High-response piezoelectricity modeled quantitatively near a phase boundary

Abstract

Interconversion of mechanical and electrical energy via the piezoelectric effect is fundamental to a wide range of technologies. The discovery in the 1990s of giant piezoelectric responses in certain materials has therefore opened new application spaces, but the origin of these properties remains a challenge to our understanding. A key role is played by the presence of a structural instability in these materials at compositions near the “morphotropic phase boundary” (MPB) where the crystal structure changes abruptly and the electromechanical responses are maximal. Here we formulate a simple, unified theoretical description which accounts for extreme piezoelectric response, its observation at compositions near the MPB, accompanied by ultrahigh dielectric constant and mechanical compliances with rather large anisotropies. The resulting model, based upon a Landau free energy expression, is capable of treating the important domain engineered materials and is found to be predictive while maintaining simplicity. It therefore offers a general and powerful means of accounting for the full set of signature characteristics in these functional materials including volume conserving sum rules and strong substrate clamping effects.