A Non-Linear Model for Elastic Dielectric Crystals With Mobile Vacancies

Report No. ARL-RP-253
Authors: J. D. Clayton
Date/Pages: July 2009; 20 pages
Abstract: A framework is developed for electromechanical behavior of dielectric crystalline solids subjected to finite deformations. The theory is formulated in the context of electrostatics; however, vacancies in the lattice may carry an electric charge, and their concentrations may be large. The material is treated as a continuous body with a continuous distribution of point vacancies, but volumes and charges of individual defects enter the description. The deformation gradient is decomposed multiplicatively into terms accounting for recoverable thermoelasticity and irreversible volume changes associated with vacancies. Thermodynamic arguments lead to constitutive relations among electromechanical quantities framed in the elastically unloaded intermediate configuration, with the Cauchy stress tensor consistently non-symmetric as a result of electrostatic effects. The requirement of non-negative dissipation imposes constraints on vacancy migration. Following postulation of a quadratic form for the free energy potential, a kinetic equation for vacancy flux is derived in the intermediate configuration, with diffusion driven by gradients of vacancy concentration, electrostatic potential, hydrostatic pressure, and crystal structure. Effects of geometric non- linearity (i.e. finite elastic strains and large vacancy concentrations) are found to affect vacancy diffusion in a body subjected to biaxial lattice strain, for example a film device with lattice mismatch at its interfaces.
Distribution: Approved for public release
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Last Update / Reviewed: July 1, 2009