solution properties of almandine-pyrope garnet as determined by
TRANSCRIPT
American Mineralogist, Volume 77, pages 765-773' 1992
Solution properties of almandine-pyrope garnet as determined byphase equilibrium experiments
ANonBl, M. Kozror-.* StnvrN R. Bonr'BNU.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 fromphase equilibrium experiments at temperatures of 900 and 1000 "C and pressures from 8to 14 kbar for the assemblage garnet + rutile * sillimanite + ilmenite + q:uartz (GRAIL).
Almandine (Alm) has essentially ideal behavior in almandine-pyrope garnet over the com-position range Almrn-Almu, at the above experimental conditions. In all experimentalproducts a systematic partitioning of Fe and Mg between garnet and ilmenite was seenwith ln Kax 1.59. This partitioning does not appear to be temperature sensitive. Theresults of this study support the use of garnet mixing models that incorporate ideal or
nearly ideal Fe-Mg parameters.
INrnonucrroN
Garnet is an important and abundant mineral in theEarth's crust and mantle and is the essential constituentin many metamorphic reactions that have been calibratedas thermobarometers (see Essene, 1989, for a review).Much information on the metamorphic history of rockshas been obtained through the use of such thermobarom-eters and through the interpretation ofgarnet zoning.
For precise estimates of pressure and temperature, theend-member reaction of the geobarometer must be wellcalibrated, and the solid-solution properties of garnet,predominantly a mixture of almandine, pyrope, grossu-lar, and spessartine, must be well known. This is especial-ly important for P-T studies that employ garnet zoning.The almandine-pyrope join (FerAlrSirO' r-MgrAlrSirO'r)is one of the most important limiting garnet solid solu-tions because most garnets occurring in pelites are com-posed predominantly of these two components, and sev-eral exchange geothermometers are based on thepartitioning of Fe and Mg between garnet and some otherphase such as biotite or orthopyroxene.
The thermodynamic mixing properties of garnet havebeen inferred from cationic size considerations, variousFe-Mg exchange experiments, and metamorphic para-geneses. Depending on the type of analysis, almandine-pyrope mixing properties have been postulated to benearly ideal (Aranovich and Podlesskii, 1983, 1989; Ber-man, 1990; Hackler and Wood, 1989; Hodges and Spear,1982; Newton and Haselton, 198 l) or significantly non-ideal (Ganguly and Saxena, 1984, 1987; Geiger et al.,1987; Moecher et al., 1988; Perkins, 1979). However, todate there have been no direct determinations of activity-
* Present address: The College of Wooster, Department of Ge-ology, Wooster, Ohio 44691, U.S.A.
0003-004x/92l0708-o765$02.00 7 65
composition relationships for iron magnesium garnet sol-id solutions. The only other experimental work is thestudy of Geiger et al. (1987), who measured the excessenthalpy of almandine-pyrope garnets. Examples of Fe-Mg exchange experiments are the studies of O'Neill andWood (1979) and Hackler and Wood (1989), who deter-mined the Fe-Mg exchange between garnet and olivine.However, those experiments do not permit the garnet andolivine mixing properties to be deduced separately.
This study was undertaken to determine the mixingparameters of almandine-pyrope garnet by means of thephase equilibrium technique (Koziol and Newton, 1989;Koziol, 1990; Wood, 1988). This study complements thatof Bohlen et al. (1983), in which the end-member reac-tion for the GRAIL geobarometer, on the basis of theequilibrium between garnet rutile and aluminosilicate il-menite quartz, was experimentally determined. This studywas also designed to complement the work of Koziol andNewton (1989) and Koziol (1990), who determined themixing properties of grossular-rich garnet.
