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

## TL;DR

This study explains the boron anomaly in SrF2-borate glasses by combining three theories to show how SrF2 affects glass structure and properties.

## Contribution

The integration of MRN, TCT, and Percolation Theory provides a novel framework to decode the boron anomaly in SrF2-borate glasses.

## Key findings

- SrF2 induces phase separation into F⁻-rich and B⁴⁺-rich domains, increasing Urbach energy.
- Percolation Theory identifies a critical SrF2 threshold at 10 mol% that changes network behavior.
- The triple-theory approach enables eco-friendly glass design with tailored opto-mechanical properties.

## Abstract

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 \documentclass[12pt]{minimal}
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\begin{document}$${\text{F}}^{-}$$\end{document}-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, \documentclass[12pt]{minimal}
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\begin{document}$${\text{F}}^{-}$$\end{document} disrupts the network (forming BO2F2/BO3F defects), causing non-monotonic N4% (minimum 27.3% at X = 5 mol%) and modulus anomalies. Above 10 mol%, \documentclass[12pt]{minimal}
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\begin{document}$${\text{F}}^{-}$$\end{document} 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.