American Mineralogist, Volume 69, pages 298-306, 1984

Entropies of kyanite, andalusite, and sillimanite: additional constraints on the pressureand temperature of the Al2SiOs triple point

Rrcneno A. Rosrp eNo Bnuce S. HrurNcwey

U.S. Geological Survey959 National Center, Reston, Virginia 22092

Abstract

The low-temperature heat capacities of kyanite (Minas Gerais, Brazil), andalusite(Espirito Santo, Brazil), and sillimanite (Reinbolt Hills, Antarctica) were measured with anautomatic, adiabatically shielded calorimeter between approximately l0 and 380 K. At29E.15 K the entropies are E2.30-r0.13, 91.39-+0.14, and 95.79-ro.l4 J/(mol .K) forkyanite, andalusite, and sillimanite, respectively. our values are 1.8, 2.0 and0.4vo smallerthan those of Todd (1950). Our calculated slope for the andalusite-sillimanite phaseboundary is in significantly better agreement with the phase boundaries of Holdaway(1971), than with those of Richardson, Gilbert and Bell (1969) and strongly suggest that Aland Si are ordered in sillimanite to at least ll00 K.

The thermal Debye temperatures, d$, calculated from our heat capacity data in the range? < 18 K are 1lfi), E55, and 730 K for kyanite, andalusite, and sillimanite respectively. Forandalusite and sillimanite our values for Ofi are in moderate agreement with thosecalculated from the room temperature adiabatic elastic stifness constants ofVaughan andWeidner (1978), 838 and 800 K, respectively.

Introduction

The usefulness of a mineral system in the interpretationof geologic processes is dependent upon its geologicdistribution and upon the confidence that we place in ourknowledge ofthe physical and chemical properties ofthatsystem. The Al2SiO5 polymorphs, kyanite, andalusite,and sillimanite, commonly occur in metamorphosed peli-tic sediments, and because of the relatively simple chem-istry of the mineral systemo the Al2SiO5 polymorphsdefine one of the most important fixed (invariant) pointsfor establishing a quantitative petrogenetic grid for meta-morphic petrology. However, because the Gibbs freeenergies of the three Al2SiOs polymorphs difer by solittle and because of kinetic problems in some areas of theexperimental studies of this sytem, the location of theunivariant reaction boundaries and of the invariant (tri-ple) point are not known with the certainty necessary tomake this mineral system a fully effective tool for thepetrologist.

Most petrologists accept either the phase diagram ofHoldaway (1971) or that ofRichardson et al. (1969); a fewcite the work of Althaus (1967) or Brown and Fyfe (lg7l).Zen (1969) and Holdaway (1971) have summarized, theearly work on the stability of the Al2SiO5 polymorphs andhave provided extensive analyses of the experimentalstudies, citing the known and potential sources for error.Relatively few studies have been published since Zen'sreview (e.g., Holdaway, l97l Anderson et aI. 1977:

Winter and Ghose, 1979; and Schneider, 1979;Day andKumin, 1980).

The phase diagrams of the Al2SiO5 system given byHoldaway (1971), Richardson et al. (1969), Althaus(1967), and Brown and Fyfe (1971) differ in the location ofthe triple point and in the slopes of the univariant reactionboundaries. The univariant reaction boundaries deter-mined from phase-equilibria experiments also difer fromthe slopes predicted from the calorimetrically derivedthermochemical data provided from the low-temperatureheat-capacity measurements of Todd (1950), the heat-content measurements of Pankratz and Kelley (1964) andthe enthalpy of solution results of Anderson and Kleppa(1969), Navrotsky et al. (1973) and Anderson etal. (1971.).Several authors (e.g., Zen, 1969; Holdaway, l97l; andAnderson, Newton, and Kleppa, 1977) have proposedthat one or more of the Al2SiO5 polymorphs is partiallydisordered in aluminum and silicon in order to producegeneral agreement between the calorimetric data and thephase-equilibria data.

The univariant reaction boundaries located by phase-equilibria studies are, in general, based upon only a fewexperimental phase-reversal brackets through whichmany reaction curyes of varying slopes could be con-structed. The reaction boundaries selected in the variousstudies represent the workers' best estimates of thelocations and slopes of the reaction boundaries; however,the choices are not unique.

A combination of (1) the calorimetrically determined0003--fi x)o84l03 g__029E$02. 00 29'3

entropies (Si - S3, where S$ is the zero-point entropy),(2) entropy estimates for various models of order-disor-der in Al-Si, and (3) data for the molar volumes (as afunction of temperature and pressure) of the AlzSiOspolymorphs can provide estimates of the slopes of theunivariant reaction boundaries (dPldT : AS/AI4 thathave greater precision than those derived solely fromphase-reversal brackets. However, the calorimetricallyderived entropies at 298.15 K for the Al2SiO5 polymorphsthat are available in the literature are based upon heatcapacity measurements that cover only the range oftemperatures from 54.4 to 296.5 K (Todd, 1950) andtherefore they have a much larger uncertainty than thoseavailable from modern measurements extending down to5 K. Also, the molar volume data available in the litera-ture are not consistent (e.g., Skinner et al., 1961, andWinter and Ghose, 1979) and consequently increase theuncertainty with which the univariant reaction bound-aries may be determined.

We have measured the heat capacities of andalusite,kyanite, and sillimanite between about 6 and 375 K inorder to reduce the uncertainty in the calorimetricallydetermined entropy (Si - S3). We have combined ourresults with the heat-content data of Pankratz and Kelley(1964), have calculated heat capacity functions withwhich we may improve the estimates of the slopes of theunivariant reactions, and have compared these resultswith phase-equilibria data in order to evaluate the contri-bution of order-disorder in AVSi and to further restrictthe location of the triple point in the Al2SiO5 mineralsystem.

Materials and sample preparation

Kyanite. The kyanite used for our heat capacity studieswas obtained from Ward's Natural Science Establish-ment (Ward's) and came from Minas Gerais, Brazil. Thepolycrystalline aggregate contained coarse light blue tocolorless crystals as much as 2 cm long with a heavybrown (limonite?) stain. The sample was crushed in analumina mortar and the -10 +20 mesh fraction (-2.0+0.8 mm) was retained. The material was boiled in a60/40 HF ' HCI solution for t hour, rinsed several timeswith distilled water, dried at 130oC, and then handpickedfree of any remaining impurity phases trnder a binocularmicroscope. The final sample consisted of transparentneedle-shaped crystals, some bent, and ranged fromcolorless to light blue. The sample was analyzed byatomic absorption and by inductively coupled argonplasma (Icer) spectroscopy for Fe, Cr, and Mn. Theanalysis gave Fe2O3 : 0.18+0.05 wt.%o, Cr 90 ppm, andMn <5 ppm. The sample weight for our calorimetricstudies was 42.328 g corrected for bouyancy.

Andalusite. Andalusite was also purchased fromWard's. The source was listed as Santa Theresa, EspiritoSanto, Brazil. The material was in the form of water-rounded, transparent single crystals 0.5 to I cm in diame-

299

ter and were either bottle green or pink. The individualcrystals were examined under a binocular microscope,and those crystals showing rutile or other inclusions werediscarded. Analysis by atomic absorption and ICAP gaveFe2O3 : 0.36i0.05 wt.Vo, andless than 5 ppm for Cr andMn. The sample weight corrected for buoyancy was44.59E g.

