Monte Carlo simulations of grain size effects on the transition temperature of Ising systems: Comparison with mean field approximation in ferroelectrics

Abstract

Simple effective field arguments assuming an anisotropic layer of thickness L_c covering the ferroelectric bulk grain of perovskite ceramics are used to determine an expression for the transition temperature T_c(L) as a function of the grain linear size L. Experimental data for BaTiO₃ ceramics as a function of grain size are described reasonably well by the expression of T_c(L) obtained this way. In order to show that the decrease of the transition temperature with the grain size of the sample is mainly due to surface effects, we have also performed Monte Carlo simulations of the critical temperature dependence with the grain size for finite Ising systems under free surface boundary conditions. We find that the behavior is comparable with the one previously reported experimentally for ferroelectric materials and that it can be described by a very similar expression.