Resolving the boron anomaly in SrF₂-borate glasses using combined MRN-TCT-percolation framework

This study resolves the longstanding "boron anomaly" by integrating Modified Random Network (MRN), Topological Constraint Theory (TCT), and Percolation Theory. SrF₂ (acting dually as network disruptor/charge compensator) was substituted in 50B₂O₃-(20-X)PbO-(X)SrF₂-20CaO-10ZnO glasses (X = 0-20 mol%) via melt-quenching technique. MRN reveals SrF₂-induced phase separation into [Formula: see text]-rich disordered domains (XRD: 45° hump) and B⁴⁺-rich ordered domains (28° hump), explaining increased Urbach energy (from 0.291 to 0.389 eV). TCT quantifies (B³⁺ to B⁴⁺) conversion (N4% increase from 33.8% to 77.9%), where percolating BO₄ tetrahedra enhance rigidity. This increases Young's modulus (from 61.98 to 83.25 GPa) despite density loss and widens direct (from 2.964 to 3.215 eV) and indirect (from 2.537 to 2.652 eV) bandgaps. Percolation Theory identifies a critical threshold at 10 mol% SrF₂: below this, [Formula: see text] disrupts the network (forming BO₂F₂/BO₃F defects), causing non-monotonic N4% (minimum 27.3% at X = 5 mol%) and modulus anomalies. Above 10 mol%, [Formula: see text] saturation enables charge compensation (stabilizing BO₄⁻ units). This triple-theory synergy decodes the anomaly and enables eco-friendly glass design with tailored opto-mechanical properties.