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 ofthe phases, as outlined by Cressey et al.(1978) and Schmid et al. (1978). The thermodynamic ba-sis of this technique has been discussed by Wood (1988).The univariant equilibrium of interest is
3FeTiO, + AlrSiOs + 2SiOr: Fe.AlrSirOr2 + 3TiO2. (1)ilmenite sillimanite qurtz almmdine rutile
In a simple system, when garnet is a solid solution andthe other phases have limited or no solid solution, the
766
activity of almandine in garnet can be determined usingthe relationship
rPoI LVo dP : R?" ln K (2)
atP
where the standard state is the pure phase at the temper-ature and pressure ofinterest, Po is the equilibrium pres-sure of the end-member equilibrium at T, the tempera-ture of the experiment, P is the pressure of the experiment,AZ0 is the volume change of Reaction l, and K is de-fined as
,. a or^'(a*")t1\ :
;_ tj,l(ar ,*)3 . a"u.(ao,)2 '
When the integral on the left side of Equation 2 is eval-uated, the activity of almandine in garnet at the temper-ature and pressure of interest is determined. Equation 2has been integrated using volume data from Berman(1988). In garnet, the cations mix over three sites performula unit, giving the following relationship betweenactivity and mole fraction:
afil, : (X^,-"y",-)' (4)
where Xis the mole fraction of FerAlrSirO,, in the binarysolution and 7 is the activity coefficient of FerAlrSirO,r.Measurement of the garnet composition in equilibriumwith rutile, ilmenite, sillimanite, and quartz over a rangeof P and Z permits calculation of 7o,- and the activity-composition relationships. For optimal accuracy in thesemeasurements, compositions must be reversed and allphases well characterized by microprobe analysis. In ad-dition, the end-member curve must be well known. TheGRAIL end-member equilibrium, Equation l, has beentightly reversed by Bohlen et al. ( I 983), grearly aiding theprecision of the determination of yer-.
ExpnnrtvrnurAr- METHoDS
Starting materials
Natural quartz from Brazil and natural sillimanite(0.950/o FerOr) from Molodezhnaya Station, Antarctica,were used as starting materials. The rutile and ilmeniteused were part of synthetic samples from the study ofBohlen et al. (1983). Two ilmenite-geikielite solid solu-tions (IlmrrGeiko. and IlmrrGeikor) were synthesized fromfinely disseminated mixtures of reagent-grade Fe metal,sintered FerO., TiOr, and MgO. These mixtures were re-acted in evacuated silica tubes at 900'C for 3 d. Eachpreparation yielded ilmenite close to the desired com-position and a small amount ( <<0. l0lo) of rutile that couldbe detected optically and in backscattered electron (BSE)imaging but could not be detected by X-ray diffractionanalysis.
Garnet used in this study was synthesized from glassof the desired composition. Each glass sample was pre-pared from a mixture of reagent-grade SiOr, AlrO. (co-rundum), FerOr, and MgO and melted in a graphite cru-cible at 1325 "C for 25 min. These conditions were arrived
KOZIOL AND BOHLEN: ALMANDINE-PYROPE SOLUTION PROPERTIES
at after some experimentation and varied with the size ofthe graphite crucible and the integrity of the heating ele-ments in the furnace used. The resulting homogeneousglass was dark greenish black with no color changes in-dicative of an fo,g.radient, nor were there traces of metalprecipitation. The glass was finely powdered, loaded intoan Au capsule 5 mm in diameter, with 2 wto/o graphite, Iwto/o quartz, and I mL HrO, and synthesized at 900 'C,
I 5 kbar, for l-2 d. These syntheses yielded homogeneousgarnet except for the composition Alm.oPyroo, which wassynthesized at 1070 oC and 19.2 kbar to yield homoge-neous garnet. All garnet samples were characterized op-tically, by X-ray diffraction, and by electron microprobeanalysis. All garnet products had a small amount ofgraphite, and some had a trace (<<0.10/o) of quartz. Elec-tron microprobe analyses confirmed that the garnets wereof the desired composition with l itt le variation,with actual compositions AlmronPrpr, (+0.2 molo/o),Almro rPrprn, ( + 2. 9 molo/o), Almrn oPrpo o u (+ 2.6 molo/o).
Apparatus and experimental procedure
Starting mixes of the GRAIL assemblage in stoichio-metric proportions appropriate for Equation I were pre-pared using appropriate garnet and ilmenite composi-tions. The garnets were chosen so as to approach the finalcomposition from the almandine-rich and almandine-poordirections, and the ilmenites were chosen to be close tothe composition in exchange equilibrium with the antic-ipated final gamet composition. For experiments per-formed at 1000 'C, the finely ground sample was encap-sulated without any special precautions to eliminatemoisture. About 4 wto/o HrO was added to the capsule forexperiments performed at 900'C. The AgroPdro samplecapsule, sealed by arc welding, was placed into a 3-mmPt capsule with about 100 mg of Fe metal and 5 mL ofHrO. This outer capsule was also sealed by arc welding.
All experiments were performed in a piston-cylinderapparatus, using an assembly of 2.54 cm in diameter withNaCl pressure medium and Pt-Pte'Rh,o thermocouples.Experiments above 9.8 kbar were made in the low-tem-perature assembly of Bohlen (1984), and experiments be-low this pressure were made in a high-temperature as-sembly where Pyrex sleeves are next to the graphitefurnace. Details of this assembly and its calibration arediscussed by Bohlen (1984). Experimental conditions andresults are listed in Table l.
