Lattice dynamics of BaTiO₃, PbTiO₃, and PbZrO₃: a comparative first-principles study

Abstract

The full phonon dispersion relations of lead titanate and lead zirconate in the cubic perovskite structure are computed using first-principles variational density-functional perturbation theory, with ab initio pseudopotentials and a plane-wave basis set. Comparison with the results previously obtained for barium titanate shows that the change of a single constituent (Ba to Pb, Ti to Zr) has profound effects on the character and dispersion of unstable modes, with significant implications for the nature of the phase transitions and the dielectric and piezoelectric responses of the compounds. Examination of the interatomic force constants in real space, obtained by a transformation which correctly treats the long-range dipolar contribution, shows that most are strikingly similar, while it is the differences in a few key interactions which produce the observed changes in the phonon dispersions. These trends suggest the possibility of the transferability of force constants to predict the lattice dynamics of perovskite solid solutions.