American Mineralogist, Volume 62, pages 475490, 1977

Titanium-containing silicate garnets. I. The distribution of Al, Fet*, and Ti4+ betweenoctahedral and tetrahedral sites

Fne,Nr E. HuccrNs. Drvrn Vrnco e.Np H. Gpnsenn HucrsNsoLzl

Geophysical Laboratory, Carnegie Institution of WashingtonWashington, D. C.20008

Abstract

The distribution of ferric iron between octahedral and tetrahedral sites in syn-thetic titanium garnets of compositions between CaeFerTi, .rSir.u.O,z (50:50 by weightCarFerSirOtr: CasFerTirOtr), and both CarAlrSirO,, and CasFezSiaO,, have been measured by6?Fe Mdssbauer spectroscopy. By using an ideal cation-exchange model in conjunction withthe ferric distribution data, the distribution of aluminum and titanium in the garnet structurecan also be obtained. The distribution of Al, Fe3+, and Tia+ between the sites approachesequilibrium only at temperatures in excess of 1200"C over a period of weeks; it appears,however, that the relative preference for the tetrahedral site must be in the order Al 2 Fe > Ti.This order of preference is inconsistent with crystal-chemical guidelines based only on ionicsize and charge, and an additional factor, electronegativity, is necessary to rationalize theinferred site preferences.

At temperatures of l050oC and below, the measured ferric distribution in these garnetssynthesized from glasses is inconsistent with an equilibrium distribution, because the samedistribution is observed at different temperatures for a given composition. It is thereforeinferred that such temperature-independent distributions result irom the extremely slowkinetics for the cation exchange, that eflectively eliminates observing any change in thedistribution during the synthesis of the garnets. Such frozen-in, initial distributions appear toreflect the crystallization path. In particular, the presence of CaSiOg or CaTiOr as inter-mediate and metastable products in the crystallrzation process is correlated with the observedcation distribution in garnets synthesized below 1050'C. The ferric distributions in titaniumgarnets formed from gels or in natural garnets associated with serpentized peridotites differsignificantly from those in garnets synthesized from glasses, and most probably reflect quitedifferent crystallization reactions.

lntroduction

Natural titanium-rich garnets, usually known asmelanites or schorlomites, differ markedly from othernatural garnets. For instance, their main petrologicoccurrence is in undersaturated alkaline igeneousrocks, unlike most other garnets, which are foundpredominantly in metamorphic environments. In ad-dition, the chemistry of titanium-rich garnets is alsosignificantly more complicated, because silicon doesnot completely fill the tetrahedral sites and there isusually an excess of divalent cations (X) and a defi-ciency of trivalent cations (Y) indicated by chemicalanalyses when compared with the usual garnet for-

I Permanent address: Mineralogisch-Petrographisches Institutder Universit?it. Miinchen, West Germanv.

mu'la, XxYzSisOr2. For these reasons, the crystalchemistry of natural titanium garnets poses a numberof interesting problems not encountered with othersilicate garnets. In particular, the relative site prefer-ences of Al, Fe3+, and Ti between the octahedral sitesand those tetrahedral sites not occupied by silicon,and the oxidation states of iron and titanium in thegarnets are two problems that have been extensivelydiscussed in the literature. Almost without exception,such discussions have been based on studies ofa suiteof natural samples of different compositions and par-ageneses lacking sufficient control of the several vari-ables to give definitive answers.

The present study of titanium garnets differs fromprevious investigations in that an attempt has beenmade to establish an experimental framework in

+ t )

4'r6 HUGGINS ET AL: TITANIUM-CONTAINING SILICATE GARNETS

which the crystal chemistry of titanium garnets maybe interpreted. In this paper, the relative site prefer-ences of Al. Fe8+. and Tin+ for the octahedral ortetrahedral sites in the garnet structure are discussed;in subsequent papers, the phase equilibria, the in-trinsic oxygen fugacities, and the oxidation states oftitanium and iron in natural melanites and schorlo-mites will be discussed.

The distribution of Al, Fe, and Ti in the garnetstructure can, in principle, be resolved by combinedX-ray and neutron diffraction studies. Such studies ofnatural garnets have not been reported, however, andattempts to establish the site distribution of thesecations have been based on results of other tech-niques or crystal-chemical principles. Unfortunately,vibrational spectra of titanium garnets and studies ofcorrelations between the elements in garnets do notyield an unambiguous assignment of the cations tothe sites.

Vibrational spectra of titanium garnets were origi-nally interpreted (Tarte, 1959) as indicating the re-placement of Si in the tetrahedral sites by Ti. Sub-sequently, however, Tarte (1965) and Howie andWoolley (1968), although maintaining this inter-pretation, expressed reservations about its unique-ness. Recently, Dowty and Mark (1968), Moore andWhite (1971), and Dowty (1971) suggested that thevibrational spectra could actually be better inter-preted as Al'+ or Fe3+ replacing Si in the tetrahedralsites.

Attempts to ascertain the location of Tin+ in thegarnet structure have also been based on elementalcorrelations from chemical analyses of natural gar-nets and, in particular, from the relationships be-tween Si, Fe8+, Al3+, and Tin+ in zoned crystals. Insuch analyses, an inverse relationship noted betweenSi and Tia+ (Kunitz , 19361' Howie and Woolley, 1968)was offered as evidence that Tia+ principally replacesSi in the structure. Contrasting inverse elemental cor-relations, however, such as that between Tia+ andFe3+ (Lehij?irvi,1967; Isaacs, 1968), indicate that thisexplanation is not suffhcient for all cases. In any case,the ratio of Ti to the number of tetrahedrally coordi-nated sites not occupied by Si is uniformly in excessof l:1, demonstrating that Si is not the only elementbeing replaced by Ti.

M6ssbauer studies of natural garnets (Dowty,l97l; Burns, 1972) showed that ferric iron can enterthe tetrahedral sites, but did not resolve the questionof whether Tia+ or Al filled the remaining tetrahedralsites. Burns and Burns (1971) reported Mdssbauerdata from some titanian garnets of different para-

geneses, most of which indicated the presence of bothoctahedral and minor tetrahedral ferric iron. How-ever, garnets from serpentinized peridotites exhibitonly octahedral ferric iron in their Mdssbauer spectra(Burns and Burns, 1971), indicating that ferric ironwas completely absent from the tetrahedral sites. Incontrast, Burns (1972) reported the Mdssbauer spec-trum of a garnet of composition Ca3[Fe8+Ti](Fe3+Siz)Orz that had been synthesized by heatingcoprecipitated gels for 20 hours at 1050'C (Ito andFrondel, 1967), which indicated that ferric ironcompletely filled the tetrahedral sites not occupiedby silicon. Hence, it might be inferred that the cationdistribution observed in titanian garnets can bedetermined by the conditions of synthesis.