Experimental products
The products of all experiments were characterized op-tically and by X-ray diffraction and electron microprobeanalysis. Microprobe analyses were obtained on an ARL-SEMQ electron microprobe with wavelength-dispersivespectrometers. Standards used were synthetic almandinegarnet, Kakanui pyrope and synthetic TiOr, FerOr, andmagnesium aluminum spinel. An accelerating potentialof 15 kV and sample current of 30 nA were standardoperating conditions. Counting times were 20 s, and usu-ally 2-3 counting periods were taken and averaged for
KOZIOL AND BOHLEN: ALMANDINE.PYROPE SOLUTION PROPERTIES 767
TABLE 1. Experimental conditions and results
P Time InitialExp. (kbao (h)
FinalXMXo,.
Calculated Activitydrr^ coeff .
3.23B3.543.13A3.83.6A3.683.413.623.38A3.3883.42A.3.42B3.743.70A3.683.72
947898
1174848
1 1 8168142142959592
1231 1 6243
0.800.950.800.700.950.700.950.700.800.600.800.600.700.800.600.60
0.8880.8080.8250.8230.8680.800o.7770.7400.7080.691o.7210.6540.6140.6750.6130.6s3
0.9660.9440.9470.9490.9590.9480.932o.9240.8970.9140.9200.9050.8690.8770_8850.899
0.9790.9740.9680.9680.9690.9710.9860.9780.9790.98'0.9830.9810.9840.9700.985o.972
0.9100.8440.8510.8480.8860.8280.8300.7910.7810.7480.7780.7160.7020.7540.6890.711
0.9650.8810.8710.8660.8500.8500.8240.8150.7660.7660.752o.7520.7030.6940.690o.712
1.06(6)1.04(6)1.02(6)1.02(6)0.s6(5)1.0q6)0.99(6)1.03(6)0.s8(6)1.02(6)0.e7(6)1.0s(6)1.00(6)0.92(5)1.0q6)1.00(6)
14.012.512.312.21 1 . 91 1 . 911 .411.210.210.29.9o o8.88.68.58.0
Note; All experiments performed at 1000 rc except for experiment 3.72, which was conducted at 900 €. Initial ilmenite composition was llml@ ex@ptfor experiments 3.74, 3.7O,3.68, and 3.72, where it was llms.
' Estimated rutile activity.
each analysis. Spectrometer data were reduced using theprocedure ofBence and Albee (1968). Single garnet anal-yses representative ofthe average composition are givenin Table 2. The averaged results for ilmenite and rutileare given in Tables 3 and 4, respectively.
Microprobe analyses of the products revealed a small
TABLE 2, Selected electron microprobe analyses of garnet
amount of Fe and Al in rutile and a small amount of Aland a significant and systematic solution of Mg in ilmen-ite (see below). In addition, there was a small but signif-icant amount (0.9-2.0 wto/o) of TiO, in all garnet analysesfrom experimental products. This level of TiO, was notseen in analyses of the almandine standard, nor in anal-
Exp 9.72 3.238 3.64 3.683.54 3.13A 3.41
sio,Al2o3FeOMgoCaOTio,
Total
38.521.631.28.50 .11 . 1
r 0 1 . 0
2.9681.9582.O110.980.0070.0657.989
3.62
36.020.640.1
1 . 8o.21 . 3
100.0
2.9421.9872.7350.2180.014o.0777.973
3.38A
36.721.O37.34.10.11 . 3
100.5
2.9411.9772.4980.4910.0050.087.992
3.388
Wl"/c37.120.938.33.50.01 .6
101.4Cations
2-9531.9572.5480.420.0030.0937.974
3.424
36.420.738.03.60.01 . 5
100.2
2.9321.9712.5620.4330.0020.0917.991
3.428
36.420.839.42.40.11 . 0
100.1
2.9561.9932.6770.2880.0060.0287.977
3.74
37.520.736.94.10.01 . 2
100.4
2.9891.9492.4590.490.0040.0727.963
3.704
37.321.036.04.80 .11 .6
100.8
2.9571.9582.3780.5630.0080.1007.964
3.68
siAIFeMgCaTi
Total
Exp.
