Structure and dynamics of perovskite‐type crystals

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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.