Defects and the central peak near structural phase transitions

The effect of defect or impurities on the static and dynamic response, near a displacive structural phase transition, depends on the symmetry and dynamics of the defect cell. It is shown that a small concentration of defect cells, in which the order parameter relaxes on a slow time scale between different equivalent orientations, may account for the narrow "central peak" as well as for the temperature dependence of the "soft-mode" frequency in the perovskites near structural phase transitions. The case of a frozen defect cell is also discussed. Calculations are performed for the pure and impure systems using mean-field theory, and corrections are discussed using the universality hypotheses and renormalization-group calculations for dynamic critical behavior.