Optimized standard state and solution properties of minerals

Abstract

 An internally consistent set of standard state and mixing properties has been derived for olivine, orthopyroxene, garnet, cordierite, and ilmenite in the system FeO-MgO-CaO-Al₂O₃-TiO₂-SiO₂-H₂O from analysis of relevant phase equilibrium and thermophysical data. Solubility of Al₂O₃ in orthopyroxene is accounted for in addition to Fe-Mg mixing. Added confidence in the retrieved properties stems from the representation within reasonable uncertainties of data for seven linearly dependent Fe-Mg exchange equilibria, as well as net transfer equilibria, among the above phases. Critical to successful analysis was the extension of the mathematical programming technique to include bulk composition constraints which force an observed assemblage of fixed composition to be stable at experimentally studied conditions. The final optimization reproduces the extremely tight constraints on endmember properties while invoking very simple macroscopic solution models that afford an excellent opportunity for extrapolation beyond the data considered in this study. Compatibility among the experimental data is improved markedly by incorporation of recently published C_p data on pyrope and forsterite. Electrochemical data defining the oxygen fugacity of Fe-Fa-Qz, Fa-Mt-Qz, and Mt-Hm allow excellent compatibility of almandine thermochemical properties derived from phase equilibrium data obtained at both reducing (Fe-Wst) and oxidizing (Hm-Mt) conditions. Analysis of the combined data involving endmembers and solid solutions removes many of the ambiguities in mixing property magnitudes that arise in analyses of more restricted sets of data. In addition, the consideration of the solid solution data allows further refinement of some endmember properties. Nonideal mixing parameters, although correlated, are well defined by the combination of experimental data, with GOlex>GIlmex>GGtex >GOpxex>GCdex, and 0.7<WOlG<4.1 kJ/atom of isomorphous Fe-Mg at 1000 K. Experiments defining the Al₂O₃ solubility of Opx in equilibrium with Gt and Cd+Qz define negative Fe-Al interactions that have an important effect on Fe-Mg partitioning in Opx. Applications of this data set to high-grade metamorphic rocks are described in a companion paper, published as part II of the present work.