Sillimanite. The sillimanite sample was separated froma pegmatite lens in a granulite-facies rock from theReinbolt Hills, Antarctica (Sample number 556, alsoSmithsonian NMNH #137011, Grew, 1980). The sourcematerial was first crushed to -20 mesh (0.83 mm), soakedfor 14 hours in 40 percent HF(aq), and the larger grains ofsillimanite were picked free. The remaining material wascrushed to -48 mesh (0.29 mm), passed thru tetrabro-moethane to remove feldspars and quartz, passed severaltimes thru a Franzl magnetic separator to remove ilmen-ite. sieved to remove material smaller than 0.10 mm (150mesh), boiled in 25% HF(aq) for 3 hours, and finallyhandpicked under a binocular microscope. Grew (1980)reported a range of 0.76 to 1.30 wt.%o Fe2O3 for variousgrains of sillimanite from sample 556 with an average of1.23. A complete analysis of sample 556 is given by Grew(1e80).

Apparatus and experimental results

The heat capacity measurements were made by meansof the calorimeter and cryostat described by Robie andHemingway (1972), Robie, Hemingway, and Wilson(1976). Our experimental results are listed in their chrono-logical order of measurement in Tables 1 through 3 forkyanite, andalusite and sillimanite respectively. Figure Ishows values for kyanite, and Figure 2 shows the difier-ences C!,(andalusite) - Ci(kyanite), and Cf,(sillimanite)- CiGyanite). Our experimental measurements below 30K were plotted as CtT versus ?2 and extrapolatedsmoothly to 0 K. Figure 3 gives examples for kyanite andandalusite. The heat capacities measured between 20 and-385 K were smoothed by computer, using the smooth-ing spline procedure described by Robie, Finch, andHemingway (1932). The two data sets were joined

smoothly and used to produce tables of the thermody-namic properties (Tables 4, 5, and 6). No correctionswere made to our data for deviation from the exactcomposition AlzSiOs. Over the range of temperaturescommon to our results and those ofTodd (1950), 5l to 298K, our values for Sisa - S3r agree within 1.3% forkyanite, 0.9Vofor andalusite, and0.2Vo for sillimanite. At298.15 K, the entropies of kyanite, andalusite, and silli-manite are 83.20=0.13. 91.39-f0.14, and 95.79!0.14J/(mol' K), respectively. The correction for FezOr foreach phase would be less than 0.17o.

I Any use of trade names in this report is for descriptivepurposes only and does not constitute endorsement by the U.S.Geological Survey.

ROBIE AND HEMINGWAY: KYANITE, ANDALUSITE' SILLIMANITE

300 ROBIE AND HEMINGWAY: KYANITE, ANDALUSITE, SILLIMANITE

rerP. " . : : : i . ,

reop. . . l i l i . ,K J / ( e o l ' K ) K J / ( n o l ' K )

Table l. Experimental molar heat capacities of kyanite fromMinas Gerais. Brazil

The agreement between the thermal and the elastic valuesfor the Debye temperature is excellent (within 2%) forandalusite but is less satisfactory for sillimanite. This isprobably due to the greater amount of iron in solidsolution in the sillimanite as compared with the andalusitesample, which would lead to a larger specific heat at lowtemperatures, as compared with pure Al2SiO5, and thusto a smaller value of Ofi. Our values for the Debyetemperatures ditrer significantly from those given byKieffer (1982). Her values were calculated from estimatedmean sound velocities.

Molar volumes of Al2SiO5 polymorphs

In Table 7, we have summarized the available unit-cellparameters and molar volume data at 25'C for sillimanitefrom Brandywine Springs, Delaware, for andalusite fromMinas Gerais, Brazil, and for kyanite from Burnsville,North Carolina. These materials are the most widelystudied and demonstrate only too well the differencebetween precision and accuracy in X-ray unit-cell data.For each of these materials, the single-crystal cell para-meters of Winter and Ghose (1979) are significantly largerthan are the other values. which have been obtainedprimarily from power diffractometry using an internalstandard. It is tempting to conclude that the difference inthe cell parameters is related to determination proce-dures, i.e., single-crystal or powder techniques. However

Table 2. Experimental molar heat capacities of andalusite fromSanta Theresa, Espirito Santo, Brazil

reDP. . ,1 : : i . , re rp .

K J / ( ! o l ' K ) K

f , e a t - E e a tc a p a c l t t r e ! P '

c a p a c l E y

J / ( r o l ' K ) K J , / ( ! o 1 . K )

reop . " , f i l i . ,

K J / ( D o l ' K )

S e r l e s I

3 0 4 . 2 8 r 2 4 . 23 0 E . 8 9 1 2 5 . 53 r 3 . 8 8 t 2 7 . r3 1 8 . 9 0 t 2 4 . 73 2 4 . r 7 1 3 0 . 33 2 9 . 4 5 r 3 1 . 83 3 4 . 7 r r 3 3 . 53 3 9 . 9 7 1 3 4 . 91 4 5 . 2 1 1 3 6 . 6

S e r L e s 2

3 5 0 . 3 3 r 3 7 . 63 5 5 . 5 2 r 3 8 . 93 5 0 . 4 8 r 4 0 . 13 6 5 . 4 6 1 4 1 . 33 t 0 . 6 3 t 4 2 . 5

S e r l e a 3

5 2 . 1 6 3 . 5 7 96 5 . 4 1 7 . 4 6 47 3 . 6 5 t O . 7 78 0 . 4 9 1 3 . 8 58 7 . 0 3 1 6 . 9 99 3 . 3 8 2 0 . 1 69 9 . 5 4 2 3 . 4 2

r 0 5 . 6 3 2 6 . A Or r 1 . 6 5 3 0 . 3 0L L 7 . 6 4 3 3 . 8 2r 2 3 . 6 0 3 7 . 2 7L 2 9 . 5 2 4 0 . 8 6r 3 5 . 4 2 4 4 . 4 4r 4 l . 3 l 4 1 . 8 91 4 7 . 1 7 5 r . 3 3r 5 3 . 0 r s 4 . 8 3r 5 8 . 8 3 5 8 . 2 01 6 4 . 6 4 6 r . 6 0

S e r L e s 4

1 5 9 . 1 6 5 8 . 4 61 6 4 . 8 3 6 r . 8 01 7 0 . 0 8 6 4 . 8 1r 7 5 . 4 2 6 7 . 8 11 8 1 . 0 9 7 0 . 9 8r a 6 . 7 4 7 1 . 9 7r 9 2 . 3 8 7 7 . 0 01 9 8 . 0 2 7 9 . 9 52 0 3 . 6 6 8 2 . 8 92 0 9 . 2 4 A 5 . 7 22 r 4 . 9 0 8 8 . 4 82 2 0 , 5 0 9 1 . 0 7

