Journal of Petrology Advance Access originally published online on April 29, 2005
Journal of Petrology 2005 46(9):1859-1880; doi:10.1093/petrology/egi037
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Experimental Investigation and Optimization of Thermodynamic Properties and Phase Diagrams in the Systems CaO–SiO2, MgO–SiO2, CaMgSi2O6–SiO2 and CaMgSi2O6–Mg2SiO4 to 1·0 GPa
1 DEPARTMENT OF EARTH AND PLANETARY SCIENCES, McGILL UNIVERSITY, 3450 RUE UNIVERSITÉ, MONTRÉAL, QC, H3A 2A7, CANADA
2 CENTRE FOR RESEARCH IN COMPUTATIONAL THERMOCHEMISTRY, ÉCOLE POLYTECHNIQUE DE MONTRÉAL, P.O. BOX 6079, SUCCURSALE CENTRE-VILLE, MONTRÉAL, QC, H3C 3A7, CANADA
RECEIVED FEBRUARY 17, 2004; ACCEPTED MARCH 14, 2005
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSEXPERIMENTAL RESULTS AT 1{middle...THERMODYNAMIC MODELSTHERMODYNAMIC OPTIMIZATION AND...DISCUSSIONCONCLUSIONREFERENCES |
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Using experimental results at 1·0 GPa for the systems CaO–SiO2, MgO–SiO2, CaMgSi2O6–SiO2 and CaMgSi2O6–Mg2SiO4, and all the currently available phase equilibria and thermodynamic data at 1 bar, we have optimized the thermodynamic properties of the liquid phase at 1·0 GPa. The new optimized thermodynamic parameters indicate that pressure has little effect on the topology of the CaO–SiO2, CaMgSi2O6–SiO2, and CaMgSi2O6–Mg2SiO4 systems but a pronounced one on the MgO–SiO2 binary. The most striking change concerns passage of the MgSiO3 phase from peritectic melting at 1 bar to eutectic melting at 1·0 GPa. This transition is estimated to occur at 0·41 GPa. For the CaMgSi2O6–SiO2 and CaMgSi2O6–Mg2SiO4 pseudo-binaries, the size of the field clinopyroxene + liquid increases with increasing pressure. This change is related to the shift of the piercing points clinopyroxene + silica + liquid (from 0·375 mol fraction SiO2 at 1 bar to 0·414 at 1·0 GPa) and clinopyroxene + olivine + liquid (from 0·191 mol fraction SiO2 at 1 bar to 0·331 at 1·0 GPa) that bound the clinopyroxene + liquid field in the CaMgSi2O6·SiO2 and CaMgSi2O6·Mg2SiO4 pseudo-binaries, respectively.
KEY WORDS: CaO–SiO2; CaMgSi2O6–Mg2SiO4; CaMgSi2O6–SiO2; experiments; MgO–SiO2
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSEXPERIMENTAL RESULTS AT 1{middle...THERMODYNAMIC MODELSTHERMODYNAMIC OPTIMIZATION AND...DISCUSSIONCONCLUSIONREFERENCES |
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The system CaO–MgO–SiO2 (Fig. 1) has been extensively studied in the past at low (Bowen, 1914
; Schairer & Yoder, 1962; Kushiro, 1972a; Longhi & Boudreau, 1980) and high pressures (Kushiro, 1969) because it includes forsterite, enstatite and diopside, which are major constituents of peridotitic (
85%) and basaltic rocks. The sub-system diopside–forsterite–silica has been very useful in providing a framework for the understanding of complex phase equilibria of natural basaltic rocks. The recognition that silica-saturated liquids may be generated by partial melting of peridotites at pressures up to 2·0 GPa PH2O (Kushiro, 1969) is an excellent example of how experiments in this subsystem (dry and wet) have provided insight into the petrogenesis of igneous rocks.
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However, such relatively simple phase diagrams are recognized to be of limited use because they cannot be applied directly to natural magmas and rock systems (Hess, 1992
; Langmuir et al., 1992). Much effort in recent decades has been employed in making thermodynamic databases at low and high pressures (e.g. Berman, 1988; Holland & Powell, 1990; Saxena et al., 1993) that will render the calculation of such complex phase equilibria possible. In igneous petrology these databases have been mostly used to predict the stability fields of minerals in the upper and lower mantle (Saxena & Eriksson, 1983a, 1985; Fei et al., 1990; Saxena, 1996), but attempts have also been made to calculate, for example, the mineralogy of condensates from a solar-composition gas (Saxena & Eriksson, 1983b) and the composition of the Earth's core (Saxena et al., 1994).
