ON THE MOTION OF VERTICES IN 2-DIMENSIONAL GRAIN-GROWTH

Relations are derived for the motion of vertices in the standard model of ideal grain growth in two dimensions. The translational and rotational motions of the vertices are determined by the curvatures of the adjoining grain boundaries, and their derivatives. In addition, there is a necessary constraint of these curvatures, in that they must sum to zero. The case of anomalous initial conditions (of relevance to topological changes) is analysed, and the singular behaviour of the vertex velocity is determined for such a case. Similar rules govern the motion of vertices and lines in three-dimensional grain growth.