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1.
Robert G. Berman 《Geochimica et cosmochimica acta》1984,48(4):661-678
A thermodynamic model is proposed for calculation of liquidus relations in multicomponent systems of geologic interest. In this formulation of mineral-melt equilibria, reactions are written in terms of the liquid oxide components, and balanced on the stoichiometry of liquidus phases. In order to account for non-ideality in the liquid, a ‘Margules solution’ is derived in a generalized form which can be extended to systems of any number of components and for polynomials of any degree. Equations are presented for calculation of both the excess Gibbs free energy of a solution and the component activity coefficients.Application to the system CaO-Al2O3-SiO2 at one atmosphere pressure is achieved using linear programming. Thermodynamic properties of liquidus minerals and the melt are determined which are consistent with adopted error brackets for available calorimetric and phase equilibrium data. Constraints are derived from liquidus relations, the CaO-SiO2 binary liquid immiscibility gap, solid-solid reactions, and measured standard state entropies, enthalpies, and volumes of minerals in this system.Binary and ternary liquidus diagrams are recalculated by computer programs which trace cotectic boundaries and isothermal sections while checking each point on a curve for metastability. The maximum differences between calculated and experimentally determined invariant points involving stoichiometric minerals are 17°C and 1.5 oxide weight per cent. Because no solid solution models have been incorporated, deviations are larger for invariant points which involve non-stoichiometric minerals.Calculated heats of fusion, silica activities in the melt, and heats of mixing of liquids compare favorably with experimental data, and suggest that this model can be used to supplement the limited amount of available data on melt properties. 相似文献
2.
The energetics of multicomponent diffusion in molten CaO-Al2O3-SiO2 (CAS) were examined experimentally at 1440 to 1650°C and 0.5 to 2 GPa. Two melt compositions were investigated: a haplodacitic melt (25 wt.% CaO, 15% Al2O3, and 60% SiO2) and a haplobasaltic melt (35% CaO, 20% Al2O3, and 45% SiO2). Diffusion matrices were measured in a mass-fixed frame of reference with simple oxides as end-member components and Al2O3 as a dependent variable. Chemical diffusion in molten CAS shows clear evidence of diffusive coupling among the components. The diffusive flux of SiO2 is significantly enhanced whenever there is a large CaO gradient that is oriented in a direction opposite to the SiO2 gradient. This coupling effect is more pronounced in the haplodacitic melt and is likely to be significant in natural magmas of rhyolitic to andesitic compositions. The relative magnitude of coupled chemical diffusion is not very sensitive to changes in temperature and pressure.To a good approximation, the measured diffusion matrices follow well-defined Arrhenius relationships with pressure and reciprocal temperature. Typically, a change in temperature of 100°C results in a relative change in the elements of diffusion matrix of 50 to 100%, whereas a change in pressure of 1 GPa introduces a relative change in elements of diffusion matrix of 4 to 6% for the haplobasalt, and less than 5% for the haplodacite. At a pressure of 1 GPa, the ratios between the major and minor eigenvalues of the diffusion matrix λ1/λ2 are not very sensitive to temperature variations, with an average of 5.5 ± 0.2 for the haplobasalt and 3.7 ± 0.6 for the haplodacite. The activation energies for the major and minor eigenvalues of the diffusion matrix are 215 ± 12 and 240 ± 21 kJ mol−1, respectively, for the haplodacite and 192 ± 8 and 217 ± 14 kJ mol−1 for the haplobasalt. These values are comparable to the activation energies for self-diffusion of calcium and silicon at the same melt compositions and pressure. At a fixed temperature of 1500°C, the ratios λ1/λ2 increase with the increase of pressure, with λ1/λ2 varying from 2.5 to 4.1 (0.5 to 1.3 GPa) for the haplodacite and 4 to 6.5 (0.5 to 2.0 GPa) for the haplobasalt. The activation volumes for the major and minor eigenvalues of the diffusion matrix are 0.31 ± 0.44 and 2.3 ± 0.8 cm3 mol−1, respectively, for the haplodacite and −1.48 ± 0.18 and −0.42 ± 0.24 cm3 mol−1 for the haplobasalt. These values are quite different from the activation volumes for self-diffusion of calcium and silicon at the same melt compositions and temperature. These differences in activation volumes between the two melts likely result from a difference in the structure and thermodynamic properties of the melt between the two compositions (e.g., partial molar volume).Applications of the measured diffusion matrices to quartz crystal dissolution in molten CAS reveal that the activation energy and activation volume for quartz dissolution are almost identical to the activation energy and activation volume for diffusion of the minor or slower eigencomponent of the diffusion matrix. This suggests that the diffusion rate of slow eigencomponent is the rate-limiting factor in isothermal crystal dissolution, a conclusion that is likely to be valid for crystal growth and dissolution in natural magmas when diffusion in liquid is the rate-limiting factor. 相似文献
3.