Most of the phase equilibria predictions mentioned above have been made under subsolidus conditions because little is still known about the thermodynamic properties of melts at high pressures. This lack of information forced petrologists to adopt an approach that relies on the calculation of equilibria using empirical thermodynamic models (Ghiorso et al., 1983, 1994; Ghiorso & Sack, 1995; Ghiorso, 1997; Hirschmann et al., 1998) or simple partition coefficients (D) of individual elements (or components; Nielsen & Dungan, 1983; Nielsen, 1985) to quantify petrogenetic processes such as partial melting or fractional crystallization. None the less, reliable thermodynamic data exist for the liquid phase of many binary and multi-component systems at atmospheric pressure (see, for example, the FactSage database; Bale et al., 2002), which sets the stage for a systematic study of high-pressure equilibria that may serve to quantify magmatic processes. Moreover, it is expected that this kind of study will help petrologists to understand better how pressure affects the structure of melts in simple and complex systems.
The best system to begin with is the CaO–MgO–SiO2 ternary. This ternary has been thermodynamically modeled at 1 bar by Berman (1983), Gaye & Welfringer (1984), Huang et al. (1995) and more recently by Jung (2003). Unfortunately, no attempt was made to model the system at high pressure. In this study, the systems CaO–SiO2 (lime–silica), MgO–SiO2 (periclase–silica), CaMgSi2O6–SiO2 (diopside–silica), and CaMgSi2O6–Mg2SiO4 (diopside–forsterite) that compose the CaO–MgO–SiO2 ternary have been experimentally determined at 1·0 GPa and the thermodynamic properties and phase diagrams optimized at 1 GPa.
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METHODS |
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Starting materials
Starting materials consisted of mechanical mixtures of pure oxides and/or end-member silicates. The end-member silicates were prepared in 10 g batches (to avoid weighing errors) by mixing in appropriate proportions the desired powders in an agate mortar filled with isopropyl alcohol for about 60 min. The alcohol was driven off from the MgSiO3 composition by heating at 900°C for 1 h. Ground mixtures of CaCO3 + SiO2 and CaCO3 + MgO + SiO2 were dried and decarbonated at 1000°C for 12 h. Silicate compounds were synthesized as follows.
Mg2SiO4: the ground oxide mixture was fired five times (with intermediate dry grinding in an agate mortar) at 1400°C for a total of 50 h, and three times (with intermediate grinding) at 1500°C for a total of 60 h.
MgSiO3: ground oxide mixtures were fired at least twice (with intermediate dry grinding in an agate mortar) at about 1500°C for a total of 50 h, and one mixture was fired at 1550°C for 180 h.
Ca2SiO4: the mixture was fired three times at 1500°C for a total of 24 h with intermediate grindings in an agate mortar.
CaSiO3: the ground oxide mixture was fired three times (with intermediate dry grinding in an agate mortar) at 1400°C for a total of 280 h.
CaMgSi2O6: the ground oxide mixture was fired at 1500°C for a total of 2 h, and some CaMgSi2O6 glass was recrystallized at 1000°C for 24 h.
The final phases were analysed with an electron microprobe to check homogeneity and composition. Each material was found to be stoichiometric and no unreacted simple oxide was found based upon microscopic observations in oil and X-ray diffractometry. The Mg2SiO4 was forsterite, the Ca2SiO4 was 
-Ca2SiO4, the MgSiO3 was a mixture of clino- and protoenstatite, the CaSiO3 was pseudowollastonite, and the CaMgSi2O6 was diopside. The SiO2 used was made of ß-cristobalite and 
-quartz. The final starting materials were prepared in batches of 5, 2 or 1 g by mixing mechanically simple oxides and/or silicates in desired proportions for about 60 min in an agate mortar filled with isopropyl alcohol. The latter was driven off at 900°C for 1 h, which converted most of the -Ca2SiO4 to ß-Ca2SiO4 (larnite). The final starting material powders were kept in a drying oven at 110°C prior to use.
Experimental procedures
Experiments performed below 1740°C were carried out in platinum capsules. Each container was tightly packed with about 10 mg of starting material powder and a flat crimp was applied gently to remove air space as much as possible. Following this, the capsules were fired with a torch to about 1000–1300°C for 1 min and quickly sealed by arc welding to eliminate water. Experiments located close to or above the melting point of platinum (1769°C) were carried out with rhenium (Hudon et al., 2002) or molybdenum capsules. Molybdenum capsules and lids were machined from 99·97% molybdenum rods. Each container was tightly packed with about 10 mg of starting material powder, closed with a lid and wrapped with a 0·0127 mm thick molybdenum foil. At high temperature and pressure the foil alloys with the lid and the container, which provides an additional seal. Rhenium capsules were preferred over molybdenum capsules because the latter slightly contaminate the charge.
