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

TL;DR

This paper introduces two ring-based quantitative methods to analyze local structural ordering and anisotropy in amorphous and crystalline silicon dioxide, linking ring symmetry to material properties.

Contribution

It proposes novel geometric and spatial correlation analysis techniques for rings, enhancing understanding of structural motifs beyond pair correlations in silica.

Findings

Symmetric rings are linked to crystal symmetry.

Amorphous silica mainly consists of distorted rings.

Local structural anisotropy contributes to intermediate-range order.

Abstract

Rings comprising chemically bonded atoms are essential topological motifs for the structural ordering of network-forming materials. Quantification of such larger motifs beyond short-range pair correlation is essential for understanding the linkages between the orderings and macroscopic behaviors. Here, we propose two quantitative analysis methods based on rings. The first method quantifies rings by two geometric indicators: roundness and roughness. These indicators reveal the linkages between highly symmetric rings and crystal symmetry in silica and that the structure of amorphous silica mainly consists of distorted rings. The second method quantifies a spatial correlation function that describes three-dimensional atomic densities around rings. A comparative analysis among the functions for different degrees of ring symmetries reveals that symmetric rings contribute to the local structural order in amorphous silica. Another analysis of amorphous models with different orderings reveals anisotropy of the local structural ordering around rings; this contributes to building the intermediate-range ordering.