Heat capacity of magnesium aluminosilicate melts

00167037/93/56.00

Geochimieo d Cosmochimica Acfa Vol. 57, pp. 1267-1275 Copyright 8 1993 Pcrgamon Pres Ltd. Printed in U.S.A.

+ .oO

Heat capacity of magnesium aluminosilicate melts PHILIPPE COURTIAL and PASCAL RICHET Lahoratoire de Physique des Gkomateriaux, Institut de Physique du Globe, 4 place Jussieu, 75252 Paris Cedex 05, France (Received March 12, 1992; accepted in revisedform Augusf 6, 1992)

Abstract-The heat capacities of six melts of the system MgO-A1203-SiOz have been determined from drop calorimetry measurements made between 900 and 1800 K. These and previously published data show that within the glass-forming region of this system the heat capacity is a linear function of composition. The partial molar heat capacities of SiOz and MgO are temperature independent and equal to the values obtained previously for Al-free melts, whereas that of A1203 increases with temperature and is consistent with the heat capacity of pure alumina liquid. Although melts of the system MgO-A1203-Si02 behave as ideal solutions with respect to the heat capacity, available measurements for other liquids show that this conclusion is not generally valid for aluminosilicates. Some thermochemical and structural implications of this behavior are also discussed. present in the melt (e.g., RICHET and BOTTINGA, 1984a, 1985). We have thus undertaken systematic calorimetric measurements on simple ternary aluminosilicate systems to determine more thoroughly these interactions in order to establish a reliable model of calculation of the heat capacity. In this paper, we present the results obtained for six liquids of the system MgO-A1203-Si02 whose compositions were selected to lie on a network of joins starting from all three endmembers. In this way, the composition dependence of the heat capacity and partial molar heat capacities can be examined without having to resort to statistical analyses of the data obtained with multiparameter fits. Among ternary aluminosilicate systems of geochemical interest, magnesium aluminosilicates show the most profound nonideal thermodynamic behavior, as clearly exemplified by the wide extent of liquid immiscibility ( GREIG, 1927;HAGEMAN and OONK, 1986). Ironically, we will show that the heat capacity of these liquids follows an almost ideal behavior. It must be emphasized at once, however, that the partial molar heat capacity of liquid A1203 determined for this system agrees with the heat capacity of pure A&O3 liquid but not with values obtained from other aluminosilicate liquids. In other words, aluminosilicate liquids are indeed markedly nonideal with respect to the heat capacity, especially when alkali elements are also present in the melt.

INTRODUCTION ALUMINUM IS A MAJOR constituent of naturally occurring silicate melts that exerts a profound influence on their physical properties. The measurements of ROSSINet al. ( 1964) and RIEBLING ( 1964, 1966), for instance, have shown that the viscosity strongly depends not only on the Al203 concentration, but that it depends on it in a more complicated fashion than on the Si02 content. The density is not as sensitive a function of the structure as the viscosity, but even in this case a nonlinear composition dependence has been discussed ( BOTTINGA et al., 1982). This behaviour has long been referred to the dual structural role of aluminum as either a network former element, substituting to silicon in tetrahedral positions, or as a network modifier, acting like alkaline or alkaline-earth elements to break up the tetrahedral network (e.g., BOTTINGAand WEILL, 1972). The isobaric heat capacity of silicate melts (C,,) is another important property of interest for thermal modelling of magmatic processes, phase equilibria calculations, or theoretical investigations of physical properties of liquids (e.g., YODER, 1976; CARMICHAELet al., 1977; RICHET, 1984). Hence, the influence of aluminum on the heat capacity must also be determined, regardless of particular interpretations as to its structural role. As a matter of fact, the heat capacity of a liquid includes an important configurational contribution, and it might be expected that calorimetric measurements will shed some light on the kind of structural changes that are induced by temperature variations (e.g., RICHET and NEUVILLE, 1992). To fulfill geochemical purposes, a model of calculation of the heat capacity as a function of temperature and composition is needed. For Al-free silicate liquids, available enthalpy data for a variety of compositions are generally consistent with linear variations of the heat capacity with composition, even though the temperature dependence of the heat capacity may also depend specifically on composition ( RICHET and BOTTINGA, 1985). However, available data for aluminosilicate liquids are inconsistent with this simple, linear variation of Cd with composition, with variations which seem to depend specifically on the nature of alkali or alkaline-earth cations

