Investigation of specific features of the lattice dynamics and the ferroelectric transition in perovskite crystals

The specific features of diffuse X-ray scattering in BaTiO3, KNbO3, and PbTiP3 perovskite crystals have been investigated. The former two perovskite compounds in cubic, tetragonal, and orthorhombic phases exhibit anomalous sheets due to diffuse X-ray scattering, whereas no similar sheets are observed in the case of diffuse X-ray scattering in PbTiO3. For these compounds, the phonon spectra are calculated in the quasi-harmonic approximation within the polarizable-shell model, and the mechanism of stabilization of the soft mode above the temperature of the phase transition to the ferroelectric state is considered. It is demonstrated that, in the cubic phase of BaTiO3 and KNbO3 crystals, there exist quasi-one-dimensional "soft" modes of vibrations of ions in M-O-M-O- chains, where M = Ti or Nb. In PbTiO3, this feature of the soft mode has not been revealed. The pair correlation functions of simultaneous atomic displacements in BaTiO3, KNbO3, and PbTiO3 are determined and used to calculate the intensity of diffuse X-ray scattering. The results obtained are in good agreement with experimental data. This is a strong argument in support of the hypothesis that the specific features of diffuse scattering are associated with the existence of quasi-one-dimensional correlations of atomic displacements in the soft optical mode and that the ferroelectric transition in perovskites is a displacive ferroelectric phase transition. The possible influence of the specific features revealed in the phonon spectra of the perovskite crystals on the processes of nuclear magnetic resonance and X-ray absorption (extended X-ray absorption fine structure spectra) is briefly discussed.