A phase-field study on the hysteresis behaviors and domain patterns of nanocrystalline ferroelectric polycrystals

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.