Thermodynamics of mixing and ordering in the pyrope–grossular solid solution

Static lattice energy calculations have been combined with cluster expansion formalism to predict pair-wise ordering interactions in the pyrope–grossular solid solution. The ordering interactions, the Js, have been then used to calculate the activity-composition relations over a wide temperature range with the help of the Cluster Variation Method. It is shown that short-range ordering in the system is driven by size mismatch. The prediction of the right signs and magnitudes of the ordering interaction energies requires separation of the mixing enthalpy into the configuration-dependent (chemical) and the configuration-independent (elastic) components. The study predicts the existence of a miscibility gap below 500ºC