Abstract
Effects of elastic coupling between a ferroelectric thick film and a supporting substrate or underlayer with finite thickness on the apparent longitudinal piezoelectric coefficients are analysed in this work. General analytical solutions of the effective d33 converse piezoelectric coefficients of a film–substrate couple are given as a function of the electromechanical properties, crystalline structure and orientation, as well as the thickness ratio of the couple. Computations of effective d33 coefficients as a function of the thickness ratio are performed for typical tetragonal and rhombohedral lead zirconate titanate ferroelectric films with a composition near its morphotropic phase boundary. These results are compared with those for thin films with the same compositions, where the substrate clamping effect is dominant.
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