Relaxation time distribution function

The distribution function of relaxation time in disordered dielectrics has been calculated in the random field theory framework. For this purpose, we first consider the dynamics of single two-orientable electric dipole in a random electric field E in a disordered ferroelectric. The obtained dependence tau(E) made it possible to express the relaxation time distribution function F(tau) via the random field distribution function f(E). This function has been calculated self-consistently in the random field theory framework. Nonlinear random field contribution and effects of spatial correlations between the dipoles have also been taken into account. It was shown that nonlinear contribution of random field gives asymmetric shape of F(tau) while in linear case it is symmetric. Comparison of calculated F(tau) curves with those extracted from empirical Cole-Cole (CC), Davidson-Cole (DC), Kohlrausch-William-Watts (KWW) and Havriliak-Negami (HN) functions had shown, that they correspond to mixed ferroelectric-dipole glass (ferro-glass) phase with coexistence of shea and long-range order. Different forms of F(tau) are determined by linear (CC) or nonlinear (DC, KWW, HN) contributions of random field.