Linear elasticity and piezoelectricity in pyroelectrics

Abstract

We present a new, first-principles theory of linear elasticity and piezoelectricity in pyroelectrics, materials including ferroelectrics, which possess a spontaneous polarization. The constitutive relations for the polarization, the electric displacement, the magnetic intensity, and the total stress are found to contain linear terms proportional to either the spontaneous polarization ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{P}}}^{S}$ or the spontaneous electic field ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}}^{S}$. The terms involving ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{P}}}^{S}$ are found to cancel from the differential equations and boundary conditions when ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{P}}}^{S}$ is homogeneous. If ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{P}}}^{S}$ is not homogeneous, linear terms proportional to spatial derivatives of ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{P}}}^{S}$ remain in the Maxwell equations. The terms involving ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}}^{S}$ lead to a new effective piezoelectric stress tensor of lower symmetry than the normal piezoelectric stress tensor, because it can couple to rotation as well as to strain. The terms involving ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{E}}}^{S}$ also produce a new effective elastic stiffness tensor of lower symmetry than the usual stiffness tensor in that it can couple to both strain and rotations. The reduced symmetry allows it to have as many as 45 different components instead of the usual 21.