Strain analysis of phase transitions in (Ca,Sr)TiO3perovskites

A single Landau free energy expansion is used to describe phase transitions in perovskites, from a cubic parent structure to tetragonal and orthorhombic structures with space groups related to the M3 and R25 points of the Pm3̅m reciprocal lattice. This expansion permits relationships between symmetry-adapted forms of the spontaneous strain and individual order parameter components to be predicted. Data from the literature for (Ca,Sr)TiO3 perovskites are analyzed in the light of these predictions. Shear strains for I4/mcm, Pnma, and Cmcm structures tend to conform to the predicted pattern. The Pm3̅m↔I4/mcm transition has nearly tricritical character as a function of temperature in CaTiO3 and more nearly second-order character as a function of composition at the Sr-rich end of the solid solution. Coupling with the volume strain appears to be both temperature and composition dependent, which may be a general feature of phase transitions in perovskites. Renormalization of fourth-order terms by changing the volume coupling coefficients could be responsible for the unusual order parameter evolution shown by CaTiO3 and for changes in thermodynamic character of the phase transitions as a function of composition. The pattern of strain variations also correlates closely with patterns of variations in heat capacity from the literature, suggesting revisions to the subsolidus phase diagram for the (Ca,Sr)TiO3 solid solution above room temperature.