The origin of piezoelectric enhancement in compositionally graded ferroelectrics with sinusoidal variation

Abstract

The direct piezoelectric effect of [Formula: see text] Ba1− xSr xTiO3 graded ferroelectrics, whose compositions change in a sinusoidal form, is investigated via an extended phase-field method. The obtained results demonstrate that the piezoelectric coefficient can be significantly enhanced by controlling the amplitude of sinusoidal variation. The origin of piezoelectric enhancement is investigated by considering the formation of polarization domain structures and their behaviors under strain. Although a ferroelectric tetragonal phase or a paraelectric cubic phase primarily form in homogeneous Ba1− xSr xTiO3 ferroelectrics with a different content x, interestingly, an unusual ferroelectric monoclinic phase can be formed in compositionally graded ferroelectrics, giving rise to the coexistence of multiple phases. The monoclinic phase emerges as a result of the process that reduces built-in electric potential induced by a large gradient of polarization. In turn, the formation of the monoclinic phase gives rise to transient zones that make the polarization field more susceptible to external strains, thereby enhancing the piezoelectric response. We further demonstrate that the piezoelectric enhancement strongly depends on the volume fraction of the monoclinic phase in compositionally graded ferroelectrics, suggesting a route for the rational design of polarization domains and piezoelectric effects.