sio,Al2o3FeOMgoGaOTio,
Total
38.020.934.65.70.31 . 5
101.0
2.9791.9372.2720.6670.0240.0877.966
38.121.634.06.70.01 . 5
101.9
2.9471.9742.20o.7730.0010.0867_981
38.021.632.67.10.31 . 2
r00.8
2.9581.9782.122o.8220.030.0717.981
Wlc/o37.820.933.86.20.11 . 9
100.7Cations
2.9661.9322.2140.7230.0050.1 147.954
38.221.230.58.20.41 .5
100.0
2.9671.941.9810.9490.0320.0877.956
39.221.529.99.10.01 .3
101 .0
2.9971.9361.911.0350.0030.0767.957
38.02',t.332.17.60.01 .4
100.4
2.9641.962.0910.8790.0010.087.975
39.021.329.39.90.00.9
100.4
2.9941.9291.8781.1330.0030.0517.988
SiAIFeMgCaTi
Total
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 3.6A3.8 3.68 3.41
FeOTio,Alro3Mgo
Total
FeTiAIMg
TotalPoints
Exp.
44.153.30.42.5
100.3
0 .9100.9870.0110_0932.0015
3.62
46.352.60.60.4
99.9
0.9650.9860.018o.0171.9854
3.38A
46.152.30.61 . 1
100.1
0.9630.9820.0180.0392.001c
3.388
Yllo/o46.453.10.61 . 0
1 0 1 . 1Cations
0.960.9880.0180.0352.0023
3.424
46.053.10.70.9
100.6
0.9510.9880.0200.0321.9903
3.428
46.553.00.60.6
100.7
0.9680.9910.0180.0232.003
3.74
45.952.60.60.9
100.0
0.9590.9880.0140.0351.9952
3.70A
44.953.2o.71 . 3
100.1
0.9310.9920.0200.0481.9904
3.68
FeOTio,Al,o3Mgo
Total
FeTiAIMg
TotalPoints
44.5s3.20.71 . 5
99.9
0.9230.9930.0190.0581.9922
43.653.4o.72.3
100.0
0.8980.9890.0210.0831.9905
44.053.40.71 . 8
99.9
0.9060.9900.0210.0641.9803
Wl"/"44.253.70.61 . 7
100.2Cations
0.9150.9970.0190.0611.992
44.053.80.52.1
100.4
0.9050.9950.0190.0771.9964
42.3s3.91 . 13.0
100.3
0.8650.9910.0250.1 091.989c
43.652.9o.72.9
100.1
0.8980.9790.0190.1 062.O025
43.053.00.52.7
99.2
0.9750.9680.0190.0971.9594
Nofe.- All experiments performed at 1000 .C except for experiment 3.72.
TABLE 4. Electron microprobe analyses of rutile
Exp. 3.72 3.238 3.54 3.13A 3.8 3.6A 3.68 3.41
FeOTio,Al,o3Mgo
Total
FeTiAIMg
TotalPoints
Exp.
1 . 397.80.90.0
100.0
0.0140.9800.0130.0011.0083
3.62
0.998.50.70.0
100.1
0.0100.9870.0100.01.0082
3.38A
1 . 298.00.80.0
100.0
0.0130.9800.0130.01.006c
3.42A
wtc61 . 5
97.91 . 00.0
100.4Cations
0.0170.9800.0160.01.0122
3.428
1 . 597.31 . 10.0
99.9
0.0160.9740.0170.01.0072
3.74
0.0140.9800.0170.01 . 0 1 12
3.70A
1 . 297.71 . 00.0
o o o
0.0140.9800.0160.01.0092
3.68
o.799.10.40.0
100.2
0.0070.9910.0070.01.005
1 . 298.21 . 10.0
100.5
FeOTio,Al2o3Mgo
Total
FE
TiAIMg
TotalPoints
0.997.8o.40.0
99.1
0.0750.9680.0070.00.9902
1.097.60.70.0
o o e
0.0110.9690.0100.00.990
0.899.00.50.0
100.3
0.0090.9900.0080.01.0072
Wlo/c0.9
98.70.60.0
100.2Calions
0.0100.9880.0090.01.0073
0.899.00.50.0
100.3
0.0090.9900.0080.01.0073
1 . 497.00.90.0
99.3
0 .0160.9650.0140.00.9942
0.798.40.40.0
99.5
0.0070.9790.0070.00.9933
Notej All experiments performed at 1000 € except for experiment 9.72.
yses of the synthetic garnet used as starting material. Boh-len et al. (1983) postulated that the 1.5 wto/o TiO, theyobtained in their analyses was the result of fine inter-growths of rutile with garnet. We believe the Ti is part ofthe garnet structure because we did not see any rutilegrains in BSE images, even at high power, and the Sication totals of the garnet were always slightly reducedcompared with analyses of standards and synthetic garnetsamples.
