American MineralooistVol. 57, pp. t69z-tit0 (1972\

INTERPRETATION OF THE SPIN-ALLOWED BANDS OFFe2' IN SILICATE GARNETS

Wrr,r,reu B. Wlrrrp aND RAyMoND K. Moonp,l

Materials Research Labor,atory and Dep,artment of Geo,saiences,T h,e P ennsglu a"ruia State U niu er sitE,

U niu ersity Park, P mnsyluania I 6 802

Assrnecr

The three intense near-infrared bands of Fe2+ in silicate garnets at approximately4500, 6000, and 7800 cm-l are assigned to transitions from the d," orbital ground stateto the d.,,-n, ils"t &rtd d,o orbitals respectively. The temperature dependence of theband intensities implies that the transitions are vibronically coupled by phononswith frequencies of 835 and 695 cm-l. The mean frequency is a measure of Dq forthe S-fold siie and decreases with increasing mean X-O distance. The frequencydifrerence between the il,. and. d1, orbitals is shown to be a measure of the distortionof the 8-fold site. Revised crystal field stabilization energies for Fe2+ in garnet are10.26 to 10.72 kcal/mole.

INrnonucrrom

The electronic spectra of transition metal ions in garnets have beenstudied by many workers (Clark, 1957; Manning, 1g67a, 1g67b, 196g;Burns, 1969, 1970; Moore and White, lg72). The garnets exhibit someof the most complex spectra of any known silicate minerals. Previouswork has established the relationship of the spectral bands to energylevels of Fez*, Fe3*, Mn2*, Cr3*, and VB* on mainly the 6-fold andS-fold sites of the garnet structure. Most impor[ant is the spectrumof Fe2*. It is generally agreed that Fer. is responsible for a group ofthree strong bands in the near infrared due to spin-allowed transi-tions and for a number of weak sharp bands in the visible due tospin-f orbidden transitions.

The present paper is concerned only with the three spin-allowedbands of Fe2* on the &fotd site in garnet. The object is to providea detailed assignment for these bands in terms of the arrangementof the orbitals in the site and to relate the frequencies of these bandsto the crystal chemistry of the garnets. Crystal chemical and crystal-Iographic data are available in an extensive set of structural refine-ments (Novak and Gibbs, 1971) and in a review article (Geller, 1967).

'Present address: Department of Natural Sciences, Radford College, Radford,Virginia.

Fe* BANDS IN SILICATE GARNETS 1693

Exppnrrvrpxrer,

A suite of 13 garnets from ugrandite and pyralspite families were studied.Chemical analyses were reported in the first part of this study (Moore andWhite, 1972) and are not repeated here. Measured lattice parameters andcalculated molecular proportions of the end members are listed in Table 1. AIIspecimens were optically homogeneous single crystals. The crystals were slicedand ground to approximately 0.25 to 0.50 mm thickness. The samples were

S:;;"i""}';f;;$. to a glass finish on three-micron srit for optical absorption

The absorption spectra between 0.3 and 2.6 microns were collected on boththe Beckman DK-2A and the Cary 14 spectrophotometers. The spectra runas a function of temperature were obtained using the Cary 14 with a cold celland Iiquid nitrogen; and for high-temperature work a soldering gun variaccombination was used with thermocouple measurement of the temperature.All variable temperature measurements were obtained in triplicate to insureconstant temperature and accurate intensity variations.

Oprrcar, Spncrn,l

The three strong bands in the near infrared appear best in thespectra of the pyralspites. A typical spectrum is shown in Figure1. All pyralspites examined show this group of three bands (labeleda, b, and c) in Figure 1 near 4300, 5900, and 770O cm-l. From theirintensity and half width it seems safe to infer that these are spin-allowed transitions. Freouencies and intensities for all specimens arelisted in Table 2.

The same bands appear in the spectra of grossularite but are ofmuch lower intensity because of the low concentration of ferrousiron. Usually the weak a-band was not observed. Frequencies andintensities for the other two bands are listed in Table 2.

