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Publication Citation: Grain Size Distribution in Two Dimensions in the Long Time Limit

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Author(s): Geoffrey B. McFadden; C.S. Pande; K.P. Cooper;
Title: Grain Size Distribution in Two Dimensions in the Long Time Limit
Published: July 08, 2008
Abstract: It is shown that the inclusion of a "noise" term in the growth rate of individual grains leads to a stochastic model that provides a more realistic description of grain growth phenomenon. The resulting Fokker-Planck equation for the grain size distribution is solved numerically due to the difficulties in obtaining an analytical solution. The analysis is limited to two dimensions and assumes quasi-stationary distributions in the long time limit. The resulting grain size distribution is shown to be in agreement with that obtained from computer simulations, indicating the validity of the stochastic approach.
Citation: Acta Materialia
Volume: 56
Pages: pp. 5304 - 5311
Keywords: Fokker-Planck equation, grain growth, grain size distribution function, similarity solution, thin films
Research Areas: Math
PDF version: PDF Document Click here to retrieve PDF version of paper (285KB)