Semi-empirical modelling of Young’s Modulus in aluminoborosilicate glasses from Network Chemistry and Topology

Understanding the relationship between atomic structure and mechanical properties of aluminoborosilicate glasses is essential for optimizing the performance of nuclear waste confinement matrices. In this study, the elastic behavior of Na 2 O–CaO–Al 2 O 3 –B 2 O 3 –SiO 2 glasses was systematically investigated using nanoindentation. The Young’s modulus (E) ranges from 56 to 93 GPa depending on the Na/Ca ratio and B 2 O 3 content. Ca-rich glasses exhibit the highest stiffness, reflecting enhanced structural compaction and stronger Ca–O bonds compared to Na–O. The correlation between E and molar volume (V m ) confirms that network rigidity is primarily governed by atomic packing density. Solid-State Nuclear Magnetic Resonance (NMR) spectroscopy ( 11 B and 27 Al) provides quantitative information for calculation of Non-Bridging Oxygen (NBOs) fractions. These data reveal three distinct mechanical regimes: 1) Na-rich glasses, where Na⁺ acts as a depolymerizing modifier; 2) Ca-rich glasses, where Ca²⁺ maintains network stiffness despite higher NBO content; and 3) mixed Na–Ca glasses showing non-linear and complex elastic behavior. Several semi-empirical regression models were developed to estimate E directly from glass composition using physically meaningful descriptors, namely the theoretical ionic volume V i ‾ , the dissociation energy per unit volume G i ‾ , and the cation field strength (CFS). Depending on the availability of experimental boron speciation data, the models were calibrated on datasets of 118 to 160 glass compositions. The best practical formulation, applicable when experimental boron speciation data are unavailable, reached R² = 0.80 with a root mean square error of about 8 GPa. These models provide practical tools for describing and predicting Young’s modulus in complex aluminoborosilicate and nuclear glasses without requiring density measurements.