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An assessment of the one-bar liquidus phase relations in the MgOSiO2 system
CaiphadVol. 18, No. 2, pp. 157-184.1994 Copyright (D 1994 Elsevier Science Ltd Printed in Great Britain. All rights resewed 0364-5918/‘94 $7.00 + 0.00
Pergamon
0364-5916(94)
00066-g
AN ASSESSMENT OF THE ONE-BAR LIQUIDUS PHASE RELATIONS IN THE MgO-SiO, SYSTEM
V. Swamy’, S. K. Saxenat, and B. St&man2 1 Instituteof EarthSciences,Theo&al Geochemi.sl?y, Uppsda University,Norbyv@en18 B, S - 152 36. Upps& Sweden 2 Divisionof PhysicalMebhrgy. RoyalIdtute of Technology Stockholm, S - 10044. Sweden
ABSTRACT
An assessment of the thermodynamic properties of the liquid phase in the MgO-SiOs system at one bar is performed using the calphad technique. The liquid is described using a two-sublattice ionic liquid model. The thermodynamic data for the solid phases used are from previous evaluations considering high pressure and high temperature phase equilibria and the available calorimetric data. With the assessed parameters, the experimental phase relations are reproduced very well and a good agreement is obtained with the calorimetric data on enthalpy of fusion.
Introduction The availability of a large amount of high-temperature and high-pressure phase equilibria data and calorimetric data for the MgO-Si02 system has resulted in a number of thermodynamic assessments of this binary. Thermodynamic properties of the subsolidus phases to high pressures and high temperatures were recently assessed by Fei et al. (l), Saxena and Shen (2) and Shi et al. (3). Swamy et al. (4) evaluated the SiO, system including the liquid and the high-pressure solids. We present here an assessment of the thermodynamic pmpetties of the MgO-SiO, liquid at 1 bar using data for the solids from above sources, compiled in Saxena et al. (5), and by adopting the two-sublattice model of Hillert er al. (6) for the liquid phase. The recent evaluations of the MgO-Si02 phase relations at one bar were done by Blander and Pelton (7). who applied a modified quasichemical liquid model, by Howald and Scanlon (8) using a Redlich-Kister model for the liquid, and by Hillert and Wang (9). who applied a two-sublattice model for the liquid and a compound energy model for per&se (in order to model solid solubility of SiO2 in periclasc). Our assessement differs from these in that in the assessment we include enthalpy of fusion data for the liquidus phases and for reasons discussed below disregard solid solubility of SiO, in per&se. The one-atmosphere phase diagram of the MgO-SiO, system was first presented by Bowen and Andersen (10). The crystalline phases of the system are: periclase (MgO), forsterite (Mg$iO&, the pyroxene (MgSiOs) polymorphs (protoenstatite, otthoenstatite and clinoenstatite) and the silica polymorphs (cristobalite, tridymite. &quartz and a-quartz). Bowen and Andersen (10) found that forsterite melts congruently at 2163 K and pmtoenstatite melts incongruently at 1830 K to yield forsterite and liquid. As the phase relations were not examined for 60 years after the first determination by Bowen and Andersen, Chen and Presnall(l1) redetermined Original
version received on 7 June 1993, Revised version on 22 September 157
1993
158
V. SWAMY
et al.
some critical parts of the phase diagram. The results obtained by the latter workers agree completely with the results of Bowen and Andersen. G&g (12) fast observed liquid immiscibility in the silica-rich portion of the binary which was later investigated by Ol’shanskii (13) and Hageman and Oonk (14). While most of the solid phases of the system have near-stoichiometric compositions, there have been conhadictory experimental results on the solid solubility of SiO, in periclase. Schlaudt and Roy (15) mported that 0.11 mole fraction Mg$IiO, (corresponding to 0.09 mole fraction Sit&J could be accommodated in MgO at the eutectic temperattne of 2123 K. However, other workers observed very low or no solubility of silica in periclase (e.g., 16-18). The stability fields of the SiO, polymotphs are rather well established. The stability relations of the pyroxene polymorphs. especially dun of clinoenstatite, however, are not yet clear. The available experimental data on the clinoenstatite (P2t/c)-orthoenstatite (Pbca) transition (19-21) do not agme well with one another. An extrapolation of the high-pressure data of Boyd and England (21) to one bar yields a temperature of 903 K for this transition (3). The orthoenstatite-pnstatite (Pbcn) transition is located between 1248 K and 1268 K (22). Additionally, them is a high-temperatute clinoenstatite (C2Jc) which is the liquidus phase with a narrow stability field at pressures just above 1 bar (23). However, as its stability at 1 bar is not known accurately, we assume pro~statite to be the liquidus mineral at 1 bar as done by most previous workers (e.g., 25). There have been a number of direct and indirect determinations of enthalpies of fusion of the liquidus minerals (e.g., 8.24-27). For periclase, the CODATA recommended values for the temperature and enthalpy of fusion am respectively 3lOOQ5 K and 77.0 kJAnol(28). Navtotsky er al. (24) using transposed-temperature drop calorimetry determined an enthalpy of fusion of 114+20 kJ/mol for forsterite at its melting temperature. From dmp calorimetric and solution calorimetric data, Richet and Bottinga (26) obtained an enthalpy of 73.2~16.0 kJ/mol for the metastable congruent melting of enstatite. Richet er al. (27) estimated an enthalpy of fusion of 8.92~tl.OkJ/mol for cristobalite at the melting temperature of 1999 K.
