Nonlinear dielectric susceptibility in doped incipient ferroelectrics

The theory of dc-electric field nonlinear susceptibility in the doped incipient ferroelectrics is developed in a random field approach. The calculations of the susceptibility chi(E, T) had shown that the coefficients chi(nl) ((k)) (T, n ) in power serie of susceptibility chi(E, T ) = Sigmachi(nl) ((k)) E-2k (k = 0 and k = 1, 2, 3...correspond respectively to linear and nonlinear susceptibility of the first, second etc. order) diverge at the same temperature T = T-m that depends on the impurity dipoles concentrations. The critical indexes of the divergency for the concentration of the dipoles which correspond to mixed ferroglass phase with coexistence of short- and long-range polar order were shown to be the same as those calculated in mean field approximation. The comparison of the theory with experimental data obtained for KTa1-xNbxO3 (0.0075 less than or equal to x less than or equal to 0.05) is performed. The calculations describe the main peculiarities of temperature, electric field and concentrational dependence of observed nonlinear dielectric susceptibility. Since the temperature T m corresponds to the transition from dipole glass to ferroglass phase the transition is proven to be equilibrium one in the disordered ferroelectrics.