Structural distortions in families of perovskite-like crystals

The crystallographic and group theoretical analysis of the structural phase transitions in perovskite and perovskite-like crystals is reviewed. We include ABX(3) perovskites and their relative crystals of ReO3 type (G(0) = O-h(1)), elpasolites, cryolites and their relatives (G(0) = O-h(5)) layered crystals of TIAIF(4) series (G(0) = D-4h(1)), Aurivillius and Ruddlesden-Popper series (G(0) = D-4h(17)). The structures in their initial phase G(0) often contain n layers (n = 1, 2,3) of vertex linked octahedra. The distorted phases produced by one kind of tilt and by superposition of tilts in the slabs are enumerated. Most of the tilts correspond to symmetry changes, which can be associated to definite librational lattice modes irreducible representations of the G(0) group. The softening of modes associated to the PT has been found experimentally in many perovskites, elpasolites and layered crystals with n = 1. In contrast, no such soft modes have been found yet for even-layered (n = 2) crystals. Examples of successive phase transitions due to the superposition of tilts in these types of crystals have been collected.