The problem of the diffusion of solute atoms around screw dislocations was treated. In particular, the diffusion equation in two dimensions with radial symmetry in an elastic field of a screw dislocation subject to conservation of flux at the interface of a new phase was derived and solved. An incoherent second-phase precipitate growing under the action of the stress field of a screw dislocation was considered. The second-phase growth rate as a function of the supersaturation and a strain energy parameter was evaluated in two dimensions. The calculations showed that an increase in the amplitude of the dislocation force, e.g. the magnitude of the Burgers vector, enhanced the second-phase growth in an alloy. Moreover, the reduction in concentration of solute atoms was calculated as a function of radius around a second phase which grew cylindrically (in the radial direction) so that its radius varied as the square root of time for various levels of the dislocation force amplitude.

Diffusion-Controlled Phase Growth on Dislocations. A.R.Massih: Philosophical Magazine, 2009, 89[33], 3075-86