Electromechanical coupling in nonpiezoelectric materials due to nanoscale nonlocal size effects: Green’s function solutions and embedded inclusions

Abstract

In a piezoelectric material, an applied uniform strain can induce an electric polarization (or vice versa). Crystallographic considerations restrict this technologically important property to noncentrosymmetric systems. It has been shown both mathematically and physically that a nonuniform strain can potentially break the inversion symmetry and induce polarization in nonpiezoelectric materials. The coupling between strain gradients and polarization, and conversely between strain and polarization gradients, is investigated in this work. While the conventional piezoelectric property is nonzero only for certain select materials, the nonlocal coupling of strain and electric field gradients is (in principle) nonzero for all dielectrics, albeit manifesting noticeably only at the nanoscale, around interfaces or in general in the vicinity of high field gradients. Based on a field theoretic framework accounting for this phenomena, we (i) develop the fundamental solutions (Green's functions) for the governing equations, and (ii) motivated by eventual applications for quantum dots, solve the general embedded mismatched inclusion problem with explicit results for the spherical and cylindrical shape. Expectedly, our results for the aforementioned problems are size dependent and indicate generation of high electric fields reaching values of approximately hundreds of kV/m in selected sizes and locations---even in isotropic centrosymmetric nonpiezoelectric materials.