Importance of considerations of mixing properties in establishing an internally consistent thermodynamic database: thermochemistry of minerals in the system Mg 2 SiO 4 -Fe 2 SiO 4 -SiO 2

A thermodynamic solution model is developed for minerals whose compositions lie in the two binary systems Mg2SiO4-Fe2SiO4 and Mg2Si2O6-Fe2Si2O6. The formulation makes explicit provision for nonconvergent ordering of Fe2+ and Mg2+ between M1 and M2 sites in orthopyroxenes and non-zero Gibbs energies of reciprocal ordering reactions in both olivine and orthopyroxene. The calibration is consistent with (1) constraints provided by available experimental and natural data on the Fe-Mg exchange reaction between olivine and orthopyroxene ± quartz, (2) site occupancy data on orthopyroxenes including both crystallographic refinements and Mossbauer spectroscopy, (3) enthalpy of solution data on olivines and orthopyroxenes and enthalpy of disordering data on orthopyroxene, (4) available data on the temperature and ordering dependence of the excess volume of orthopyroxene solid solutions, and (5) direct activity-composition determinations of orthopyroxene and olivine solid solutions at elevated temperatures. Our analysis suggests that the entropies of the exchange [Mg(M2)Fe(M1)⇔Fe(M2)Mg(M1)] and reciprocal ordering reactions [Mg(M2)Mg(M1)+ Fe(M2)Fe(M1)⇔Fe(M2)Mg(M1)+Mg(M2)Fe(M1)] cannot differ significantly (± 1 cal/K) from zero over the temperature range of calibration (400°–1300° C). Consideration of the mixing properties of olivine-orthopyroxene solid solutions places tight constraints on the standard state thermodynamic quantities describing Fe-Mg exchange reactions involving olivine, orthopyroxene, pyralspite garnets, aluminate spinels, ferrite spinels and biotite. These constraints are entirely consistent with the standard state properties for the phasesα-quartz,β-quartz, orthoenstatite, clinoenstatite, protoenstatite, fayalite, ferrosilite and forsterite which were deduced by Berman (1988) from an independent analysis of phase equilibria and calorimetric data. In conjunction with these standard state properties, the solution model presented in this paper provides a means of evaluating an internally consistent set of Gibbs energies of mineral solid solutions in the system Mg2SiO4-Fe2SiO4-SiO2 over the temperature range 0–1300° C and pressure interval 0.001–50 kbars. As a consequence of our analysis, we find that the excess Gibbs energies associated with mixing of Fe and Mg in (Fe, Mg)2SiO4 olivines, (Fe, Mg)3Al2Si3O12 garnets, (Fe, Mg)Al2O4 and (Fe, Mg)Fe2O4 spinels, and K(Mg, Fe)3AlSi3O10(OH)2 biotites may be satisfactory described, on a macroscopic basis, with symmetric regular solution type parameters having values of 4.86±0.12 (olivine), 3.85±0.09 (garnet), 1.96±0.13 (spinel), and 3.21±0.29 kcals/gfw (biotite). Applications of the proposed solution model demonstrate the sensitivity of petrologic modeling to activity-composition relations of olivine-orthopyroxene solutions. We explore the consequences of estimating the activity of silica in melts forming in the mantle and we develop a graphical geothermometer/geobarometer for metamorphic assemblages of olivine+orthopyroxene+quartz. Quantitative evaluation of these results suggests that accurate and realistic estimates of silica activity in melts derived from mantle source regions,P-T paths of metamorphism and other intensive variables of petrologic interest await further refinements involving the addition of “trace” elements (Al3+ and Fe3+) to the thermodynamic formulation for orthopyroxenes.