Distinguishing noisy crystalline structures using bond orientational order parameters

  • Jan Haeberle
  • Matthias Sperl
  • Philip BornEmail author
Regular Article


The bond orientational order parameters originally introduced by Steinhardt et al. (Phys. Rev. B 28, 784 (1983)) are a common tool for local structure characterization in soft matter studies. Recently, Mickel et al. (J. Chem. Phys. 138, 044501 (2013)) highlighted problems of the bond orientational order parameters due to the ambiguity of the underlying neighbourhood definition. Here we show the difficulties to distinguish common structures like FCC- and BCC-based structures with the suggested neighbourhood definitions when noise is introduced. We propose a simple improvement to the neighbourhood definition that results in robust and continuous bond orientational order parameters with which we can accurately distinguish crystal structures even when noise is present.

Graphical abstract


Soft Matter: Self-organisation and Supramolecular Assemblies 


  1. 1.
    E. Allahyarov, K. Sandomirski, S.U. Egelhaaf, H. Löwen, Nat. Commun. 6, 7110 (2015)ADSCrossRefGoogle Scholar
  2. 2.
    U. Gasser, E.R. Weeks, A. Schofield, P.N. Pusey, D.A. Weitz, Science 292, 258 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    J.H. Chu, I. Lin, Phys. Rev. Lett. 72, 4009 (1994)ADSCrossRefGoogle Scholar
  4. 4.
    O. Arp, D. Block, A. Piel, A. Melzer, Phys. Rev. Lett. 93, 165004 (2004)ADSCrossRefGoogle Scholar
  5. 5.
    A.P. Nefedov et al., New J. Phys. 5, 33 (2003)ADSCrossRefGoogle Scholar
  6. 6.
    A. Panaitescu, A. Kudrolli, Phys. Rev. E 90, 032203 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    T. Aste, M. Saadatfar, A. Sakellariou, T.J. Senden, Physica A: Stat. Mech. Appl. 339, 16 (2004)ADSCrossRefGoogle Scholar
  8. 8.
    P.J. Steinhardt, D.R. Nelson, M. Ronchetti, Phys. Rev. B 28, 784 (1983)ADSCrossRefGoogle Scholar
  9. 9.
    W. Lechner, C. Dellago, J. Chem. Phys. 129, 114707 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    W. Mickel, S.C. Kapfer, G.E. Schröder-Turk, K. Mecke, J. Chem. Phys. 138, 044501 (2013)ADSCrossRefGoogle Scholar
  11. 11.
    G.E. Schröder-Turk, R. Schielein, S.C. Kapfer, F.M. Schaller, G.W. Delaney, T. Senden, M. Saadatfar, T. Aste, K. Mecke, AIP Conf. Proc. 1542, 349 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    P.N. Pusey, J. Phys. (Paris) 48, 709 (1987)CrossRefGoogle Scholar
  13. 13.
    P.R. ten Wolde, M.J. Ruiz-Montero, D. Frenkel, Phys. Rev. Lett. 75, 2714 (1995)ADSCrossRefGoogle Scholar
  14. 14.
    P. Rein ten Wolde, M.J. Ruiz-Montero, D. Frenkel, J. Chem. Phys. 104, 9932 (1996)ADSCrossRefGoogle Scholar
  15. 15.
    I. Volkov, M. Cieplak, J. Koplik, J.R. Banavar, Phys. Rev. E 66, 061401 (2002)ADSCrossRefGoogle Scholar
  16. 16.
    C. Desgranges, J. Delhommelle, Phys. Rev. B 77, 054201 (2008)ADSCrossRefGoogle Scholar
  17. 17.
    F. Rietz, C. Radin, H.L. Swinney, M. Schröter, Phys. Rev. Lett. 120, 055701 (2018)ADSCrossRefGoogle Scholar
  18. 18.
    F.A. Lindemann, Phys. Z. 11, 609 (1910)Google Scholar
  19. 19.
    R.W. Cahn, Nature 413, 582 (2001)ADSCrossRefGoogle Scholar
  20. 20.
    C. Rycroft, Voro++: a three-dimensional Voronoi cell library in C++, Technical Report LBNL-1432E, Lawrence Berkeley National Lab. (LBNL), Berkeley, CA, U.S.A., January 2009Google Scholar
  21. 21.
    S. Fortune, Voronoi diagrams and Delaunay triangulations, in Computing in Euclidean Geometry, Lecture Notes Series on Computing, Vol. 4 (World Scientific Publishing Co. Pte. Ltd, 1995) pp. 225--265Google Scholar
  22. 22.
    J.P. Troadec, A. Gervois, L. Oger, Europhys. Lett. 42, 167 (1998)ADSCrossRefGoogle Scholar

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© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institut für Materialphysik im WeltraumDeutsches Zentrum für Luft-und RaumfahrtKölnGermany
  2. 2.Institut für Theoretische PhysikUniversität zu KölnKölnGermany

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