Homogeneous nucleation of a solid-solid dilatational phase transformation

problem of homogeneous coherent nucleation of a spherical particle in an iufmite matrix is considered. A LandauXlinzburg type potential is used to describe the material response. The underlying Landau potential is taken to be of the 2-3-4 type and the gradient energy contribution is taken to be quadratic. The nucleation problem is posed as an energy extremum problem and the finite element method, in conjunction with a perturbed Lagrangian algorithm, is used to obtain solutions with nucleus structure. The present nonlinear model spans the range from classical to nonclassical nucleation and exhibits many of the physical phenomena associated with nonclassical nucleation including divergence in radius and interface thickness of the critical nucleus and vanishing of the nucleation energy as the instability temperature is approached