On the Boroxol Ring Fraction in Melt-Quenched B$_2$O$_3$ Glass

TL;DR

This study develops a machine-learned potential to simulate B$_2$O$_3$ glass formation, revealing the boroxol ring fraction's dependence on quench rate and matching experimental estimates.

Contribution

The paper introduces a DFT-accurate machine-learned potential enabling realistic simulations of B$_2$O$_3$ glass with boroxol rings, addressing previous modeling challenges.

Findings

Boroxol ring fraction exceeds 30% at low quench rates.

A minimum energy configuration occurs at 75% boroxol fraction.

Boroxol fraction increases as quench rate decreases.

Abstract

An atomistic structural model for melt-quenched B$_2$O$_3$ glass has eluded the simulation community so far. The difficulty lies in the abundance of the six-membered boroxol rings - an intermediate-range order motif suggested through Raman and NMR spectroscopy - which is challenging to obtain in atomistic molecular dynamics simulations. Here, we report the development of a DFT-accurate machine-learned potential for B$_2$O$_3$ and employ quench rates as low as 10$^{9}$ K/s to obtain B$_2$O$_3$ glasses with more than 30% of boron atoms in boroxol rings. Also, we show that the pressure, and consequently the boroxol fraction, in the deep potential molecular dynamics (DPMD) simulations critically depends on the range of the geometry descriptor used in the embedding neural network, and at least a 9 $\unicode{x212B}$ range is required. The boroxol ring fraction increases with decreasing quench rate. Finally, amorphous B$_2$O$_3$ configurations display a minimum in energy at a boroxol fraction of 75%, intriguingly close to the experimental estimate in B$_2$O$_3$ glass.