Experimental Investigation and Optimization of Thermodynamic ...

JOURNAL OF PETROLOGY

VOLUME 46

NUMBER 9

PAGES 1859–1880

2005

doi:10.1093/petrology/egi037

Experimental Investigation and Optimization of Thermodynamic Properties and Phase Diagrams in the Systems CaO---SiO2, MgO---SiO2, CaMgSi2O6---SiO2 and CaMgSi2O6---Mg2SiO4 to 10 GPa PIERRE HUDON1*, IN-HO JUNG2 AND DON R. BAKER1 , DEPARTMENT OF EARTH AND PLANETARY SCIENCES, McGILL UNIVERSITY, 3450 RUE UNIVERSITE

1

AL, QC, H3A 2A7, CANADA MONTRE COLE POLYTECHNIQUE DE MONTRE AL, CENTRE FOR RESEARCH IN COMPUTATIONAL THERMOCHEMISTRY, E

2

AL, QC, H3C 3A7, CANADA P.O. BOX 6079, SUCCURSALE CENTRE-VILLE, MONTRE

RECEIVED FEBRUARY 17, 2004; ACCEPTED MARCH 14, 2005 ADVANCE ACCESS PUBLICATION APRIL 29, 2005 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 þ liquid increases with increasing pressure. This change is related to the shift of the piercing points clinopyroxene þ silica þ liquid ( from 0.375 mol fraction SiO2 at 1 bar to 0.414 at 1.0 GPa) and clinopyroxene þ olivine þ liquid (from 0.191 mol fraction SiO2 at 1 bar to 0.331 at 1.0 GPa) that bound the clinopyroxene þ liquid field in the CaMgSi2O6 SiO2 and CaMgSi2O6 .Mg2SiO4 pseudo-binaries, respectively.

INTRODUCTION

KEY WORDS: CaO---SiO2; CaMgSi2O6---Mg2SiO4; CaMgSi2O6---SiO2; experiments; MgO---SiO2

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. 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

*Corresponding author. E-mail: [email protected]

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Fig. 1. The optimized CaO---MgO---SiO2 system at 1 bar ( Jung, 2003). Temperatures in parentheses are congruent melting points. Ak, akermanite; Crs, cristobalite; Di, diopside; Fo, forsterite; Mnt, monticellite; Mrw, merwinite; Opx, orthopyroxene; Per, periclase; Pig, pigeonite; Ppx, protopyroxene; Pwo, pseudowollastonite; Tri, tridymite; Wo, wollastonite.

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.

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HUDON et al.

SYSTEM CaO---MgO---SiO2 AT 1.0 GPa

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.

METHODS Starting materials Starting materials consisted of mechanical mixtures of pure oxides and/or end-member silicates. The endmember 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 þ SiO2 and CaCO3 þ MgO þ 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 gCa2SiO4, the MgSiO3 was a mixture of clino- and protoenstatite, the CaSiO3 was pseudowollastonite, and the CaMgSi2O6 was diopside. The SiO2 used was made of b-cristobalite and a-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 g-Ca2SiO4 to b-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 pistoncylinder 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.

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

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Table 1: Experimental conditions and results for the system CaO---SiO2 at 1.0 GPa Sample

Capsule

Starting material

T ( C)

0.28 0.28

Lim þ g-Lar

1780 þ 6/---5

60

Lim þ b/g-Lar

2100 þ 5/---8

5

Hat* þ Lar þ Gl

0.28 0.40

Lim þ b/g-Lar

2130 þ 4/---7

5

Lar þ Gl

Lim þ Crs/Qtz

1470 þ 1/---2

300

Lar þ Pwo

0.40 0.40

b/g-Lar þ Pwo

1480 þ 3/---3

15

Lar þ Pwo

b/g-Lar þ Pwo

1490 þ 2/---4

15

Lar þ Gl (þPwo, tr)

