Dependence of the Permittivity and of the Electrocaloric Effect on the Ferroelectric Ceramics Grain Size

We consider the problem of determining the permittivity and the electrocaloric effect in the model of a ferroelectric ceramics grain. We assume that a grain consists of a spherical ferroelectric core coated with a dielectric shell and placed into a dielectric matrix. The transition layer thickness is assumed small as compared to the grain size. The dependence of the polarization on the electric field in the core is given by the nonlinear Ginzburg–Landau equation. The polarization reversal is induced by a change in the electric field that is considered uniform at large distance from the grain. The electrostriction effect in the core–shell–matrix three-phase system produces an elastic field described by linear equations. To take into account the effect of domain walls on the physical characteristics of the ceramics in the given model, we propose that the Kittel–Mitsui–Furuichi approach be used. The proposed computational algorithm makes it possible to refine the dependence of the number of domains on the spherical grain size. The electrocaloric effect in the grain is represented by the combination of the primary and secondary effects that appear due to ordering of dipole moments of the ferroelectric with the perovskite structure; by way of example, we consider the barium titanate ceramics. For this material, we report on the results of calculations of the dependences of the permittivity and individual electrocaloric effect components on the grain size.