Computer Simulations Combining Finite Difference and Finite Element Methods: Solute Drag on Migrating Grain Boundaries in Three-Dimension


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The current study aims to improve our fundamental understanding of solute segregation and solute drag on migrating grain boundaries (GB) in three dimensions. Computer simulation combines finite difference and finite element methods. An exemplary case study is reported, in which a spherical grain is embedded inside a cubic grain and shrinks as a result of motion by curvature, as a preliminary to modeling grain growth in single phase materials. The results agree qualitatively with literature studies in 1-D.



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




M.C. Gao et al., "Computer Simulations Combining Finite Difference and Finite Element Methods: Solute Drag on Migrating Grain Boundaries in Three-Dimension", Materials Science Forum, Vols. 558-559, pp. 1075-1080, 2007

Online since:

October 2007




[1] D. McLean: Grain Boundaries in Metals (Clarendon Press, Oxford 1957).

[2] P. Lejcek and S. Hofmann: Crit. Rev. Sol. State. Mat. Sci. Vol. 20 (1995), p.1.

[3] G. Gottstein and L.S. Shvindlerman: Grain Boundary Migration in Metals: Thermodynamics, Kinetics, Applications (CRC Press, Boca Raton, FL 1999).

[4] A.P. Sutton and R.W. Balluffi: Interfaces in Crystalline Materials (Clarendon Press, Oxford 1995).

[5] H.V. Atkinson: Acta Metall. Vol. 36 (1988), p.469.

[6] G.S. Rohrer: Annual Rev. Mat. Res. Vol. 35 (2005), p.99.

[7] R.D. Doherty, D.A. Hughes, F.J. Humphreys, J.J. Jonas, D.J. Jensen, M.E. Kassner, W.E. King, T.R. McNelley, H.J. McQueen and A.D. Rollett: Mater. Sci. Eng. A Vol. 238 (1997), p.219.


[8] K. Lücke and K. Detert: Acta metall. Vol. 5 (1957), p.628.

[9] J.W. Cahn: Acta metall. Vol. 10 (1962), p.789.

[10] K. Lücke and H.P. Stüwe: Acta Metall. Vol. 19 (1971), p.1087.

[11] M. Hillert and B. Sundman: Acta Metall. Vol. 24 (1976), p.731.

[12] M. Hillert and B. Sundman: Acta Metall. Vol. 25 (1977), p.11.

[13] Z.K. Liu, J. Agren and M. Suehiro: Mater. Sci. Eng. A Vol. 247 (1998), p.222.

[14] M. Suehiro: Isij Int. Vol. 38 (1998), p.547.

[15] M. Suehiro, Z. K. Liu and J. Agren: Metall. Mater. Trans. A 1998, 29, 1029.

[16] D. Fan, S.P. Chen and L.Q. Chen: J. Mater. Res. Vol. 14 (1999), p.1113.

[17] M. Hillert: Acta Mater. Vol. 47 (1999), p.4481.

[18] R. Le Gall and J.J. Jonas: Acta Mater. Vol. 47 (1999), p.4365.

[19] A. Michels, C.E. Krill, H. Ehrhardt, R. Birringer and D.T. Wu: Acta Mater. Vol. 47 (1999), p.2143.

[20] J.W. Cahn and A. Novick-Cohen: Acta Mater. Vol. 48 (2000), p.3425.

[21] M. Hillert and M. Schalin: Acta Mater. Vol. 48 (2000), p.461.

[22] M. Hillert, J. Odqvist and J. Agren: Scripta Mater. Vol. 45 (2001), p.221.

[23] M.I. Mendelev and D.J. Srolovitz: Phil. Mag. A Vol. 81 (2001), p.2243.

[24] M.I. Mendelev and D.J. Srolovitz: Acta Mater. Vol. 49 (2001), p.589.

[25] A. Vilenkin: Interface Sci. Vol. 9 (2001), p.323.

[26] P.R. Cha, S.G. Kim, D.H. Yeon and J.K. Yoon: Acta Mater. Vol. 50 (2002), p.3817.

[27] M. Jahazi and J.J. Jonas: Mater. Sci. Eng. Vol. 335 (2002), p.49.

[28] R. Kirchheim: Acta Mater. Vol. 50 (2002), p.413.

[29] M.I. Mendelev and D.J. Srolovitz: Model. Sim. Mat. Sci. Eng. Vol. R79 (2002), p.10.

[30] Y.J.M. Brechet and G.R. Purdy: Acta Mater. Vol. 51 (2003), p.5587.

[31] N. Ma, S.A. Dregia and Y. Wang: Acta Mater. Vol. 51 (2003), p.3687.

[32] N. Maruyama, G.D. W. Smith and A. Cerezo: Mater. Sci. Eng. Vol. 353 (2003), p.126.

[33] M. Hillert: Acta Mater. Vol. 52 (2004), p.5289.

[34] W.A. Soer, J.T.M. De Hosson, A.M. Minor, J.W. Morris and E.A. Stach: Acta Mater. Vol. 52 (2004), p.5783.

[35] M. Hillert: Z. Metallkd. Vol. 96 (2005), p.104.

[36] M.I. Mendelev, D.J. Srolovitz, G.J. Ackland and S. Han: J. Mater. Res. Vol. 20 (2005), p.208.

[37] A.L. Korzhenevskii, R. Bausch, R. Schmitz: Acta Mater. Vol. 54 (2006), p.1595.

[38] A.P. Kuprat: SIAM J. Sci. Comput. Vol. 22 (2000), p.535.

[39] A. Kuprat, D. George, G. Straub and M.C. Demirel: Comput. Mater. Sci. Vol. 28 (2003), p.199.

[40] J. Gruber, D.C. George, A.P. Kuprat, G.S. Rohrer and A.D. Rollett: Scripta Mater. Vol. 53 (2005), p.351.