Solution Properties of Almandine-Pyrope Garnet As

American Mineralogist, Volume 77, pages 765-773' 1992

Solution properties of almandine-pyropegarnet as determinedby phaseequilibrium experiments

ANonBl, M. Kozror-.* StnvrN R. Bonr'BN U.S. Geological Survey, MS 910, 345 Middlefield Road, Menlo Park, California 94025, U.S.A.

AesrRAcr The thermodynamic mixing properties of almandine-pyrope garnet were derived from phaseequilibrium experiments at temperaturesof 900 and 1000 "C and pressuresfrom 8 to 14 kbar for the assemblagegarnet + rutile * sillimanite + ilmenite + q:uartz(GRAIL). Almandine (Alm) has essentiallyideal behavior in almandine-pyropegarnet over the com- position range Almrn-Almu, at the above experimental conditions. In all experimental products a systematic partitioning of Fe and Mg between garnet and ilmenite was seen with ln Kax 1.59. This partitioning does not appearto be temperaturesensitive. The results of this study support the use of garnet mixing models that incorporate ideal or nearly ideal Fe-Mg parameters.

INrnonucrroN composition relationships for iron magnesiumgarnet sol- work is the Garnet is an important and abundant mineral in the id solutions. The only other experimental (1987), the excess Earth's crust and mantle and is the essentialconstituent study of Geiger et al. who measured garnets. Examples of Fe- in many metamorphic reactionsthat have beencalibrated enthalpy of almandine-pyrope of O'Neill and as thermobarometers(see Essene,1989, for a review). Mg exchangeexperiments are the studies (1989),who deter- Much information on the metamorphic history of rocks Wood (1979)and Hackler and Wood garnet olivine. has been obtained through the use of such thermobarom- mined the Fe-Mg exchangebetween and permit the garnetand eters and through the interpretation ofgarnet zoning. However, those experimentsdo not For preciseestimates of pressureand temperature, the olivine mixing properties to be deduced separately. the mixing end-member reaction of the geobarometermust be well This study was undertaken to determine garnet the calibrated, and the solid-solution properties of garnet, parametersof almandine-pyrope by means of predominantly a mixture of almandine, pyrope, grossu- phaseequilibrium technique (Koziol and Newton, 1989; that lar, and spessartine,must be well known. This is especial- Koziol, 1990;Wood, 1988).This studycomplements reac- ly important for P-T studies that employ garnet zoning. of Bohlen et al. (1983),in which the end-member geobarometer, on the basis of the The almandine-pyropejoin (FerAlrSirO'r-MgrAlrSirO'r) tion for the GRAIL garnet il- is one of the most important limiting garnet solid solu- equilibrium between rutile and aluminosilicate This tions becausemost garnets occurring in pelites are com- menite quartz, was experimentally determined. study posed predominantly of thesetwo components, and sev- was also designedto complement the work of Koziol and (1989) (1990), the eral exchange geothermometers are based on the Newton and Koziol who determined garnet. partitioning of Fe and Mg betweengarnet and some other mixing properties of grossular-rich phase such as biotite or orthopyroxene. The displaced-equilibriumtechnique The thermodynamic mixing properties of garnet have involves the de- been inferred from cationic size considerations,various The displaced-equilibrium technique pressure(at constant temper- Fe-Mg exchange experiments, and metamorphic para- termination of a changein result ofsolid so- geneses.Depending on the type of analysis, almandine- ature) ofa univariant equilibrium as a et al. pyrope mixing properties have been postulated to be lution in one ofthe phases,as outlined by Cressey (1978). thermodynamicba- nearly ideal (Aranovich and Podlesskii,1983, 1989;Ber- (1978)and Schmidet al. The Wood (1988). man, 1990;Hackler and Wood, 1989;Hodges and Spear, sis of this techniquehas beendiscussed by is 1982;Newton and Haselton, 198l) or significantlynon- The univariant equilibrium of interest ideal (Ganguly and Saxena, 1984, 1987; Geiger et al., + 3TiO2. (1) 1987;Moecher et al., 1988;Perkins, 1979).However, to 3FeTiO, + AlrSiOs+ 2SiOr: Fe.AlrSirOr2 date there have been no direct determinations of activity- ilmenite sillimanite qurtz almmdine rutile

