Abstract
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 BaTiO${}_{3}$. 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 ${\ensuremath{\varepsilon}}_{\mathrm{eff}}$($E$) was determined by taking into consideration the local field distribution. A remarkable agreement between the model and experimental data was obtained for BaTiO${}_{3}$ 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 ${\ensuremath{\varepsilon}}_{\mathrm{eff}}$($E$) in nanoceramics.
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