The 2-dimensional simulation of the grain-boundary migration of regular polygons was carried out by using finite-element methods. A straight-line element was used to represent the grain boundaries, where surface tension acted. The driving force for boundary migration was the free-energy reduction per unit volume of atoms crossing the boundary. It was found that polygons with less than 6 edges shrank and finally disappeared, while those with more than 6 edges grew. The steady-state grain-boundary shape between triple-points could be approximated by circular arcs. The migration velocity of the grain boundary was inversely proportional to the grain radius; thus indicating that the square of the radius was proportional to time. The constant of proportionality increased with the number of edges of the polygon.

2-Dimensional Simulation of Grain Boundary Migration by Finite Element Method B.N.Kim, T.Kishi: Journal of the Japan Institute of Metals, 1997, 61[12], 1347-51