[Symmetry in perovskite variants]

The relationships among the huge number of derivative structures of the perovskite type are rationalized in a concise manner using group-subgroup relations between space groups. One family tree of such relations is given for perovskites having tilted coordination octahedra. Further group-subgroup relations are concerned with distortions of the octahedra, such as Jahn-Teller distortions or with atoms shifted from the octahedron centres. In these cases, the space-group symmetry reductions must allow site symmetry reductions of the occupied sites in the perovskite structure. On the other hand, subgroups in which the perovskite sites split into different independent sites are necessary for derivative structures with atom substitutions, such as in the elpasolites A(2)EMX(6). In addition, substitutions and distortions can be combined in adequate subgroups. Substitutions may also involve the occupation of atom sites of perovskite by molecular groups such as N(CH(3))(4)(+) or other organic cations, or by molecules like acetonitrile. If they are ordered, their molecular symmetry requires further space-group symmetry reductions. The anions can be replaced by cyanide ions or by NO(2)(-) ions; space-group symmetry then depends on the temperature-dependent degree of order. The relationships can be used to predict if and what kind of twinning may occur in phase transitions and whether second-order phase transitions are possible.