Octahedral tilting in cation-ordered perovskites – a group-theoretical analysis

Abstract

Group-theoretical methods are used to enumerate the structures of ordered perovskites, in which 1:2 and 1:3 ordering of B and B′ cations is considered in combination with the ubiquitous BX 6 (or B′X 6) octahedral tilting. The cation ordering on the B-cation site is described by irreducible representations of the Pm\bar 3m space group of the cubic aristotype: Λ1 ( k = 1/3,1/3,1/3) for the cation ordering pattern in the 1:2 compound A 3 BB_2^{\prime}X 9 and M_1^ + ( k = 1/2,1/2,0) for the cation ordering in the 1:3 compound A 4 BB_3^{\prime}X 12. The octahedral tilting is mediated by the irreducible representations M_3^ + and R_4^ +. Ten distinct structures have been identified in the 1:2 case and 11 structures for 1:3.