Relaxor ferroelectrics: From Cross superparaelectric model to random field theory

A brief review is presented of recent results derived from the random field theory approach to describing relaxor ferroelectric properties. The key point in this approach is that the random field originating f rom chemical disorder of relaxor ferroelectrics destroys long range polar order, which could otherwise exist at temperatures below the Burns temperature T_d. As a result, polar clusters appear of size R_c (the correlation radius of Burns reference phase), corresponding to the Cross superparaelectric phase. The relaxor properties can be calculated by averaging the electric field dependence of the paraelectric Burns reference phase with the random field distribution function of a suitable property. The distribution functions for the cases of linear and non-linear random field contributions are calculated using the statistical physics framework for electric dipoles, point charges and dilatational centres as random field sources. These calculations allow explanation of the observed Vogel–Fulcher law and non-Debye character of the dynamic dielectric response; of stiff and soft response to dc field of non-linear susceptibility; of unusual R_c temperature dependence; as well as of dielectric response anomalies in 1:1 family relaxors. The correlation radius and relaxation time distribution functions are calculated using the random field distribution function. Calculated phase diagrams for mixed relaxors, allowing for non-linear and spatial correlation effects, give a good fit to the experimental results. Comparison of calculated and observed properties leads to the conclusion that a mixed ferroglass phase with coexisting short and long polar order is the most probable state for all relaxors, the degree of mixing being the essential factor for a relaxor.