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 BX6 (or B'X-6) octahedral tilting. The cation ordering on the B-cation site is described by the irreducible representation R-1(+) of the Pm (3) over barm 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.