Spot analyses were taken at different points within thesame grain of garnet, rutile, or ilmenite and among sev-eral different grains. Garnets were almost always com-positionally zoned. The original seed compositions wereretained in the core, but the garnet grains developed arim, varying between 2 and l0 pm in thickness, that hada new composition. This new composition differed fromthe starting composition by as much as 17 mol0/0. Thethree or four analyses with good stoichiometry that werefarthest removed from the original composition wereconsidered indicative of the final composition attained.Ilmenite and rutile were unzoned.
Each garnet analysis was cast into mole fractions sep-arately and recalculated on a site by site basis, where Xo,--- X...(Xor)t't.X.,. The microprobe data of Bohlen et al.(1983) were used to calculate the activity of sillimaniteby the relationship cr,, : Xru : Xr,.Xou and a.,, was foundto be 0.97 at 1000'C. The activity of rutile, always within0.03 of unity, was taken to be equal to the mole fractionof rutile, calculated as XR, : Xr,/X-u where X.", was thetotal number of cations in the analysis. The ilmenite molefraction was calculated as Xo..Xr, (on a cation basis).
DrscussroN
Results of experiments
The results ofexperiments conducted at 1000 and 900'C are given in Table l For an experiment at a givenpressure and temperature, the activity of almandine ingarnet may be calculated by Equation 2, and this valuefor each set of experimental conditions is noted in TableI as calculated an*. Xo,-, as measured by electron mi-croprobe analysis, cannot be compared directly to thisvalue because the other phases involved in the experi-ments are not at unit activity, as noted above, and theiractivity values must be substituted into Equations 2 and3. The extent of nonideal mixing in ilmenite geikielite aspredicted by the model of Anderson and Lindsley (1981)is negligible at these compositions at 1000'C; thereforethis correction to the ideal activity of ilmenite was ig-nored. Starting with the definition of K the equilibriumconstant (Eq. 3), we define K' as the cube root of theapparent equilibrium constant ofReaction l:
K', : 4jnoi'i]'48"
(5)arr^ ' (Q"r) t "
where a'fff corresponds to X^- measured by the experi-ments. In effect, K' is the mole fraction of almandineobtained after accounting for solid solution in the other
769
grt + ru
l----->-
l---------->
flfl
i lm + sil
+q l z
mole fraction almandine
Fig. 1. P-Xo'- diagram at constant temperature of 1000 'C.
Solid line: displacement in pressure of the GRAIL equilibrium(Eq. l) by solid solution in almandine gamet, calculated byEquation 2, assuming ideal mixing in garnet. Experimental dataobtained in this study are also plotted. Filled boxes: startingcomposition of almandine-pyrope garnet. Arrow tips: K' or finalcomposition of garnet adjusted for the reduced activities of il-menite, rutile, and sillimanite. See text for details.
phases. The value of K' is compared against ao,- calcu-lated from Equation 2, as described above. Equation 4may be rewritten as
a?i^: K "Yo,^ (6)
where afi| is the calculated value and'y^,- is the activitycoefficient. A graphical presentation ofthe data at 1000'C is given as Figure l. In this and all further figures,values for K, the adjusted mole fraction of almandine,are plotted. In this isothermal section, the calculated dis-placement of the univariant reaction (Eq. l) if Mg-Femixing in the garnet were ideal is shown by the solid line.The change in the garnet compositions from initial (filledboxes) to final (arrow heads) is also shown. The final com-positions are very close to the curve for ideal mixing, andtherefore there is little to no excess free energy of mixingfor iron magnesium garnet solutions at 1000 "C. Verylimited data were obtained at 900 'C, but one half rever-sal indicates that iron magnesium garnets behave simi-larly at this temperature.
In considering the uncertainties of these results, onemust include uncertainties in electron microprobe anal-ysis. Uncertainties in the compositions of garnet, rutile,ilmenite, and sillimanite cause an estimated uncertaintyof approximately +Q.917 in the value for K', the adjustedmole fraction of almandine. The main factors contrib-uting to the uncertainty in the calculated ao'- from Equa-tion 2 are the uncertainty in Po, the pressure of the end-
KOZIOL AND BOHLEN: ALMANDINE-PYROPE SOLUTION PROPERTIES
' 15
1 3
G'lt.:l
O i 1
fat,ooLo.