‘Thermodynamic functions and the liquid model Thermochemical data for a phase can be reptesented in terms of its enthalpy of formation at 1 bar and 298.15 K, A!f&,ss.t~ the entropy at 1 bar and 298.15 K, S”t,29s,t5, and the heat capacity at constant pressure expressed as a polynomial on temperatute, C,(T),. for the compound from 298.15 K. We use the following formulation for the heat capacity, CP(7) [see Saxena et al. (S)]: CP(T) = a + bT + CT-* + dT* + eTm3+ fl-ln + gT-I.
Ul
The liquid phase is described by adopting the two-sublattice ionic liquid model of Hillert et al. (6). In this model the liquid phase consists of two sublattices. one for the cations and another for the anionic species. The liquid is represented by the formula (Mg*+)p (o?-,SiO., 4m.Si02)q, where p and q are the number of sites on each sublattice. Here q=2. and in order to maintain electroneutrality, p=4ySi044-+2y02- where y is the site fraction. The Gibbs energy per formula unit is given by [see Hillert et al. (6)]: Cm = yOa- S;Mg?@-
+ ySi04”- “Y;Mg42+(Si044)2+2ySi0, SGSiO,
+ 2RT (y@ In yOa-+ ySi044- In ySi04q + ySi0, In ySi0;) + EGm.
PI
The excess Gibbs energy, EGm , depends on the interactions between species in the anionic sublattice. We use the same approach as that of Hillert and Wang (9) to describe the excess Gibbs energy. Accordingly, only the
ASSESSMENT
159
OF THE MgO-SiO,SYSTEM
interaction of SiO, with Os- and SiOd4- is considered. The same interaction energy parameters L(Si044--Si0,) and f@--SiO,), counted per negative charge as “L(SiO, 4--Si0,)=2nL(02~-Si02). and with terms upto ‘L (in order to account for the asymmetry in the miscibility gap) are included. Thus we have: EC, = yO*ySiO,
[“L+~L(y02- -ySiO,) + 2L(@2- -ySi02)* + ‘L(yO*- -ySi02)3]
+ 2ySiOb4- ySi0, [0L+‘LCySi044-- ySi0,)+2L( ySi044- - ySiO,)* + 3L(ySi044- -ySi02)3J.
[31
The L parameters vary linearly with temperature.
TABLE 1
Thermodynamic Roperties of the Phases in the MgO-SiOz System at 298.15 K and 1 Bar Phase a-quartz hum
Tridymite Cristobahte SiO, Liquid Periclase MgO Liquid Forsterite Protoenstatite Orthoenstatite Clinoenstatite
AHo/J/mol
S”J/mol/K
Cp“J/mol/K
-9 10700.00 -910497.00 -906913.00 -906034.00 -901013.00 -601490.00 -531270.00 -2174140.00 - 1545794.00 - 1546290.00 -1548715.00
41.460 41.700 45.116 46.060 49.033 26.940 49.479 94.110 66.960 66.270 63.230
44.589 44.589 44.254 44.299 44.217 37.28 1 37.222 118.638 81.595 82.225 81.772
Experimental
data
The experimental data were reviewed by Hillert and Wang (9). We use the phase diagram information from Bowen and Andersen (lo), data on liquid immiscibility from Hageman and Oonk (14) and Greig (12), the activities of MgO and SiO, in the liquid by Kambayashi and Kato (29) and the enthalpies of fusion data discussed earlier. All the solids in the system are treated as stoichiometric compounds. As mentioned earlier, measurements of solubility of SiO, in periclase by different workers gave contradictory results and in some assessments the solubility of silica in periclase was considered (e.g., 7.9). We accept the results of Henriksen and Kingery (18) which show very low solubility of SiO, in MgO.
