TEE AMERICAN MINERAI,OGIST, VOL. 56, JANUARY-FEBRUARY, 1971

VIBRATIONAL SPECTRA OF THE COMMONSILICATES: I. THE GARNETS

RaylroNo K. Moonp aNl Wrr,r,ralr B. WnrrB, MaterialsReseorch Laboratory and. Department of

Geochemistry and, Mineralogy,

AND

Tnoues V. LoNc, Department of Chemistry, The PennsyhaniaState Unitersity, (Jnitersity Park, Pennsylaania 16802.

Assrnlcr

Infrared spectra have been measured on 22 specimens of silicate garnet and Ramanspectra on 6 specimens. Seventeen IR modes were found as predicted by a factor groupanalysis. Not all of the predicted 25 Raman lines were found. The factor group splitting ofthe tetrahedral vibrations correlates with the occupancies of the octahedral and cubal sites.The site group splitting was used to measure the distortion of the garnet tetrahedral site.

fnrnooucrror.r

The number of papers presenting infrared spectra of silicate mineralsis immense. Many of these are listed in Lyon's (1962-a) bibliography.One of the most recent and complete such collections is Lyon's (1962-b)unpublished catalog of infrared spectra of silicate minerals prepared inconnection with lunar exploration techniques. fnterpretation of thesespectra has been by mainly empirical arguments. Shifts in frequency andintensity with composition can be measured and form the most rigorousapproach developed to date. This technique was applied systematicallyto the layer silicates by Stubican and Roy (1961) and to the olivine andspinel families independently by Tafte (1962). It has become known asthe "method of isomorphous substitution."

The justifications for beginning a new round of refinements on thevibrational spectra of the common silicates are the following:

1. Infrared data can now be obtained in the range of 400-50 cm-lthus providing information on the low-frequency vibrations not usuallyavailable in the earlier studies.

2. Measurement of the Raman spectra yields a whole new set of in-formation which, in centro-symmetric crystals, is nonoverlapping withany of the infrared frequencies.

3. Theoretical methods can be used which will predict the numberand selection rules of all vibrational modes.

This paper presents vibrational spectra and interpretation for silicateminerals with the garnet structure. The high symmetry and presence ofonly isolated SiOe tetrahedra in garnet make the theoretical analysis of

J4

SPECTRA OF TIIE GARNIJTS 55

the vibrations more useful than would be the case with most othersil icates.

Compared with other sil icates, the infrared spectra of sil icate garnetshave been litt le investigated. Only the recent paper bv Griff ith (1969)reports the Raman spectra of the sil icate garnets. Infrared spectrahave been reported by Launer (1952), Wickersheim, Lefever, andHanking (1960), Wickersheim (1961) and Tarte (1965). The first twopapers deal qualitativelv with spectra in the range 650 to 1200 cm-l inwhich only two to five of the infrared bands are observed. Wickersheim(1961) presents the infrared spectrum of one natural sil icate garnet(almandine) in the range 250 to 1200 cm-1 and the spectra of impuritySiO+ bands in YIG in the range 600 to 1000 cm-l. Tarte's paper is themost comprehensive and presents spectra (in the range of 300 to 1000cm-l) of a large number of natural silicate garnets (including high-titanium garnets) as well as that of synthetic germanate garnets. Onlyqualitative interpretations were attempted on an incomplete set of bands.

Investigations of the infrared spectra of the yttrium and rare earthgarnets have been carried out by Wickersheim (1961) and McDevitt(1969). Excellent papers on rare earth garnets uti l izing factor group andsite group methods for the analvsis of Raman spectra have been pub-lished very recently. (Hurrell, Porto, Chang, Mitra, and Bauman, 1968,Koningstein and Toaning-Ng, 1968, and Koningstein and Mortensen,1e68).

