Abstract

A range of methods, based on Monte Carlo and lattice dynamics simulations, are presented for the calculation of the thermodynamic properties of solid solutions and phase diagrams. These include Monte Carlo simulations with the explicit interchange of cations, the use of the semigrand-canonical ensemble and configurational bias techniques, hybrid Monte Carlo/molecular dynamics, and a new configurational lattice dynamics technique. It is crucial to take account of relaxation of the local atomic environment and vibrational effects. Examples studied are (i) the enthalpy and entropy of mixing, the phase diagram and the spinodal of MnO/MgO. The available experimental data disagree widely for this system; (ii) the enthalpy of mixing of CaO/MgO, where the size mismatch between the cations is considerably larger than in (i); (iii) the postulated high-pressure orthorhombic to cubic phase transition in (Mg,Mn)SiO₃ perovskite, where we show that impurity cations can have a much larger effect than that expected from a mean-field treatment or linear interpolation between end-member compounds.