...
Dimensional changes parallel to the interface are restricted, and in-plane compatibility stresses are generated.
Consider substitutional binary allow diffusion. The system contains three components, species 1, species 2, and vacancies. Sites can only be created or destroyed at sources
Write the Gibbs-Duhem relation based on the assumption of local equilibrium. A net flux vacancy flux develops in a direction opposite that of the fastest-diffusing species. Nonequilibrium vacancy concentrations would develop in the diffusion zone if they were not eliminated by dislocation climb.
Relate chemical potential gradients to concetration gradients
The local volume expansion arising from the local change of composition contributes to diffusion via the derivative of the average site volume.
Consider the self-diffusivity of species 1 in a chemically homogeneous solution corresponding to *D1. Compare this with the intrinsic diffusivity of the same species in a chemically inhomogeneous solution at the same concentration, corresponding to D1.
The primary difference between D1 and *D1 is a thermodynamic factor involving the concentration dependence of the activity coeffient of component 1.
A thermodynamic factor arises because mass diffusion has a chemical potential gradient as a driving force, but the diffusivity is measured proportional to a concentration gradient and is influenced by the nonideality of the solution.
Describe fluxes by Fick's-law expressions involving two different intrinsic diffusivities, D1 and D2, in a local coordinate system (local C-frame) fixed to the lattice plane through which fllux is measured.
The planes move normal to one another at different rates in a nonuniform fashion due to the Kirkendall effect.
When there is no change in the total specimen volume, the overall diffusion that occurs during the Kirkendall effect can be described in terms of a single diffusivity measured in a single reference frame.
Diffusion in a Volume-Fixed Frame (V-Frame)