Grain Growth in one Dimension: the Mean Field Approach
- ISSN: 16629752
- DOI: 10.4028/www.scientific.net/MSF.94-96.337
Abstract
In order to assess the accuracy of the mean field approximation to the kinetics of grain growth, we introduce a one-dimensional model of a polycrystal, in which the grains are segments in a line, with periodic boundary conditions, each grain having two adjacent grains. The size of each grain changes with time according to a given law, the rate of change depending on the size of the grain and on the sizes of the adjacent grains, in such a way that small grains shrink, eventually disappearing, and large grains expand, with conservation of total size. In a mean field approximation, the adjacent grains are replaced by grains of average size. The evolution of various initial distributions under the two approaches, i.e. the discrete and the mean field approaches, is compared. Large differences between the two approaches are found for particular initial distributions, while for other distributions the differences are minor. The kinetics is, in general, faster in the discrete approach, and leads to broader distributions than in the mean field approximations. Steady state distributions within the mean field approach are seen to evolve in the discrete approach. No tendency for a steady state to be reached has been observed, the distributions becoming in general broader due to growth. features.
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