Garnet-orthopyroxene and orthopyroxene-clinopyroxene relationships in simple and complex systems

Use of simple mixing models of orthopyroxene and garnet solid solutions enables extrapolation of experimentally determined equilibria in the MgSiO₃-Al₂O₃ system to uninvestigated parts of pressure-temperature-composition space. Apparent discrepancies in the experimental data for simple and multicomponent systems may be explained by considering the effect of CaO and FeO on reducing pyrope activity in the garnet solid solutions. Equilibration pressures of natural garnet-orthopyroxene assemblages may be calculated, provided temperatures are known, from a combination of the experimental data on the MgSiO₃-Al₂O₃ system and analyses of coexisting natural phases. Despite the presence of a compositional gap in the system, the solubility of enstatite in diopside coexisting with orthopyroxene can also be approximately treated by an ideal solution model. An empirical approach has been developed to take account of Fe²⁺ on the orthopyroxene-clinopyroxene miscibility gap in natural systems in order to calculate equilibration temperatures of 2-pyroxene assemblages. The model presented reproduces almost all of the available experimental data for multicomponent systems to within 60° C.