Synthesis and phase-equilibrium studies of tita-nium iron silicate garnets (Ito and Frondel, 1967;Huckenholz, 1969) are inconclusive because compo-sitions more titanium-rich than CarFe2Ti'.uSi1.uO12are not stable at I atm (Huckenholz, 1969), and soeither Fe3+ or Tia+ or both could make up the silicondeficiency. The replacement of Fe8+ by Al3+ in suchgarnets further reduces the maximum amount of tita-nium that can be substituted in the garnet (Hdlzl,1975), and again such studies are not informative forassessing site preferences. If Zro+ fills the octahedralsite in the garnet structure, Tin+, can enter the tetrahe-dra l s i te , as ev idenced by the fo rmat ion o fCa"Zrr(TiFer)O', (Ito and Frondel,1967). Studies ofother titanium-substituted, nonsilicate garnet systems(Espinosa, 1964; Geller et al., 1965), have indicated,on the basis of measurements of the magnetic proper-ties of the garnets, that the substitution of Tia+ inyttrium iron garnet may be an order-disorder phe-nomenon, with ferric iron favoring the tetrahedralsite over titanium. The possibility that this kind ofphenomenon might also be found in titanium-con-taining silicate garnets and hence that natural garnetsmay be used as geothermometers has not been in-vestigated.

In this paper, results of a 5'Fe Mdssbauer study ofsynthetic garnet solid-solutions between the composi-tion CarFerTir.o2sir.6EO12 (hereafter referred to asTIAN) and either CagAlzSiaO,, (GR) or CarFerSirO,(AN) are presented. The composition Ca'Fe2Tir.o"Sir.u8or2 was used because it is close to the maximumextent of solid solution between CasFezSisO'z andthe hypothetical garnet CaaFezTieOrr, and corre-sponds to a 50:50 mixture by weight of CarFerSirOl2and CarFezTisOrz. The Mdssbauer effect provides in-formation directly concerning the site distribution ofiron: however. the site distributions of Ti and Al

HUGGINS ET AL.: TITANIUM-CONTAINING SILICATE GARNETS

Table l Compositions of synthetic garnets investigated in this study

477

AN-TIAN join GR-TIAN ioin

( x ) * S l p f u t T i p f u F e p f u (:) S i p f u T i p f u Fe p fu A 1 p f u

Andrad i te

T i t a n

0 .0000 . 387Q.4870 . 5870 . 7 0 60 . 8 5 41 .000

3 . 0 0 0z . + ) L2 ? r l

2 . t 682 . 0001 . 7 9 11 . 584

0 .0000 .5490 . 6 8 90 . 8 3 2I . 000t . 209l . + l o

2. 0002. 0002. 0002. 0002 . 0002 .0002 . 000

Gross u I a r

T l tan

0. 000

o .265n ? q q

0 .4560 . 5 5 8U . O O Z

o . 7 7 r0 . 8 8 31 . 000

3 . 0001 . t ) 4

2 . 4 9 22 , 3542 .2 t12 .0621 . 9 0 9L . 7 4 9r . ) o q

0 . 0000 .246o . 3 7 50 . 5080 .6460 . 7 8 90 . 9381 . 0 9 1L . Z ) L

r .416

0 .000 2 .0000 . 3 4 7 1 . 6 5 30 . 5 2 9 t . 4 7 L0 . 7 1 8 7 . 2 8 20 . 9 1 3 1 . 0 8 71 . 1 1 5 0 . 8 8 5L . 3 2 4 0 . 6 7 6L . 5 4 r 0 . 4 5 9r . 7 6 6 0 . 2 3 42 .000 0 .000

*Mole f rac t lon T IAN.fPer fomula un l t (12 oxygens) .

can be inferred by difference or by using a thermody-namic model for the cation-exchange processes. Bymeasuring samples prepared at different tempera-tures, the temperature dependence of the site dis-tribution can be evaluated, from which the potentialof natural titanium garnets as geothermometers maybe assessed. In addition, the crystallochemical fac-tors such as ionic charge, ionic radius, and electro-negativity, which may determine the relative distribu-tion of cations between the octahedral and tetra-hedral sites in the garnet structure, are reexamined.

Experimental

Synthesis and composition of garnets

The samples used in this study were, for the mostpart, originally prepared in studies of the phase equi-libria across the joins between AN and the hypothet-ical garnet CarFerTirO,, (Huckenholz, 1969), and be-tween GR and TIAN (Hdlzl, 1975; H<ilzl andHuckenholz, in preparation). In both studies, thegarnet starting materials were glasses prepared byrapidly quenching mixtures of the required amountsof oxides melted at temperatures between 1400' and1500'C over a period of hours in air. Single-phasegarnets were crystallized from the glasses at sub-solidus temperatures using one of three methods. Forthe AN-TIAN compositions and for compositionsalong the GR-TIAN join stable at l050oC, 5 g quan-tities of material were prepared in air and held at1050'C for several weeks using platinum crucibles.To ensure homogeneous products, the glasses wereground intermittently. For compositions on theGR-TIAN join that are not stable at 1050"C (Hdlzl,1975), 500 mg quantities of garnets were crystallized

at 800oC in standard hydrothermal equipment under1 kbar of water pressure. The glasses were placed ingold capsules along with sufl icient PtO, and HrO toensure a wet, oxidizing environment. The crystall iza-tion times in these runs were between 2 and 4 weeks.Finally, all other crystall ization and heating experi-ments were made on -50 mg quantit ies of glass orgarnet crystals held in Pt envelopes, using quenchingfurnaces. The durations of the experiments are givenin Tables 2, 3, and 6. More detailed experimentaldescriptions, including phase characterizations, aregiven by Huckenholz (1969), H6lz l (1975), and Hdlz land Huckenholz (in preparation).

The compositions of the samples investigated arelisted in Table l. Compositions across the GR-TIANjoin can be represented by the general formula

CasAlr-r"Fe2rTi1.42rsis-r.nrOn 0 < x < I

and those across the AN-TIAN join by

CarFerTi"Sie-yOrz 0 < y < 1.42

By making the substitution 1.42x : y in the latterformula, the two joins can be expressed in terms ofthe same compositional parameter, x.