V. SWAMY
100
et al.
TABLE 2 Coefficients for Heat Capacity, C,(7). J.mol-‘.K-1
Cp(T) = a + bT + CT-~ + dT2 + CT-~ + fl’-lR + gT-’ Phase c (10-4)
d(l@)
18.2800
-18.0986
540.5800
1.2050
113.1000
a
b UC’?
298.15-848K
81.1441
848-4OOOK
18.8120
'298.15-848 K
81.1441
18.2800
-18.0986
848-4OC0K
18.8120
1.2050
113.1000
66.6993
5.2119
e(lO-‘)
f
g(lO-‘)
H+
a-quartz 698.458
o.cxm
1.202
0.000
-1.213
540.5800
0.000
698.458
o.GuO
0.0000
1.202
O.WM
-1.213
-213.2338
-35.4183
O.OMl
o.ooo
0.000
-3083.8590 -1911.8161
31256.50
0.000
0.000
0.000
99.4385
0.000
o.Oal
0.000
o.oooo 10.532243
o.ooo
0.000
o.oooo
0.000
0.000
o.OaI
0.0000
1.I440
0.000
0.2411
O.OCKlO
0.m
0.84
&I~~ 0.84
Tridymitc 298.154000K Cristobalite 298.15523 K 5234OMIK
9011209
-1.62024
14.9325
440.5322
SiO2 Liquid 298.15-1480K
13.1932
1.6186
14804000 K
81.3100
O.oooO
45.4900
4.7730
-216.OWO
4.6536
-103.3800
Xi20.6124 0.0000
Pcriclnsc 298.154ooo K MgO Liquid 298.15-1100K
41.4811
llOO-3OMIK
18.3112
300&5100K
94.2000
o.Ooal
165.8ooo
18.55W
-210258
O.OCKI
o.O@l
0.0000
516.2028
0.000
0.000
o.Oow
o.coOO
o.Oal
o.ooo
o.OOcn3
-391.1000
0.0000
2.8610
O.C@O 0.5610
-19.4688 -1118.3100 o.oooo
Porstcrite 298.1540&l K Protoenstntite 298.154000K
144.3100
1.8919
-134.9500
0.0000
4.6265
0.000 -1.9563
144.4500
1.8820
-135.oooo
O.CNIO
4.6120
0.000 -1.9380
138.0791
8.1088
O.OOW
O.ooO -1.8888
Ortboenstatite 298.154000K Cliaoeastatite 298.15-4oooK
40.5900
-135.2318
t - Enhlpy of transition.kJ/mol.
Thermodynamic data and assessment Thermodynamic data for quartz, tridymite, cristobalite, liquid silica, periclase. forsterite and pyroxenes are from earlier assessments (l-4). The Cp for liquid MgO used by Hillert and Wang (9) is 84 J.mol.‘.K-1 which is the same as the CODATA ncommendation
(28). This value, however, is taken as similar to the Cp of liquid Be0
We optimized the thermochemical properties of liquid MgO by adopting a Cp of 94.2 J.mol-‘.K-1 which is the partial molar heat capacity derived by Lange and Navmtsky (30) for liquid MgO through systematic analysis of a large amount of data on multicomponent liquids. Our data on enthalpy and temperamre of fusion of periclase using these data am in close agreement with the CODATA recommended values (28). The thermodynamic data
ASSESSMENT
OF THE MgO-SiO,
SYSTEM
161
for all the phases are listed in Tables 1 and 2. The parameters for the liquid phase were allowed to vary during the optimization wormed using the program Purrot fmn Thcmw-Cdc databank package (31). This optimizer works by minimizing an error sum and is capable of handling all kinds of experimental data simultaneously.
TABLE 3 Assessed Model Patameters for the Liquid Phase Parameter
Assessed values
OL ‘L
148550 - 73.5653 1102 176615 - 59.3847
*L ‘L
-2500
0GM~2+(Si0,4-h-4”GMg0 Liq-20GSiOzLiq -322263+ 63.7227
I
I
I
I
I I
q ltlcgmanhOonk1986 FIG. 1 The calculated high temperamte patt of the MgO-SiO, phase diagram. Experimental data on liquid immiscibility from Hageman and Oonk (14) are also shown. Per - periclase, Fo forsterite. Pen -protoenstatite, Crs cristobalite. Trd - tridymite.
