Introduction

Abstract

The linear piezoelectric effect,which occurs in elastic dielectrics, is a physical phenomenon widely used in technology. The classical continuum theory [1] incorporating the effect is about seventy-five years old and is today universally employed in the analysis and design of crystal oscillators, filters and transducers [2,3]. In systematic derivations of the classical, phenomenological theory, piezoelectricity is usually expressed as an interaction between mechanical strain and one of the electrical variables: the electric field [3] the electric displacement [4] or the electric polarization [5]. There is, however, no fundamental reason for restricting attention to the interaction of the strain, a second rank tensor, with only a first rank electrical quantity (field, displacement, polarization). It is not illogical to examine the consequences of considering an additional, linear, electromechanical effect: an interaction between the strain and, say, the polarization gradient — a second rank tensor quantity. The added complexity is justified by the fact that the resulting mathematical theory [6] has interesting novel properties: (1) it accomodates the mathematical representation of a surface energy of deformation and polarization which is absent from the classical theory but which has been measured in the laboratory [7] and calculated from atomic considerations [8]; (2) it can account [9] for an apparent anomaly observed in measurements of the electrical capacitance of thin, dielectric films [10]; (3) the additional electromechanical effect is not confined to non-centrosymmetric materials, as is the classical piezoelectric effect; (4) the resulting equations, rather than the classical ones, are the correct, long wave limit [9,11] of the equations of the modern dynamical theory of crystal lattices of electronically polarizable atoms [12,13,14,15].