Buckling the equatorial anion plane: octahedral anion distortions in ferroic perovskites and related systems resolved via neutron diffraction

A framework for describing anion displacements from perfect octahedra in perovskites has been developed for use with neutron diffraction data sets. We describe the distortions as noncoplanar arrangements, or buckling, of oxygen ions in any central plane of the octahedron, ignoring the central cation. Nonplanar distortions of octahedra have been calculated for perovskite structures contained within the Inorganic Crystal Structure Database. We find that antiferroelectric materials have buckling angles larger than ~2° and ferroelectric materials have buckling angles between 0° and 1°. The trend is found as a function of solid solution composition and temperature for common antiferroelectrics. For example, the described method resolves a structural difference between the end members PbTiO₃ and PbZrO₃, which exhibit ferroelectric and antiferroelectric responses, respectively. This technique is applicable to other structures containing anion octahedra, e.g., pyrochlores, spinels, and tungsten bronzes.