Symmetry classification of the layered perovskite-derived A n B n X 3n+2 structures

Abstract

The effects of combinations of octahedral tilts on the symmetries of layered A n B n X 3n+2 structures were considered. Two complementary approaches were used to deduce the symmetries. The space groups associated with different tilt systems were determined for structures with different layer thicknesses (n values) and for structures with different layer stacking arrangements. For the most symmetrical tilts about the orthorhombic axes of the A n B n X 3n+2 structure, maximal group/subgroup relations were established. Comparison of these results with experimental data available in the literature suggests that the symmetries of most observed A n B n X 3n+2 compounds are fully determined by the tilt systems adopted by rigid BX 6 octahedra. The most common tilt system observed at room temperature is a combination of an in-phase tilt about an orthorhombic axis parallel to the pseudo-fourfold axis of the octahedron with a tilt about an orthorhombic axis perpendicular to the layers.