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

The full phonon dispersion relations of lead titanate and lead zirconate in the cubic perovskite structure are computed using first-principles variati onal density-functional perturbation theory, with nb initio pseudopotential s and a plane-wave basis set. Comparison with the results previously obtain ed 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 unst able modes, with significant implications for the nature of the phase trans itions and the dielectric and piezoelectric responses of the compounds. Exa mination of the interatomic force constants in real space, obtained by a tr ansformation which correctly treats the long-range dipolar contribution, sh ows that most are strikingly similar, while it is the differences in a few key interactions which produce the observed changes in the phonon dispersio ns. These trends suggest the possibility of the transferability of force co nstants to predict the lattice dynamics of perovskite solid solutions.