American Mineralogist, Volume 7 5, pages 319-327, tg90

Activity-composition relationships of binary ca-Fe and ca-Mn garnetsdetermined by reversedo displaced equilibrium experimenti

ANonrl, M. Kozror,*Department of the Geophysical Sciences, University of Chicago, 5734 S. Ellis Avenue, Chicago, Illinois 60637, U.S.A.

AnsrucrActivity-composition (a-X) relationships of grossular-spessartine and grossular-alman-

dine garnets have been determined by reversed phase-equilibrium experiments at 900 "Cand 1000 "C and ll to 18 kbar in the assemblage garnet-plagioclase-kyanite-quartz. Theaddition of 2 to 4 wto/o LirMoOo promoted equilibration. The results indicate that gos-sular-spessartine garnets mix ideally. Cell-edge measurements indicate no excess volumeof mixing. It is therefore reasonable to consider Mn as an ideal diluent of ternary Ca-Fe-Mg garnets. For grossular-almandine, activity-composition relationships are nearly idealat 900'C and 1000 oC but can also be described with an asymmetric (subregular) Margulessolution model. When the data obtained at 900'C and 1000'C are considered togeiher,the calculated free-energy parameters are Wr: Wc^p": -1.09 kJlmol of cation ia W,: Wr*^: 2.59 kJ/mol of cation. These results, together with those of high-temperatureoxide melt calorimetry, indicate that excess

"otropy of Cu-Fe mixing in garnet is effectively

zefo.

INrnooucrroN

A common approach used to determine the metamor-phic and tectonic histories ofterranes is to apply geother-mometers and geobarometers to unravel the pressure-temperature-time paths of rocks. The geothermometersand geobarometers are based on thermodynamic expres-sions of equilibrium between coexisting phases. Althoughknowledge of the thermodynamic properties of the end-member phases has improved markedly through recentanalysis of phase equilibrium and calorimetric data (Hol-land and Powell, 1985; Berman, 1988), progress on thesolution properties of minerals has been slower. Garnetis a participating mineral in many useful geothernome-ters and geobarometers; its solution properties are essen-tial in calculations of the pressures and temperaturesrecorded by metamorphic rocks. Uncertainty in the ac-tivity-composition (a-X) relations of a mineral such asgarnet may be one of the largest remaining uncertaintiesin thermobarometry, as discussed by Essene (1999).

Most garnets within the crust of the Earth are complexmulticomponent solutions of the major substituents Ca,Fe2+, Mg2+, and Mn2+ on the eight-coordinated X siteand Al3+, Fe3+, and Cr3+ on the octahedral y site(Meagher, 1982). To construct a reliable thermodynamicmodel of mixing, a formidable amount of experimentalwork is needed to constrain the free energy of mixing ofcomponents in this complex solid solution. Initially it isimportant to define the mixing properties of the principalbinary joins, such as grossular-almandine, grossular-py-

* Present address: U.S. Geological Survey, MS 910, 345 Mid_dlefield Road, Menlo Park, California94025, U.S.A.

rope, and grossular-spessartine, which can be used to for-mulate a comprehensive mixing model (Ganguly andSaxena, 1987 , p. 98-1 02).

There are several ways to constrain mixing behavior ofbinary garnets. Experiments that determine the displace-ment of an equilibrium as a function of a given mineralcomposition are an important source of information, butonly if pressure and temperature are well controlled, min-eral compositions are well known and reversals are pre-cise. Measurement of the displacement of the reaction 3anorthite : grossular * 2 kyanite + qvafiz by dilutinggrossular with other components, first performed by Hen-sen et al. (1975), provides estimates of activity-compo-sition relationships for a range of garnet compositions.This technique has been used by Cressey et al. (1978) forthe Ca-Fe join, by Wood (1988) for the Ca-Mg join, andby Koziol and Newton (1989) for a limited range of Ca-Fe-Mg solid solutions.

Cressey et al. (1978) measured the free energy ofgros-sular-almandine solutions over 850-1 100 'C and 0.12 <Xa = 0.79. Most final garnet compositions were deducedfrom garnet cell-edge information. They concluded thatthe activity-composition relationship was nearly ideal withslight negative deviations for Fe-rich compositions andpositive deviations for Ca-rich compositions. An appar-ent temperature dependence of mixing properties wasascribed to excess entropy. Later theoretical studies havequestioned whether equilibrium was attained in these ex-periments (Ganguly and Saxena, 1984; Anovitz and Es-sene,1987).