Properties of these garnets, such as refractive in-dices, density, and cell parameters, are described else-where (Huckenholz, 1969; Virgo and Huckenholz,197 4; H 6lzl, 197 5 ; H6lzl and Huckenholz, in prepara-

tion). The extent of stable garnet formation in the com-positional field AN-GR-CarAlrTirOrr-Ca3Fe2TirOrr,based on the studies of Huckenholz (1969) and Hdlzl(1975), is shown in Figure l. The compositions alongthe two joins discussed in this paper approach thelimit of stable garnet formation in this system.

4't8 HUGGINS ET AL: TITANIUM-CONTAINING SILICATE GARNETS

Table 2. M<issbauer data for the AN-TIAN ioin at 1050.C

Peak l Ine w id ths Area ra t los Cat ion s i te occupanc ies

(x ) T / t * A_. .x*( "c /days)

A A * * * ^ +- v l : : c j l j Ffur Ferv,r\rt t r l rv Iz

0 . 0000 . 3870.4870 . 5 8 70 . 7 0 60 .8 541 .000

1050 / 1551050 /5810s0/ 1051050 /5810s0/88r0s0/68r0s0 / 30

0 . 2 7o . 3 2n ? ?

0 . 3 40 . 34o . 3 40 . 3 4

o . 2 80 . 3 5o . 3 4o . 3 40 . 3 50 . 3 50 . 36

1 . 0 0I . 0 3r . 0 2L . 0 2r . 0 2I . 0 10 . 9 9

I . 0 0o . 7 50 . 7 20 . 6 70 . 6 30 . 5 10 . 4 1

0 . 3 00 . 6 0

0 . 6 00 . 2 40 . 14

o. i s0 . 3 10 . 3 10 . 3 10 . 3 3o . 3 2

2 . O 0I . 5 0t . 4 4r . 3 4r . 2 61 . 0 2o . 8 2

0 . 0 00 . 5 00 . 56o . 6 6o . 7 40 . 9 81 . 1 8

0 . 000 . 0 50 . 1 30 . 1 8o . 2 6o . 2 30 . 2 4

*TmPera ture in "c and t ime ln days o f exper imenta l condLt ions fo r c rysEa l l l za t lon f rm g lass .* *Rman numera l subscr ip t re fe rs to coord lna t ion number o f s l te .

* * *Subscr lp t C re fe rs to cmpos i te peak a t h igh veLoc i ty .tArea@ru + Ayr ) /a rea(46) .

t i ln th ts jo ln Fe IV and T iu , occupanc les must be equa1.

M'6ss baue r e x pe riment qtion

From 57Fe M6ssbauer experiments, the oxidationstate and location of iron cations within a crystalstructure can often be identified, and values for theferrous-ferric ratio and the ratio of iron between twoor more sites can be estimated if more than one typeof iron cation is present.

In this study, Mdssbauer experiments were per-formed in transmission geometry using u'Co in a pal-ladium matrix as the source of 7 rays. The energyspectrum was provided by the Doppler effect result-ing from the source moving at a constant accelerationwith respect to the stationary sample absorber. Thesource velocity varied by +4.2 mm/sec, Two mirror-image spectra of each sample were recorded simulta-neously in a 1024 multichannel analyzer, i.e. 512channels per spectrum. The velocity calibration andzero-velocity point of the spectra were achieved by

periodically measuring reference spectra of ironmetal foil.

The sample absorbers were prepared from mix-tures of finely powdered garnets and 100-125 mg ofLucite (Fisher Scient i f ic Company, Fair lawn, N.J.) ,which were hot-pressed at 150'C into 1.25 cm diame-ter disks of about 0.1 cm thickness. Enough garnetwas added to the Lucite so that the areal density ofiron was between 3 and 5 mg/cm2. This concentra-tion usually resulted in an absorption effect for thelargest peak of 6 to l0 percent (Fig. 2).

Data were usually accumulated until at least250,000 counts/channel were obtained. The spectraldata were then analyzed by means of a least-squaresfitting program on a Univac 1108 computer. Theprogram fits a specified number of Lorentzian-shapedpeaks to the data by an iterative procedure until a testfor convergence is satisfied. A typical fitted spectrum(one of the two mirror spectra) of a titanium garnet is

F"vr

Table 3. Mdssbauer data for the GR-TIAN ioin at 800o and 1050.C*

Peak l ine w id ths Area ra t ios S i te occupancLes

(r) T / t( 'cTaays)

A . -IVA Error (pfu)

0 . L 7 40 . 2 6 50 . 3590 .4570 . 5580 . 5 5 80 . 6 6 20 , 7 7 L0 . 883r . 000

800/L7800 / 18800/88O0/ 20800/ 14

L050/7 s1050 / 120L050 / L20L05o /7 510s 0/ 30

0 . 3 90 . 3 70 . 3 80 . 3 60 . 3 5o . 3 70 . 360 . 3 7U . J O

0 . 8 50 . 8 20 . 7 7

0 . 7 00 . 7 00 . 6 3

0 . 4 8

0 .0490 .095U . I O )

0 . 238U . J J )

0 . 3 3 50 , 4900 . 6 9 40 . 9 1 8

n 2 1 0

0 . 4 3 50 . 5 5 3u . o / o0 , 7 8 I0 . 7 8 10 . 8 3 40 . 8480 . 848

+0. 005+0 . 008+ 0 . 0 r 1+0 . 014+0 . 017+ 0 . 0 1 7+ 0 . 0 2 0+0 . 023+0 .026

0 . 4 8 0 . 3 60 , 4 3 0 . 3 40 . 4 0 0 . 3 40 . 3 9 0 . 3 4o . 3 7 0 . 3 40 . 3 4 0 . 3 40 , 3 5 0 . 3 50 . 3 5 0 . 3 60 . 3 3 0 . 3 5

See Tab le 2 .

0 . 98n oo0 . 9 91 . 0 11 . 0 11 . 001 . 0 21 d t

0 . 9 9

*Symbols as de f ined in Tab le 2 .

HUGGINS ET AL.: TITANIUM.CONTAINING SILICATE GARNETS

Table 4. Ordering schemes considered for garnets across the GR-TIAN join

OrderLns scheme* Equat ion for RtEquat ionr o r r 1 g . 4

479

A L > > F e > > T l

A 1 > > F e = T l

A 1 > > T i > > F e

A 1 = T i > > F eF e > > A I > > T iF e = A 1 > > T iF e > > T i > > A 1F e > > T i = A 1

T l > > A 1 > > F eT i > > A 1 = F eT l > > F e > > A 1T i = F e > > A 1A 1 = F e = T i

R = 1 . 0 0R = ( 2 - L . a L 6 1 , ) / 2 1R = 1 . 0 0n = 0 . s855 / IR = 1 . 0 0

(3) aboveR = 0 . 2 9 2R = L - 0 . 7 0 8 xJ4; atove(4) above

(3) above(3) above(3) aboveR = 0 . 5 8 5 5

! = 2 / ( 2 + 1 .416x )

( 0 . 0 < x < 0 . 5 8 5 5 )( 0 . 5 8 5 5 < x < 1 . 0 )( 0 . 0 < x < 0 . 5 8 5 5 )( 0 . 5 8 5 5 < x < 1 . 0 )( 0 . 0 < x < 1 . 0 )

( 1 )

( 2 )

( 3 )

( 4 )( s )

( 6 )( 7 )

* In terms of preference for tetrahedral s i tes, xbefore any J; I = I means completeLy dlsordered:

lsee equat ion 1 in text .

