Field-dependent permittivity in nanostructured BaTiO3 ceramics: Modeling and experimental verification

The grain size (GS) effect on the electric field dependence of the dielectric constant in ferroelectric nanoceramics was studied using a detailed model and the predicted behavior compared to experimental data obtained for BaTiO3. In the finest ceramics the permittivity reduces below 1000 and a tendency to linearization of the permittivity vs field dependence is observed. The composite structure of ferroelectric ceramics corresponding to ferroelectric grain cores separated by nonferroelectric grain boundaries determines a progressive increase of the electrical inhomogeneity of the system with decreasing GS. The local electric field was computed at various applied voltages for different GSs by a finite element approach, and then the effective permittivity-field response epsilon(eff)(E) was determined by taking into consideration the local field distribution. A remarkable agreement between the model and experimental data was obtained for BaTiO3 ceramics. The local field distribution explains with considerable accuracy the reduction of permittivity and tunability observed with decreasing GS as well as the tendency towards linearization of epsilon(eff)(E) in nanoceramics.