Phenomenological theory of the deformation of rotated octahedra in perovskites

A phenomenological theory of the macrostrain in perovskites-that undergo phase transitions in which the octahedra are tilted is presented. Examination of the literature shows that the octahedra are deformed as well as rotated, and that the deformation is roughly proportional to the square of the angle of rotation of the octahedra. A Landau expansion is used that reproduces the deformation in phases with tetragonal, orthorhombic and rhombohedral symmetries. Five parameters are required; these are similar to the electrostrictive coefficients that relate macrostrain to the spontaneous polarisation in ferroelectrics. The magnitudes of these parameters are determined in three cases; barium cerate, yttrium-doped barium cerate and sodium magnesium fluoride. The deformation of the octahedra has a greater effect on the macrostrain than the rotation of the octahedra.