Temperature changes in the crystal structure of barium titanium oxide

Barium titanium oxide, which is tetragonal at room temperature, changes about 120 degrees C to a cubic structure. This change has been followed in detail by means of X-ray powder photographs taken in a 19 cm. powder camera at intervals of a few degrees over a range covering the transition point. The unit cell, which contains the formula number of atoms, retains its identity throughout the transition, and the atomic parameters are unaltered. The change is simply in the axial lengths, and these vary continuously with the temperature, though not linearly, the variation becoming more rapid near the transition point. While the linear expansion coefficients along and perpendicular to the tetrad axis are large and of opposite sign, the volume expansion coefficient is small and positive. There is no discontinuous change either of linear spacing or of volume detectable at the transition point, but there is a sharp discontinuity in the linear expansion coefficients, and a marked increase in the volume expansion coefficient which is probably, though not certainly, discontinuous. The transition suggests a typical $\lambda $-point change. The specific heat has not been determined, but the thermal expansion curve has the characteristic $\lambda $ shape. Co-existence of cubic and tetragonal structures, in proportions depending on the temperature, occurs over a range of some degrees near the transition point, and is attributed to the effect of local stresses in facilitating or hindering a change between two structures whose energy difference is very small in this temperature range. Below room temperature, observations made down to - 183 degrees C suggest that the structure may have a second transition point somewhere below this and become cubic again, the change being of the same nature as that at 120 degrees C. It is argued that the room-temperature structure can only be explained by the existence of directed bonds, and that the breaking of these bonds with increasing temperature is responsible for the 120 degrees C transition. The low-temperature transition is explained by postulating a more complete set of bonds, probably an octahedral complex, which partially breaks down at this temperature to give the square formation observed in the room-temperature structure. The possible nature of the directed bonds is discussed qualitatively. The condition which makes possible the formation of such bonds is likely to be the abnormal volume available to the Ti atom, which is due to the effect of the large Ba ion in forcing apart the oxygen lattice. The directed bond system will only contribute a small part to the attractive energy of the lattice, which is mainly ionic in character. The hypothesis that directed bonds exist, whatever their origin, is used for a tentative explanation of anomalous variations of intensity of the X-ray lines observed at temperatures near the transition point.