Ordered double perovskites -- a group-theoretical analysis

Group-theoretical methods are used to enumerate the structures of ordered double perovskites, A(2)BB'X(6), in which the ordering of cations B and B' into alternate octahedra 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 the irreducible representation R(1)(+) of the Pm3;m space group of the cubic aristotype, while the octahedral tilting is mediated by irreducible representations M(3)(+) and R(4)(+). There are 12 different structures identified, and the corresponding group-subgroup relationships are displayed. Known structures are briefly reviewed.