Melting and thermodynamic properties of pyrope (Mg3Al2Si3O12)

Geochimm ef Cosmoch~mrco Acla Vol. 55, pp. 1005-1010

COl6-7037/91/$3.00

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U.S.A.

Copyright 6 1991 Pergamon Press plc. Printed in

Melting and thermodynamic

properties of pyrope ( Mg3A12Si3012)

CHRISTOPHE T~QuI,’ RICHARD A. ROBIE,~ BRUCE S. HEMINGWAY,’ DANIEL R. NEUVILLE,’ and PASCAL RICHET’ ‘Institut de Physique du Globe, 4 place Jussieu, 75252 Paris cedex 05, France ‘US Geological Survey, 959 National Center, Reston, VA 22092, USA (Received July 13, 1990; accepted in revised form January 15, 199 1)

Abstract-The heat capacity of Mg3A12Si3012 glass has been measured from 10 to 1000 K by adiabatic and differential scanning calorimetry. The heat capacity of crystalline pyrope has been determined from drop-calorimetry measurements between 820 and 1300 K. From these and previously published results a consistent set of thermodynamic data is presented for pyrope and Mg3A12Si30L2 glass and liquid for the interval O-2000 K. The enthalpy of fusion at 1570 + 30 K, the metastable congruent 1-bar melting point, is241 f 12 kJ/mol. 11.4587 (5) A (Cu source with Si as an internal standard). This figure is in the range 1 I .45 1-I 1.462 A of the parameters of synthetic samples reviewed by GEIGER et al. ( 1989) whose preferred value for “pure” pyrope is 11.454 A. The only significant impurity in the final product was quartz, as evidenced by its 10 1 reflection at 3.34 8, in the X-ray pattern. From the intensity of this reflection as compared to that observed for pyrope samples mixed with known amounts of quartz, a quartz fraction of 1.5 + 0.5 wt% was determined. The results were corrected for the quartz content with the enthalpy equations of RICHET et al. ( 1982). This correction is about +0.08%. The main effect of the iron content of our sample is an increase in the molar mass which was taken as 404.54 g, i.e., a figure 0.35% higher than the molar mass of pure pyrope. In addition, almandine (FejAlzSi301z) has a slightly higher molar C,, than pyrope (WATANABE, 1982), but no allowance was made for this effect because the correction would be of the order of only -0.02%. The drop-calorimetry measurements on crystalline pyrope were made with the high-temperature set-up and ice calorimeter described by RICHES et al. ( 1982), with modifications reported by RICHET and BOTTINGA ( 1984). From measurements under the same conditions on a-A1203, inaccuracies of the order of 0.2 and 0.5% are estimated for the measured relative enthalpies and the derived heat capacities. respectively ( RICHET et al., 1982). The low-temperature and DSC measurements were made on a synthetic glass prepared from an oxide mix as described in RICHET and BOTTINGA ( 1984). To prevent partial crystallization on cooling, 5-g samples were quenched from 1920 K to room temperature in a few seconds by immersing the bottom of the platinum crucible in water. The density of the quenched material investigated was 2.765 (2) g/cmj. In view of the good agreement between the electron microprobe analyses (Table 1) and the nominal composition, the nominal molar mass was used to derive the molar C, values. The lowtemperature C, measurements were made on 38.6854 g of this glass with the adiabatic calorimeter and procedures previously described by ROBIE and HEMINGWAY ( 1972) and HEMINGWAY et al. ( 1984). Errors on the adiabatic C, values are about f 10% below 10 K, *0.5% between 10 and 50 K, and *0.2% above 50 K. The DSC measurements were performed as reported by KRUPKA et al.( 1979), with estimated inaccuracies of * 1%.

