Metallurgical and Materials Transactions A

, Volume 46, Issue 11, pp 4908–4920 | Cite as

Recent Developments in Modeling Heteroepitaxy/Heterogeneous Nucleation by Dynamical Density Functional Theory

  • Frigyes Podmaniczky
  • Gyula I. Tóth
  • György Tegze
  • László GránásyEmail author
Symposium: ICASP-4 (International Conference on Advanced Solidification Processing)


Crystallization of supersaturated liquids usually starts by epitaxial growth or by heterogeneous nucleation on foreign surfaces. Herein, we review recent advances made in modeling heteroepitaxy and heterogeneous nucleation on flat/modulated surfaces and nanoparticles within the framework of a simple dynamical density functional theory, known as the phase-field crystal model. It will be shown that the contact angle and the nucleation barrier are nonmonotonous functions of the lattice mismatch between the substrate and the crystalline phase. In continuous cooling studies for substrates with lattice mismatch, we recover qualitatively the Matthews–Blakeslee mechanism of stress release via the misfit dislocations. The simulations performed for particle-induced freezing will be confronted with recent analytical results, exploring thus the validity range of the latter. It will be demonstrated that time-dependent studies are essential, as investigations based on equilibrium properties often cannot identify the preferred nucleation pathways. Modeling of these phenomena is essential for designing materials on the basis of controlled nucleation and/or nano-patterning.


Contact Angle Heterogeneous Nucleation Lattice Mismatch Critical Thickness Misfit Dislocation 
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.



This work includes techniques developed in the framework of the EU FP7 Collaborative Project “EXOMET” (Contract No. NMP-LA-2012-280421, co-funded by ESA), and by the ESA MAP/PECS projects MAGNEPHAS III, PARSEC, and GRADECET.