EXPERIMENTAL METHODS The compositions of the investigated melts are plotted in Fig. I. Most of these liquids are not excellent glass farmers and cannot be supercooled over wide temperature intervals. Compositions generally close to eutectics have thus been chosen to investigate temperature ranges as wide as possible, in such a manner that important mineral compositions were also included. The samples were synthetic materials prepared from oxide mixes through repeated cycles of grinding and fusion, as described previously ( RICHETand BOTTINGA,1984a). The MgSiOXsample is the same as that used in low-temperature heat capacity measurements by RICHET et al. ( 1993). The chemical compositions were checked by electron microprobe analyses (see Table I), even though the nominal values are thought more accurate. They are simply indicated by the labels MgY.x, where Y and x give the mole fraction of SiOz and A&O,, respectively. Most of the calorimetric data will be referred to formula weights (gfw) for which the oxide mole fractions sum to 1 (Table 1). 1267

1268

P. Courtial and P. Richet

FIG. 1. Compositions investigated. The 3/ I and I / 1 binary joins dealt with in Figs. 4 and 7 are shown by the solid lines. Solid squares: compositions of Table 1; open square, solid circles and open diamond: compositions investigated by RICHETet al. ( 1982) R~CHETand BOTTINGA ( 1984b), and RICHET and NEUVILLE( t992), respectively.

Heat capacities have been determined through relative-enthalpy measurements made with the drop method. The synthesized materials were loaded in Pt-Rh 15% crucibIes and heated at temperature T before being dropped into an ice calorimeter in which the relative enthalpy HT - Hz73released during cooling was measured. The calorimetric apparatus and procedures have already been described in detail ( R~CHETet al., 1982). With the exception of MgSiOs liquid, ail the melts investigated vitrified on cooling in the calorimeter. Heatcapacity dete~inations from dro~lo~met~ m~uremen~ on glass-forming liquids are valid only if cooling down to the calorimeter temperature takes place in a reproducible fashion, regardless of the initial temperature. That this condition is actually met in our experiments has been discussed in detail by RICHETand BOITINGA ( 1986). For the materials investigated in this study, the imprecision of the

measured enthalpies is 0.05-O. 10%. This is smaller than the instrumental inaccuracies of less than 0.2 and 0.5% for the measured relative enthalpies and derived heat capacities, respectively, indicated by the measurements made on o-AlzOs with the same apparatus ( RICHET et al., 1982). Additiona errors originate in possible, minor deviations of the actual from the nominal compositions, and in the slight differences between the C, values given by the various (simpfe) analytiCat expressions that can be fitted to the enthalpy data. As discussed pmviously (e.g., RICWETand BOITINGA, 1985), these errors seem small and the overail inaccuracy of the C, data should be about l%, with the greater errors for the heat capacities of glasses (C,), because of the restricted temperature intervals that were investigated below the glass transition. To improve the accuracy of extrapolations down to 273 K of the glass C, data, the room-temperature heat capacities as

Table 1. Comparison between nominal and analysed compositions temperatures (T,)of the investigated materiaW SiOz Mg53.12

Nom. Anal. Mg60.10 Nom. AnaI. Mg59.13 Nom. Anal. Mg50.18 Nom. Anal. Mg65.15 Nom. Anal. Mg50.00 Nom. Anal.

54.82 55.32 (09) 61.79 62.20 (07) 59.09 60.54 (56) 49.01 48.82 (39) 62.92 62.02 (13) 59.85 60.04 (24)

AW3 20.66 20.62 17.48 17.56 22.10 20% 29.94 30.45 24.14 24.23 0. 0.03

(03) (09) (65) (20) (12)

MgO 24.52 23.74 (IO) 20.73 20.20 (06) 18.81 18.41 (57) 21.05 21.22 (141 12.94 14.23(13) 40.15 39.47 (22)

Total

(wt 461, and liquidus

At&? gfw (gl TIOW 2.882

58.031

1640

2.900

58.340

1630

2.980

59.992

1670

3.040

61.295

1720

3.095

62.307

1740

2.500

50.198

1840

99.96 (15) 100.20 (11) 100.13 (86) 100.67 (66) 100.65 (13) 99.80 (04)

*Andyws IIIWJCwith an automated Can&ax etecuon microprobe operated at 15 kV and 10 nA. Totals include NasO,KaO,GO, Ti%, Fe0 and crZ&. bI@, is the nominal numberof atoms per gfw =~~er~~.(l~)

