Raman, i.r. reflection, and emission spectra of sodium β-alumina

Spctrocbimia Acta, Vol. 3Sh pp. 685 to 694 @Pngunon Press Ltd., 1979. Printed in Great Britain

Raman,

is. refkctiob and emission spectra of !mdium /3ahnnina* Roow Fancrrt and J. B. BATES

Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, U.S.A. (Receiwd 6 February 1978) Abstract-The Raman, i.r. reflection, and emission spectra of single crystal sodium /&ahunina were measured over a wide range of temperatures. Symmetry assignments of the normal modes based on the stoichiometric crystal structure are proposed. The vibrational dynamics are analyzed in terms of a model invoking a vibrationally decoupled single spine1 block, and simiiaritiesin the distribution of normal mode frequencies in MgAlsO, and Nab-Af20s are discmsed. Temperature dependent ef%cts on the spectra are also presented. SYMMEl-RY BASED VlBR.4TlONALANALYSIS

INTRODUCTION

Solids which exhibit superionic conductivity are of current interest because of their potential use as electrolytes in batteries. These materials are characterized by high ionic conductivity at temperatures well below the melting point due to the unusually high mobility of a constituent ionic species. The class of @huninas provide several examples of superionic conductors; the technologically most important and most widely studied being sodium /Lahtmina (NajLAIsOs). Many techniques including i.r. [l, 23 and Raman spectroscopy [S-S] have been used to investigate the properties of jLalumina Polar&d i.r. reflection spectra of Na and A&AlsOs measured at 300 K were reported by BARKERer al. [2] and a linear chain model was proposed to account for low frequency vibrations of the sodium and columnar oxygen ions. The sodium ion vibration associated with the attempt mode has been studied in detail by Raman scattering [33 and i.r. reflectivity [2, 63. However, additional low frequency Raman bands assigned to combined vibrations of sodium ions and columnar oxygen and the i.r. and Raman bands which arise from modes of the spine1 block have not been carefully examined. In this paper, we report the results of an extensive study of the pdarixed Raman, i.r. reflection, and ir. emission spectra of Na&Al,Os measured over a temperature range from 12 to 1073 K. The spectra are compared to the modes predicted from full (D& factor group selection rules, and it is shown that a model based on a lower factor group symmetry appropriate to the spine1 block sublattice adequately describes those regions of the spectra which arise primarily from intramolecular modes of the spine1 block. Similarities in the vibrational normal mode frequencies between Nab-AlsOs (MgAlsO,) will be described.

Sodium /?-alumina crystallixes in the hexagonal system in the space group gb (Ws/mmc) with one formula unit in the primitive cell [7]. The stoichiometric formula t$it is given by NasO . 1lA1sOJ, but the crystal contains an excess of Na+ ions (-25x), which is responsible for its high ionic conductivity. As illustrated in Fig 1, the structure consists of alternating layers of spinel-like blocks composed of ahiminum and oxygen atoms separated by mirror planes, with two blocks and two mirror planes in a primitive unit cell. A spine1 block consists of four layers of oxygen atoms in closest cubic packing with both octahedrally and tetrahedrally coordiited aluminum atoms. Each

(a)

(b)

and spine1

*Research sponsored by the Department of Energy under contract with Union Carbide Corporation. tPermanent address: Department of Chemistry, University of Oklahoma, Norman, OK 73019, U.S.A.

Fig 1. Perspective drawings of the unit cell of Nab-AlsO3 and surrounding~toms: (a) cell with octahedrafly coordinated aluminum ions (small circles); (b) cell with tetrahedrally coordiited aluminum ions. Sodium ions (large shaded circles) are shown on Reevers-Ross &es. Large opm circles represent oxygen ions in (a) and (b). 685

Roosa Faecxi and J. B. BATBS

686

parentheses is in the SchoenGea notation describing the point symmetry of the site [9]. The reps in Table I were derived from correlation diagrams using a technique reviewed by FATELEY et al. [ll]. The tables by BOYLE [12] were used in some cases to determine the correct choice for a site orientation. In the present situation, non-equivalent sites of the same symmetry have the same orientation and therefore the same r. The results in Table l(B) can be used to determine the reps for sets of atoms. For example, the reps contributed by the four non-equivalent sets of aluminum atoms are givenby