Experiments were performed with a 1·91 cm piston-cylinder apparatus (Boyd & England, 1960) using the high-temperature assembly described by Hudon et al. (1994). Experimental details concerning preparation of the assembly, pressurization and heating procedures, thermocouple type, thermal gradient and pressure calibration have been described by Hudon et al. (2002). Temperature fluctuations were usually within ±5°C (see exceptions in Tables 1–4). All the temperatures were converted to the International Temperature Scale of 1990 (ITS-90; Adams, 1914; Sosman, 1952; Preston-Thomas, 1990). Pressures were controlled within ±0·056 GPa. Experiments were terminated by turning off the power and quenched to 100°C at a rate of about 1500°C/min. Thermocouple and capsule locations were examined after each experiment to verify if they shifted with respect to each other. Samples that were located at a distance corresponding to a temperature difference of more than 10°C from the measured temperature were rejected.
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Sample identification
Quenched samples were kept in their capsules, cast in epoxy and polished longitudinally for identification of the products under the petrographic microscope or in backscattered electron images. In a few cases samples were removed from their capsules and phases were identified in oil with a petrographic microscope or by X-ray diffraction. Some phases were identified by electron probe microanalysis using the JEOL 8900 probe at McGill University. Analyses were performed by wavelength-dispersive spectrometry (WDS) using an accelerating voltage of 15 kV, a 20 nA beam current and a 1 µm spot size. Counting times were of 20 s on peaks and 10 s on backgrounds, and data were reduced with the ZAF corrections using synthetic enstatite (Mg), wollastonite (Ca), diopside (Ca, Mg) and silica glass standards.
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EXPERIMENTAL RESULTS AT 1·0 GPa |
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Experimental conditions and observed phases of selected experiments in the CaO–SiO2, MgO–SiO2, CaMgSi2O6–SiO2 and CaMgSi2O6–Mg2SiO4 systems at 1·0 GPa are given in Tables 1, 2, 3 and 4, respectively. In many instances quench textures in glassy samples or the lack of sufficiently large pockets of glass (>10 µm) prevented reliable analysis of the glass; the quenching technique was thus adopted to locate the liquidi and solidi of all systems studied. Equilibrium phases were distinguished from quench ones by their shape and from electron microprobe analysis. For each sample a few grains were usually selected in different portions of the charge and analyzed at their rims and cores; if the analyses were identical (within 0·5 cation %) and if the stoichiometry was acceptable (i.e. cation proportions were within 0·5% of the expected values), the phase was considered to be equilibrated.
Attainment of equilibrium
Equilibrium was experimentally demonstrated in the CaO–SiO2, MgO–SiO2, CaMgSi2O6–SiO2, and CaMgSi2O6–Mg2SiO4 systems at 1·0 GPa by reversal experiments (Tables 1, 2, 3 and 4, respectively). These were performed by equilibrating one or two samples of each system at a temperature above and below the eutectic (for the binaries) or the piecing point (for the pseudo-binaries). All reversals were consistent with experiments taken directly to high pressures and temperatures from ambient conditions.
The CaO–SiO2 system
The 1·0 GPa CaO–SiO2 phase diagram includes the crystalline phases Ca3SiO5, Ca2SiO4 and CaSiO3, and possesses a small immiscibility field in the silica-rich portion of the binary. The liquidus phase relations were constrained by experiments spanning the binary at temperatures to 2130°C. The eutectic temperature for Ca3SiO5 (hatrurite), Ca2SiO4 and liquid was determined to be 2115 ± 21°C, and the silica-rich side of the Ca2SiO4 liquidus was bracketed. However, it was impossible to constrain the overall CaO–SiO2 phase diagram in this study. Attempts to determine the melting points and liquidi of the CaO, Ca3SiO5 and Ca2SiO4 phases were unsuccessful, but experimental results suggest that their melting points lie above 2130°C. No solid solutions were found in Ca2SiO4 and no attempts were made to determine which polymorph was produced. Seven allotropes are actually known for this composition: , ß (larnite), 'Low(2a,b,2c), 'Low(a,3b,c), 'High, , and the high-T–high-P K2NiF4 type (Remy et al., 1995). At 1 atm the stable polymorph at the melting point is the -phase, which transforms to the 'High-phase at 1437°C. According to Remy et al. (1995), the -phase is stable at the 1·0 GPa melting point and transforms to the 'High-phase at 1681°C. However, in our optimization at 1·0 GPa, the phase transition at 1681°C was not adopted because no volumetric data are known for the 'High-phase at 1·0 GPa. The compound Ca3Si2O7 (rankinite) was not observed. The metasilicate polymorph was identified by its characteristic irregular shape to be pseudowollastonite (Huang & Wyllie, 1975a) and was found to melt congruently at 1553 ± 11°C. This value is in good agreement with the temperature of 1568 ± 15°C calculated from the pseudowollastonite melting curve determined by Huang & Wyllie (1975a) [pressure corrected for friction effects by Huang & Wyllie (1975b) and Huang et al. (1980)]. The eutectics involving pseudowollastonite are located at about 44 ± 2 mol % SiO2 at 1487 ± 11°C and 61 ± 1 mol % SiO2 at 1455 ± 10°C. Data dealing with the miscibility gap and the quartz melting point are taken from Hudon et al. (2004) and Hudon et al. (2002), respectively.
