Influence of sintering temperature on grain size and electrocaloric effect of barium titanate ceramics

A theoretical study of the polarization distribution and mechanical stresses in a ferroelectric ball located in an unlimited dielectric space has been carried out. The ball is covered with a dielectric and air shell. The external electric field far from the ball is assumed to be uniform. The polarization in the ball satisfies the nonlinear Landau–Ginzburg equation, which takes into account the presence of electrostriction. It is also assumed that for a small ball, the effect of local elastic stresses on polarization can be replaced by their homogenized value over the volume of the ball. Under this assumption, the distribution of the stress and the electric field can be obtained both in the ball and outside it. The dependence of the Curie–Weiss temperature on the radius of the ball is derived. The resulting solution is used to simulate the properties of microgranular ceramics. Along with the developed theoretical model, a series of experiments was carried out to measure the temperature dependence dielectric constant and the electrocaloric effect (ECE) for BaTiO$_3$ ceramics synthesized at different temperatures. The change in temperature during ECE was measured by direct methods. The greatest value of the ECE was achieved for ceramics synthesized at 1350$^\circ$C. The magnitude of the change in temperature with a change in the electric field by 2 mV/m was $\Delta T$ = 0.42 K. The observed experimental results demonstrate the possibility of using the theoretical four-phase model of ceramics to predict the dependence of the properties of ceramics on the sintering temperature.