1 00.90.80.77 f0.6
770 KOZIOL AND BOHLEN: ALMANDINE-PYROPE SOLUTION PROPERTIES
member equilibrium (Eq. l), and the uncertainty in P,the pressure of the experiment. The end-member curvewas precisely bracketed by Bohlen et al. (1983) to within200 bars, and the piston-cylinder apparatus employed inthe Menlo Park laboratory is precise to + 100 bars (lab-oratory unpublished data). The 20 uncertainty of +600bars in the difference between Po and P leads to an un-certainty of +0.026 (for large differences) to +0.034 (forsmall differences) in the calculated value of co,-. Thecombination of uncertainties stemming from composi-tion and pressure determination leads Io a 2o uncertaintyof +0.06 in the value of 7o,- as listed in Table l.
Fe-Mg exchange between garnet and ilmeniteA systematic partitioning of Fe and Mg between garnet
and ilmenite was noted and followed as the experimentsprogressed. This exchange can be described by the reac-tion
Yr almandine + geikielite : % pyrope + ilmenite. (7)
The distribution coefficient, K", is defined as
0.4
U . J
otr(sc D o D';
=x
0.1
0.00.00 0.05
XMg
0 .10
in i lmenite
Other studies have experimentally determined the parti-tioning of Fe and Mg (or Mn) between ilmenite and aniron magnesium silicate (Bishop, 1980; Pownceby et al.,1987), but there is little information on Fe-Mg partirion-ing between garnet and ilmenite (but see Green and So-bolev, 1975). Although these experiments were not de-signed to measure the Ko of this exchange, we did note asystematic partitioning of Fe and Mg with an average orbest f,t Ko of 4.9, or ln Ko of I .59 (Fig. 2A). These exper-iments were performed over a range of pressures, buttheir results can be compared because the volume changeof this reaction is extremely small (+0.019 J/bar). Thedata in Figure 24, are reversed in terms of garnet molefraction but all final ilmenite-geikielite compositions wereapproached from ilmenite-rich compositions (pure il-menite except for the most magnesian compositions; seeTable l). Still, the very regular results at 1000 "C areanother indication that equilibrium between garnet andilmenite was approached.
Green and Sobolev (197 5) performed synthesis exper-iments on a pyrolite and an olivine-basanite compositionand obtained microprobe analyses of coexisting garnetand ilmenite. They found regular partitioning of Fe andMg between these two phases with a Ko of approximately4.0 + 0.5. This value did not appear to be sensitive totemperature, pressure, or composition. The compositionsthey investigated were more magnesian [Mg(Mg + Fe) ofEarnet : 0.41-0.73; of ilmenite : 0.15-0.471 than thoseof this study (see Fig. 2B). Although it was suggested pre-viously (Koziol and Bohlen, 1990) that this exchangemight be a geothermometer, Green and Sobolev (1975)have shown that the Ko for garnet ilmenite is insensitiveto temperature over the range 900-1100 .C.
E q E
E
Green & Sobolev (1975)
f u G o o
I!
I
JII
I
l r
II
I
this study
0.6
X Mg in i lmeniteFig. 2. Experimental data for the distribution of Mg2* be-
tween coexisting garnet and ilmenite. X Mg: mole fraction of theMg end-member of garnet or ilmenite. (A) Final compositionsobtained in this study at 1000 "C (filled squares). Arrows indicateextent of change of selected initial garnet-ilmenite pairs to finalcompositions as listed in Table l. A K" value of 4.9 best fits allthe data. (B) Comparison of data from this study (filled squares)to the data ofGreen and Sobolev (1975) (open squares) obtainedat 950-1050 €.
Mixing properties of iron magnesium garnets
The data in this study were collected over a range ofpressures and compositions, and the activity coefficientscannot be compared directly unless there is no excessvolume of mixing in almandine-pyrope garnets. Thecomprehensive unit-cell measurements of Geiger et al.(1987) show a very slight asymmetry in the volumes ofmixing that may be neglected for the purposes of thispaper. As noted above and in Figure 1, our experiments
1 . 0
0.8
o
F 0.6ct)
g o-4x
0.2
(8)
o.40.0 F
0.0
KOZIOL AND BOHLEN: ALMANDINE-PYROPE SOLUTION PROPERTIES 7 7 1
indicate that the excess free energy of mixing of iron mag-nesium garnet solutions is close Io zeto, at least at 1000and 900'C. Because our data cover only a limited rangeof compositions and temperature, the results from otherstudies are considered here in order to constrain furtherthe mixing properties of this solid solution.
