Correlation between ferroelectric domain size and grain size in ferroelectric ceramics: A phase-field study

Abstract

The properties of ferroelectric ceramics depend on their grain/domain size heavily and former experiments find that their domain size monotonously increases with grain size increasing and the slope of the increase is drastically different at small and large grain sizes. However, a theoretical understanding of the relationship between the domain and grain size is still lacking. In this work, the domain structure of ferroelectric ceramics at different grain sizes is investigated by a phase-field model. Consistent with experiments, it is found that the domain size increases sharply with grain size increasing at small grain sizes and then slowly at larger grain sizes. Analysis shows that at small grain sizes, the increase is sharp because the electrostatic energy leads to the formation of a vortex-like structure with four domains in each grain forcing the domain size to approximately equal to half of the grain size as a result of the strong geometric constraint. At large grain sizes with much weaker geometric constraints, the electrostatic energy can be minimized by forming more than four domains which reduces the slope. In addition, the elastic energy contributes to a further reduction of the slope at large grain sizes. The dielectric permittivity at different grain sizes is calculated and it is found that the permittivity first increases and then decreases with grain size decreasing. This work provides a theoretical understanding of the relationship between the domain and grain size of ferroelectric ceramics and could shed light on the designing of high-performance ferroelectric ceramics.