Determination of excess free energy, excess enthalpy,and confirmation ofexcess entropy are needed for Ca-Fegarnet to formulate an accurate mixing model. Geiger et

0003{04xl90/030443 I 9$02.00 319

320 KOZIOL: ACTIVITY-COMPOSITION RELATIONSHIPS OF BINARY GARNETS

al. (1987) have measured the excess enthalpy often gros-

sular-almandine solutions by alkali borate calorimetry at760 'C. They found that the enthalpy of mixing of Ca

and Fe2+ was nearly ideal. Consideration of all the dataofCressey et al. (1978) and Geiger et al. (1987) Ied topredictions of excess entropy in the models of Gangulyand Saxena (1984) and Anovitz and Essene (1987). How-ever, ifonly the best-constrained data at 1000 "C ofCres-sey et al. (1978) are combined with the data of Geiger etal. (1987), then excess entropy is virtually zero (Ganguly

and Saxena, 1984, p. 9l).This study attempts to resolve these discrepancies by

constraining the excess free energy of Ca-Fe garnets andby demonstrating the attainment of equilibrium throughreversed compositions. The use of NaCl pressure mediafor more accurate measurements and of a molten oxysaltflux to promote equilibration of the experimental chargeshave resulted in an improved description of the a-Xproperties of Ca-Fe mixing and a determination of Ca-Mn mixing.

The displaced equilibrium technique

The displaced equilibrium technique involves the de-termination of a change in pressure (at constant temper-ature) ofa univariant equilibrium as a result ofsolid so-lution in one of the phases (Cressey et al., 1978; Schmidet al., 1978). The thermodynamic basis of this techniquehas been discussed by Wood (1988). The univariant equi-librium ofinterest is

3 anorthite : grossular + 2 kyanite (or sillimanite)CaAtrsirOs CasAlrsi3Op AlrSiOr ( l )

+ quanzsio,

When only garnet is a solid solution and the other phases

are the pure components at unit activities, the activity ofgrossular in garnet can be determined using the relation-ship

L* o* dP: Rrrn ag;

where F is the equilibrium pressure of the end-memberequilibrium at T, T is the temperature of the experiment,P is the pressure of the experiment, Alrc is the volumechange ofReaction l, and aS is the activity ofthe gros-

sular component in garnet. When the integral on the leftside is evaluated, the activity ofgrossular in garnet at Iand P is determined. Following Koziol and Newton(1989), Equation 2 has been integrated using volume datafrom Holland and Powell (1985) that incorporate expan-sivity and compressibility terms. In garnet, the cationsmix over three sites per formula unit, giving the followingrelationship between activity and mole fraction:

agl: (X'.r^)' (3)

where X* is the mole fraction of CarAlrSirO,, in the bi-

nary solution and T* is the activity coefrcient of

CarAlrSirO,r. Measurement of the garnet compositions in

equilibrium with anorthite, AlrSiOr, and quartz over a

range of P and 1" permits calculation of "y* and the activ-

ity-composition relationships. For optimal precision' the

end-member curve must be well known; see Koziol and

Newton (1988).

(2)

ExpnnrvrnNTAl, PRoCEDURE

Apparatus

All experiments were performed in a piston-cylinder

apparatus, using a 3/+-in. ( I .9 I -cm) diameter assembly with

a NaCl pressure medium and a WRer-WRe' thermocou-ple. Procedures have been described by Koziol and New-

ton (1989). Temperature uncertainties with these ther-

mocouples are about +10 "C (Perkins et al., 1981).

Experiments performed at 1000 oC and ll.l kbar were

very close to the melting curve of NaCl (Clark, 1959)'

which was the effective lower pressure limit of the exper-

iments. A correction of -200 bars was applied to the

nominal pressure of the piston-out experiments to be in

accord with the work of Koziol and Newton (1988). Sil-

ver capsules, 1.5-mm diameter and with a 0.153-mm wall

thickness. were used. Two capsules, containing mixtures

of anorthite, kyanite, and quartz and each with garnet

crystals of a diferent composition, were placed side by

side in the salt assembly, with the thermocouple tip be-

tween them. Care was taken that the capsules did not

touch the graphite sleeve or each other. The thermocou-ples were protected from contamination by the silver

sample capsules by a thin layer of AlrO3 cement.

Synthesis and characterization of garnets

Garnets were crystallized from stoichiometric mixtures

of glasses of end-member composition as described by

Geiger et al. (1987) and Koziol and Newton (1989). Pre-

vious workers (Snow, I 943; Yoder and Keith, I 95 1 ; Mot

tana, 1974) made spessartine glass by melting a mixture

of oxides in a gas-mixing furnace. An alternative method

was devised in the present study for melting large batches

of oxide mix. A finely ground mixture of MnO, AlrOr,

and SiO, oxides of the stoichiometry of spessartine was

with loose granular MnO. This setup was placed in a

vertical furnace with a strong flow of nitrogen, monitored

by observing an outflow stream ofbubbles through water.