The enthalpy of mixing of almandine-pyrope garnethas been determined by Geiger et al. (1987) using calori-metric methods. They found that almandine-pyrope solidsolutions have apparently large excess enthalpies of mix-ing, most pronounced near the almandine-rich end of theseries. Large uncertainties are associated with these ca-lorimetric measurements. Modeling the data asymmet-rically, they obtained Wf : 12.06 kI, Wil^ : -5.25 kJfor one cation of mixing. Such significant excess enthal-pies of mixing, if combined with our results, may indicatea sizable excess entropy of mixing, by the relationshipAG* : AHU - 7AS".. However, the limitations of thesetwo sets of data make such a conclusion highly uncertain.
Fe-Mg partitioning studies constrain a linear combi-nation of the mixing properties of the two phases, suchas biotite garnet (Ferry and Spear, 1978), olivine garnet(O'Neill and Wood, 1979;Hackler and Wood, 1989), andcordierite garnet (Aranovich and Podlesskii, 1983). Ifthesolution properties of the other phase are well known,then the almandine-pyrope mixing properties can be cal-culated. In this way Ferry and Spear (1978) concludedthat almandine-pyrope garnets were nearly ideal at Fe-rich compositions, based on their garnet-biotite exchangeexperiments. Similarly, O'Neill and Wood (1979) andHackler and Wood (1989) suggested almandine pyrope isnearly ideal from garnet-olivine partitioning data, as didAranovich and Podlesskii (1983) from garnet-cordieriteexchange experiments. Berman (1990) has employed anumber of garnet-orthopyroxene Fe-Mg exchange studiesto extract iron magnesium garnet properties by mathe-matical programming analysis. He obtained 2."., : 0.08kJ/mol, W-"r": l.24kI/mol for one cation of mixing.
A number of researchers have used compositional dataof coexisting Fe-Mg phases from natural occurrences, wellcharacterized petrologically in terms of temperature andpressure, to constrain garnet properties (Dahl, 1980;Hodges and Spear, 1982; Hoinkes, 1986). Others havecombined petrologic data with experimental data (Chat-terjee, 1987; Ganguly and Saxena, 1984, 1987). A recentanalysis by Williams and Grambling (1990) examinedcoexisting garnet and biotite pairs from rocks in northernNew Mexico where metamorphic conditions are wellknown. Fe and Mg content of the garnets and ln Ko ofgarnet-biotite partitioning were clearly linked to the spes-sartine content ofgarnet. Because ofthis, parameters forMg-Fe and Mg-Mn mixing in garnet cannot be indepen-dently determined, but a range of paired values is per-mitted. Ideal mixing of Mg-Fe in garnet is allowed, butWilliams and Grambling prefer slightly nonideal mixingand adopt the values of Hackler and Wood (1989) ofWr"*": 0.7 kJ/mol of cation, W*"r" : 2.12 kJ/mol ofcatron.
mole fraction almandine
Fig. 3. Activity coefrcient of almandine (r^-) vs. mole frac-tion almandine for a portion of the alrnandine-pyrope join, asdetermined from representative mixing models and the experi-mental data ofthis study. Filled squares: data collected at 1000'C, plotted at the adjusted garnet composition (see Table l) withuncertainties (described in text) shown by brackets. Solid curves:predictions of various mixing models, as noted. Dotted line:ideal mixing behavior.
A comparison of representative nearly ideal and non-ideal mixing models with our experimental results is madein Figure 3. This graph of the adjusted mole fraction ofalmandine against the activity coefficient of almandine(ro,J is a plot of the values of 7o'^ at 1000 'C, predicted
by the mixing models of Berman (1990), Hackler andWood (1989), and Ganguly and Saxena (1984). It alsoincludes the experimental data, plotted as squares, as wellas an indication ofthe uncertainties in the data (brackets).Although only a small portion of the join could be in-vestigated, it is clear that the experimental data are con-sistent with the models of Hackler and Wood (1989) andBerman (1990).
Implications for geobarometrY
In general, these results provide confirmation of nearlyideal mixing behavior of almandine-rich garnets andtherefore improve our confidence in estimates of tem-perature and pressure calculated from garnet geother-mometers and geobarometers. These results support Ber-man's (1990) garnet model and other models (Hodges
and Spear, 1982; Newton and Haselton, 1981) that in-corporate nearly ideal Fe-Mg mixing.
