Local structure characterization with the bond-orientational order parameters q4, q6, … introduced by Steinhardt et al. [Phys. Rev. B 28, 784 (1983)
https://doi.org/10.1103/PhysRevB.28.784] 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 $q_l^{\prime }$. These $q_l^{\prime }$ 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. Schröder-Turk et al., Europhys. Lett. 90, 34001 (2010)
https://doi.org/10.1209/0295-5075/90/34001; S. Kapfer et al., Phys. Rev. E 85, 030301–R (2012)
https://doi.org/10.1103/PhysRevE.85.030301].
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2013
American Institute of Physics
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