> > J means conpletely orderedlx and ; in tetrahedral s i tes

a lL x i n t e t r ahed ra l s i t ein acc6rd vt i th bulk rat lo.

shown in Figure 2. Three peaks are apparent vis-ually-although four peaks actually contribute to thespectral profile. The spectrum consists of two com-ponents, an octahedral ferric absorption and a tet-rahedral ferric absorption, each contributing twopeaks to the spectrum. The low-velocity peaks of thetwo components are well separated, but the high-velocity peaks overlap considerably, resulting in anapparent three-peak spectrum. The areas of the twopeaks of each component should be equal; hence, thearea of the composite peak at highest velocity shouldequal the sum of the areas of the tetrahedral peak atlowest velocity and the octahedral peak at inter-mediate velocity.

In this study, all spectra were fitted to three peaksof Lorentzian line-shape. As discussed previously(Weber et al.,1975), this fitting procedure requires noconstraints on any of the peak parameters and doesnot provide area ratios significantly different fromthose obtained with a constrained, four-peak fit. Asalso discussed previously, the quality of the data, andthe least-squares fitting procedure were evaluated us-ing the statistical parameters developed by Ruby(1973) and Dollase (1975). The following criteriawere adopted as indicating acceptable data and fit.First, the error in Mtsnn (Ruby, 1973), which is ameasure of the quality of the data, had to be less than0.05 percent. Secondly, the results from fitting thetwo mirror-image spectra obtained in each experi-

ment had to give closely similar parameters. Thirdly,the sum of the areas of the two resolved low-velocitypeaks had to be within a3 percent of the area of thecomposite, high-velocity peak. If the data and fit metthese requirements, the procedures outl ined by Dol-lase (1975) were used to estimate errors in the variousparameters.

For site distribution data, it is particularly impor-tant to assess the error in the area ratio. R. defined asfollows:

R : 2(area Avt)/area (Atu -f Av + Ac): Fevr/(Ferv * Fevr) (l)

where l1y, Ay1,a,fld,4c,, respectively, are the resolvedoctahedral, tetrahedral, and composite Mdssbauerpeaks (Fig. 2), and where Fevr and Ferv, respectively,are the octahedral and tetrahedral site occupancies offerric iron. By equating directly peak areas and siteoccupancies, it is assumed that the recoil-free frac-tions for ferric iron in the two sites are equal and thatno thick absorber corrections are necessarv. Based on

Table 5. Values for the distribution coefficients K, and K, for theGR-TIAN ioin

o r d p r n F i F r ? a h e d r a l

A 2 s i t e p r e f e r e n c eKr

f . 0 5 0 2 , 2 0 + O . 2 O 0 . 1 5 + 0 . 0 58 0 0 0 . 7 0 + 0 . 1 0 1 , 1 5 + 0 . I 0

A 1 > F e > T l

T i > F e > A l

480 HUGGINS ET AL.: TITANIUM-CONTAINING SILICATE GARNETS

Table 6. Supplementary experiments*

!/!( 'c l days )

Peak llne wldthg Area ra t los( x ) S i te occuDanc ies

4c4vrAtv

(a) GR-TIAN jo in at 800"C

0 .662 800 /14 0 .35o .77 r 8OO/ r4 0 .350.883 800/L2t 0.33

(b) AN-TIAN jo in above 1200'C

0 . 3 30 . 3 50 . 3 5

0 . 3 40 . 3 50 . 360 . 35o . 3 70 . 3 7

0 . 360 . 3 60 . 3 6

0 . 360 . 36

n ? 7

v . 5 t

0 , 3 7

o . 3 7

1 . 0 11 . 0 2I . 0 0

0 . 9 91 . 0 2L . O 2L . 0 2L . O 2r . 0 l

1 . 0 11 . 0 0

0 . 6 2u . ) o0 .48

0 . 7 50 . 7 0u . oo0 . 5 9v . ) a0 .46

u . ) o0 . 5 1

0 . 5030 . 6 7 80 . 9 1 8

+0 .023+0 .026

Fevr Error

0 . 8 2 Io .8640 .848

0 . 0 50 , 0 90 . 1 50 . 1 8v . z )

0 . 3 4

Ffuf FeIV,TIVI Tl tv K2

0 . 387o.4870 . 5 8 70 . 7 0 60 .854r . 000

t225 /7L22o /8L220 / 7t 275 /3t260 / 71245/ 5

L220/LotL230/40tt z45 / s

0 . 3 40 . 3 3o . 3 2o . 3 20 . 3 30 . 3 3

1 . 5 0I . 40L . 3 21 . 1 81 . 04o . 9 2

0 . 5 00 . 6 00 . 6 80 . 8 20 . 961 . 0 8

0 . 3 00 . 350 .43n ? ,o . 2 80 . 2 7

(c ) GR-TIAN jo in above 1200 'C

o , 7 7 L0 . 8 8 31 .000

0 . 3 4 0 . 3 80 . 3 3 0 . 3 6

See Tab le 6 (b ) .

+ 0 . 0 2 3+0 .026

*Syobo ls as de f lned ln Tab le 2 .tHeat lng exper lments on garnets c rys ta l l l zed a t l05O.C.

Dollase's scheme, the error in the area of peak l1ywould exceed t l0 percent when the tetrahedral occu-pancy of ferric iron was only about l0 percent of thetotal iron; however, the error in R was always be-tween I and 2 percent regardless of composition.Hence, the errors in the site occupancies of ferric ironin this study are estimated to be i0.03 cation performula unit for the AN-TIAN series. Errors in Fes+

Co3AlrTi .O,.

Co.Fe, Ti, o,uSi,..roO,zCo.Fe, Si30r2 Co.FerTi.O,,

Fig. l Diagram locating the'joins from along'which composi-tions were used in this study. The maximum extent of stable garnetformation in the system Ca.FerSLOrr-CarAlrSirOrr-CarFe2TirO,r-CarAlrTi3012 is also shown.

site occupancies for compositions across theGR-TIAN join are less than *0.03 cation per for-mula unit because of the smaller amounts of totali ron .