Manning (1967a) assigned this group of bands to Fe2* on the8-fold site. This assignment is substantiated by Figure 2 in whichis plotted the absorbance of the band per unit thickness as a functionof FeO content. The Beer's law plot shows that all three bands varynearly linearly with increasing ferrous iron content. The scatter in theindividual points may be due to inaceuracies in the chemical analysisfor FeO, since the scatter is in the same direction for each band.Analysis for FeO in silicate garnets is difficult and Figure 2 suggeststhat a spectrophotometric analysis could be used to give better re-sults.

No evidence was found for the 2900 cm-1 band reported by Clark(1957) in agreement with Manning's (1967a) observation. Calcula-tions based on the assumption that the 2900 cm-l band is due to Fe,*(such as those of Bloomfield, Lawson and Rey, 1961) should be re-examined.

1694 W. B. WHITE AND N. K. MOORE

TABLE 1. LATTICE PARAMETER AND MOLECULAR PROPORTIONS FOR GARNET SPECIMENS

l - + r i ^ ^Sample- Yaraneter(A)

SpPy

AL-77

AL-7 6

A1-68

AL-67*

A I - ) T

Py-7Lx

Py-59*

sp-70

Sp-53rt

Gr-90

Gr-87

Gr-74

11 . 5019

LL,5L27

IL .5292

LL.5767

11 .5150

11 .5302

tL.5026

11 .6116

I I . ) / I

11 .8478

tr.84L2

11 , 8512

1 .8 .0

8 . 0

2 2 . 6

2 3 . O

3 3 . 6

7 L . 4

5 9 . 1

6 . 8

0 . 9

0 . 5

7 7 , O

7 6 . 0 3 . 6

6 7 . 8 5 . 0

6 7 . 5 3 . 0

5 1 . 0 0 . 9

1 6 . 0 0 . 9

3 7 . 5 L . 7

2 2 . 4 7 0 . 0

4 5 . 5 5 3 . 0

3 . 2 0 . 6

6 . 0 0 . 6

4 . 7 2 , 6

4 . 6 0 . 4

1 3 . 0

J . J I . J

6 . 4

1 3 ; 1 ; . I . 4

3 , 4 1 . 0

r . 7

0 . 8

o . 7

8 9 . 9 6 . 4

8 7 . 3 6 . 4

7 3 . 6 1 8 . 4

7 . 3

*Assumes all iron is one valency state, Fe# in pyralspite ancl Fe# in

ugrand i tes .

Agreement in frequency values of the band maximum with thosereported by Manning (1967a) is good. The frequencies of this set ofbands vary little with the pyralspite composition.

Molar extinction coemcients were calculated from the slopes of thelines in Figure 2 and are shown on the figure. These are based one : A/ (lC), where C is the concentration of Fe2* ions in moles perliter of garnet host. These are of the correct order of magnitude ex-pected f.or d-d transitions.

The behavior of the a, b, and c bands with varying temperatureswas measured. The results for specimen Ll-77 are shown in Figure 1.At temperatures down to 78 K the main effect is a general lowering ofintensity, a slight sharpening of the bands, and a mild frequency shift.No additional fine structure was observed. The frequency shifts aresmall and difficult to measure from these relatively broad bands. Thefrequency changes, related to the value at 78 K are shown in Figure3. Of interest is the observation that the b- and c-bands increase in

FE- BANDS IN SILICAl'E GARNETS 1605

lrloz.

E o.4oU'dt

o.8

o.7

o . 6

o . 5

o . l

o .o

A t -77

tII'I

\ \ b

l l

t \

r\ \ ..--..i \

\ "? t , \

l \ ' . \i \ t \ oi t \ - r- \ ,

\,,. \e.

\ aa

. : \ \

i \t i \I i \ / \

: ' : \ / \l ' . \ . / . . \

i ' . . . . ' - -

. . "" ' . . . . \ g ' loK

\ "" . . . . . . . . "" " .5zloK

\\. .-.\\. -./

\.. /"'\..' r \ t ' \ .

\ / . \ ?8"K

o.3

o . 2

l o o o r 5 0 0 2 0 0 0 2500

WAVELENGTH (nonome te rs )

Fra. 1. Nea,r infrared spectra of a pyralspite Afo.zzPyo.rGh.ss4sAn6.ss4 at varioustemperatures.

1696 W. B. WHITE AND N. K. MOONE

TABLE 2. FREQUENCIES 0F THE SPIN-AILOWED a' b' AND c BANDS IN THE

SAMPLES STIIDIED. ABSORBANCES/m ARE PRESENTED IN PARENTHESES.