and * Presentaddress: The Collegeof Wooster, Department of Ge- In a simple system, when garnet is a solid solution ology,Wooster, Ohio 44691, U.S.A. the other phases have limited or no solid solution, the 0003-004x/92l0708-o765$02.00 765 766 KOZIOL AND BOHLEN: ALMANDINE-PYROPE SOLUTION PROPERTIES activity of almandine in garnet can be determined using at after some experimentation and varied with the size of the relationship the graphite crucible and the integrity of the heating ele- ments in the furnace used. The resulting homogeneous rPo glass was dark greenish with I LVo dP : R?" ln K (2) black no color changesin- atP dicative of an fo,g.radient, nor were there tracesof metal precipitation. glasswas powdered, where the standard state is the pure phaseat the temper- The finely loaded into ature and pressureofinterest, Po is the equilibrium pres- an Au capsule5 mm in diameter, with 2 wto/ographite, I wto/oquartz, 'C, sure of the end-member equilibrium at T, the tempera- and I mL HrO, and synthesizedat 900 I kbar, yielded ture of the experiment,P is the pressureof the experiment, 5 for l-2 d. Thesesyntheses homogeneous garnet except for the composition Alm.oPyroo,which was AZ0 is the volume changeof Reaction l, and K is de- oC fined as synthesizedat 1070 and 19.2 kbar to yield homoge- neous garnet. All garnet sampleswere characterizedop- a ,. : or^'(a*")t tically, by X-ray diffraction, and by electron microprobe 1\ ;_ tj,l (ar,*)3. a"u.(ao,)2' analysis. All garnet products had a small amount of graphite, and some had a trace (<<0.10/o)of quartz. Elec- When the integral on the left side of Equation 2 is eval- tron microprobe analysesconfirmed that the garnetswere uated, the activity of almandine in garnet at the temper- of the desired composition with little variation, ature and pressureof interest is determined. Equation 2 with actual compositions AlmronPrpr, (+0.2 molo/o), has been integrated using volume data from Berman AlmrorPrprn, ( + 2.9 molo/o),Almrn oPrpo (+ 2.6 molo/o). (1988). In garnet, the cations mix over three sites per ou formula unit, giving the following relationship between Apparatus and experimental procedure activity and mole fraction: Starting mixes of the GRAIL assemblagein stoichio- afil, : (X^,-"y",-)' (4) metric proportions appropriate for Equation I were pre- pared using appropriate garnet and ilmenite composi- whereXis the mole fraction of FerAlrSirO,,in the binary tions. The garnetswere chosenso as to approachthe final solution and is 7 the activity coefficient of FerAlrSirO,r. composition from the almandine-richand almandine-poor Measurement of the garnet composition in equilibrium directions, and the ilmenites were chosen to be close to with rutile, ilmenite, quartz sillimanite, and over a range the composition in exchangeequilibrium with the antic- of P and Z permits calculation of 7o,- and the activity- ipated final gamet composition. For experiments per- composition relationships. For optimal accuracyin these formed at 1000 'C, the finely ground sample was encap- measurements,compositions must be reversed and all sulated without any special precautions to eliminate phaseswell characterizedby microprobe analysis.In ad- moisture. About 4 wto/oHrO was added to the capsulefor dition, the end-member curve must be well known. The experiments performed at 900'C. The AgroPdrosample GRAIL end-member equilibrium, Equation l, has been capsule, sealedby arc welding, was placed into a 3-mm tightly reversedby Bohlen ( grearly et al. I 983), aiding the Pt capsulewith about 100 mg of Fe metal and 5 mL of precision of yer-. the determination of HrO. This outer capsulewas also sealedby arc welding. All performed piston-cylinder ExpnnrtvrnurAr- METHoDS experiments were in a apparatus,using an assemblyof 2.54 cm in diameter with Starting materials NaCl pressure medium and Pt-Pte'Rh,o thermocouples. Natural quartz from Brazil and natural sillimanite Experiments above 9.8 kbar were made in the low-tem- (0.950/oFerOr) from Molodezhnaya Station, Antarctica, peratureassembly of Bohlen (1984),and experimentsbe- were used as starting materials. The rutile and ilmenite low this pressure were made in a high-temperature as- used were part of synthetic samples from the study of sembly where Pyrex sleeves are next to the graphite Bohlen et al. (1983). Two ilmenite-geikielitesolid solu- furnace. Details of this assembly and its calibration are tions (IlmrrGeiko. and IlmrrGeikor)were synthesizedfrom discussedby Bohlen(1984). Experimental conditions and finely disseminated mixtures of reagent-gradeFe metal, results are listed in Table l. sintered FerO., TiOr, and MgO. These mixtures were re- acted in evacuated silica tubes at 900'C for 3 d. Each Experimental products preparation yielded ilmenite close to the desired com- The products of all experimentswere characterizedop- position and a small amount ( <<0.l0lo) of rutile that could tically and by X-ray diffraction and electron microprobe be detectedoptically and in backscatteredelectron (BSE) analysis.Microprobe analyseswere obtained on an ARL- imaging but could not be detected by X-ray diffraction SEMQ electron microprobe with wavelength-dispersive analysis. spectrometers.Standards used were synthetic almandine Garnet used in this study was synthesizedfrom glass garnet, Kakanui pyrope and synthetic TiOr, FerOr, and of the desired composition. Each glass sample was pre- magnesium aluminum spinel. An acceleratingpotential pared from a mixture of reagent-gradeSiOr, AlrO. (co- of 15 kV and sample current of 30 nA were standard rundum), FerOr, and MgO and melted in a graphite cru- operating conditions. Counting times were 20 s, and usu- cible at 1325"C for 25 min. Theseconditions were arrived ally 2-3 counting periods were taken and averaged for KOZIOL AND BOHLEN: ALMANDINE.PYROPE SOLUTION PROPERTIES 767

TABLE1. Experimentalconditions and results

P Time Initial Final Calculated Activity Exp. (kbao (h) Xo,. XM drr^ coeff . 3.23B 14.0 94 0.80 0.888 0.966 0.979 0.910 0.965 1.06(6) 3.54 12.5 78 0.95 0.808 0.944 0.974 0.844 0.881 1.04(6) 3.13A 12.3 98 0.80 0.825 0.947 0.968 0.851 0.871 1.02(6) 3.8 12.2 117 0.70 0.823 0.949 0.968 0.848 0.866 1.02(6) 3.6A 11.9 48 0.95 0.868 0.959 0.969 0.886 0.850 0.s6(5) 3.68 11.9 48 0.70 0.800 0.948 0.971 0.828 0.850 1.0q6) 3.41 11.4 118 0.95 o.777 0.932 0.986 0.830 0.824 0.99(6) 3.62 11.2 168 0.70 0.740 o.924 0.978 0.791 0.815 1.03(6) 3.38A 10.2 142 0.80 0.708 0.897 0.979 0.781 0.766 0.s8(6) 3.388 10.2 142 0.60 0.691 0.914 0.98' 0.748 0.766 1.02(6) 3.42A. 9.9 95 0.80 o.721 0.920 0.983 0.778 0.752 0.e7(6) 3.42B oo 95 0.60 0.654 0.905 0.981 0.716 o.752 1.0s(6) 3.74 8.8 92 0.70 0.614 0.869 0.984 0.702 0.703 1.00(6) 3.70A 8.6 123 0.80 0.675 0.877 0.970 0.754 0.694 0.92(5) 3.68 8.5 116 0.60 0.613 0_885 0.985 0.689 0.690 1.0q6) 3.72 8.0 243 0.60 0.6s3 0.899 o.972 0.711 o.712 1.00(6) Note; All experimentsperformed at 1000 rc except for experiment3.72, which was conductedat 900 €. Initialilmenite composition was llml@ex@pt for experiments3.74, 3.7O,3.68, and 3.72,where it was llms. ' Estimated rutile activity.