No ferrous iron was detected in the Mdssbauerspectra of any of the garnets, although l0-15 percentof the iron was in the ferrous state in the glasses.Owing to the oxidizing nature of the conditions underwhich the garnets were synthesized, it is assumed thatTi3+ is also absent.

Results

AN-TIAN join at 1050"C

The Mdssbauer data and derived ferric site occu-pancies for samples along the AN-TIAN join arelisted in Table 2. With increasing titanium content,the octahedral iron content decreases as shown graph-ically in Figure 3. Also shown in Figure 3 are calcu-lated curves for the theoretical random distributionand for the ordered distributions corresponding to alltitanium in either tetrahedral or octahedral coordina-tion. By plotting between the random curve and thecurve for the distribution that corresponds to all tita-nium in the octahedral sites, the data indicate thattitanium enters the octahedral site in preference toferric iron. It should be noted that the data show a

():. Gornei + ..... .. + corior

HUGGINS ET AL.: TITANIUM.CONTAINING SILICATE GARNETS

l , / = a ] f f T Y r n r n . / s e c

Fig. 2 Mi issbauer spectrum of TIAN (x : 1.0) . The data are f i t ted to three peaks: ,4y1, tetrahedralcomponent at low veloci ty ; ,4vr ,

octahedral component at low veloci ty ; and Ag, a composi te peak, resul t ing f rom the superposi t ion of the octahedral and tetrahedral

components at h igh veloci t ; .

481

ZnHFttVDrJriltr

0.03

FL

trZntflUU-

Jtrl 'F

ot lLIv. -2

- 4,2

break in the trend between x = 0.7 and 0.85, which isalso reflected in the values of K2, the distributioncoemcient, defined as follows:

K, : [Fe"rl[Tirv]/[Ferv][Tivr] Q)

Values of K, (Table 2) suggest that either the distribu-tion is not at equilibrium or cation exchange of Fe8+and Ti4+ between the distinct sites does not conformto an ideal distribution model.

GR-TIAN join at 1050" and 800oC

The Mcjssbauer results for the GR-TIAN join arelisted in Table 3. The data show a trend (Fig. 4) withincreasing titanium content that is very similar to thatof the AN-TIAN join. Also shown in Figure 4 are

calculated curves for the extreme order or disorderschemes listed in Table 4. These curves show thecalculated value for R at a given composition for aparticular ordering scheme. Figure 4 shows that theexperimental data do not match any of theseschemes, although the data for low-titanium samples(x < 0.6) do plot close to the random model (Al : Fe: Ti). It is therefore inferred that the distribution isan order-disorder phenomenon.

Although Mdssbauer experiments only providedata relating to the site distribution of ferric iron, byutilizing the compositional constraints on the join itis possible to evaluate the data in terms of an idealcation-exchange model involving the distribution ofand Tio+. Al3+. and Fe3+ between the distinct sites. A

HUGGINS ET AL.: TITANIUM.CONTAINING

o 4

AN T I A N

Fig. 3. Plot of the ferric distribution parameter, R, as a functionof the compositional parameter, ,r, for samples along theAN-TIAN join synthesized at 1050'C. Also shown are curvescorresponding to a random distribution of Fe8+ and Tin+ (K, : 1 1and to the ordered distributions where Ti enters the tetrahedral site(K, : o1 or the octahedral s i te (Kr= 0)

somewhat related approach was taken by Navrotsky(1975) in evaluating the site distributions, based onlyon Fe2+ M6ssbauer data, of Fe'+, Ti3+, and Tia+ inpseudobrookites between FeTirOu and Tiaob.

In the synthetic GR-TIAN join, the followingcompositional constraints are present:

Al * Fe + Ti : 2 t- 1.42x (3)

A l v r + F e v r * T i v r : 2 ( 4 )

Alrv + Fely * Ti* : 1.42* (5)

A l r v + A l v r : A l : 2 - 2 x ( 6 )

A l o r T i > > F e T i > > F e

0 .6 0 .8 r . o' T I A N

Fig. 4. Plot ofthe ferric distribution parameter, R, as a functionof the compositional parameter, x, for samples along theGR-TIAN join synthesized at 10500 or 800'C. Curves corre-sponding to the ordering schemes listed in Table 4 are also shown.

SILICATE GARNETS

Ferv * F€vr : Fe = 2x (7)

Tirv + Tivr = Ti : 1.42x (8)

Hence, only two site occupancies (for different ele-ments) need be measured for complete knowledge ofall the site occupancies. The M6ssbauer data providesite occupancies for only one element. The lack ofknowledge concerning one more site occupancy canbe translated into a relationship between Kt and Kr,the distribution coefficients for Al-Fe and Ti-Fe ex-change, respectively. The latter is defined in equation(2) above; the former is defined as follows:

l(, : [Ally][Feur]/[Alur][Ferv] (9)

By manipulation of eqs. (2) and (6-9), the octahedraloccupancies may be expressed in terms of Kr, Kr, x,and Rr", as follows:

A l v r : Q - 2 x ) / ( l * K r R r " )

Tivr :

Fevt

1.42x/(l * KzRr")

: 2x/(l + Rn") (.l'2)

where Rp" is the ratio Ferv/Fevr. By substitutingthese values in equation (4), an expression relating Ktand K2 is obtained:

(2 - 2x)/(l * K1Rp") + 1.42x/(l + K2RF")+ 2 x / ( l * R r " ) : 2 ( 1 3 )

Thus, at a given value of x, a measured value of Rr"defines a relationship between Kt and Kr. If mixing ofcations at the distinct crystallographic positions con-forms to an ideal cation-exchange model, the valuesof K, and K, should be constant at any given temper-ature; therefore, curves relating K, and K, for eachvalue ofx should intersect at a unique point reflectingthe most appropriate values of Kt and K, at thattemperature. When the measured Rr" values are sub-stituted into equation (13), the"curves shown in Fig-ure 5 result, and the assumption of ideal cation-exchange behavior appears to be satisfied, because aunique point is in fact obtained for each temperature.Not only do the data seem to provide a test of theideality of cation exchange between the sites in thesolid-solution series, but the most appropriate valuesof K, and K, (Table 5) at the two temperatures andhence complete site occupancy data can also be deter-mined. The ferric data and the calculated curves de-fined by values of Kr and K, are compared in Figure6 .