Smple Band a Band b Band c

AL-77

A1 -76

Al-68

A1-6 7

A1-51

Sp- 70

sp-5 3

Py-7 L

Py-59

Py-Cr ( I I I )

Gr-87

Gt-7 4

Gr-90

4 3 8 1 ( 1 . 0 7 )

4 3 0 3 ( 1 . 1 7 )

43L2 (L .02 )

4348 (0 .90 )

439o (o .49 )

4244 (0 .39 )

4310 (0 . 18 )

46s1 (0 .10 )

4s33 (0 . 64 )

4666 (0 .20 )

587 4 ( r . 44 \

s 8 6 8 ( 1 . 4 4 )

s884 (1 . 30 )

59L7 (L.L2)

6011 (0 . 68 )

s924 (O .49)

s 9 s 1 ( 0 . 4 e )

62L r (O ,22 )

6068 (0 . 80 )

5L39 (0 .27 )

s76o (0 .03 )

5830 (0 . 09 )

5800 (0 . 07 )

7 663 (2 .40 )

7 633(2 ,48)

7 668(2.L9)

7 657 (r .99)

7 77 0 ( r . 62 )

7 1 7 0 ( o . 8 4 )

7 7 52 (L . r 7 )

7 8 8 8 ( 0 . 4 2 )

7 7 6 4 ( L . 3 0 )

783r(0,42)

8150 (0 . o8 )

8 2 3 3 ( 0 . 1 8 )

8 2 1 0 ( 0 . 1 3 )

frequency with decreasing temperature (the expected result from thestronger crystal field resulting from shortened metal-oxygen distancesdue to thermal contraction), but the a-band decreases in frequencywith decreasing temperature.

INrpnpnnrarroN oF THE SPECTRAAssignnuents

The cubal coordination polyhedron based on a drawing by Prandl(1966) is shown in Figure 4. The distorbed cube has site symmetry Dz.The Iabeling of the three 2-fold axes of Ds is arbitrary in so far asthe crystal is concerned but is not arbitrary if one wants to use theusual labeling for spectroscopic terms and the descent-of-symmetrytables, both of which assume particular conventions for labeling ofthe coordinate system. It should also be noted that these 2-fold axesare proper symmetry elements of the space group, Ia\d,. They arenot merely pseudo-symmetries of the coordination polyhedron. One2-fold axis is unique in that it lies in the center of a face of the

2 . 8

2 . 4

2 . O

o .8

o.4

Feh BANDS IN SILICATE GABNETS

t o 2 0

/

1697

€ ( c 1 = 1 . 1 1

^ rc/

G 1 1 1 = 9 . 5 7

bEJ

Es\ 1 . 6LrJ()zctE t . zoacl

o

a/at r ' / € (o )=o .so

3 0 4 0WETGHT pERCENT FeO

.Frc' 2' Beer's Law plots for the spin-allowed bands of the pyrarspites. solidpoints represent samples for which Feo was determined by chemical analysis.open points represent samples for which totar iron was calculated as Feo.

1698 W. B. WHITE AND R. K. MOORE

I

EC)

.= BoE

2tI

?

( {min = 76o8 cm- l )

jc

( { r ; n r 5 8 6 6 c m - l )

lb

( ' O r , n = 4 3 9 9 t t - t ,

o

TEMPERATURE ( "K )

Fro. 3. Frequency shift in near-infrared spin-allowed bands as a function

temperature.

Fe,, BANDS IN SILICATE GARNETS 1699

Divalent iron has a single quintet ground state which is split by anoctahedral crystal field into a lower 6T2o level and an upper uzo levelwith an energy separation of about 10,0b0 cm-1. See "lorr"s (tgOZ) to,typical values in crystalline hosts.

Assuming that the oxygens behave as point electrostatic charges,the- splitting of the quintet term in a cubai fierd is -g/9 of the octa-hedral value if the interatomic distances remain constant (Fig. b).

Frc. 4. The cubal site inaxes to the crystallographicof Prandl (1966).

garnet showing the relation of the site symmetryaxes. Oxygens numbered according to convention

c a ( x )

c " ( y I

- - t o r o l

1700 W. B. WHITE AND R. K. MOORE

5 erd yz

5l d, z-rz

F e + + i n M g o

5t.

