Crystal-chemical aspects of phase transitions in barium titanate

Structural aspects of phase transitions in barium titanate are analysed from a crystal-chemical point of view. The respective discussion is focused on two possible sources of ferroelectric deformation of TiO68− octahedron. First, gradual changes of π-electron localisation are considered. Under an assumption of a mean field related to actual crystal symmetry, an adequate model is proposed. The values of bond orders are evaluated from resonance structures. They are compared with respective bond lengths. Another source of the ferroelectric deformation, which is taken into consideration, relates to the Ti-ion movements between eight potential minima on the cube diagonals. The analysis of the problem is grounded within adiabatic (local field) approximation and follows ideas of an eight-site model. The crystal structure is treated as a result of averaging of atomic positions according to the postulated disorder. Comparison of the X-ray interatomic distances with the values calculated from the disorder model is made. The collected data generally prove that the ferroelectric deformation of the TiO68− octahedron, which is observed in barium titanate, contains two components. One is related to the changes of structural disorder degree and should be considered as a main factor. The other includes the effects attributed to the changes of π-electron localisation.