Although the test for ideal cation exchange (Fig. 5)and the fit of the data to the distribution curves (Fig.6) were satisfactory, there are a number of factors

(10)

(11 )

o 0 2 0 4G R

1te..,

F e = T i > A l

( e q 3 )

4t,

)i"r,

( e q 6 )

F e > > T i o n d A l

HUGGINS ET AL.: TITANIUM-CONTAINING SILICATE GARNETS 483

suggesting that this result might be misleading. First,the ferric distribution data for the two joins lie onalmost the same trends (compare Figs. 3 and 4).Secondly, the cation distribution in the AN-TIANjoin does not conform to an ideal cation-exchangemodel, and the values of K, are not compatible withthose for the GR-TIAN join (compare Tables 2 and5). Thirdly, the site preferences in the GR-TIAN joinbecome reversed between the two temperatures(Table 5). Because ofthese factors, additional heatingexperiments were made in order to evaluate the effectof temperature on the site distribution and to obtainsome understanding of the kinetics of the exchangereactlon.

The data and curves in Figure 6 suggested an initialtest of the distribution model because, as indicated inthis figure, there should be a large difference in Rbetween samples synthesized at 800oC and thosesynthesized at'l050oC at the titanium-rich end of theGR-TIAN join. Subsequently, crystallization experi-ments at 800"C were carried out at this end of thejoin; the M6ssbauer data for these samples are sum-marized in Table 6a. The ferric distribution data arealmost identical with those for samples of the samecomposition but synthesized at 1050'C. The nearcoincidence of the data for the samples crystallized atthe two different temperatures strongly suggests thatat these temperatures the observed distribution doesnot approach equilibrium and that factors other thantemperature alone are controlling the distribution.Further discussion of this result is oresented later inthe paper.

Experiments with high-temperature runs

Only at temperatures of 1200"C and above is theiron distribution observed to change significantly.Figure 7 illustrates the subtle changes induced byheating at l220oC for 40 days a sample originallycrystallized at 1050'C. The Mdssbauer data for sam-ples synthesized or heated for periods up to 6 weeksat temperatures in excess of 1200'C are listed inTable 6b and 6c for the AN-TIAN and GR-TIANjoins, respectively.

The K, values for the AN-TIAN join at -1250'Cappear to fit a single ideal isotherm curve, defined bya K, value of about 0.30 (Fig. 8). The data scattersomewhat about this curve, and this scatter may in-dicate that equilibrium has stil l not been completelyattained. The ferric distribution at -1250'C clearlyconforms more closely to an ideal distribution thanthat at 1050'C. For the three samples on theGR-TIAN join, which are stable at 1225"C, a ther-

oo |

* , t

F ig. 5. Plot of the re lat ionship between the two dist r ibut ion

coefficients, K, and Kr, defined by the Mcissbauer ratio, Rr", for

garnets a long the GR-TIAN jo in. The points of intersect ion at the

different temperatures define the most appropriate values of K'

and Kz for the samples.

modynamic analysis based on an ideal cation-ex-change model was carried out; this analysis was sim-ilar to that for the samples synthesized at 1050' and800'C. The K' us. K, plot (Fig. 9) gave a well-definedpoint of intersection, which defined values of 1.35 *0.25 for K, and 0.25 + 0.05 for K2. At this temper-ature (-1225"C), the values for K, for the differentjoins are compatible, unlike the situation at 1050'C.

These results suggest that at temperatures above1200'C the cations between the different sites in thegarnet structure are approaching a distribution thatconforms to an ideal cation-exchange model. At suchhigh temperatures, the equil ibrium preferences of thethree cations for the tetrahedral sites in the garnet

structure, as defined by the values ofKt and K2, areinthe order Al > Fe ) Ti. From the values of K' and K,

at -1250"C, using the relationship

Fig. 6. Comparison of the ferric distribution parameter, R, andcalculated isotherms defined by the values of r(t and K, listed inTable 5 for the CR-TIAN ioin.

o 0 2 a 4

ut r

d

o

o

o

qbo

6

6

E

O

;

a - ,

a o

= d

z*< 3 ,- n

t -

^ ( ,@ c )

. . oJ N

G ;d b

l ' E

6b '

- A ' =

: o 3> - j

. qr t r

d i-n

I r o

oo

Eo -o >:

ooo

HUGGINS ET AL,: TITANIAM-CONTAINING SILICATE GARNETS

lonprsau

O o O n@ loo

o

oo

E

oo

oFoo

ott)

uorlorosqo luouosau lonprsau

HUGGINS ET AL.: TITANIUM-CONTAINING SILICATE GARNETS

LGE : RT ln K i

(where AG6 is the free energy of exchange, Z is thetemperature in oK, and R is the gas constant), a LGBvalue of - I kcallmole can be estimated for Al-Feexchange and -4 kcallmole for Fe-Ti exchange.These values are similar to those estimated for othercation-exchange phenomena found in oxides and sili-cates (e.9. Virgo and Hafner, 1969; Seifert and Virgo,1975) .

Discussion

Kinetics of the order-disorder phenomena andge o the rmomet ry im pl i cations

One of the reasons for investigating the site prefer-ences of titanium-containing garnets was to assesstheir potential as geothermometers and indicators ofthermal histories of rocks containing such garnets.This study shows that samples synthesized or heatedat temperatures above 1200'C for up to 6 weeks havean internal cation distribution that approaches thatpredicted from an ideal cation-exchange model com-patible with data from both joins. Thus, it is est!mated that at such temperatures a period of at least Ior 2 months is probably required for an equilibratedstate to be reached. The time needed to reach equilib-rium at temperatures of 1050'C or below, therefore,may be on a time scale of years. This inference issupported by the similarity of the cation distributionsin samples synthesized at 800o and 1050'C, despitesynthesis times of up to 4 months for certain samples.

In addition, the maximum possible change in theratio R (Eq. l) is not very large except at the tita-nium-rich ends of the joins. Based on the order ofpreference for the tetrahedral site, Al ) Fe ) Ti,determined at high temperatures, the range of valuesof R that can be expected for the AN-TIAN join isdefined by the curves where Kz - 0.3 and K" - 0 (Fig.8). For the GR-TIAN join, values of K, and K, canbe expected to be limited to ) I and ( l, respectively.Hence, the area in which data for this join should plotis bounded by the curves denoted by Al >> Fe : Tiand Al : Fe ) Ti in Figure 4. This range is prob-ably much greater than that found in practice, how-ever, because it is unrealistic to expect complete or-dering for one pair of elements while the second pairof elements shows complete disordering. Further-more, it can be anticipated that the different values ofthe distribution coefficient as a function of temper-ature are probably mostly associated with Al and Ti,rather than Fe. This fact is a direct result of theintermediate position of ferric iron in the order of site

r o

o , 2 0 4 0 6 0 8 l ox T I A N

Fig. 8. Plot ofthe ferric distribution parameter, R, as a function

of the compositional parameter, x, for samples along the

AN-TIAN join synthesized at temperatures above l200oC. Curves

corresponding to different values of the distribution coefficient, Kr,

are also shown.

preference. Changes in the ferric distribution as aresult of a stronger preference of Ti for the octahedralsites at lower temperatures are compensated by oppo-site changes as a result of a stronger preference of Alfor the tetrahedral site.

