Group-Theoretical Analysis of Octahedral Tilting in Perovskites

TLDR

A group‑theoretical analysis of cubic perovskite structures derived by tilting rigid octahedra, mediated by the R⁺₄ and M⁺₃ irreducible representations, is performed. The analysis identifies 15 distinct structures, fewer than the 23 previously proposed, and clarifies their group–subgroup relationships. Citation: Glazer, Acta Cryst.

Abstract

A group-theoretical analysis is made of the structures derived from the aristotype cubic perovskite ( Pm 3¯ m ) by the simple tilting of rigid octahedral units. The tilting is mediated by the irreducible representations R^+_4 and M^+_3 or the two in combination. These result in 15 possible structures, compared with the 23 possibilities suggested previously by Glazer [ Acta Cryst. (1972), B 28 , 3384–3392]. The analysis makes the group–subgroup relationships apparent.