Nucleation and successive microstructure evolution: simulation approaches for a comprehensive picture from the atomistic to the microscale

Article
  • 56 Downloads

Abstract

What determines the mechanical material properties of a material sample after solidification is strongly tied to its microstructure. Nevertheless, the precise laws governing the initial stage of this structuring process, i.e. nucleation and the successive transiental microstructure evolution scenarios remain far from being fully understood even today.

Here we show how the phase-field method, which originally established itself to tackle the free boundary problem given by microstructure evolution, can also be employed to investigate the energetics of heterogeneous nucleation in a solidifying sample. Moreover it is demonstrated, how the phase-field crystal method can shade more light in open questions regarding a quantitative formulation of nucleation statistics to thereupon simulate the phase transition phenomena in solidification from nucleation to crystallization in larger domains quantitatively.

Finally we discuss how both methods can be joined to study nucleation from the atomic to the microscale.

Keywords

phase-field modeling phase-field crystal method heterogeneous nucleation microstructure evolution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Granasy L, et al, Phys. Rev. Lett., 88 (2002) 206105.CrossRefPubMedADSGoogle Scholar
  2. 2.
    Granasy L, et. al., Phys. Rev. Lett., 98 (2007) 035703.CrossRefPubMedADSGoogle Scholar
  3. 3.
    Chen L Q, Annu. Rev. Mater. Res., 32 (2002) 113.CrossRefGoogle Scholar
  4. 4.
    Boettinger W J, Warren J A, Beckermann C and Karma A, Annu. Rev. Mater. Res., 32 (2002) 163.CrossRefGoogle Scholar
  5. 5.
    For a monograph see: Emmerich H, The Diffuse Interface Approach in Material Science — Thermodynamic Concepts and Applications of Phase-Field Models, Springer Monograph, Lecture Notes in Physics, 73 (2003).Google Scholar
  6. 6.
    For a recent review summarizing the advances of and by phasefield modeling in condensed matter physics, see: H. Emmerich, Advances of and by phase-field modeling in condensed matter physics, Advances in Physics, 57 (2008) 1.CrossRefADSGoogle Scholar
  7. 7.
    Gupta S C, The classical Stefan problem, Elsevier, North-Holland Series in Applied Mathematics and Mechanics, 45 (2003).Google Scholar
  8. 8.
    Elder K R, Katakowski M, Haataja M and Grant M, Phys. Rev. Lett. 88 (2002) 245701.CrossRefPubMedADSGoogle Scholar
  9. 9.
    Swift J and Hohenberg P C, Phys. Rev. A 15 (1993) 851.Google Scholar
  10. 10.
    Elder K R and Grant M, Phys. Rev. E 70 (2004) 051605.CrossRefADSGoogle Scholar
  11. 11.
    K. R. Elder, N. Provatas, J. Berry, P. Stefanovic and M. Grant, Phys. Rev. B, 75 (2007) 064107.CrossRefADSGoogle Scholar
  12. 12.
    Stefanovic P M, Haataja M and Provatas N, Phys. Rev. Lett., 96 (2006) 225504.CrossRefPubMedADSGoogle Scholar
  13. 13.
    Berry J, Grant M and Elder K R, Phys. Rev. E, 73 (2006) 031609.CrossRefADSGoogle Scholar
  14. 14.
    Elder K, Lecture Notes, Summer School of DFG Priority Program 1296 Heterogenous Nucleation, Herzogenrath, Germany, July 28th to August 1st (2008).Google Scholar
  15. 15.
    van Teeffelen S, Backofen R, Voigt A, Loewen H, arXiv:0902.3363v1Google Scholar
  16. 16.
    Folch R and Plapp M, Phys. Rev. E, 72 (2005) 011602.CrossRefMathSciNetADSGoogle Scholar
  17. 17.
    Emmerich H and Siquieri R, J. Phys. Condens. Matter, 18 (2006) 11121.CrossRefADSGoogle Scholar
  18. 18.
    Siquieri R and Emmerich H, Phil. Mag. 81(11) (2007).Google Scholar
  19. 19.
    Strohmenger J, Volkmann T, Gao J and Herlach D M, (2004) Materials Science and Engineering A 375 (2004) 561; Volkmann T, Strohmenger J, Gao J and Herlach D M, Applied Phys. Lett., 85 (2004) 2232.Google Scholar
  20. 20.
    Jackson K A, in Growth and Perfection of Crystals, ed. by Doremus R H, Roberts B W and Turnbull D, Wiley NY, 319 (1958).Google Scholar
  21. 21.
    Shneidman V A, Jackson K A and Beatty K M, Phys. Rev. B, 59 (1999) 3579.CrossRefADSGoogle Scholar
  22. 22.
    Prieler R, Hubert J, Li D, Verleye B, Haberkern R and Emmerich H, J. Phys. Cond. Matter., in printGoogle Scholar
  23. 23.
    Athreya B, Goldenfeld N, Dantzig J, Greenwood M and Provatus N, Phys. Rev. E, 76 (2007) 056706.CrossRefADSGoogle Scholar
  24. 24.
    Goldenfeld N, Athreya B and Dantzig J, Phys. Rev. E, 72 (2005) 020601 (R).CrossRefADSGoogle Scholar
  25. 25.
    Goldenfeld N, Athreya B and Dantzig J, J. Stat. Phys., 125 (2006) 1015.CrossRefADSGoogle Scholar
  26. 26.
    Emmerich H, Ch. Eck, Cont. Mech Thermodynamics, 17 (2006) 313.MathSciNetGoogle Scholar
  27. 27.
    Chalupecky V, Ch. Eck, H. Emmerich, EPJ ST, 149 (2007) 1.ADSGoogle Scholar

Copyright information

© Indian Institute of Metals 2009

Authors and Affiliations

  1. 1.Center for Computational Engineering Science and Institute of Minerals EngineeringRWTH Aachen UniversityAachenGermany

Personalised recommendations