I. INTRODUCTION THE PROPERTIES OF PYROPE ( Mg,A12Si~O12), the magnesian endmember garnet, are significant in view of the importance of Mg-rich garnets in igneous and high-grade metamorphic rocks as well as in the upper mantle. Pyrope is stable only at high pressure and temperature, and reliable thermodynamic data have been obtained only relatively recently because of the difficulties of securing pure samples large enough for calorimetric experiments. Available measurements include the enthalpy of formation (CHARLU et al., 1975; NEWTON et al., 1977a) and the low-temperature heat capacity (C,) by adiabatic methods ( HASELTON and WESTRUM, 1980). At higher temperatures, differential scanning calorimetry (DSC) measurements have been reported up to 600 K by WATANABE ( 1982) and to 1000 K in an abstract form by NEWTON et al. ( 1977b). To avoid the problems of extrapolations of such DSC data, we have thus determined the high-temperature heat capacity of pyrope from drop-calorimetry measurements performed between 820 and 1300 K. We have also measured the heat capacity of Mg3A12Si30j2 glass from 10 to 1000 K, recalculated the melting properties of pyrope, and determined the configurational entropy of Mg3A12Si3012 liquid. These data are useful for thermodynamic modeling of pyrope-melt equilibria and are important parameters in the quantitative modeling of the viscosity of molten garnets developed in a companion paper ( NEUVILLE and RICHET, 199 1) Finally, the data for pyrope are also part of a broader study of the high-temperature heat-capacity for minerals in the system CaO-MgO-A1203-Si02 ( RICHET and FIQUET, 199 1) . II. EXPERIMENTAL

METHODS

The pyrope used is a natural garnet from the Dora Maira massif in the Western Alps that has been described by CHOPIN ( 1984). This material has a composition that can vary from 90 to 98 mol% pyrope and includes some quartz, talc, chlorite, kyanite, and rutile. A Mgrich chunk was ground in an agate mortar and purified through magnetic separation, density separation in diiodomethane, subsequent annealing at 1270 K for 30 min, and a final density separation. Electron microprobe analyses of the starting material and of a glass made from the purified product (Table 1) indicate an essentially pure pyrope composition, with an Mg/(Mg + Fe) ratio of 98.5 mol%. An X-ray analysis of another sample from the same outcrop made by C. Geiger (Bayerische Geoinstitut, priv. comm.) yielded a lattice parameter of

III. HEAT

CAPACITIES

Crystal The drop-calorimetry results are reported in Table 2 and plotted in Fig. 1 in the form of mean heat capacities, C,,, = (H7 - HzT3)/( T - 273). In series BX, the product was heated to 1394 K, i.e., a temperature higher than the 1270 K of the short annealing of the purification procedure of the sample at which pyrope was found metastable. The result of 1005

1006

C. TCqui et al. Table 1. Comparison

between nominal and electron microprobe

4203

Nominal

25.29

Glass CtyStal

compositions

(wt %)

SiO2

MgO

CaO

Fe0

Total

44.7 1 45.95(3) 45.70(9)

30.00 28.71(16) 28.02( 13)

0.00 0.18(l) 0.12(2)

0.00 0.02(l) 0.69(5)

100.00 100.20(30) 99.70(30)

Reported values are averages of 2 analyses made with an automated CAMEBAX electron microprobe(Universitt ParisVI) operatedat 15 kV and 15 nA. Totals include about 0.15 % Na20 for the glass, and 0.22 % NazO and K20 for the crystal.

this run was too high with respect to the previous results (Fig. I), and further experiments showed anomalous deviations of about 0.3% with respect to previous measurements. An X-my pattern of the product indicated partial transformation to aluminous enstatite only, without sapphirine and sillimanite whose occurence was suggested by the phase diagram of BOYD and ENGLAND ( 1962). This aluminous enstatite was similar to that observed by OHTANI et al. ( 198 1) for samples quenched at high pressures from pyrope melt, and the transformation was found complete after a 30 min heating of the pyrope sample at 1200°C. A second series of experiments (BY) with a new sample was thus made to complement the results of series BX. Our relative enthalpies are also compared in Fig. 1 to mean heat capacities calculated from the C, equations of NEWTON et al. ( 1977b) and WATANABE( 1982). Our results agree with the values given by the DSC C, equations in the temperature interval where these data overlap. All these data are consistent with the adiabatic measurements of HASELTON and WESTRUM ( 1980) near and above room temperature. The consistency between our results and those derived for pure pyrope by KISELEVA et al. (1972) from measurements on a natural garnet with 18 mol% grossular is not as good, but the 2-3% difference is nevertheless within the errors of their transposed drop-calorimetry measurements. To derive the high-temperature heat capacity of pyrope, fits were made simultaneously to the C, and H7. - H, measurements, with enthalpy data in the form

s

C, = 872.988 - 137.44 10-3T f 0.045 105/T2 - 8794.3/T0.5

+ 33.408 10-6T2,

(2)

whereas the equation of the form recommended by BERMAN (1988) was C, = 548.046 - 1220.75/TQ.5 - 24.424 106/T2 + 32.552 108/T3.

