T T'- I I i I.-Uq -7 ex.I tH 1E, IH 8' I la v jJ:5 JJ I 0 I T- I I I I- T I- II- I = I- I" I I T I - I — 0 N I I I I I I I I I T I I I I I I I I I I I I I I

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Simple Combinations: x L1 x L2 x L3 x L4 x M1 x M2 = M1 = M1 = M2 M2 - L1 L3 E2 x E2 x E2 x E2 x E2 x E2 x L1 NI2 L2 - M2 L3 - M1 MIm=LN L4 - L1 I1 L M2 - L1 + L + L4 + L4 + + L2 + NI2 Ni1 F1 F1 F1 F1 F1 F1 F1 F1 F1 F1 F1 F1 F1 F1 Fs F3 F3 F3 F3 F3 x F1 A1 x F2 = A2 x P3 = A3 x 4 = A4 x Hi - H2 x H2 = H1 x H3 = H1 x H4 - E1 x L1 = L2 x L2 = L1 x L3 = L4 x L4 = L3 X MI1 = L1 x M2 = L3 x F3 = A1 + E1 + E1 + E2 + E2 + H2 + H3 + H2 + H2 + M1 + Ml + M2 + M2 + L2 + L4 + El + F1 + F2 + F1 + F2 + F3 + F4 + F3 + F4 + H4 + H4 + H4 + H3 + 2 M1 + 2 M2 + F1 + F2 F2 x F2 F2 x F3 = F2 x F4 = F2 x H1 F2 x H2 F2 x H3 = F2xH4 = F2 x L = F2 x L2 F2 x L3 = F2 x L4 = F2 x M1 = F2 x M2 A1 A4 A3 HI HI H2 HI L1 L2 L3 L4 L1 L3 + E1 + F1 + F2 + E2 + F3 + F4 + E2 + F3 + F4 (I.R.) + H2 + H4 + H2 + H3 + H3 + H4 + H3 + H4 + M1 + M1 + M2 + M2 + L2 + 2 M1 + L4 + 2 M2 x F4 x HI x H2 x H3 x H4 = A2 = H2 = H1 = H1 - HI + E1 + H3 + H2 + H2 + H3 + F1 + F2 + H4 + H3 + H4 + H4 F4 F4 F4 F4 F4 x F4 x HI x H2 x H3 x H4 = A1 = H2 1 H -H2 - H1 + E1 + + H3 + + H3 + + H3 + + H3 + F1 + F2 H4 H4 H4 H4 -68

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN F3 F3 F3 F3 F3 F3 x L1 x L2 x L3 x L4 x M1 xM2 - L4 = L3 = L2 - L1 - L3 - L L 1 + M2 + M2 + M1 + L4 + 2 M2 + L2 + 2 M1 F4 x L1 F4 x L2 = F4 x L3 = F4 x L4 - F4 x M1 - F4 x M2 L3 + M2 L4 + M2 L1 + M1 L2 + M1 L3 + L4 + 2 M2 L1 + L2 + 2 MI A1 x A1 A1 x A2 A1 x A3 A1 x A4 A1 x E1 A1 x E2 A1 x F1 A1 x F2 A1 x F3 A1 x F4 A1 x H1 A1 x H2 A1 x H3 A1 x H4 A1 x L1 A1 x L2 A1 x L3 A1 x L4 A1 x MI A1 x M2 - Al - A2. A3 = A4 - El E2 - FI = F2 - F3 = F4 - H1 - H2 = Hg = H4 = Ll = L2 - L3 = L4 _ Ml = M2 A2 x A2 = A1 A2 x A3 A4 A2 x A4 A3 A2 x E1 E1 A2 x E2 E2 A2 xF1 = F2 A2 X F2 = F A2 x F3 F4 A2 x F4 F3 A2 x H1 = H3 A2 x H2 = H4 A2 x H2 = H A2 x H4 H2 A2 x L = L2 A2 x L2 =L1 A2 x L3 L4 A2 x L4 L3 A2xM1 x M1 A2 x M2 M2 A3 x A3 = A1 A2 x A4 = A2 A3 x E1 E2 A3 x E2 E1 A3 x F1 F3 A3 x F2 = F4 A3 x F3 F1 A3 xF4 - F2 A3 x H1 - H A3 x H2 = H4 A3 x H3 H3 A3 x H4 H2 A3 x L1 -L3 A3 x L2 L4 A3 x L3 L1 A3 x L4 =2 A3 x M1 =M2 A3 x M2 = M A4 x A4 A4 x E1 A4 x E2 A4 x F1 A4 x F2 A4 x F3 A4 x F4 A4 x EI A4 x H2 A4 x H3 A4 x H4 A4 x L1 A4 x L2 A4 x L3 A4 x L4 A4 x M1 = A1 = E2 - E1 -F4 -F3 = F2 = F1 - H2 = H1 = H4' L4 = L3 - L2 = L1 = M2 A4 x M2 - M1 -69