S e r l e 6 5

2 2 5 . 7 6 9 3 . 5 22 3 0 . 9 5 9 5 . 8 62 3 6 . 0 8 9 8 . 2 92 4 L . 2 7 r 0 0 . 52 4 6 . 7 4 l O 3 . l2 5 2 . 2 0 1 0 5 . I2 5 1 , 6 6 r O 7 . 22 6 3 . r 0 1 0 9 . 42 6 8 . 5 4 1 1 1 . 52 7 3 . 9 6 r 1 3 . 62 1 9 . 3 5 1 1 5 . 82 8 4 . 7 5 l l t . 52 9 0 . L 2 1 r 9 , 42 9 5 . 4 9 1 2 1 . s3 0 0 . 8 4 L 2 3 . 23 0 6 . 2 0 L 2 4 . 93 1 1 , 5 4 L 2 6 . 5

S e r l e s

8 . 1 69 . 0 0

1 1 . 2 01 2 . 3 8r 5 . 3 2t 7 . o 21 8 . 9 12 0 . 9 72 3 . 2 ' '2 5 . 8 52 8 . 7 23 r . 9 43 5 . 5 33 9 . 5 64 4 , 0 94 9 . 1 65 4 . 8 06 0 . 9 66 1 . 3 4

S e r l e a

7 . 4 21 0 . 2 1

S e r i . e g

a . 3 79 . 0 59 . 8 5

1 0 . 3 51 0 . 8 41 1 . 3 51 2 . 2 9t 2 . 7 7L 3 . 2 1r 3 . 7 7t 4 . 2 1

o . 0 2 4 20 . 0 r 0 90 . 0 0 6 60 . 0 r 1 3o . o 3 5 2o . 0 5 2 60 . 0 8 4 3o . t 2 2 40 . 1 6 7 4o . 2 1 7 50 . 3 5 5 0o , 5 6 1 7o . 9 4 2 91 . 4 0 02 . 0 8 52 . 8 5 34 . 0 4 35 . 8 8 48 . 1 7 5

0 . 0 r 5 70 . 0 1 5 4

0 . 0 1 7 2o . o o 8 8o . 0 1 4 1o . o l 7 3o . o l 8 3o . o l o 30 . 0 r 2 9o . o l 4 4o . 0 l 3 l0 . 0 2 4 90 . 0 3 3 2

Debye temperatures of lcyanite, andalusite, andsillimanite

We have calculated the Debye temperatures Ofi, fromour heat capacity data for temperatures below approxi-mately 18 K for the three Al2SiO5 polymorphs. Theresultant values are l100+25, 855+20, and 730-+50 K forkyanite, andalusite, and sillimanite, respectively. Figure3 gives a comparison between our observed heat capaci-ties and those calculated from the above values of efi forkyanite and andalusite. The excessively large scatter ofthe C! data below 20 K is a consequence ofthe very smallheat capacities of the Al2SiO5 polymorphs and the factthat the sample is only a very small percentage of the totalheat capacity (calorimeter plus sample). For example, at20 K the heat capacity of the kyanite sample was only5.1% of the total measured heat capacity.

We have also calculated the Debye temperature ofandalusite and sillimanite from the single-crystal elasticconstant data of Vaughan and Weidner (1978), using themethods described by Robie and Edwards (1966). Thesecalculations yield 838 and 8fi) K for the elastic Debyetemperature of andalusite and sillimanite, respectively.

5 5 . 0 9 7 . 4 4 9 2 2 6 . 3 9 9 6 . 4 75 9 . 9 6 9 . 4 3 8 2 3 r . 9 1 9 E . 8 56 1 . 7 L 1 1 . 5 8 2 3 ' r . 4 6 l 0 l . l7 0 . 0 0 t 4 . t 3 2 4 3 . 0 0 1 0 3 . 37 5 . r 3 L 7 . 2 4 2 4 8 . 5 3 1 0 5 . 66 2 . 1 9 2 0 . 4 7 2 5 4 . 0 5 1 0 7 . 88 8 . 3 1 2 3 . 7 L 2 5 9 . 5 ' r 0 9 . 89 4 . 4 4 2 7 . 0 6 2 6 5 . 0 6 I 1 1 . 9

l o o . 5 l 3 0 . 4 6 2 1 0 . 5 4 1 1 3 . 7r 0 6 , 5 3 3 3 . 8 9 2 7 6 . O L I 1 5 . 71 t 2 . 5 1 3 7 . 3 0 2 A t . 4 7 l l 8 . oI 1 8 . 4 5 4 0 . 8 5 2 8 5 . 9 3 1 t 9 . 5r 2 4 . 3 5 4 4 . 2 9 2 9 2 . 3 a 1 2 r . 4t 3 0 . 2 2 4 7 . 5 8 2 9 t . a O L 2 3 . 21 3 6 . 0 5 5 0 . 9 3 3 0 3 . 2 0 r 2 4 . 91 4 1 . 8 5 5 4 . 2 2 3 0 8 . 5 9 1 2 6 . 4r 1 7 - 6 2 5 7 . 3 5 3 r 3 . 9 5 1 2 8 . 11 5 3 . 3 7 6 0 . 5 r 3 r 9 . 3 2 t 2 9 . 6l 5 9 . l o 6 3 . 1 o 3 2 4 . 6 6 t 3 l . l1 5 4 . 8 1 6 6 . 7 4 3 3 0 . 0 O L 3 2 . 9L 7 0 . 4 9 6 9 . 5 E 3 3 5 . 3 1 1 3 4 . 3r 7 6 . 1 6 1 2 . 7 0 3 4 0 . 6 0 1 3 5 . 71 8 r . 8 0 7 5 . 5 7 3 4 5 . 8 9 1 3 6 . 7t a ? . 4 2 7 8 . 5 0 3 5 1 . 1 5 1 3 8 . 11 9 3 . O 3 8 r . 3 3 3 5 6 . 4 2 1 3 9 . 31 9 8 . 6 3 A 3 . 9 2 3 6 L . 6 7 r 4 0 . 62 0 4 . 2 L 8 6 . 5 0 3 6 6 - 9 2 t 4 t . 92 0 9 . 7 7 8 9 . 0 2 3 7 2 . L 4 L 4 3 . 22 r 5 . 3 2 9 L . 6 2 3 1 7 . 3 6 r 4 4 . 62 2 0 . 8 6 9 4 . 1 1

S e r I e s I S e r l e a I s e r l e 6 2

5 . 8 8 0 . 0 1 2 66 . 4 6 0 . 0 2 t 66 . 9 6 0 . 0 3 0 57 . 5 7 0 . 0 2 1 38 . 4 0 0 . 0 2 2 39 . 2 8 0 . 0 3 1 6

1 0 . 2 3 0 , 0 3 9 01 1 . 3 3 0 . 0 3 7 5

S e r l e a 3

1 3 . 5 5 0 . 0 5 1 41 4 . 6 8 0 . 0 7 4 0L 5 . 7 2 0 . 0 9 5 1L 7 . O 2 0 . L 2 2 6r 8 . 7 6 0 . r 8 0 32 0 . 6 5 0 . 2 5 7 42 2 . 8 4 0 . 3 6 5 22 5 . 3 1 0 . 5 3 3 22 8 . 0 8 0 . 7 8 9 33 I . 2 0 1 . I 9 73 4 . 6 9 t . 7 9 93 8 . 6 r 2 . 6 8 94 2 . 9 9 3 . 7 7 44 7 . 9 2 5 . 0 9 85 3 . 4 3 5 . 8 4 15 9 . 5 0 9 . 2 3 3

ROBIE AND HEMINGWAY: KYANITE'

Table 3. Experimental molar heat capacities of sillimanite fromReinbolt Hills, Antarctica

Teup.