CONVERSION TOo H c U B A L

q

G A R N E TC U E A L

- 4 3 5 0 c m - l

5 " , d r y

< 2OOO cm-'5t drz

G A R N E T

Frc. 5. Energy level scheme for the splitting of the Fe'* quintet term in va.rious

fields.

Using the spectrum of Fe2* in MgO as a reference point and remember-

ing ihat the crystal field varies with the inverse fifth power of the

inieratomic distance, an estimation of the average energy level sepa-

ration in garnet is given by

1o,ooo x 8/e "

(m)'ry 6,ooo cm-'.

The interatomic distances are those in MgO and the average X-O

distance in pyrope (Gibbs and smith, 1965). The calculated splitting

is almost exactly the average frequency of the three spin-allowed

bands.The distortion of the cubal site to a triangular dodecahedron lifts

the degeneracy of the cubic field levels. The labeling of the lesultant

states is obtained from the descent-of-symmetry tables of wilson,

Decius, and Cross (1955, P. 340).

T " , + A * B r * 8 "

Eo---+ A * Bt.

The center-of-gravity rule for orbital splitting is expected to hold if

the orbitals do not mix. since there are no other quintet levels and

since only the ,4 terms of the excited and ground states could interact,

one might expect t"he T2o level to split into three components whose

uo"rug" is close to the expected energy for the cubic field. what is in

IO,OOO cm- '8888 cm- l

600O cm-'

Fe'* BANDS IN SILICATE GARNETS 1Z0l

fact observed is a separation into terms spaced about 1700 cm-r apart.The middle band at 5g00 cm-1 is very close to the expected averagevalue of 6,000 cm-1.

The analysis given above is probably not as elegant as the numbersindicate, because it ignores the splitting of the ground state. If thissplitting were large, the transitions wourd increase in energy becauseof the lowering of the new ground state. No band which might cor-respond to the tr-> Br transition between the two levels derived fromEo was observed in the range of 1b00-4b00 cm-1. It was thereforeconcluded that the ground state splitting was smail, and it is so in-dicated in tr'igure 5.

The energy level diagram of tr'igure 5 differs from that publishedby Burns (1970). Burns apparently accepted. Clark's (lgEZ) reportof a band at 2900 crn:1 and assigned it to the transition between thefwo components of lhe Eo level. Burns likewise finds only 4820 cm-ras the separation of the centers of gravity of the T2s and.,Eo levels.His value seems much too low to be consistent with the average sizeof the site.

The rigorous group theoretical analysis gives the degree of splittingand the labeling of the resultant states but says nothing about theenergies of these states. Relative energies can be obtained by an actualsolution of the secular equation in the manner of Garner and Mabbs(1970) or Randii (1962). However, one may obtain an empirical fitof the relative energies by an examination of the way in which theorbitals fit into the coordination polyhedron. Figure 6 shows an alter-nate view of the S-fold site (based on Gibbs and smith, 1g6b) drawnas an undistorted eube and giving the bond lengths of pyrope. Theaxes follow the convention established in Figure 4. The orbitals havebeen inserted in their proper location in the boxes to conform to theaxis designation. The transformation properties of the orbitals in l)2symmetry are;

dx', dy', da' -+ A

dxy -+ B,

d,rz -> 8,,

dyz --+ B"

The orbital lobes of d,, and dry point to the centers of cube faces andwill suffer the least repulsion by the o'- charges. These should. belong tothe components of the cube ground state and indeed Eo + A + Blunder this axis arrangement. Deciding which orbital has the lowerenergy and thus is the ground state in the distorted cube is more difrcult.

I7O2 W. B. WHITE AND R, K. MOORE

Examination of the lengths of the cell edges in Figure 6b suggests thatd,, w.ill sense a slightly stronger field than d"" because of the contractionof the cube along the 2,4964 edge. d," will then be the ground state,but the actual energy separation will be small, in agreement with thelack of any observed. transition above 1500 cm-'.

