Fictive component model of pyroxenes and multicomponent phase equilibria

Pyroxenes are considered as ideal solid solutions of some real components (e.g. diopside or orthoenstatite) and some fictive or hypothetical components (e.g. orthodiopside or orthohedenbergite). Using the reversed experimental data in the CaO-MgO-SiO₂ system, the Gibbs free energy of formation of fictive orthodiopside and of fictive clinoenstatite have been determined in the temperature range of 1,000 to 1,600 °K. The data on free energies of components in the binary system can be used to extend the fictive component model to the ternary CaSiO₃-MgSiO₃-FeSiO₃ system. Using published phase diagrams on the pyroxene quadrilateral, Gibbs free energy of formation of fictive orthohedenbergite has been calculated. Application of the ideally mixing fictive component model to computation of phase equilibria leads to the determination of compositions of coexisting Fe-Mg-Ca pyroxenes at different temperatures.Abbreviations and symbols G_f⁰ Gibbs free energy of formation from the elements at 1 bar and temperature - G^Ex excess free energy of mixing in a solution - G molar Gibbs free energy - R gas constant - H enthalpy - S entropy - T absolute temperature - P pressure - KJ/M kilojoules per mole - j joules - Opx orthopyroxene - Cpx clinopyroxene - H hedenbergite - D diopside - E enstatite - F ferrosilite - X mole fraction - K equilibrium constant