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'X6) octahedral tilting. The cation ordering on the B-cation site is described by irreducible representations of the Pm3 m space group of the cubic aristotype: Lambda1 (k = 1/3,1/3,1/3) for the cation ordering pattern in the 1:2 compound A3BB2'X9 and M1+ (k = 1/2,1/2,0) for the cation ordering in the 1:3 compound A4BB3'X12. The octahedral tilting is mediated by the irreducible representations M3+ and R4+. Ten distinct structures have been identified in the 1:2 case and 11 structures for 1:3.