Structural evolution, strain and elasticity of perovskites at high pressures and temperatures

Octahedral tilting transitions in perovskites are usually identified by the significant lattice distortions which accompany them. The underlying mechanism of coupling between the tilts and the macroscopic strain also gives rise to large anomalies in single crystal and bulk elastic moduli. Landau theory provides an effective framework for describing these different changes in properties and relating them, quantitatively, to the evolution of the driving order parameter for the transition. This approach has been used to analyse the overall elastic behaviour of perovskites belonging to the CaTiO3-SrTiO3 (CST) solid solution, which is expected to be closely analogous to the behaviour of silicate perovskites at higher pressures and temperatures. Pm3m ↔ I4/mcm and I4/mcm ↔ Pnma transitions in CST perovskites are marked by changes in the shear modulus of ∼ 10-30%. The evolution of the order parameter and, hence, of the octahedral tilt angles through these can be followed through the variations of spontaneous strains extracted from high resolution lattice parameter data. Contributions to the elastic softening which are due to strain/octahedral tilt coupling have been calculated using a fully parameterised Landau model of the Pm3m ↔ I4/mcm transition as a function of temperature, pressure and composition. Differences between calculated elastic constants and experimental data from Dynamical Mechanical Analysis, pulse-echo ultrasonics and Resonant Ultrasound Spectroscopy suggest that a proportion of the total softening in tetragonal samples may be due to anelastic effects. The anelastic contributions are observed at frequencies of both a few Hz and 10's of MHz, and can be understood in terms of strain contributions arising from movements of transformation twin walls in response to an externally applied shear stress. Similar transitions in other perovskites are likely to display small anomalies in the bulk modulus, due to weak coupling between octahedral tilts and volume strain, but much larger anomalies in the shear modulus. The elastic properties of tetragonal and orthorhombic structures are likely to be quite different due to different anelastic contributions from twin wall displacements