(3)

Finally, RICHET and FIQUET ( 199 1) have proposed another form of the C, equation to ensure an accurate representation of experimental data as well as built-in reliable high-temperature extrapolations. For pyrope, our preferred C, equation is thus + 138.003 In TS

C, = -592.635

191.204 103/T

- 72.066 106/T2 + 79.749 108/T3.

(4)

The average absolute deviations of the experimental data from the fitted values given by Eqn. (4) are 0.10% for the adiabatic C, values of HAsELToN and WESTRUM ( 1980) above 275 K and 0.08% for the enthalpies of Table 2. A comparison with the DSC data is less straightforward since only fitted results have been reported by NEWTON et al. ( 1977b), between 350 and 1000 K, and WATANABE ( 1982), between 350 and 650

7

HT-

With the so-called C,, we obtained

HAAS

H,=

C,dT. TO

and

FISHER

(

(1) 1976) equation for

450 -

,/ 2” /= 1.’

430 -

/,a

,.// Table 2. Relative enthalpy of Pympe

HT-Hn Run BY.9 BY.6 BY.4 BY.8 BY.1 BX.1 BY.3 BX.5 BY.7 BX.3 BY.10 BX.6

T(K) 823.3 883.1 931.7 974.4 1020.2 1088.1 1119.6 1188.6 1200.1 1288.3 1339.5 1393.9

kJ/mol

Jk 573.55 644.06 700.64 752.32 808.20 891.90 928.58 1012.2 1028.1 1138.4 1204.2 1276.9

a Result not used in C, decomposition effects

/? I...’ C.’ 4”

410,d

23 1.72 260.17 283.04 303.93 326.56 360.34 375.20 409.78 415.01 459.94 486.68 516.02a fits

because

/ 390 600

900

1200

1500

T (K)

FIG. I. Mean heat capacity of crystalline pyrope. Squares: data from Table 1;solid curve: values calculated with Eqn. (4). The dashed and dotted curves are values calculated from the CD equations of of

NEWTON et al. ( 1977b) and WATANABE ( 1982). respectively, with H350-Hz73 as given by HASELTON and WESTRUM ( 1980).

Physical chemistry of pyrope

1007

Table 3. Experimental low-temperature heat capacities of quenchedMg3A12Si3012 glass (J/mol K)

Series3 44.48 26.19 49.60 33.28 55.25 41.13 61.15 49.68

Series 1

301.63 305.78 310.27 314.76 319.22 323.69 328.15 332.61 337.67 343.40 349.18

330.1 331.9 335.6 338.3 242.1 345.4 348.7 351.2 353.7 356.9 360.6

Series2 354.88 364.0 360.30 366.7 365.41 369.9 Series3 8.86 0.1150 10.11 0.2405 11.09 0.3780 12.25 0.5638 13.69 0.8577 15.23 1.288 16.95 1.867 18.84 2.638 20.95 3.664 23.30 5.049 25.91 6.839 28.85 9.168 32.13 12.23 35.80 16.11 39.91 21.00

T WI FIG. 2. C, difference between Mg,A12SiXO12 glass (Table 4) and pyrope ( HASELTONand WESTRUM, 1980).

K. Calculated at 50 K intervals with the reported equations, these fitted heat capacities deviate by 1.39% for the former dataset and by 0.79% for the latter. As shown in Fig. 3, heat capacities given by Eqn. (4) agree remarkably with the values used by HASELTON and NEWTON ( 1980), and are somewhat lower than those proposed more recently by BERMAN ( 1988). On the other hand, extrapolation of our results with Eqn. (3) appears to significantly underestimate the temperature dependence of C, above the interval of the measurements. Finally, it is well known that an expression of the form of Eqn. (2) extrapolates poorly at high temperatures. This is also shown in Fig. 3 where the values given by the equations of NEWTON et al. ( 1977b) and WATANABE ( 1982) are plotted for temperatures in excess of the intervals