each analysis. Spectrometerdata were reduced using the amount of Fe and Al in rutile and a small amount of Al procedureofBence and Albee (1968).Single garnet anal- and a significant and systematicsolution of Mg in ilmen- ysesrepresentative ofthe averagecomposition are given ite (seebelow). In addition, there was a small but signif- in Table 2. The averagedresults for ilmenite and rutile icant amount (0.9-2.0 wto/o)of TiO, in all garnet analyses are given in Tables 3 and 4, respectively. from experimental products. This level of TiO, was not Microprobe analysesof the products revealed a small seenin analysesof the almandine standard, nor in anal-

TABLE2, Selectedelectron microprobe analyses of garnet

Exp 9.72 3.238 3.54 3.13A 3.64 3.68 3.41

Wl"/c sio, 38.5 36.0 36.7 37.1 36.4 36.4 37.5 37.3 Al2o3 21.6 20.6 21.O 20.9 20.7 20.8 20.7 21.0 FeO 31.2 40.1 37.3 38.3 38.0 39.4 36.9 36.0 Mgo 8.5 1.8 4.1 3.5 3.6 2.4 4.1 4.8 CaO 0.1 o.2 0.1 0.0 0.0 0.1 0.0 0.1 Tio, 1.1 1.3 1.3 1.6 1.5 1.0 1.2 1.6 Total r01.0 100.0 100.5 101.4 100.2 100.1 100.4 100.8 Cations si 2.968 2.942 2.941 2-953 2.932 2.956 2.989 2.957 AI 1.958 1.987 1.977 1.957 1.971 1.993 1.949 1.958 Fe 2.O11 2.735 2.498 2.548 2.562 2.677 2.459 2.378 Mg 0.98 0.218 0.491 0.42 0.433 0.288 0.49 0.563 Ca 0.007 0.014 0.005 0.003 0.002 0.006 0.004 0.008 Ti 0.065 o.077 0.08 0.093 0.091 0.028 0.072 0.100 Total 7.989 7.973 7.992 7.974 7.991 7.977 7.963 7.964

Exp. 3.62 3.38A 3.388 3.424 3.428 3.74 3.704 3.68 Wlc/o sio, 38.0 38.1 38.0 37.8 38.2 39.2 38.0 39.0 Al2o3 20.9 21.6 21.6 20.9 21.2 21.5 2',t.3 21.3 FeO 34.6 34.0 32.6 33.8 30.5 29.9 32.1 29.3 Mgo 5.7 6.7 7.1 6.2 8.2 9.1 7.6 9.9 GaO 0.3 0.0 0.3 0.1 0.4 0.0 0.0 0.0 Tio, 1.5 1.5 1.2 1.9 1.5 1.3 1.4 0.9 Total 101.0 101.9 r00.8 100.7 100.0 101.0 100.4 100.4 Cations Si 2.979 2.947 2.958 2.966 2.967 2.997 2.964 2.994 AI 1.937 1.974 1.978 1.932 1.94 1.936 1.96 1.929 Fe 2.272 2.20 2.122 2.214 1.981 1.91 2.091 1.878 Mg 0.667 o.773 o.822 0.723 0.949 1.035 0.879 1.133 Ca 0.024 0.001 0.03 0.005 0.032 0.003 0.001 0.003 Ti 0.087 0.086 0.071 0.114 0.087 0.076 0.08 0.051 Total 7.966 7_981 7.981 7.954 7.956 7.957 7.975 7.988

Note; All experiments performed at 1000 'C except lor experiment 3.72. 768 KOZIOL AND BOHLEN: ALMANDINE-PYROPE SOLUTION PROPERTIES

Tmle 3. Electron microprobe analyses of ilmenite

Exp. 3.72 3.238 3.54 3.134 3.8 3.6A 3.68 3.41 Yllo/o FeO 44.1 46.3 46.1 46.4 46.0 46.5 45.9 44.9 Tio, 53.3 52.6 52.3 53.1 53.1 53.0 52.6 53.2 Alro3 0.4 0.6 0.6 0.6 0.7 0.6 0.6 o.7 Mgo 2.5 0.4 1.1 1.0 0.9 0.6 0.9 1.3 Total 100.3 99.9 100.1 101.1 100.6 100.7 100.0 100.1 Cations Fe 0.910 0.965 0.963 0.96 0.951 0.968 0.959 0.931 Ti 0.987 0.986 0.982 0.988 0.988 0.991 0.988 0.992 AI 0.011 0.018 0.018 0.018 0.020 0.018 0.014 0.020 Mg 0_093 o.017 0.039 0.035 0.032 0.023 0.035 0.048 Total 2.001 1.985 2.001 2.002 1.990 2.00 1.995 1.990 Points 5 4 c 3 3 3 2 4

Exp. 3.62 3.38A 3.388 3.424 3.428 3.74 3.70A 3.68 Wl"/" FeO 44.5 43.6 44.0 44.2 44.0 42.3 43.6 43.0 Tio, s3.2 53.4 53.4 53.7 53.8 s3.9 52.9 53.0 Al,o3 0.7 o.7 0.7 0.6 0.5 1.1 o.7 0.5 Mgo 1.5 2.3 1.8 1.7 2.1 3.0 2.9 2.7 Total 99.9 100.0 99.9 100.2 100.4 100.3 100.1 99.2 Cations Fe 0.923 0.898 0.906 0.915 0.905 0.865 0.898 0.975 Ti 0.993 0.989 0.990 0.997 0.995 0.991 0.979 0.968 AI 0.019 0.021 0.021 0.019 0.019 0.025 0.019 0.019 Mg 0.058 0.083 0.064 0.061 0.077 0.109 0.106 0.097 Total 1.992 1.990 1.980 1.992 1.996 1.989 2.O02 1.959 Points 2 5 3 4 c 5 4 Nofe.-All experiments performed at 1000 .C except for experiment 3.72.

