Despite the numerous technological applications of amorphous materials, such as glasses, the understanding of their medium-range order (MRO) structure—and particularly the origin of the first sharp diffraction peak (FSDP) in the structure factor—remains elusive. Here, we use persistent homology, an emergent type of topological data analysis, to understand MRO structure in sodium silicate glasses. To enable this analysis, we introduce a self-consistent categorization of rings with rigorous geometrical definitions of the structural entities. Furthermore, we enable quantitative comparison of the persistence diagrams by computing the cumulative sum of all points weighted by their lifetime. On the basis of these analysis methods, we show that the approach can be used to deconvolute the contributions of various MRO features to the FSDP. More generally, the developed methodology can be applied to analyze and categorize molecular dynamics data and understand MRO structure in any class of amorphous solids.

尽管非晶态材料（例如玻璃）在技术上有大量应用，但对它们的中程（MRO）结构（尤其是结构因子中的第一个尖锐衍射峰（FSDP）的起源）的理解仍然难以捉摸。在这里，我们使用持久性同源性（一种拓扑数据分析的新兴类型）来了解硅酸钠玻璃中的MRO结构。为了进行此分析，我们对环进行了自洽分类，并对其结构实体进行了严格的几何定义。此外，我们可以通过计算所有点的生命周期加权的累积总和来对余辉图进行定量比较。在这些分析方法的基础上，我们表明该方法可用于对各种MRO功能对FSDP的贡献进行反卷积。更普遍，