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 rotati onal motions of the vertices are determined by the curvatures of the a djoining grain boundaries, and their derivatives. In addition, there i s a necessary constraint of these curvatures, in that they must sum to zero. The case of anomalous initial conditions (of relevance to topol ogical changes) is analysed, and the singular behaviour of the vertex velocity is determined for such a case. Similar rules govern the motio n of vertices and lines in three-dimensional grain growth.