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

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 BX6 (or B'X-6) octahedral tilting. The cation ordering on the B-cation site is described by irreducible representations of the Pm (3) over barm space group of the cubic aristotype: Lambda(1) (k = 1/3,1/3,1/3) for the cation ordering pattern in the 1:2 compound A(3)BB'X-2(9) and M-1(+) (k = 1/2,1/2,0) for the cation ordering in the 1:3 compound A(4)BB'X-3(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.