0 A
0.2
0.4 Mole
fraction
0.6 SiO,
0.8
1.0
V. SWAMY et al.
162
TABLE 4 comparison of Experimental Phase Equilibrium and Calorimetric Data with that calculated
Using Our Data Equilibrium
Experimental
Calculated
Perichse -fwsren’te eutectic: Temperature, K Composition of liquid, x(SiOz)
2123 0.310
2128 0.300
Forsterite - protoenwatitepetite&:
1830 0.515
1830 0.523
Protoenstatite- cris&alite entectic:
Temperature, K Composition of liquid, x(SiOJ
1816 0.545
1821 0.544
Temperature, K Composition of liquids, x(Mg0)
1968 0.415. 0.020
1968 0.410, 0.014
Melting of periclase:
Temperature, K Enthalpy, kJ/mol
31OOi25 77.00
3083 75.00
Melting offorsterite:
Temperature, K Enthalpy, kJ/mol
2163 114.W20.00
2160 92.40
cOtl@l&?flt
Temperature, K Enthalpy, kJ/mol
1834 73.20.16.00
1834 68.42
Temperature, K Enthalpy, kJ/mol
1999 8.92il.00
1998 8.91
Temperature, K
1248-1268
1257
Temperature, K
Uncertain
903
Temperature, K Composition of liquid, x(SiOJ
Two liquids - cristobalite:
Idti?l~
Of PrOtOe~rarire.’
Melting of crisrobalite:
Protoe-
- orthoed:
orthoenWatitt? -cii7wenstarite:
Results The assessed model parameters for the liquid are given in Table 3. Figure 1 shows the calculated phase diagram of MgO-SiO, system. The liquid immiscibility data from Hageman and Conk (14) are shown in Fig. 1. The calculated activities of SiO, and MgO in the liquid are compared with experimental measurements by Kambayashi and Kato (29) in Fig. 2. Since a better tit of the calculated activity to experimental data would result in the substantial underestimation of the fusion enthalpy of forsterite and protoenstatite. we accept the present results. Table 4 shows that the calculated data am consistent with the experimental phase equilibria and calorimetric data.
ASSESSMENT
OF THE MgO-SiO,
I
1.0 0.9-
T=1973K
0.9-
0.8-
0.8-
0.7-
0.7-
163
SYSTEM
I
I
0.50
0.55
T=1973K
0.6-
0.5-
0.5-
0.4-
-
0.3-
5 <
0.20.1o
A
(a>
O.&l
I
o.&
I
0.50
I 0.55
0.60 A
0.40
0.25
Mole fraction 30,
0.60
Mole fraction SIO,
FIG.2 Comparison of calculatedactivity
of (a) SiO, and (b) MgO in the liquid with experimental data (circles) from Kambayashi and Kato (29)
Acknowledgements V.S. acknowledges the valuable discussions with Bengt Hallstedt. This work was financially supported by NUTEK through the CAMPADA project and by a grant from NFR to S.K.S.
References 1. Y. Fei, S. K. Saxena and A. Navrotsky, J Geophys Res 9569156928
(1990).
2. S. K. Saxena and G. Shen, J Geophys Res 97, 19813-19825 (1992).
3. P. Shi, S. K. Saxena, 2. Zhang and B. Sundman, accepted for publication in Culphad (1993). 4. V. Swamy, S. K. Saxena, B. Sundman. and J. Zhang, submitted to .I Geophys Res (1993). 5. S. K. Saxena, N. Chatterjee, Y. Fei and Ci. Shen, Thermodynamic Data on Oxides and Silicates, Springer-Verlag (1993). 6. M. Hillert, B. Jansson, B. Sundman and J. &en, Met Truns 16A, 261-266 (1985). 7. M. Blander and A. D. Pelton, Geochim Cosmochim Acta 51,85-95 (1987). 8. R. A. Howald and M. J. Scanlon, Calphad 13,33-43 (1989). 9. M. Hillert and X. Wang, Culphud 13,253-266 (1989). 10. N. L. Bowen and 0. Andersen, Amer J Sci (4th series) 37,487-500 (1914). 11. C. -H. Chen and D. C. Presnall, Ame< Mineral 60,398-406 (1975). 12. J. W. Greig, Amer J Sci 13, 16-153 (1927). 13. Ya. I. Ol’shanskii, Dokl Akad Nauk SSSR 76,93 (1951). 14. V. B. M. Hageman and H. A. J. Oonk, Phys Chem Gfurses 27, 194-198 (1986). 15. C. M. Schlaudt and R. Roy, J Amer Ceram Sot 48,248-251 (1965). 16. J. W. Henney and J. W. S. Jones, Trans Brit Ceram Sot 68,201-203 (1969). 17. D. G. Jones and D. A. Melford, Truns Brit Cerum Sot 68,241 (1969). 18. A. F. Henriksen and W. D. Kingery, Cerumurgiu Jnternut 5,11-17 (1979).
