• phase transitions;
  • distorted perovskites.

Rietveld neutron powder profile analysis of the compound Na0.5Bi0.5TiO3 (NBT) is reported over the temperature range 5–873 K. The sequence of phase transitions from the high-temperature prototypic cubic structure (above 813 K), to one of tetragonal (673–773 K) and then rhombohedral structures (5–528 K) has been established. Coexisting tetragonal/cubic (773–813 K) and rhombohedral/tetragonal (with an upper temperature limit of 145 K between 528 and 673 K) phases have also been observed. Refinements have revealed that the rhombohedral phase, space group R3c, with aH = 5.4887 (2), cH = 13.5048 (8) Å, V = 352.33 (3) Å3, Z = 6 and Dx = 5.99 Mg m−3, exhibits an antiphase, aaa oxygen tilt system, ω = 8.24 (4)°, with parallel cation displacements at room temperature. The tetragonal phase, space group P4bm, with aT = 5.5179 (2), cT = 3.9073 (2) Å, V = 118.96 (1) Å3, Z = 2 and Dx = 5.91 Mg m−3, possesses an unusual combination of in-phase, a0a0c+ oxygen octahedra tilts, ω = 3.06 (2)°, and antiparallel cation displacements along the polar axis. General trends of cation displacements and the various deviations of the octahedral network from the prototypic cubic perovskite structure have been established and their systematic behaviour with temperature is reported. An investigation of phase transition behaviour using second harmonic generation (SHG) to establish the centrosymmetric or non-centrosymmetric nature of the various phases is also reported.