The remaining three orbitals are the components of the Tro excihedstate. The lobes of d.,-o" point to the cube edges along the u and y axes'd,,-,"'shoulil interact more weakly with the ligands than either draor d.yz which point toward the ligands along the cube diagonals. There-foie, d,,.-u' should have the lowest energy of the three. This assignmentis in agreement with the qualitatively different behavior of the a-bandas a function of temperature. Examination of Figure 6d shows that the

o . d z 2 c. dx2-y2

b . d x y d . d x z o n d d Y z

Frc. 6. Schematic views of the cubal site showing the location of five d-orbitals

in the polyhedron. Bond and edge lengths are appropriate for pyrolre (a,fter

Gibbs and Smith, 1965).

ti>-r,.

,"' T

t z . z t t

Fe4 BANDS IN SILICATE GABNETS 1703

four lobes of d,no ure oriented along the four shoft (Z.lg8;.) Fe-O bonds,while the d,, lobes lie along the long (2.2$N bonds. d,, should experi-ence the strongest interaction and thus is assigned to the highest energy,while d,, is assigned to the intermediate one. These assignments aresummarized in Figure 5.

It should be noted that the distortion of the cube site also a,fiects thegeometry of the orbitals. The four lobes of d"" (and d,,) transform intoeach other by the operations of the 2-fold symmetry axes so theseorbitals retain their symmetrical shape. The same is not true of d,oarrd d,,-n,. The two ends of the r-axis lobe of d""-," (and likewise of theE-axis lobe) are interchangedby C"(z) but the a-axis lobes and y-axislobes are not related to each other by a symmetry operation. Therigorous linear combination which generates d,",-o, it a cubic site isbroken and the two pairs of lobes need not have the same shape. Thesame argument holds for d"u. The description of these two orbitals in theabove discussion in terms of cubic geometries is thus only an approxi-mation.

Selection Rules

Transitions by dipole coupling between electronic energy states aresubject to two selection rules: The spin must not change during thetransition, and the bransition must be between states of oppositeparity (LaPorte's rule). Consider now the possible selection-rulerelaxors-mechanisms which relax LaPorte's rule and allow at leastsome of the transitions to occur as weak absorptions.

P-orbital mixing and vibronic coupling are the two mechanismsmost commonly involved. The mixing of the d-orbitals with higherp-orbitals can take place only if the transition metal is not on acentro-symmetric site. The transition probability for p-d mixingtransitions is given by

where ,r.r. is the dipole moment, operator. P-o can have a finite valueonly if the integral is totally symmetric with respect to the site groupof the ion. The symmetry of the integral can be calculated by decom-posing the direct product of the irreducible representation of the ex-cited state in question, the component of the dipole moment (whichtransforms as fr, A, or a) coupling the transition, and the ground state.l

I A very readable account of the use of group theory to determine selectionrules may be found in Cotton (1971). For a, more advanced discussion seeTinkham (1964).

I7O4 W. B. WHITE AND R. K. MOONE

Although r, y, and. z are unique in any one 8-fold site, the other opera-tions of the space group mix the labels between sites, so that there isno distinction when the full cubic unit cell is considered. There areeffectively, then, only transitions of the type A + A and A + B. Allcomponents of the dipote moment belong to representations of the Btype. The products are:

A X B X A : B (antisymmetric)

B X B X A : , 4 . ( s y m m e t r i c )

Thus all of the A --> B transitions are allowed, while the A -> Atransition in Figure 5 is forbidden by the mixing mechanism. Thefact that the a-band is only a little less intense than the b- andc-bands and the fact that all molar extinction coefficients are low(e - 1), both suggest that orbital mixing is not effective. The me-chanism is formally allowed by symmetry considerations, but thedeviation of the 8-fold site from centro-symmetric symmetry is notsufficient to produce much coupling in a quantitative sense.

The selection rules for vibronic coupling are derived from

p*ororo, - [

V"-*{n^*p*"n*ond,

where ** is a vibrational excited state coupling the transition and

*oo is the vibrational ground state (always totally symmetric).Again the requirement for a finite transition probability is that theintegral be totally symmetric. That is, the direct product, of therepresentations of the five functions under the integral must belongto the,4 representation. Since the vibrational ground state is totallysymmetric, it can be ignored and the selection rule reduces to therequirement that there exists a phonon mode whose symmetry isthe same as the product representation of t ***t'ol'"n dr. Theseproducts are the same as those calculated for +'he p'd mixing me-chanism. Thus phonons of both d and B type are needed to accountfor all three spin-allowed bands.