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - E1 x E1 = A1 + A2 + E1 E1 x E2 - A3 + A4 + E2 E2 x E2 = A1 + A2 E2 E1 x F1 = F1 + F2 E2 x F1 - F3 + F4 E1 x F2 - F1 + F2 E2 x F2 F3 + F4 E1 X F3 = F3 + 4 E2 x F3 = F1 + F2 E1 x F4 = F3 + F4 E2 x F4 = F1 + F2 E1 x H1 H1 + H3 E2 x H1 - H1+ H3 E1 x H2 = H2 + H4 E2 x H2 H2 + H4 E1 x H3 = H1 + H3 E2 x H3 = HI + H3 E1 x H4 H H2 + H4 E2 x H4 - H2 + H4 H1 H1 H1 H1 H1 H1 Hi H1 H1 H1 x H1 x H2 x H3 x H4 x L1 x L2 x L3 x L4 x M1 x M2 = A1 - Fi = A2 = F1 = L1 _ Li m L1 = L2 - L1 = L1 + A3 + E14+ + F2 + F3 + + A4 + E1 + + F2 + F3 + + L3 + M1 + + L4 + M1 + + L3 + M1 + + L4 + M + + L2 + L3 + + L2 + L3 + E2 F4 2 F4 W2 M2 M2 M2 L4 L4 + F2 + F4 + + H1 + H2 + + F1 + F3 + + H1 + H2 + H1 H3 H1 H3 + H2 + H4 + H2 + H4 + H3 + H4 (Both) + H3 + H4 (Both) + 2 M1 + 2 M2 + 2 Ml + 2 M2 H2 H2 H2 H2 H2 H2 X H2 = A1 x H3 F1 x H4 -. A2 x L1 = L2 x L2 L1 x L3 = L1 + A4 + E1 + F2 + F3 + A3 + E1 + L3 + M1 +L + 14 + L4 + M + E2 + + F4 + + E2 + + M2 + M2 + M2 F2 + F3 + H1 + H2 + H3 + 4 Hi + H2 + H3 + H4 F1 + F4 + H1 + H2 + H3 + H4 (Raman) -70

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN - H2 x L4 H2 x M1 H2 x M2 = L2 - L1 L1 - L1 + L3 + L2 + L2 +M2 + L4 + L4 H3 x H3 A1 H3 x H4 = F1 H3 x L1 - L2 H3 x L2 L1 H3 x L3 L2 H3 x L4 = L1 H3 x M1 = L1 H3 x M2 L1 + A3 + F2 + L4 + L3 + L4 + L3 + L2 + L2 + A4 + L4 + L3 + L3 + L4 + L2 + L2 + E1 + F3 + M1 + M1 + M1 + M1 + L3 + L3 + E1 + M1 + M1 + MI + M1 + L3 + L3 + E2 + F4 + M2 + M2 + M2 + M2 + L4 + L4 + E2 + M2 + M2 + M2 + M2 + M2 + L4 + L4 + 2 (M1 + M2) + 2 (M1 + M2) + F2 + F4 + H1 + H2 + H3 + H4 + Hi + IH2 + H3 + H4 + 2 (M1 + M2) + 2 (M1 + M2) + F2 + F3 + H1 + H2 + H3 + H4 + 2 (M1 + M2) + 2 (Ml + M2) H4 x H4 = A1 H4x Li - L1 H4 X L2 a L2 H4 X L3 L2 H4 x L4 L1 H4x M1 = L1 H4 X M2 L1 L1 XL1 L1 xL2 L1 x L3 L x L4 L1 x M1 L1 x M2 L2 x M = A1 = A - A3 = A4 = E1 - E2 - E1 + F2 + + F1 + + F4 + + F3 + + F1,'.+ + F3 + + F1 + 11 H2 H1 H3 F2 F4 F2 1 + H4 + H3 L2 x L2 = A1 + H2(I.R) L2 x L3 = A4 + H4 L2 x L4 A3 + HL + H2 + H3 + H4 + HI + H2 + H3 + H4 + H1 + H2 + H3 + H4 + F2 + H1 + H4 + F3 + H3 + H4 + F4 + Hi + H2 (Raman) (I.R.)

- ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN L2 x M2 - L3 x L3 L3 x L4 = L3 x M- L3 x M2 L4 x M1 - L4 x M2 M1 x M1 M1 x M2 M2 x M2 - E2 A1 A2 E2 E1 E2 E1 A1 A3 A1 + F3 + F1 + F1 + F3 4 F1 + F3 -+ F1 + A2 + A4 + A2 + F4 + H1 + H2 + F4 + F2 + F4 + F2 + E1 + E2 + E1 + H1 + H4 + H3 + H1 + H1 + H1 + Hi + 2 + 2 + 2 + H2 + H3 + H4 L4 x L4 A1 2 + + H + H4 + H2 + H3 + H4 (I.R.) + H2 + H3 + H4 (Raman) + H2 + + + H4 + H2 + H3 + H4 (F1 (F3 (F1 + F2 + H1 + H2 + H3 + H4) + F4 + H1 + H2 + H3 + H4) (I.R.) + F2 + H1 + H2 + H3 + H4) FIRST Overtones:....: _:...:..-... (A1) 2 (A) 1 (A2) = 2 (A3) - 2 (A4) = 2 (E1) 2 IA1 A1 A1 A1 + E1 (F1) 2 (H1) - 2 (L1) - 2 (M1) - 2 A1 + E1 (F2) (F3) (F4) A1 + E1 + F2 (H2) - (H3) - (H4) - A1 + A4 + E1 + E2 + F2 + H + H4 2 2 2 (L2) (L3) (L4) - A1 + F2 + H1 + H4 2 2 2 (M2) A1 + E1 + F1 + 2 F2 + 2 H1 + H3 + H4 2

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN It follows from the previous analysis that the combination lines H1 x H2 and HI x H4 are active both in Raman Effect and Infra-red absorption. The author's sincere thanks are due to Professors D. Mo Dennison and G. Be B. M. Sutherland for their kind interest in this work. -73