TABLE4. Electron microprobe analyses of rutile

Exp. 3.72 3.238 3.54 3.13A 3.8 3.6A 3.68 3.41 wtc6 FeO 1.3 0.9 1.2 1.5 1.5 1.2 1.2 o.7 Tio, 97.8 98.5 98.0 97.9 97.3 98.2 97.7 99.1 Al,o3 0.9 0.7 0.8 1.0 1.1 1.1 1.0 0.4 Mgo 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Total 100.0 100.1 100.0 100.4 99.9 100.5 ooo 100.2 Cations Fe 0.014 0.010 0.013 0.017 0.016 0.014 0.014 0.007 Ti 0.980 0.987 0.980 0.980 0.974 0.980 0.980 0.991 AI 0.013 0.010 0.013 0.016 0.017 0.017 0.016 0.007 Mg 0.001 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Total 1.008 1.008 1.006 1.012 1.007 1.011 1.009 1.005 Points 3 2 c 2 2 2 2 Exp. 3.62 3.38A 3.42A 3.428 3.74 3.70A 3.68

Wlo/c FeO 0.9 1.0 0.8 0.9 0.8 1.4 0.7 Tio, 97.8 97.6 99.0 98.7 99.0 97.0 98.4 Al2o3 o.4 0.7 0.5 0.6 0.5 0.9 0.4 Mgo 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Total 99.1 ooe 100.3 100.2 100.3 99.3 99.5 Calions FE 0.075 0.011 0.009 0.010 0.009 0.016 0.007 Ti 0.968 0.969 0.990 0.988 0.990 0.965 0.979 AI 0.007 0.010 0.008 0.009 0.008 0.014 0.007 Mg 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Total 0.990 0.990 1.007 1.007 1.007 0.994 0.993 Points 2 2 3 3 2 3 Notej All experiments performed at 1000 € except for experiment 9.72. KOZIOL AND BOHLEN: ALMANDINE-PYROPE SOLUTION PROPERTIES 769 ysesof the synthetic garnetused as starting material. Boh- '15 len et al. (1983) postulatedthat the 1.5 wto/oTiO, they obtained in their analyseswas the result of fine inter- growths of rutile with garnet. We believe the Ti is part of the garnet structure becausewe did not see any rutile 13 grt + ru grains in BSE images, even at high power, and the Si cation totals of the garnet were always slightly reduced l-----> G' - compared with analysesof standardsand synthetic garnet lt .:l samples. l------> were points O i1 Spot analyses taken at different within the f at, same grain of garnet, rutile, or ilmenite and among sev- o o fl eral different grains. Garnets were almost always com- L fl positionally zoned. The original seedcompositions were o. ilm + sil retained in the core, but the garnet grains developed a +qlz rim, varying between 2 and l0 pm in thickness,that had a new composition. This new composition differed from the starting composition by as much as 17 mol0/0.The three or four analyseswith good stoichiometry that were 7f farthest removed from the original composition were 0.6 0.7 0.8 0.9 10 considered indicative of the final composition attained. mole fractionalmandine Ilmenite and rutile were unzoned. 'C. Each garnet analysis was cast into mole fractions sep- Fig. 1. P-Xo'- diagramat constanttemperature of 1000 arately and recalculatedon a site by site basis,where Xo,- Solid line: displacementin pressureof the GRAIL equilibrium gamet, by -- X...(Xor)t't.X.,. The microprobe data of Bohlen et al. (Eq. l) by solid solution in almandine calculated Equation2, assumingideal mixing in garnet.Experimental data (1983) were used to calculatethe activity of sillimanite obtainedin this study are also plotted. Filled boxes:starting by the relationshipcr,, : Xru : Xr,.Xouand a.,,was found compositionof almandine-pyropegarnet. Arrow tips:K' or final to be 0.97 at 1000'C. The activity of rutile, alwayswithin compositionof garnetadjusted for the reducedactivities of il- 0.03 of unity, was taken to be equal to the mole fraction menite,rutile, and sillimanite.See text for details. of rutile, calculated as XR, : Xr,/X-u where X.", was the total number of cations in the analysis.The ilmenite mole fraction was calculated as Xo..Xr, (on a cation basis). phases.The value of K' is compared against ao,- calcu- lated from Equation 2, as described above. Equation 4 DrscussroN may be rewritten as Results of experiments a?i^: K "Yo,^ (6) The resultsofexperiments conducted at 1000and 900 'C are given in Table l For an experiment at a given where afi| is the calculated value and'y^,- is the activity pressure and temperature, the activity of almandine in coefficient. A graphical presentation ofthe data at 1000 'C garnet may be calculated by Equation 2, and this value is given as Figure l. In this and all further figures, for each set of experimental conditions is noted in Table values for K, the adjusted mole fraction of almandine, I as calculated an*. Xo,-, as measured by electron mi- are plotted. In this isothermal section, the calculated dis- croprobe analysis, cannot be compared directly to this placement of the univariant reaction (Eq. l) if Mg-Fe value becausethe other phasesinvolved in the experi- mixing in the garnet were ideal is shown by the solid line. ments are not at unit activity, as noted above, and their The changein the garnet compositions from initial (filled activity values must be substituted into Equations 2 and boxes)to final (arrow heads)is also shown. The final com- 3. The extent of nonideal mixing in ilmenite geikielite as positions are very closeto the curve for ideal mixing, and predictedby the model of Andersonand Lindsley(1981) therefore there is little to no excessfree energyof mixing is negligibleat thesecompositions at 1000'C; therefore for iron magnesium garnet solutions at 1000 "C. Very 'C, this correction to the ideal activity of ilmenite was ig- limited data were obtained at 900 but one half rever- nored. Starting with the definition of K the equilibrium sal indicates that iron magnesium garnets behave simi- constant (Eq. 3), we define K' as the cube root of the larly at this temperature. apparent equilibrium constant ofReaction l: In considering the uncertainties of these results, one must include uncertainties in electron microprobe anal- 4jnoi'i]'48" ysis. Uncertainties in the compositions of garnet, rutile, K', : (5) arr^'(Q"r)t" ilmenite, and sillimanite causean estimated uncertainty of approximately +Q.917 in the value for K', the adjusted where a'fff correspondsto X^- measuredby the experi- mole fraction of almandine. The main factors contrib- ments. In effect, K' is the mole fraction of almandine uting to the uncertainty in the calculatedao'- from Equa- obtained after accounting for solid solution in the other tion 2 are the uncertainty in Po, the pressureof the end- 770 KOZIOL AND BOHLEN: ALMANDINE-PYROPE SOLUTION PROPERTIES