0.40 0.40

Lim þ Crs/Qtz

1756 þ 9/---7

30

Lar þ Gl

Lim þ Crs/Qtz

1887 þ 2/---5

17

Gl

0.45 0.45

Lim þ Crs/Qtz

1470 þ 1/---2

300

Lim þ Crs/Qtz

1490 þ 3/---4

240

0.45 0.45

Lim þ Crs/Qtz

1530 þ 3/---2

30

Lim þ Crs/Qtz

1545 þ 4/---5

40

Gl

0.50 0.50

Lim þ Crs/Qtz

1545 þ 4/---5

40

Pwo

Starting composition

Duration (minutes)

Phases

(mol fr. SiO2)

CS-139

Re

CS-197

Re

CS-193

Re

CS-111

Pt

CS-202

Pt

CS-199

Pt

CS-66

Mo

CS-70

Mo

CS-112

Pt

CS-132

Pt

CS-129

Pt

CS-118

Pt

CS-119

Pt

CS-116

Pt

CS-97

Pt

CS-102

Pt

CS-89

Pt

CS-130

Pt

CS-120

Pt

CS-98

Pt

CS-103

Pt

CS-138

Pt

Hat þ Lar

Lar þ Pwo Lar þ Pwo þ Gl Lar þ Gl

Lim þ Crs/Qtz

1560 þ 2/---2

38

Gl

0.55 0.55

Lim þ Crs/Qtz

1430 þ 1/---7

60

Pwo þ Qtz (þGl, tr)

Lim þ Crs/Qtz

1450 þ 4/---1

360

0.55 0.55

Lim þ Crs/Qtz

1470 þ 3/---6

60

0.55 0.60 0.60 0.60

Pwo þ Gl (þQtz, tr) Pwo þ Gl

Lim þ Crs/Qtz

1530 þ 3/---2

30

Pwo þ Gl

Lim þ Crs/Qtz

1545 þ 4/---5

40

Gl

Lim þ Crs/Qtz

1430 þ 1/---7

60

Pwo þ Qtz (þGl, tr)

Lim þ Crs/Qtz

1450 þ 1/---4

360

Pwo þ Qtz þ Gl

Lim þ Crs/Qtz

1460 þ 2/---2

240

Pwo þ Gl

CS-90

Pt

0.60

Lim þ Crs/Qtz

1470 þ 3/---6

60

Pwo þ Gl

CS-73

Pt

0.60 0.70

Lim þ Crs/Qtz

1475 þ 5/---4

60

Gl

CS-104

Pt

CS-137

Re

CS-140

Re

Lim þ Crs/Qtz

1740 þ 4/---2

60

Qtz(tr) þ Gl

0.70 0.70

Lim þ Crs/Qtz

1760 þ 8/---6

60

Qtz(tr) þ Gl

Lim þ Crs/Qtz

1780 þ 6/---5

60

Gl

0.40

Lim þ Qtz

1515 þ 3/---4

60

[Lar þ Liq]

1475 þ 7/---2

300

1475 þ 2/---5

60

1435 þ 2/---2

360

Reversal experiments CS-142

CS-144

Pt

Pt

0.60

Lim þ Qtz

Lar þ Pwo [Liq] Pwo þ Qtz (þGl, tr)

*Approaches the composition of Ca3SiO5 (hatrurite). Lim, lime; Hat, hatrurite; b-Lar, b-larnite; g-Lar, g-larnite; Lar, larnite (polymorph not determined); Pwo, pseudowollastonite; Crs, cristobalite; Qtz, quartz; Gl, glass; Liq, liquid; tr, traces. Phases in parentheses were not considered in final run products. Identification of bracketed phases is based on previous experiments performed at the same P---T conditions and similar run durations.

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 mm 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.

EXPERIMENTAL RESULTS AT 1. 0 GPa 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 mm)

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HUDON et al.