The shear viscosity of 66 liquids in the systems CaO-Al2O3-SiO2 (CAS) and MgO-Al2O3-SiO2 (MAS) have been measured in the ranges 1-104 Pa s and 108-1012 Pa s. Liquids belong to series, nominally at 50, 67, and 75 mol.% SiO2, with atomic M2+/(M2++2Al) typically in the range 0.60 to 0.40 for each isopleth. In the system CAS at 1600°C, viscosity passes through a maximum at all silica contents. The maxima are clearly centered in the peraluminous field, but the exact composition at which viscosity is a maximum is poorly defined. Similar features are observed at 900°C. In contrast, data for the system MAS at 1600°C show that viscosity decreases with decreasing Mg/(Mg + 2Al) at all silica contents, but that a maximum in viscosity must occur in the field where Mg/2Al >1. On the other hand, the viscosity at 850°C increases with decreasing Mg/(Mg + 2Al) and shows no sign of reaching a maximum, even for the most peraluminous composition studied. The data from both systems at 1600°C have been analysed assuming that shear viscosity is proportional to average bond strength and considering the equilibrium:
Al[4]-(Mg,Ca)0.5⇔(Mg,Ca)0.5-NBO+AlXS 相似文献
4.
John R Beckett 《Geochimica et cosmochimica acta》2002,66(1):93-107
Activity coefficients of oxide components in the system CaO-MgO-Al2O3-SiO2 (CMAS) were calculated with the model of Berman (Berman R. G., “A thermodynamic model for multicomponent melts with application to the system CaO-MgO-Al2O3-SiO2,” Ph.D. dissertation, University of British Columbia, 1983) and used to explore large-scale relationships among these variables and between them and the liquid composition. On the basis of Berman’s model, the natural logarithm of the activity coefficient of MgO, ln(γMgOLiq), and ln(γMgOLiq/γSiO2Liq) are nearly linear functions of ln(γCaOLiq). All three of these variables are simple functions of the optical basicity Λ with which they display minima near Λ ∼ 0.54 that are generated by liquids with low ratios of nonbridging to tetrahedral oxygens (NBO/T) (<0.3) and a mole fraction ratio, XSiO2Liq/XAl2O3Liq, in the range 4 to 20. Variations in ln(γCaOLiq) at constant Λ near the minimum are due mostly to liquids with (XCaOLiq + XMgOLiq)/XAl2O3Liq < 1. The correlations with optical basicity imply that the electron donor power is an important factor in determining the thermodynamic properties of aluminosilicate liquids.For a constant NBO/T, ln(γCaOLiq/γAl2O3Liq) and ln(γMgOLiqγAl2O3Liq) form curves in terms of XSiO2Liq/XAl2O3Liq. The same liquids that generate minima in the Λ plots are also associated with minima in ln(γCaOLiqγAl2O3Liq) and ln(γMgOLiqγAl2O3Liq) as a function of XSiO2Liq/XAl2O3Liq. In addition, there are maxima or sharp changes in slope for NBO/T > 0.3, which occur for XSiO2Liq/XAl2O3Liq ranging from ∼0 to ∼6 and increase with increasing NBO/T. The systematic variations in activity coefficients as a function of composition and optical basicity reflect underlying shifts in speciation as the composition of the liquid is changed. On the basis of correlations among the activity coefficients, it is likely that the use of CaO, an exchange component such as SiMg−1 and two of MgO, CaAl2O4, or MgAl2O4 would yield significant savings in the number of parameters required to model the excess free energy surface of liquids over large portions of CMAS relative to the use of oxide end members.Systematic behavior of thermodynamic properties extends to small amounts of other elements dissolved in otherwise CMAS liquids. For example, ln(XFe2+Liq/XFe3+Liq) at constant oxygen fugacity is linearly correlated with ln(γCaOLiq). Similarly, ln(CS), where CS is the sulfide capacity is linearly correlated at constant temperature with each of the optical basicity, ln(aCaOLiq) and ln(γCaOLiq), although the correlation for the latter breaks down for low values of Λ. The well-known systematic behavior of sulfide capacity as a function of optical basicity for systems inside as well as outside CMAS suggests that ln(γCaSLiq) is also a simple function of optical basicity and that the relationships observed among the activity coefficients in CMAS may hold for more complex systems. 相似文献
5.
S.K. Saxena 《Geochimica et cosmochimica acta》1981,45(6):821-825
Using the model of fictive ideal components, Gibbs free energies of formation of pyrope and Al2O3-enstatite have been determined from the experimental data on coexisting garnet and orthopyroxene and orthopyroxene and spinel in the temperature range of 1200–1600 K. The negative free energies in kJ/mol are:
TK | 1200 | 1300 | 1400 | 1500 | 1600 |
Pyrope | 4869.92 | 4747.05 | 4614.26 | 4462.63 | 4311.00 |
Al2O3-enstatite | 1257.25 | 1244.28 | 1191.93 | 1158.67 | 1125.64 |