On a stochastic theory of grain growth

On the analytical solution for self-similar grain size distributions in two dimensions

“…As expected, that analysis led to a Fokker-Planck equation for the size distribution, which can yield a unique self-similar asymptotic state that could be reached from any arbitrary initial state. The Fokker-Planck equation was obtained using a stochastic formulation first proposed by Pande [3] and employing von Neumann-Mullins law and the results of Rios and Glicksman [4]. We also showed that the boundary conditions are sufficient to determine the "strength" of the diffusion term D in terms of the parameters already determined by Rios and Glicksman [4].…”

“…In Pande and Cooper [2] we showed why models based on a mean field approach cannot explain many properties of grain growth observed experimentally, no matter what form of growth rate is assumed. Hence, there is a need for a new approach, namely a stochastic treatment [3,[8][9][10][11].…”

The analytical modeling of normal grain growth

“…]+ D_1_~(RN-l aF) at -aRLR 2 R N -1 aR aR This equation is known as a FokkerPlanck equation, and it has been solved in closed form with appropriate constraints. 24 The second term on the righthand side of this equation is the general diffusion term for N-dimensional grains (N = 1,2, or 3).…”

“…----~----~------~----~-A comparison of measured grain size data in iron21 with the Rayleigh and log-normal distribution functions 24. The similarity of the size distributions at different annealing times illustrates the self-similar scaling behavior of grain growth.…”

Kinetics of Normal Grain Growth Depending on the Size Distribution of Small Grains

“…On normal grain growth, there have been extensive studies including the curvature-driven growth model, 1) diffusion-like growth model, 2) statistical analysis, 3) stochastic model 4) and numerical simulations. [5][6][7][8][9][10][11][12] Despite a variety of the analyzing methods, most of the studies predict an n-value of 2, and thereby n ¼ 2 has widely been recognized as the theoretical grain growth exponent for normal grain growth.…”