Phase Transitions in Perovskite Crystals

Atomic displacements are analysed that occur at phase transitions in perovskites caused by the condensation of zone boundary modes. It is shown that for phases in which modes with wave vectors at the M‐point, ½ (a* + (a* + b*), and the R‐point, ½(a* + b* + c*), have condensed, static displacements associated with a normal mode with wave vector ½ + c* of the X‐point are also present. Such induced displacements are to be expected from Landau's theory of continuous phase transitions when terms that couple the parameters X , R , and M me included in the free energy expression. Such an expression is applied to (Na, K)NbO 3 , and the results derived from it are compared with the experiment.