Model for growth and coarsening of two phase systems under diffusional control

Abstract

A model is described which is capable of simulating the two-dimensional evolution of microstructure in two phase systems undergoing diffusion controlled growth and surface tension driven coarsening. To solve the diffusion equation in the matrix phase, an integral equation method is employed. Thus, although it is necessary to describe the shapes of the second phase particles using a number of elements, it is not necessary to discretise the matrix phase as the particles evolve. This allows the computation times to be kept within reasonable limits. The boundary condition at the interface and the variation of the interfacial concentration with interface curvature are accounted for in a rigorous fashion. It is shown that the method can handle the ‘soft’ impingement of overlapping diffusion fields. A treatment of the ‘hard'’ physical impingement of particles is developed. To demonstrate the accuracy and stability of the method, the results from the model are compared with the exact solution for a spherical particle growing in a circular domain; it is shown that the agreement is reasonable. The results from a number of example computations are presented, which include (a) growth of a single particle in a finite domain, (b) soft and hard impingement of two particles in a finite domain, (c) coarsening of a significant number of particles at constant volume fraction, and (d) simultaneous nucleation, growth, and coarsening of second phase particles. Where appropriate, the results are compared with those from other models which have been published in the literature. The advantages and disadvantages of the present model are discussed.