Direct Free Energy Minimisation Techniques Using Quasiharmonic Lattice Dynamics

Analytic and numerical approaches to calculation of derivatives of the free energy with respect to internal and external strains of a crystal are compared using lattice dynamics in the quasiharmonic approximation. The two approaches give very similar results. The analytic values are calculated by a code written by Kantorovich 1] which gives derivatives of free energy with respect to all internal and external strains for a crystal with an arbitrary unit cell. As well as the thermodynamic potentials at a given geometry and properties which can be directly derived from them, this enables direct calculation of quantities such as the elastic constants and thermal expansion coeecient. It also enables calculation of the optimised geometry of crystals with many degrees of freedom avoiding the problems presented by a numerical minimisation of the free energy in many dimensions. We have looked at simple ionic crystals (MgO, MgF2) using a rigid ion model, comparing them with some experimental results.