Series4 177.46 215.3 181.83 220.3 186.19 225.9 190.55 230.9 194.91 235.5 199.28 240.1 203.64 244.8 208.01 249.9 212.41 254.1 216.83 258.6 221.28 263.1 225.80 267.5 230.40 271.7 235.08 275.9 239.86 280.2 244.70 284.6 249.62 288.5 254.58 292.5 259.56 297.1 264.61 301.5 269.70 305.6

Series4 58.14 45.32 63.15 52.68 67.59 59.31 72.44 66.66 77.89 74.90 83.14 82.98 88.43 91.11 93.72 99.28 98.88 107.3 103.95 115.2 108.92 122.6 113.82 129.9 118.64 137.1 123.39 144.0 128.09 150.8 132.74 157.3 137.34 163.8 141.91 170.1 146.44 176.3 150.94 182.5 155.41 188.3 159.86 193.7 164.28 199.3 168.69 204.6 173.08 210.0

Series 5

274.66 279.70 284.58 289.48 294.34 299.20 304.07 308.91 313.74 318.56

309.9 313.4 317.2 321.6 325.0 330.1 331.9 334.2 337.5 341.9

investigated. To ensure correct high-temperature extrapolations with this widely used form of equation, the heat capacity of pyrope as given by Eqn. (4) for T = 1700 and 2000 K had to be included in the data base to obtain the coefficients reported for Eqn. (2). Glass

The low-temperature CDof pyrope glass (Table 3) shows the usual sigmoid variation with temperature. The thermodynamic functions reported in Table 4 were derived from the listed C, values obtained from the data of Table 3 with an interpolating spline. The absolute differences between the low-temperature heat capacities of the glass and crystalline forms plotted in Fig. 2 show a maximum around 80 K, whereas the relative difference continuously decreases from 10 K. These variations are typical of the coordination effects first observed by KELLEY et al. ( 1953), whereby phases with VI-fold

coordinated

aluminum

have a lower heat capacity

than the phases made up of AlO

tetrahedra,

as is likely the

case of Mg3A12Si3012 glass. Below 400 K, the DSC results given in Table 5 are about 800

1600

1200

0.8% higher than the adiabatic 2000

T WI FIG.

3. Heat capacity of pyrope. Solid curve: values given by our

recommended Eqn. (4); dashed curve: C, as given by Eqn. (3); open and solid squares: values obtained from the equations of HASELTON

and NEWTON( 1980) and BERMAN( 1988), respectively; open and solid triangles: extrapolations of the equations of NEWTON et al. ( 197713)and WATANABE( 1982), respectively, outside the temperature range of the DSC measurements.

results. On the average, these

results are also 0.8% higher than the values derived from the drop-calorimetry

data of RICHET and BOTTINGA ( 1984), but

in both cases the disagreement limits of the techniques.

is within the respective

Even though the precision

data gets lower when approaching in C, apparent

above

the glass transition

error

of DSC

1000 K, the rapid increase

930 K likely shows the beginning

(Fig. 3) whose completion

peratures leads to a value of 660 J/mol

of

at higher tem-

K for the heat capacity

of the liquid. This increase is thus consistent

with the obser-

C. Ttqui et al.

1008

Table 4. Smoothed low-temperature thermodynamic properties of quenched Pyrope glass (J/m01 K)

:: 40 45 50 60 70 80 90 100

0.013 0.230 1.225 3.180 6.183 10.19 15.24 21.10 27.38 33.89 48.01 62.93 78.16 93.56 109.0

0.004 0.049 0.299 0.895 1.908 3.374 5.311 7.722 10.57 13.79 21.19 29.7 1 39.10 49.20 59.86

0.003 0.039 0.242 0.711 1.487 2.589 4.024 5.785 7.834 10.11 15.23 20.98 27.17 33.69 40.45

0.001 0.010 0.057 0.184 0.420 0.784 1.287 1.936 2.734 3.675 5.961 8.734 11.93 15.51 19.41

