Simulations of Microstructural Evolution

"We formulate the mathematical solution to late-stage multi particle diffusion in finite systems. The transition from finite system behavior to that for an infinite system is established. Large-scale simulations are reported regarding the dynamics of phase coarsening. Even in the case of a small volume fraction (Vv = 10-4), the particle size distribution is broader than that for the well-known Lifshitz-Slyozov limit at zero volume fraction. We also report the first simulation studies of extremely low volume fraction, for which corresponding experiments, as well as other simulations, do not exist at present for comparison. However, in the case of moderate volume fractions (Vv = 0.1), the fiucutations in the volumetric growth rate of particles are extracted from our simulations. These simulations provide additional insight into the statistical nature of diffusion interactions, including multiparticle stochastics during microstructural evolution.IntroductionPredicting microstructure evolution in alloys remains one of the cornerstones of materials science. Phase coarsening is a common process in microstrucural evolution that leads to a decrease in the excess total interfacial energy of the system. The system typically consists of separate and identifiable units, or domains, such as second-phase particles distributed in a matrix. During phase coarsening, larger particles grow at the expense of small particles. Over time, this ""competition"" results in an increase in the average size of the particle population, and in a concomitant decrease in the number of particles.Particle size and microstructure of many cast alloys depend on similar coarsening processes. Indeed, properties of these materials, such as strength, toughness, ductility, and electrical conductivity, depend on the material's average particle size and particle size distribution (PSD). Understanding and controlling microstructures in two-phase systems are clearly of widespread technological importance."