ANDALU S ITE, SILLIMANITE

T e m p e r o t u r e , i n K e l v r n s

Fig. l. Experimental molar heat capacities (open diamonds)of kyanite from Minas Gerais, Brazil. Solid triangles, data ofTodd (1950).

lusite, and sillimanite at high temperatures' and

Schneider (1979) has measured the cell parameters of

andalusite to l0(X)'C. The results of the three investiga-

tions for andalusite are shown in Figure 4. The agreement

between the three investigations is unsatisfactory.The effect of pressure upon the molar volume can be

estimated from the compressibilities at 298 K, (F : ll

V(dVldP)"i. Brace et al. (1969) obtained 0.70, 0'67' and

0.65 Mbar-l for kyanite, andalusite, and sillimanite,

respectively. The compressibilities (adiabatic) of andalu-

site and sillimanite are 0.63 and 0.60 Mbar-l obtained

30r

TmP. Heatcapaclty

J / ( r c r ' K )

Eeetc6paclEy

J / ( n o 1 ' K )

Teop. Hea tcapacl ty

J / ( o o 1 . K )

Serte€ I Serled 3 (cont) Sel led 4 \ lFf

c

>-t

OoLoO

to0)

f_

303.05 124.5 152.80307.86 125.9 1s8 .523L2.82 t27.3 164.23317.80 L28.4 L69.92323.00 130.0 175.593 2 8 . 1 9 r 3 r . 4 1 8 1 . 2 4333.36 132.7 186.89338.52 134.4 L92.533 4 3 . 7 0 1 3 5 . 5 1 9 8 . 1 6348.85 136.7 203.78

209.37Serles 2 2L4.96

220.533 5 2 , 8 0 L 3 7 . 7 2 2 6 . 1 1357.93 138.6 23L.69362.88 140.1 237.27367.84 141.5 242.85172.96 142.7 248.42378.06 143.6 2s3 .98

2s9.52SerLeB 3 265.07

270.6355.09 8 .723 276.L659.98 10 .84 281.6864.73 13 .12 287.1870.01 1s .80 292.6576.LO 19.03 298.1182.11 22 .29 303.5688.17 25 .60 308.9994.23 28.93

100.25 32 .32LO6.22 35.72tt2.L4 39.15118.03 42 .62123.89 45 .00129.72 49.321 3 5 . 5 3 5 2 . 5 814r .31 55 ,82L47.07 58 .93

6 . 4 7 0 . 0 4 67 . 2 9 0 . 0 5 08.09 0 .0669 . 0 1 0 . 0 5 6

1 0 . 1 1 0 . 0 5 3rt.24 0.06012.50 0 .068r3 .88 0 .082r 5 . 3 8 0 . 1 1 91 7 . 0 5 0 . 1 7 718.9r 0 .26520.97 0 .39423.26 0 .56425.82 0 .8202A.67 1 .1983 r . 8 7 L . 7 6 635.45 2 .56439.45 3.70143.94 5.01448.99 6.52054.61 8 .55360.70 11 .2167.O2 L4.2973.36 17 .5079.63 20 .9585.80 24 .309 r . 9 0 2 7 . 6 L97.92 30 .97

Serles 5

L15.24 73 .93180.61 76 .62185.73 79 . t2190.90 8r .63196.34 84 .1620L.75 86.50207, I5 89 .002 t 2 . 5 4 9 1 . 3 92r7 .9L 93 .65223.2A 96.02228.63 98.29233.98 tOO.5239.32 rO2.7

62.065 5 . 1 56 8 . 1 371.0674.O476.9019.648 2 . 3 584.9287.4389.8492.4594.8391. r799,48

1 0 1 . 7r 0 3 . 9106.1108.2110.1LL2.2114. t115.81 1 7 . 61 1 9 . 5tzL.4L 2 2 . 9L24.5t26.1

the data for the Burnsville, North Carolina, kyaniteinclude single-crystal data by Skinner et al. (1961) andBurnham (1963) that agree closely with one another andwith the powder data but that are significantly less thanthe values of Winter and Ghose (1979).

Furthermore, based on the work of Hubbard et al.(1975) one might expect systematic differences betweensingle crystal and powder measurements at the level of afew parts in 105, not the 60 parts in 105 observed betweenthe Winter and Ghose (1979) and Skinner et al. (1961)

data.The molar volumes at 298 K that we have adopted for

use in our calculations are 44.15=0.05, 51.52t0.05, and49.86+0.05 cm3/mol for kyanite, andalusite, and silliman-ite, respectively, and were obtained from unit-cell vol-umes of Table 7 and using a value for Avogadro's number= (6.022094!0.000008) x 1023 mol-r (Deslattes et al',r974).

Skinner et al. (1961) and Winter and Ghose (1979) haveboth measured the unit-cell parameters of kyanite, anda-

tos 2OO lOOT e n p e n o c u . e , l n h e l v r n e

Fig. 2. ACi for andalusite - kyanite (circles)

sillimanite - kyanite (triangles) versus temperature.

Y

o

Lo

6 .o

a6g

and for

- - . . \

t/II \

\

/'

*/

"--/

2u'

/

302

5. Stg

o. s6g

s. so2

& 600

ROBIE AND HEMINGWAY: KYANITE, ANDALUSITE, SILLIMANITE

Ya a.os6o

g. og1

Lo

Cf, (andalusite) : 290.4 - 0.01052r - 2627.ET- s

- 1.109 x 106T'2 Q)

Ci (sillimanite) :226.1 + 0.014077 - 1376.07-.s

- 2.440 x 1ge7-z (3)Holdaway (1971) pointed out that the Brandywine

Springs sillimanite used by Richardson et al. (1969) intheir phase-equilibrium studies contained appreciableamounts of fibrolite (fibrous sillimanite) and, as such,might be the cause of the difference in the phase bound-aries obtained by Richardson et al. in contrast to his owndeterminations. Holdaway's premise is supported by theexamination of the Brandywine Springs sillimanite byhigh voltage transmission electron microscopy, whichshowed that the fibrolite patches contained quartz as a

Table 4. Molar thermodynamic properties of kyanite (Al2SiO5).[Formula weight 162.047 g/mol]

T e ! p , E e a t E o t r o p t E o t h a l p y c l . b b s e E e r g ye e p a c l t y f u D c t l o o f u n c t l o D

t . ; rs i -s i r tu i -n l r r r -<c i -u iv rK J / ( o o l . K )

6 t@ 2gg

Tcapo^acu.c2

Fig. 3. CIT versus T2 for Al2SiO5 polymorphs. Straight linesare calculated using the indicated Debye temperatures (dp).Squares, data for kyanite; triangles, data for andalusite.

from the elastic constant data of Vaughan and Weidner(1978), and 0.90 to 0.70 Mbar-t for andalusite (isother_mal) obtained from the unit-cell parameters of Ralph,Finger, and Ghose (l9Sl). From these data and the

The Al2SiO5 triple point

We wish to use our new entropy data together with theexisting high-temperature heat content values of pankratzand Kelley (1964) and the high-temperature molar volumedata of Skinner et al. (1961), Winter and Ghose (1979),and Schneider (1979) to see whether we can distinguishwhich of the proposed triple points (or phase diagrams)gives the best agreement.

