Persistent homology: A tool to understand medium-range order glass structure

Glass structure remains puzzling to scientists, especially due to the challenges in characterizing their structural order beyond the first coordination shell, i.e., the so-called medium-range order. Structural method development is therefore needed to advance our understanding of, e.g., structure-property relations in these disordered materials. To this end, we here review the fundamentals, applications and perspectives of an interesting new approach, namely persistent homology, which is a type of topological data analysis. This method allows for the analysis of both ring- and void-type structures in materials without making any assumptions of the network structure. As discussed herein, it has recently been used to analyze atomic position data (as obtained from atomistic simulations or reverse Monte Carlo) of glasses, especially regarding their medium-range order structure. We also discuss the opportunities in coupling persistent homology analyses with machine learning calculations as well as the open questions and challenges that require further investigations.