Apparent Ionic Charges and Vibrational Eigenmodes of BaTiO3and Other Perovskites

Abstract

The polarization associated with the vibrations of a complex lattice can be discussed by assigning apparent charges to the individual ions. These apparent charges can be calculated for a lattice of electrically polarizable ions by a consideration of the local dipole fields if polarization due to short-range forces is neglected, and such calculations are made for several cubic perovskites. Using these calculations as criteria for reasonable values of apparent charges results in the severe restriction of the range of the displacements permissible for the polar vibrational modes compatible with the experimentally observed mode dipole strengths. The apparent ionic charges and polar eigenmodes of SrTi${\mathrm{O}}_3$, BaTi${\mathrm{O}}_3$, KTa${\mathrm{O}}_3$, and KCo${\mathrm{F}}_2$ are discussed in this manner. For BaTi${\mathrm{O}}_3$, the magnitude of the spontaneous polarization is correctly predicted, and the displacements predicted for the very low-frequency mode in the cubic phase are closely similar to those which occur at the cubic-tetragonal phase transformation.