STATISTICAL-THEORY OF 2-DIMENSIONAL GRAIN-GROWTH .2. KINETICS OF GRAIN-GROWTH

A statistical theory of two-dimensional grain growth is derived from first principles. It describes the time evolution of the distribution function of the grain radii as a solution of a two-parametric continuity equation depending, besides on the time, on the radius R and on the number n of sides of the grains. Here beside the growth rate of an individual grain which is determined by the von Neumann-Mullins equation, also the changing rate of n (e.g. by neighbour switching) had to be evaluated. For solution of the continuity equation, additionally a topological relationship (mean number of sides as function of R) is required to be known. Since this relationship depends on the microstructure (see Part I), it causes a certain ambiguity in the final kinetic equations. For comparison, a simplified model using circular grains is treated which is based on heuristic assumptions but gives better insight into the "physical meaning" of the suppositions and results of the theory. The literature on this subject is thoroughly discussed. In particular, the physical principle of volume conservation during grain growth, which is connected with the fulfillment of the basic topological law nBAR = 6, was shown for several investigations not to be satisfied on the level of the basic equations.