Group-theoretical analysis of octahedral tilting in ferroelectric perovskites

Group-theoretical methods are used to analyze perovskite structures where both ferroelectric cation displacements and simple tilting of octahedral units are present. This results in a list of 40 different structures, each with a unique space-group symmetry. The list is compared with that of Aleksandrov & Bartolome [ Phase Transit. (2001), 74, 255-335] and a number of differences are found. The group-subgroup relationships between the structures are also determined, along with an indication of those phase transitions that must be first order by Landau theory.