Table 2: Experimental conditions and results for the system MgO---SiO2 at 1.0 GPa Sample

Capsule

Starting material

T ( C)

0.30 0.30

Per þ Fo

1920 þ 2/---2

5

Per þ Fo

Per þ Fo

1940 þ 1/---2

3

Per þ Gl

0.30 0.30

Per þ Fo

2090 þ 6/---5

5

Per þ Gl

Per þ Fo

2130 þ 4/---7

5

Gl

0.33 0.33

Fo

1930 þ 2/---2

5

Fo þ Gl

Fo

1940 þ 1/---2

5

Fo þ Gl

0.33 0.40

Fo

1950 þ 2/---2

5

Gl

Per þ Crs/Qtz

1825 þ 4/---0

30

Fo þ Gl

0.40 0.465

Per þ Crs/Qtz

1849 þ 1/---1

12

Gl

Fo þ Pen/Cen

1650 þ 3/---3

60

Fo þ En (þGl, tr)

0.465 0.465

Fo þ Pen/Cen

1660 þ 3/---4

30

Fo þ En

Fo þ Pen/Cen

1665 þ 4/---2

30

Fo þ Gl

0.465 0.465

Per þ Crs/Qtz

1686 þ 1/---2

240

Fo þ Gl

Per þ Crs/Qtz

1696 þ 1/---3

60

Gl

0.49 0.49

Per þ Crs/Qtz

1660 þ 3/---4

30

Fo þ En

Fo þ Pen/Cen

1665 þ 4/---2

30

Gl

0.50 0.50

Pen/Cen

1660 þ 2/---2

5

En

Pen/Cen

1670 þ 0/---2

5

Gl

0.53 0.53

Pen/Cen þ Crs/Qtz

1640 þ 5/---5

240

En þ Qtz (þGl, tr)

Pen/Cen þ Crs/Qtz

1650 þ 2/---2

30


0.53 0.53

Pen/Cen þ Crs/Qtz

1660 þ 3/---4

30

Gl

Pen/Cen þ Crs/Qtz

1665 þ 4/---2

30

0.5555 0.5555

Pen/Cen þ Crs/Qtz

1640 þ 5/---5

240


Pen/Cen þ Crs/Qtz

1650 þ 2/---2

30


Pen/Cen þ Crs/Qtz

1660 þ 3/---4

30

Qtz þ Gl (þEn, tr)

Per þ Crs/Qtz

1750 þ 2/---1

30

Qtz þ Gl

1756 þ 9/---7

30

Gl


Duration (minutes)

Phases

(mol fr. SiO2)

MS-333

Re

MS-336

Re

MS-373

Re

MS-384

Re

MS-366

Re

MS-337

Re

MS-357

Re

MS-86

Mo

MS-44

Mo

MS 286

Pt

MS-313

Pt

MS-317

Pt

MS-78

Pt

MS-74

Pt

MS-314

Pt

MS-318

Pt

MS-300

Pt

MS-299

Pt

MS-218

Pt

MS-321

Pt

MS-315

Pt

MS-319

Pt

MS-219

Pt

MS-322

Pt

MS-316

Pt

MS-73

Pt

0.5555 0.60

MS-169

Mo

0.60

Per þ Crs/Qtz

0.49

Fo þ Pen/Cen

Gl

Reversal experiments MS-395

MS-396

Pt

Pt

0.53

Pen/Cen þ Qtz

1680 þ 3/---4

18

[Liq]

1630 þ 1/---2

45

Fo þ En

1680 þ 3/---4

18

[Liq]

1630 þ 1/---2

45

En þ Qtz

Per, periclase; Fo, forsterite; Pen, protoenstatite; Cen, clinoenstatite; En, enstatite (polymorph not determined); other abbreviations and notes are the same as in Table 1.

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.

