Explaining an anomalous pressure dependence of shear modulus in germanate glasses based on Reverse Monte Carlo modelling

Unlike traditional silicate glasses, germanate glasses often feature non-monotonic variations in material properties (e.g., elastic moduli and glass transition temperature) with varying chemical composition, temperature, and pressure. However, the underlying atomic-scale structural origins remain poorly understood. This is because, in most oxide glasses, the structural changes are quantified through solid-state NMR spectroscopy, but unfortunately the only NMR active germanium isotope (⁷³Ge) has very unfavorable NMR properties. Here, we circumvent this problem by using high-energy X-ray and neutron total scattering coupled with ab initio molecular dynamics simulations as input for Reverse Monte Carlo modeling. In detail, we study the structure and properties of two sodium germanate glasses (10Na₂O-90GeO₂ and 20Na₂O-80GeO₂) subjected to permanent densification through hot compression up to 2 GPa at the glass transition temperature. While density as well as Young's and bulk modulus increase with pressure as expected, shear modulus first increases and then decreases slightly at higher pressures. The refined atomistic structure models suggest that the glasses feature a distribution of 4, 5, and 6 coordinated Ge with a majority of 4 and 5 coordinated species. Only minor changes in the Ge–O coordination occur upon hot compression, but a notable transformation of edge- to corner-sharing Ge-polyhedra is found. This anomalous polyhedral packing causes a lower number of angular constraints upon higher pressure treatment, explaining the non-monotonic trend of shear modulus with pressure. We also find that the rings become smaller and less circular upon compression, contributing to the volumetric compaction. These findings may aid the future design of germanate glasses with tailored properties and the general understanding of structure-property relations in oxide glasses.