In order to calculate the entropy changes at hightemperature, we have combined our heat-capacity dataabove 250 K with the heat content data ofpankratz andKelley (1964) and have fit these combined data sers ro anextended Maier-Kelley equation (Haas and Fisher, 1976)

Cl : u+ bT + cT-2 + dT-r/z + e71by least squ€ues with the constraint that the derivedequation joins smoothly with our measured low tempera-ture 0! and entropy. The P term was not significant andtherefore was omitted in the fitting process. The resultingequations, which are valid for the temperature range of250 to 1600 K, are:

Ci kyanite) : 303.9 - 0.01339? - 290,437-.0s

51 0l 52 02 53 03 54 04 55 0

o . o o l 5o . o l 20 . 0 3 9o . t 4 20 . 2 8 90 . 5 2 1o . 9 4 7L . 4 1 52 . t 9 23 . L 2 7

5 , 6 7 48 . 9 9 8

1 3 . 1 8r 7 . 9 82 3 . L 7

2 A . 7 53 4 . 5 24 0 . 4 64 6 . 4 15 2 . 2 95 8 . 1 55 3 . 9 36 9 . 5 17 4 . a 78 0 . 1 5

4 5 . 2 69 0 , 0 29 4 . 5 19 9 . 0 9

1 0 3 . 41 0 7 . 3l l l . 2l l 5 . o1 1 8 . 5t 2 2 . O

o . o o 0 5o . o o 4o . o l 3o . 0 3 80 . o 8 40 . t 5 5o . 2 5 5o . 4 2 50 . 6 3 80 . 9 1 5

1 . 6 9 72 . 8 L 24 . 2 7 76 . l o 28 . 2 6 L

1 0 . 7 31 3 . 4 8t 6 . 4 7r 9 . 6 92 3 . 0 92 6 . 6 53 0 . 3 53 4 , l 73 8 . 0 t4 2 . 0 4

4 6 . 0 85 0 . I 65 4 . 2 65 8 . 3 86 2 . 5 16 6 . 5 47 0 . t 67 4 . 8 87 8 . 9 88 3 . O 5

E t . l o9 1 . 1 29 5 . 1 09 9 . 0 6

1 0 3 , 01 0 6 . 9l l o . 71 1 4 . 5

7 2 , 0 6E 2 . 3 0

0 . o o o 4o . 0 0 3o . o l o0 . 0 3 2o . 0 5 7o . t 2 2o . 2 0 10 . 3 3 1o . 4 9 60 . 7 1 0

1 . 3 1 32 . 1 6 53 . 2 1 24 . 6 3 56 . 2 2 5

8 . 0 r 79 . 9 8 5

1 2 . l ot 4 . 3 41 6 . 6 7r 9 . 0 82 1 . 5 52 4 . 0 62 6 . 5 92 9 . L 1

3 1 . 6 93 4 . 2 13 6 . 7 61 9 . 2 64 L . 7 44 4 . t 94 6 . 5 04 4 . 9 75 r . 3 15 3 . 5 1

5 5 . 8 65 8 . 0 76 0 . 2 45 2 . 3 16 1 . 4 56 6 . 4 96 8 . 4 87 0 . 4 34 7 . 3 55 3 . r 9

o . o o o lo . o o l0 . 0 0 3o . 0 0 6o , o t 70 . 0 3 40 . 0 5 80 . 0 9 40 . 1 4 20 . 2 0 5

g . 3 8 4o . 6 4 71 . 0 0 6L . 4 6 72 . O 3 5

2 . 7 L 23 . 4 9 34 . 3 7 55 . 3 5 26 . 4 2 17 . 5 7 38 . 8 0 4

l o . l lL L . 4 'l 2 . 9 0

1 4 . 3 9r 5 . 9 21 7 . 5 0L 9 . 1 22 0 . 1 12 2 . 4 52 4 . L 72 5 . 9 02 f . 6 62 9 . 4 1

3 r . 2 43 3 . 0 53 4 . 8 73 6 . 7 03 8 . 5 34 0 . 3 84 2 . 2 34 4 . 0 82 1 . 1 |2 9 . 1 1

6 07 08 09 0

t o o

l l 0t20r 3 01 4 0r 5 0r 6 01 7 01 8 01 9 02 0 0

2 r o2202302 4 02502602 7 02 8 02903 0 0

3 l o 1 2 5 . 03 2 0 I 2 8 . I3 3 0 r 3 t . o3 4 0 1 3 4 . 03 5 0 1 3 6 . 63 6 0 1 3 9 . 03 7 0 1 4 r . 33 8 0 t 4 3 . 72 7 3 . t 5 L r z . 72 9 8 . r 5 t 2 L . 6-8.952 x tO5T-2 (1)

ROBIE AND HEMINGWAY: KYANITE, ANDALUSITE' SILLIMANITE 303

Table 5. Molar thermodynamic properties of andalusite(Al2SiO5). [Formula weight 162.047 g/mol]

T e r p . f , e . t E n t r o p y E n t h E l p y G l b b o € a e r 8 y

c a p a c l . t y f u n c t l o o f u D c t l o n

r . ; <s i -s i r 1u i -u l t r r - t c i -u i r r r

K J / ( o o I . K )

for the andalusite --+ sillimanite transition. From the dataof Skinner et al. (1961), AVio+a : -0.232 and AVi123 :-0.240 J/bar. whereas the data of Winter and Ghose(1979), yield AWo+e : -0.193 and AVi123 : 0'197 Jlbat'Above 800 K The measurements by Schneider (1979) onandalusite lie between those by Skinner et al. (1961) andthose by Winter and Ghose (1979), as shown in Figure 4;

and therefore we have simply taken a graphical averagefor AVi from Skinner et al., Winter and Ghose, andSchneider, i.e., AVisa6 : 0.213t0.017 and LVr:rn =-0.218t0.019 J/bar. Using the Clapeyron equation at Ibar we get

dP I dT : (2. 84 t 0. 30 J lK)l (- 0.213-10.0 17 J/bar)

: -13.3-+2.3 bar/K at l(X8 K, and at 1123 K'

dptdT = (2.E010.30 J/Ky(-0.218-r0.02 J/bar)

: -12.8+2.3 batlK'

Table 6. Molar thermodynamic properties of sillimanite(Al2SiO5). [Formula weight 162.M7 g/mol]

T e o p . H e e t E n t r o P y E n t h s l P y G l b b s e n e r g y

c a p e c l t y f u n c t l o n f u n c t l o n

r c ; s i - s 6 ( H i - H 6 ) / r - ( G ; - H 6 ) / r

K e l v l . n J / ( D o l ' K )