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Table 3: Experimental conditions and results for the system CaMgSi2O6---SiO2 at 1.0 GPa Sample

Capsule


Starting material

T ( C)

Duration (minutes)

Phases

(mol fr. SiO2)

PCC-14

Pt

0

Di

1506

CMS-101

Pt

0

Di

1510 þ 1/---2

5

Di

CMS-89

Pt

0

Di

1515 þ 0/---2

5

Gl

0 0.1

Di

1519 þ 1/---0

5

Gl

Diglass þ SiO2glass

1400 þ 3/---2

60

Cpx þ Qtz

0.1 0.1


1440 þ 3/---4

30

Cpx þ Qtz þ Gl


1460 þ 2/---2

240

0.1 0.1


1475 þ 5/---4

60

Cpx þ Gl


1500 þ 13/---14

240

Cpx þ Gl

0.1 0.1


1505 þ 4/---4

60


1515 þ 0/---2

5

PCC-18

Pt

CMS-119

Pt

CMS-103

Pt

CMS-69

Pt

CMS-44

Pt

CMS-65

Pt

CMS-86

Pt

CMS-90

Pt

CMS-3

Pt

CMS-7

Pt

CMS-11

Pt

CMS-15

Pt

CMS-19

Pt

CMS-4

Pt

CMS-64

Pt

CMS-8

Pt

CMS-12

Pt

CMS-16

Pt

CMS-45

Pt

CMS-87

Pt

CMS-29

Pt

CMS-26

Pt

CMS-75

Pt

CMS-98

Pt

CMS-74

Pt

CMS-71

Re

0.25 0.25 0.25 0.25 0.25 0.35 0.35 0.35 0.35 0.35 0.47

12

Di

Cpx þ Qtz þ Gl

Cpx þ Gl Gl

Di þ Crs/Qtz

1446 þ 2/---3

60

Cpx þ Qtz þ Gl

Di þ Crs/Qtz

1475 þ 3/---4

60

Cpx þ Qtz þ Gl

Di þ Crs/Qtz

1495 þ 3/---2

60

Cpx þ Gl

Di þ Crs/Qtz

1505 þ 3/---3

60

Cpx þ Gl

Di þ Crs/Qtz

1515 þ 3/---3

60

Gl

Di þ Crs/Qtz

1446 þ 2/---3

60

Cpx þ Qtz þ Gl

Di þ Crs/Qtz

1470 þ 1/---2

300

Cpx þ Qtz þ Gl

Di þ Crs/Qtz

1475 þ 3/---4

60

Cpx þ Qtz þ Gl

Di þ Crs/Qtz

1495 þ 3/---2

60

Cpx þ Gl

Di þ Crs/Qtz

1505 þ 3/---3

60

Gl

Di þ Crs/Qtz

1475 þ 5/---4

60

Cpx þ Qtz þ Gl

0.47 0.47

Di þ Crs/Qtz

1505 þ 4/---4

60

Qtz þ Gl

Di þ Crs/Qtz

1533 þ 9/---5

60

Gl

0.47 0.55

Di þ Crs/Qtz

1543 þ 4/---3

60

Gl

Di þ Crs/Qtz

1600 þ 8/---4

60

Qtz þ Gl Gl

0.55 0.7 0.7

Di þ Crs/Qtz

1620 þ 3/---4

20

Di þ Crs/Qtz

1760 þ 4/---3

60

Qtz þ Gl

Di þ Crs/Qtz

1780 þ 6/---5

60

Gl

0.55

Di þ Crs/Qtz

1525 þ 1/---7

18

[Liq]

1445 þ 1/---2

45

Cpx þ Qtz þ Gl

Reversal experiments CMS-111

Pt

Di, diopside; Cpx, clinopyroxene; other abbreviations are the same as in Table 1.

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: g, b (larnite), a0 Low(2a,b,2c), a0 Low(a,3b,c), a0 High, a, and the high-T---high-P K2NiF4 type (Remy et al., 1995). At 1 atm the stable polymorph at the melting point is the a-phase, which transforms to the a0 High-phase at 1437 C.

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HUDON et al.


