Effect of crystal orientation on piezoelectric response of single-crystal piezoelectric layers

The piezoelectric response of a piezoelectric material is strongly dependent on the relative direction between external loading and the poling direction. In this study, we present a three-dimensional finite element model to analyze the effect of the angle between the loading direction and the poling direction on the deformation state and electric displacement in a piezoelectric layer. The results show that, under the action of electric loading, the apparent longitudinal piezoelectric coefficient can be determined from the ratio of the displacement difference to the potential difference between the top and bottom surfaces, which is a function of the crystal orientation. The deformation-induced electric potential difference between the top and bottom surfaces of the piezoelectric layer is dependent on the expansion/shrinkage of side surfaces when subject to mechanical loading.