member equilibrium (Eq. l), and the uncertainty in P, 0.4 the pressure of the experiment. The end-member curve was preciselybracketed by Bohlen et al. (1983)to within 200 bars, and the piston-cylinder apparatusemployed in the Menlo Park laboratory is precise to + 100 bars (lab- U.J oratory unpublished data). The 20 uncertainty of +600 o bars in the difference between Po and P leads to an un- tr certainty of +0.026 (for large +0.034 (for (s differences)to cD small differences) in the calculated value oD of co,-. The '; combination of uncertainties stemming from composi- tion and pressuredetermination leadsIo a 2o uncertainty = of +0.06 in the value of 7o,- as listed in Table l. x 0.1 Fe-Mg exchangebetween garnet and ilmenite A systematicpartitioning of Fe and Mg betweengarnet and ilmenite was noted and followed as the experiments 0.0 progressed.This exchangecan be described by the reac- 0.00 0.05 0.10 tion XMg in ilmenite Yralmandine + geikielite : pyrope + ilmenite. (7) % 1.0 The distribution coefficient,K", is defined as

(8) 0.8 o E Other studies have experimentally determined the parti- Eq F 0.6 E tioning of Fe and Mg (or Mn) between ilmenite and an ct) iron magnesiumsilicate (Bishop, 1980;Pownceby et al., Green& Sobolev(1975) o 1987),but there is little information on Fe-Mg partirion- fuGo ing between garnet and ilmenite (but see Green and So- g o-4 lr I bolev, 1975).Although these experimentswere not de- I x I I signed to measurethe Ko of this exchange,we did note ! a I systematicpartitioning of Fe and Mg with an averageor 0.2 J best f,t Ko of 4.9, or ln Ko (Fig. I of I .59 2A). Theseexper- I this study iments were performed over a range of pressures,but I their results can be compared becausethe volume change 0.0F of this reaction is extremely small (+0.019 J/bar). The 0.0 o.4 0.6 data in Figure 24, are reversed in terms of garnet mole fraction but all final ilmenite-geikielitecompositions were X Mg in ilmenite approached from ilmenite-rich compositions (pure il- Fig. 2. Experimentaldata for the distributionof Mg2*be- menite except for the most magnesiancompositions; see tweencoexisting garnet and ilmenite. X Mg: molefraction of the Table l). Still, the very regular results at 1000 "C are Mg end-memberof garnetor ilmenite.(A) Final compositions another indication that equilibrium between garnet and obtainedin this studyat 1000"C (filled squares). Arrows indicate ilmenite was approached. extentof changeof selectedinitial garnet-ilmenitepairs to final compositionsas listedin Table l. A K" valueof 4.9 bestfits all Green and Sobolev (1975) performed synthesisexper- the data.(B) Comparisonof datafrom this study(filled squares) iments on a pyrolite and an olivine-basanite composition to thedata ofGreen and Sobolev (1975) (open squares) obtained and obtained microprobe analyses of coexisting garnet at 950-1050€. and ilmenite. They found regular partitioning of Fe and Mg betweenthese two phaseswith a Ko of approximately 4.0 + 0.5. This value did not appearto be sensitiveto Mixing properties of iron magnesiumgarnets temperature,pressure, or composition. The compositions The data in this study were collected over a range of they investigatedwere more magnesian[Mg(Mg + Fe) of pressuresand compositions, and the activity coefficients Earnet: 0.41-0.73; of ilmenite : 0.15-0.471than those cannot be compared directly unless there is no excess of this study (seeFig. 2B). Although it was suggestedpre- volume of mixing in almandine-pyrope garnets. The viously (Koziol and Bohlen, 1990) that this exchange comprehensive unit-cell measurementsof Geiger et al. might be a geothermometer, Green and Sobolev (1975) (1987) show a very slight asymmetryin the volumes of have shown that the Ko for garnet ilmenite is insensitive mixing that may be neglected for the purposes of this to temperatureover the range900-1100 .C. paper. As noted above and in Figure 1, our experiments KOZIOL AND BOHLEN: ALMANDINE-PYROPE SOLUTION PROPERTIES 771

