The European Physical Journal B

, Volume 70, Issue 3, pp 403–412 | Cite as

A phase-field/Monte-Carlo model describing organic crystal growth from solution

Investigation of the diffusion-influenced growth of hydroquinone crystals
  • J. KundinEmail author
  • C. Yürüdü
  • J. Ulrich
  • H. Emmerich
Computational Methods


In this paper work we present a phase-field/Monte-Carlo hybrid algorithm for the simulation of solutal growth of organic crystals. The algorithm is subsequently used for an investigation of diffusion effects on the growth mechanisms. This method combines a two-scale phase-field model of the liquid phase epitaxial growth and a Monte-Carlo algorithm of the 2D nucleation and thus is faster than previous purely Monte Carlo simulations of crystal growth. The inclusion of supersaturation and diffusion in the method allows the study of crystal growth under various growth conditions. Parameters used in the hybrid algorithm are bound to the energetic parameters of crystal faces, which can be estimated from a detailed study of the actual crystal structure based on a connected nets analysis, which allows the prediction of the shape and morphology of real crystals. The study of the diffusion effect is carried out based on an example of a hydroquinone crystal, which grows from the water solution at various supersaturations. The dependencies of the growth rate and the nucleation rate on the supersaturation indicate the change of the growth mechanism from spiral growth to 2D nucleation. The difference in the growth rate for various faces is in agreement with the crystal morphologies derived from the attachment energy method and observed experimentally. The main result of the simulation is the evaluation of engineering limits for choosing appropriate external process conditions.


68.35.Ct Interface structure and roughness 68.43.Mn Adsorption kinetics 68.55.Ac Nucleation and growth: microscopic aspects 


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  1. 1.
    D. Winn, M.F. Doherty, AIChE Journal 44, 2501 (1998)CrossRefGoogle Scholar
  2. 2.
    Cerius 2 User Guide, version 4.2 (Molecular Simulations Inc., San Diego, 2000)Google Scholar
  3. 3.
    J.J. Lu, J. Ulrich, Cryst. Res. Technol. 38, 63 (2003)CrossRefGoogle Scholar
  4. 4.
    J.J. Lu, J. Ulrich, Cryst. Res. Technol. 40, 839 (2005)CrossRefGoogle Scholar
  5. 5.
    P. Hartman, P. Bennema, J. Cryst. Growth 49, 145 (1980)CrossRefADSGoogle Scholar
  6. 6.
    S.X.M. Boerrigter, H.M. Cuppen, R.I. Ristic, J.N. Sherwood, P. Bennema, H. Meekes, Cryst. Growth Des. 2, 357 (2002)CrossRefGoogle Scholar
  7. 7.
    S.X.M. Boerrigter, G.P.H. Josten, J. van der Streek, F.F.A. Hollander, J. Los, H.M. Cuppen, P. Bennema, H. Meekes, J. Phys. Chem. A 108, 5894 (2004)CrossRefGoogle Scholar
  8. 8.
    R.F.P. Grimbergen, P. Bennema, H. Meekes, Acta Cryst. A 55, 84 (1999)CrossRefGoogle Scholar
  9. 9.
    S. Piana, J.D. Gale, J. Am. Chem. Soc. 127, 1975 (2005)CrossRefGoogle Scholar
  10. 10.
    L. Balykov, V. Chalupecky, C. Eck, H. Emmerich, G. Krisnamoorthy, A. Rätz, A. Voigt, Multiscale modeling of epitaxial growth: from discrete-continuum to continuum equations, in Analysis, Modeling and Simulation of Multiscale Problems, edited by A. Mielke (Hrsg.) (Springer, Berlin, Heidelberg, 2006)Google Scholar
  11. 11.
    G. Krishnamoorthy, H. Emmerich, V. Chalupecky, Estimation of critical dislocation distances, A quantitative study beyond BCF theory, Eur. Phys. J. Special Topics 149, 19 (2007)CrossRefADSGoogle Scholar
  12. 12.
    V. Chalupecky, C. Eck, H. Emmerich, Eur. Phys. J. Special Topics 149, 1 (2007)CrossRefADSGoogle Scholar
  13. 13.
    S. Dost, B. Lent, Single Crystal Growth of Semiconductors from Metallic, Solutions (Elsevier, Amsterdam, 2007)Google Scholar
  14. 14.
    W.K. Burton, N. Cabrera, F.C. Frank, Phil. Trans. R. Soc. A 243, 299 (1951)zbMATHCrossRefADSMathSciNetGoogle Scholar
  15. 15.
    J. Kundin, M. Radke de Cuba, S. Gemming, H. Emmerich, Physica D 238, 117 (2009)zbMATHCrossRefADSMathSciNetGoogle Scholar
  16. 16.
    J. Kundin, H. Emmerich, Eur. Phys. J. B 63, 2536 (2008)CrossRefGoogle Scholar
  17. 17.
    F. Liu, H. Metiu, Phys. Rev. E 49, 2601 (1994)CrossRefADSGoogle Scholar
  18. 18.
    A. Karma, M. Plapp, Phys. Rev. Lett. 81, 4444 (1998)CrossRefADSGoogle Scholar
  19. 19.
    J.W. Mullin, O. Söhnel, Chem. Eng. Sci. 32, 683 (1977)CrossRefGoogle Scholar
  20. 20.
    J. Torrent-Burgues, J. Cryst. Growth 140, 107 (1994)CrossRefADSGoogle Scholar
  21. 21.
    R.W. Wilcox, J. Crystal Growth 65, 133 (1983)CrossRefADSGoogle Scholar
  22. 22.
    J.W. Christian, The Theory of transformation in Metals and Alloys (Pergamon Press, London, 1965)Google Scholar
  23. 23.
    S.C. Wallwork, H.M. Powell, J. Chem. Soc. Perkin Trans. 2, 641 (1980)Google Scholar
  24. 24.
    F. Puel, G. Fevotte, J.P. Klein, Chem. Eng. Sci. 58, 3729 (2003)CrossRefGoogle Scholar
  25. 25.
    K.-X. Li, Q.-X. Yin, W. Chen, J.-K. Wang, J. Chem. Eng. Data 51, 127 (2006)CrossRefGoogle Scholar
  26. 26.
    L.N. Trevani, E. Calvo, H.R. Cortia, J. Chem. Soc. Faraday Trans. 93, 4319 (1997)CrossRefGoogle Scholar
  27. 27.
    S.V. Lindemann, V.E. Shklover, Y.T. Struchkov, Cryst. Struct. Comm. 10, 1173 (1981)Google Scholar
  28. 28.
    W. Chen, Q.-X. Yin, J.-K. Wang, X.-N. Li, VDI-Berichte 1901, 441 (2005)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • J. Kundin
    • 1
    Email author
  • C. Yürüdü
    • 2
  • J. Ulrich
    • 2
  • H. Emmerich
    • 1
  1. 1.Computational Materials Engineering (CME), Institute for Minerals Engineering, Center for Computational Engineering Science, Jülich-Aachen Research Alliance, RWTH Aachen UniversityAachenGermany
  2. 2.Verfahrenstechnik/TVT, Centre of Engineering Science, Martin Luther University Halle WittenbergHalle SaaleGermany

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