The oxides were melted at 1280-1330 "C for lG-l5 min

and quenched in water. The resulting quenched glass was

clear, orange-brown, and a rosy orange color in small

chips, similar to the color described by Mottana (1974).

The crucible lid made of MnO remained green except on

its outer surface, which became brownish. The MnO bufl

er was therefore effective. The refractive index ofthe glass

KOZIOL: ACTIVIry-COMPOSITION RELATTONSHIPS OF BINARY GARNETS 321

variedamongbatchesfroml.665tol.6T3(+0.002).Ox- TABLEl. Compositionsandceildimensionsofsyntheticgarnetsidesmel tedunderf lowingni t rogenwi thout theMnobuffer produced a glass ofa dark ied-brown or burgundy Actuat ::Xtlilf No. or Motarvotume.color, indicating substantial oxidation of Mn. composition (mot% grs) anatyses a A.

- - iil;;j

-

An oxide mix composed of reagent calcite, AlrOr, andSiO, equivalent to the composition of grossular was driedat I l0 "C, heated to 800 "C overnight to drive off COr,and then melted at 1350 oC in a vertical platinum-woundfurnace for 20 min. The resulting glass was finely groundand remelted to a clear glass. Following the procedure ofBohlen et al. (1983b), almandine glass was made from afinely ground mixture of high-purity hematite, AlrOr, andqtf,artz, melted in graphite crucibles at 137 5 .C and onebar until the Fe was reduced to Fe2+ and there was incip-ient Fe metal saturation. The glass used in this study wasthe same as that used in the experimental study of Pat-tison and Newton (1989). It was clear forest green in colorand had no magnetite microcrystals and negligible Fedroplets.

Pure spessartine garnet was synthesized at 1250 "C and20 kbar for 2l h. The synthesis produced very pale green-brown crystals with a refractive index greater than 1.780but less than 1.800, in accord with previous syntheses(Matthes, l96l; Hsu, 1968; Mottana,1974). Nine gros-sular-spessartine garnets and four grossular-almandinegamets were synthesized at 1250 'C and 26 kbar in largevolume (0.5 to 0.6 g) graphite containers with a soft-glasspressure medium. Synthesis duration was 2448 h. Theresulting material was more than99o/o isotropic. The syn-thetic garnets were homogeneous and very close to theirintended compositions, as determined by electron micro-probe analysis. Some syntheses had a trace amount ofquartz, observable only as a crystal or two in an oil-im-mersion grain mount. Table I gives measured composi-tions and cell dimensions for grossular-spessartine andgrossular-almandine garnets.

Experirnental technique

Starting materials consisted of 30 wto/o garnet seeds l0-30 pm in size and 70 wIo/o of a finely ground mixture ofsynthetic anorthite, natural kyanite, and quartz with 24wto/o LirMoOo added as a flux. The anorthite, kyanite, andquartz were the same as the materials used by Koziol andNewton (1988, 1989). The compositions of the garnetseeds were chosen so as to obtain a reversal by approach-ing the final composition from both grossular-rich andgrossular-poor directions. Experimental durations weregenerally 3 to 4 d for experiments at 1000 "C and 7 to 8days for experiments at 900 .C. Thermocouple and fur-nace integrity were checked during the experiments bymonitoring power requirements of the furnace assem-blies. Experimental charges were solid dark gray pelletswhen removed from the capsules. Several small chips ofeach charge were prepared for analysis by electron mi-croprobe.

Final garnet compositions were determined by energy-dispersive spectroscopy (ens) on an ARL electron micro-probe (Li-drifted Si detector) and on a 1987 Cameca elec-

Grossular-spesgartine2.5 31 1 1 .815(2) 12.418(6)2.2 1 9 11 .778(11 12.302(3)0.9 31 11 .735(2) 12.168(6)3.0 19 11 .710(2) 12.088(6)3.3 31 1 1.688(3) 12.022(9)2.1 30 11.662(2) 1 1.940(6)3.4 40 11 .638(2) 1 1 .867(6)1 .0 24 11.626(21 11.830(6)1 .3 29 11 .618(1) 11 .805(3)

11.615(2) 11.798(6)Grossular-almandine

Grss 8spsr4 2Grsro"Sps.,Grs.o rSps.."Grs.r.Sps*"Grs*"Spqo,Grsro,Spsr.