mirror plane contains one or more sodium ions and one columnar oxygen atom which is bonded to two tetrahedrally coordinated altqinum atoms in the adjacent spine1 blocks above and below the plane. In the stoichiometric compound, each mirror plane would contain one Na+ ion located on a 2d (Beever+Ross) site (see below). The excess Na+ ions preferentially occupy the 6h (mid-oxygen) sites, but some of the excess ions may occupy the 2b (anti-Beevers-Ross) sites, especially at elevated temperatures [8]. The fifty-eight atoms in the stoichiometric unit cell give rise to 171 k=O optics modes which can be characterized according to the Deb factor group of the crystal using standard group theoretical techniques. The important crystallographic data, taken from the work of PETERS ef al. 171..and the results of the analysis are given in Table 1. The irreducible representations (reps) contributed by atoms at the various sites are denoted by r(C,), for example, where the symbol in

I-Al= r(C3 + 21-(CS,)+ r(k),

since the Al atoms occupy one set of C, sites, two sets of CSVsites, and one set of D3, sites. The contribution to T(Dsh), the reps for vibrational motion of Na/.?-A1203 at k==O, from various atom groups in the unit cell can be determined from the results in Table l(C). The reps

Table 1. Irreducible representation for atom diiplacemcnts and k = 0 selection rules in sodium fl-alumina A.

Crystallographic

Data

(a)

Atom

Occupied

00)

12(k)

csbd)

Al(l)

O(2)

12(k)

cs

Al (2)

‘3v(‘d)

Al

.

O(3)

4(f)

O(4)

4(e)

O(S)

2(c)

c3v D3&)

Na(l)(d)

2(d)

Dyl

B.

Irreducible

r(c,)

=

2A

+A lg

UC2J= r (C3J=

Representations + 28 29

AIQ+A2Q Alg

r(D3,)-

+B 19

+B

for

+ 29

3E

+ 3E

+59+ +5g

+B19

2g

.

Irreducible

c3v Djd (C;)

Na(2)

6th)

C2” (C;l)

+A

lu

Sites

+ 2A

+E2g

+A +A +A +A

r A!L rO ?Na(l)-

for

Atom Sets

2u 2u 2u

+B +B

I”+

2B2u+

35”+

3E2u

lu

+B2u+

2El”

+E2u

+B2u

+Elu

+E2”

2u 2u

+El” +B2u

and Selection

=

r(cs)+

2r(c3V)+r(D3d)

-

2r(cs)+

2r(c3V)+r(D3h)

T(D3h)

c3v

4(f)

2(a)

+E2~

Representations

cs

Al (4)

r(D3d)=

C.

Symnttry(c)

4(f)

(3)

2E2g

Blg

Site

12(k)

Occupied

19

19

(1)

+E\u

Rules

+E2”

Raman, i.r. reflection, and emission spectra of sodium /?-alumina

687

Table 1 (Cont.) i sb

=

3A2Q+

ll;Elu+

14E2u =

L

-

rO(5)+rNa(l)

r

=

P sb +T mp-w

OP

Raman

106 19 +

lOA,9+

and

Infrared

38 29 + 13E19 + 13Ez9+ 3A,u +

28, g+

E

19

E29

2A2”+’

ao2+a2 ; c2 (a’c, (a’

3B,u+ llB2u+

2Elu

(e)

Activity

A19

2E2g+

llA2”+

A

2u

c

ac) 2

-a

2

Elu

(a*,a)

,ae’)

‘*From Ref. 3. (b’Nwnber of equivalent sites and Wyckoff notation. @‘Siteorientation in parentheses See text. “the ordered position on Reevers-Ross sites was assumed. “‘The ad, and c are orthogonal axes, where c is the crystallographic c axis.

for the 171 optic modes of the stoichiotnetric are given by &dil+rO(S)+

rNatI)-mg

unit cell

(2)

