Grain growth of uniform boundaries with scaling

摘要

The equation of continuity for grain growth is derived from a Fokker-Planck formulation; the equation contains no term corresponding to diffusion or random walk of grains along a size axis. It is shown that such a term cannot arise form grain switching events contrary to the assumption of most sto- chastic theories of grain growth. A development is given of curvature driven grain growth for uniform boundaries utilizing the scaling analysis of Hunderi and Ryum. In two dimensions the addition of the von Neumann-Mullins relation allows the determination of the reduced grain size(x) distribution function P(x) from the average number of sides s(x) as a function of x and vice versa (given a structural kinetic par- ameterβ). A non-Hillert P(x) is shown to require a non-linear s(x). It is argued, with Hunderi and Ryum, that P(x) very likely has a cutoff. Three distributions P(x) and their corresponding s(x) are discussed.