Review of polyhedral distortions as a multi-scale minimization of the electric polarization and their correlations with physical properties

The Jahn-Teller (JT) and non-Jahn-Teller polyhedral distortions are reviewed within the same context, based on a multi-scale minimization of the electric polarization by handling formal ionic valences and valence electron density. This model is applied to tetragonal distortions of octahedra, particularly in K₂NiF₄ structures with different formula types, along with doping. The predictions are always in good agreement with the observed data. In particular, the ferrodistortive order of JT distortions is obtained from formal charge polarizations, while the antiferrodistortive one is adopted when only the valence electron density is involved. The correlations between physical properties and octahedral elongations through the crystal structures on one side and chemical compositions on the other side are discussed according to this model for high-T_c cuprate superconductors and CMR manganites.