Non-Fickian current enabling the uphill diffusion of impurities diffusing by the mechanism of mobile impurity-defect pairs

TL;DR

This paper derives equations for non-Fickian impurity diffusion mediated by mobile impurity-defect pairs, predicting uphill diffusion in inhomogeneous cases and suggesting it could be observed in FCC metals.

Contribution

It introduces a new theoretical framework for non-Fickian diffusion, including uphill diffusion, in impurity systems with inhomogeneous defect distributions.

Findings

Equations predict uphill diffusion in inhomogeneous impurity systems.

Non-Fickian behavior occurs at small scales and can also happen at any scale in inhomogeneous cases.

Uphill diffusion may be observable in about one third of impurities in FCC metals.

Abstract

Equations governing the diffusion mediated by the mobile pairs have been derived. In addition to known non-Fickian (n-F) behavior observable at small spatiotemporal scale under homogeneous defect distribution the equations predict another type of n-F diffusion that may take place only in the inhomogeneous case and can be operative at any scale. In the limit of slowly varying inhomogeneity the n-F diffusion current has been identified and shown to be able to induce the uphill diffusion. It has been argued that the latter should be observable in about one third of impurities in FCC metals.