Exppnrurxr.q.l Mrrno us

A suite of 19 garnets of varying composition was assembled. Elernental analyses rvereperformed by emission spectrographic methods, and ferrous/ferric ratio determined by rvetanalytic methods. Cell edges ancl refractive indices were measured. The chemical composi-tion was normalized into mole ratios of the three dominant end members of the pl,rope(Py)-almandine (Al)-spessarite (Sp) series and the grossularite (Gr)-andradite (An)-uvarovite (Uv) series. A code name was attached to each specimen according to the dom-inant end member. The code names, the cell edges, and the molecular proportions are listedin Table 1. These same garnet crystals were used to investigate the optical spectra of thetransition metal ions and full details of the characterization are reported there (Moore andWhite, in preparation).

Specimens for infrared measurements $'ere ground to fine powders. Spectra in the rangeof 2000-300 cm-r were obtained on a Perkin Elmer Model 621 spectrophotometer usingthe powders vacuum-pressed into KBr discs. Spectra in the range o{ 600-50 cm-r were ob-tained on a Beckmann IR-1l spectrophotometer from powders slurried directly ontopolyethylene slabs.

. Raman spectra were measured from 2-3 mm cubes of single crystal oriented to have

[100] faces. A Spex model 1400 double monochromator was used with a 30 mW Spectra-Physics Model 112 He-Ne laser as a source. The He-Ne excitation rvavelength of 6328 Aoccurs in a transmission window of the optical spectrum. Measurement of the Ramanspectra of irbn-containing garnets would have been very dilicult with conventional sourcesbecause of the high absorbance in the blue. Polarization measurements were made by in-

56 MOORE, WHITI', AND LONG

Terr,n 1. L,q,rrrcr P.maltnrrn .tNo Mor,ncur,en Pnopontrolts or rnp

ENo-Mnunrns ron Eacu SlncrutN

SampleLattice

parameterAnGrAIPy

P\l-7 7Al-76Al-68Lt-67At-51Py-71Py-59Sp-70Sp-53Gr-92Gr-928Gr-90Gr-89Gr-87Gr-74An-94An-93AnTi-84Uv-44

4 . 6 0 . 41 3 . 0

J . J I J

6 41 3 . 1 t . 43 . 4 1 . 01 . 7

0 . 8o . 7

9 2 0 4 69 2 | 4 . 48 9 . 9 6 . 48 9 0 6 38 7 . 3 6 . 47 3 . 6 1 8 44 5 94.05 . 5 9 3 . 0

1 1 5 8 4 . 02 9 . O 1 9 . 0

tt.4991r.5211 1 . 5 3 311.5231 1 . 5 3 0rr.525r1.502tr.60711 . 571t| .84411 .84811 .8431r.847tt 8431 1 . 8 5 712.033t2.o4912 tOlr1 .920

1 8 . 08 . 0

2 2 . 62 3 033 .61 1 t

59. 16 . 80 . 9J I

3 . 0

77 .07 6 067 .867 .55 1 . 01 6 . 03 7 . sa a A

45 .50 . 50 . 73 24 36 . 0

1 0

3 . 65 03 . 00 90 . 91 1

7 0 05 3 . 0

0 60 . 50 . 62 . 60 . 50 50 . 4t 4

0 5t 2

4 . O6 . 6

serting a half-wave plate in the laser beam and rotating a polarizer placed between thepolarization scrambler and the entrance slit.

RBsurrs

Infrared. Spectra. The IR spectra of all pyralspites are similar, as are thespectra of all ugrandites. Typical examples, the spectrum o{ an alman-dine, Al-77, and an andradite, An-93 are shown in Figure 1. The bandsare given a simple alphabetical Iabel for identification. Band frequenciesfor all 19 specimens are l isted in Table 2. Two weak bands appear be-tween the D and E bands in the high-titanium and high-chromiumgarnets. Other than these, a maximum of 17 bands are observed in theinfrared.

