Development of a force field for modeling lithium borosilicate glasses

Abstract

A force field (FF) with a Buckingham function was developed for modeling lithium borosilicate (LBS) glasses using molecular dynamics (MD) simulations. The parameter set of the FF for two-body interaction between Li and O (Li-O) was optimized to reproduce both theoretically calculated force and energy using the density functional theory (DFT) and experimental properties, such as density and mechanical moduli. Bayesian optimization based on a machinelearning technique was employed to efficiently find the best parameter set in a wide parameter space. The accuracy of the MD simulation using the optimized FF of Li-O together with the previously reported FFs for Si-O, B-O, and O-O pairs was examined by comparing with experimentally measured boron coordination numbers (𝑁 𝐵 ) in a variety of LBS glasses. Consequently, it was found that the combination of the FFs is not accurate enough to reproduce the boron coordination change with varying glass compositions. Therefore, the parameter set of the B-O pair was extended to be composition-dependent to reproduce the experimental data on the N 𝐵 . It was confirmed that the empirical parameter correction as a function of 𝐾 = [SiO 2 ]/[B 2 O 3 ] and 𝑅 = [Li 2 O]/[B 2 O 3 ] ratios enables modeling LBS glass consistently with experimental NMR data.

Modeling Short-Range and Three-Membered Ring Structures in Lithium Borosilicate Glasses Using a Machine-Learning Potential

“…The 4 B and 5 Si ratios were almost maintained even after the energy minimization, as shown in Figure 2b, confirming that the glass structures obtained by MLP were at least in a local minimum of the energy landscape of the glass structures. Because the borosilicate glasses obtained with DeepMD in our previous study did not contain 5 Si, 28 training more data on the structures wherein lithium and silicon are involved is expected to improve the MLP for modeling the LBS glasses. Accordingly, this study focused on the boron coordination and the threemembered rings (3MR) composed of boron atoms.…”

“…21−24 Analogously, a composition-dependent force field for lithium borosilicate glass was also proposed by modifying the Buckingham-type force field, 25−27 whose parameters were optimized to reproduce force and energy evaluated by DFT calculations. 28 The empirical force field for LBS glasses is hereafter abbreviated as FMP-LBS. 28 These extended empirical force fields can reproduce 3 that planar three-membered rings such as boroxol rings are seldom in glass structures modeled by force fields with two-body interactions.…”

“…28 The empirical force field for LBS glasses is hereafter abbreviated as FMP-LBS. 28 These extended empirical force fields can reproduce 3 that planar three-membered rings such as boroxol rings are seldom in glass structures modeled by force fields with two-body interactions. 29 A recent progressive advancement of machine-learning (ML) technologies provides us with another approach to investigate glass models more precisely.…”

“…Although a possible alternative method to obtain adequately large and well-equilibrated glass structures is the classical molecular dynamics (CMD) simulation, CMD simulations often fail to reproduce borosilicate glass structures. Contrary to silicate glasses, borosilicate glasses including modifiers are difficult to be modeled accurately with simple functional force fields because boron atoms flexibly vary the oxygen coordination number, 3-fold ( 3 B) or 4-fold coordinated ( 4 B). − To accurately model sodium borosilicate glasses using CMD simulations, several force fields were extended by employing composition-dependent parameters. − Analogously, a composition-dependent force field for lithium borosilicate glass was also proposed by modifying the Buckingham-type force field, − whose parameters were optimized to reproduce force and energy evaluated by DFT calculations . The empirical force field for LBS glasses is hereafter abbreviated as FMP-LBS .…”

“…Contrary to silicate glasses, borosilicate glasses including modifiers are difficult to be modeled accurately with simple functional force fields because boron atoms flexibly vary the oxygen coordination number, 3-fold ( 3 B) or 4-fold coordinated ( 4 B). − To accurately model sodium borosilicate glasses using CMD simulations, several force fields were extended by employing composition-dependent parameters. − Analogously, a composition-dependent force field for lithium borosilicate glass was also proposed by modifying the Buckingham-type force field, − whose parameters were optimized to reproduce force and energy evaluated by DFT calculations . The empirical force field for LBS glasses is hereafter abbreviated as FMP-LBS . These extended empirical force fields can reproduce 3 B/ 4 B ratios in alkaline borosilicate glasses; however, it is known that planar three-membered rings such as boroxol rings are seldom in glass structures modeled by force fields with two-body interactions …”