Lattice Theory of the Elastic Dielectric

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Abstract
A homogeneously deformed and uniformly polarized elastic dielectric is considered. For small displacements of the medium from the deformed and polarized state, the equation of motion and the equation for the change in polarization due to the displacement are derived to the first order in the deformation parameter and the macroscopic electric field, using Toupin's general theory of the elastic dielectric. Born and Huang's treatment of the vibrations of an ionic lattice is extended to the case where the lattice is homogeneously deformed and has a uniform electric field. The equation of motion and the equation for the change in polarization due to small displacements from the deformed and polarized state are derived on lattice theory. A comparison of lattice-theoretical equations at long wavelength with the continuum-mechanical equations yields the expressions for the electrical susceptibility, the piezoelectric constants, and the second-order elastic constants together with their linear coefficients of variation with the deformation and the electrical field.

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