indicate that the excessfree energyof mixing of iron mag- o nesium garnet solutions is close Io zeto, at least at 1000 E and 900'C. Becauseour data cover only a limited range G -E1 of compositions and temperature, the results from other o studies are consideredhere in order to constrain further o c. the mixing properties of this solid solution. ol The enthalpy of mixing of almandine-pyrope garnet :g hasbeen determined by Geigeret al. (1987)using calori- Q) ().1o metric methods. They found that almandine-pyropesolid = solutions have apparently large excessenthalpies of mix- ': (, ing, most pronounced near the almandine-rich end of the 6r series. Large uncertainties are associatedwith these ca- lorimetric measurements.Modeling the data asymmet- molefraction almandine : Wil^ : -5.25 kJ rically, they obtained Wf 12.06kI, Fig. 3. Activity coefrcientof almandine(r^-) vs. molefrac- for one cation of mixing. Such significant excessenthal- tion almandinefor a portion of the alrnandine-pyropejoin, as pies of mixing, if combined with our results,may indicate determinedfrom representativemixing modelsand the experi- a sizable excessentropy of mixing, by the relationship mentaldata ofthis study.Filled squares:data collected at 1000 AG* : AHU - 7AS".. However, the limitations of these 'C, plottedat theadjusted garnet composition (see Table l) with two setsof data make such a conclusion highly uncertain. uncertainties(described in text)shown by brackets.Solid curves: Fe-Mg partitioning studies constrain a linear combi- predictionsof variousmixing models,as noted.Dotted line: nation of the mixing properties of the two phases,such idealmixing behavior. as biotite garnet (Ferry and Spear, 1978), olivine garnet (O'Neill and Wood, 1979;Hacklerand Wood, 1989),and cordieritegarnet (Aranovich and Podlesskii,1983). Ifthe A comparison of representativenearly ideal and non- solution properties of the other phase are well known, ideal mixing models with our experimentalresults is made then the almandine-pyrope mixing properties can be cal- in Figure 3. This graph of the adjusted mole fraction of In this way Ferry and Spear(1978) concluded almandine against the activity coefficient of almandine culated. 'C, that almandine-pyrope garnets were nearly ideal at Fe- (ro,J is a plot of the values of 7o'^ at 1000 predicted rich compositions, basedon their garnet-biotite exchange by the mixing models of Berman (1990), Hackler and experiments.Similarly, O'Neill and Wood (1979) and Wood (1989), and Ganguly and Saxena(1984). It also Hacklerand Wood (1989)suggested almandine pyrope is includes the experimental data, plotted as squares,as well nearly ideal from garnet-olivine partitioning data, as did as an indication ofthe uncertaintiesin the data (brackets). Aranovich and Podlesskii (1983) from garnet-cordierite Although only a small portion of the join could be in- exchangeexperiments. Berman (1990) has employed a vestigated,it is clear that the experimental data are con- number of garnet-orthopyroxeneFe-Mg exchangestudies sistentwith the modelsof Hackler and Wood (1989)and to extract iron magnesium garnet properties by mathe- Berman(1990). matical programming analysis.He obtained 2."., : 0.08 for geobarometrY kJ/mol, W-"r": l.24kI/mol for one cation of mixing. Implications A number of researchershave usedcompositional data In general,these results provide confirmation of nearly of coexistingFe-Mg phasesfrom natural occurrences,well ideal mixing behavior of almandine-rich garnets and characterizedpetrologically in terms of temperature and therefore improve our confidence in estimates of tem- pressure, to constrain garnet properties (Dahl, 1980; perature and pressure calculated from garnet geother- Hodges and Spear, 1982; Hoinkes, 1986).Others have mometers and geobarometers.These results support Ber- combined petrologic data with experimental data (Chat- man's (1990) garnet model and other models (Hodges terjee,1987; Ganguly and Saxena,1984, 1987).A recent and Spear, 1982; Newton and Haselton, 1981) that in- analysisby Williams and Grambling (1990) examined corporate nearly ideal Fe-Mg mixing. coexistinggarnet and biotite pairs from rocks in northern A barometer that is rather sensitive to values of the New Mexico where metamorphic conditions are well activity of almandine is the garnet-rutile-sillimanite-il- known. Fe and Mg content of the garnets and ln Ko of menite-quartz geobarometer or GRAIL (Bohlen et al., garnet-biotite partitioning were clearly linked to the spes- 1983).The GRAIL barometerhas a small volume change sartine content ofgarnet. Becauseofthis, parametersfor compared with many others and a rather flat slope. Boh- Mg-Fe and Mg-Mn mixing in garnet cannot be indepen- len et al. (1983) formulated this geobarometerwith ex- dently determined, but a range of paired values is per- perimental reversals of the end-member reaction and a mitted. Ideal mixing of Mg-Fe in garnet is allowed, but nonideal model for garnet solid solution from Perkins Williams and Grambling prefer slightly nonideal mixing (1979), which provides for a temperature-dependent and adopt the values of Hackler and Wood (1989) of symmetric model for Fe-Mg mixing in garnet: Wr"*": Wr"*": 0.7 kJ/mol of cation, W*"r" : 2.12 kJ/mol of 14.57- 5.A2TfC, kJ/mol, onecation of mixing).In their catron. analysisof the GRAIL barometer,Bohlen et al. (1983) 772 KOZIOL AND BOHLEN: ALMANDINE-PYROPE SOLUTION PROPERTIES stated that a nonideal garnet model was necessaryfor cording to recentwork by Kohn and Spear(1991), un- estimating the correct pressures for kyanite- and silli- certainties in the mixing properties of garnet account for manite-bearing assemblages.Otherwise, pressuresin the a significant amount of the uncertainty in the final pres- sillimanite field would be calculated for kyanite-bearing sure estimate, especially for the garnet-AlrSiOs-quafiz- rocks, or pressuresin the andalusite field would be cal- plagioclase and garnet-plagioclase-clinopyroxene-quartz culated for sillimanite-bearing rocks. The effect of using