Shortcomings of the Bond Orientational Order Parameters for the Analysis of Disordered Particulate Matter

TL;DR

This paper critically examines the limitations of traditional bond-orientational order parameters in analyzing disordered particulate systems and proposes a robust alternative based on Minkowski structure metrics.

Contribution

The authors identify fundamental flaws in the conventional bond-orientational order parameters and introduce a morphometric approach using Minkowski structure metrics as a more reliable measure.

Findings

Neighborhood selection significantly affects ql values

Discontinuity in neighborhood leads to robustness issues

Minkowski structure metrics provide a more stable analysis

Abstract

Local structure characterization with the bond-orientational order parameters q4, q6, ... introduced by Steinhardt et al. 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 neighboring spheres NN(p) around a given central particle p; we show that procedure to select the spheres constituting the neighborhood NN(p) can have greater 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 ql'. These ql' are of a similar mathematical form as the conventional bond-orientational order parameters and are mathematically equivalent to the recently introduced Minkowski tensors [Europhys. Lett. 90, 34001 (2010); Phys. Rev. E. 85, 030301 (2012)].