Reprinted from JOURNAL OF THE OPTICAL SOCIETY OF AMERICA, Vol. 43, No. 11, 1100-1102, November, 1953 Printed in U. S. A. The Infrared Spectrum of Brucite [Mg(OH)2]* R. T. MARAt AND G. B. B. M. SUTHERLAND University of Michigan, Ann Arbor, Michigan (Received August 17, 1953) The infrared spectrum of single crystals of brucite [Mg(OH)2] has been examined under high resolving power between 2 and 3,u. It contains at least 16 bands most of which are shown to be OH stretching frequencies and which exhibit a variety of polarization properties. It follows that the unit cell of brucite must be much larger than had been previously assumed and that the positions of the hydrogen atoms have been incorrectly assigned from x-ray data. INTRODUCTION IN the course of a study of the infrared spectra of a number of crystalline materials (including mica) it recently became important to investigate in detail the spectrum of a crystal of known structure containing hydroxyl groups or ions. Furthermore, it was desirable to have a crystal in which the OH groups (or ions) were all oriented in the same direction and were not hydrogen bonded. According to the x-ray work of Bernal and Megaw,' magnesium hydroxide [Mg(OH)2] in the form of brucite crystals fulfills both criteria. In order to see whether the latter was fulfilled, our first action was of course to see what Coblentz2 had recorded on the spectra of crystals containing hydroxyl groups. In a research dealing with the differences between the infrared spectra of water of crystallization and water of constitution, Coblentz noted that the infrared spectrum of brucite appeared to be anomalous. All the other compounds that he had studied, containing OH groups and ions, showed a characteristic band at 2.9p, to 3.0/M, but brucite was peculiar in that it exhibited a band with a strong maximum at 2.5ku with indications of weaker maxima near 2.7/t and 3.0u. This "anomaly" was very satisfactory from our point of view since it indicated that any hydrogen bonding effect in brucite must be much weaker than it is in alcohols, for instance, where the free OH band is shifted (as in water) from 2.75,u to 3.0/.. In this paper we present the preliminary results of our work on the spectrum of brucite, using polarized radiation and high resolving power on single crystals in various orientations. This spectrum has turned out to be extremely complex and of great significance, especially in the relation of infrared to x-ray methods of investigating molecular structure in the crystalline state. EXPERIMENTAL RESULTS The most striking new feature revealed by our reexamination of the infrared spectrum of brucite is the discovery of a highly complex structure in the band observed by Coblentz near 2.5y. The spectrum of a cleaved section of brucite with the incident beam parallel to the c axis (i.e., normal to the cleavage plane) is given in Fig. 1(A). This spectrum was obtained with a Perkin-Elmer Model 21 double-beam spectrophotometer equipped with a rock salt prism. While the early work showed absorption in this interval with maximum absorption near 2.5/. [the approximate position of the most intense band in Fig. 1(A)], none of these details were available to Coblentz, who chose only a few points between 2u and 3g for his point-by-point plot. The strongest absorption band is found near 2.48,, and weaker ones are observed at roughly 2.30g,, 2.65/u, 2.83/t, and 3.07,. It is to be noted that no band is observed near 2.75/u, which is the approximate location of a "free" OH vibration band in many compounds. However, the four principal absorption maxima are located in a roughly symmetrical pattern about this wavelength. The remainder of the spectrum out to 15A for this crystal orientation is generally in agreement with that reported by Coblentz and will not be discussed further in this paper. If the crystal is inclined so that the c axis is no longer parallel to the incident beam, then a new band appears near 2.73,u, and its intensity increases with increasing angle between the c' axis and the incident beam [Fig. 1(B) and 1(C)]. Polarization spectra of a crystal tilted in this way indicate that the 2.73-/n band is present in the spectrum only when the incident electric vector has a component parallel to the c axis of the crystal. Identical results are obtained when the crystal is rotated about any axis that lies perpendicular to the c axis. All the bands that appear on the spectrum when the incident beam is parallel to the c axis are also observed z6c 0 4o n, t z2 ct 0~ 30~ 60 A B C 2 2 3 2 3 2 3 2 3 2 3 i. FIG. 1. Infrared spectrum of brucite oriented with c axis parallel to the incident beam and at angles.of 30~ and 60~. * Supported by the U. S. Army Signal Corps. t Present address, Department of Physics, Gettysburg College, Gettysburg, Pennsylvania. J. D. Bernal and H. D. Megaw, Proc. Roy. Soc. (London) A151, 384 (1935). 2 W. W. Coblentz, Investigations of Infrared Studies (Carnegie Institution of Washington, Washington, D. C., 1905-1908). 1100

