Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter
Shortcomings of the bond orientational order parameters for the analysis of disordered particulate matter
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DOI：
10.1063/1.4774084
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发表时间：
2013-01-28
影响因子：
4.4
通讯作者：
Mecke, Klaus
中科院分区：
文献类型：
--
作者：
Mickel, Walter;Kapfer, Sebastian C.;Mecke, Klaus
用键取向序参数q（4），q（6），.由Steinhardt等人[Phys. Rev. B 28，784（1983）]引入的“非线性”已经成为凝聚态物理学中的标准工具，其应用包括玻璃化、堵塞、熔化或结晶转变以及簇形成。在这里，我们讨论了这些参数的定义，显着影响他们的解释无序系统的研究中的两个基本缺陷，并提供了一个补救措施。首先，键取向序参数的定义考虑了一组最近邻（NN）球，NN（p），围绕一个给定的中心粒子p的几何排列，我们表明，邻域定义的选择可以有一个更大的影响的数值和定性的趋势q（l）比物理参数的变化，如包装分数。其次，邻域的离散性质意味着NN（p）不是粒子坐标的连续函数; q（l）继承的这种不连续性导致q（l）作为结构度量缺乏鲁棒性。这两个问题都可以通过形态测量方法来避免，从而产生鲁棒的Minkowski结构度量q（l）'。这些q（l）'具有与常规键取向序参数类似的数学形式，并且在数学上等价于最近引入的Minkowski张量[G. E. Schroder-Turk等人，欧罗巴Lett. 90，34001（2010）; S. Kapfer等人，E85，030301（R）（2012）]。(C)2013年美国物理学会。[http：//dx.doi.org/10.1063/1.4774084]
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]