where r(T)=A2.+EIU are the reps for the acoustic modes. These can be divided into contributions t?om the fifty-four atoms in the spine1 block (r,) and the four atoms in the mirror pfanes Cr,,,. The results in Table l(C) show that, based on DsL symmetry, there are predicted thirty-eight Raman active modes (IOAr, +13E,,+lS&,J and twcnty-aevcn i.r. active modes (12 .4,,+15E,&. From the spine1 block, there are predicted thirty-six Raman active modes and at least twenty-three ir. active modes (assuming all three acoustic modes derive from spine1 block motion). ExPERIMENTALPRocEDuREs The crystals used in this study were cut in thin section; from a commercially grown bottle [13] exposing faces of about 1 cm’ surface area containing the optic axis. The faces were polished with an ethanol slurry of 0.3 p alumina. The crystals tended to deave very. easily perpendicular to the optic axis partictilarly after prolonged exposure to the atmosphere and were therefore stored in mineral oil until studied. In this study, an orthogonal set of crystal axes am denoted by a&, and c where c is the crystallographic c axis. From Laue back reflection patterns, the a axis was found to be about 22’ from the (010) crystallographic axis. The Raman spectra were recorded using an instrument described elsewhere [14]. The 488.0 and 514.5 run lines of an argon ion laser operating with an output of 600 mW were used as excitation sources, and the spectral resolution was about 5 cm- r. Sample cooling between 12 and 300 K was provided by mounting the crystab on the cold finger of a closed cycle helium refrigerator. The sample temperature was determined between 12 and 70 K by measuring the ratio of the Stokes to anti-Stokes scattering intensity of the Es, phonon at -100 cm-‘. Above 70K the temperature was measured by a gold-chrome1 thermocouple attached to the

cold finger. Raman spectra above 300K were measured using a high temperature furnace in which the crystals were held in graphite cells placed inside a silver cell holder [15]. The sample temperature was estimated with a chromelalumd thermocouple located inside the silver cell holder near the sample. The i.r. reflection spectra were recorded at 300 K on a Reckman IR-12 i.r. spectrometer using a reflection accessory with a 4 : 1 linear image reduction and an average angle of incidence of 15”. Infrared emission spectra were measured at temperatures from 373 to 773 K using a Fourier transform spectrometer. The spectra were recorded as the ratio of the sample radiancy to the radiancy of the empty sample holder at the same temperature. This ratio represents qualitatively the emission spectrum or emissivity of the sampfe. The resolution in the i.r. measurem ems was about 8 cm-r. A wire grid polarizer was used in the rdlection and emission measurements to control the polarization of the light reaching the detector. RRSULTS AND MSCU6610N Symmetry based assignments The frequencies of the Raman bands observed at 12 K are listed along with the appropriate symmetry ape& assignment in Tabk 2. Representative spectra are shown in Fig. 2 for several scattering geometries. The assignments in Table 2 were based on a comparison of the polarization dependence of band intensities with the selection rules in Table l(C). The II(cc)d qxetrum was useful in distinguishing between AI, and E1, modes, since both of these modes appear in the &‘d)c spectrum. Also, several weak bands were identi6ed in the a(c spectrum that were not observed in a(a’d)c scattering. These bands arise from A ts modes in which the induced dipole moment and, therefore, the atom displacements are parallel to the c axis. There is some ambiguity in a few of the assigmnents in Table 2 since it was occasionally d&ult to distinguish the case in

RooaaFaacn andJ.B.B~m

688

Table 2. Frequencies and assignments of the bands observed in Raman spectra of sodium Balumina at 12 K Frequency

-1

(cm 1

Assignment

65

Alg

258

?. 525

E29 A

782

1gtE29

795

Al9 E

El9

773

El9 E

Al9

710

Alg

330

lgPE2g

694

Elg

327

E

657

Alg

310

471

645

Elg

163+

474

607

Alg

117

424

606

E2g

110+

Assignment

557

Al9

100

-1 (cm )

553

E2g

90T

363

Frequency

*I9

802

19

*I9

993

E29

Alg

915

*I9

19

Al9

tweak bands observed only in a(cc~ scattering

which two modes have identical or nearly identical frquencies and belong to different symmetry species from the case in which one mode appears in d&rent polarizations due to spillover resulting from misalignment of the crystal, inhomogeneities in the crystal, or breakdown of the selection rules due to the defect structure or disorder in the crystal In these measure merits, the polarization discrimination in general seemed to be good Thus, the following procedure was adopted for &rs of bands which occurred at the same frequency in different polarizations, requiring the assignment of different symmetry species If the intensity of the weaker band was roughly less than 10% of the intensity of the stronger band, the weaker feature was assumed to result from spillover of the more intense mode. This arbitrary choice somewhat simplifies the assignments but may diskninate against weak modes coincident in frequency with strongly scattering ones. The transverse optic mode frequencies determined from the re5ection spectra at 300 K, illustrated in Fig 3, and those determined from the emission spectra recorded at 473 and at 773 K and illustrated in Fig 4 are listed in Table 3. Since reliable absolute reflectivity data were unavailable, the transverse and longitudinal optic mode frquencies could not be calculated from a Kramers-Kronig transformation of the spectra Therefore, the TO mode frequencies were estimated from the lower frquency inflection points of the broad bands

and from the retlectivity maxima in the case of narrow reflection bands. The emissivity of a semi-transparent material at frequency v and temperature T is given by [16] & _(l

