Derivation of Statistical Model of Grain Growth Based on 3-D Von Neumann Equation

The derivation of an equivalent 3-D Von Neumann equation and the corresponding kinetics equation in terms of geometrical characteristics of a grain is shown and the formulation is provided in the framework of the statistical theory of grain growth. The topological relationships between number of grain faces, grain size, number of corners and edges and how these can be calculated in a real microstructure with a statistical approach are discussed. A quadratic law for the linkage between number of faces and grain size is found and compared with available experimental results. Inside the above description a basic formulation of the statistical theory will be derived based on simple geometrical and statistical principles without any independent assumption