Original ArticleComputer simulation in 3D of a phase transformation nucleated by simple sequential inhibition process

Abstract

Analytical and numerical models of nucleation and growth transformations usually suppose that nuclei are located uniform randomly, i.e., according to a Poisson point process, within the matrix. Nonetheless, nucleation might be prevented or made more difficult if a new nucleus tries to form very close to another already existent nucleus. In these circumstances, it is better to locate the nuclei according to a point process in which there is an exclusion zone around each nucleus. The 3D Sequential point process is a convenient point process to model such a situation. By changing the nuclei density, the Sequential point process can generate arrangements of nuclei in space with distinct characteristics. In this work, we compare 3D computer simulations with nuclei generated by the Sequential point process with nuclei generated by a Poisson point process. Stereological parameters, as well as the correction function (obtained from the two-point correlation function), characterize the progress of the transformation. The 3D Sequential point process can produce a range of outcomes. Transformation kinetics behavior changes from close to a transformation nucleated according to a homogeneous Poisson point process to a transformation close to a periodic arrangement of nuclei.