Topology Based Growth Law and New Analytical Grain Size Distribution Function of 3D Grain Growth
Based on topological considerations and results of Monte Carlo Potts model simulations of three-dimensional normal grain growth it is shown that, contrary to Hillert’s assumption, the average self-similar volume change rate is a non-linear function of the relative grain size, which in the range of observed grain sizes can be approximated by a quadratic polynomial. In particular, based on an adequate modification of the effective growth law, a new analytical grain size distribution function is derived, which yields an excellent representation of the simulated grain size distribution.
S.-J.L. Kang, M.Y. Huh, N.M. Hwang, H. Homma, K. Ushioda and Y. Ikuhara
P. Streitenberger and D. Zöllner, "Topology Based Growth Law and New Analytical Grain Size Distribution Function of 3D Grain Growth", Materials Science Forum, Vols. 558-559, pp. 1183-1188, 2007