Heat capacity of Mg ~uminosili~te

and the data at the lower and higher temperatures refer to the glassy or the liquid state, respectively. As usual, the glasstransition temperatures (7”) listed in Table 4 were taken as the temperatures at which the enthalpy curves of the glasses intersect those of the liquids. Another feature apparent in Fig. 2 is the abnormal scatter in the results below the glass transition temperature for Mg59.13. Experience shows that calorimetric results depend on thermal history only in the glass transition range, where the highest m~uremen~ probably include the effects of limited configumtional changes. In this case, the lowest enthaipies have thus been used for determining heat capacities. In addition, Fig. 2 shows for most of the materials a few results that are too low in the supercooled liquid field. This is because the product crystallized partially during the long heating stage of the experiments, but not during rapid cooling in the calorimeter; the result is then too low because heat capacities of crystals are much lower than those of liquids. For runs on Mg50.00 (liquid enstatite), partial crystallization set in right after the glass transition, preventing measurements over significant temperature intervals in the supercooled liquid region. According to the phase diagram of the SiO&fgO system dete~ined by BOWEN and ANDERSEN

calculated with the model of RICHET (1987) were added to the enthalpy data base.. The very good agreement, noted in our Results section, between the measured and model enthalpies of these glasses justifies this practice. Without it, the fits could not he extrapolated

accurately helow about 400 K hecause of the large measurement gap between our reference temperature, namely 273 K, and the lowest temperatures investigated, which are comprised between 800 and 900 K.

RESULTS

The experimental relative entbalpies are listed in Table 2, where runs are labelled in chronological order. The data are also plotted in Fig. 2 in the form of mean heat capacities: C, = (Hr - Hz,~)/( T - 273).

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melts

(1)

Because mean heat capacities vary only slightly with temperature, C,,, plots clearly show calorimetric data on an expanded scale, without the fitting bias that can beset the derived heat capacities. In Fig. 2, the heat capacity increases characteristic of the glass transition are thus apparent as breaks in the C, curves. For all materials inviting, the glass tmnsition took place within the temperature range studied

Table 2 Experimental rclative-cnthalpy results(kJ/gfw)* w

T(K)

HT-&

#

Mg53.12 AW.2 AW.3 AW.4 AW.7 AW.9 AW.5 AW.6 AW.10 AW.ll AW.12 AW.1 AW.8

CL2 CI.8 CL4 cr.21 CL7 CL5 CL6 Cl.11 CI. 10 a.9

Cf.15 Cl.12 CI.18” CL20 CI. 19

816.7 947.4 1010.1 1055.7 1058.5 1089.3 1134.3 1192.3 1247.3 1318.7 1662.7 1847.0

T(K)

HT- Hz73

#

TW

CG.2 CG.7 CG.19 CR.8 CG.3d CG.12 CG.17 CG.16 CR.2d CG.18 CR.3d CO.9 CR.4 CG.5 CR.1 CG.4 Co.14 CG.8 CO.10 CG.15 CG.ll CO.13

Mg59.13 818.9 892.4 937.5 981.9 984.9 1021.0 1037.3. 1037.7 1052.7 1052.8 1066.7 1104.5 1104.7 1121.0 1151.5 1196.5 1264.2 1289.8 1385.9 1759.9 1787.9 1839.1

CJ.2 Cr.3 CJ.4 CJ.5 CM. 1 CJ.6 CM.2 CJ.10 CJ.13 CJ.15 CJ.14 CJ.11

Mg5o.00 870.1 929.9 975.7 1012.2 1034.4 1047.3 1053.6 1833.8 1868.0 1880.4 1868.8 1893.4

M&O.10

36.508 41.481 45.957 49.518 52.940 56.136 61.690 66.958 73.507 106.45 124.24

Mg50.18 858.8 37.556 953.1 44.596 919.2 46.463 1011.5 48.925 1020.6 49.652 1034.8 50.773 1071.4 53.589 1093.1 55.633 1120.6 58.243 1173.5 63.697 1224.7 68.907 1271.2 73.472 1316.0 77.853 1768.8 123.76 1799.8 126.95

AV.2 AV.3 AV.4 AV.5 AV.6 AV.7 AV.8 AV.9 AV.lOb AV.1 AV.11

CZ.32c CZ. 1 cz.2 cz.3 cz.21 CZ.37 CZ.38 CZ.5 CZ.35 CZ.25 CZ.26 cz.28b CZ.30” CZ.31 CZ.29