The MgO–SiO2 system
The 1·0 GPa MgO–SiO2 phase diagram is made up of Mg2SiO4 and MgSiO3, and an immiscibility field is present in the silica-rich end. The entire phase diagram was constrained at 1·0 GPa except for the melting point of MgO (periclase). The eutectic between periclase and forsterite is located at 31·5 ± 1·5 mol % SiO2 and 1930 ± 19°C. No solid solutions were found in periclase. The congruent melting point of forsterite was fixed at 1945 ± 19°C with some difficulty because considerable partial melting was observed despite the precautions taken. None the less, the value of 1945°C agrees with the temperature of 1948°C calculated from the forsterite melting curve of Davis & England (1963, 1964). Phase relations for the metasilicate were carefully measured but no attempts were made to identify its polymorph. Some controversy exists at low pressures (<2·0 GPa) and high temperatures concerning enstatite phase transitions (Atlas, 1952; Boyd et al., 1964; Sclar et al., 1964; Boyd & England, 1965; Perrotta & Stephenson, 1965; Kushiro et al., 1968; Smith, 1969; Anastasiou & Seifert, 1972; Chen & Presnall, 1975; Biggar, 1988; Pacalo & Gasparik, 1990). The possible polymorphs at 1·0 GPa are protoenstatite, high-temperature clinoenstatite, and orthoenstatite. A recent thermodynamic study of the Ca–Mg–Fe–Al–Si–O pyroxenes by Shi et al. (1994, 1996) places the stable orthoenstatite polymorph at the liquidus; this allotrope was thus chosen. It was found to melt congruently at 1665 ± 12°C, which compares well with the value of 1672 ± 12°C calculated from the melting curve of enstatite determined by Boyd et al. (1964). Eutectics were found to lie at about 47·8 ± 1·3 mol % SiO2 and 1663 ± 12°C and at about 55·6 ± 1·5 mol % SiO2 and 1655 ± 12°C. Data concerning the miscibility gap were taken from Hudon et al. (2004).
The CaMgSi2O6–SiO2 system
This system is, like the 1 atm phase diagram, pseudo-binary at 1·0 GPa. Experiments fixed the congruent melting point of diopside at 1513 ± 11°C, which is identical to the temperature determined by Boettcher et al. (1982) and agrees within 10°C with earlier data (Boyd & England, 1963; Williams & Kennedy, 1969). Solid solutions were observed in diopside (i.e. clinopyroxene; Table 8); its enstatite component showed a tendency to increase with temperature and reached a maximum of 13·8 mol % at 1505°C. On the other hand, no solid solutions were observed in quartz. The piercing point clinopyroxene (solid solution) + quartz + liquid was found to lie at about 41 ± 1 mol % SiO2 and 1485 ± 10°C. Immiscibility data were taken from Hudon et al. (2004).
The CaMgSi2O6–Mg2SiO4 system
This system is a pseudo-binary at 1·0 GPa. Solid solutions were detected in clinopyroxene (Table 9); its enstatite component showed a tendency to increase with temperature and reached a maximum of 16·4 mol % at 1525°C. Negligible solid solutions (typically <1 mol % Ca2SiO4) were found in the olivine and for this reason it was considered to be a stoichiometric compound (Table 10). The piercing point clinopyroxene (solid solution) + olivine + liquid was located at about 33 ± 1 mol % Mg2SiO4 and 1485 ± 10°C.
