  The medium range order (MRO) in amorphous systems has been linked to complex
features such as the dynamic heterogeneity of 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 glassformers, i.e., silica and sodium
silicates, systems that are of 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 crumbled with increasing size. Using a recently
proposed four-point correlation function, we reveal that the relative
orientation of the tetrahedra shows a transition at a distance around 4
Angstroms, a structural modification that is not seen in standard two-point
correlation functions. Furthermore, we find that the length scale
characterizing the MRO is non-monotonic as a function of temperature, caused by
the competition between energetic and entropic terms. 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.
