Monte Carlo Potts Model Simulation and Statistical Theory of 3D Grain Growth


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An improved Monte Carlo (MC) Potts model algorithm has been implemented allowing an extensive simulation of three-dimensional (3D) normal grain growth. It is shown that the simulated microstructure reaches a quasi-stationary state, where the growth of grains can be described by an average self-similar volumetric rate of change, which depends only on the relative grain size. Based on a quadratic approximation of the volumetric rate of change a generalized analytic mean-field theory yields a scaled grain size distribution function that is in excellent agreement with the simulation results.



Materials Science Forum (Volumes 558-559)

Edited by:

S.-J.L. Kang, M.Y. Huh, N.M. Hwang, H. Homma, K. Ushioda and Y. Ikuhara




D. Zöllner and P. Streitenberger, "Monte Carlo Potts Model Simulation and Statistical Theory of 3D Grain Growth", Materials Science Forum, Vols. 558-559, pp. 1219-1224, 2007

Online since:

October 2007




[1] M.P. Anderson, D.J. Srolovitz, G.S. Grest, P.S. Sahni: Acta Metall. Vol. 32 (1984), p.783.

[2] M.P. Anderson, G.S. Grest, D.J. Srolovitz: Phil. Mag. B 59 (1989), p.293.

[3] A.D. Rollett, P. Manohar: In: D. Raabe et al., editors. Continuum scale simulation of engineering materials. (Weinheim, Wiley-VCH 2004), p.77.

[4] C. Ming Huang, C.L. Joanne, B.S.V. Patnaik, R. Jayaganthan: Appl. Surf. Sci. Vol. 252 (2006), p.3997.

[5] M.W. Nordbakke, N. Ruym, O. Hunderi: Acta Mater. Vol. 50 (2002), p.3661.

[6] R. Brandt, J. Svoboda, K. Lücke: In: H. Weiland et al., editors. Grain growth in polychrystalline materials III. (Warrendale (PA), TMS 1998), p.131.

[7] D. Zöllner, P. Streitenberger: Scripta Mater. Vol. 54 (2006), p.1697.

[8] P. Streitenberger, D. Zöllner: Scripta Mater. Vol. 55 (2006), p.461.

[9] G.L. Thomas, R.M.C. de Almeida, F. Graner: Phys. Rev. E Vol. 74 (2006), 021407.

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

[11] W.W. Mullins: Acta Mater. Vol. 46 (1998), p.6219.

[12] M. Hillert: Acta Metall. Vol. 13 (1965), p.227.

[13] D. Zöllner, P. Streitenberger: Mater. Sci. Forum Vol. 467-470 (2004), p.1129.

[14] P. Streitenberger, D. Zöllner: this proceedings.

[15] S. Hilgenfeldt, A.M. Kraynik, S.A. Koehler, H.A. Stone: Phys. Rev. Lett. Vol. 86 (2001) 2685.

[16] M.E. Glicksman: Phil. Mag. Vol. 85 (2005), p.3.

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