Normal-mode analysis of the structures of perovskites with tilted octahedra

An analysis of the normal modes of vibration of a cubic perovskite that have condensed to produce phases with tilted octahedra is presented. Only structures with octahedral tilts that double a repeat distance are considered; these involve small rotations of the octahedra about pseudocubic 〈100〉 directions. Phases with more than one octahedral tilt often possess atomic displacements in addition to those associated directly with the tilts. A Landau potential has been constructed which includes all parameters needed to describe the low‐symmetry phases. In addition to the spontaneous macrostrain, seven different order parameters are required to describe the possible transitions between phases with only one type of A and one type of B cation. Arguments based on the Landau expansion suggest that structural displacements associated with some of these order parameters are unlikely to be present, and that some subsets of displacements may have a higher symmetry than required by the space group of the lower‐symmetry phase. Comparison is made between these predictions and reported structural refinements. Where relevant, phases with more than one type of A or more than one type of B cation are considered.