"Grs,o rSpso.Grsil6spse52Grso. oSps". oSpessartine

Grss6 rAlm$eGrs€TAlmssGrs24 4Alm75 6Grsq oAlme5l

0.91 . 33.7o.7

34 11.753(3) 12.220(6)44 11.680(1) 11.99s(3)35 1 1 .608(1) 11 .775(3115 11.544(21 11.s80(6)

- Uncertainty (1o) in last digit is given in parentheses

tron microprobe. Operating voltage was 15 kV, with abeam current of 30 nA. Counting time was I min.

Equilibration of charges

In most experiments, the garnets changed composition,indicative of an approach to equilibrium. The originalgarnet compositions persisted in the cores of the garnetgrains, and the rims were mostly, but not entirely, of anew composition. The rims varied in thickness from about2 to l0 pm. Stringent criteria (X"r, X^, XF. + Xcuwithin0.01 of the stoichiometric value) based upon the micro-probe analyses ofthe starting garnets were used to rejectanalyses obtained when the electron beam overlappedonto anorthite, quarlz, or the quenched flux. The finalcompositions reported in Tables 2 and 3 are averages ofthree or four analyses that showed the most change ingrossular content.

With the addition of LirMoOo to the experimentalcharges, Li or Mo could have been incorporated into gar-net or anorthite. Garnets from several experiments wereanalyzed carefully for Mo. No evidence of Mo solid so-lution could be found. In the similar study on ternarygarnets by Koziol and Newton (1989), anorthites in theexperimental products were analyzed by electron micro-probe for cation stoichiometry and compared against theanalyses of synthetic anorthite used as the starting ma-terial and against anorthite grown in experiments on theend-member reaction. The data suggest about 34 molo/osolution of LiAlSirO, component in the feldspars of theexperiments using ternary garnets, as seen in the changingamount of Ca measured and the variation of AllSi ratio.However, there is an equal amount of substitution of Liin anorthite present in experiment 1.58, an experimenton the anorthite breakdown reaction. The calculatedgrossular activities are the same as if no solid solutionwere present in the feldspar, and departure from idealanorthite composition was not incorporated into the cal-

322

TABLE 2, Experimental results and grossular-spessartine garnelcompositions at 1000 and 900'C

KOZIOL: ACTIVITY-COMPOSITION RELATIONSHIPS OF BINARY GARNETS

Experi-ment

Time P(h) (kbar)'

ilme(h)

StartingP compo- Final

(kbar)- sition composition

a1ts(calcu-lated)

Experi-menl

TABue 3. Experimental results and grossular-almandine com-positions at 1000 and 900 'C

Startingcompo- Finalsition composition

a'F(calcu-lated) lca

,06

1000 rc11.0 0.201 10.143

0.020 T0.13112.7 0.392 10.195

0.107 T0.18014.1 0.392 10.233

0.048 10.22317.0 0.201 T0.40118.9 0.703 10.583

0.507 T0.573

900'c8.9 0.201 .10.110

0.020 T0.09011.6 0.392 !0.212

0.223 T0.20913.7 0.392 10.320

0.201 T0.30816.1 0.703 J0.514

0.392 10.s00

0.126 0.8810.126 0.962

0.175 0.8970.175 0.972

0.229 0.9830.229 1.027

0.398 0.995

0.s69 0.9760.569 0.993

0.107 0.9730.107 1 .156

0.189 0.9000.189 0.848

0.294 0.9190.294 0.955

0.484 0.9420.484 0.968

2.28 99 12.6

2.31 '141 12.5

2.33 96 16.0

2.81 116 18.2

2.35 69 19.0

2.32

2.44 214 12.5

2.36 168 14.7

1000 c0.244 10.1190.046 i0.1260.244 10.1820.046 T0.1800.046 T0.1800.437 J0.3150.244 10.3010.661 J0.4660.244 T0.4340.661 10.5200.437 T0.484

900 qc0.244 10.1230.046 T0.1000.437 10.2560.046 10.2440.437 10.4210.244 T0.376

0.129 1 .0810.129 '1.021

0j72 0.9440.172 0.954

0.169 0.936

0.329 1.0450.329 1.093

0.499 1.0710.499 1 .150

0.580 1 .1160.580 1 .199

0.1 19 0.9660.1 19 1 .189

0.223 0.8730.223 0.915

0.362 0.8590.362 0.962

1242.30

2.22

2.8

2.20

2.23

2.25

2.26

2.24

2.27

172

9.4

78

73

72

160

193

' Uncorrected gauge pressure.

culations. Anorthite in these experiments was not ana-lyzed, but it is assumed the same substitution applies.

AlrSiOs polymorphism

A natural kyanite was used as a starting material in theexperiments. According to the phase diagram of Holda-way (1971), at a constant temperature of 1000 oC, exper-iments below about 14 kbar are in the sillimanite stabilityfreld. However, X-ray analysis of products of lower-pres-sure experiments showed that kyanite was present meta-stably in experiments down to I I kbar.

