Grain size effect on nonlinear dielectric properties in nanostructured ferroelectric ceramics: modeling and experimental validation

The grain size effect on the electric field dependence of the dielectric constant in nanostructured BaTiO3 ceramics was studied. When reducing grain size (GS) 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 compositeformed 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 (FEM) at various external voltages. The effective permittivity-field responses ?eff(E) have been computed by taking into consideration the specific local field distribution. 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 reducingthe ceramic grain size [2]. (Fig.1) The macroscopic P(E) hysteresis loops were simulated combining the FEM approach with a Monte Carlo model capable to describe domains structures. The FEM -Monte Carlo model explained the transition from a rectangular P(E) hysteresis loops to a less saturated one with reducing grain size. This modification is related to the decrease of the local electric fieldon the bulk regions with reducing GS.