164
V. SWAMY
et al.
19. J. E. Grover, Trans Amer Geophys Union 53,539 (1972). 20. C. B. Sclar, L. C. Canison and C. M. Schwartz, Trans Amer Geophys Union 45, 121 (1964). 21. F. R. Boyd and J. L. England, Carnegie fnst WagingtonYb 64,117-120 (1965). 22. L. Atlas, J GeoZ60, 125147 (1952). 23. T. Gasparik, Amer Mineral 75,1080-1091(1990). 24. A. Navrotsky, D. Ziegler, R. Gcstrike and P. Mauiar, ContribMineral Petrol 101,122-130(1989). 25. J. FStebbins, I. S. E. Carmichael and L. K. Motet, Contrib Mineral Petrol 86,131-148 (1984). 26. P. Richct and Y. Bottinga, Rev Geophys 24, l-25 (1986). 27. P. Richet, Y. Bottinga, L. Denielou. J. P. Petitet and C. Tequi, Geochim Cosmochim Acta 46, 26392658 (1982) 28. D. Gatvin, V. B. Parker and H. J. White, Jr., CODATAThermodynamicTables, p. 356 (1987) 29. S. Kambayashi and E. Kato, J Chem Thermodynamics16,241-248(1984). 30. R. A. Lange and A. Navrotsky, ContribMineral Petrol 110,31l-320 (1992). 31. B. Sundman, B. Jansson. and J. -0. Andersson, Calphad 9,153-190 (1985).
Pergamon
0364-5916(94)
00066-g
AN ASSESSMENT OF THE ONE-BAR LIQUIDUS PHASE RELATIONS IN THE MgO-SiO, SYSTEM
V. Swamy’, S. K. Saxenat, and B. St&man2 1 Instituteof EarthSciences,Theo&al Geochemi.sl?y, Uppsda University,Norbyv@en18 B, S - 152 36. Upps& Sweden 2 Divisionof PhysicalMebhrgy. RoyalIdtute of Technology Stockholm, S - 10044. Sweden
ABSTRACT
An assessment of the thermodynamic properties of the liquid phase in the MgO-SiOs system at one bar is performed using the calphad technique. The liquid is described using a two-sublattice ionic liquid model. The thermodynamic data for the solid phases used are from previous evaluations considering high pressure and high temperature phase equilibria and the available calorimetric data. With the assessed parameters, the experimental phase relations are reproduced very well and a good agreement is obtained with the calorimetric data on enthalpy of fusion.
Introduction The availability of a large amount of high-temperature and high-pressure phase equilibria data and calorimetric data for the MgO-Si02 system has resulted in a number of thermodynamic assessments of this binary. Thermodynamic properties of the subsolidus phases to high pressures and high temperatures were recently assessed by Fei et al. (l), Saxena and Shen (2) and Shi et al. (3). Swamy et al. (4) evaluated the SiO, system including the liquid and the high-pressure solids. We present here an assessment of the thermodynamic pmpetties of the MgO-SiO, liquid at 1 bar using data for the solids from above sources, compiled in Saxena et al. (5), and by adopting the two-sublattice model of Hillert er al. (6) for the liquid phase. The recent evaluations of the MgO-Si02 phase relations at one bar were done by Blander and Pelton (7). who applied a modified quasichemical liquid model, by Howald and Scanlon (8) using a Redlich-Kister model for the liquid, and by Hillert and Wang (9). who applied a two-sublattice model for the liquid and a compound energy model for per&se (in order to model solid solubility of SiO2 in periclasc). Our assessement differs from these in that in the assessment we include enthalpy of fusion data for the liquidus phases and for reasons discussed below disregard solid solubility of SiO, in per&se. The one-atmosphere phase diagram of the MgO-SiO, system was first presented by Bowen and Andersen (10). The crystalline phases of the system are: periclase (MgO), forsterite (Mg$iO&, the pyroxene (MgSiOs) polymorphs (protoenstatite, otthoenstatite and clinoenstatite) and the silica polymorphs (cristobalite, tridymite. &quartz and a-quartz). Bowen and Andersen (10) found that forsterite melts congruently at 2163 K and pmtoenstatite melts incongruently at 1830 K to yield forsterite and liquid. As the phase relations were not examined for 60 years after the first determination by Bowen and Andersen, Chen and Presnall(l1) redetermined Original
version received on 7 June 1993, Revised version on 22 September 157
1993
158
V. SWAMY
et al.