Quenched flux and extraneous phases

The LirMoOo dissolved some kyanite, quattz, and alittle garnet to make an intergranular melt. This meltquenched to a Mo-rich aluminosilicate glass, which couldbe easily avoided during electron microprobe analysis.

Zoisite was identified in quenched charges in the an-orthite breakdown study of Koziol and Newton (1988),but was not found in this study. However, X-ray analysisshowed the presence of various amounts of an unknownphase represented by a single peak with a dvalue of 3.420A. ttre presence of another phase should not affect thereaction between garnet and the assemblage anorthite,kyanite, and quartz, as long as the latter four phases arepresent and in equilibrium. The unknown phase may cor-respond to the presence ofbrightly reflective beadlets inthe interstitial melt areas and may be a molybdate ormolybdenum silicate formed during quenching. No otherextraneous phases were detected.

2.37 166 167

' Uncorrected gauge Pressure.

Rasur-rs oF EXPERTMENTS

Volume relations

There is some discrepancy in the published value ofthe unit-cell constant of spessartine. Ito and Frondel(1968) and Skinner (1956) l ist l l .62l + 0'001 A, butsmaller values have been obtained by Hsu (1968)' Mot-

tana(1974), and Dasgupta etal.(1974). These values arel l . 6 i 4 + 0 .001 A . t t . o t z + 0 .003 A , and l l . 619 +

0.001 A respectively. Spessartine synthesized from stoi-chiometric glass for this study has a unit-cell constant ofl l . 615 + 0 .002 A .

Cell volumes and compositions of the synthetic gros-

sular-spessartine solid solutions are in Table l. Figure Iis a plot of composition against volume. A straight line

between the volumes of pure spessartine and grossular

reproduces all measurements, indicating no excess vol-ume of mixing. In general the volumes of these garnets

are smaller that the volumes of four grossular-spessartinegarnets measured by Ito and Frondel (1968). Their gar-

nets were synthesized from gels and may have containedsmall amounts of Mn3+ or HrO. Mn3* has an ionic radiusof 0.58 A 6ow spin) or 0.65 A @igh spin) as comparedto 0.53 A for Al3* (Shannon and Prewitt, 1969), and itspresence in spessartine could account for the larger unitcell.

Unit-cell constants of the four synthetic grossular-al-mandine solid solutions and the garnets of Geiger (1986)

are in Figure 2. As in Geiger's study, the garnets of thisstudy were synthesized in graphite crucibles at high pres-

0.6610.437

J0.497 0.54810.479 0.s48

1.1021.144

Spessartine-Grossular

323

Almandine-Grossular

This studyGeiger (1986)

11 .4 -0.0

Mole fraction grossular

Fig. 2. Volumes of grossular-almandine garnets. Opensquares: data from this study (see Table l). Filled diamonds:data from Geiger (1986). Ideal mixing is shown by the straightline drawn between almandine (l l.5l I J/bar) from Bohlen et al.(1983a) and grossular (12.531 J,/bar) from Skinner (1956). Un-certainties in compositions and volumes as in Fig. 1.

the volume ideality of the join. Uncertainties in the dataare discussed below. To illustrate activity-compositionrelationships, mole fraction versus (4fl)'/3 is plotted in Fig-ures 3a and 3b for grossular-spessartine. Any deviationfrom ideality is smaller than experimental uncertainties.

Reversals of grossular-almandine compositions wereobtained at 1000 and 900 oC over the range ll to 18kbar. The results are in Table 3. It was difficult to locateequilibrated garnet rims in the experiments at 900 .C,

and the reversal brackets are broad. The kinetics of thereaction are very slow at 900'C, and this discouragedexperiments at lower temperatures.

The data are plotted in activity-composition diagrams(Ftg. 4a,4b) to illustrate possible non-ideal behavior. Asa first approximation, the grossular-almandine join is es-sentially ideal at both temperatures and does not requirea complicated expression to relate composition and ac-tivity.

Error analysisIn formulating activity-composition relationships, one

must take account of uncertainties in both the calculatedactivities and the measured compositions. The uncertain-ty in composition is determined by the width or separa-tion of the reversal bracket and also by the uncertaintyof electron microprobe analysis, which is about 10.008in X* (A. Koziol, unpublished data). For example, inexperiment 2.30 (Table 3) the midpoint of the reversalbracket is X* : 0.122, but the bracketing compositionsare X*: 0.1l9 and X* : 0.126. The uncertainty on thefinal garnet composition is judged to be the square rootofthe sum ofsquares of(a) one-halfthe reversal bracketwidth and (b) +O.OOS in X* in both bracketing compo-sitions, for an estimated error of +0.012 for X* in thiscase.

