Structures and phase transitions in perovskites--a group-theoretical approach.

Applications of computer-based group-theoretical methods to perovskite crystallography are reviewed. Such methods furnish a systematic account of the effects on the high-symmetry parent structure of diverse distortions. New results are presented for elpasolites (ordered double perovskites) when both ferroelectric cation displacement and simple octahedral tilting are allowed. Group-theoretical results prove invaluable in assisting experimental studies of perovskites since, if the nature of the distortion is known, they limit the possible structures or, in relation to more extensive studies, constrain the sequences of structures that may occur. Spontaneous strains and the estimation of order parameters are briefly discussed. Group-theoretical methods are undoubtedly a powerful aid to the study of perovskite crystallography, and their computer implementation makes them more accessible than hitherto.