893.7 37.635 957.5 42.129 1040.8 48.110 1108.0 53.376 1167.2 58.800 1168.4 58.882 1229.8 64.620 1324.2 73.246 1421.0 77.835 1651.6 103.87 1836.8 121.32

Mg65.15 521.3 888.1 952.4 1028.5 1104.4 1132.7 1155.8 1186.0 1207.3 1273.6 1323.2 1395.3 1407.3 1777.4 1820.0

14.097 39.432 44.183 49.901 59.800 58.187 60.298 63.163 65.270 71.854 76.457 82736 83.560 120.87 125.12

a simk, ~~-~~~~ set-up 6 Additional expaimcntmade d Resulttoo high because of limited contiprationat changes on cooling

HT-Hz73

33.390 38.730 41.890 45.104 45.582 48.019 49.150 49.197 50.510 50.340 51.497 54.525 54.540 56.140 58.760 63.190 69.490 71.599 80.660 117.01 119.59 124.97

31.883 35.697 38.475 40.665 43.005 43.301 120.01 124.93 128.79 131.43

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V

53.12(-l)

PtG. 2. Mean heat capacity of some magnesium ~lum~nosilicates showing the glass t~n~tion between IO50 and 1 t 50 K, depending on ~orn~~t~on. Solid curves are vahzes as given by the data of Table 3. For cfarity, the data have been displaced upwards or downwards by the numbers indicated in parentheses.

( 19 14 ), incongruent melting of enstatite begins at I830 K (to 5% forsterite plus liquid) and ends at 1850 R, A few measurements were also attempted at temperatures higher than 1850 K even though they were higher than the nominal capabilities of our furnace. If enstatite had crystallized only on cooling to 273 K, the measured relative enthalpies would be intermediate between the two limiting curves plotted in Fig. 3, depending on the crystallized Ii-action; with complete

glass formation, the enthalpies would plot on the lower curve, whereas total c~s~l~i~tion would correspond to the higher curve. Our data plotted in Fig. 3 would suggest that more than half of the hquid crystallized on cooling in a nonreproducible manner which prevented heat capacity determinations. Su~~sin~y, however, this crystallizing fmction seems to depend on the initial temperature of the liquid before the quench, which could be related to the observation made by BOWEN and ANDERSEN ( i 9 I4 ) that forsterite and “silica” can ahso crystahii on coobng Iiquid MgSi03 _~nfo~~nate~y, the contents of the crucible could not be examined after the experiments to check the relevance of this observation to our results.

The calorimetric data could be reproduced to within their error margins with least-squares fits made with usual MaierKelIey equations, C,; = a + bT + c/T2, H,- - I& RG. 3. Roiative enthalpy of orthoenstatite and MgSR& glass and liquid. Experimental data at the higheat temperatures platted as solid squares The lower and upper curves shown for the amorphous phases refer to the entkalpy of the liquid relative to the glass and crystalline

phases at 273 K, respectively. The notations T,, T,, and Ak+refer to the calorimetric glass transition temperature, the metastabIe congruent melting point, and the enthalpy of fusion, respectively. Values calculated from the heat capacities of orthoenstatite, as given by BERMAN and I3noW ( 1985), of Mg!SiOI glass fmm Table 2, and of higSi0~ hquid from the model values of RKHET and BOTTINGA ( 1985); enthaipy of vitrification (Fw,) of MgSiQ at 974 K from HERVIG et al. ( 1985 1. Note that the uncertainties of ah the data are negIigibIe in a plot drawn at that scale.

= Rz73 -+ aT -k bTZf2 - c/T,

(21 (3’5

where the constant i& is an adjustable parameter only for the liquids. For @asses, it is determined by the constraint Hr - ffz73 = 0 for T = 273.15 K. These fitted enthalpy and C, equations are given in Tabie 3 for the liquid and glassy phases, along with the average absolute deviations (AAD) oftbe fitted values from the experimental enthalpies. Direct comparison of these results with other experimental data cannot be made, these materials having not been studied previously. The only exception is MgSO,OOf enstatite f , which was run by Rifferential Scanning Calorimetry (DSC) in the glass form by STEeBfNs et al. ( 1984) and adiabatic calorimetry by RICHET

Heat capacity of Mg aluminosilicate

1271

melts

Table 3. Coeffkients of HT - Hz73= R273 + aT + bl?2 - c/T + 2d10” (J/gfw)andC, = a + bT + cfl + dt’lQ.5(J/gfwK)* R273

a

1O’b

d

m-5,

A”

AT(K)

AAD

Mg53.12 liquid -47202 glass -22178

88.555 57.994

4.624 0. 15.722 -15.708

0. 0.