No previous author has examined the full infrared range for thenatural silicate garnets; the most complete previous work is that ofTarte (1965) in which he reports twelve bands in the range 300 to 4000cm-r. The same number of bands was found in this range in the presentstudy.

Hurrel et al. (1968) obtained the infrared spectrum o{ yttrium alumi-num garnet over the entire infrared range and observed a total of fi.fteen

SPDCTRA OF THD GARNETS

t {cnr )

.)/

Frc. 1. Typical infrared spectra for an almandine (A1-77) and an andradite(An-93). The Ietter code on the bands refers to Table 2.

bands. They postulated that the two missing bands are weak and pos-sibly degenerate with other modes. Their data for YAG are also listed inTable 2.

Raman Spectra. Only six samples were examined by Raman experiments.The band frequencies are presented in Table 3. The spectra of samples4l-68 and An-93 as typical examples are shown in Figure 2. A maximumof twenty bands were observed in the spectra (Gr-90).

Koningstein and Mortensen (1968) report the Raman spectra of YAG,YbAG and YGaG at room temperature and 100oK. They observed amaximum of 22 bands in the YAG sample. Koningstein and Toaning-Ng(1968) obtained the spectrum of a Thulium Gallium Garnet at 80-85oKand observed a maximurn of 12 bands. Hurrel et al. (1968) obtained thespectrum of YAG at 90oK and observed all but three of the predicted25 modes. In the latter two papers, polarization data for the Ramanspectra were obtained and bands were assigned to particular irreduciblerepresentations.

Tnronprrcer, Ar.rerysrs

The Factor Group Method. The first necessity in ana"lyzing the garnetspectra is to determine the number of vibrational modes and the selection

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58

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zH

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tsl

F

SPECTRA OIT TTIE GARNETS

'Ienr,a 3. RaueN Snllrs (rN crr) or Ga4Nnrs

59

Sp-70 Gr-90

rules that control them. Crystalline solids that do not contain well de-fined molecular units can best be analyzed by the factor group method.Factor group analysis takes into account all atoms in the solid whereasthe more commonly used site group method [c/. Duke and Stephens(1964) for an analysis of the vibrations of the isolated SiOn groups inolivine using the site group method] accounts only for the motions of themolecular units. Although factor group analysis is commonly used in thePhysics literature for analysis of the vibrational spectra of crystals, it isdifficult to point to a satisfactory review article. Mitra and Gieiisse (1964)and White and DeAngelis (1967) discuss the method in some detail. Fora complete mathematical treatment see Maradudin and Vosko (1968).

Application to the Garnet Structure. Garnet is cubic, space groupIa3d(O6r0), with 8-4sBz(CO+)a units per unit cell. The srnallest Bravaiscell is primitive with 4 formula units per unit cell. In the garnet structurethe A atoms are S-fold coordinated with Dz site symmetry, the B atoms

1o

J

+56789

101 1T213l41 516t 718T9202 l222324

87s8M816751728700679659631581562552501476{+ol

425J ' J

358. t l /

888859826759l J +

6956626385925705575335 1 6483+zo4163783483303 r z

287257160128

890843806

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6 1 1562

s17468400

917 918839 841796 798

749 748

665 659625

600J O O 5 / I

60 MOORE. WHITE. AND LONG

Frc. 2. Raman spectra for an almandine (,{I-68) and an andradite (An-93). The two

spectra of andradite represent trvo intensity settings of the spectrometer. The numbers on

the bands refer to Table 3.

are 6-fold coordinated with So site symmetry, and the C atoms (primarilySi) are 4-fold coordinated with Sa site symmetry.

There are 3n degrees of freedom in a crystal, where n is the number ofatoms in the unit cell. The full body-centered cell contains 480 degreesof freedom or 240 degrees of freedom in the primitive cell. It is convenientto perform the analysis on the full cell with factor group 01.

