While the short-range order structure and properties of phosphate-based glasses have been extensively studied, limited studies have focused on their medium-range order (MRO) structure, including the structural origin of the first sharp diffraction peak (FSDP) in the structure factor. In this work we perform molecular dynamics simulations, based on a machine learning interatomic potential, of calcium phosphate and calcium aluminophosphate glasses to investigate their MRO structures. We do so based on both classical ring analyses and persistent homology, clarifying the relation between different MRO features and the position of the FSDP. Furthermore, by classifying loops based on geometric descriptors (roundness and eccentricity), we show that the density distribution of loops with an eccentricity between 0.6 and 0.8 and those exhibiting high roundness are found at similar $Q$ values as the FSDP. Compositional variations, especially with increasing Ca/P ratio, systematically leads to larger loops, including more loops with high eccentricity. Overall, our work provides new insights into the geometry of MRO structures identified by persistent homology and classical ring analysis in phosphate glass networks.

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• Glasses
• Data analysis
• Machine learning
• Molecular dynamics
• X-ray scattering