-rXl-0 1-rt

’

(31

where the reflectivity, r, and transmissivity, t, are also functions of v and r In regions where t is small, Eqn. (3) reduces to E-l-r,

(4)

so that the emission spectrum is a measure of the reflectivity at very near zero angle of incidence. The procedure used to determine the TO mode frequencies from the emission spectra was analogous to that used with the relktion data The agreement between the frequencies measured from the relkction spectra at 300K and those observed in the emission spectra at 473 K is generally good, especially for the weaker reflection bands. The discrepancies between these data are largely due to errors in estimating the TO frquenties from the inflection points of the broad reflection and emission bands rather than the difference in temperature between the two measurements. The emission band observed at -510 cm-’ in the Ellc spectrum(Fig. 4) was not apparent in the corresponding

689

Raman, i.r. reflection, and emission spectra of sodium g-alumina

SODIUM BETA ALUMINA TP (2’K

900

800

700

600

500

400

300

2Qo

(00

FREOUENCY km-‘)

Fig. 2. Raman spectra of sodium jhhunina in various scattering geometries. The spectra have been vcrtically disphcd for clarity of preseutation. Full scale intensity in each case is 1000 cps. reflection spectrum (Fig. 3) nor was it reported in the earlier study [Z]. It is interesting to consider the vibrational -modes of Na/LAlrOs above 250 cm-‘. Since similar vibrational frequency diitribution patterns were observed in the lithium, sodium, potassium, and rubidium isomorphs [4], it is reasonable to assume that these higher frequency modes originate in the spine1 blocks. A comparison of the number of Raman active modes predicted to originate in the spinel block (Table l), lOA,,+ 13E,,+ 13E2, with the number of observed Raman bands (Table 2), 12A1,+8E1,+3Es, shows that less than half of the predicted total number of degenerate modes was identified. On the other hand, the predicted number of ix. active spine1 block modes, lOAr,+ 13E,, agrees well with the number of i.r. bands identified above 250 cm- ’ in the reflection spectra (Table 3), 12Ar,+ 16EI, The structure of Nafi-A1sOJ depicted in Fig. 1 suggests that, to a Crst approximation, the vibrational modes within a spine1 block may be considered to be dynamically decoupled from the modes of adjacent blocks. As far as these modes are concerned, /3-alumina can be viewed as a layer com-

pound with a primitive unit cell consisting of one spine1 block. A schematic diagram of this reduced lattice model is shown in Fig 5. The reduced lattice is formed from. the alternate spine1 block layers, ignoring the columnar oxygen ions. By comparing the coordiites of equivalent positions, it can be shown that the unit cell of the reduced structure belongs to the space group, D&,. The selection rules for the optic modes of the reduced structure can be determined from the correlation diagram in Table 4. From the results also given in Table 4, the predicted Raman active modes are lOA,,+ 13E, and the predicted i.r. active modes are lOAs.+ 13E, These predictions agree much better with the observed number of Raman and i.r. bands of each symmetry type occurring above 250 cm-‘. It should be noted from the correlation diagram in Table 4 that both the El, and El, modes under Dbk become E, modes under a Dsd symmetry designation. The AI, and Al, modes are unchanged, while the El, modes of Dhhare simply relabeled as E, modes under D3,+The reduced lattice model provides a rather satisfactory resolution of the problem of the discrepancy between the number of observed and calculated Raman

690

Rooaa Faac~ and J. B. BATES

II

I

I

I

I

IJI

I

9008007m600soo4003m400

I

I

I 300

FREQUENCY km-’

