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

A model is described which is capable of simulating the two-dimensional evo lution of microstructure in two phase systems undergoing diffusion controll ed growth and surface tension driven coarsening. To solve the diffusion equ ation in the matrix phase an integral equation method is employed. Thus alt hough 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 ph ase as the particles evolve. This allows the computation times to be kept w ithin reasonable limits. The boundary condition at the interface and the va riation of the interfacial concentration with interface curvature are accou nted for in a rigorous fashion. It is shown that the method can handle the 'soft' impingement of overlapping diffusion fields. A treatment of the 'har d' physical impingement of particles is developed. To demonstrate the accur acy and stability of the method, the results from the model are compared wi th 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 o f example computations are presented which include (a) growth of a single p article 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 coar sening of second phase particles. Where appropriate, the results are compar ed with those from other models which have been published in the literature . The advantages and disadvantages of the present model are discussed.