Table 4: Experimental conditions and results for the system CaMgSi2O6 ---Mg2SiO4 at 1.0 GPa Sample

Capsule


Starting material

T ( C)

Duration (minutes)

Phases

(mol fr. Mg2SiO4)

CMS-46

Pt

0.10

Di þ Fo

1475 þ 5/4

60

Cpx þ Ol

CMS-85

Pt

0.10 0.10

Di þ Fo

1505 þ 4/4

60

Cpx þ Gl

CMS-91

Pt

CMS-2

Pt

CMS-6

Pt

CMS-10

Pt

CMS-14

Pt

CMS-18

Pt

CMS-22

Pt

CMS-1

Pt

CMS-5

Pt

CMS-9

Pt

CMS-13

Pt

CMS-17

Pt

CMS-21

Pt

CMS-28

Pt

CMS-61

Pt

CMS-73

Pt

CMS-66

Pt

0.23 0.23 0.23 0.23 0.23 0.23 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.50 0.50 0.60

Di þ Fo

1515 þ 0/2

5

Di þ Fo

1446 þ 2/3

60

Gl Cpx þ Ol

Di þ Fo

1475 þ 3/4

60

Cpx þ Ol

Di þ Fo

1495 þ 3/2

60

Cpx þ Ol

Di þ Fo

1505 þ 3/3

60

Cpx þ Ol

Di þ Fo

1515 þ 3/3

60

Cpx þ Ol þ Gl

Di þ Fo

1525 þ 3/3

60

Gl

Di þ Fo

1446 þ 2/3

60

Cpx þ Ol

Di þ Fo

1475 þ 3/4

60

Cpx þ Ol

Di þ Fo

1495 þ 3/2

60

Cpx þ Ol

Di þ Fo

1505 þ 3/3

60

Cpx þ Ol þ Gl

Di þ Fo

1515 þ 3/3

60

Cpx þ Ol þ Gl

Di þ Fo

1525 þ 3/3

60

Cpx þ Ol þ Gl

Di þ Fo

1533 þ 9/5

60

Gl

Di þ Fo

1680 þ 12/11

60

Ol þ Gl

Di þ Fo

1700 þ 7/4

60

Gl

Di þ Fo

1500 þ 13/14

60

Cpx þ Ol

CMS-84

Pt

0.60

Di þ Fo

1505 þ 4/4

60

Cpx þ Ol

CMS-106

Pt

Di þ Fo

1533 þ 2/3

20

Ol þ Gl

CMS-68

Re

0.60 0.60

Di þ Fo

1760 þ 8/5

60

Ol þ Gl

CMS-72

Re

Di þ Fo

1780 þ 6/5

60

Gl

CMS-107

Pt

0.60 0.90

Di þ Fo

1533 þ 2/3

20

Ol þ Gl

CMS-135

Re

0.90

Di þ Fo

1940 þ 1/2

3

0.60

Di þ Fo

Gl

Reversal experiments CMS-113

Pt

1550 þ 0/2

18

[Ol þ Gl]

1480 þ 1/4

45

Cpx þ Ol þ Gl

Ol, olivine; other abbreviations are the same as in Tables 1---3.

According to Remy et al. (1995), the a-phase is stable at the 1.0 GPa melting point and transforms to the a0 Highphase 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 a0 Highphase 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

1865


VOLUME 46

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 (2845

MgO (per)y

298---3098 >3098

MgO (liquid)y

298---3098 >3098

SiO2 (b-crs)z

298.15---1996 >1996

SiO2 (b-qtz)z

298.15---3000 >3000

SiO2 (liquid)z

298.15---1996 >1996

Mg2SiO4 (fo)y MgSiO3 (proto)x

298.15---3000 298.15---3000

b

c (105)

e (108)

