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

The direct piezoelectric effect of BaTiO3↔ Ba1−xSrxTiO3 graded ferroelectrics, whose compositions change in a sinusoidal form, is investigated via an extended phase-field method. obtained results demonstrate that the coefficient can be significantly enhanced by controlling amplitude variation. origin enhancement considering formation polarization domain structures and their behaviors under strain. Although ferroelectric tetragonal phase or paraelectric cubic primarily form homogeneous ferroelectrics with different content x, interestingly, unusual monoclinic formed compositionally giving rise to coexistence multiple phases. emerges as result process reduces built-in electric potential induced large gradient polarization. In turn, gives transient zones make field more susceptible external strains, thereby enhancing response. We further strongly depends on volume fraction suggesting route for rational design domains effects.