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Rings comprising chemically bonded atoms are essential topological motifs forthe structural ordering of network-forming materials. Quantification of suchlarger motifs beyond short-range pair correlation is essential forunderstanding the linkages between the orderings and macroscopic behaviors.Here, we propose two quantitative analysis methods based on rings. The firstmethod quantifies rings by two geometric indicators: roundness and roughness.These indicators reveal the linkages between highly symmetric rings and crystalsymmetry in silica and that the structure of amorphous silica mainly consistsof distorted rings. The second method quantifies a spatial correlation functionthat describes three-dimensional atomic densities around rings. A comparativeanalysis among the functions for different degrees of ring symmetries revealsthat symmetric rings contribute to the local structural order in amorphoussilica. Another analysis of amorphous models with different orderings revealsanisotropy of the local structural ordering around rings; this contributes tobuilding the intermediate-range ordering.

Ring-originated anisotropy of local structural ordering in amorphous and crystalline silicon dioxide