110 120 130 140 150 160 170 180 190 200

124.2 139.1 153.5 167.5 181.1 194.0 206.3 218.4 230.0 241.1

70.96 82.41 94.12 106.0 118.0 130.1 142.3 154.4 166.5 178.6

47.38 54.40 61.47 68.55 75.60 82.60 89.52 96.34 103.1 109.7

23.59 28.01 32.64 37.46 42.43 47.53 52.75 58.06 63.45 68.90

210 220 230 240 250 260 270 280 290 300

251.7 261.8 271.3 280.3 289.1 291.6 305.9 313.7 320.9 327.6

190.6 202.6 214.4 226.2 237.8 249.3 260.7 271.9 283.1 294.1

116.2 122.6 128.9 135.0 141.0 146.8 152.6 158.2 163.7 169.0

74.41 79.97 85.55 91.17 96.80 102.4 108.1 113.7 119.4 125.0

273.15 298.15

308.4 326.4

264.2 292.0

154.4 168.0

109.9 124.0

5

10 :; 25

temperature and the rapid crystallization of the supercooled liquid above the glass transition, measurements could be made only between 1083 and 1226 K and between 1844 and 1863 K. A constant C, of 682.2 J/mol K was derived from the data for these narrow temperature intervals. Subsequent measurements on wider temperature intervals for two other compositions have shown that C, varies linearly with composition along the join Si02-Mg3A12Si3012 ( COURTIAL et al., 1990), with a slight linear temperature dependence for the C, of Al-bearing compositions. For the sake of consistency with the other data for this join, the following equation for liquid pyrope has been obtained from the original data of RICHET and BOTTINGA (1984) between 1083 and 1863 K: C, (J/mol HT

-

HT~

= -338,979

+ 63O.OOT + 17.5 10m3T2.

This enthalpy equation reproduces the experimental an average absolute deviation of 0.10%. IV. ENTROPY

(7b)

data with

AND MELTING PROPERTIES

Matching Properties The enthalpy of fusion ( AHI) of pyrope can be calculated from the enthalpy

of vitrification,

determined

by solution

Table 5. DSC C, measurements for quenched Mg3AlzSi3Ole glass (J/mol K) C,

Series 1

of the glass transition at about 1070 K in drop-calorimetry experiments ( RICHET and BOTTINGA, 1984). As usual for silicate glasses, the onset of the glass transition corresponds to the temperature range where the heat capacity of the glass approaches the Dulong and Petit harmonic limit (Fig. 4). These DSC data can also be compared to hightemperature heat capacities calculated with the empirical model of RICHET ( 1987). With an average absolute deviation of 0.54% from the experimental data, the model values are within their stated + 1% accuracy. The available adiabatic, DSC, and drop-calorimetry data do not warrant an equation of the form of Eqn. (4) since they do not need to be extrapolated at higher temperatures. With an equation of the form proposed by HAAS and FISHER ( 1976), we obtained vation

c, = 513.773 + 71.191 10-37. (5)

The average absolute deviations of the experimental results from the fitted values are 0.2 1% for the data of Table 1 above 274 K, 0.78% for those of Table 3, and 0.12% for the data of RICHET and BOTTINGA ( 1984) between 874 and 1056 K. Liquid The relative enthalpy of liquid pyrope was measured by and BOTTINGA ( 1984). Owing to the high liquidus

RICHET

(7a)

(J/mol)

T(K)

- 58.566 105/T2- 2439.0/T”-5.

K) = 630.00 + 3.5 10e3T,

339.7 349.5 359.4 369.2 379.1 388.9 398.8 408.6 418.5 428.4 438.3 448.3 458.2 468.2 478.1 488.0 497.0

353.3 358.0 363.2 367.8 372.7 377.4 382.3 385.9 390.6 194.2 397.7 400.9 404.2 408.1 412.7 415.8 419.3

Series 2 410.7 468.2 478.1 414.2 488.0 416.5 498.0 420.0 507.9 422.7 517.9 425.6 527.8 428.4 537.8 430.6 547.7 433.1 557.6 435.0 567.6 437.0 577.5 439.5 587.5 442.6 597.4 444.1 607.4 447.9 617.3 450.0 627.2 452.7 637.2 455.8 646.1 458.4

‘f(K)

C,

Series 3 617.3 450.3 627.2 452.8 631.2 454.5 647.1 456.4 657.1 458.8 667.0 459.6 677.0 462.8 686.9 464.8 696.8 465.2 706.8 467.4 716.7 468.8 726.7 470.2 736.6 471.8 745.6 471.3 Series 4 746.4 47 1.O 756.3 472.9 766.3 415.4 776.2 412.9 786.2 476.7 796.1 479.8 806.0 481.2 816.0 483.9 825.9 484.3 835.9 486.7 844.8 484.1 Series 5 835.9 486.5 845.7 486.2 855.4 489.2 865.1 488.7 874.8 488.0 884.5 488.9 893.2 489.4 Series 6 884.5 486.1 894.2 485.5 903.9 487.6