The invariance conditions for the atoms in the garnet structure andthe reducible representations are tabulated in Table 4. From the re-ducible representation of the primitive cell, the vibrational degrees offreedom are classified among the irreducible representations of the factorgroup in Table 5. Seventeen infrared and twenty-five Raman activemodes are predicted by the selection rules. Similar methods of classifyingthe normal modes for the garnet structure were apparently used byHurrel et aI. (1968), and Koningstein and Mortensen (1968).

Site Group Analysis. The complete factor group analysis yields the truesymmetry of the various normal modes and the correct selection rules.but it is not very instructive when one wants to assign the normalmodes to specific atomic motions.

SPECTRA OF THE GARNETS 61

Te.eln 4. IxveueNcn CoNorrroNs ron GanNnr Splcn Gnoup Ia3il,Onro

3Cz6Cz 6& 3on 6aa

o-site, 56o, (1641)

Cs,C*4 0

x0 0 0 1 6t6

q-5 q-

0 4 0

000E C z2 4 0 0 0 8 0

&,,sn,8

d-site, Sroo (24Si)

(-2,,1

8 0 c 0 0 0D

2 4 0c-site, D2o, (24Ca)

Crra, Crot -

8 C

a9 6 0 0 0 0 0 0 0 0 0

h-site, C1oo (96O)

160 16

- 8-48- 8

IRED:xpr2 240

The garnet structure contains discreet SiOr tetrahedra which behavenearly independently of the other components of the structure. Thebinding of the SiOa tetrahedra by the 6- and S-fold cations can be con-sidered weak compared to the binding of the Si-O bonds themselves.This model, although only a very rough approximation in the garnet

TasrB 5. Cl.tsstntc.trroN ann SrlRcrroN Rur,ns lon FuloanrNrel Moors ol Glnnrr

Translatory*(SiOr)

InternalSn Dz Se

-4. A- 8- 4

Selectionrules

^/

T-

I

I

l l u

Tzu

0 0 01 1 01 1 02 3 03 2 01 0 10 1 11 1 23 3 32 2 3

RamanInactiveRamanInactiveRaman

InactiveInactiveInactiveInfraredInactive

" Translatory motions of individual cation sublattices.b Total translatory modes: sum of Sn*Dz*So.

MOORE, WHITE, AND LONG

structure, can be used as a starting point to determine the behavior ofindependent SiOa tetrahedra.

Using this model, the number of translatory (essentially cation mo-

tions), rotatory (tetrahedral rocking motions) and internal degrees offreedom (tetrahedral independent motions) are:

Units Intranal Transl'atory

12(SiOt 108 368 8 O 2 4

tzA 0 36

The classifi.cation of each type of mode is given in Table 5.The site symmetry of the tetrahedral site in garnet is Sa whereas the

normal molecular group is ?a. It is possible therefore to determine thesite splitt ing or removal of degeneracy by a descent in symmetry method:

Rotatory

3600

12AE12Es12T2872T2e

The degeneracies of the Za modes are removed to some extent by thelowering of the symmetry of the site. In addition, the selection rules arechanged. Therefore in the l imiting case where the tetrahedra act inde-pendently of the lattice, we would expect 5 IR active internal modes and9 Raman active internal modes.

By the reversal of the above process the factor group representationsto which these internal modes belong can be determined. An example ofthis method for z1 mode is given below:

Mod.e Sr

vr 12A

2TE

This information for all tetrahedral modes is summarized in Table 6.

