Inverse Domain‐Size Dependence of Piezoelectricity in Ferroelectric Crystals

Piezoelectricity of ferroelectric crystals is widely utilized in electromechanical devices such as sensors and actuators. It is broadly believed that the smaller the ferroelectric domain size, the higher the piezoelectricity, arising from the commonly assumed larger contributions from the domain walls. Herein, the domain-size dependence of piezoelectric coefficients of prototypical ferroelectric crystals is theoretically studied based on thermodynamic analysis and phase-field simulations. It is revealed that the inverse domain-size effect, i.e., the larger the domain size, the higher the piezoelectricity, is entirely possible and can be just as common. The nature of the domain-size dependence of piezoelectricity is shown to be determined by the propensity of polarization rotation inside the domains instead of the domain wall contributions. A simple, unified, analytical model for predicting the domain-size dependence of piezoelectricity is established, which is valid regardless of the crystalline symmetry, the materials chemistry, and the domain structures of a ferroelectric crystal, and thus can serve as a guiding tool for optimizing piezoelectricity of ferroelectric materials beyond the "nanodomain" engineering. In addition, the theoretical approach can be extended to understand the microstructural size effect of multifunctional properties in ferroic and multiferroic materials.