The unfavorable kinetics, at least for these re-stricted compositions, and the small range of valuesexpected for changes in the ferric distribution wouldappear to preclude the calibration ofa useful geother-mometer based on Mdssbauer measurements of theferric distribution in titanian garnets. However, thevery slow kinetics for the order-disorder phenome-non may be used to indicate the crystallization proc-ess, because at low temperatures the distribution gen-erated upon formation may be effectively "frozen-in." This aspect is discussed in detail in the nextsection.

Fig. 9. Plot of the relationship between the two distributioncoefficients, K, and K", defined by the Mdssbauer data for garnetsalong the GR-TIAN join stable above l200oC.

o 8

o oAN

K 2

K r - t t - t 6 , K 2 - o 2 - O 3

HUGGINS ET AL.: TITANIUM.CONTAINING SILICATE GARNETS

The extremely sluggish rate of cation exchange inthe synthetic garnets is similar to that in the feldspars,because in both minerals the order-disorder exchangereactions involve both trivalent and quadrivalent cat-ions in tetrahedral sites. The activation energy forcation exchange must reflect the strength of the bondsbeing broken. As bond strength depends on ioniccharge, among other factors, and inversely on thecoordination number, the activation energy forAl-Fe-Ti exchange in garnets and Al-Si exchange infeldspars can be expected to be two to three timesgreater than that for Fe'z+-Mg exchange between oc-tahedral sites in chain sil icates. Hence, on the basis ofthe standard Arrhenius equation describing rate con-stants, temperatures would have to be two or threetimes greater for Al-Fe-Ti exchange in garnets tooccur at the same rate as Fe2+-Mg exchange in chainsil icates. Such a difference is indeed found when the"cut-off ' temperatures for the two exchange proc-esses are compared. The cut-off temperatures arethose at which cation exchange is too slow to be con-veniently measured in the laboratory, -500-700K

for Fd+-Mg exchange in chain sil icates (Virgo andHafner, 1969; Seifert and Virgo, 1975) and -1500K

for Al-Fe-Ti exchange in garnets.

Influence of crystallization path on the cqtiondistribulion at low temperatures

Despite the excellent f it of the data to ideal cation-exchange models (Figs. 4 and 5), the cation distribu-tions in the GR-TIAN join, as well as in theAN-TIAN join, do not appear to have reached equi-l ibrium when crystall ized at temperatures of l050oCand below. Indeed, because of the sluggish kinetics, itis l ikely that the observed cation distributions areeffectively init ial distributions, which were generatedat the beginning of crystall ization and do not changesignificantly during the remaining time of crystall iza-tion. Such distributions may be regarded as frozen-in.

The distinct breaks in the trends of the ferric distri-bution against composition (Figs. 3 and 4) indicatethat more than one crystall ization mechanism isneeded to account for the observed init ial distribu-tions. The closely similar trends of the two joins,however, suggest that these init ial distributions, andhence the crystall ization mechanism, are determinedprimarily by the titanium content. There appear to beat least two possible mechanisms that could give riseto an init ial distribution dependent only on titaniumcontent: (l) crystall ization directly from the glass,and (2) crystall ization from the glass ura metastablephases. For the first mechanisrn to be operative, the

glass "structure" and garnet structure should be quitesimilar, so that the cation distribution in the glass canbe retained upon crystallization. Both Mdssbauerand vibrational (infrared) studies show, however,that the glass and garnet are structurally different.Mdssbauer spectra of the glasses (Fig. 10) uniformlyshow a broad absorption doublet, which has parame-ters intermediate to those of octahedral and tetrahe-dral ferric iron in a titanian garnet. Such spectra werefound to be identical regardless of whether the com-position was that of AN or TIAN, or from along theGR-TIAN join. These results suggest that the garnetand glass structures are not directly related. Sim-ilarly, vibrational spectra of the garnets and glassesindicate the lack of an obvious structural relation-ship. As can be seen in Figure 11, the main Si-Ostretching vibrations in the garnets compared withthose of the respective glasses are aI significantlylower frequencies. This observation suggests thatthere may be Si-O-Si linkages in the glass, because itis well known that Si-O polymerization effectivelyincreases the frequency of vibration. Less direct evi-dence that the garnets and their glass are structurallyquite different is the fact that in neither join does agarnet crystallize directly from the glass (Hucken-holz,1969; H6lzl, 1975), Instead, depending on com-position, the subliquidus phases for these garnet com-positions are gehlenite, pseudowollastonite, orperovskite. Hence, significant structural rearrange-ment and movement of ions are necessary if the gar-nets are to crystallize directly from the glasses, andany relative ordering of the Al, Fe, and Ti cationsbetween the octahedral and tetrahedral sites in theglasses is unlikely to be retained in the correspondinggarnets.

For the above reasons, the alternative hypothesisinvolving the formation of metastable phases in thecrystallization process must be evaluated. Evidencefor this process is provided by Huckenholz (1969),who reported that, for low-titanium compositions,wollastonite and hematite were found in addition togarnet in synthesis runs of short duration. On furtherheating, these phases diminished with time, until onlygarnet remained. Furthermore, glasses of high tita-nium content usually contained perovskite uponbeing quenched. Both wollastonite and perovskiteoccur prominently in the high-temperature break-down reactions that separate liquid and garnet fieldsin the garnet phase diagrams (Huckenholz, 1969;Hdlzl, 1975). Whether CaSiO, or CaTiOs is found ata given composition depends entirely on the TilSiratio.

HUGGINS ET AL,: TITANIUM.CONTAINING SILICATE GARNETS

o oV e l o c i t y , m m / s e c

Fig. 10. M tissbauer spectrum of glass of andradite garnet composition. The spectrum is fitted to only a single dou blet ( I S = 0.3 I , eS :l . f9; c/. t i tanium garnets, Virgo and Huckenholz, 1974; Huggins et al. ,1975).

