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 a(H) = 5.4887 (2), c(H) = 13.5048 (8) Angstrom, V = 352.33 (3) Angstrom(3), Z = 6 and D-x = 5.99 Mg m(-3), exhibits an antiphase, a(-)a(-)a(-) oxygen tilt system, omega = 8.24 (4)deg...