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Title:Theory for atomic diffusion on fixed and deformable crystal lattices
Author(s):Fried, Eliot; Sellers, Shaun
Subject(s):Atomic Diffusion
Fixed Crystal Lattices
Deformable Crystal Lattices
Abstract:We develop a theoretical framework for the diffusion of a single unconstrained species of atoms on a crystal lattice that provides a generalization of the classical theories of atomic diffusion and diffusion-induced phase separation to account for constitutive nonlinearities, external forces , and the deformation of the lattice. In this framework, we regard atomic diffusion as a microscopic process described by two independent kinematic variables: (i) the atomic flux, which reckons the local motion of atoms relative to the motion of the underlying lattice, and (ii) the time-rate of the atomic density, which encompasses nonlocal interactions between migrating atoms a nd characterizes the kinematics of phase separation . We introduce generalized forces power-conjugate to each of these rates and require that these forces satisfy ancillary microbalances distinct from the conventional balance involving the forces that expend power over the rate at which the lattice deforms. A mechanical version of the second law, which takes the form of an energy imbalance accounting for all power expenditures (including those due to the atomic diffusion and phase separation), is used to derive restrictions on the constitutive equations. With these restrictions, the microbalance involving the forces conjugate to the atomic flux provides a generalization of the usual constitutive relation between the atomic flux and the gradient of the diffusion potential. a relation that in conjunction with the atomic balance yields a generalized Cahn-Hilliard equation.
Issue Date:1999-06
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 910
1999-6012
Genre:Technical Report
Type:Text
Language:English
URI:http://hdl.handle.net/2142/112618
ISSN:0073-5264
Sponsor:Energy Department; EPSRC (UK)
Rights Information:Copyright 1999 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04


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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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