The Correlation Theory of 2D Normal Grain Growth


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Computer simulations of 2D normal grain growth have shown that size correlations between adjacent grains exist in 2D grain structures. These correlations prevail during the coarsening process and influence on the kinetics of the process and on the grain size distribution. Hillert’s analysis starts with the assumption that all grains in the structure have the same environment. Since computer simulations contradict this assumption, the mean-field theory for normal grain growth needs to be modified. A first attempt was made by Hunderi and Ryum, who modified Hillert’s growth law to include the effect of spatial grain size correlations. In the 1D case the distributions derived by means of the modified growth law agreed well with simulation data. However, the distribution derived for 2D grain growth retained unwanted properties of the Hillert distribution. We review some recent progress in developing a mean-field statistical theory. A paradox related to curvilinear polygons is shown to support the expectation that the grain size distribution has a finite cutoff.



Materials Science Forum (Volumes 467-470)

Edited by:

B. Bacroix, J.H. Driver, R. Le Gall, Cl. Maurice, R. Penelle, H. Réglé and L. Tabourot




M.W. Nordbakke et al., "The Correlation Theory of 2D Normal Grain Growth", Materials Science Forum, Vols. 467-470, pp. 1081-1086, 2004

Online since:

October 2004




[1] M. Hillert: Acta metall. Vol. 13 (1965), p.227.

[2] S.P. Marsh, M.E. Glicksman: Acta mater. Vol. 44 (1996), p.3761.

[3] K. Marthinsen, O. Hunderi and N. Ryum: Acta mater. Vol. 44 (1996), p.1681.

[4] C.V. Thompson: Solid State Physics, edited by H. Ehrenreich and F. Spaepen (Academic Press, 2001), pp.269-314.

[5] P.R. Rios: Scripta mater. Vol. 40 (1999), p.665.

[6] P. R Rios, K. Lücke: Scripta mater. Vol. 44 (2001), p.2471.

[7] V. E. Fradkov, D.G. Udler: Adv. Phys. Vol. 43 (1994), p.739.

[8] W.W. Mullins: Acta mater. Vol. 46 (1998), p.6219.

[9] O. Hunderi, N. Ryum: J. Mater. Sci. Vol. 15 (1980), p.1104.

[10] P. Streitenberger: Scripta mater. Vol. 39 (1998), p.1719.

[11] O. Hunderi, N. Ryum: Acta mater. Vol. 44 (1996), p.1673.

[12] M.W. Nordbakke, N. Ryum and O. Hunderi: Acta mater. Vol. 50 (2002), p.3661.

[13] D. Weygand: Simulation numérique de la croissance de grains (PhD thesis, University of Grenoble, 1998).

[14] C. Maurice: Recrystallization and Grain Growth, edited by G. Gottstein and D.A. Molodov (Springer-Verlag, 2001). Trans Tech Publications Ltd Brandrain 6 Fax: +41 - 1 922 10 33 CH-8707 Uetikon-Zuerich e-mail: ttp@ttp. net Switzerland Web: http: /www. ttp. net.