The vibrational spectrum of the garnet structure has been ex-amined theoretically by Hurrell et al. (L9ffi) and by Moore, White,and Long (1971). There are 98 vibrational modes for the entirestructure. However, it seems likely that only vibrations involvingthe cation on the S-fold site would be effective in vibronic coupling.These are:

f1zc) - Azo'l A"* + E, + E, + TTb * 3Tr* * 2Tro * 2Tr*

The symmetry notation is that appropriate to the full factor grcup.

Fes' BANDS IN SILICATE GA?NETS 1705

When reduced to the S-fold site symmetry these modes become

I(DJ : 6,4. + 1081 + 10,B' + 10.83.

Phonon modes occur in all Dz representations, and so all transi-tions are formally allowed by vibronic coupling.

Vibronic coupling implies a particular dependence of the bandintensities on temperature. Holmes and McOlure (1957) proposeda dependence of the form

/ : 1 . ( 1 + r - u , , )where / is the oscillator strength

^ fI : 4.32 X 10-" J e(v) dv

/e is the oscillato,r strength at 0 K and d is the vibrational frequencyof the coupling phonon in temperature units.

Oscillator strengths for the a, b, and c bands are plotted in Figure7. The shapes of the curves are as expected for vibronic coupling,and they can fit to a function of the form

l : 1 . ( 1 + o e - u " ) .

The best-fit parameters are

0.1 x 10-6

68

1200 K

(835 cm-l) (835 cm-') (695 cm-')

The vibrational frequencies are in reasonable agreement with ob-served infrared frequencies of 862 cm-1 and 630 cnr*1 (Moore, et al.,1971) .

Cnvsrar, Cnniurcer, Rer,erroNs

Site Size and Site Distortion

If the mean of the Fe2* frequencies is a measure of Dq in the&fold site, there should be an inverse relationship between the meanfrequency and the mean metal oxygen distance. Four of the measuredgarnets, Ll-77, Py-71, Sp-70, and Gr-90 were selected as beingthe most representative of the end member compositions. The mean

Jo

ot

0

0.1 x 10-5 0.5 x t0-6

146 14

1200 K 800 K

1706 W. B, WHITE AND R. K. MOONE

22.O

20.o

| 8 .0

t 6 . o

t 4 . o

t 2 . o

I O.O

8 . O

6 . O

4 . O

2 . O

o.ot 0 0 3 0 0 5 0 0

T E M P E R A T U R E ( O K )

Frc. 7. Dependence of oscillator strength of spin-allowed bands on temperature.

of the three Fe2* bands is plotted against (X-O) distances as re-ported by Novak and Gibbs (1971) in Figure 8. Although the totalshift is small, only 450 cm-1, and therefore difficutt to measure fromsuch broad bands, the result is as expected. Pyrope with the smallestsite has the highest frequency and grossular with the largest sitehas the lowest frequency. An attempt to further refi.ne the relation-ship by calculating a mean site size from weighted averages ofShannon-Prewitt (1969) ionic radii of the X-cations

(x-o) : PNr, (n" , *Ro)

where Nya is mole fraction of ith S-fold cation and R a is its radius,

@

o><

'+-

Fe"' BANDS IN SILICATE GARNETS 1707

and Ro is 4-coordinated radius of O2-, did not produce anythinguseful. The curve was similar to Figure 8, but the individual pointswere too scatt€red to calculate n, in the crystal field relation

Dq - R'-o-".

Variations in site distorbion which produce unknown variations inthe splitting of the ground state in addition to the limited precisionpossible in the measurements severely limit the calculation.

The assignments for the individual orbitals of Fe'* in the S-foldsite place the d,* orbitals along the shori X-O bond and Lhe dou orbitalalong the long X-O bond. It might be expected, therefore, that theseparation in frequency between the c-band (assigned tn d,,") andthe Lband (assigned lo d,s") would be a measure of the differencein X-O bond lengths and therefore a measure of the distoriion ofthe 8-fold site. This frequency difference is plotted against the a (X-O)values of Novak and Gibbs (1971) for the four definable end mem-bers in Figure 9. The relationship is very good within the limitations

I

Eo

()zUJfoUJ(rlr

z

5u ssoo

2 .25 2.30 2.3s 2.40 2.45

< x- o> (A)Fro. 8. Mean of ?r, orbital energies of Fea as function of mean X-O distance.