  1. 1.
    K.F. Kelton and L. A. Greer: Nucleation in Condensed Matter. Pergamon Materials Series, vol. 15 (Elsevier, Amsterdam, 2010).Google Scholar
  2. 2.
    B.A. Grzybowski, K.J.M. Bishop, C.J. Campbell, M. Fialkowski and S.K. Smoukov: Soft Matter, 2005, vol. 1, pp. 114–28, and references therein.CrossRefGoogle Scholar
  3. 3.
    J. Aizenberg, A. J. Black and G.M. Whitesides, Nature, 1999, vol. 398, pp. 495–98.CrossRefGoogle Scholar
  4. 4.
    C.X. Cui, Y.H. Chen, P. Jin, B. Xu, Y.Y. Ren, C. Zhao, and Z.G. Wang: Physica E, 2006, vol. 31, pp. 43–47.CrossRefGoogle Scholar
  5. 5.
    K.-H. Chen, C.-Y. Chien, W.-T. Lai, T. George, A. Scherer and P.-W. Li: Cryst. Growth Des., 2011, vol. 11, pp. 3222–6.CrossRefGoogle Scholar
  6. 6.
    A.J.M. Mackus, M.A. Verheijen, N. Leick, A.A. Bol and W.M.M. Kessel: Chem. Mater., 2013, vol. 25, pp. 1905–11.CrossRefGoogle Scholar
  7. 7.
    G.I. Tóth, J. R. Morris and L. Gránásy, Phys. Rev. Lett., 2011, vol. 106, art. no. 045701.Google Scholar
  8. 8.
    W. Cheng, N. Park, M. T. Walter, M. Hartman, and D. Luo, Nat Nanotechnol., 2008, vol. 3, pp. 682–690.CrossRefGoogle Scholar
  9. 9.
    S. Auer and D. Frenkel: Phys. Rev. Lett., 2003, vol. 91, art. no. 015703.Google Scholar
  10. 10.
    D. Winter, P. Virnau, and K. Binder: Phys. Rev. Lett., 2009, vol. 103, art. no. 225703.Google Scholar
  11. 11.
    M. Heni and H. Löwen: J. Phys.: Condens. Matter, 2001, vol. 13, pp. 4675–96.Google Scholar
  12. 12.
    A. Esztermann and H. Löwen: J. Phys.: Condens. Matter, 2005, vol. 17, pp. S429–S441.Google Scholar
  13. 13.
    S. Toxvaerd: J. Chem. Phys., 2002, vol. 117, pp. 10303–10.CrossRefGoogle Scholar
  14. 14.
    E.B. Webb III, G.S. Grest and D.R. Heine: Phys. Rev. Lett., 2003, vol. 91, art. no. 236102.Google Scholar
  15. 15.
    L. Gránásy, T. Pusztai, D. Saylor, and J.A. Warren: Phys. Rev. Lett., 2007, vol. 98, art. no. 035703.Google Scholar
  16. 16.
    J.A. Warren, T. Pusztai, L. Környei, and L. Gránásy: Phys. Rev. B, 2009, vol. 79, art. no. 014204.Google Scholar
  17. 17.
    S. van Teeffelen, C.N. Likos, and H. Löwen: Phys. Rev. Let., 2008, vol. 100, art. no. 108302.Google Scholar
  18. 18.
    T. Neuhaus, M. Marechal, M. Schmiedeberg, and H. Löwen: Phys. Rev. Lett., 2013, vol. 110, art. no. 118301.Google Scholar
  19. 19.
    A.L. Greer, A.M. Brunn, A. Tronche, P.V. Evans and D.J. Bristow: Acta Mater., 2000, vol. 48, pp. 2823–35.CrossRefGoogle Scholar
  20. 20.
    T.E. Quested and A. L. Greer: Acta Mater., 2005, vol. 53, pp. 2683–92.CrossRefGoogle Scholar
  21. 21.
    S.A. Reavley and A.L. Greer, Philos. Mag., 2008, vol. 88, pp. 561–79.CrossRefGoogle Scholar
  22. 22.
    K.R. Elder, M. Katakowski, M. Haataja and M. Grant: Phys. Rev. Lett., 2002, vol. 88, art. no. 245701.Google Scholar
  23. 23.
    H. Emmerich, H. Löwen, R. Wittkowski, T. Gruhn, G.I. Tóth, G. Tegze, and L. Gránásy: Adv. Phys., 2012, vol. 61, pp. 665–743, and references therein.CrossRefGoogle Scholar
  24. 24.
    G.I. Tóth, G. Tegze, T. Pusztai, and L. Gránásy: Phys. Rev. Lett., 2012, vol. 108, art. no. 025502.Google Scholar
  25. 25.
    L. Gránásy, F. Podmaniczky, G.I. Tóth, G. Tegze, and T. Pusztai: Chem. Soc. Rev, 2014, vol. 43, pp. 2159–73.CrossRefGoogle Scholar
  26. 26.
    Z. Fan: Proc. J. Hunt Int. Symposium, Z. Fan and I.C. Stone, eds., Brunel University Press, Uxbridge, 2001, pp 29–44.Google Scholar
  27. 27.
    Z. Fan: Metall. Mater. Trans. A, 2013, vol. 44A, pp. 1409–18.CrossRefGoogle Scholar
  28. 28.
