Modelling of the grain size effect on nonlinear dielectric properties in nanostructured ferroelectric ceramics,

The grain size effect on the electric field dependence of the dielectric constant in nanostructured BaTiO3 ceramics was studied. When reducing grain size down to 100 nm, the permittivity diminishes below 1000 and a tendency towards linearization of the permittivity vs. field dependence and lack of saturation is observed [1]. To explain these features, the highly inhomogeneous nature of the nanostructured ceramic was considered. The ceramic was described as a composite formed by grains with ferroelectric core and low-permittivity linear dielectric grain boundary. The role and contribution of the grain boundaries increases when reducing grain size at nanoscale. A complex model for describing the grain size influence on the tunability response in dense nanostructured ceramics was proposed. Virtual ceramic microstructures with progressive reduction of grain size were generated and the local electric fields have been computed by finite element approach at various external voltages. The effective permittivity-field responses eff(E) have been computed by taking into consideration the specific local field distribution [2]. A remarkable agreement between the experimental tunability features and model calculations was obtained in describing the reduction of permittivity and tunability and tendency of linearization of the eff(E) when reducing the ceramic grain size (Fig.1).