Frequencies of Py (pyrope), Al (almandine), and Sp (spessa.rtite) are meansof three observed bands. Frequency of Gr (groszular) is that of middle band,since low frequency band is not observed in this garnet.

1708 W. B. WHITE AND R. K. MOORE

( R L o n c - R s h o . r ) ( E )

Frc. 9. The relation between the seoaration of the b- and c-bands and thedistortion oi th" 8-fold rit".

of the small number of points. The increased distortion of the dodeca-hedral site in grossular is very clearly reflected in the optical spectrum'

Crystal Fielil Stabi,lizati,on Energies

The relative stability of transition ions in the S-fold site of garnetand their partitioning between garnets and co-existing biotite wasdiscussed by Schwarcz (1967). Burns (1970, p. 85) also made acalculation of the CFSE for Fe2* in the S-fold site of garnet. Burnsapparently accepted Clark's (1957) 29O0 cm-1 band (although heplots 3100 curl on his energy level diagram) and assigned it to theupper component of Lhe Eo ground state split, by the D2 distortionof the cubal field.l This assignment implies a large splitting of thecubic ground state which present data and assignments argue againstand leads to a value of the CFSE of 4,160 cm-l or 11.9 kcal.

Fe2* has a single electron otrtside the half-filled shell. Placing this

t As noted earlier, neither we nor Manning were able to observe the 2900 cm-lband, although Clark's figures show it to be quite intense. Clark's figures showspectra very similar to ours and Manning's, except for the numerical value ofthe lowest frequency band. Clark also reports a band at 2500 cm-t in diopside,whereas all further measurements show this band to fall near 4500 cm-1 (See

Burns, 1970, for summary of pyroxene spectra). We conclude that the low fre-quency bands reported by Clark suffer from a calibrational or calculationalerror and that the true value of these bands in pyrope, almandine, and diopsideare about 2000 cm-l hieher than he reported.

I

g

Fe* BANDS IN SILICATE GANNETS 1709

electron in the lowest energy orbital (d,') leads to an extra stabiliza-tion energy composed of a cubic field part and an additional partdue to the ground state splitting. From Figure 5 it can be seen that

e f / .OFSE : z 1 1""

* vt I v") - 1 (sround state splitting)-lo L \ 3 / 2 ' o - '

' - ' J

* | (sror,,,a state sPlitting)

The ground state splittirrg i. t"t rri"n, but has been shown to beless than 1500 cur1. Ignoring this term will lead to CFSE's that aretoo small by a factor of one-fifth LheEo orbital splitting, or no morethan 30O cm+.

The calculated CFSE's for the three end-member garnets forwhich all three bands can be measured are:

Py 3750 (cm-')AI 3583Sp 3588

lO.72kcal mole-'t0.2410.26

These values are lower than those proposed by Burns because ofthe smaller contribution from the ground state splitting.

An examination of element partitioning in mineral assemblagessuch as the eclogites or schists where garnet co-exists with, mineralswith small divalent cations such as pyroxene or chlorite shows thatthe CFSE and ionic size effects work in opposite directions. Thefavorable CFSE in the smaller octahedral sites in pyroxene andolivine will tend to enrich those minerals in small cations with largeCFSE such as Ni'?*. On the other hand, larger divalent cations suchas Mn2* (for which CFSE = 0 anyway) may be enriched in thegarnet phase. Measurement of the element, distribution betweengarnet and pyroxene and garnet and chlorite (Matsui and Banno,1969/1970) shows the Ni?* is highly depleted in garnet, while Co'*,Fe'*, and Mn'* are enriched. The favorable CFSE of Co'* andFe2' in the ferromagnesian minerals fails to overcome the size effectin garnet.

Acrwowr,rncrvrnNrs

This work was supported by the National Science Foundation under Grants

GP 3232 and GA 29440.

RprrnrNcng

Br,oortrrnr,o, Prrrr,p, A. W. LawsoN, AND Cnenr,ps Rov (1961) Crystal field

splitting and covalent bonding in Fea silicate garnets. J. C'\rcm. Ph'Es.3+,

74F',7ffi.Bunxs, Rocon G. (1969) Optical absorption in silicates. /n S' K. Runcorn (ed'),

The A'ppli,cation o! Mode.rn Phgsics to the Earth anil Planetary literiors.