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THERMODYNAMIC MODELS |
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TOPABSTRACTINTRODUCTIONMETHODSEXPERIMENTAL RESULTS AT 1{middle...THERMODYNAMIC MODELSTHERMODYNAMIC OPTIMIZATION AND...DISCUSSIONCONCLUSIONREFERENCES |
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Pure compounds
The Gibbs free energy of formation of a phase from its elements at any temperature T (K) and pressure P (bar) is given by
 | (1) |
is the enthalpy of formation from the elements at 1 bar and 298·15 K, 
is the entropy at 1 bar and 298·15 K, CP(T) is the heat capacity at constant pressure, and V(P,T) is the molar volume at pressure P (bar) and temperature T (K). The heat capacity CP(T) is expanded as a polynomial in temperature as
 | (2) |
is calculated using the high-temperature Birch–Murnaghan model as formulated by Saxena et al. (1993). In this model, which uses a third-order Birch–Murnaghan equation of state, the term 
is replaced by 
for computational convenience. The relation between the two terms is
 | (3) |
 | (4) |
 | (5) |
 | (6) |
 | (7) |
 | (8) |
 | (9) |
is the molar volume at 298·15 K and 1 bar, and (T) is the thermal expansion expressed as the polynomial
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Liquid phase
For the liquid phase, the Modified Quasichemical Model of Pelton & Blander (1984
, 1986) has been used. A summary of this model, which has been further developed, has been given in the recent review by Pelton et al. (2000) and Pelton & Chartrand (2001). This model was chosen because it is particularly well adapted to systems containing substantial short-range ordering such as molten silicates. Short-range ordering is taken into account by considering second-nearest-neighbor pair exchange reactions. For example, for the CaO–MgO–SiO2 liquid these reactions are
 | (11) |
 | (12) |
 | (13) |
gA,B of these reactions, which may be expanded as empirical functions of composition.
The second-nearest neighbor ‘coordination numbers’ of Ca, Mg and Si used in the Modified Quasichemical Model have been given by Wu et al. (1993a, 1993b) and Eriksson et al. (1994). The asymmetric ‘Toop-like’ extension of binary model parameters (Pelton, 2001) is used to calculate the Gibbs energy of the ternary liquid, with SiO2 as the ‘asymmetric component’.
Olivine solid solution
The olivine solid solution has two distinct octahedral sublattices (or sites), called M2 and M1:
 | (14) |
The end-members of the olivine solid solution in the CaO–MgO–SiO2 system are -larnite, Ca2SiO4, monticellite, CaMgSiO4, inverse-monticellite, MgCaSiO4, and forsterite, Mg2SiO4. For the olivine solid solution, the model is developed within the framework of the Compound Energy Formalism (CEF; Hillert et al., 1988). The Gibbs energy expression in the CEF per formula unit of a solution is as follows:
 | (15) |
and 
represent the site fractions of constituents i and j on the M2 and M1 sublattices. Gij is the Gibbs energy of an ‘end-member’ (i)M2(j)M1SiO4, in which the M2 and M1 sublattices are occupied only by i and j cations, respectively. SC is the configurational entropy assuming random mixing on each sublattice, given by
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 | (17) |
 | (18) |
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Clinopyroxene (diopside) solid solution
Diopside, CaMgSi2O6, can dissolve MgSiO3 to form the clinopyroxene solid solution. Like olivine, the pyroxene has two distinct octahedral sublattices, M2 and M1. However, unlike olivine, the amount of Ca on the M1 sites is negligibly small, so that the formula unit of pyroxenes can be written as (Ca2+,Mg2+)M2(Mg2+)M1Si2O6.
In the CaO–MgO–SiO2 system, the end-members of the pyroxene solid solution are diopside, CaMgSi2O6, and the imaginary phase clinoenstatite, Mg2Si2O6, and the mixing of cations occurs only on the M2 sites. The Gibbs energy of a pyroxene solution is expressed using equations (15)–(19) of the Compound Energy Formalism.
There are three other pyroxene solid solutions with different crystal structures: (1) orthopyroxene, where the end-members are the imaginary phase, which has orthopyroxene structure, CaMgSi2O6, and orthoenstatite, Mg2Si2O6; (2) protopyroxene, where the end-members are the imaginary phase, which has protopyroxene structure, CaMgSi2O6 and protoenstatite, Mg2Si2O6; (3) low-clinopyroxene, where the end-members are the imaginary phase, which has low-clinopyroxene structure, CaMgSi2O6, and low-clinoenstatite, Mg2Si2O6. These are modeled the same way as the clinopyroxene solid solution.
Other solid solutions
There are other solid solutions in the CaO–MgO–SiO2 system: monoxide (CaO and MgO) and wollastonite (CaSiO3 and MgSiO3). The thermodynamic properties of these solutions were modeled at 1 bar, but not at 1·0 GPa because they are less important in the present study.
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THERMODYNAMIC OPTIMIZATION AND RESULTS |
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The Gibbs energies of pure compounds were mostly taken from the assessment by Berman & Brown (1985)
, with small corrections being made to the enthalpies of formation, 
, to reproduce the phase diagram data. All these corrections are within the uncertainty quoted by Berman & Berman. The volumetric data are taken from the previous studies by Saxena et al. (1993), Shi et al. (1994, 1996) and Hudon et al. (2002, 2004). The thermodynamic and volumetric data are listed in Tables 5 and 6, respectively.
