Soft-mode phase transitions from first principles

First-principles electronic structure calculations of oxides have been performed now for several years: they have reproduced many aspects of the wide variety of behaviour of oxide compounds, including their vibrational properties and phase stability. The structural phase transitions of magnesium silicate perovskite have been investigated using a variety of first-principles approaches. These include the determination of the equilibrium structures of cubic, tetragonal and orthorhombic phases and their relative energies, the response of these structures to pressure and the calculation of vibrational frequencies of each phase. Inspection of the vibrational modes showed that the mechanism of the phase transition could be traced. As expected, the modes most active in the phase transition involve rotation of oxygen octahedra, and the extent to which these may be described as 'rigid-unit modes' (RUMs) was calculated. Recent calculations on RUMs in barium zirconate perovskite are also presented.