John Wiley and Sons, New York.

1710 W B. WHITE AND R. K. MOORE

- (1970) Mineralogical Applicati.otts ol Crastal Fiekl Theoru. CambridgeUniversity Press, Cambridge.

Cr,enr, Snwnx P. (ig57) Absorption spectra of some silicates in the visibleand near infrared. Amer. Mi.neral. 42, 732-742.

Corror'r, F. Ar,sunr (LgZl) Chemi,cal Appli,cati,ons of Group Theorg, pnd, ed'John Wiley and Sons, New York.

Genxnn, C. D., aNo F. E. Manss (1970) Studies in eight coordination. Part I.Crystal field energies in the D:a point group. J. Chem. Soc. (A),7711-L716.

Gnr,r,rn, S. (1967) Crystal chemistry of the garnets. Z. Kristallogr. t2s, 147.Grnns, G. V., arvo J. V. Surlrrr (1965) Refinement of the crystal structure of

synthetic pyrope. Amer. Mi,neral. So, 2023-2039.Ilor,uns, Ownr'r G., eNo DoNar,n S. McCrunn (1957) Optical spectra of hydrated

ions of the transition metals. J. Chem. Phgs. 26, 1686-1694.Hunnnr,r,, J. P., S. P. S. Ponro, I. F. CuaNc, S. S. Mrrne aNn R. P. Beuuerl

(1968) Optical phonons of yttrium aluminum garnet. Phgs. Reu. 773, f!51-856.

Joxos, G. D. (1967) Jahn-Teller splittings in the optical absorption spectra ofdivalent iron compounds. Phgs. Reu. 155,259-%1.

MawNrNc, P. G. (1967a) The optical absorption spectra of the garnets almandine-pyrope and spessartine and some structural interpretations of mineralogicalsignificance. Can. Mineral. g, ZB7-251.

Mar.rr.rrNc, P. G. (1967b) The optical absorption spectra of some andraditesand the identification of the oAr -) 'A' 'E(G) transition in octahedrallybonded Fe3'. Can. J. Earth 56". 4, 103$-1047.

Mewwrrvo, P. G. (1969) Optical studies of grossular, andradite (var. colophonite)and uvarovite. Can. M,i,neral. 0,723-729.

Mersur, Yosnrro, ewo Srronpr Bewxo (1969/1970) Partition of divalent transi-tion metals between coexisting ferromagnesian minerals. Chem. Geol. s,259-265.

Moonn, R. K., eNr W. B. Wnrre (1972) Electronic spectra of transition metalions in silicate garnets. Can. Mineral (in press).

ervl T. V. Lorvo, (1971) Vibra,tional spectra of the commonsilicates. L The Garnets. Amer. Mineral. 56, 5+-71.

Nover, G. A., er.rn G. V. Grsss (1971) The crystal chemistry of the silicategarnets. Amer. Mineral. s6, 7gl-825.

Pnerrrnr,, Wor,r'nerr (1966) Verfeinerung der Kristallstruktur des Groszulars mitNeutronen-und Rtintgenstrahlbeugung. Z. Kristallogr. 123, 81-116.

RaNnr6, Mrrex (1962) Ligand field splitting of d orbitals in eight coordinatedcomplexes of dodecahedral structure. J. Chem. Phgs. 36, 2094-2M7.

Scuwencz, flpxnv P. (1967) The effect of crystal field stabilization on thedistribution of transition metals between metamorphic minerals. Geochi,m.C osmoch'im. Acta 31, 503-517.

SrreNNow, R. D., eno C. T. Pnnwrrr (1969) Effeetive ionic radii in oxides andfluorides. Acta Crystallogr. B2S, 925-946.

Trwrrreu, Mrcnepr, (1064) Group Theory and, eturntum Mecltani,cs. McGrawMcGraw Hill Book Co., New York.

Wrr,sorv, E. G. Jn., J. C. Dncrus exp p. C. Cnoss (1985) Molecular Vibrations,McGraw Hill Book Co.. New York.

Manuscript recei,ued, Mag 10, 1972; accepted lor pubtitatinn, June Ig, Img.