Anomalies of Elastic and Electromechanical Characteristics of Crystals in Second-Order Phase Transitions

In the preceding chapters we have seen that, according to a simple treatment based on the Landau theory, the temperature dependence of the dielectric constant (dielectric permittivity) experiences anomalies of three types in second-order phase transitions. If the transition is a proper ferroelectric transition, i.e., if the order parameter exhibits the transformation properties of a component (or components) of the polarization vector, then one or more components of the permittivity tensor goes to infinity at T = T_c, obeying the Curie-Weiss law in a certain vicinity of this point. If the transition is an improper ferroelectric transition, i.e., if the transformation properties of the order parameter differ from those for polarization but have a certain specific form (see Chap. 4), then the dielectric constant remains slightly temperature dependent in both phases, but one or more components of it increase discontinuously upon transition into the polar phase. Finally, in the most general case, when the order parameter has no specific transformation at all with respect to an electric field, the temperature dependence of the dielectric constant undergoes only a kink at T = T_c.1 In order to establish these differences, we did not need to know either the physical meaning of the order parameter or the character of interactions leading to a phase transition; it was sufficient to take into account the symmetry properties of a crystal and the order parameter.