Theory of phase transitions in disordered ferroelectrics allowing for nonlinear and spatial correlation effects

The order parameter, ferroelectric phase transition temperature, and critical concentrations of random-site electric dipoles, point charges and dilatational centres in disordered ferroelectrics are calculated. The calculations are carried out by the random-field method with a random-electric-field distribution function, allowing for nonlinear and spatial correlation effects. Essential differences from the linear case are revealed. First, the aforementioned effects lead to the transformation of the second-order phase transition into one of first order and vice versa for alpha(3) > 0 and alpha(3) < 0 respectively, where as is the third-order nonlinearity constant. Second, for alpha(3) > 0 the phase transition temperature T-c, has a maximum as a function of the random-field-source concentration; its maximal value appears to be larger than that in the mean-field approximation. At the same time, for alpha(3) < 0 the maximum is absent and the T-c-value is smaller than that in the linear case (i.e. at alpha(3) = 0). This means that nonlinear and spatial correlation effects enhance the long-range order in disordered ferroelectrics for (alpha(3) > 0 and inhibit it for alpha(3) < 0. It is shown that the critical concentrations of electric dipoles, point charges and dilatational centres are the same as in the linear case. The application of the theory developed to various disordered ferroelectrics is discussed.