7 4

1089-1847 877-1058

0.08 0.03

Mg60.10 liquid -45642 glass -224%

87.004 58.649

4.246 14.792

0. -16.182

0. 0.

7 3

1108-1837 894-1041

0.04 0.01

Mg59.13 liquid-38986 glass -35302

78.126 78.732

11.922 -1.224

0. -37.810

0. 11 0. 6

1W-1839 819-1067

0.14 0.11

Mg50.18 liquid-54824 glass -24903

100.98 64.390

0. 13.488

0. -18.607

0. 0.

7 7

1093-1800 859-1071

0.08 0.07

Mg65.15 liquid-52547 glass -20959

97.581 57.538

0. 19.944

0. -12.289

0. 0.

7 6

1156-1820 521-1133

0.08 0.09

-1165.

5

277-1054

Mg50.00 glass -9659.3 109.63

-10.880

1.8849

0.15b

aR273 is an adjustable paramctex for liquidsonly,seetext.N is thenumber of experimental data in thetemperature interval AT andAAD theaverage absolute deviation of thefitteddatafromthe expcrimentalcnthalpics b AAD of 0.66 96 for thefittedD.S.C. measurements of ST!ZBBINS eral. (1984) calculated at 50 K intervalsbetween 400 and850 K: AAD of 0.08 % for the21 adiabatic measurements of RICHETet al. (1993) bctwcen 277 and355 K.

et al. ( 1993). Over the temperature interval where these measurements overlap, the heat capacities are consistent. Heat Capacity of Glasses

Temperature Dependence of the Heat Capacity of Liquids

The heat capacity of a material is simply related to the partial molar heat capacities (Cpi) of its oxide constituents by CD = C Xicppi,

range from 6 to 30% of C,. These AC, data do not correlate simply with Tg, broadly increasing with lower Si02 contents but depending little on the amount of AlzO,.

(4)

where Xi is the mole fraction of oxide i. For silicate glasses, the heat capacity increases continuously with temperature, as for any other solid materials. The composition dependence of the heat capacity is very simple, however, since the available calorimetric data are consistent with an ideal solution model, i.e., composition independent partial molar heat capacities (e.g., BACON, 1977; STEBBINS et al., 1984; RICHET, 1987). In Eqn. 4, one has thus Cpi = C’:i, whose temperature dependence is adequately reproduced by Eqns. like 2. As a matter of fact, the enthalpies calculated from the C, set derived by RICHET ( 1987) deviate little (AAD = 0.26%) from the experimental values of glasses in Table 3. This provides yet another example of this extensively discussed additive behavior, which does not warrant further comments in this paper.

The temperature dependence of C, also changes significantly at T,, becoming slight enough that expressions simpler than Eqn. 2 must be used. With a few exceptions, data for melts are generally consistent with constant or slightly increasing CP’s. In any case, only measurements on wide temperature intervals may allow detection of possible temperature dependent heat capacities (e.g., RICHET and BOTTINGA, 1985). This was another reason for studying the glass transition in order to investigate supercooled liquids up to the temperatures at which crystallization could no longer be eventually avoided. As discussed previously (RICHET and BCYITINGA, 1984b), there seems to be no significant loss in accuracy when data must be interpolated over this crystallization gap up to the stable liquid range. [The only apparent exception is liquid pyrope, for which a constant C, was reported from measurements made over the very restricted temperature ranges 1083-1226 and 1844-1863 K ( RICHET and BOTTINGA, 1984b). A slightly temperature dependent C, was actually redetermined by TBQUI et al. ( 199 1) for reasons of consistency with the data on Mg53.12 and Mg60.10.