A complete critical evaluation and thermodynamic modeling of phase diagrams and thermodynamic properties of the CaO–MgO–SiO2 system at 1 bar were performed by Jung (2003) based on the previously optimized model parameters for the binary sub-systems CaO–MgO (Wu et al., 1993a), CaO–SiO2 (Eriksson et al., 1994), and MgO–SiO2 (Wu et al., 1993b). In the optimization of the CaO–MgO–SiO2 system at 1 bar by Jung (2003), the thermodynamic properties of the olivine solid solution were optimized using a Gibbs energy of pseudo-end-member GMgCa and three excess model parameters. In the case of the clinopyroxene solid solution, the thermodynamic properties were optimized using a Gibbs energy of pseudo-end-member GMgMg and two excess model parameters. Finally, to reproduce the overall CaO–MgO–SiO2 system, three small optimized ternary model parameters were added to the liquid phase. The thermodynamic model with model parameters can explain all available and reliable thermodynamic, cation distribution, and phase equilibrium data within experimental error limits from 25°C to above the liquidus temperatures over the entire composition range at 1 bar.
The pressure-dependent model parameters for the binary liquid CaO–SiO2 and MgO–SiO2 were optimized using the experimental data of the present study. Then the prediction was made for the phase equilibria of the CaO–MgO–SiO2 system. Because the liquid was predicted slightly more stable (the melting temperature of diopside was predicted to be 1500°C with no additional parameters instead of the real melting temperature of 1513°C), a small pressure-dependent ternary parameter was added. This parameter does not affect the calculations of the miscibility gaps from our previous study (Hudon et al., 2004). In the case of the olivine and clinopyroxene solid solutions, no additional pressure-dependent model parameters were added because the change of thermodynamic properties of these solutions within a few GPa seems to be very small. Consequently, only the Gibbs energies of their end-members are varied according to their volumetric properties.
The database of the model parameters is given in Table 7 and can be used along with software for Gibbs energy minimization such as FactSage (Bale et al., 2002) to calculate any thermodynamic property, phase diagram section or phase equilibrium of interest at 1 GPa. The optimized phase diagrams of the CaO–SiO2, MgO–SiO2, CaMgSi2O6–SiO2, and CaMgSi2O6–Mg2SiO4 systems at 1 bar and 1·0 GPa are shown in Figs 2, 3, 4 and 5, respectively.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSEXPERIMENTAL RESULTS AT 1{middle...THERMODYNAMIC MODELSTHERMODYNAMIC OPTIMIZATION AND...DISCUSSIONCONCLUSIONREFERENCES |
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The CaO–SiO2 binary
For the CaO–SiO2 binary (Fig. 2), the optimization at 1·0 GPa is valid for the portion
0·43 mol fraction SiO2 because no liquidus data were collected for compositions <0·40 mol fraction SiO2 as a result of the high temperatures for lime and larnite. Moreover, no volumetric data are known for the 'High-larnite and hatrurite at 1·0 GPa. In terms of consistency, the optimized CaO–SiO2 phase diagrams at 1 bar and 1·0 GPa are in agreement with the experimental data collected at 0·7 and 2·7 GPa by Huang et al. (1980). Pressure has little effect on the topology of the CaO–SiO2 system: the 1 bar and 1·0 GPa phase diagrams are similar. Little can be said about the CaO-rich part of the binary because this portion was not constrained at 1·0 GPa. The pseudowollastonite melting point at 1 bar (1540°C) and 1·0 GPa (1549°C) is almost identical (within error). To first order, this suggests that the volume of fusion is nearly zero.
The MgO–SiO2 binary
For the MgO–SiO2 binary (Fig. 3), the optimization at 1·0 GPa is valid for the portion 0·33 mol fraction SiO2 because the melting point of periclase is unknown at 1·0 GPa. In terms of consistency, the optimized MgO–SiO2 phase diagrams at 1 bar and 1·0 GPa are in agreement with the experimental data of Taylor (1973) at 1·5 GPa and Dalton & Presnall (1997) at 5·0 GPa. However, discrepancies are observed with data gathered between 0·7 and 2·5 GPa by Chen & Presnall (1975). At 1·0 GPa, those workers placed the solidus between forsterite and orthoenstatite at 1664°C, which is in excellent agreement with the optimized value of 1659°C. The problem comes from the orthoenstatite–ß-quartz solidus: their experimental data suggest that it is located between 1695 and 1713°C (i.e. at about 1705°C) whereas the optimization places the solidus at 1646°C. Preference was given to the 1646°C solidus because the temperature range (1695–1713°C) for which Chen & Presnall (1975) placed their solidus is positioned above the orthoenstatite melting point [which is 1668°C according to the present study, and 1672 ± 12°C according to Boyd et al. (1964)]. Moreover, at 1·2 and 2·0 GPa, the Chen & Presnall (1975) orthoenstatite liquidus is strongly asymmetric on both sides of the orthoenstatite composition, which is thermodynamically implausible because the limiting slope of the liquidus line prevents such behavior. Chen & Presnall (1975) made their solidus and liquidus determinations using two starting compositions (46·5 mol % SiO2 and 55·55 mol % SiO2) that are located relatively close to the MgSiO3 composition. The same compositions were among those used in the present study and it was always difficult to detect the melting of MgSiO3 for these compositions even with the aid of backscatter imaging. The same problem was encountered by Boyd et al. (1964) during the determination of the MgSiO3 melting curve: to overcome the difficulty they put some platinum black in their starting compositions. In the present study, it was found easier to make solidus determinations by using starting compositions located away from the MgSiO3 composition because quench melts were then hard to confuse with MgSiO3 crystals. For these reasons, Chen & Presnall (1975) may have misinterpreted some of their experimental run products, which may explain their high-temperature orthoenstatite–ß-quartz solidus and their asymmetric orthoenstatite liquidus.
