Monte Carlo simulations for describing the ferroelectric-relaxor crossover in BaTiO₃-based solid solutions.

The properties induced by the M(4+) addition (M = Zr, Sn, Hf) in BaM(x)Ti(1-x)O(3) solid solutions have been described on the basis of a 2D Ising-like network and Monte Carlo calculations, in which BaMO(3) randomly distributed unit cells were considered as being non-ferroelectric. The polarization versus temperature dependences when increasing the M(4+) concentration (x) showed a continuous reduction of the remanent polarization and of the critical temperature corresponding to the ferroelectric-paraelectric transition and a modification from a first-order to a second-order phase transition with a broad temperature range for which the transition takes place, as commonly reported for relaxors. The model also describes the system's tendency to reduce the polar clusters' average size while increasing their stability in time at higher temperatures above the Curie range, when a ferroelectric-relaxor crossover is induced by increasing the substitution (x). The equilibrium micropolar states during the polarization reversal process while describing the P(E) loops were comparatively monitored for the ferroelectric (x = 0) and relaxor (x = 0.3) states. Polarization reversal in relaxor compositions proceeds by the growth of several nucleated domains (the 'labyrinthine domain pattern') instead of the large scale domain formation typical for the ferroelectric state. The spatial and temporal evolution of the polar clusters in BaM(x)Ti(1-x)O(3) solid solutions at various x has also been described by the correlation length and correlation time. As expected for the ferroelectric-relaxor crossover characterized by a progressive increasing degree of disorder, local fluctuations cause a reducing correlation time when the substitution degree increases, at a given temperature. The correlation time around the Curie temperature increases, reflecting the increasing stability in time of some polar nanoregions in relaxors in comparison with ferroelectrics, which was experimentally proved in various types of relaxors.