A barometer that is rather sensitive to values of theactivity of almandine is the garnet-rutile-sillimanite-il-menite-quartz geobarometer or GRAIL (Bohlen et al.,1983). The GRAIL barometer has a small volume changecompared with many others and a rather flat slope. Boh-len et al. (1983) formulated this geobarometer with ex-perimental reversals of the end-member reaction and anonideal model for garnet solid solution from Perkins(1979), which provides for a temperature-dependentsymmetric model for Fe-Mg mixing in garnet: Wr"*":14.57 - 5.A2T fC, kJ/mol, one cation of mixing). In theiranalysis of the GRAIL barometer, Bohlen et al. (1983)
o
EG
- E 1o
o
c .o l:gQ)o( ) . 1
=':(,6 r
772 KOZIOL AND BOHLEN: ALMANDINE-PYROPE SOLUTION PROPERTIES
stated that a nonideal garnet model was necessary forestimating the correct pressures for kyanite- and silli-manite-bearing assemblages. Otherwise, pressures in thesillimanite field would be calculated for kyanite-bearingrocks, or pressures in the andalusite field would be cal-culated for sillimanite-bearing rocks. The effect of usingan ideal model is to reduce pressure estimates.
We conducted a reexamination of GRAIL assemblagesas reported in the literature to check that ideal Fe-Mgmixing was consistent with field evidence. Well-charac-terized assemblages from the studies of Aggarwal andNesbitt (1987), Baker (1985), Fletcher and Greenwood(1979), Hattori (1967),l^abotka (1980), and Stiiubti (1989)that preserved two AlrSiO, polymorphs or that were es-timated to have equilibrated near an AlrSiO, phaseboundary were chosen. Temperatures estimated by thegarnet-biotite geothermometer of Ferry and Spear (1978)were recalculated using Berman's ( I 990) garnet model, orin some cases the author's estimates were used. Pressureswere calculated with the calibration of Bohlen et al. (1983)using Perkins's garnet model (given above) and using anideal garnet solution model, where all cation interactionsare assumed to be zero. Such a model ignores the de-monstrable nonideality of Fe-Ca and Mg-Ca (see Ber-man, 1990) and represents the end-member case. Resultswere compared against the aluminosilicate diagram ofHoldaway (197l) with modifications to the kyanite-silli-manite boundary by Bohlen et al. (1991). We find thattemperatures calculated using different solution modelsfor garnet in the garnet-biotite geothermometer are vir-tually the same. Estimated pressures are slightly lowerthan those estimated by the previous calibration, but arealways close (within I kbar) to the kyanite-sillimanitephase boundary. Ideal mixing in almandine-pyrope gar-net is compatible with the reported GRAIL paragenesesin the papers cited.
Another thermobarometer that is affected by assumediron magnesium garnet mixing properties is spinel-quartz-garnet-sillimanite (Bohlen et al., 1986), which can be usedto estimate either temperature or pressure. This ther-mobarometer is based on experimental reversals of theequilibrium 3 hercynite * 5 quartz : almandine + sil-limanite, and the formulation is independent of any gar-net or spinel solution model, as explained by Bohlen etal. (1986). However, the activity of almandine in garnetmust be determined, and the use of the nonideal garnetmodel of Ganguly and Saxena (1984) was suggested byBohlen et al. (1986). The use of a nearly ideal garnetmodel has the efect of increasing the estimated temper-ature and lowering the estimated pressure calculated fromthe thermobarometer.
CoNcr,usroN
The determination of solid-solution properties of min-erals greatly improves the calibration of many geother-mometers and geobarometers. This new determination ofalmandine-pyrope mixing especially aids the many for-mulations of thermobarometers that involve garnet. Ac-
cording to recent work by Kohn and Spear (1991), un-certainties in the mixing properties of garnet account fora significant amount of the uncertainty in the final pres-sure estimate, especially for the garnet-AlrSiO s-quafiz-plagioclase and garnet-plagioclase-clinopyroxene-quartzgeobarometers. This uncertainty is not eliminated by thework presented here and in similar studies; however, itis greatly reduced, and investigation of the P-Ihistory ofmetamorphic terranes may proceed with more assurance.
AcrNowr,nncMENTS
This work was supported by a NRC postdoctoral fellowship to A.M.K.at the U.S. Geological Survey, Menlo Park. We thank Craig Manning andCarey Huggins for valuable help and advice in the lab, kwis Calk for hisgenerous help with the microprobe analyses, and Richard Erd for assis-tance with XRD measurements. Reviews by L.Y. Aranovich, R.G. Ber-man, H.T. Haselton, and H. Shaw greatly improved the manuscript.
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KOZIOL AND BOHLEN: ALMANDINE-PYROPE SOLUTION PROPERTIES