Simulation of mineral solid solutions at zero and high pressure using lattice statics, lattice dynamics and Monte Carlo methods

We discuss how two techniques, based on (1) lattice statics/lattice dynamics simulations and (2) Monte Carlo methods may be used to calculate the thermodynamic properties of oxide mixtures at zero and high pressure. The lattice statics/lattice dynamics calculations involve a full free energy structural optimization of each of a number of configurations, followed by thermodynamic averaging. Strategies for generating a suitable set of configurations are discussed. We compare results obtained by random generation with those obtained using radial distribution functions or explicit symmetry arguments to obtain approximate or exact weightings respectively for individual configurations. The Monte Carlo simulations include the explicit interchange of cations and use the semigrand canonical ensemble for chemical potential differences. Both methods are readily applied to high pressures and elevated temperatures without the need for any new parametrization. Agreement between the two techniques is better at high pressures where anharmonic terms are smaller. We compare in detail the use of each technique for properties such as enthalpies, entropies, volume and free energies of mixing at zero and high pressure and thus calculation of the phase diagram. We assess the vibrational contributions to these quantities and compare results with those in the dilute limit. The techniques are illustrated throughout using MnO-MgO and should be readily applicable to more complicated systems