Glass Transitions From the data of Table 3, one obtains the parameters listed in Table 4, which show that the glass transition takes place when the glass C, becomes close to the harmonic limit of C’,, the iscchoric heat capacity, namely 3R per gram atom ( =25.0 J/g atom K) where R is the gas constant. This is in agreement with previous data for silicates summarized by RICHET and BCFITINGA( 1986). The marked increases in C, at the glass transition listed in Table 4, AC, = (CM - C,,) / C,,, are also consistent with those previously observed for silicates, which

Table4. Heatcapacity at the glass transition (J/gatom K) T, 6) Mg53.12 Mg60.10 Mg59.13 Mg50.18 Mg65.15 Mg50.00

1077 1089 1067 1080 1139 1056

Cps 25.54 25.31 24.87 25.45 25.62 24.98

CPl 32.48 31.60 30.48 33.22 31.58 33.43’

ACP(%) 27 25 23 30 23 34

*Model valueof R~CHET andBOTIWGA (1985). cf. Table 5

P. Courtial and P. Richet

1272

it reproduces slightly better the data, the improvement of this fit over the originally selected constant C, was not deemed significant in the former publication.]

Although

Composition Dependence of the Heat Capacity of Liquids The binary joins covering the widest composition ranges investigated in this study are those between pure SiOz and ~A1203 .( 1 - x) MgO compositions (Fig. I ) . As shown in Fig. 4, these data indicate that, within experimental un~~nti~, the com~s~tion dependence of C, is linear down to pure SiO, Iiquid even though the temperature dependence becomes stronger when the alumina content increases. In ather words, the partial molar heat capacity of SiO* is temperature and composition independent along these joins, as found previously for Al-free silicate melts over temperature intervals which can span more than 1000 K ( RICHET and BOTTINGA, 1985). To examine the composition dependence of the partial molar heat capacities of MgO and A1203, we have simply plotted in Fig. 5 the heat capacities of liquids along the MgOA&O3join as given by linear exhalation of the trends shown in Fig. 4 for SiOz-xA1203.( I - x)MgO compositions. The uncertainties ofthese extrapolated values could be somewhat higher than those of the data plotted in Fig. 4. Nevertheless, a linear variation is again observed in Fig. 5, without a significantly higher scatter in the data. This indicates that the partial molar heat capacities of both MgO and A1203 do not depend on composition. For SiOz-rich magnesium aluminosilicates, the available data are thus consistent with an ideal solution model for the heat capacity. interestingly enough, the partial molar heat capacity of MgO derived from these linear variations is 85.94 J f mol K. Within its estimated 1% unce~ainty, it is thus indistinguishable from the value 85.78 J/m01 K previously determined for Al-free melts (RICHET and BOTTINGA, 1985). For the sake of consistency, the partial molar heat capacities of SiOz and MgO were constrained to the temperature independent

FIG. 5. Extrapolated heat capacities atong the join MgO-A1203. Solid and open squares: data at 1800and 1200 K, respectively, from linear fits of the data of Fig. 4, where the value given for MgO is the temperature and composition independent partial molar heat capacity obtained by RICHET and BOTTINGA ( 1985) for Al-free melts; Bal. I800 K: heat capacity ofpure AIzO, liquid as obtained by BARKHATOV et al. ( 1973) from drop-calorimetry measurements; Sal. and LN: model values of STEBBiNset al. f 1984) and LANGE and NAVROTSKY ( 1992), respectively.

values obtained for Al-free melts. Although the partial molar heat capacity of A1209 also does not depend on composition in the range covered by this study, it does depend on temperature. The value given in Table 5 was determined from a simultaneous least-squares fit of the data for all the compositions represented in Fig. 1, which was made as described previously by RICHET and BOTTINGA( 1985 ) . Of course, the Gibbs-Duhem equation is obeyed with this ideal solution model, and with the data listed in Table 5 all input relative enthalpies are reproduced with an average absolute deviation of 0.12%. No signi~~ntly better quality of fit was obtained when the partial mofar beat capacities were also considered as adjustable parameters, whereas a temperature independent value for A1203 could not reproduce the experimental data to within their experimental uncertainties. Comparison with Previous Models

140 -

1800K

-I

The first model of prediction of the heat capacity of geochemical interest for melts has been the ideal solution model of CARMICHAELet al. (1977), which was mainly based on their own measurements on seven compositions. This model has been extended and updated by STEBBINSet al. ( 1984) with their own measurement (STEBBINSet at., 1982, 1983) and data from our iaboratory. More recently, LANGE and NAVROTSKY( 1992) have added to this data base direct hightemperature heat-capacity measurements on iron-bearing Table 5. Comparisonbetween model partialmolar heat capacities(J/mo~K) Oxide

moi % SiO, FIG. 4. Heat capacity of liquids along the SiQ-xA1203.( 1 - x)MgO joins shown in Fig. I. The solid and open symbols refer to 1800 and I200 K, respectively. Data from the individual fits of Table 3.

