Local structure characterization with the bond-orientational order parameters q4, q6, … introduced by Steinhardt et al [Phys. Rev. B 28, 784 (1983)] has become a standard tool in condensed matter physics, with applications including glass, jamming, melting or crystallization transitions, and cluster formation. Here, we discuss two fundamental flaws in the definition of these parameters that significantly affect their interpretation for studies of disordered systems, and offer a remedy. First, the definition of the bond-orientational order parameters considers the geometrical arrangement of a set of nearest neighboring (NN) spheres, NN(p), around a given central particle p; we show that the choice of neighborhood definition can have a bigger influence on both the numerical values and qualitative trend of ql than a change of the physical parameters, such as packing fraction. Second, the discrete nature of neighborhood implies that NN(p) is not a continuous function of the particle coordinates; this discontinuity, inherited by ql, leads to a lack of robustness of the ql as structure metrics. Both issues can be avoided by a morphometric approach leading to the robust Minkowski structure metrics
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28 January 2013
Research Article|
January 22 2013
Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter
Walter Mickel;
Walter Mickel
a)
1Theoretische Physik,
Friedrich-Alexander-Universität Erlangen
, Staudtstr. 7, D-91058 Erlangen, Germany
2
Université de Lyon
, F-69000, Lyon, France and CNRS, UMR5586, Laboratoire PMCN, Lyon, France
3Institute for Stochastics,
Karlsruhe Institute of Technology
, D-76128 Karlsruhe, Germany
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Sebastian C. Kapfer;
Sebastian C. Kapfer
b)
1Theoretische Physik,
Friedrich-Alexander-Universität Erlangen
, Staudtstr. 7, D-91058 Erlangen, Germany
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Gerd E. Schröder-Turk;
Gerd E. Schröder-Turk
c)
1Theoretische Physik,
Friedrich-Alexander-Universität Erlangen
, Staudtstr. 7, D-91058 Erlangen, Germany
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Klaus Mecke
Klaus Mecke
d)
1Theoretische Physik,
Friedrich-Alexander-Universität Erlangen
, Staudtstr. 7, D-91058 Erlangen, Germany
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a)
Electronic mail: waltermickel@web.de.
b)
Electronic mail: kapfer@ens.fr.
c)
Electronic mail: Gerd.Schroeder-Turk@physik.fau.de.
d)
Electronic mail: Klaus.Mecke@physik.fau.de.
J. Chem. Phys. 138, 044501 (2013)
Article history
Received:
September 28 2012
Accepted:
December 13 2012
Citation
Walter Mickel, Sebastian C. Kapfer, Gerd E. Schröder-Turk, Klaus Mecke; Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter. J. Chem. Phys. 28 January 2013; 138 (4): 044501. https://doi.org/10.1063/1.4774084
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