Modeling of particle coarsening and precipitation free zones

Previous simulation studies of the effect of volume fraction on the precipitate coarsening process have treated precipitates as point sources or sinks of solute atoms. These studies have demonstrated that, although the average particle size varying with time as $t^{1/3}$ is still valid, the coarsening rate constant is an increasing function of volume fraction. In this study we extend these simulation methods to model particle coarsening near grain boundaries. An essential feature of the new model is the solute depletion that occurs at grain boundaries. The simulation results are shown to quantitatively reproduce the following aspects of particle coarsening near grain boundaries in certain alloys: (a) precipitate free zones (PFZs) form near grain boundaries, (b) the width of PFZs increases with time and is proportional to the square root of time, (c) particles at the edge of PFZs are larger than those inside the grain. This novel model is shown to be well suited to describe particle coarsening near grain boundaries. In addition, it reinforces the credibility of the theories built into our mathematical model, i.e., the formation of PFZs near grain boundaries is caused by diffusion of solute atoms. (paper)