Statistical Derivation of Basic Equations of Diffusional Kinetics in Alloys with Application to the Description of Diffusion of Carbon in Austenite

TL;DR

This paper derives fundamental equations for diffusional kinetics in alloys using a statistical approach, providing new microscopic expressions for diffusivity and applying them to carbon diffusion in austenite.

Contribution

It introduces a generalized kinetic equation considering interaction effects and derives an explicit diffusivity expression for interstitial atoms, advancing the understanding of diffusion in alloys.

Findings

Derived a microscopic diffusivity expression for interstitial atoms.

Applied the theory to carbon diffusion in austenite.

Provided insights into carbon-carbon interactions and transition state entropy.

Abstract

Basic equations of diffusional kinetics in alloys are statistically derived using the master equation approach. To describe diffusional transformations in substitution alloys, we derive the "quasi-equilibrium" kinetic equation which generalizes its earlier versions by taking into account possible "interaction renormalization" effects. For the interstitial alloys Me-X, we derive the explicit expression for the diffusivity D of an interstitial atom X which notably differs from those used in previous phenomenological treatments. This microscopic expression for D is applied to describe the diffusion of carbon in austenite basing on some simple models of carbon-carbon interaction. The results obtained enable us to make certain conclusions about the real form of these interactions, and about the scale of the "transition state entropy" for diffusion of carbon in austenite.