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

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 funct ion 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 transiti on temperature with the grain size of the sample is mainly due to surface e ffects, we have also performed Monte Carlo simulations of the critical temp erature dependence with the grain size for finite Ising systems under free surface boundary conditions. We find that the behavior is comparable with t he one previously reported experimentally for ferroelectric materials and t hat it can be described by a very similar expression.