  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)].
