Advection-diffusion model for the stagnation of normal grain growth in thin films

This paper presents an advection-diffusion model to describe the stagnation of normal grain growth in thin films. The underlying advection-diffusion model describes grain growth in a two-dimensional topological-class/size space. Grain boundary grooving and the correlation between neighbouring grains are introduced into the model to represent stagnation. Grain boundary grooving causes the stagnation of grain growth, and the correlation between neighbouring grains accelerates the effects of stagnation. Numerical solution of continuity equations gives a grain size distribution that is close to log-normal, and fits experiments well. The time development of average grain size also shows the stagnation of grain growth.