SiOz Mgob 403

CpO=a+lO-3bT’ a b

et al. (1984)

81.37 0 85.78 0 130.2 35.7

80.0 99.7 157.6

STEBBINS

LANOEand NAVROTSKY (1992)

82.6 94.2 170.3

aThis wor& estimated mdnties of about 1% for the partialmolar heat capacities cahlated from the listed coe&ients b Value for At-free melt obtained by RICKET and BOTIWGA(1985)

Neat capacity of Mg aluminosilicate meits liquids and derived a new set of partial molar heat capacities. In all of these models, the partial molar heat capacities are consideti independent of temperature and composition and were determined from data bases with a majority of measurements for stable liquids. They are included in Table 5 along with our own data for magnesium aluminosilicates. The difference between these model values concerns not only AlzOa, but also MgO. As a result, the model values of STEBBINSet al. ( 1984) and LANGE and NAVROTSKY (. 1992 ) tend to overestimate the heat capacities determined in this study by 2 to 6%~~with the greatest dilferences at the lowest temperatures. A rn~n~~~on of these di&rences is given in Fig. 5 by the various ideal model values plotted outside their composition range of validity. DISCUSSiON

NonideWy of Aluminosilicates As apparent in Fig. 5, the partial molar heat capacity of A&O3 obtained for Mg-rich aluminosilicates are consistent with bath the heat capacity of pure A1203 liquid and its temperature dependence, as determined by BARKHATO~ et al. f 1973 ) from drop-calorimetry measurements made between 2300 and 3100 K. Even though the reported uncertainty of these data is about 595, the wide temperature range of the m~urements should ensure a reliable extrapolation down to 1800 K at least. In other words, this consistency suggests that an ideal solution model would be valid throughout the whole system MgO-A1203Si02 and that the linear variation of the heat capacity indicated by the solid lines in Fig. S are thus likely estimates. However, the manner in which liquidus temperatures increase and the glass-forming ability of melts deteriorates when the alumina content increases makes measurements impracticable with our calorimetric setup outside the composition range investigated in this study.

1273

If ~urn~nosiIi~t~ were generally behaving as ideal solutions with respect to the heat capacity, then the partial molar heat capacity of A1203 as given in Table 5 could be used in conjunction with the values previously obtained for all the other oxides considered by. RKHET and IWM'INGA ( 1985). For calcium aluminosilicates, however, this approach would not account far the available measurements, which indicate in particular a stronger temperature dependence for the partial molar heat capacity of Al& in Ca- than in Mg-bearing melts {RICHET and BOITINGA, 1984% RICHET and NEUVILLE, 1992; Court&l, unpubl. data). Likewise, a comparison of the values calculated in this manner with ex~rn~~l data for the join SiQ-NaAlz04 shows serious ~ment, especially at the lowest temperatures where C, does not vary linearly down to pure SiOz liquid (Fig. 6). In fact, the temperature dependence of the heat capacity is so much stronger for alkali than for alkaline-earth aluminosilicates that this feature alone would make an ideal solution model inappropriate. In other words, the nonideal behavior of aluminosilicates in these ternary systems is the result of specific interactions between aluminum and alkali or other alkaline-earth elements. Note that these complexities are also apparent when dealing with more complex compositions where these different kinds of intemc~ons are borne out in the same manner (NEUVILLE et al., 1993). The present results have some bearing on the enthalpy-ofmixing measurements made by HERVIGet al. ( 1985) on magnesium aluminosilicate glasses. The additivity of the liquid heat capacities implies that enthalpies of mixing are temperature independent in the MgO-Alz03-Si02 system. On the other hand, the relatively high glass transition temperatures of magnesium aluminosilicates (Table 4) su~ests that all the samples investigated by HERWGet al. ( f 985 ) were not fully relaxed at 974 K, the tempemture of their solution calorimetry measurements. This leaves open the possibility that a correction for varying fictive temperatures should be applied to these results to obtain the actual enthalpies of mixing (e.g., RKHET and BO-ITINGA, 1986). If the spread in the glass transition temperatures reported in Table 4 is representative of magnesium aluminosilicates, however, this effect would be almost negligible since it would amount to less than 1 W.