6 07 08 09 0

r 0 0

5l o1 52 02 53 03 54 04 55 0

l l o1 2 01 3 0t 4 01 5 01 6 01 7 01 8 01 9 02 0 0

2 l o2202lo2402502602 t o2 8 0290300

o . o o o ,o . 0 0 6o . 0 2 10 . 0 5 80 . 1 2 E0 . 2 4 5o . 4 2 30 . 6 7 81 . 0 0 81 . 4 1 0

2 . 4 4 63 . 7 6 65 . 3 3 87 . 1 3 49 . 1 t 2

1 1 . 2 41 3 . 4 9r 5 . 8 3r 8 . 2 52 0 . 7 |2 3 . 2 r2 5 . 7 32 8 . 2 53 0 . 8 03 3 . 3 3

3 5 . 8 43 8 . 3 34 0 . 8 04 3 . 2 14 5 . 6 44 8 . 0 r5 0 . 3 45 2 . 6 35 4 . 8 95 7 . 1 1

5 9 . 2 86 t . 4 16 3 . 5 05 5 . 5 56 7 . 5 56 9 . 5 17 1 . 4 37 3 . 3 r5 1 . 0 65 6 . 7 0

o . o o o 3o . o o 2o . o o 70 . 0 1 70 . 0 3 70 . 0 7 00 . 1 2 00 . t 9 20 . 2 9 10 . 4 1 7

0 . 7 6 r| . 2 3 41 . 8 3 72 . 5 6 73 . 4 2 0

4 . 3 A 75 . 4 5 r6 . 6 3 27 . 8 9 49 . 2 3 7

1 0 , 6 51 2 . 1 41 3 . 6 8t 5 . 2 7t 6 . 9 2

1 8 . 6 12 0 . 3 32 2 . 0 92 3 . 8 82 5 . 6 92 7 . 5 32 9 . 3 83 1 . 2 53 3 . 1 43 5 . 0 6

3 6 . 9 53 8 . 8 64 0 . 7 84 2 . t L4 4 . 6 44 6 . 5 74 8 . 5 05 0 . 4 32 9 . 9 73 { . 6 9

0 . 0 0 20 . 0 1 50 . 0 4 80 . 1 1 6o . 2 4 30 . 4 5 3o . 7 6 41 . 1 8 9L . 7 3 22 . 3 9 24 . 0 5 66 . r 4 6I . 6 L 7

l t , 4 2L 4 . 5 2

2 9 . 0 33 3 . 0 23 7 . 1 04 L . 2 64 5 . 4 A4 9 . 7 45 4 . 0 2

5 8 . 3 35 2 . 6 46 6 . 9 4

7 5 . 5 27 9 . 1 94 4 . 0 2a a . 2 39 2 . 4 r9 6 . 5 5

1 0 0 . 7t 0 4 . 71 0 8 . 81 L 2 . 71 1 5 . 7l 2 0 . 6t 2 4 . 5

8 5 . 3 59 5 . 7 9

0 . 0 0 1o . 0 0 40 . 0 1 2o . o 2 90 . 0 5 80 . 1 0 50 . 1 7 6o . 2 7 50 . 4 0 60 , 5 7 01 . 0 0 51 . 5 8 72 . 3 0 73 . 1 5 14 . 1 4 0

5 . 2 3 56 . 4 3 47 , 7 3 09 . 1 1 2

t 0 . 5 71 2 . 1 0t 3 . 5 91 5 . 3 4L 7 . O 41 8 . 7 8

2 0 . 5 62 2 . 3 42 4 . 2 22 6 . 0 92 7 . 9 82 9 . 4 93 r . 8 23 3 . 7 63 5 . 7 13 7 , 6 7

3 9 . 6 44 1 . 6 14 3 . 5 84 5 , 5 64 7 . 5 34 9 . 5 15 1 . 4 83 2 . 4 33 7 . 3 1

0 . 0 0 2O . O I I0 . 0 3 50 . 0 8 70 . 1 8 50 . 3 4 80 . 5 8 80 . 9 r 41 . 3 2 6I . 8 2 13 . 0 5 04 . 5 5 06 . 3 1 0a . 2 6 3

1 0 . 3 8

L 2 . 6 31 4 . 9 9L 7 . 4 2t 9 . 9 22 2 . 4 52 5 . 0 02 7 . 5 73 0 . 1 43 2 . 7 03 5 . 2 4

3 7 . 7 64 0 . 2 6a 2 . 7 24 5 . 1 54 7 . 5 44 9 . 8 95 2 . 2 05 4 . 4 75 5 . 7 05 8 . 8 8

6 1 . 0 26 3 . 1 25 5 . 1 76 7 . t 96 9 . 1 57 1 . 0 87 2 . 9 75 2 . 9 25 8 . 4 8

o . o o 3 30 . o 2 50 . 0 8 5o . 2 6 40 . 5 E 2l . l r 51 . 9 3 03 . O 2 74 . 2 9 55 . 4 2 2

9 . 5 5 5r 3 . 9 11 E . E 62 4 . L l2 9 . 7 0

3 5 . 3 44 l . l l4 6 . 8 25 2 . 4 15 7 . 9 86 3 . 4 16 8 . 6 77 3 . 4 6I 8 . 9 68 3 . 7 9

E 8 . 6 09 2 . 9 09 7 . L 9

l o r . 31 0 5 . 3l o 9 . l1 1 2 . 81 1 6 . 41 1 9 . 81 2 3 , 0

o . o o l oo . o o 80 . o 2 8o . 0 7 5o . 1 6 50 , 3 1 4o . 5 4 30 . 8 7 11 . 2 9 8| . 8 2 7

3 . 2 0 85 . O O O1 . L 7 59 . 7 0 1

1 2 . 5 3

l 5 . 6 31 8 . 9 52 2 . 4 62 6 . L 12 9 . 9 53 3 . 8 t3 1 . 8 14 r . 9 44 6 . 0 75 0 . 2 5

5 4 . 6 55 8 . 6 66 2 , 4 96 7 . I I7 r . 3 37 5 . 5 37 9 . 7 28 3 . 8 98 E . 0 39 2 . L 1

9 6 . 2 3l o o . 3r 0 4 . 31 0 8 . 3t t 2 . 2t l 6 . r1 1 9 . 9t 2 3 . 7

8 1 . 0 39 1 . 3 9

3 l o 1 2 6 . 0320 128.93 3 0 1 3 r . 93 4 0 1 3 4 . 53 5 0 1 3 6 . 93 6 0 1 3 9 . 33 7 0 1 4 1 . 73 E O 1 4 4 . 02 7 3 . L 5 1 l 4 . 22 9 8 . 1 5 L 2 2 . 6

5l o1 52 02 53 03 54 04 55 06 07 08 09 0

1 0 0

1 1 01 2 01 3 0

0 . o 0 6o . o 4 20 . 1 4 20 . 3 7 6o . 8 2 2

. 5 5 2

. 5 5 9- 6 t 5

. 4 t 4

. 1 8 2I I . 3 I1 6 . 0 12 1 . 1 82 6 . 6 43 2 . 2 8

3 8 . 0 2 1 7 . 4 7L 3 . 7 8 2 1 , 4 24 9 . 5 0 2 5 . r 5

5 0 . 6 26 5 . 9 97 L . 2 37 6 . 3 28 r . 2 38 5 . 9 4

separate phase (Bell and Nord, 1974). Bell and Nordconcluded that "parts of the Brandywine Springs silli-manite are technically rocks, not minerals" and that "theexistence of quartz makes the Brandywine Springs silli-manite less than desirable for thermochemical studies."However, Holdaway's conclusion that fibrolite is lessstable than sillimanite would appear to be the majorreason for the discordant results.

