Thermodynamics of mixing in MgSiO3-Al2O3 perovskite and ilmenite from ab initio calculations

The thermodynamic mixing functions of MgSiO3-Al2O3 solid solutions in perovskite and ilmenite structures were modeled based on the results of ab initio calculations applied to a set of supercell structures containing 64 and 48 exchangeable sites, respectively. The sampled structures were constructed from the supercells of the end-members MgSiO3 perovskite and Al2O3 corundum by inserting double AlAl and MgSi defects, respectively, at all possible distances. From these calculations the pairwise effective interactions were derived and used to calculate enthalpy differences between successive configurations produced in Monte Carlo simulation runs. The temperature dependent enthalpies of mixing of the solid solutions were evaluated as averages over the Monte Carlo runs while the free energies of mixing were calculated with the method of thermodynamic integration. The phase equilibria of perovskite, ilmenite and garnet in the Mg-Si-Al-O system were calculated using the computed models of mixing and the standard thermodynamic properties of the end-members from the data base of Fabrichnaya (1999). The obtained activity-composition models are in good agreement with available experimental constraints, thereby showing that the thermodynamic effects of mixing in silicate solid solutions with coupled substitutions can be reliably predicted based on ab initio calculated total energies of a small set of supercell structures. (C) 2010 Elsevier B.V. All rights reserved.