d

635090.0 657730.8

37.75000 13.22032

58.79117 62.76000

0.0 0.0

11.47146 0.0

133.9040 0.0

1.029788 0 .0

0.0 0.0

555594.0 578234.8

65.69076 41.16108

58.79117 62.76000

0.0 0.0

11.47146 0.0

133.9040 0.0

1.029788 0 .0

0.0 0.0

601500.0 642428.3

26.95140 13.75885

61.10965 66.94400

0.0 0.0

6.21154 0.0

296.1990 0.0

0.058466 0 .0

0.0 0.0

545345.0 565026.3

27.00404 11.22636

72.79556 66.94400

0.0 0.0

5.22752 0.0

296.1990 0.0

0.058466 0 .0

— —906377.0 936216.9

46.0288 5.116827

83.5136 85.7720

0.0 0.0

24.55360 0.0

374.693 0.0

2.8007219 0 .0

908627.0 ---950177.9

44.2068 ---1.72091 50.8291

80.0120 85.7720

0.0 0.0

35.46684 0.0

240.276 0.0

4.9156837 0 .0

83.5136 85.7720

0.0 0.0

---24.55360 0.0

---374.693 0.0

2.8007219 0 .0

---896796.0 ---926635.5 ---2177699.3 ---1533278.0

9.917131 94.00993 81.7000

238.6414 101.1900

0.0 0.01505673

107.6400

0.0 ---25.75452 ---25.75452

---2001.261 0.0

MgSiO3 (ortho)x

298.15---3000

---1545080.0

MgSiO3 (l-cli)x Ca2SiO4 (a-lar)*

298.15---3000 298.15---3000

---1543953.0 ---2278596.0

66.6660 69.3700 144.7480

104.3000 209.6800

0.01858268 0.01588268 0.0

---25.75452 ---79.89400

Ca2SiO4 (a0 -lar)* Ca2SiO4 (g-lar)*

298.15---3000 298.15---3000

---2304009.1 ---1625506.6

123.4143 109.6946

230.8367 255.2200

0.0 0.0

---79.89400 0.0

CaSiO3 (pwo)*

298.15---3000 298.15---3000

---1634676.4 ---3866291.2

141.1561 149.0727

0.0 0.0

---58.57595 ---36.59348

Ca2MgSi2O7 (ak)x

298.15---3000 298.15---3000

---3199747.0 ---3866291.2

142.5000 212.000

305.4100 387.0639

0.0 0.0

---71.65973 0.0

---1604.931 ---2938.769

CaMgSiO4 (mnt)x¶

298.15---3000

---2253375.0

108.30

226.34

0.0

---11.7970901

---1542.74

CaSiO3 (wo)* CaMgSi2O6 (di)x

f (103)

86.93646 79.81426

0.0 0.0 ---701.9000 ---1033.088 ---2340.800 ---417.2320 ---690.2950

---1.162433 0 .0 0 .0

3.14218 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0 .0 12.974799

0.0 0.0

12.974799 1.4104000

0.0 0.0

9.4073495 4.8434942

0.0 0.0

9.2183754

0.0 0.0

---0.407904 ---0.2328588

0.0

*Eriksson et al. (1994). yWu et al. (1993b). zHudon et al. (2002). xBale et al. (2002); Jung (2003). ¶End-member of olivine solid solution. per, periclase; b-crs, b-cristobalite; b-qtz, b-quartz; fo, forsterite; proto, protoenstatite; ortho, orthoenstatite; l-cli, lowclinoenstatite; a-lar, a-larnite; a0 -lar, a0 -larnite; g-lar, g-larnite; pwo, pseudowollastonite; wo, wollastonite; ak, akermanite; di, diopside; mnt, monticellite.

The parameter Y is expressed by Y ¼ Vð1;T Þ =VðP;T Þ where V(1,T ) is calculated using Z o Vð1;T Þ ¼ V29815 exp

ð8Þ

T

aðT ÞdT

All the Gibbs energies of end-members of slag and solid solutions are expressed in the same way as described above. The optimized thermodynamic and volumetric properties of pure compounds are given in Tables 5 and 6, respectively.

ð9Þ

29815

o and V29815 is the molar volume at 298.15 K and 1 bar, and a(T ) is the thermal expansion expressed as the polynomial

aðT Þ ¼ a0 þ a1 T þ a2 T 1 þ a3 T 2 :

ð10Þ

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)

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VOLUME 46

NUMBER 9

SEPTEMBER 2005

Table 6: Volumetric properties of solid and liquid phases o V29815

Phase

a(T ) ¼ a0 þ a1T þ a2T1 þ a3T2

b(T ) ¼ b0 þ b1T þ b2T2 þ b3T3 (105 Pa)

