Intermixing tendencies in garnets: Pyrope and grossular

The composition-temperature-pressure phase diagram of pyrope-grossular solid solutions, in which Mg and Ca are guest species in a highly rigid aluminosilicate framework, is predicted using simple models for the mixing enthalpy and the vibrational excitations. The models are expected to elucidate general phase separation tendencies in mixtures of guest species. Size mismatch of guest species is shown to give a positive enthalpy of mixing, and vibrational effects are shown to favor phase separation at the side of the smaller guest species, while at the side of the larger guest species mixing is favored. This gives rise to asymmetrical miscibility gaps that are displaced toward the side of the smaller species; in the case of pyrope-grossular, toward pyrope. It is shown that a realistic description of phase stability can be obtained using very few electronic density functional total energy calculations, making it of particular relevance for large unit-cell systems.