Pressure has much more effect on the topology of MgO–SiO2 binary. The most striking change concerns passage of the metasilicate from peritectic melting at 1 bar to eutectic melting at 1·0 GPa (see close-up views of the MgSiO3 + liquid fields at 1 bar and 1 GPa in Fig. 3c and d). The melting point of MgSiO3 rises by 110°C between 1 bar and 1·0 GPa whereas it rises by only 9°C for pseudowollastonite in the same pressure range. The protoenstatite–orthoenstatite polymorphic transition explains this difference. The molar volume of orthoenstatite is smaller than the protoenstatite one, which makes the melting slope of orthoenstatite steeper than the protoenstatite one and results in the peritectic to eutectic transition. On the other hand, the presence at 1 bar of both the six- and four-fold (compressible) Mg2+ cations in the liquid phase makes the MgO–SiO2 melt compressible (the four-fold cations are thought to adopt a more compact arrangement at high pressure by increasing their coordination to six; see Matsui & Kawamura, 1980; Kubicki et al., 1992). This factor should counteract the volume change undergone by the solid and make the MgSiO3 melting slope shallower, which would delay the peritectic to eutectic transition. However, this effect seems to be negligible at 1 GPa because the melting point of MgSiO3 rises substantially (by 110°C) between 1 bar and 1 GPa.
Boyd et al. (1964) experimentally determined the MgSiO3 melting curve and estimated that the pressure at which the melting changes from incongruent to congruent is less than 0·54 GPa. Taylor (1973) located the eutectic between Mg2SiO4 and MgSiO3 at 1·5 GPa and predicted by interpolation to the 1 bar melting point that the change occurs at about 0·4 GPa. Chen & Presnall (1975) performed experiments along the Mg2SiO4–SiO2 join between 0·7 and 2·5 GPa and found by interpolation a pressure of 0·13 GPa. Experimental results obtained and optimized in this study were linearly extrapolated between 1 bar and 1·0 GPa to give a pressure of 0·41 GPa. This value agrees with the Boyd et al. (1964) data and is virtually identical to the Taylor (1973) estimate (0·4 GPa). The low-pressure estimate (0·13 GPa) of Chen & Presnall (1975) can be linked to the problems they had identifying the orthoenstatite melting and locating the solidus at high pressure.
According to Bowen (1928), the peritectic melting of enstatite to forsterite + liquid can lead to the generation of silica-saturated magmas by fractional crystallization of silica-undersaturated magmas. The limiting pressure of 0·41 GPa shows that this petrogenetic process can occur in shallow to intermediate magma chambers. The presence of other elements such as Fe and Al (Chen & Presnall, 1975), or volatiles such as H2O (Kushiro, 1968, 1972b; Kushiro & Yoder, 1968; Warner, 1973) can obviously modify this interpretation.
The CaMgSi2O6–SiO2 pseudo-binary
For the pseudo-binary CaMgSi2O6–SiO2 (Fig. 4) experimental data at 1·0 GPa were reproduced within experimental error limits from 25°C to above the liquidus temperatures, and the optimization at 1·0 GPa is valid for the whole phase diagram. Unfortunately, no experimental data exist at other pressures for comparison.
The topology of the phase diagram is virtually the same at 1 bar and 1 GPa. The only notable difference lies in the size of the clinopyroxene + liquid field. The piercing point clinopyroxene + silica + liquid, which bounds the clinopyroxene + liquid field, shifts from 0·375 mol fraction SiO2 at 1 bar to 0·414 at 1·0 GPa, which represents an increase of 3·9 mol % SiO2.