    O. Galkin and P. Vekilov, Proc. Natl. Acad. Sci. USA, 2000, vol. 97, pp. 6277–81.CrossRefGoogle Scholar
  29. 29.
    P.G. Vekilov: Cryst. Growth Des., 2004, vol. 4, pp. 671–85.CrossRefGoogle Scholar
  30. 30.
    P.R. TenWolde and D. Frenkel: Science, 1997, vol. 277, pp. 1975–78.CrossRefGoogle Scholar
  31. 31.
    V. Talanquer and D.W. Oxtoby: J. Chem. Phys., 1998, vol. 109, pp. 223–7.CrossRefGoogle Scholar
  32. 32.
    G.I. Tóth and L. Gránásy, J. Chem. Phys., 2007, vol. 127, art. no. 074710.Google Scholar
  33. 33.
    T. Kawasaki and H. Tanaka, Proc. Natl. Acad. Sci. USA, 2010, vol. 107, pp. 14036–41.CrossRefGoogle Scholar
  34. 34.
    T.H. Zhang and X.Y. Liu, J. Am. Chem. Soc., 2007, vol. 129, pp. 13520–26.CrossRefGoogle Scholar
  35. 35.
    H.J. Schöpe, G. Bryant, and W. van Megen: Phys. Rev. Lett., 2006, vol. 96, art. no. 175701.Google Scholar
  36. 36.
    J.F. Lutsko and G. Nicolis, Phys. Rev. Lett., 2006, vol. 96, art. no. 046102.Google Scholar
  37. 37.
    T. Schilling, H.J. Schöpe, M. Oettel, G. Opletal, and I. Snook: Phys. Rev. Lett., 2010, vol. 105, art. no. 025701.Google Scholar
  38. 38.
    G.I. Tóth, T. Pusztai, G. Tegze, G. Tóth, and L. Gránásy: Phys. Rev. Lett., 2011, vol. 107, art. no. 175702.Google Scholar
  39. 39.
    K.R. Elder, N. Provatas, J. Berry, P. Stefanovic, and M. Grant: Phys. Rev. B, 2007, vol. 75, art. no. 064107.Google Scholar
  40. 40.
    S. van Teeffelen, R. Backofen, A. Voigt, and H. Löwen: Phys. Rev. E, 2009, vol. 79, art. no. 051404.Google Scholar
  41. 41.
    U.M.B. Marconi and P. Tarazona; J. Chem. Phys., 1999, vol. 110, pp. 8032–44.CrossRefGoogle Scholar
  42. 42.
    H. Löwen; J. Phys.: Condens. Matter, 2003, vol. 15, pp. V1–V3.Google Scholar
  43. 43.
    A.J. Archer and M. Rauscher, J. Phys. A: Math. Gen., 2004, vol. 37, pp. 9325–33.CrossRefGoogle Scholar
  44. 44.
    G.I. Tóth, G. Tegze, T. Pusztai, G. Tóth, and L. Gránásy: J. Phys.: Condens. Matter, 2010, vol. 22, art. no. 364101.Google Scholar
  45. 45.
    G. Tegze, G. Bansel, G.I. Tóth, T. Pusztai, Z. Fan, and L. Gránásy: J. Comput. Phys., 2009, vol. 228, pp. 1612–23.CrossRefGoogle Scholar
  46. 46.
    R. Backofen and A. Voigt: J. Phys.: Condens. Matter, 2009, vol. 21, art. no. 464109.Google Scholar
  47. 47.
    L. Gránásy, G. Tegze, G.I. Tóth, and T. Pusztai: Philos. Mag., 2011, vol. 91, pp. 123–49.CrossRefGoogle Scholar
  48. 48.
    J.W. Matthews and A.E. Blakeslee: J. Cryst. Growth, 1974, vol. 27, pp. 118–25.Google Scholar
  49. 49.
    R.J. Asaro and W.A. Tiller: Metall. Trans., 1972, vol. 3, pp. 1789–96.CrossRefGoogle Scholar
  50. 50.
    K.R. Elder and M. Grant: Phys. Rev. E, 2004, vol. 70, art. no. 051605.Google Scholar
  51. 51.
    M. Castro: Phys. Rev. B, 2003, vol. 67, art. no. 035412.Google Scholar
  52. 52.
    R. Backofen and A. Voigt: J. Phys.: Condens. Matter., 2010, vol. 22, art. no. 364104.Google Scholar
  53. 53.
    G. Tegze, L. Gránásy, G.I. Tóth, F. Podmaniczky, A. Jaatinen, T. Ala-Nissila, and T. Pusztai: Phys. Rev. Lett., 2009, vol. 103, art. no. 035702.Google Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2015

Authors and Affiliations

  • Frigyes Podmaniczky
    • 1
  • Gyula I. Tóth
    • 1
    • 2
  • György Tegze
    • 1
  • László Gránásy
    • 1
    • 3
    Email author
  1. 1.Wigner Research Centre for PhysicsBudapestHungary
  2. 2.Department of Physics and TechnologyUniversity of BergenBergenNorway
  3. 3.BCASTBrunel UniversityUxbridgeUK

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