Uncertainties in the activity of grossular calculated fromEquation 2 are sensitive to uncertainties in ,F, the pres-

KOZIOL: ACTIVITY-COMPOSITION RELATIONSHIPS OF BINARY GARNETS

o.ct

qtE3o

GtlaoEf

o

12.5

12.3

12.1

1 1 . 9

.0 0.2 0.4 0.6 0.8 1.0mole fraction grossular

Fig. l. Volumes of spessartine-grossular garnets. Data arefrom Table 1. Ideal mixing is shown by the straight line drawnbetween spessartine (l 1.798 J,/bar) from this study and grossular(12.531 J/bar) from Skinner (1956). Horizontal bars show 2ocompositional uncertainty as determined from energy-dispersiveelectron-microprobe analysis. Uncertainties in measured vol-ume are about the size of the symbols.

sures, where the oxygen fugacity should be quite low.M0ssbauer resonance analyses of Geiger's pure alman-dine indicated that less than one percent of the total Fepresent was Fe3+ (Geiger et al., 1987). No Mossbaueranalyses were performed on the gamets in this study.However, since the unit-cell constants and volumes ofthese garnets agree with those of Geiger (1986), the Fe3+contents are probably very small and should not affectthe phase-equilibrium results.

In their work on the grossular-almandine join, Cresseyet al. (1978) derived a volume-composition curve thatshowed a slight negative deviation from ideality for onedatum at GrsroAlmro and positive deviation at the moregrossular-rich end. This implies strong variation of thepartial molar volume of grossular , Vo, over the join. Thevolume-composition relationship has been reexaminedusing the data ofthis study and that ofGeiger (1986). Aplot of composition versus volume (Fig. 2) indicates somepositive deviation from ideal behavior at high grossularcontent, but the deviation is not large. Depending on thevalues chosen for the molar volumes of almandine andgrossular, the derived Margules parameters describing ex-cess volume of mixing change significantly. In addition,although small, yet variable, amounts of Fe3+ do notgreatly aflect the phase-equilibrium data, they do affectthe measured volumes of the garnets. Because of the smallexcess volumes of mixing measured and these uncertain-ties, the correction to the activity of grossular in garnetfor V* [Eq. 6 of Cressey et al. (1978)] was ignored.

Activity of grossular in binary garnets

Experimental reversals of compositions of grossular-spessartine garnets were obtained at 1000 and 900'C.Experimental conditions and compositions of garnets arein Table 2. The activities of grossular listed were calcu-lated from Equation 2. There is no excess volume cor-rection for grossular activity in these garnets because of

12.6

12.4

12.2

12.O

1 1 . 8

1 1 . 670

1 1 .

1 . 00.80.60.40.2

324

ro: 0.4

P attCD EI)S-

0.2

c',: 0.4

? oC'' EDo

(l,

: 0.4? oCD ED

(E

0.2

0.2 0.4 0.6

mole fraction grossular

0.2

0.00.60.40.2

0.0 -0.00.60.40.20.0

mole fraction grossularFig. 3. Activity-composition relationship for the grossular

component in grossular-spessartine garnets shown by a plot ofmeasured X- against the cube root ofcalculated activity ofgros-sular. Data (filled squares) are from Table 2. Ideal mixing be-havior is shown by the straight line. Uncertainties in X* andactivity (unfilled boxes) are discussed in the text. (a) Data ob-tained at 900 "C. (b) Data obtained at 1000'C.

sure of the end-member reaction, and in P, the pressureof the experiment. Koziol and Newton (1988) judged theposition of the anorthite breakdown curve to be deter-mined within +450 bars at 1000'C and +510 bars at900 "C. The uncertainty in the pressure of the experi-ments of this study is t300 bars. The square root of thesum of squares of these values results in estimated un-certainties of +540 bars at 1000 "C and +590 bars at 900"C for the pressure term in Equation 2. Therefore gros-

KOZIOL: ACTIVITY-COMPOSITION RELATIONSHIPS OF BINARY GARNETS

0.2 0.4 0.6

mole fraction grossular

mole fraction grossularFig. 4. Activity-composition relationship for the grossular

component in grossular-almandine garnets shown by a plot ofmeasured X* against the cube root ofcalculated activity ofgros-sular. Data (filled squares) are from Table 3. Ideal mixing be-havior is shown by the straight line. Uncertainties in X* andactivity (unfilled boxes) are discussed in the text. (a) Data ob-tained at 900 "C. O) Data obtained at 1000'C.

sular activities calculated from Equation 2 have uncer-tainties of about 100/0. Uncertainties in Are have littleeffect and have been neglected.