1

Fig. 3. Polarized near-normal incidence reflectivity spectra of sodium p-alumina with faces cut parallel to and pqawkAw.to

active modes with a simultaneous close agreement between the number of observed and calculated i.r. active modes. Furthermore, the preservation of the inversion center in the reduced structure is in agreement with the result that few coincidences were found between the Raman and i.r. frequencies observed above 250 cm-l. Comparison with spine/ The frequency distribution of the normal modes in spinel, MgA120*, may be expected to provide some additional insight into the origin of the spine1 block modes of Nab-A120J. The spine1 blocks in Na/?-AI,OB are structurally identical to the MgA&O, spine1 provided aluminum atoms are substituted for magnesium atoms in the latter. This substitution involves a small mass difference although the bonding may be expected to be somewhat different. It is therefore instructive to look for similarities in the distribution of normal mode frequencies in MgA&O* and Na&4120,. The i.r. reflection and Raman spectra of MgAIzOd havi been measured [ 171, and symmetry based normal mode assignments have been given by WHITIZet al. [17, 181. Raman measurements of oriented single crystals revealed an Al, mode at 772 cm- ‘, an E, mode at 410 cm-‘, and 7”, modes at671,491 and 311 cm-‘. The reflectivity spectrum was analyzed by a KramersKronig technique and showed the T,, fundamentals

the optic axis.

at 670.485,428, and 305 cm- ‘. The search for similarities ‘in the normal mode frequency distributions between MgA120, and Nafi-AlzOS will be considerably simplii by @in viewing /hhunina as a structure with one spine1 block per primitive cell. Examination of the correlatiqn tables reveals that reduction of the Oh group to D3, gives the following correlations: Al,,+A,, EI,,+EF T2,+E,+A1, and TlU+E,+A2,_ Therefore, as similarities in the frequency distribution of the normal modes between MgAllOI and Nag-A&OS are sought, it should be noted that each triply degenerate T mode of spine1 resulta in an A and an E type mode of /Lalumina The observed correlations are described in Fig. 6. In MgAlz04 there are three sets of closely spaced pairs of bands originating from T,, and Tzo modes and three relatively isolated bands derived from modes of Al, El, and T,, symmetry. Each of the sets of T,,- T2,, band pairs in spine1 may be correlated with a pattern of four bands in Na&AlzOo associated with modes of Al, E, E, and At, symmetry in order of descending frequency in each case. The band structure from 435 to 525 cm-’ is somewhat complicated due to the superposition of the E, and Alu modes of Nab-A1203 correlated with the ‘isolated’ T,, mode of spinel. There is very apparent correlation between the Ai, mode at 772 cm-’ in MgAl,O, and the mode of corresponding symmetry at 782 cm- 1 in Nap-A120J. The only major discrepancy in comparing the spectra of these two

691

Raman, ix. rciktion, and emission spectra of sodium ~-alumina

I

I SODIUM

BETA

ALUMINA

573.K

‘1 I2u.J

900

600 FREOUENCY

Fig. 4. Pohizcd

300

(cm-‘1

ix. emission spectra of sodium jhdumina with faces cut pnrallel to and perpendicular to the optic axis.

systems in this way is the very intense El, mode at 410 cm-’ of the spine1 structure which has no obvious counterpart in spectrum of /Ul,O~. The correlation illustrated in Fig. 6 can serve only as a qualitative guide toward interpretating the spectra of Nab-Al,OS because of the more complex structure and lower symmetry of this material as compared to MgA120*. However, if only the more intense modes of NajLAi208 are considered, there are several rather

strilci~g similarities

in the normal mode frequency distributions of the two structures.

l&ma1 f$Tects Since Na-/?A&0 exhibits high ionic conductivity above 300 K, it is of interest to study the temperature e&&s on the frequencies, intensities, and bandwidths of the normal modes of Na&Al,Os. Such &ects on the motion of the Na+ ions [3] as well as other low fre-

692

ROGER FIWCH and J. B. Br;rps Table 3. Frequencies (cm-‘) of the Al. and Et. modes of sodium p-alumina determined from the polarized reflection and emission spectra

AZu (E /I c) Reflect

300 K

1060

E,

Emission

ion

Reflect

473

773 K

1150

1145

1070

1060

890 865

86s

855

300 K

L,

ion

(E I c) Emission

473 K --

773 K

1055

1050

825

820

810

768

770

760

718

715

710

920

777

770

765

670

673

665

720

720

715

630

630

625

640

655

655

590

600

595

530

550

545

555

560

550

510

510

500

435

440

435

445

450

435

390

390

395

387

375

375

337

373

310

307

295

302

287

295

Fig 5. Schematic diagrams of the Dsr and reduced Dj, structures of sodium B-alumina The solid circles in (a) represent the columnar oxygen ions. The unit cells in (a) and (b) are shown in dotted outline, and the shaded areas represent layers of spine1 blocks.

