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 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.