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 ABX₃ perovskites and their relative crystals of ReO₃ type (G₀ = O¹ _h), elpasolites, cryolites and their relatives (G₀ = O⁵ _h), layered crystals of T1AlF₄ series (G₀ = D¹ _4h), Aurivillius and Ruddlesden-Popper series (Go = D¹⁷ _4h). The structures in their initial phase G₀ 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 G₀ 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.