Three-dimensional nucleation with diffusion-controlled growth: Simulation of hierarchical diffusion zones overlap

We show that a major difficulty persists for the comprehensive description of multiple nucleation on active sites followed by three-dimensional diffusion-controlled growth, namely the unfeasible consideration of a uniform height for all diffusion zones, which is required for proper consideration of the process in analogy to a two-dimensional transformation within the standard model. Through numerical simulations of the Monte Carlo type we illustrate that a hierarchical model of overlap, with earlier diffusion zones prevailing over later ones, may lead to overcoming this major limitation. The results obtained have been compared with those given by current formulations of the standard model, showing that hierarchical overlap of diffusion zones offers a robust and improved description of multiple nucleation with three-dimensional diffusion-controlled growth.