some critical parts of the phase diagram. The results obtained by the latter workers agree completely with the results of Bowen and Andersen. G&g (12) fast observed liquid immiscibility in the silica-rich portion of the binary which was later investigated by Ol’shanskii (13) and Hageman and Oonk (14). While most of the solid phases of the system have near-stoichiometric compositions, there have been conhadictory experimental results on the solid solubility of SiO, in periclase. Schlaudt and Roy (15) mported that 0.11 mole fraction Mg$IiO, (corresponding to 0.09 mole fraction Sit&J could be accommodated in MgO at the eutectic temperattne of 2123 K. However, other workers observed very low or no solubility of silica in periclase (e.g., 16-18). The stability fields of the SiO, polymotphs are rather well established. The stability relations of the pyroxene polymorphs. especially dun of clinoenstatite, however, are not yet clear. The available experimental data on the clinoenstatite (P2t/c)-orthoenstatite (Pbca) transition (19-21) do not agme well with one another. An extrapolation of the high-pressure data of Boyd and England (21) to one bar yields a temperature of 903 K for this transition (3). The orthoenstatite-pnstatite (Pbcn) transition is located between 1248 K and 1268 K (22). Additionally, them is a high-temperatute clinoenstatite (C2Jc) which is the liquidus phase with a narrow stability field at pressures just above 1 bar (23). However, as its stability at 1 bar is not known accurately, we assume pro~statite to be the liquidus mineral at 1 bar as done by most previous workers (e.g., 25). There have been a number of direct and indirect determinations of enthalpies of fusion of the liquidus minerals (e.g., 8.24-27). For periclase, the CODATA recommended values for the temperature and enthalpy of fusion am respectively 3lOOQ5 K and 77.0 kJAnol(28). Navtotsky er al. (24) using transposed-temperature drop calorimetry determined an enthalpy of fusion of 114+20 kJ/mol for forsterite at its melting temperature. From dmp calorimetric and solution calorimetric data, Richet and Bottinga (26) obtained an enthalpy of 73.2~16.0 kJ/mol for the metastable congruent melting of enstatite. Richet er al. (27) estimated an enthalpy of fusion of 8.92~tl.OkJ/mol for cristobalite at the melting temperature of 1999 K.
‘Thermodynamic functions and the liquid model Thermochemical data for a phase can be reptesented in terms of its enthalpy of formation at 1 bar and 298.15 K, A!f&,ss.t~ the entropy at 1 bar and 298.15 K, S”t,29s,t5, and the heat capacity at constant pressure expressed as a polynomial on temperatute, C,(T),. for the compound from 298.15 K. We use the following formulation for the heat capacity, CP(7) [see Saxena et al. (S)]: CP(T) = a + bT + CT-* + dT* + eTm3+ fl-ln + gT-I.
Ul
The liquid phase is described by adopting the two-sublattice ionic liquid model of Hillert et al. (6). In this model the liquid phase consists of two sublattices. one for the cations and another for the anionic species. The liquid is represented by the formula (Mg*+)p (o?-,SiO., 4m.Si02)q, where p and q are the number of sites on each sublattice. Here q=2. and in order to maintain electroneutrality, p=4ySi044-+2y02- where y is the site fraction. The Gibbs energy per formula unit is given by [see Hillert et al. (6)]: Cm = yOa- S;Mg?@-
+ ySi04”- “Y;Mg42+(Si044)2+2ySi0, SGSiO,
+ 2RT (y@ In yOa-+ ySi044- In ySi04q + ySi0, In ySi0;) + EGm.
PI
The excess Gibbs energy, EGm , depends on the interactions between species in the anionic sublattice. We use the same approach as that of Hillert and Wang (9) to describe the excess Gibbs energy. Accordingly, only the
ASSESSMENT
159
OF THE MgO-SiO,SYSTEM
interaction of SiO, with Os- and SiOd4- is considered. The same interaction energy parameters L(Si044--Si0,) and f@--SiO,), counted per negative charge as “L(SiO, 4--Si0,)=2nL(02~-Si02). and with terms upto ‘L (in order to account for the asymmetry in the miscibility gap) are included. Thus we have: EC, = yO*ySiO,
[“L+~L(y02- -ySiO,) + 2L(@2- -ySi02)* + ‘L(yO*- -ySi02)3]
+ 2ySiOb4- ySi0, [0L+‘LCySi044-- ySi0,)+2L( ySi044- - ySiO,)* + 3L(ySi044- -ySi02)3J.