AssrcNlrBNrs

Raman Spectra. The assignments of the Raman spectra were based onpolarization data obtained from a single crystal of sample Gr-90. Thecrystal was cut into a cube with {001} faces. The crystal was placed inthe sample holder such that the incident beam direction was parallel toa crystallographic axis, and the scattered radiation parallel to an or-thogonal axis. Polarizers were inserted in the incident beam and in the

Mode

Y l

v 2

U z

v4

Sr

12Ar2A+r2Bt2B+t2El 2B+ l2D

OnTa1 t

1 n

SPF:,CTRA OF TI]E GARNDTS

'Ieeln 6. fNlonNar, Monr Drsrntlurtoll

63

Or Internal Y4u

n

AzsLE

TkTzeI

Ifl2rr

r l u

Tz"

2J

567J

z

576

I01100110T

01tz

3101J

L

0I127

10132

^ yr, y2 etc. are Herzberg's (1945) notation for the viblational motions of a regular

tetrahedrai molecule. zr is the symmetric stretch, /2 the symmetric bend, z3 the antisym-

metric stretch, and z+ the antisymmetric bend.

scattered beam. By rotating the analyzer 90o the polarizability com-

for the incident and scattered beams lespectively, and the letters outside

the brackets represent the direction of the incident and scattered beams

respectivelv. Under the experimental conditions, the Ak and -E* modes

are observable under parallel polarizers but not under crossed polarizers,

while the Z2* modes are observable under crossed, but not parallel

polarizers. A summary of the experimental conditions for the observation

of these modes is presented in Table 7.

Examples of the polarized spectra are presented in Figure 3' The

,41g and E* modes do not completely extinct when the polarizers are

Teer,n 7. Por-a.rvesrr-rrv ConpoNnrts elo CoxnrrroNs FoR THE

Expnnrm:rran Olsonvarron or rnn R.cMaN Moors

ModePolarizability

component

Experimentally observable

y(rtc)z y(rcy)z

Tze

*tc, ),y, zz

" ^ , - - ) _ ^ t { _ ' r q q

) t t * - | ) )

rcy, rz, jz

yesyes

no

nonoyes

MOORIi. WI]ITD. AND LONG

F R E Q U E N C Y ( c n T )

Frc. 3. Raman spectra of a grossularite (Gr-90)garnet in two polarization directions.

crossed [x(yr)z]. This is partly due to internal reflections, caused byinternal fractures in the crystal, and to misalignment of the crystal(intentional in this case). Koningstein and Toaning-Ng (1968) haveshown that, when a garnet crystal is rotated away from axis alignmentwith the incident and scattered radiation, the .E* polarizability com-ponents transform to all possible quadratic combinations, whereas theAu polarizability components remain the same. In Figure 3, the E*modes have nearly the same intensity under both experimental condi-tions, while the three,4 1* modes decrease in intensity markedly undercrossed polarizers [x(yr)z]. The spectra were run numerous times withmore precise alignment of the crystal, and the experimental conditionsoutlined in Table 7 were nearly attained. The spectra in Figure 3 areused for illustration because they exhibit the most complete set of ob-served bands.

A summary of the assignments is given in Table 8, along with theresults for YAG as determined by Hurrel et al. (1968). These assignmentsare tentative. The frequencies of the observed bands are plotted as afunction of the lattice parameter in Figure 4. The lines indicate possiblecorrelations. The assignment of these Raman bands to particular sitemotions is based partly on the consensus that the high-frequency bandsrepresent molecular motions of the tetrahedra and on the site groupcharacteristics.

I

SPECTRA OF THE GARNETS

Taeln 8. RaueN AssroxunNrs

65

Band(Gr-90) Representation Site motion Band (YAG)' Representation

Tzen

Le

Tze

Tze

I

Tzetl

Tzs

lze

A .t . L e

L g

Tze

561544537531436408403

373340310296

A E

Tze

Tzs

lze

TuD

Lg

DLg

A ETze'r-

88885982675973469s

662638592.t /u

533516

483426416378

vr &nd zg

857783758719714690

243218162IM

TzeT:e

D g

Tze

vz &fid vE

lzsTzeA E

Rotatory

348330312287

ThTaTze

LB

Sa Trans.

257160t28

li

Tzslze

Dz Trans.

'Hurrel et aL.(J968).