T(K)

C,

Series 6 913.6 490.9 923.3 491.6 933.0 495.9 941.7 496.5 Series 7 933.0 497.6 942.7 495.2 952.3 494.9 962.0 499.4 971.7 503.9 981.4 504.6 990.0 510.7 Series 8 933.0 497.6 942.7 497.3 952.3 499.1 962.0 501.1 971.7 504.7 981.4 506.8 990.0 510.5 Series 9 339.7 353.2 349.5 358.4 359.4 363.3 369.2 368.1 379.1 372.7 388.9 377.6 398.8 381.7 408.6 386.4 418.5 390.9 428.4 394.1 438.3 398.8 448.3 402.8 458.2 406.2 468.1 410.4 478.1 413.8 48X.0 417.8 497.0 421.4

1009

Physical chemistry of pyrope Table 6. Entropy of Mg3AlzSi3012 forms T (K) crystal crystal Liquid Liquid Glass Glass

S (J/m01K)

298 266.21 + 0.P 1570 1006.6+ 4.P 1570 1160.7+ 12~ 1020d 869.7 f 12b 346.3 I! 12b 298 54.3 + 13e 0

a HASELTONand WESTRUM (1980) b From the coefficients of eqn (4) c From the entropy of fusion of 154.1 J/mole K d Assumed fictive temperature of the glass sample investigated in solution calorimeay (YODER,1975) e From the data of Table4

.

400’ 500

’

600

I

.

700

’

’ ’ .

900

800

’

1000 Configurational Entropy

T (K) FIG. 4. High-temperature DSC data for MgjAlzSixOlz glass. The different symbols correspond to the different seriesindicated in Table 3. The dashed line is the Dulong and Petit limit for C,.

calorimetry on the crystal and glass forms, corrected to the melting point with the relevant relative-enthalpy data for the crystal, glass, and liquid. Pyrope melts congruently only above 40 kbar (DAVIS, 1964), and in this report we have used the 1-bar metastable congruent melting point derived by RICHET ( 1988) from Clausius-Clapeyron arguments, namely Tf = 1570 + 30 K. With this melting point and the C, Eqn. (4), one obtains AHH,= 241.9 & 12 kJ/mol from the enthalpy of vitrification of 147.9 kJ/mol at 975 K (YODER, 1975). To get this figure we have assumed a fictive temperature of 1020 K for the glass used in solution calorimetry and included the correction of +9 kJ/mol applied by NEWTON et al. (1977a) to the original enthalpy of solution of the crystal ( CHARLU et al., 1975). This enthalpy of fusion is slightly lower than the AH, = 243.1 + 8 kJ/mol obtained by RICHET and BOTTINGA ( 1984) with a 1-bar melting point of 1500 K obtained from extrapolations of the high-pressure melting curve and of the C, equation of the crystal. The difference is greater for the entropy of fusion which, at 154.1 + 7.6 J/mol K, is 8 kJ/mol lower than the previous result. 1400,

I

1200 I 1000

LiquY

I

-

y^ 5

800

E 3

600

; 400 Sconf

200

_---

--__-_/

0

400

800

1200

_----

1600

2000

T WI FIG. 5. Absolute entropy of pyrope and Mg,Al&O12 glass and liquid (solid curves) and configurational entropy of amorphous Mg,AlzSi30,2 (dashed curve) as a function of temperature.