Raman, i.r. reflection, and emission spectra of sodium @furnina

693

Table 4. Correlation diagram and symmetry species of the vibrational modes for the D3, reduced lattice model A.

Correlation

Diagram

!!3&2L1.

%h

%h

:lg>,,

i:pju

at2+a2;c2

19

A 2u B > 2u

::I> Aig Eg

::>

rop(Dy)=

A 2u c

(ala’-aa;aa’) (a’c,ac)

yg+

3A2g+ 13Eg+ 3AIU+ ‘DAzu+ ‘3E

quency modes [S] have been described previously. The higher frequency modes originating in the spine1 block also display a temperature dependent behavior as illustrated by the results shown in Fig 7. The increase in intensity of the low frequency modes with increasing temperature can be attributed to the Bose population factor in the expression for the Raman scattering cross section [19]. As expected the Raman and i.r. emission fmqueGm(Fig.4jgenemhy~tithknneesiRg temperature. The bandwidth of the Al, mode at 258 cm-’ doubled over the temperature range of Fig 7,

”

while the widths of the other modes increased less dramatically. The a(cckr’ spectrum in Fig. 2 shows that the two A I,, bands at 258 and the 327 cm-’ are asymmetric, with the low frquency wing broadened in both cases. There is also apparent a very broad band extending over several hundred wavenumbers which underlies the two A,, peaks and probably originates in a continuum of . . rmllt~~~ two Al, bands could ark from a Farm-like anharmanic interaction [20] behveen the discrete Al, states

800 A,,

-___-

AQ

-----

TOD-

-r 600

-

5

5 3

500

-

ii

E

129 ____<:__---Thl

___-

:.,_r:c_-se-.-

Tlu

400 -

_* ---. . . .

Ez9

A(9 Eu E9 &I Aau k 2u

300 -

2ooL

WA1204

co;,

NOB-A120s CD:,,,

Fig 6. Energy level diagram describing the correlation of the distribution of normal mode frequencies between Nab-Al,@ (treated as a D& space group structure) and MgA1204.

ROGERFancu and J. B. Berm

694 I

I

I

I1

I

SODIUM

900

600

700

III

I

III

BETA ALUMINA

600

500 FREQUENCY

400

Fig. 7. Raman scattering from the A,, and Et, modes of Nt@-AlsO, is 1000 cps. and

the continuum of multipltonon states. The temperadependence of the Fano-resonance anharmonic interaction could be responsible for the very large change in width of the 258 cm-’ band compared to to those of other modes for which this type of interaction is absent. ture

Acknowledgmenr-One of us (R.F.) wishes to thank the Oak Ridge Associated Universities for financial assistanoc provided through the Faculty Research Participation Program. REFERENCES [I]

[2] [3] [4] [5l [6l

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1478 (1974).

300

200

m0

(Cm-‘)

at two temperatures. Full scale intensity

C. R. Prrrmts, M. BOATMAN,J. W. Moo~a and M. D. Acta Cryst. 27B, 1826 (1971).

GLICK,

W. L. Ranr, F. REXDING= and S. LAPLACA, in SuperG. D. MAHAN and W. L. Roru (Eds). Plenum Press, New York (1976). [91 Intemationai Tables of X-ray Crystallography. The Kynoch Prass, Birmingham, Vol. I (1969). [W E. B. Wriso~, JR., J. C. Dactus and P. C. CROSS, in Molecular Vibrations. McGraw-Hill, New York (1955). [ill W. G. FAIELIX, N. T. McDnvrrr and F. F. B~NTLY, Appf. Spectrosc. 25,155 (1971). [I21 L. L. Bone, Acre Cryst. 27A. 76 (1971). [I31 Union Carbide Corporation Crystal Products Department, San Diego, CA 92123, U.S.A. [I41 J. B. BATBSand J. C. PIGG, J. Chem. Phys. 62, 4227 (1975). [RI A. S. QIJL~T,Appl. Spectrosc. U.82 (1971). M. C. MCMAHAN, J. Opt. Sot. Am. 40,376 (1950). ::: M. P. O’HORO, A. L. Fnrsr~~o and W. B. WHITE, J. Phys. Chem. Soli& 34,23 (1973). [W W. B. Wmnr and B. A. DEANGBLIS,Spectrochim. Acta

ionic Condwtors,

g;

23A, 985 (1967). R. LONWN, Adu. Phys. 13.423 (1964). J. F. Scorr, Phys. Rev. Lett. 24.1107 (1970).