Structure and dynamics of perovskite‐type crystals

Abstract

The connection between Landau's theory of phase transitions and the lattice-dynamical theory of a displacive transition in a crystal is discussed. At a second-order displacive transition the frequency of one normal mode becomes zero. By investigating the displacements of the atoms from special positions of the lattice for a number of crystals having the distorted perovskite structure, we have shown that several modes are involved in the various transitions, except in the case of LaAlO₃, where the transition is probably second-order or nearly so, and is associated with a mode of low frequency. The wave vector of this mode is at the point (1/2 1/2 1/2) of the Brillouin zone, and its irreducible representation is Γ₂₅.