High-temperature single-crystal X-ray diffraction study of tetragonal and cubic perovskite-type PbTiO₃ phases

A high-temperature single-crystal X-ray diffraction study of a synthetic PbTiO₃ perovskite was carried out over the wide temperature range 298-928 K. A transition from a tetragonal (P4mm) to a cubic () phase has been revealed near 753 K. In the non-centrosymmetric P4mm symmetry group, the difference in relative displacement between Pb and O along the c-axis is much larger than that between Ti and O. The Pb and Ti cations contribute sufficiently to polarization being shifted in the opposite direction compared with the shift of O atoms. Deviation from the linear changes in Debye-Waller factors and bonding distances in the tetragonal phases can be interpreted as a precursor phenomenon before the phase transition. Disturbance of the temperature factor U_eq for O is observed in the vicinity of the transition point, while U_eq values for Pb and Ti are continuously changing with increasing temperature. The O site includes the clear configurational disorder in the cubic phase. The polar local positional distortions remain in the cubic phase and are regarded as the cause of the paraelectricity. Estimated values of the Debye temperature Θ_D for Pb and Ti are 154 and 467 K in the tetragonal phase and decrease 22% in the high-temperature phase. Effective potentials for Pb and Ti change significantly and become soft after the phase transition.A high-temperature single-crystal X-ray diffraction study of PbTiO₃ perovskite was carried out at temperatures between 298 and 928 K. Deviation from linear changes in Debye-Waller factors in the tetragonal phases was observed before the phase transition.