Continuum Models of Grain Growth

Abstarct

Many solid materials consist of small crystallites called grains, which are domains of the same phase with different spatial orientations of their crystalline lattices. The grains are separated from each other by the grain boundaries (GBs), which are 2d extended defects with positive excess free energy and, therefore, thermodynamically unstable. Due to their global instability, curved GBs are known to move toward the centers of their curvatures. However, overall, the GBs move such as to increase the average size of the grain $\overline{R}$ and reduce the total GB area and thus the total free energy of the system.