The andalusite-sillimanite transition (at I bar) takesplace at 1048120 K on the basis of Holdaway's highpressure reversals and the unpublished measurements ofWeill as reported by Holdaway (1971). Richardson et al.(1969) placed the andalusite-sillimanite phase boundaryintersection with the l-bar axis at ll23 K. From our heatcapacity and entropy data and equations (2) and (3), weget ASi6a6 :2.84=0.3 and ASirzr : 2.80+0.3 J/(mol ' K)

1 4 01 5 01 6 01 7 01 8 01 9 0200

z t o 9 0 . 4 62 2 0 9 4 . 8 I2 3 0 9 8 . 9 82 4 0 1 0 3 . 02 5 0 I 0 6 . 82 6 0 1 1 0 . 52 7 0 l l 4 . o2 8 0 1 1 7 . 42 9 0 1 2 0 . 73 0 0 1 2 3 . 7

3 1 0 1 2 6 . 73 2 0 1 2 9 . 53 3 0 L 3 2 . 23 4 0 1 3 4 . 83 5 0 1 3 7 . 33 5 0 1 3 9 . 83 7 0 L 4 2 . 22 7 3 . t 5 1 l 5 . I2 9 8 . r 5 r 2 3 . 2

304 ROBIE AND HEMINGWAY: KYANITE, ANDALT]SITE, SILLIMANITE

Table 7. X-ray unit-cell paxameters and molar volumes of kyanitefrom Burnsville, North Carolina; andalusite from Minas Gerais.

Brazil; and sillimanite from Brandywine Springs, Delaware

t 0 .71192 0 .78473 0 .55724 89 ,977 l0 l . l2 l 106.006 293. . t6 44 ,14 Burnhan0.00005 0.00004 0.00006 0.005 0.005 0.003 0.04 o.or i isort

l0 l . l5 105.00 293.41 44 .17 Sk inner0 .08 0 .08 0 .32 0 .05 e t a l . (1961)

101.22 105.98 292,92 44 .10 St inne.0 .08 0 .03 0 ,21 0 .03 e t a l . (1961)

101.32 105.97 292.7 44.07 Richardson0 . 0 3 0 . 0 3 0 . 3 0 . 0 5 e t a l . ( 1 9 6 g )

l 0 l . l 0 1 0 5 . 9 9 2 9 4 . 2 4 4 . 2 9 H o l d a w a y0 , 2 0 . 0 3 ( t 9 7 1 )

l 0 l . l l 1 0 6 . 0 3 2 9 3 . 5 0 4 4 . 2 0 t { t n l e r a n d0 . 0 ? 0 . 0 1 0 . 0 9 0 . 0 1 c h o s e ( t 9 7 9 )

sillimanite phase boundary must exhibit substantial cur-vature. The slope from Richardson et al., (1969) isapproximately -24.1 bars/K. Our slope calculation(-14.1x.2.4 bar/K at 973 K and I bar) provides a com-pletely independent check of the value, -12-+4 bar/K,obtained by Anderson, Newton, and Kleppa (1977) onthebasis of the diference in the enthalpies of solution ofandalusite and sillimanite in 2PbO.B2O3 at 973 K. Thegeneral agreement between our results and those ofAnderson et al. (1977), together with the direct measure-ments of Holdaway, appear to be sufficient grounds forconcluding that the andalusite-sillimanite phase boundaryof Richardson et al., is incorrect. In our calculations weassumed that S3 : 0, i.e., there was no frozen-in disorderin sillimanite at low temperatures (see also the neutronstructural refinement of Peterson and McMullen, 1980).Our data strongly suggest that sillimanite is AVSi orderedat least below llfi) K.

The kyanite-andalusite boundary has been reversed byNewton (1966b) (hydrothermally) at 6.6-r-0.4 kbar and1023 K. Holdaway (1971) has also reversed this boundaryat666-+16Kand2.4kbar,746-+26 K and 3.6 kbar. andgives an "apparent" reversal at847'+17 K and 4.8 kbar.From our entropy data and equations (l) and (2) wecalculate ASiozr : 8.20-+0.3 J/(mol ' K). The correctionnecessary to calculate ASie4 at 6.6 kbar is quite uncer-tain, because of the large diferences between the valuesof dAIz"/dZ obtainable from the measurements of Skinneret at. (1960), and those of Winter and Ghose (1979). Againwe have averaged the two diferent sets of V(fl data to getAsioa (6.6 kbar) : (8.20+0.3) + 0.34-+0.26 = 8.54-10.40J/(mol . K). The average value for AViozr is 0.763-10.003J/bar. The calculated slope is ll.ZbarlKat1023 K and 6.6kbar. If we assume a constant slope the kyanite-andalu-site boundary would occur at 434 K and I bar pressure.At 434 K and I bar ASi3a : 9.26+0.3 J/(mol.K) and

a b c c B y v V "nn nn nm des des des t : ; io cm3

Source

( y a n l t e , B u . n s v i l l e , N o r t h C a r o l i n d

t 0 .7121 0 .7846 0 .5577 89 .970.0002 0.0002 0.0005 0.08

0.7123 0 .7844 0 .5568 89 .900.0002 0 .0002 0 .0002 0 .08

0.7124 0 .7843 0 .5s56 89 .920.0001 0,0002 0.0005 0.05

r 0 .7121 0 .7851 0 .5588 90 .130.0002 0.0002 0.0002

t 0,7'1252 0.78520 0.55724 89.990.00012 0 .000t0 0 ,00010 0 .02

A n d . l u s i t e , t l l n a s c e . a i s , B r a z i l

0.77950 0 .78996 0 ,555800.0001 0.0001 0.0001

r 0 .77942 0 .78985 0 .55590.00002 0.00002 0,0002

0.7795 0 .790t 0 . s5510.0002 0.000? 0.0002

t 0 .77980 0 ,79031 0 .555660.00007 0.00010 0.00005

0.78003 0.790t 2 0. s55470.00012 0 .000t4 0 .00007

342.25 51 .53 Sk lnner0 .09 0 .04 e t a l . (1951)

342.23 51.52 Burnhan and0.1 2 0 .02 Buerger

( l s6 l )

341.9 51 .47 Ho ldawav0,2 0 .03 ( t e7 l )

-

342,44 51 ,56 l { in te r and0.05 0 .01 chose (1979)

342.35 5 l .54 Brace e t a l .0 .09 0 .01 (1969)

