A phase field model of the impingement of solidifying particles

We propose a model of the impingement of solidifying crystalline particles, the ensuing grain boundary formation, and grain coarsening. This model improves upon previous theoretical descriptions of this phenomenon, in that it has the proper behavior under rotations and is easy to implement numerically. Also, insight into the model is straightforward since the parameters are physically motivated, and anisotropy in both the liquid–solid and grain boundary energies can be introduced in a natural manner. A one dimensional analytic solution is presented