Variable-temperature single-crystal X-ray diffraction study of tetragonal and cubic perovskite-type barium titanate phases.

A variable-temperature single-crystal X-ray diffraction study of a synthetic BaTiO3 perovskite has been performed over the temperature range 298-778 K. A transition from a tetragonal (P4mm) to a cubic (Pm3m) phase has been revealed near 413 K. In the non-centrosymmetric P4mm symmetry group, both Ti and O atoms are displaced along the c-axis in opposite directions with regard to the Ba position fixed at the origin, so that Ti(4+) and Ba(2+) cations occupy off-center positions in the TiO6 and BaO12 polyhedra, respectively. Smooth temperature-dependent changes of the atomic coordinates become discontinuous with the phase transition. Our observations imply that the cations remain off-center even in the high-temperature cubic phase. The temperature dependence of the mean-square displacements of Ti in the cubic phase includes a significant static component which means that Ti atoms are statistically distributed in the off-center positions.