ConfigurationalHeat Capacity

mol % SiO, FIG. 6. Heat capacityalong the join SiOz~NaA12C& I Solid and open squares experimentaldata from RICHET et al. ( 1982) and RICHET and BOTTINGA ( 1984a) at 1800 and 1200 K, respectively;Sal. and LN: model values of STEBBINSet al. ( 1984) and LANGE and NAVROTSKY ( I992 ); 1800 and I200 Kz values calculatedwith the data of Table 5 and the partialmolar heat capacityof Na& obtained for AI-free meltsby RICHETand BOTTINGA(~%~).

The configurational heat capacity ( Cyf) represents an energy that is used to change the structure of a liquid in response to temperature variations. For silicates, a much simplifying feature is that C* can be taken as the &‘,difference between liquids and glasses at the glass tuition tern~m~~ ( mCHET et al., 1986). In fact, the uncertainties of the heat capacity of glasses are somewhat higher just below the glass transition than at lower temperatures because of the aforementioned possible effects of thermal history in this temperature range. Within experimental uncertainties, the deviations of the data of Table 4 from 3R are not significant, and we will thus assume in the following that, on a g atom basis, the configurational heat capacity is given by

I274

P. Courtial and P. Richet

mol % SiO, FIG. 7. Configurational heat capacity along the same SQxAlrO3.( I - x)MgO joins shown in Figs. I and 4. The solid and open symbols refer to 1800 and 1200 K, respectively. For comparison, the value calculated for MgSiOs from the C, model of RICHET and BOTTINGA( 1985) is included as an open diamond.

Finahy, aluminum is essentiahy fourfold coordinated in magnesium aluminosilicate glasses ( MERZBACHER et al., 1990), whereas magnesium seems to have a coordination of the order of 6 ( RICHET et al., 1993). Part of the reason why both the partial molar heat capacity of AlzOs and its temperature dependence are so specific could thus originate in temperature-induced changes of aluminum or magnesium towards higher and lower coordination numbers, respectively, in a manner that would depend on the alkali or alakalineearth cations present in the melt. The existence of high coordination states for network-foxing cations has been detected recently (e.g., STEBBINS et al., 1992). The diflicuity is that one cannot guess a priori the way coordination changes influence the configurational heat capacity, in contrast to their influence on the density or viscosity. High-temperature structural data are thus needed to complement the thermochemical information.

Acknowledgments-We

thank D. Neuville and C. T&qui for their help at various stages of this study, and A. Navrotsky and J. I? Stebbins for comments. Contribution CNRS-INSU-DBT 489.

~dit~~ria~handling: P. Hess The values calculated with Eqn. 5 are plotted in Fig. 7 for +( 1 - x)MgO joins. Since the heat capacity of liquids is an additive function of composition for magnesium aluminosilicates, the configurational heat capacity conforms to the same trend. On the g atom basis used in Fig. 7, one observes in addition that the data for different joins at the same temperature plot on the same straight line. Hence, Cry depends only on the Si/( Mg + Al) ratio, with a fivefold increase between 100 and 42 molW SiO*. The liquids investigated in this study encompass a wide range of degrees of ~lyme~~tio~, and their viscosity, for instance, spans many orders of magnitude even along joins like SiOz-MgA1204 (RIEBUNG, 1964). These linear variations of CgWfthus suggest that the temperature-induced structural changes taking place in magnesium aluminosilicate melts depend mainly on the basic structural units that do not change much with composition, not on the details of the structure. Hence, it is tempting to assume that most of the configurational heat capacity is associated with short-range oxygen-cation interactions. SiOrxAlaOs

BOTTINGA et al. ( 1982) concluded that the composition dependence of the molar volume was not linear for aluminarich silicate melts, in accordance with the marked changes in the viscosity-com~sition ~Iationship that have been reported at ratios of aluminum over network-maiming cations of about unity (e.g., RIEBLING, 1964). Again, these features do not seem to correlate with the linear variations of the heat capacity. On the other hand, liquid immiscibility in silicate melts can be viewed as the result of competing cations trying to optimize in different ways their oxygen coordination. That the configurational heat capacity of magnesium aluminosilicates is roughly twice as great as that of their alkali counterparts is thus consistent with the much wider extent of liquid immiscibility they show.

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