Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter
Mickel W, Kapfer S, Schröder-Turk G, Mecke K (2013)
Publication Status: Published
Publication Type: Journal article
Publication year: 2013
Journal
Publisher: AMER INST PHYSICS
Book Volume: 138
Journal Issue: 4
DOI: 10.1063/1.4774084
Abstract
Local structure characterization with the bond-orientational order parameters q(4), q(6), ... 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 q(l) 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 q(l), leads to a lack of robustness of the q(l) as structure metrics. Both issues can be avoided by a morphometric approach leading to the robust Minkowski structure metrics q(l)'. These q(l)' are of a similar mathematical form as the conventional bond-orientational order parameters and are mathematically equivalent to the recently introduced Minkowski tensors [G. E. Schroder-Turk et al., Europhys. Lett. 90, 34001 (2010); S. Kapfer et al., Phys. Rev. E 85, 030301(R) (2012)]. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4774084]
Authors with CRIS profile
Sebastian Kapfer
Lehrstuhl für Theoretische Physik
Gerd Schröder-Turk
Lehrstuhl für Theoretische Physik
Klaus Mecke
Lehrstuhl für Theoretische Physik
Additional Organisation(s)
Involved external institutions
France (FR)How to cite
APA:
Mickel, W., Kapfer, S., Schröder-Turk, G., & Mecke, K. (2013). Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter. Journal of Chemical Physics, 138(4). https://doi.org/10.1063/1.4774084
MLA:
Mickel, Walter, et al. "Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter." Journal of Chemical Physics 138.4 (2013).
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