Certification of boroxol ring population in vitreous B2O3 glass using theoretical simulations

Population of boroxol rings in vitreous borate glass (v-B${}_2$O${}_3$) is still debated due to several conflicting results from experiments and simulations. To address this issue, we examined structural models of v-B${}_2$O${}_3$ using a combination of classical and $ab$ $initio$ molecular dynamics (MD) simulations. For the classical MD simulations, both analytical and machine-learning force fields (MLFF) were utilized to construct multiple v-B${}_2$O${}_3$ models with varying amounts of boroxol rings, followed by $ab$ $initio$ MD and energy minimization using density functional theory. These diverse structures were compared with available experimental data, such as neutron and X-ray diffraction patterns, nuclear magnetic resonance (NMR), and Raman spectroscopy. Consequently, only models with more than 70% of boron atoms within boroxol rings reproduced these experimental data, confirming that a various boroxol rings should exist in v-B${}_2$O${}_3$. Specifically, NMR and Raman spectra of the v-B${}_2$O${}_3$ models with fewer boroxol rings did not show the characteristic spectra observed experimentally even when their structures were sufficiently relaxed. We therefore conclude that the population of boron atoms within boroxol rings should be more than 70%, and could be as high as 80%. Finally, we updated the MLFF using the structural data that included a certain amount of boroxol rings obtained through this work. Consequently, it was demonstrated that accurate MLFF produces a certain amount of boroxol rings, while a quenching rate comparable to experimental condition is required to generate a reasonable population of boroxol rings.