Dissipative phenomena and acoustic phonons in isothermal crystals: A density-functional theory study

Abstract

We derive the nonlinear transport equations for isothermal crystalline solids using a density-functional theory based free energy and the Poisson bracket formalism. The model is comprised of three characteristic time scales: A fast one of sound waves and two slow ones of diffusive phenomena. It also combines long-range elastic features with a density field $\ensuremath{\rho}$ having an atomistic resolution. At the level of linearized hydrodynamics, our results are identical to transport equations obtained from the Mori projection operator treatment when the coupling of mass density and phonons becomes weak. At the linear level, we also show that Fick's law breaks down without dislocations in accordance with Cahn's theory of stress effects on diffusion in solids. In contrast, with no bilinear couplings between the density and the displacement fields, it is possible to use a nonlinear local theory to describe diffusion and elastic effects using just a single scalar field $\ensuremath{\rho}$, which is numerically efficient. We show how a variety of phenomenological phase field crystal models---which have recently demonstrated their power in materials science applications---can be derived, and how their parameters can be related to more microscopic ones.