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A phase field crystal study of heterogeneous nucleation – application of the string method

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  • Metals as Model Systems
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Abstract

We use the simplified string method in order to examine two dimensional heterogeneous nucleation at a wall and on a substrate. The material is described by a phase field crystal model and the influence of the wall or substrate is included by an external potential. Tuning the external potential we show that we can control the contact angle in equilibrium and misfit to a substrate. The nucleation barrier is reduced by a wall, but cannot be explained by classical nucleation theory due to non-classical nucleation paths. For small misfits a substrate also decreases the nucleation barrier, while large misfits increases the nucleation barrier.

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References

  1. K. Fisher, W. Kurz, Fundamentals of Solidification (Trans. Tech, Uetikon-Zürich, 1986)

  2. C. Herring, The Physics of Powder Metallurgy (McGraw-Hill, New York, 1951)

  3. L. Gránásy, T. Pusztai, G. Tóth, Z. Jurek, M. Conti, B.R. Kvamme, J. Chem. Phys. 119, 10376 (2003)

    Article  ADS  Google Scholar 

  4. L. Gránásy, T. Pusztai, D. Saylor, J. Warren, Phys. Rev. Lett. 98, 1 (2007)

    Article  Google Scholar 

  5. J.A. Warren, T. Pusztai, L. Környei, L. Gránásy, M. Cheng, Phys. Rev. B 79, 1 (2009)

    Article  Google Scholar 

  6. J.F. Lutsko, Phys. Rev. E 74, 1 (2006)

    MathSciNet  Google Scholar 

  7. J. Krug, Phys. A 313, 47 (2002)

    Article  ADS  Google Scholar 

  8. P. Politi, C. Castellano, Phys. Rev. E 66, 031605 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  9. R. Backofen, A. Voigt, J. Cryst. Growth 303, 100 (2007)

    Article  ADS  Google Scholar 

  10. P. Otto, F. Penzler, A. Rätz, T. Rump, A. Voigt, Nonlinearity 17, 477 (2004)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  11. A. Redinger, O. Ricken, P. Kuhn, A. Rätz, A. Voigt, J. Krug, T. Michely, Phys. Rev. Lett. 100, 1 (2008)

    Article  Google Scholar 

  12. K. Elder, M. Katakowski, M. Haataja, M. Grant, Phys. Rev. Lett. 88(24), 245701 (2002)

    Article  ADS  Google Scholar 

  13. K. Elder, M. Grant, Phys. Rev. E 70, 051605 (2004)

    Article  ADS  Google Scholar 

  14. K.R. Elder, N. Provatas, J. Berry, P. Stefanovic, M. Grant, Phys. Rev. B 75, 1 (2007)

    Article  Google Scholar 

  15. S.V. Teeffelen, R. Backofen, A. Voigt, H. Löwen, Phys. Rev. E 79, 1 (2009)

    Google Scholar 

  16. H. Emmerich, H. Löwen, R. Wittkowski, T. Gruhn, G.I. Tóth, G. Tegze, L. Gránásy, Adv. Phys. 61, 665 (2012)

    Article  ADS  Google Scholar 

  17. H. Emmerich, L. Gránásy, H. Löwen, Eur. Phys. J. Plus 126(10), 1 (2011)

    Google Scholar 

  18. A. Jaatinen, T. Ala-Nissila, Phys. Rev. E 82, 1 (2010)

    Article  Google Scholar 

  19. K.A. Wu, A. Karma, J. Hoyt, M. Asta, Phys. Rev. B 73, 1 (2006)

    MATH  Google Scholar 

  20. L. Gránásy, G. Tegze, G.I. Tóth, T. Pusztai, Philosophical Mag. 91, 123 (2011)

    Article  ADS  Google Scholar 

  21. G.I. Tóth, G. Tegze, T. Pusztai, G. Tóth, L. Gránásy, J. Phys.: Cond. Matter 22, 364101 (2010)

    Google Scholar 

  22. R. Prieler, J. Hubert, D. Li, B. Verleye, R. Haberkern, H. Emmerich, J. Phys.: Cond. Matter 21, 464110 (2009)

    ADS  Google Scholar 

  23. D. Sheppard, R. Terrell, G. Henkelman, J. Chem. Phys. 128, 134106 (2008)

    Article  ADS  Google Scholar 

  24. G. Henkelman, H. Jónsson, H. Jo, J. Chem. Phys. 113, 9978 (2000)

    Article  ADS  Google Scholar 

  25. E. Vanden-Eijnden, M. Venturoli, J. Chem. Phys. 130, 194103 (2009)

    Article  ADS  Google Scholar 

  26. W. Ren, E. Vanden-Eijnden, W.E., Phys. Rev. B 66, 5 (2002)

    Google Scholar 

  27. R. Backofen, A. Voigt, J. Phys.: Cond. Matter 22, 364104 (2010)

    ADS  Google Scholar 

  28. W. Ren, E. Vanden-Eijnden, J. Chem. Phys. 126, 164103 (2007)

    Article  ADS  Google Scholar 

  29. J. Dzubiella, C. Likos, J. Phys.: Cond. Matter 15, 147 (2003)

    ADS  Google Scholar 

  30. S. Praetorius, A. Voigt, Macromol. Theory Simul. 20, 541 (2011)

    Article  Google Scholar 

  31. R. Backofen, A. Rätz, A. Voigt, A. Rätz, Philosophical Mag. Lett. 87, 813 (2007)

    Article  ADS  Google Scholar 

  32. S. Vey, A. Voigt, Comput. Vis. Sci. 10, 57 (2007)

    Article  MathSciNet  Google Scholar 

  33. D. Mumford, J. Shah, Comm. Pure Appl. Math. 42, 577 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  34. B. Berkels, A. Rätz, M. Rumpf, A. Voigt, J. Sci. Comput. 35, 1 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  35. R. Backofen, A. Voigt, J. Phys.: Cond. Matter 21, 464109 (2009)

    ADS  Google Scholar 

  36. Y.M. Yu, R. Backofen, A. Voigt, J. Crystal Growth 318, 18 (2011)

    Article  ADS  Google Scholar 

  37. A. Jaatinen, C.V. Achim, K.R. Elder, T. Ala-Nissila, Phys. Rev. E 80, 1 (2009)

    Article  Google Scholar 

  38. Y.-M. Yu, A. Voigt, Appl. Phys. Lett. 94, 043108 (2009)

    Article  ADS  Google Scholar 

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Backofen, R., Voigt, A. A phase field crystal study of heterogeneous nucleation – application of the string method. Eur. Phys. J. Spec. Top. 223, 497–509 (2014). https://doi.org/10.1140/epjst/e2014-02105-3

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  • DOI: https://doi.org/10.1140/epjst/e2014-02105-3

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