键取向序参量在无序颗粒物分析中的应用
Shortcomings of the Bond Orientational Order Parameters for the Analysis of Disordered Particulate Matter
摘要：
用键取向序参量q4，q6，.由Steinhardt等人引入的“凝聚态”已经成为凝聚态物理中的标准工具，其应用包括玻璃化、堵塞、熔化或结晶转变以及团簇形成。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，键取向的序参量的定义考虑了一组相邻的球NN（p）周围的一个给定的中心粒子p的几何排列，我们表明，程序来选择构成的邻域NN（p）的球可以有更大的影响，ql的数值和定性的趋势比的物理参数，如包装分数的变化。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; ql继承的这种不连续性导致ql作为结构度量缺乏鲁棒性。这两个问题都可以通过导致鲁棒Minkowski结构度量ql '的形态度量方法来避免。这些ql'具有与常规键取向序参量类似的数学形式，并且在数学上等价于最近引入的Minkowski张量[Europhys. Lett. 90，34001（2010）; Phys.Rev.E. 85，030301（2012）]。
英文摘要：
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)].
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