  The problem of heterogeneous nucleation of second-phase in alloys in the
vicinity of elastic defects is considered. The defect can be a dislocation line
or a crack tip residing in a crystalline solid. We use the Ginzburg-Landau
equation to describe the spatiotemporal evolution of the order parameter in the
environs of the defect. The model accounts for the elasticity of the solid and
the interaction of order parameter field with the elastic field of the defect.
A finite volume numerical method is used to solve the governing partial
differential equation for the order parameter. We examine the nature of the
phase transition in the vicinity of the defects.
