Use of stereology to derive a new kinetic equation for mean curvature driven grain growth

摘要: Abstract The idea that normal grain growth driven by surface tension may be described theoretically the hypothesis local velocity of an element boundary is proportional to its mean curvature dates back more than half a century. von Neumann was first derive this relation and used it predict rate evolution two dimensional cell structure. MacPherson Srolovitz extended development describe in three dimensions; however, their result couched terms did not facilitate tests theory. In paper expected value theorems established stereology are invoked extend provide new equation predicts change volume grains microstructure which, while preserving rigor generality result, expresses quantities can measured microstructures. This illustrated with set measurements based upon theory derived from simulation successfully predictions. It interesting also exhibits “ n -6 rule” similar to, but identical with, contained Neumann’s