S i l l l m n i t e , B r a n d y w i n e S p r l n g s , D e l a w a . e

0.74805 0.75709 0.576780.0002 0,0002 0.0002

0.1481 0 ,7672 0 .57690.0002 0.0002 0.0002

0.7479 0 .7670 0 .57700.0002 0.0001 0.0001

0. i485 0 .76 i3 0 .57690.0002 0.0002 0;0002

0. i4831 0 ,76710 0 .57 i000.00004 0.00004 0.00004

t 0 .74883 0 .75808 0 .577740.00007 0.00007 0.00005

3 3 0 . 9 t 4 9 . 8 3 S k i n n e r0 . 1 7 0 . 0 3 e t a l . ( 1 9 6 1 )

3 3 1 . 1 4 9 . 8 5 A r a n a k i a n d0 . 2 0 . 0 3 R o y ( l 9 6 3 )

3 3 1 . 0 4 9 . 8 3 R t c h a . d s o n0 . i 0 . 0 2 e t a l . ( 1 9 6 9 )

3 3 1 . 3 3 4 9 . 8 7 N a v f o t s k y0 . 1 7 0 . 0 3 e t a l . ( 1 9 7 3 )

3 3 1 . 2 2 4 9 . 8 7 C d r e r o n0 . 0 3 0 . 0 1 ( t e r 6 )

332.29 50.03 l{ lnter and0 . 0 5 0 . 0 1 c h o s e ( 1 9 7 9 )

t Single-cfystal neasurements

* Yincey County, North Carol lna--probably Burnsvj i ler i lC

Our calculated slope (at I bar) for the temperaturerange covered by the Richardson et al. and the Holdawaydata is thus in excellent agreement with Holdaway's(1971) experimental value, - 13.9 bar/K. However. if wecalculate the slope at Holdaway's triple point (774 K and3.76 kbar) we set dPldT = l(3.44 -(-7.75 x l0-5)(3760)l(-0.191) : -19.5-+3.8 bar/K where the secondterm in the numerator is the change in AS77a between Iand3.76 kbar. The additional + 0.5 bar/K uncertainty inthe slope at the triple point arises because of the uncer-tainty in d,AVldT. To be compatible with the measuredheat capacity and molar volume data the andalusite-

o.3a2ms .og t@ 8e6 lego t2@ l4e6

T.6o.FE!uF. K

Fig. 4. Unit-cell volumes of andalusite at high temperaturesSources of experimental data: circles, Winter and Ghose (1979);solid line Schneider (1979); inverted triangles, Skinner, Clark,and Appleman (1961).

E

oE

o

aob

6. 356

0. 354

o.352

9.355

L 3aA

o,316

6. ?1a

2

/

/rz

/

z,4

'/

,z

ROBIE AND HEMINGWAY: KYANITE, ANDALUSITE, SILLIMANITE 305

aui,r* r.r

aci,rm t'r

asi,rr, .l/1'or.r1

slge U(nol.()

ori,rro r':

Table 8. Selected thermodynamic properties of kyanite,andalusite, and sillimanite at 298.15 K and a comparison of theenthalpies of reaction (Ali?,szo) at 970 K calculated from datagiven in this study with the results from molten salt calorimetry.

-259L.90

-2441.72

- 497.00r0 .2 5

91.39t0. I4

3 .46( 3 .34)a 'b

0 3 . 0 6( 2 .80)b

a. Ander.on and Ueppe (1969)

b. Anderson, ileeton, and K1eppe (1977)

Llflnq = 0.740-+0.003 J/bar from which the calculatedslope is 12.5 barlK. Based on a combination of theequilibrium measurements and the calorimetric and molarvolume data we adopt 450+15 K as the I bar interceptand 11.8t0.7 bar/K as the slope for the kyanite-andalu-site boundary.

Newton (1966a, 1969) has also reversed (hydrothermal-ly) the kyanite-sillimanite equilibrium at 1023 K and8.510.4 kbar. The Clapeyron slope (at 1023 K and I bar)calculated from our entropy data and the average of theAV| measurements of Skinner et al. (1961) and of Winterand Ghose (1979) for this reaction is

dPldT : (1 1.0810.30 J/K)/(0.551 +0.005 J/bar): 20.1+0.4 bar/K

At 8.5 kbar ASrozr : I 1.05 J/K and the calculated slope isessentially unchanged and the I bar intercept for thekyanite-sillimanite boundary would thus be 6001 15 K.Above 1100 K we might expect a slight positive curvatureof this phase boundary as a consequence of the Al-Sidisordering in sillimanite. The reaction boundary calcu-lated from our data shows reasonable agreement with theresults of Richardson et al. (1969), and Newton (1966a,1969).

In Table 8, we summarize the values for the thermody-namic properties of the Al2SiO5 polymorphs derived fromour measurements and calculations. These values are inagreement with the equilibrium reversals of Newton(1966a,b, 1969), and Holdaway (1971), the solubilitymeasurements of Weill (1966), and the calorimetricallydetermined enthalpy change of the kyanite --+ sillimanitetransition (Anderson and Kleppa, 1969), the andalusite -->

sillimanite transition (Anderson et al. 1977), and for thekyanite -> andalusite change obtained by combining datain these last two named studies.

The phase-equilibrium data only provide informationon the differences in AG and do not fix the absolutevalues. To be consistent with the work of Haas, Robin-son, and Hemingway (1981), we have arbitrarily adoptedtheir value of A.Eli,zqe for sillimanite as our referencevalue.

The phase diagram calculated from the data in Table 8together with the high-temperature heat capacity func-tions and the average ofthe AVt values of Skinner et al.(1961), and of Winter and Ghose (1979) is shown in Figure5, together with selected phase-equilibria results. Thecalculated triple point is at 790t25 K and 4.0t0.5 kbar.

Acknowledgments

We are very much indebted to E.S. Grew, UCLA, for provid-ing us with the granulite from which the sillimanite sample wasextracted and to our USGS colleague H.T. Haselton, Jr., formany stimulating discussions.

5OO 600 700 800 900 1 000 I I 00

T € n g e r t t u r e K

Fig. 5. Phase diagram Al2SiO5. Phase boundaries calculatedfrom (l) data in Table 8; (2) molar volume data of Skinner, Clark,and Appleman (1961) and of Winter and Ghose (1979); (3) heat-capacity equations listed in text. Experimental results are fromHoldaway (1971, open horizontal rectangles); Newton (1966a,b,

1969, vertical rectangles); and Evans, 1965, open circles)' Thefilled horizontal rectangle is the unpublished data of Weillreported by Holdaway (1971).

-2596,01r1 .70

-2445.t211.69

- 506.0Efr.24

82,30!o .13

0

0

-25E7.7711.73

-2440.90{ . 7 2

- 492.60

95.79r0. t4

6 . 5 2( 5 . 9 4 ) e( 6 . 3 5 ) D

O L400

S I L L I T A i l I T E

306 ROBIE AND HEMINGWAY: KYANITE, ANDALUSITE, SILLIMANITE

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Manuscript received, March 9, 19E3;acceptedfor publication, September 14, 19E3.