KP0

0 KP,T (103)

3

(cm /mol) a0 (106)

a1 (109)

a2 (102)

a3 (102) 43.37 0.0 95.0 0.0

16.76 20.92

33.62 0.0

5.44 0.0

0.0012 0.0

11.25 20.92

36.4 0.0

8.35 0.0

0.0850 0.0

26.978 23.700

24.3616 0.0

4.0248 0.0

2.75739 0.0

SiO2 (liquid)z

25.269

Mg2SiO4 (for)*

43.665 32.4605

24.6421 20.1

21.8347 13.9

0.0 0.1627

44.46 38.71

21.8623 4.4633

0.47869 0.03435

36.7653 0.0

23.6466 0.0

0.20099 0.0

CaO (lime)* CaO (liquid)y MgO (per)* MgO (liquid)y SiO2 (b-crs)z SiO2 (b-qtz)z

MgSiO3 (proto)x MgSiO3 (ortho)x MgSiO3 (l-cli)x

31.2737 31.2437

Ca2SiO4 (a0 -lar)y

52.19367 52.19367

Ca2SiO4 (g-lar)y CaSiO3 (pwo)*

52.19367 39.92717

CaSiO3 (wo)*

40.07718 66.10208

Ca2SiO4 (a-lar)y

CaMgSi2O6 (di)x Ca2MgSi2O7 (ak)* CaMgSiO4 (mnt)*¶

92.810 51.46911

0.0 0.0

0.0 0.0

0.0 0.0

33.94 24.85

4.66398 8.071

0.14588 0.52386

25.1 0.0

9.821 0.0 1.50966

0.0 2.48638

55.412

0.5191

0.0 0.0

b0 (106)

b1 (1010)

b2 (1014)

b3 (1017)

0.8605 0.0

1.25 0.0

3.33 0.0

0.328 0.0

4.00 0.0

0.0 0.0

0.5875 0.0

1.101 0.0

1.37 0.0

0.48 0.0

4.1 0.0

0.04 0.0

0.0 0.0

6.0 1.0

0.0 0.0

0.0 1.702

4.0 5.2

2.559 0.0002

29.4578 1.14126

4.62 4.2

0.00299 0.00015

4.28415 0.0

4.53 0.0 0.0

0.00055 0.0

5.13000 1.77000

0.0 33.8 409.241 172.78 488.85 0.0 0.0 0.0 186.336 236.5 236.5

10.954 0.7427

0.0 24.0

102.114 1.24

0.0 0.69

0.90860 0.8892

6.91731 1.3584

0.24728 3.1613

0.93760 0.0

0.00004 0.0

0.0 0.0 0.86311 0.9135 0.9082

0.0 441.13

10.0 0.0

1.000 0.72388

0.0 0.0 1.4726 0.8944 0.8384 0.0 0.72179

16.5567 0.0 0.0 0.0

0.0 0.0

2.4303 0.1275

1.450 1.3598

0.1165 0.0

0.2291 0.0

4

0.14437

4

5.0

0.0 4 4

4

0.0 0.0 0.0 0.0 0.0005 0.0 0.0

*Saxena et al. (1993). yThis study. zHudon et al. (2002). xShi et al. (1994, 1996). ¶End-member of olivine solution.

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 ðCaCaÞ þ ðSiSiÞ ¼ 2ðCaSiÞ;

DgCaMg

ð11Þ

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 ðMgMgÞ þ ðSiSiÞ ¼ 2ðMgSiÞ;

ðCaCaÞ þ ðMgMgÞ ¼ 2ðCaMgÞ;

DgMgSi

DgCaMg

ð12Þ

The olivine solid solution has two distinct octahedral sublattices (or sites), called M2 and M1: ðCa2þ ; Mg2þ ÞM2 ðCa2þ ; Mg2þ ÞM1 SiO4

ð13Þ

where (A---B) represents a second-nearest-neighbor A---B pair. That is, A---B pair is equivalent to A---O---B pair where O is oxygen. The parameters of the model are the Gibbs energies DgA,B of these reactions,

ð14Þ

where cations shown within a set of parentheses occupy the same sublattice. The end-members of the olivine solid solution in the CaO---MgO---SiO2 system are a-larnite, Ca2SiO4,

1868

HUDON et al.