DrscussroNGrossular-spessartine

The data indicate that grossular and spessartine mixideally or nearly so, and activities of both components in

KOZIOL: ACTIVITY-COMPOSITION RELATIONSHIPS OF BINARY GARNETS 325

this binary solution can be assumed to be ideal for thepu{poses of thermodynamic calculations.

Mn-substitution in natural garnet can be considerablein low-grade parageneses, and possible perturbation ofgeothermometers by Mn, especially the garnet-biotitegeothermometer, has been discussed by several authors(Hodges and Spear, 1982; Perchuk,1982; Williams andGrambling, 1985). To define the perturbation, the Mn-Ca, Mn-Fe, and Mn-Mg interactions must be well under-stood. Lacking previous experimental data, an upper lim-it of 5.67 kJ/mol has been proposed for a symmetricallynonideal Ca-Mn join, based on differences in ionic radii(Ganguly and Kennedy, 1974). Mn-Fe mixing has beenapproximated by an ideal model (Ganguly and Saxena,1984) but Mg-Mn mixing in garnet has been consideredstrongly nonideal, with Zr*" : 13.4 + 2.5 kJ/mol for asymmetric model (Ganguly and Kennedy, 1974). Hodgesand Spear (1982) concluded that Mn mixes ideally ingarnet with respect to the other cations, based on para-genetic analysis ofa near-triple point occurrence ofAlrSiO,polymorphs. Hoinkes (1986) noted that regression anal-ysis of his garnet-biotite ln Ko data implied ideal mix-ing of spessartine with Fe-Mg garnet at amphibolite faciesconditions.

Experimental work by Pownceby et al. (1987) placesfurther constraints on Fe-Mn mixing in garnet. Theiranalysis of the partitioning of Fe and Mn between garnetand ilmenite, treated as symmetrical solutions, indicatesthat W'lk" - Wff-n: 1.26 kJlmol. This result, togetherwith experimental data on Fe-Mn ilmenite solutions (H.O'Neill, unpublished data; cited in Pownceby et al., 1987),indicates that Fe-Mn mixing in garnet is nearly ideal,with minor positive deviations.

Grossular-almandine

To a first approximation this join also is ideal, but abetter description of the join may be obtained by fittingan asymmetric Margules model to the activity data:

R?"ln "y, : ( l - X,)' lW, + 2X{W2 - W,)1, (4)

where Wr, W, are the two Margules parameters. Sincethe results for both 900'C and 1000 oC are very similar,the data at both temperatures were combined. Leastsquares analysis gives W*: - 1.09 kJ/mol of cation, Wr": 2.59 kJlmol of cation.

Previous estimates of excess free energy for the Ca-Fegarnetjoin are based on theoretical as well as experimen-tal dala. An upper limit of 5.7 kJ/mol for the excess freeenergy of this join was based on the difference in ionicradii between the two cations (Ganguly and Kennedy,1974). More recently, Bohlen et al. (1983a) obtained ex-perimental data on the reaction fayalite + anorthite :garnet (grsrr ralmuu r) over the temperature range 750-1050.C. Their data imply that the mixing properties of thisone composition is nearly ideal.

Ganguly and Saxena (1984) used paragenetic, experi-mental, and calorimetric data to constrain the mixingproperties of (Fe,Ca,Mg,Mn)rAlrSirOr2 garnets. The pri-

mary input to the model was experimental and parage-netic data on Fe-Mg partitioning between garnet andanother phase, such as clinopyroxene or biotite. Theiranalysis ofthe data ofCressey et al. (1978) indicated thatexcess entropy in Fe-Ca garnets could be modeled with asingle (symmetric) parameter, unlike the asymmetricmodel suggested by Cressey et al. (1978). Retaining onlythe 1000 oC experiments of Cressey et al. (1978) that wereperformed with crystalline starting materials, Ganguly andSaxena obtained, by a second regression, enthalpy param-eters of W"*" = -2.6 + 1.7 kJ/mol and Wr"* I 19.3 +2.8 kJ/mol for one cation mixing.