Two of the three,41* Raman active modes arise from internal tetra-

hedral motions, one from zr and one from vz.The third,4r* mode arises

from rotatory or rocking motions of the tetrahedra. There is general

agreement that the z1 would be higher in frequency than v2, and that the

rotatory modes are generally the lowest frequency. Based on this as-

sumption, we can assign the three,4rn modes to the site and rotatory

motions. vr and v3 may be tentatively listed together for purposes of

illustration. The zr symmetric stretch yields an Au and an ,Es type

Raman active mode, while z3 yields an E* and three lz* type Raman

active modes. Therefore, six modes are predicted in the Raman spectra(Ak,2Es, and 3f2s). Hurrel el al. 's work on YAG, where the grouping

of the high-frequency bands is more obvious, shows this aggregate of the

six modes of zr and /a quite clearly. In the Gr-90 sample the six highest

frequencv modes also contain this set of zr and,/a modes.

MOO]IE, WHITE, AND LONG

IE3

c)zlrlfalrJEL

8 0 0

7 0 0

5 0 0

4 0 0

i l i i - 3_

j i it : r Il l I a! r | |! t I a

,i ,ii- i- hi *i-

T?i-?-?-rI ii I

- l.=-

i? ! i , .I i l ! ! ii i i i iiii i ii i i ? ?i i i i ii r r i ?i l ! . I

! i i i i i i i"i 'li" i-o i t o loa o , l| | r lL O E i

( 9 r < !

t i

Frc. 4

i l . 4 0 i l . 6 0 1 1 . 8 0 l 2 . o o

LATT tcE PARAMETER (o . ) ( i )

Raman frequencies of garnets as a function of cell edge. Near-horizontal linesare intended to match corresponding bands.

SP]],CTRA OF THE GARNETS

I

E

()zUl

U

I

8 0 0

7 0 0

--ll=-::__::_-_-_-_-_-__-_*_-_____.i;______=__:___,;:__-:-.

t 2 0 0

L A T T I c E P A R A M E T E R ( o . ) ( i )

Frc. 5. Infrared frequencies of garnets as a function of cell edge'

To assign the remaining bands to specific motions as was done for zr

and za is less valid, since for these lower frequency bands the interaction

between site motions could be an important factor' However, the as-

signment is tentatively completed by the same method as was outlined

ubor.. such assignments are summarized in Table 8. This table includes

the bands and assignments of YAG (Hurrel et al' !968) '

assigned to the tetrahedral site.

Similar plots of the frequencies of the remaining bands against the

MOORE, WHITE, AND LONG

Taslr 9. INlnenrn Assrcxunxrs

Band Site Site motion

SrSrSrSr

ABCD

y2 Arrd v4

SaSr

Sn

EF'

G

SeSaD2D.

HIJKLMNoP

a

average radii of the ions occupying the octahedral and dodecahedral(cubal) sites and against the average weight of the ions occupying thesesites indicate that bands H and,l can be related to the oct;hed;l site,and bands J and K to the dodecahedral (cubal) site. The remaining bandsdo not yield reasonable plots for anv parameter or are observed in toofew specimens to observe valid variations, and thus cannot be assigned.These site assignments are summarized in Table 9 and are similar tothose found by Tarte (1965).

Based on the assignments of Table 6, we would expect three infrared-active tetrahedral stretching vibrations at high frequencies. The groupof four bands (A-D) at high frequencies consist of three very strong Lands(B, C and D) and a weak shoulder (n) tnig. 11. The origin of the 1 bandis not clear at the present time. The various rare earth garnets (McDevitt,1969) exhibit only the expected 3 bands in this region.

The bands E-G can be related to the vz and za infrared-active modes byanalogy to the Raman spectra. Four bands are predicted from thesemodes; however, due to the strong interactions of the lower bandsbetween site motions, the fourth member cannot be definitely identified.

