Theory of normal grain growth in normalized size space

Simple mean-field deterministic theory of normal grain growth in both 3-dimension and 2-dimension cases is presented, predicting the Rayleigh size distribution. The main idea is an application of standard thermodynamics to normalized size space with unit length proportional to average size. In the normalized space, the change of normalized free energy caused by the size change of an arbitrary grain is independent of the reservoir, which consists of all the other grains. Such 'decoupling' enables us to use the original Burke-Turnbull approach to relate driving force to velocity of grain growth in the normalized space