  The evolution of grain structures in materials is a complex and multiscale
process that determines the material's final properties. Understanding the
dynamics of grain growth is a key factor for controlling this process. We
propose a phenomenological approach, based on a nonlinear, discrete mass
transfer equation for the evolution of an arbitrary initial grain size
distribution. Transition rates for mass transfer across grains are assumed to
follow the Arrhenius law, but the activation energy depends on the degree of
amorphization of each grain. We argue that the magnitude of the activation
energy controls the final (sintered) grain size distribution, and we verify
this prediction by numerical simulation of mass transfer in a one-dimensional
grain aggregate.
