First-Principles Theories of Piezoelectric Materials

Piezoelectrics have long been studied using parameterized models fit to experimental data, starting with the work of Devonshire in 1954 [1]. Much has been learned using such approaches, but they can also miss major phenomena if the materials properties are not well understood, as is exemplified by the realization that low-symmetry monoclinic phases are common around morphotropic phase boundaries, which was missed completed by low-order Devonshire models, and can only appear in higher-order models [2]. In the last 15 years, a new approach has developed using first-principles computations, based on fundamental physics, with no essential experimental input other than the desired chemistry (nuclear charges). First-principles theory laid the framework for a basic understanding of the origins of ferroelectric behavior [3–7] and piezoelectric properties [8–11]. The range of properties accessible to theory continues to expand as does the accuracy of the predictions. We are moving towards the ability to design materials of desired properties computationally. Here, we review some of the fundamental developments of our understanding of piezoelectric material behavior and the ability to predict a wide range of properties using theoretical methods. This is not meant as a review of the literature. Comprehensive reviews of the literature of theoretical studies of ferroelectrics are given by Resta [12] and Rabe and Ghosez [13].