Rings consisting of chemically-bonded atoms are essential topological motifs in the structural order of network-forming materials. Here, we propose two analysis methods based on rings: (1) quantitative characterization of ring shapes and (2) evaluation of the local structure order around rings. In the first method, we quantify the geometric shape of a ring using a set of our proposed indicators, namely, the roundness and roughness, in addition to the conventional ring size. Our findings reveal that the structure of amorphous silica consists of distorted rings, some of which resemble polymorphisms in silica crystals. The second method is based on a spatial correlation function, which describes three-dimensional atom densities around rings. It allows us to visualize the anisotropy of the local structure order around rings in amorphous silica. Furthermore, through a comparative analysis of the amorphous silica models made with different constraints, we show that the local anisotropy originates from centrally located rings. Moreover, we demonstrate that the anisotropy contributes to building the intermediate-range structure order in the amorphous silica characterized by the first sharp diffraction peaks observed in diffraction experiments.

中文翻译：

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非晶和结晶二氧化硅中局部结构有序的环起源各向异性

由化学键合原子组成的环是网络形成材料结构顺序中必不可少的拓扑基序。在这里，我们提出了两种基于环的分析方法：（1）环形状的定量表征和（2）环周围局部结构顺序的评估。在第一种方法中，除了传统的戒指尺寸外，我们还使用一组我们提出的指标，即圆度和粗糙度来量化戒指的几何形状。我们的研究结果表明，无定形二氧化硅的结构由扭曲的环组成，其中一些类似于二氧化硅晶体中的多晶型现象。第二种方法基于空间相关函数，它描述了环周围的三维原子密度。它使我们能够可视化无定形二氧化硅中环周围局部结构顺序的各向异性。此外，通过对不同约束条件下无定形二氧化硅模型的比较分析，我们表明局部各向异性源自中心位置的环。此外，我们证明了各向异性有助于在无定形二氧化硅中建立中间范围的结构顺序，其特征是在衍射实验中观察到的第一个尖锐衍射峰。