Phase transitions in disordered ferroelectrics with two types of random site electric dipole

Abstract

Phase transitions in a highly polarizable crystal of cubic symmetry induced by two types of random site electric dipole orientated correspondingly along the (100)- and (111)-type directions are considered. The distribution function of random electric fields produced by these dipoles was calculated. This function made it possible to obtain the order parameters, the critical concentrations of dipoles and the transition temperatures for ferroelectric phase transitions with tetragonal and rhombohedral symmetries. All these quantities were calculated as functions of the ratio of dipole moments and the concentrations of the two types of dipole considered. It was shown that, at certain concentrations and dipole moment ratio, the order parameters of both aforementioned ferroelectric phases had to coexist. The mean values of random elastic fields produced by the random electric fields considered through the electrostriction effect are calculated. It was found that in crystals such as KTaO3 the elastic fields of Eg symmetry may be larger than those of T2g symmetry. The eight-well adiabatic potential of the cluster, which includes the impurity dipole and its nearest neighbours, was shown to be transformed into a six-well potential under the action of Eg symmetry deformations. This transformation was supposed to be the main reason for the tetragonal symmetry phase transitions observed earlier in K1- eta Lieta Ta1- xi Nbxi O3 ( eta <or=0.06; xi <or=0.028) even at very low lithium ion concentrations. The calculation of the transition temperature confirmed this supposition and made it possible to explain qualitatively the transition temperature concentrational dependence observed in the aforementioned mixed disordered system.