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: XX YiM2 YjM1 Gij TSC þ G E G¼ ð15Þ i

j

YiM2

where and YiM1 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 X X M2 M2 M1 M1 Yi ln Yi þ Yj ln Yj SC ¼ R ð16Þ i

j

j

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.

THERMODYNAMIC OPTIMIZATION AND RESULTS

k

XXX þ YkM2 YiM1 YjM1 Lk:ij i

Other solid solutions

j

and G E is the excess Gibbs energy, given by XXX GE ¼ YiM2 YjM2 YkM1 Lij:k i

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.

ð17Þ

k

where Lij:k and Lk:ij are interaction energies between cations i and j on one sublattice when the other sublattice is occupied by k. The dependence of the interaction energies on composition can be expressed by Redlich---Kister power series: Xm Lij:k ðYjM2 YiM2 Þm Lij:k ¼ ð18Þ m

Lk:ij ¼

Xm

Lk:ij ðYjM1 YiM1 Þm :

m

ð19Þ

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 (Ca2þ,Mg2þ)M2(Mg2þ)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

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 o , to reproduce the phase diagram formation, DH29815 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 pseudoend-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.

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Table 7: Optimized model parameters of solutions ( J/mol); P is in GPa Liquid: CaO---MgO---SiO2 G [MgO(liquid)]

volumetric properties: MgO (liquid)

G [CaO(liquid)]

volumetric properties: CaO (liquid)

G [SiO2(liquid)]

volumetric properties: SiO2 (liquid)

Binary parameters: 5 7 DgCaSi ¼ 158218 þ 19.456T 7070.96P 37932 YSiO2 --- 90148YSiO þ (439893 133.888T þ 2662.86P)YSiO 2 2 7 DgMgSi ¼ 86090 10180P (48974 37.656T þ 10615.37P)YSiO2 þ (328109 125.52T þ 8911.75P)YSiO 2 DgCaMg ¼ 45330.96 30582.75YCaO

Ternary parameters: q001 MgSi;Ca ¼ 41840 q001 CaSi;Mg ¼ 83680 q021 CaSi;Mg ¼ 29288 þ 6276P Olivine: (Ca2þ,Mg2þ)M2[Ca2þ, Mg2þ] M1SiO4 GMgMg ¼ G [Mg2SiO4(fo)]

volumetric properties: Mg2SiO4 (fo)

GCaCa ¼ G [Ca2SiO4 (g-lar)]

volumetric properties: Ca2SiO4 (g-lar)

GCaMg ¼ G [CaMgSiO4 (mnt)]

volumetric properties: CaMgSiO4 (mnt)

GMgCa ¼ GCaMg þ 146440

volumetric properties: CaMgSiO4 (inverse-mnt)

LCaMg:Ca ¼ 0LCaMg:Mg ¼ 32235.53 1 LCaMg:Ca ¼ 1LCaMg:Mg ¼ 4279.92

no pressure-dependent excess parameters were added

0


LCa:CaMg ¼ 0LMg:CaMg ¼ 28032.8 12.55T

0

2þ

2þ M2

Clinopyroxene: (Ca ,Mg )

2þ M1

[Mg ]


Si2O6

GCaMg ¼ G [CaMgSi2O6(di)]

volumetric properties: CaMgSi2O6 (di)

GMgMg ¼ G (MgMgSi2O6) ¼ 2fG [MgSiO3 (l-cli)]g þ 4694.5 --- 3.70T 0 LCaMg:Mg ¼ 25304.0 þ 2.358T

volumetric properties: 2 [MgSiO3 (l-cli)] no pressure-dependent excess parameters were added

LCaMg:Mg ¼ 3018.6

1


The expressions of model parameters for the liquid are shown in the section ‘Liquid phase’. Model parameters at 1 bar optimized by Jung (2003). Abbreviations are the same as in Table 5.

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 pressuredependent 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.

DISCUSSION 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