1101 T. T. MARA AND G. B. B. M. SUTHERLAND Vol. 43 when the beam is normal to the c axis, and in addition the 2.73-/u band and its overtone are present. The polarization effects for this orientation are very marked. The polarized spectra from 2/u to 3.25/u are shown in Fig. 2. The bands at 2.30,u, 2.73,u (and probably also that at 2.83A) exhibit maximum intensities when the electric vector is parallel to the c axis. The absorption near 2.48/t changes contour for the two polarization directions, and it appears to have a diminished intensity when the electric vector is parallel to the c axis. The 2.65/u and 3.07,u display their maximum intensities for the electric vector perpendicular to the c axis. Since a rock salt prism does not have large dispersion below 8/u, a LiF prism was used to scan the 2/u- to 3.2-At region. Portions of the spectra with this higher resolution are given in Fig. 3. These spectra are for orientations of the crystal with the c axis parallel and perpendicular to the direction of the incident beam. It is immediately seen that the absorption maxima in Figs. FIG. 2. Polarized infrared spectra of brucite with incident electric vector E parallel and perpendicular to the c axis. o.L) (n z ct MICRONS. FIG. 3. Portions of infrared spectra of brucite for crystal c axis oriented parallel and perpendicular to the incident beam. the c axis. Those values that are in brackets represent bands which may be present for a particular orientation but which may be obscured by neighboring absorptions. Between the time of Coblentz's and our observations, other infrared studies of brucite have also been made by Plyler,3 Yeou Ta,4 Duval and Lecomte,5 and Louisfert,6 But none of this work revealed anything more than Coblentz had in the region of the OH stretching fundamental. DISCUSSION If the structure of brucite had been as postulated by Bernal and Megaw, then the OH stretching frequency should have given rise to a single sharp absorption line near 2.75g,. This follows from their contention that TABLE I. Infrared absorption bands of brucite. E lc axis ElIc axis 2.06t/ 2.06t1 2.19 2.19 P 2.24 2.24 2.32 2.32 P (2.45) 2.45 P 2.47 (2.47) N (2.49) 2.49 P 2.53 2.53 P 2.64 (2.64) N 2.71 2.71 P 2.74 P 2.83 2.83 P(?) 2.97 2.97 3.01 3.01 3.06 3.06 N 3.08 P 8 E. K. Plyler, Phys. Rev. 28, 284 (1926). 4 M. Yeou Ta, Compt. rend. 211, 467 (1940). 5C. Duval and J. Lecomte, bull. Soc. chim. 8, 713 (1941); Bull. soc. franc. mineral. 66, 284 (1943). 6 J. Louisfert, J. phys. radium 8, 21 (1947). 1 and 2 are composed of several bands. The absorption complex near 2.5/i is especially interesting, since it consists of four individual absorption maxima, only one of which is common to both orientations. Also, the frequency shift in the band near 3.07/. is of interest. While the high resolution spectrum of the absorption near 2.73/, is not reproduced here, we can report that it is composed of at least two bands at 2.71tA and 2.74M, each of which exhibits its maximum intensity when the c axis is oriented perpendicular to the incident beam. In all, sixteen bands have been observed between 2M and 3.1/i in the spectrum of brucite, and all of these are listed in Table I. Those listed in the first column are observed in the spectrum when the incident electric vector is perpendicular to the c axis, and those in the second column appear when the electric vector is parallel to the c axis. The polarization properties are also given, where P(N) indicates maximum absorption for the incident electric vector E parallel (normal) to

November 1953 THE INFRARED SPECTRUM OF BRUCITE [Mg(OH)21 1102 the unit cell contains only two OH ions and from the rules set up by Bhagavantam and Venkatarayuda,7 Halford,8 and Hornig9 for the infrared spectra of crystals. That is the OH normal modes of a unit cell would consist of simply the in-phase and out-of-phase OH vibrations. One of these gives a zero net dipole moment change and hence is infrared inactive, leaving only one infrared active frequency associated with the hydroxyl vibrations. This band should show perfect polarization, with the change of moment parallel to the c axis. Such a band is indeed observed by us, but there are in addition at least 15 other bands in the immediate neighborhood exhibiting a variety of polarization properties. It might be argued that these represent combination vibrations with low lattice frequencies involving the Mg++ ions. However, this cannot be so, for we have examined the spectrum of Mg(OD)2 and 7 S. Bhagavantam and T. Venkatarayuda, Proc. Indian Acad. Sci. A9, 224 (1939). 8 R. S. Halford, J. Chem. Soc. 14, 8 (1946). 9 D. F. Hornig, J. Chem. Soc. 16, 1063 (1948). the complex pattern of bands is moved by a constant factor (nearly V2) to longer wavelengths. It follows that most of the bands observed between 2t, and 3.1,g are true OH stretching frequencies, although a small number of them could conceivably be combinations of OH stretching fundamentals with OH deformation lattice modes. This means that the unit cell for brucite must be very large indeed, containing at least as many OH- ions as there are OH stretching fundamentals observed. Furthermore, from the polarization properties of these bands it is certain that the positions of the hydrogen atoms have been incorrectly assigned from the x-ray data. A full treatment of the problem together with a discussion of interesting features of the brucite spectrum at other wavelengths is reserved for a later paper. Our purpose here was twofold: (a) To show that one of the pebbles picked by Coblentz on the infrared beach as of some interest is indeed a very fascinating one when examined by modern instruments; (b) to demonstrate the much greater sensitivity of the infrared method (as compared to the x-ray method) in deciding about the positions of hydrogen atoms in crystals.