Kinematics, electromechanics, and kinetics of dielectric and piezoelectric crystals with lattice defects

摘要: A mathematical framework is formulated to address the electromechanical behavior of dielectric and piezoelectric solids containing lattice imperfections. The macroscopic displacement gradient encompasses recoverable elasticity, deviatoric plasticity arising from dislocation glide, volumetric deformation attributed point vacancies in crystal. linear connection on spatial manifold deformed vectors describes gradients stretch rotation at microscale caused by continuous distributions various classes crystal defects. It shown that parallel transport a director vector with respect this about closed loop yields discontinuity contributions torsion (physically, dislocations) its curvature rotational defects such as domain walls, vacancy concentration). Classical balance laws electrostatics mass momentum conservation are invoked. free energy function dependent upon distortion, polarization, temperature, defect densities suggested. Thermodynamically consistent kinetic relations for glide diffusion then derived, chemical potential latter depending density, electric potential, hydrostatic pressure, energy. theory also explicitly considers rearrangement surface substance. Two forms contribution investigated detail: logarithmic common mixing theory, quadratic analogous convex strain used continuum elasticity theory. For case, analytical solution equation one dimension, steady state, illustrates effects charge, energy, mechanical stress distribution thin film. specific example given how compressive residual stresses observed experiments may be correlated equilibrium concentration within grains polycrystalline film, influencing electrical performance.