The residual entropy of the glass at 0 K is the configurational entropy ( Sconf ) frozen in at the glass transition (e.g., RICHET et al., 1986). This important datum can be determined from an entropy cycle beginning with the crystalline phase at 0 K, going up to the melting point at 1570 K, and then coming down to 0 K through the supercooled liquid and glass phases (Fig. 5 ). In Table 6 the entropies of the crystal, liquid, and glass forms are listed for the relevant temperatures. The final result is a residual entropy of 54.3 + 13 J/mol K for a glass with a fictive temperature of 1020 K (i.e., the assumed fictive temperature of the glass investigated in solution calorimetry). With the usual assumption (e.g., RICHET et al., 1986), G”+(T)

= C,/(T) - C,,(T,),

(8)

the configurational entropy can be calculated at any temperature (Fig. 5). At 1035 K, for example, Sconfis 56.3 f 13 J/mol K. Within its large experimental errors this result agrees with the value 61.5 + 3 J/mol K which has been derived at this temperature from the viscosity of liquid Mg3A12Si3012 ( NEUVILLE and RICHET, 199 1). Such an agreement has been observed previously for feldspar and pyroxene compositions ( RICHET et al., 1986; NEUVILLE and RICHET, 199 1). But the example of pyrope clearly illustrates the better accuracy of the result obtained from the viscosity data over that of the calorimetric determination, which is a small difference between two large numbers. In this respect, the enthalpy of vitrification contributes most heavily to the errors of the enthalpy of fusion and configuration entropy. In addition, samples as well as the low-temperature calorimetric apparatus were different for the crystal and glass used in this study and in that of HASELTON and WESTRUM ( 1980). The consequence is that systematic entropy errors do not cancel out a priori in the calculation of the residual entropy. HASELTON and WESTRUM ( 1980) noted that their synthetic pyrope has a higher room-temperature entropy than grossular under the same conditions. The expected trend is that Ca-bearing phases have higher heat capacities than their magnesian counterparts as a result of the lower vibrational frequencies associated with the higher mass of Ca relative to Mg. This was observed only for T > 200 K, and the higher roomtemperature entropy of pyrope was attributed by HASELTON and WESTRUM ( 1980) to the unusually large coordination

C. Ttqui et al.

1010

of Mg in garnets. The consistency between the rheological and calorimetric residual entropies of Mg3AlzSi301z glass could be seen as an independent evidence in favour of this argument. But this evidence is rather weak in view of the aforementioned uncertainties of the calorimetric entropies. Acknowledgments-We thank C. Chopin for donating the natural pyrope; H. RCmy for the electron-microprobe analyses; M. C. Sichere and L. Mamou for their help with our X-ray diffraction work; C. Geiger for his refinement of the lattice parameter of pyrope; and H. T. Haselton, B. 0. Mysen, and M. P. Ryan for helpful comments on the manuscript. Contribution CNRS-INSU-DBT 205. Editorial handling: B. J. Wood REFERENCES BERMANR. G. ( 1988) Internally consistent thermodynamic

data for minerals in the system Na~0-K20-Ca0-Mg0-Fe0-Fe203-A1203Si02-Ti02-H20-C02. J. Petrol. 29, 445-522. BOYDF. R. and ENGLANDJ. L. ( 1962) Mantle minerals. Carnegie Inst. Washington Yrbk. 61, 107-l 12. CHARLU T. V., NEWTONR. C., and KLEPPA 0. J. (1975) Thermochemistry of high-pressure garnets and clinopyroxenes in the system CaO-MgO-A1,03-Si02 from high-temperature solution calorimetry. Geochim. Cosmochim. Acta 39, 1487-1497. CHOPINC. ( 1984) Coesite and pure pyrope in high-grade blueschists of the Western Alps: a first record and some consequences. Contrib. Mineral. Petrol. 86, 107-I 18. COURTIALP., NEUVILLED. R., T~QLJIC., and RICHET P. (1990) Heat capacity of liquids in the systems CaO-A&O,-Si02 and MgOA120j-Si02. Terra Abstr. 2, 5. DAVIS,B. T. C. ( 1964) The system diopside-forsterite-pyrope at 40 kbars. Carnegie Inst. Washington Yrbk. 63, 165- 17 1. GEIGERC. A., KRAUSEC., Ross C. R., JR., AMTHAUERG., and LANGERK. ( 1989) Characterization of almandine, pyrope, pyropealmandine and pyrope-grossular solid solutions. Terra Abstr. 1, 290. HAAS J. L., JR. and FISHERJ. R. (1976) Simultaneous evaluation and correlation of thermodynamic data. Amer. J. Sci. 276, 525545. HASELTONH. T. and NEWTONR. C. (1980) Thermodynamics of pyrope-grossular garnets and their stabilities at high temperatures and high pressures. J. Geophys. Rex 85, 6976-6982. HASELTONH. T. and WESTRUME. F. ( 1980) Low-temperature heat capacities of synthetic pyrope, grossular, and pyropeeOgrossulaao. Geochim. Cosmochim. Acta 44,701-709. HEMINGWAY B. S., ROBIER. A., KITTRICKJ. A., GREWE. S., NELEN J. A., and LONEON D. ( 1984) The heat capacities of osumilite from 298.15 to 1000 K, the thermodynamic properties of two natural chlorites to 500 K, and the thermodynamic properties of petalite to 1800 K. Amer. Mineral. 69, 701-710.

