Journal of Materials Science

, Volume 44, Issue 9, pp 2206–2217 | Cite as

Phase field modeling of grain growth: effect of boundary thickness, triple junctions, misorientation, and anisotropy

  • I. M. McKenna
  • M. P. Gururajan
  • P. W. Voorhees
Festschrift in honour of Prof T R Anantharaman on the occasion of his 80th birthday
First Online:
Received:
Accepted:

Abstract

Phase-field models based on multiple order parameters are used extensively to study grain growth in polycrystalline materials. However, if simulations are to be carried out using experimentally obtained microstructures as the initial condition, and the resultant microstructures are to be carefully compared with those obtained from experiments, then the parameters used in the numerical simulations need to be benchmarked with analytical solutions. Furthermore, the models themselves need to be modified to incorporate the dependence of grain boundary energy on misorientation across the boundary as well as the anisotropy in the boundary energy for any given misorientation that stems from the planes of different grains that make up the boundary. In this article, we address both these issues and present some preliminary results from our 2D and 3D simulations.

Keywords

Grain Boundary Phase Field Triple Junction Boundary Energy Shrinkage Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

Acknowledgements

We thank Yunzhi Wang and Dave Rowenhorst for useful discussions, and the Office of Naval Research (ONR-CNV0044048) for financial support.

References

  1. 1.
    Gottstein G, Shvindlerman LS (1999) Grain boundary migration in metals: thermodynamics, kinetics, application. CRC Press, New YorkGoogle Scholar
  2. 2.
    Sutton AP, Balluffi RW (1997) Interfaces in crystalline materials. Oxford University Press, OxfordGoogle Scholar
  3. 3.
    Humphreys FJ, Hatherly M (2004) Recrystallization and related annealing phenomena, 2nd edn. Elsevier, New YorkGoogle Scholar
  4. 4.
    Fionova LK, Artemyev AV (1993) Grain boundaries in metals and semiconductors. de physique edition, Les Ulis CedexGoogle Scholar
  5. 5.
    Kang S-KL (2005) Sintering: densification, grain growth and microstructure. Elsevier, New YorkGoogle Scholar
  6. 6.
    Moelans N, Blanpain B, Wollants P (2008) Phys Rev B 78(024113):1Google Scholar
  7. 7.
    von Neumann J (1952) Metal interfaces. American Society of Metals, Cleveland, p 65. A written note to the paper of C. S. SmithGoogle Scholar
  8. 8.
    Mullins WW (1956) J Appl Phys 27:900CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    MacPherson RD, Srolovitz DJ (2007) Nature 446:1053PubMedCrossRefADSGoogle Scholar
  10. 10.
    Thornton K, Agren J, Voorhees PW (2003) Acta Mater 51:5675CrossRefGoogle Scholar
  11. 11.
    Chen L-Q (2002) Annu Rev Mater Res 32:113CrossRefGoogle Scholar
  12. 12.
    Gururajan MP, McKenna IM, Voorhees PW (2008) Manuscript in preparationGoogle Scholar
  13. 13.
    Chen LQ, Yang W (1994) Phys Rev B 50:15752CrossRefADSGoogle Scholar
  14. 14.
    Chen L-Q, Wang Y (1996) J Mater 48(12):13Google Scholar
  15. 15.
    Abinandanan TA, Haider F (2001) Philos Mag A 81(10):2457CrossRefADSGoogle Scholar
  16. 16.
    Fan D, Geng C, Chen L-Q (1997) Acta Mater 45(3):1115CrossRefGoogle Scholar
  17. 17.
    Fan D, Chen L-Q, Chen SP (1997) Mater Sci Eng A 238:78CrossRefGoogle Scholar
  18. 18.
    McKenna IM, Gururajan MP, Voorhees PW (2008) Manuscript in preparationGoogle Scholar
  19. 19.
    Gruber J, Ma N, Wang Y, Rollett AD, Rohrer GS (2006) Model Simulat Mater Sci Eng 14:1189CrossRefADSGoogle Scholar
  20. 20.
    Vedantam S, Patnaik BSV (2006) Phys Rev E 73:1CrossRefGoogle Scholar
  21. 21.
    Kim SG, Kim DI, Kim WT, Park YB (2006) Phys Rev E 74(061605):1MATHGoogle Scholar
  22. 22.
    Vanherpe L, Moelans N, Blanpain B, Vandewalle S (2007) Phys Rev E 76(056702):1Google Scholar
  23. 23.
    McKenna IM, Ma N, Gururajan MP, Wang Y, Voorhees PW (2008) Manuscript in preparationGoogle Scholar
  24. 24.
    Allen SM, Cahn JW (1979) Acta Metall 27:1085CrossRefGoogle Scholar
  25. 25.
    Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in Fortran, 2nd edn. Cambridge University Press, CambridgeMATHGoogle Scholar
  26. 26.
    Fan D, Chen L-Q (1997) Philos Mag Lett 75(4):187CrossRefADSMathSciNetGoogle Scholar
  27. 27.
    Cahn JW, Hilliard JE (1958) J Chem Phys 28(2):258CrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • I. M. McKenna
    • 1
  • M. P. Gururajan
    • 1
    • 2
  • P. W. Voorhees
    • 1
  1. 1.Department of Materials Science and EngineeringNorthwestern UniversityEvanstonUSA
  2. 2.Department of Applied MechanicsIndian Institute of Technology – DelhiHauz KhasIndia

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