Structures and phase transitions in perovskites – a group-theoretical approachThis article is dedicated to Helen D. Megaw (1907–2002), in appreciation of her many contributions to the crystallography of inorganic and mineral compounds, including her seminal studies of perovskites. Some of the material was presented by CJH in the Megaw memorial session at the 21st European Crystallography Meeting, Durban, South Africa, August 2003.

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.