geobarometers.This uncertainty is not eliminated by the an ideal model is to reduce pressureestimates. work presented here and in similar studies; however, it We conducteda reexamination of GRAIL assemblages is greatly reduced,and investigation of the P-Ihistory of as reported in the literature to check that ideal Fe-Mg metamorphic terranesmay proceedwith more assurance. mixing was consistent with field evidence. Well-charac- terized assemblagesfrom the studies of Aggarwal and AcrNowr,nncMENTS Nesbitt (1987), Baker (1985), Fletcher and Greenwood This work was supportedby a NRC postdoctoralfellowship to A.M.K. (1979),Hattori (1967),l^abotka(1980), and Stiiubti(1989) at the U.S. GeologicalSurvey, Menlo Park. We thank Craig Manning and that preserved two AlrSiO, polymorphs or that were es- Carey Huggins for valuable help and advice in the lab, kwis Calk for his timated to have equilibrated near an AlrSiO, phase generous help with the microprobe analyses, and Richard Erd for assis- R.G. Ber- boundary were tance with XRD measurements.Reviews by L.Y. Aranovich, chosen. Temperatures estimated by the man, H.T. Haselton, and H. Shaw greatly improved the manuscript. garnet-biotite geothermometerof Ferry and Spear(1978) were recalculatedusing Berman's ( I 990) garnet model, or RrrnnnNcns crrED in some casesthe author's estimateswere used.Pressures (1987) were calculatedwith the calibration of Bohlen et al. (1983) Aggarwal, P., and Nesbitt, B.E. Pressureand temperature condi- tions ofmetamorphism in the vicinity ofthree massivesulfide deposits, using Perkins's garnet (given model above) and using an Flin Flon-Snow Iake belt, Manitoba. Canadian Joumal of Earth Sci- ideal garnet solution model, where all cation interactions ences.24.2305-2315. are assumed to be zero. Such a model ignores the de- Anderson, D.J., and Lindsley, D.H. (1981) A valid Margules formulation monstrable nonideality of Fe-Ca and Mg-Ca (see Ber- for an asymmetric ternary solution: Revision of the olivine-ilmenite man, 1990) thermometer, with applications. Geochimica et Cosmochimica Acta, and representsthe end-membercase. Results 45,847-851. were compared against the aluminosilicate diagram of Aranovich, L.Y., and Podlesskii,K.K. (1983) The cordierite-garnet-silli- Holdaway (197l) with modificationsto the kyanite-silli- manite-quartzequilibrium: Experimentsand applications.In S.K. Sax- manite boundary by Bohlen et al. (1991). We find that ena, Ed., Kinetics and equilibrium in mineral reactions,p. 173-198. temperatures calculated using different solution models Springer-Verlag, New York. - ( I 989) Geothermobarometry for garnet garnet-biotite of high-grademetapelites: Simutta- in the geothermometer are vir- neouslyoperating reactions. Geological Society Sp€cial Publication, 43, tually the same. Estimated pressuresare slightly lower 45-61. than those estimated by the previous calibration, but are Baker, A.J. (1985) Pressuresand temperaturesofmetamorphism in the always close (within I kbar) to the kyanite-sillimanite easternDalradian. Joumal ofthe Geological Society oflondon, 142, 137-148. phase boundary. Ideal mixing in almandine-pyrope gar- Bence,A.E., and Albee, A.L. (1968) Empirical correction factors for the net is compatible with the reported GRAIL parageneses electron microanalysisof silicatesand oxides. Journal of Geology, 76, in the papers cited. 382-403. Another thermobarometer that is affectedby assumed Berman, R G. (1988) Internally-consistentthennodynamic data for min- iron magnesiumgarnet mixing propertiesis spinel-quartz- eralsin the systemNarO-KrO-CaO-MgO-FeO-FerO,-Al,Or-SiOr-TiOr- H,O-CO,. Journal of Petrology, 29, 445-522. garnet-sillimanite(Bohlen et al., 1986),which can be used -(1990) Mixing properties of Ca-Mg-Fe-Mn garnets. American to estimate either temperature or pressure. This ther- Mineralogist, 75, 328-344. mobarometer is based on experimental reversals of the Bishop, F.C. (1980) The distribution ofFez* and Mg betweencoexisting equilibrium 3 hercynite * 5 quartz : almandine + sil- ilmenite and pyroxenewith applicationsto geothermometry.American of Science.280. 46-77 limanite, and the formulation is independent gar- Journal . of any Bohlen, S.R. (1984) Equilibria for precisepressure calibration and a fric- net or spinel solution model, as explained by Bohlen et tionless fumace assembly for the piston-cylinder apparatus. Neues al. (1986).However, the activity of almandinein garnet Jahrbuch fiir Mineralogie Monatshefte, 9, 404-412. must be determined, and the use of the nonideal garnet Bohlen, S.R., Wall, V.J., and Boettcher,A.L. (1983) Experimental inves- geological model of Ganguly and Saxena(1984) was suggestedby tigations and applications of equilibria in the system FeO- TiOr-Al,Or-SiOr-HrO. American Mineralogist, 68, 1049-1058. Bohlen et al. (1986). The use of a nearly ideal garnet Bohlen, S R, Dollase, W.A., and Wall, V.J. (1986) Calibration and ap- model has the efect of increasingthe estimated temper- plications of spinel equilibria in the system FeO-AlrOr-SiOr. Joumal ature and lowering the estimatedpressure calculated from of Petrology,27, | 143-l | 56. the thermobarometer. Bohlen, S.R., Montana, A., and Kerrick, D.M. (1991) Precisedetermi- nations ofthe equilibria kyanite = sillimanite and kyanite + andalusite CoNcr,usroN and a revised triple point for Al,SiO, polymorphs. American Miner- alogist,76,677-680. The determination of solid-solution properties of min- Chatterjee,N. (1987) Evaluation of thermochemical data on Fe-Mg ol- erals greatly improves the calibration of many geother- ivine, orthopyoxene, spinel and Ca-Fe-Mg-Al garnet. Geochimica et Cosmochimica mometers and geobarometers.This new determination of Acta. 51. 25 I 5-2525. Cressey,G., Schmid, R., and Wood, B.J. (1978) Thermodynamic prop- almandine-pyrope mixing especially aids the many for- erties of almandine-grossulargarnet solid solutions. Contributions to mulations of thermobarometersthat involve garnet. Ac- Mineralogy and Petrology, 67, 397-404. KOZIOL AND BOHLEN: ALMANDINE-PYROPE SOLUTION PROPERTIES I t)