[31
The L parameters vary linearly with temperature.
TABLE 1
Thermodynamic Roperties of the Phases in the MgO-SiOz System at 298.15 K and 1 Bar Phase a-quartz hum
Tridymite Cristobahte SiO, Liquid Periclase MgO Liquid Forsterite Protoenstatite Orthoenstatite Clinoenstatite
AHo/J/mol
S”J/mol/K
Cp“J/mol/K
-9 10700.00 -910497.00 -906913.00 -906034.00 -901013.00 -601490.00 -531270.00 -2174140.00 - 1545794.00 - 1546290.00 -1548715.00
41.460 41.700 45.116 46.060 49.033 26.940 49.479 94.110 66.960 66.270 63.230
44.589 44.589 44.254 44.299 44.217 37.28 1 37.222 118.638 81.595 82.225 81.772
Experimental
data
The experimental data were reviewed by Hillert and Wang (9). We use the phase diagram information from Bowen and Andersen (lo), data on liquid immiscibility from Hageman and Oonk (14) and Greig (12), the activities of MgO and SiO, in the liquid by Kambayashi and Kato (29) and the enthalpies of fusion data discussed earlier. All the solids in the system are treated as stoichiometric compounds. As mentioned earlier, measurements of solubility of SiO, in periclase by different workers gave contradictory results and in some assessments the solubility of silica in periclase was considered (e.g., 7.9). We accept the results of Henriksen and Kingery (18) which show very low solubility of SiO, in MgO.
V. SWAMY
100
et al.
TABLE 2 Coefficients for Heat Capacity, C,(7). J.mol-‘.K-1
Cp(T) = a + bT + CT-~ + dT2 + CT-~ + fl’-lR + gT-’ Phase c (10-4)
d(l@)
18.2800
-18.0986
540.5800
1.2050
113.1000
a
b UC’?
298.15-848K
81.1441
848-4OOOK
18.8120
'298.15-848 K
81.1441
18.2800
-18.0986
848-4OC0K
18.8120
1.2050
113.1000
66.6993
5.2119
e(lO-‘)
f
g(lO-‘)
H+
a-quartz 698.458
o.cxm
1.202
0.000
-1.213
540.5800
0.000
698.458
o.GuO
0.0000
1.202
O.WM
-1.213
-213.2338
-35.4183
O.OMl
o.ooo
0.000
-3083.8590 -1911.8161
31256.50
0.000
0.000
0.000
99.4385
0.000
o.Oal
0.000
o.oooo 10.532243
o.ooo
0.000
o.oooo
0.000
0.000
o.OaI
0.0000
1.I440
0.000
0.2411
O.OCKlO
0.m
0.84
&I~~ 0.84
Tridymitc 298.154000K Cristobalite 298.15523 K 5234OMIK
9011209
-1.62024
14.9325
440.5322
SiO2 Liquid 298.15-1480K
13.1932
1.6186
14804000 K
81.3100
O.oooO
45.4900
4.7730
-216.OWO
4.6536
-103.3800
Xi20.6124 0.0000
Pcriclnsc 298.154ooo K MgO Liquid 298.15-1100K
41.4811
llOO-3OMIK
18.3112
300&5100K
94.2000
o.Ooal
165.8ooo
18.55W
-210258
O.OCKI
o.O@l
0.0000
516.2028
0.000
0.000
o.Oow
o.coOO
o.Oal
o.ooo
o.OOcn3
-391.1000
0.0000
2.8610
O.C@O 0.5610
-19.4688 -1118.3100 o.oooo
Porstcrite 298.1540&l K Protoenstntite 298.154000K
144.3100
1.8919
-134.9500
0.0000
4.6265
0.000 -1.9563
144.4500
1.8820
-135.oooo
O.CNIO
4.6120
0.000 -1.9380
138.0791
8.1088
O.OOW
O.ooO -1.8888
Ortboenstatite 298.154000K Cliaoeastatite 298.15-4oooK
40.5900
-135.2318
t - Enhlpy of transition.kJ/mol.
