The overall hysteresis behavior of nanocrystalline ferroelectric polycrystals demonstrates unique characteristics against conventional ferroelectric ceramics. The existence of low-permittivity paraelectric grain boundary and its influence to the microstructure of grains can be a key factor leading to such characteristics, especially the grain size-dependent properties. A two dimensional (2D) polycrystalline phase-field model, which distinguishes the grain boundary from the ferroelectric grain, has been developed to investigate the microstructural evolution and hysteresis behavior of nanocrystalline barium titanate (BaTiO3) polycrystals. The results show apparent grain-size dependence on the hysteresis and noticeable vortex polarization structure that dominates the grains as the grain size reduces to tens of nanometers. By studying the hysteresis and domain patterns, it is observed that the grain size-dependent properties are significantly attributed to the grain boundary in two ways: the “dilution effect” due to its low permittivity and paraelectric property that are intensified with increased volume concentration, and the extrinsic effect due to the existence of depolarization field, leading to the superparaelectric domain structure. We conclude that this grain-size dependent microstructural mechanism can well explain various experimentally observed properties of nano-grained ferroelectric polycrystals.

As the grain size decreases to the nanometer range, the characteristics of the ferroelectric nanoceramic can be ultimately determined by the competition between two effects: the intrinsic effect that is associated with the local properties of the grain boundary and the extrinsic effect that arises from the dynamics of domain structure which is highly influenced by the depolarization field caused by the grain boundary. In this work we investigate such a competition with a phase-field simulation based on the time-dependent Ginzburg-Landau kinetic equation. The study is performed on poled/unpoled nanoceramics under high- and low-amplitude bipolar alternating electric field with selected grain size and loading frequency. Our calculations for poled $\mathrm{BaTi}{\mathrm{O}}_3$ at 100 Hz show that, for the grain size from 170 to 50 nm, its properties are dominated by the extrinsic effect, and from 50 to 10 nm, they are dominated by the intrinsic one. As the grain size decreases, the dielectric and piezoelectric constants at the remnant state continuously rise in the extrinsic-dominated region and then drop sharply in the intrinsic-dominated region. Our frequency calculations from 10 to 2500 Hz at the grain size of 100 nm indicate that the high-frequency behavior is very similar to that of the small grain-size, intrinsic-dominated one, whereas the low-frequency behavior is closely related to that of the large grain-size, extrinsic-dominated part, with the demarcation line occurring around 400 Hz. For the unpoled ceramics under small-signal loading, the intrinsic effect is dominant over the entire range of grain size and frequency.