Dahl, P.S.(1980) The thermal-compositionaldependence of Fer*-Mg dis- and Ca-Mn gamets determined by reversed,displaced equilibrium ex- tributions between coexisting garnet and pyroxene: Applications to geo- periments. American Mineralogist, 75, 3 19-327. thermometry. American Mineralogist, 65, 854-866. Koziol, A.M., and Bohlen, S.R. (1990) Garnet (almandine-pyrope)geo- Essene,E.J. (1989) The current status of thermobarometry in metamor- barometry. Geological Society of America Absrracts with Progra.m, 22, phic rocks. Geological Society SpecialPublication, 43, l-44. 471. Ferry, J.M., and Spear,F.S. (1978) Experimental calibration of the par- Koziol, A.M., and Newton, R.C. (1989) Grossular activity-composition titioning of Fe and Mg between biotite and garnet. Contributions to relationships in temary garnets determined by reversed displaced-equi- Mineralogy and Petrology, 66, ll3-117. librium experiments.Contributions to Mineralogy and Petrology, 103, Fletcher, C.J.N., and Greenwood, H.J. (1979) Metamorphism and srruc- 423-433. ture ofPenfold Creek area,near QuesnelIake, British Columbia. Jour- I-abotka,T. (1980)Petrology of a medium-pressureregional metamorphic nal of Perology, 20, 7 43-794. terrane, Funeral Mountains, Califomia. American Mineralogist, 65, 670- Ganguly, J., and Saxena,S.K. (1984) Mixing propertiesof aluminosilicate 689. garnets: Constraints from natural and experimental data, and applica- Moecher, D.P., Essene,E.J., and Anovitz, L.M. (1988) Calculation and tions to geothermo-barometry.American Mineralogist, 69, 88-97. application of clinopyroxene-gamet-plagioclase-quartz geobarometers. -(1987) Mixtures and mineral reactions, 286 p. Springer-Verlag, Contributions to Mineralogy and Petrology, 100, 92-106. Berlin. Ne*on, R.C., and Haselton,H.T. (1981)Thermodynamics of the gamet- Geiger, C.A., Newton, R.C., and Kleppa, O.J. (1987) Enthalpy of mixing plagioclase-AlrSios-quartzgeobarometer- In R.C. Newton, A. Navrot- of synthetic almandine-grossular and almandine-pyrope garnets from sky, and B.J. Wood, Eds., Thermodynamics of minerals and melts, p. high-temperaturesolution calorimetry. Geochimica et Cosmochimica 13| - | 47. Springer-Verlag,New York. Acta.5l. 1755-1763. O'Neill, H.SI.C., and Wood, B.J. (1979) An experimentalstudy of Fe-Mg Green, D.H., and Sobolev, N.V. (1975) Coexistinggarnets and ilmenites partitioning between garnet and olivine and its calibration as a geo- synthesized at high pressures from pyrolite and olivine basanite and thermometer. Contributions to Mineralogy and Petrology, 70,59-70. their significancefor kimberlitic assemblages.Contributions to Min- Perkins, D., III. (1979) Application of new thermodynamic data to min- eralogy and Petrology, 50, 217-229. eral equilibria. Ph.D. thesis,University of Michigan, Ann Arbor, Mich- Hackler, R.T., and Wood, B.J. (1989) Experimental determination of Fe lgan. and Mg exchange between gamet and olivine and estimation of Fe-Mg Pownceby,M.I., Wall, V.I., and O'Neill, H.SI.C. (1987) Fe-Mn partition- mixing properties in gamet. American Mineralogist, 74,994-999. ing between gamet and iknenite: Experimental calibration and appli Hattori, H. (1967) Occurrenceof sillimanite-garnet-biotite gneissesand cations. Contributions to Mineralogy and Petrology,97 , 116-126. their significance in metamorphic zoning in the South Island, New Schmid, R., Cressey,G., and Wood, B.J. (1978) Experimental determi- Znalarrd.New Zealand Journal of Geology and Geophysics,10, 269- nation of univariant equilibria using divariant solid-solutron assem- 299. blages.American Mineralogist, 63, 511-515. Hodges, K.Y., and Spear, F.S. (1982) Geothermometry, geobarometry Stiiubli, A. (1989) Polyphasemetamorphism and the development of the and the AlrSiO, triple point at Mt. Moosilauke, New Harnpshire. Main Central Thrust. Journal of Metamorphic Geology, 7, 73-93. American Mineralogist, 67, 1 ll8- | 134. Williams, M.L., and Grambling, J.A. (1990) Manganese,ferric iron, and Hoinkes, G. (1986) Effectofgrossular content in gamet on the partitioning the equilibrium betweengarnet and biotite. American Mineralogist, 75, of Fe and Mg betweengamet and biotite: An empirical investigation E86-908. on staurolite-zonesamples from the Austroalpine Schneeburgcomplex. Wood, B.J. (1988) Activity measurementsand excessentropy-volume Contributions to Mineralogy and Petrology, 92,393-399. relationshipsfor pyrope-grossulargarnets. Journal of Geology,96, 721- Holdaway, M.J. (1971) Stability of andalusiteand the aluminum silicate 729. phasediagram. American Joumal of Science,27 l, 97-131. Kohn, M.J., and Spear,F.S. (1991) Error propagationfor barometers:2. Application to rocks. American Mineralogist, 76, 138-147. MeNuscnrrr rucErvED Aucusr 20, l99l Koziol, A.M. (1990) Activity-composition relationshipsof binary Ca-Fe M,lroscnrrr AccEFTEDMencs 13. 1992