DIFFUSE PHASE-TRANSITION IN FERROELECTRICS WITH MESOSCOPIC HETEROGENEITY - MEAN-FIELD THEORY

The diffuse phase transition in ferroelectrics with mesoscopic heterog eneity has been discussed within the context of a superparaelectric mo del by using the Ginzburg-Landau formalism. In the Curie region ferroe lectries with mesoscopic heterogeneity are treated as ''superparaelect rics'' consisting of a mass of polar clusters, each of which has Ising character. Based on the mean-field theory, the influence of the finit e-size effects of polar clusters on their structural instability has b een discussed by considering a coherent lattice coupling between two s tructurally different regions. In particular, we have analytically der ived the explicit solutions of the distribution of local polarizations . In turn, the processes of polar nanophase precipitation and coarseni ng have been also discussed in conjunction with the local chemical or structural inhomogeneity. Moreover, we have also analyzed the relation ship between the local polarization distribution and the static dielec tric susceptibility in ferroelectrics with the nanometric scale hetero geneity. The width of the Curie region is dependent upon the distribut ion of the sum of localized correlation length, which reflects the siz e distribution of heterogeneity. The presented analysis reveals that t he diffuse phase transition is closely associated with the existence o f nanometric polar clusters and their physical size distribution. Intr iguingly, our theoretical results bear a very close resemblance to mos t experimental observations.