487

c\

oo

oo

E

Hence, it is postulated that the init ial, frozen-incation distributions in the garnet and the break in thedistribution trends are determined by the followingcrystall ization paths (Fig. l2):

Si-rich compositions: glass +(CaSiO, * glass * garnet) + garnet

Ti-rich compositions: glass +(CaTiOr* glass * garnet) + goftet

The reaction between the metastable CaSiO, orCaTiO, and glass would then give rise to the observeddistribution of cations in the garnet. We suggest thatthese metastable phases act as nucleation sites for theformation of the garnet; because CaSiOa does not f ixAl, Fe, or Ti in a given coordination site, the distribu-

tion of these cations in the Ti-poor garnets is close torandom. Conversely, because CaTiO, does contain Tiin octahedral coordination, Ti-rich garnets formedvia metastable CaTiO, may contain a disproportion-ately large amount of octahedrally coordinated Ti inthe in i t ia l d is t r ibut ion.

In view of the influence of the crystall ization pathon the init ial cation distribution in garnets discussedabove, it is instructive to compare the cation distribu-tion in garnets formed in other ways with the well-defined trend for the ratio R as a function oftitaniumcontent established in this study. The result obtainedby Burns (1972) for the composition CarFerTiSirO,2,which indicates that no titanium is present on thetetrahedral sites, differs significantly from the trendfor garnets crystallized from glasses, and may reflect

488 HUGGINS ET AL.' TITANIUM-CONTAINING SILICATE GARNETS

l loo rooo 900 800 700 600

i loo 1000 900 800 700 600

Wove number in cm- l

Fig. I I Compar ison ofv ibrat ional spectra ofgarnets and glasses

showing Si-O stretching bands at higher frequencies for glasses.

a completely different trend for samples synthesizedby sintering coprecipitated gels at l050oc for 20hours (lto and Frondel , 1961). Similarly, natural gar-nets from serpentinized peridotites (Burns and Burns,l97l; Huggins et al., 1977) appear to lack ferric ironin tetrahedral coordination in the Mdssbauer spec-trum, and may lie on yet another initial ferric distri-bution trend.

C r y s tal- che micql c onside rat ions

The order of tetrahedral site preferences inferredfor synthetic titanium silicate garnets, Al > Fe ) Ti,may be compared with the site preferences found inother synthetic garnets. A number of studies usingdifferent techniques have shown that aluminum fa-vors the tetrahedral site relative to iron in YrFeu-"Al,O,, (e.g., Geller et al., 1964; Borghese, 1967;Czerlinsky and Macmillan, 1970.) In this garnetsolid-solution series, the data do not conform to anideal solid solution model (Fischer et al., 1975), andthere appears to be some disagreement between re-sults obtained with different techniques. The relativesite preferences of iron and titanium have been stud-ied in Yr-,Ca,Ti,Fer-,O,, (Espinosa, 1964; Geller elal., 1965) and in CarFer-"Tiz"Vr-,O,, (Nakayama etal., l97l). In both series of garnets, titanium was

found to favor strongly the octahedral site relative to

ferric iron; in neither study, however, was a detailedthermodynamic analysis of the data attempted. The

site preferences of other cations, which have been

evaluated in synthetic garnets, include Ga (Geller el

al., 1966; Czerlinsky, 1969; Mueller and Ghose, 1970)

and Zro+. Sno+, Sc3+, Cr8+, and In3+ (Geller, 1967).

Gallium has a stronger preference than either Al or

Fe for the tetrahedral site, whereas the other five

cations are found exclusively in octahedral sites.

Hence the experimentally determined preferences for

the tetrahedral sites in garnets are in the order Ga )

Al ) Fe > Ti >> Sc, In , Zr ,Sn, Cr . Of thesenine

cations only Cr3+ has an octahedral site preference

arising from crystal-field effects, so that in at-

tempting to rationalize the order for the remain-

ing eight cations, this factor need not be con-

sidered. The fact that garnets of the formulaeA?+ 832+ Ctr+Op, A3+ 832+ Ct+Or2, A3+ Bt+ Co+ Dtr+On' and

AZ+ B3+ Cl+ D3+O,z have all been synthesized indicatesthat ionic charge is not the dominant factor in deter-mining site preferences. If ionic size were the onlycriterion, the predicted order of tetrahedral site pref-

erences would be Al )) Ti ) Ga ) Fe )) Sn ) Zr )Sc ) In, based on Shannon and Prewitt 's (1969)

ionic radii. This order is indeed essentially correct,because all ions l isted above that are larger than Fe3+are lound exclusively in octahedral coordination;however, the inferred order for those cations found in

both octahedral and tetrahedral coordination, Ga(0.62) > Al (0.53) > Fe (0.645) > Ti (0.605) , is notcompatible with ionic size. Dowty (1971) proposed

that electronegativity might be an additional factorthat determines cation site preferences in titaniumsilicate garnets. We therefore suggest that the experi-mentally established order of tetrahedral site prefer-

Fig. 12. Crystallization paths suggested for the GR-TIAN join

to account for initial cation distribution in the sarnet.

co

oo.n-o

.t.V

ence reflects electronegativity as well as ionic size.With this factor the following order may be pre-dicted, Fe (1.9) > Ga (1.7) > Al, Ti (1.6), based onBatsanov's (1968) electronegativity scale; hence it isquite conceivable that the influence of both factorswould explain the observed order of site preferences.The use of electronegativity as a factor determiningsite preference suggests that cations with a largerelectronegativity favor the tetrahedral site over theoctahedral site in the garnet structure.

Conclusions

In this study, the relative preferences of Al, Fe, andTi for the tetrahedral sites in garnets have been dem-onstrated to be in the order Al > Fe ) Ti andconfirm the predictions made by Hartman (1969).This result can be rationalized if both ionic size andelectronegativity are considered as important factorscontrolling the site preferences. The kinetics for ex-change appear to be very slow; garnets formed fromglasses at temperatures less than l050oC appear tohave their initial cation distribution frozen-in despiteheating times of up to 4 months. Indeed, it appearsthat the distribution of ferric iron in the garnet struc-ture is probably determined mainly by the formationreaction, unless sufficiently long heating times andhigh temperatures have been used, when equilibriummay have been approached.

AcknowledgmentsThe authors are grateful to E. Hdlz l (Univers i ty of Munich) for

supply ing the synthet ic garnets on the GR-TIAN jo in. The au-thors a lso acknowledge discussions and reviews ofprel iminary andf inal vers ions of th is manuscr ipt by R. H. Mccal l is ter , L W.Finger, H. S. Yoder, Jr . , B. J. Wood, and S. S. Hafner.

The last-named author (H.G.H.) grateful ly acknowledges thesupport given him by the Deutsche Forschungsgemeinschaft tocarry out parts of th is study.

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Manuscript receiued, June 28, 1976; accepted

for publication, Nouember 18, 1976.