Diffusion-controlled phase growth on dislocations

We treat the problem of diffusion of solute atoms around screw dislocations. In particular, we express and solve 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. 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. Our calculations show that an increase in the amplitude of the dislocation force, e. g. the magnitude of the Burgers vector, enhances the second-phase growth in an alloy. Moreover, we calculate the reduction in concentration of solute atoms as a function of radius around a second phase which grows cylindrically (in the radial direction) so that its radius varies as the square root of time for various levels of the dislocation force amplitude.