The CaMgSi2O6–Mg2SiO4 pseudo-binary
In the case of the CaMgSi2O6–MgSi2O4 pseudo-binary (Fig. 5), the optimization is valid for the whole phase diagram except for compositions with 0·80 mol fraction SiO2 and below the liquidus (see Fig. 5b). For these compositions, very complex phase equilibria involving clinopyroxene, orthopyroxene, pigeonite, and olivine solid solutions occur in the phase diagram. These were not modeled at 1 bar by Jung (2003) and for this reason we did not intend to explore this area of the phase diagram at 1·0 GPa. The optimization shows that we have apparently failed to observe the liquid phase in the experiments performed in the clinopyroxene + olivine + liquid field. As a matter of fact, backscatter imaging reveals the presence of possible glass pockets for these experiments, but their size is too small (2–3 µm) to be unambiguously interpreted as glass; for this reason, these ‘glass pockets’ were not reported in the experimental results. The most important problem with the optimization of the CaMgSi2O6–Mg2SiO4 pseudo-binary concerns the olivine liquidus. The olivine liquidus generated by the optimization is about 75°C too low in relation to our experimental brackets, which is larger than the uncertainties associated with the thermocouples (about 20°C at this temperature range). The only way to solve this problem is to raise the melting temperature of forsterite by about 75°C, which is considerable. As mentioned earlier, the melting of forsterite can take place over a 46°C temperature interval at 1·0 GPa. By taking this interval into consideration, we still end up with a melting temperature of 1955°C, which agrees very well with the temperature of 1948°C calculated from the forsterite melting curve of Davis & England (1963, 1964), but appears to be too low with respect to the olivine liquidus. Numerous attempts to solve this problem by performing new forsterite melting point determinations at 1·0 GPa were unsuccessful and we therefore decided to keep the forsterite melting point at 1955°C. In terms of consistency, the optimized phase diagrams at 1 bar and 1·0 GPa are in agreement with the experimental data collected at 2·0 GPa by Kushiro (1964) and at 4·0 GPa by Davis (1964).
Like the CaMgSi2O6–SiO2 system, the topology of the CaMgSi2O6–Mg2SiO4 pseudo-binary is virtually the same at 1 bar and 1 GPa; the only difference lies in the size of the clinopyroxene + liquid field. The piercing point clinopyroxene + silica + liquid shifts from 0·191 mol fraction SiO2 at 1 bar to 0·331 at 1·0 GPa, which represents an increase of 14 mol % SiO2. This large increase may be due to the relatively low temperature of the olivine + liquid liquidus. A new determination of the olivine melting curve could confirm this possibility.
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CONCLUSION |
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TOPABSTRACTINTRODUCTIONMETHODSEXPERIMENTAL RESULTS AT 1{middle...THERMODYNAMIC MODELSTHERMODYNAMIC OPTIMIZATION AND...DISCUSSIONCONCLUSIONREFERENCES |
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The thermodynamic modeling for the CaO–MgO–SiO2 system was performed at 1·0 GPa based upon new experimental results at 1·0 GPa and new thermodynamic optimizations at 1 bar. The experimental data at 1·0 GPa were reproduced within experimental error limits from 25°C to above the liquidus temperatures for the entire CaO–SiO2, MgO–SiO2, CaMgSi2O6–SiO2 and CaMgSi2O6–Mg2SiO4 systems. We believe that the optimized model parameters can predict the phase equilibria in the CaO–MgO–SiO2 system up to pressure of several GPa with the accuracy within 50°C.
Pressure is found to have little effect on the topology of the CaO–SiO2, CaMgSi2O6–SiO2, and CaMgSi2O6–Mg2SiO4 systems but a pronounced impact on the MgO–SiO2 binary. These contrasting behaviors are mainly associated with the polymorphic transition undergone by the magnesium metasilicate at high pressure. The amphoteric nature of the Mg2+ cation in the liquid makes the melt compressible in the MgO–SiO2 system, which should slow the rise of the MgSiO3 melting point with pressure but despite this, the melting point of MgSiO3 is observed to rise by 110°C between 1 bar and 1 GPa, which suggests that the compressibility effect experienced by the liquid is negligible compared with that affecting the metasilicate. In addition to this, pressure is also found to have a marked effect on the size of the clinopyroxene + liquid field in the CaMgSi2O6–SiO2 and CaMgSi2O6–Mg2SiO4 pseudo-binaries.
The present optimized phase diagrams can be applied to low-pressure fractionation of basaltic magmas. Moreover, the information gathered about pressure effects on melt structure is encouraging and this can be considered as an important first step to better understand multi-component systems.
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ACKNOWLEDGEMENTS |
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We thank Paul Asimov, Surendra Saxena and an anonymous reviewer for their critical reading and constructive comments. This work benefited the financial support of NSERC and Reinhardt scholarships, Leroy and McGregor fellowships, and a GSA research grant (no. 4957-92) to P.H. and NSERC operating grant (no. OGP0089662) to D.R.B.
* Corresponding author. E-mail: pierreh{at}eps.mcgill.ca
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