Srnucrunar ConRBr,q,rroNs

Based on the assignments in the previous sections, some structuralcharacteristics of the tetrahedral site can be determined. The infrared

SPECTRA OF THE GARNETS 69

9 0

6 0

5 0

IEo

(,=F

J

Gah

o-

oE.

t

Fo

L

---*(!(r",'-""1"-:."" ---.^'..-st:"

- - - - c o c r c o " \ \ -

i l . so l 2 .OO

L A T T I C E P A R A M E T E R ( o . )

Frc. 6. The relation of the factor group splitting to cell

edge for various garnets.

bands (8, C and. D) assigned to zr are of particular interest. The site and

factor group splitting characteristics of this mode have been discussed.

In the garnets in which the tetrahedral sites are coupled through octa-

hedral and dodecahedral (cubal) cations, the factor group splitting

would be expected. to be of a Iarger magnitude than the site group

splitting. The Sr site in natural silicate garnets is only slightly distorted

from true ?a slmmetr)'. Based on this, the three strong high-frequency

bands in the infrared can be assigned to the two types of splitting as

follows [C-D] is the site group splitt ing, and lB-(C+D)/21 is thefactor

group splitting. The factor group splitting values have been plotted

against the lattice parameter in Figure 6. In addition, values calculated

from the reported frequencies of these bands for various rare-earth

garnets (McDevitt, 1969) as well as for a few germanium garnets (Tarte,

1965) are also plotted. Our data are shown as filled circles. When the 8-

fold cation is varied, the factor group splittings fall onto rather nice

curves for each octahedral cation. The smallest dodecahedral cations

correspond to the largest factor group splitting. This implies that the

coupling between tetrahedral motions is stronger when the dodeca-

hedral distarices are smaller. On the other hand, variations in the octa-

hedral cation seem to have little effect on the lactor group splitting.

The series ca-B-Si and ca-B-Ga in Figure 6 form nearly horizontal

lines, the factor group splitting being nearly constant for each set of

data.The tetrahedral site in garnets shares two of its edges with the dodeca-

70 MOOR]i,, WHITF:,, AND LONG

E

z

FE

@

o

U

L u _ F e

Y b - F e OO Y b - G o O / /

y - F 6 - - :Y - G o O - 2 / r , i s o

O z '

Y b - A IO - / - D y - F e

- "o t -a to

oS m - F e

P y - S l

A n - S ia

G r - S iO z '

oo t 5 0 0 2 0 0

D I F F E R E N C E I N

0 . 2 5 0 0 3 0 0 0 3 5 0

L E N G T H S O F T E T R A H E D R A L E D G E S ( i )

Fro. 7 Relation of the site group splitting to the distortion of theCO+ tetrahedron of various garnets.

hedral (cubal) site and has four unshared edges. The length of the twoshared edgep is less than the value for the four unshared edges. Therefore,the difference between these two values is a measure of amount oftetrahedral distortion, since in an undistorted tetrahedron (za) allsix edges would have the same length.

In Figure 7 , the average value for the site group splitting of thegrossularite and pyrope samples as well as the value for a number of rare-earth garnets (McDevitt, 1969) are plotted against the difference in thetetrahedral edges. The structural data are from Gibbs and smith (1965)for pyrope, Prandt (1966) for grossularite, Novak (private communica-tion) for andradite, and Euler and Bruce (1965) foi the rare-earth qar-nets. The latter data are only accurate to *0.04 A based on their re-ported randoln experimental errors. rt is seen that the infrared sitesplitting provides a measure of the S+ distortion of the tetrahedral site.

AcKNowtEDGMENT'rhis

work was supported by the Air Force Materials command, wright-patterson AirForce Base, under contract No. F 33615-69-c-1105. we are indebted to G. Novak forproviding us with his crystallographic data in advance of publication.

Rrlpnnmcns

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M anuscript receitd, Iune 10, 1970 ; occepted. Jor publi.cati.on, Iuly 22, 1970.