Diffusion-controlled phase growth on dislocations

TL;DR

This paper models the diffusion of solute atoms around screw dislocations to understand how dislocation stress fields influence second-phase precipitate growth, providing analytical solutions and growth rate predictions.

Contribution

It presents a mathematical framework for diffusion-controlled phase growth on dislocations, including solutions for the diffusion equation and growth rate analysis in 2D and 3D.

Findings

Dislocation stress fields enhance precipitate growth.

Growth rate depends on supersaturation and strain energy.

A link between supersaturation and precipitate size is established.

Abstract

We treat the problem of diffusion of solute atoms around screw dislocations. In particular, we express and solve the diffusion equation, in radial symmetry, in an elastic field of a screw dislocation subject to the flux conservation boundary condition at the interface of a new phase. We consider an incoherent second-phase precipitate growing under the action of the stress field of a screw dislocation. The second-phase growth rate as a function of the supersaturation and a strain energy parameter is evaluated in spatial dimensions d=2 and d=3. Our calculations show that an increase in the amplitude of dislocation force, e.g. the magnitude of the Burgers vector, enhances the second-phase growth in an alloy. Moreover, a relationship linking the supersaturation to the precipitate size in the presence of the elastic field of dislocation is calculated.