Revealing hidden medium-range order in silicate glass formers using many-body correlation functions

The medium-range order (MRO) in amorphous systems has been linked to complex features such as the dynamic heterogeneities in supercooled liquids or the plastic deformation of glasses. However, the nature of the MRO in these materials has remained elusive, primarily due to the lack of methods capable of characterizing this order. Here, we leverage standard two-body structural correlators and advanced many-body correlation functions to probe numerically the MRO in prototypical network glass formers, i.e., silica and sodium silicates, systems that are of great importance in natural as well as industrial settings. With increasing Na concentration, one finds that the local environment of Na becomes more structured and the spatial distribution of Na on intermediate length scales changes from blob-like to channel-like, indicating a growing inhomogeneity in the spatial Na arrangement. In parallel, we find that the Si-O network becomes increasingly depolymerized, resulting in a ring size distribution that broadens. The radius of gyration of the rings is well described by a power law with an exponent around 0.75, indicating that the rings are progressively more crumpled with increasing size. Using a recently proposed four-point correlation function, we reveal that the relative orientation of the tetrahedra shows a surprising transition at a distance around 4 angstrom, a structural modification that is not seen in standard two-point correlation functions. The order induced by this transition propagates to larger distances, thus affecting the structure on intermediate length scales. Furthermore, we find that, for Na-rich samples the length scale characterizing the MRO is nonmonotonic as a function of temperature, caused by the competition between energetic and entropic terms which makes that the sample forms complex mesoscpic domains. Finally, we demonstrate that the structural correlation lengths as obtained from the correlation functions that quantify the MRO are correlated with macroscopic observables such as the kinetic fragility of the liquids and the elastic properties of the glasses. These findings allow to reach a deeper understanding of the nature of the MRO in network glass formers, insight that is crucial for establishing quantitative relations between their MRO and macroscopic properties.