Thermodynamic data and assessment Thermodynamic data for quartz, tridymite, cristobalite, liquid silica, periclase. forsterite and pyroxenes are from earlier assessments (l-4). The Cp for liquid MgO used by Hillert and Wang (9) is 84 J.mol.‘.K-1 which is the same as the CODATA ncommendation
(28). This value, however, is taken as similar to the Cp of liquid Be0
We optimized the thermochemical properties of liquid MgO by adopting a Cp of 94.2 J.mol-‘.K-1 which is the partial molar heat capacity derived by Lange and Navmtsky (30) for liquid MgO through systematic analysis of a large amount of data on multicomponent liquids. Our data on enthalpy and temperamre of fusion of periclase using these data am in close agreement with the CODATA recommended values (28). The thermodynamic data
ASSESSMENT
OF THE MgO-SiO,
SYSTEM
161
for all the phases are listed in Tables 1 and 2. The parameters for the liquid phase were allowed to vary during the optimization wormed using the program Purrot fmn Thcmw-Cdc databank package (31). This optimizer works by minimizing an error sum and is capable of handling all kinds of experimental data simultaneously.
TABLE 3 Assessed Model Patameters for the Liquid Phase Parameter
Assessed values
OL ‘L
148550 - 73.5653 1102 176615 - 59.3847
*L ‘L
-2500
0GM~2+(Si0,4-h-4”GMg0 Liq-20GSiOzLiq -322263+ 63.7227
I
I
I
I
I I
q ltlcgmanhOonk1986 FIG. 1 The calculated high temperamte patt of the MgO-SiO, phase diagram. Experimental data on liquid immiscibility from Hageman and Oonk (14) are also shown. Per - periclase, Fo forsterite. Pen -protoenstatite, Crs cristobalite. Trd - tridymite.
0 A
0.2
0.4 Mole
fraction
0.6 SiO,
0.8
1.0
V. SWAMY et al.
162
TABLE 4 comparison of Experimental Phase Equilibrium and Calorimetric Data with that calculated
Using Our Data Equilibrium
Experimental
Calculated
Perichse -fwsren’te eutectic: Temperature, K Composition of liquid, x(SiOz)
2123 0.310
2128 0.300
Forsterite - protoenwatitepetite&:
1830 0.515
1830 0.523
Protoenstatite- cris&alite entectic:
Temperature, K Composition of liquid, x(SiOJ
1816 0.545
1821 0.544
Temperature, K Composition of liquids, x(Mg0)
1968 0.415. 0.020
1968 0.410, 0.014
Melting of periclase:
Temperature, K Enthalpy, kJ/mol
31OOi25 77.00
3083 75.00
Melting offorsterite:
Temperature, K Enthalpy, kJ/mol
2163 114.W20.00
2160 92.40
cOtl@l&?flt
Temperature, K Enthalpy, kJ/mol
1834 73.20.16.00
1834 68.42
Temperature, K Enthalpy, kJ/mol
1999 8.92il.00
1998 8.91
Temperature, K
1248-1268
1257
Temperature, K
Uncertain
903
Temperature, K Composition of liquid, x(SiOJ
Two liquids - cristobalite:
Idti?l~
Of PrOtOe~rarire.’
Melting of crisrobalite:
Protoe-
- orthoed:
orthoenWatitt? -cii7wenstarite:
Results The assessed model parameters for the liquid are given in Table 3. Figure 1 shows the calculated phase diagram of MgO-SiO, system. The liquid immiscibility data from Hageman and Conk (14) are shown in Fig. 1. The calculated activities of SiO, and MgO in the liquid are compared with experimental measurements by Kambayashi and Kato (29) in Fig. 2. Since a better tit of the calculated activity to experimental data would result in the substantial underestimation of the fusion enthalpy of forsterite and protoenstatite. we accept the present results. Table 4 shows that the calculated data am consistent with the experimental phase equilibria and calorimetric data.
ASSESSMENT
OF THE MgO-SiO,
I
1.0 0.9-
T=1973K
0.9-
0.8-
0.8-
0.7-
0.7-
163
SYSTEM
I
I
0.50
0.55
T=1973K
0.6-
0.5-
0.5-
0.4-
-
0.3-
5 <
0.20.1o
A
(a>
O.&l
I
o.&
I
0.50
I 0.55
0.60 A
0.40
0.25
Mole fraction 30,
0.60
Mole fraction SIO,
FIG.2 Comparison of calculatedactivity
of (a) SiO, and (b) MgO in the liquid with experimental data (circles) from Kambayashi and Kato (29)
Acknowledgements V.S. acknowledges the valuable discussions with Bengt Hallstedt. This work was financially supported by NUTEK through the CAMPADA project and by a grant from NFR to S.K.S.
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