Abstract
We compare two methods for the characterization of local order in samples undergoing crystal nucleation and growth. Particles with a crystal-like surrounding need to be identified to follow the nucleation process. Both methods are based on the knowledge of the particle positions in a small volume of the sample. (i) Local bond-order parameters are used to quantify the orientation of the nearest neighbors of a particle, while (ii) the graph method determines the topological arrangement of the nearest neighbors and the bonds between them. Both methods are used to detect crystal-like particles and crystal nuclei in a supercooled fluid surrounding and to determine the structure of small crystal nuclei. The properties of these nuclei are of great interest for a deeper understanding of crystal nucleation, and they can be studied in detail in colloidal model systems that allow to follow the evolution of the nuclei with single particle resolution.
Similar content being viewed by others
References
K.F. Kelton, Crystal nucleation in liquids and glasses, edited by H. Ehrenbach, D. Turnbull, Solid State Physics, vol. 45 (Academic Press, Boston, 1991), p. 75
U. Gasser, J. Phys.: Cond. Mat. 21, 203101 (2009)
U. Gasser, E.R. Weeks, A. Schofield, P.N. Pusey, D.A. Weitz, Science 292, 258 (2001)
P. Rein ten Wolde, M.J. Ruiz-Montero, D. Frenkel, Phys. Rev. Lett. 75, 2714 (1995)
P.N. Pusey, W. van Megen, Nature 320, 340 (1986)
P.N. Pusey, W. van Megen, P. Bartlett, B.J. Ackerson, J.G. Rarity, S.M. Underwood, Phys. Rev. Lett. 63, 2753 (1989)
K. Schaetzel, B.J. Ackerson, Phys. Rev. E 48, 3766 (1993)
B.J. Ackerson, K. Schaetzel, Phys. Rev. E 52, 6448 (1995)
V. Prasad, D. Semwogerere, E.R. Weeks, J. Phys.: Cond. Mat. 19, 113102 (2007)
J.C. Crocker, D.G. Grier, J. Coll. Interface Sci. 179, 298 (1996)
K. Sandomirski, E. Allahyarov, H. Lowen, S.U. Egelhaaf, Soft Matter 7, 8050 (2011)
F. Ziese, G. Maret, U. Gasser, J. Phys.: Condens. Matter 25, 375105 (2013)
P.J. Steinhardt, D.R. Nelson, M. Ronchetti, Phys. Rev. B 28, 784 (1983)
J.S. van Duijneveldt, D. Frenkel, J. Chem. Phys. 96, 4655 (1992)
S. Auer, D. Frenkel, J. Chem. Phys. 120, 3015 (2004)
C. Desgranges, J. Delhommelle, Phys. Rev. B 77, 6 (2008)
U. Gasser, A. Schofield, D.A. Weitz, J. Phys.: Condens. Matter 15, S375 (2003)
M. Leocmach, H. Tanaka, Nature Comm. 3, 8 (2012)
W. Lechner, C. Dellago, J. Chem. Phys. 129, 5 (2008)
D.S. Franzblau, Phys. Rev. B 44, 4925 (1991)
S.W. Provencher, Comput. Phys. Comm. 27, 213 (1982)
A.-P. Hynninen, M. Dijkstra, Phys. Rev. E 68, 021407 (2003)
J.-P. Hansen, I.R. McDonald, Theory of simple liquids, 2nd edn. (Academic Press, London, 1986)
G. Voronoi, J. Reine Ang. Math. 133, 97 (1908)
J.L. Finney, J. Comput. Phys. 32, 137 (1979)
J.P. Troadec, A. Gervois, L. Oger, Europhys. Lett. 42, 167 (1998)
B. O'Malley, Molecular Dynamics Investigation of Crystallization in the Hard Sphere System, Ph.D. thesis (Royal Melbourne Institute of Technology, 2001)
W. Mickel, S.C. Kapfer, G.E. Schroder-Turk, K. Mecke, J. Chem. Phys. 138, 7 (2013)
P.N. Pusey, E. Zaccarelli, C. Valeriani, E. Sanz, W.C.K. Poon, M.E. Cates, Phil. Trans. Royal Soc. a-Math. Phys. Eng. Sci. 367, 4993 (2009)
S. Auer, D. Frenkel, Ann. Rev. Phys. Chem. 55, 333 (2004)
S. Auer, D. Frenkel, Adv. Polym. Sci. 173, 149 (2005)
P. Rein ten Wolde, M.J. Ruiz-Montero, D. Frenkel, J. Chem. Phys. 104, 9932 (1996)
S. Auer, D. Frenkel, Nature 413, 711 (2001)
B. O'Malley, I. Snook, J. Chem. Phys. 123, 054511 (2005)
Y.H. Chui, R.J. Rees, I.K. Snook, B. O'Malley, S.P. Russo, J. Chem. Phys. 125, 114703 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gasser, U., Ziese, F. & Maret, G. Characterization of local structures with bond-order parameters and graphs of the nearest neighbors, a comparison. Eur. Phys. J. Spec. Top. 223, 455–467 (2014). https://doi.org/10.1140/epjst/e2014-02102-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2014-02102-6