KELLEYK. K., TODDS. S., ORR L. R., KING E. G., and BONNICKSON

K. R. ( 1953) Thermodynamic properties of sodium-aluminum and potassium-aluminum silicates. C;SEur. Mine.yRept. Inv., 4955. KISELEVAI. A., TOP~R N. D., and MEL’CHAKOVAL. V. (1972) Experimental determination of heat content and heat capacity of gr&sularite, andradite and pyrope. Geokhimiya, 1372- 1379. KRUPKA K. M.. ROBIER. A.. and HEMINGWAYB. S. (1979) Hightemperature heat capacities of corundum, periclase, an&thite, CaA12Si208glass, muscovite, pyrophilite, KAlSi308 glass, grossular. and NaAISijOs glass. Amer. Mineral. 64, 86- 101. NEUVILLED. R. and RICHET P. ( 199 1) Viscosity and mixing in molten (Ca, Mg) pyroxenes and garnets. Geochim. Cosmochim Acta 55, 101 l-1019 (this issue). NEWTONR. C., CHARLLJT. V., and KLEPPA 0. J. (1977a) Thermochemistry of high-pressure garnets and clinopyroxenes in the system CaO-MgO-A1203-Si02. Geochim. Cosmochim. Acta 41, 369-377. NEWTONR. C., THOMPSONA. B., and KRUPKA K. M. ( 1977b) Heat capacity of synthetic Mg,A1$i30,2 from 350 to 1000 K and the entropy of pyrope. Eos 58, 523. OHTANIE., IRIFUNET., and FUJINOK. ( 198 I ) Fusion of pyrope at high pressures and rapid crystal growth from the pyrope melt. Nature 294, 62-64. RICHETP. ( 1987) Heat capacity of silicate glasses. Chem. Geol. 62, 111-124. RICHET P. ( 1988) Superheating, melting and vitrification through decompression of high-pressure minerals. Nature 331, 56-58. RICHETP. and BOTTINGAY. ( 1984) Anorthite, andesine, diopside. wollastonite, cordierite and pyrope: thermodynamics of melting, glass transitions, and properties of the amorphous phases. Earth Planet. Sci. Lett. 67, 4 15-432. RICHETP. and FIQUETG. ( 199 I ) High-temperature heat capacity and premelting of minerals in the system CaO-MgO-A120,-SiO?. J. Ge0phv.r. Rex 96, 445-456. RICHETP., BOTTINGAY., DEN&LOUL., PETITETJ. P.. and TBQUI C. ( 1982 ) Thermodynamic properties of quartz, cristobalite and amorphous SiOz: drop calorimetry measurements between 1000 and 1800 K and a review from 0 to 2000 K. Geochim. Cosmochim. Acta 46,2639-2658. RICHETP.. ROBIER. A., and HEMINGWAYB. S. (1986) Low-temperature heat capacity ofdiopside glass ( CaMgSi,06): a calorimetric test of the configurational entropy theory applied to the viscosity of liquid silicates. Geochim. Cosmochim. Acta 50, 152 I- 1533. ROBIER. A. and HEMINGWAYB. S. ( 1972) Calorimeters for heat of solution and low-temperature heat capacity measurements. US Geol. Surv. Prof: Paper, 755. YODERH. S., JR. ( 1975) Heat of melting of simple systems related to basalts and eclogites. Carnegie Inst. Washington Yrbk. 74,5 15519. WATANABEH. ( 1982) Thermochemical properties of synthetic highpressure compounds relevant to the Earth’s mantle. In High-Pressure Research in Geophysics (eds. S. AKIMOTO and M. H. MANGHNANI),pp. 441-464. D. Reidel.