The Piezodielectric Effect and Electrostriction in Anisotropic or Isotropic Media

Abstract

A phenomenological theory of the piezodielectric effect in homogeneous isotropic or anisotropic solids is presented. This theory rests upon the assumption that the changes in the dielectric constants ${\ensuremath{\epsilon}}_{\mathrm{ij}}$ are linear in the six components of applied mechanical stress. It is shown that 36 piezodielectric moduli are required for a complete description of the piezodielectric effect. The number of independent moduli is two in isotropic solids, eight in alpha-quartz and tourmaline, and twelve in Rochelle salt. The matrices for the piezodielectric and piezooptical moduli are identical in all crystal classes which we have considered. The term electrostriction is applied to the case in which the components of strain are quadratic functions of the applied electrical field. The character of electrostriction in any solid is predicted by considering the piezodielectric effect together with the first and second laws of thermodynamics. The relation of electrostriction to the piezodielectric effect is very similar to the relation of the converse piezoelectric effect to the direct piezoelectric effect. The equations for the components of "electrostrictive strain" in isotropic solids and alpha-quartz are given in detail. General expressions for "electrostrictive stress" are derived. The equations of motion of a perfectly elastic, piezoelectric and electrostrictive solid which is subjected to mechanical and electrical fields are then stated. From considerations of crystalline symmetry and Neumann's hypothesis it can be seen that every solid may exhibit electrostriction whereas relatively few solids are piezoelectric.