Anovitz and Essene (1987) analyzed experimental datain the CaO-FeO-AlrO3-SiOr-TiO, system to determine Ca-Fe mixing properties of garnet. The experimental deter-minations of the reactions almandine + 3 rutile : 3 il-menite + sillimanite + quartz (GRAIL) (Bohlen et al.,1983b) and 3 anorthite: grossular + 2 AlrSiO, + quartz(GASP) (Koziol and Newton, 1986) were used to calcu-late the P-Iposition of 2 garnet * 6 rutile : 6 ilmenite+ 3 anorthite * 3 quartz (GRIPS) with its garnet ofgrsr..almuur. This reaction is also tightly determined ex-perimentally (Bohlen and Liotta, 1986). Self-consistentformulation of all of these data places constraints on thea-X relations of the grs-alm join. To be consistent withthe studies cited above and with the calorimetry data ofGeiger et al. (1985), Anovitz and Essene (1987) set theirexcess entropy parameter to a symmetric W : 6.3 J/(mol'K) and derived the excess enthalpy parameters W*r.:0.628 + 0.321 kl/mol and Wr"*: 17.081 + 0.440 W/mol for one cation mixing.

The mixing of almandine with grossular and alman-dine with pyrope has been studied by Geiger et al. (1987)using high-temperature oxide-melt solution calorimetry.They found that the grossular-almandine solid solutionhas small excess enthalpy and that almandine-pyrope sol-id solutions have significant excess enthalpies of mixing,especially near the almandine-rich end of the join. Theresults for grossular-almandine were expressed by anasymmetric Margules model, with enthalpy parameters(W) of W.n

" : - 3.03 kJ and Wr*o : 4.56 kJ for I mol

of cation. Geiger et al. (1987) suggested that excess en-tropy is close to zero in this join.

Low-temperature heat-capacity measurements, neededto obtain directly the excess entropy of solid solutions,require very large quantities of sample, and to date onlyone garnet solid solution (prpeogrsoo) has been measured(Haselton and Westrum, 1980). This study showed a con-siderable excess entropy of mixing in the pyrope-grossu-lar join, but the one solid solution measured is insufficientto define the behavior of the whole join. Given the lackof adiabatic calorimetric data for grossular-almandine,displaced-equilibrium measurements in conjunction withthe solution calorimetry may be used to obtain an esti-mate of excess entropy.

A comparison of the present data obtained at 1000'Cto the models of Ganguly and Saxena (1984), Anovitzand Essene (1987), and Geiger et al. (1987) is made in

326 KOZIOL: ACTMTY-COMPOSITION RELATIONSHIPS OF BTNARY GARNETS

0.40 . 3o.20.1.0

(6

B 1-4atoorr 1.2otr,9 1.0.9o8 o.e'tE 0.69 n

1000'C cangulyandSaxena\

al. (1987)

Anovitz and Essene (1987)

0.6 0 .7

Mole fraction grossular

Fig. 5. A plot of the activity coefrcient of grossular (7*)determined in this study at 1000 'C against composition for aportion ofthe grossular-almandinejoin, and comparison to pre-vious studies. Data are from Table 3. The value of 7* at themidpoint of each reversal is plotted as a small square. Width ofthe error box is determined by uncertainty in composition (X*).Uncertainty in 7* due to uncertainty in the calculated activityis shown as vertical extent ofthe boxes. The solid curves are theasymmetric Margules models for each study, as noted. The re-sults of this study (see text) have the parameters (in U/mol ofcation) W.": - 1.09 and Wr.: 2.59.

Figure 5, which plots composition versus activity coeffi-cient. The data from this study agree with the trend pre-dicted by the calorimetric measurements of Geiger et al.(1987) with the assumption of negligible excess entropy.The temperature baseline of the present experiments istoo short and the reversals at 900 "C too broad to clarifyor verify this assumption with any confidence.

In conclusion, the present displaced-equilibrium mea-surements of the excess free energy of grossular-alman-dinejoin show that this garnetjoin is nearly ideal. Thesenew data can be used with ternary (Ca,Fe,Mg) activitydata to construct a comprehensive formulation of ternarybehavior. The ideal mixing of Ca and Mn determined inthis study, when combined with the ideal behavior of Fe-Mn garnets (Pownceby et al., 1987), makes it reasonableto consider Mn as an ideal diluent of Ca-Fe-Mg garnets.The energetics of Mn-Mg interactions in garnet are un-known, but the combined content of these componentsin crustal garnets is usually small, so that the effect of thisinteraction may be negligible.

AcxNowlsrcMENTs

This work is part of the Ph.D. thesis research of Andrea M. Koziol. D.Perkins and R. Berman are thanked for constructive reviews. Studentsupport for A.M K. was provided by the Materials Research Laboratory(NSD at the University of Chicago. The experiments were performed inthe laboratory of Robert C. Newton, with support by National ScienceFoundation $ants NSF-EAR-8411192 and NSF-EAR-87-07156 to R.C.Newton.

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MaNuscrrp,r REcETvED JuNe 23, 1989MeNuscrrsr AccEprED NovsMBrn 28, 1989

KOZIOL: ACTMTY-COMPOSITION RELATIONSHIPS OF BINARY GARNETS