Improved empirical force field for multicomponent oxide glasses and crystals

In this paper, the self-consistent PMMCS force fields (FFs) [Pedone et al., J. Phys. Chem. B 110, 11780 (2006)] widely used for the simulation of a large variety of silicates, aluminosilicate and phosphate crystals, and multicomponent oxide glasses have been revised and improved by the inclusion of two types of three-body interactions acting between T-O-T bridges ($T=\mathrm{Si}$ and P) and network former-network former repulsive interactions. The FFs named Bertani–Menziani–Pedone (BMP)-harm and BMP-shrm better reproduce the T-O-T bond angle distributions (BADs) and network former-oxygen distances. Consequently, the prediction of $Q^n$ distributions (Q stands for quaternary species, and $n$ is the number of bridging oxygens around it), neutron total distribution functions, solid-state nuclear magnetic resonance spectra of spin active nuclei (${}^{29}\mathrm{Si}$, ${}^{17}\mathrm{O}$, ${}^{31}\mathrm{P}$, ${}^{27}\mathrm{Al}$), and the density have also been hugely improved with respect to the previous version of our FF. These results also highlight the strong correlation between the T-O-T BADs and the other short and intermediate structural properties in oxide glasses, which have been largely neglected in the past. In addition to the improvement of the structure, the FF has been revealed to reproduce well the ionic conductivity in mixed alkali aluminosilicate glasses and the elastic properties. The systematic comparison with other interatomic potential models, including the polarizable core-shell model, carried out in this paper showed that our potential model is more balanced and effective for simulating a vast family of crystalline and amorphous oxide-based systems.

Figure 1

Experimental vs calculated T-O-T angles (left) and density (right) of the crystal phases used in fitting procedure obtained using the PMMCS (green symbols), BMP-shrm (cyan symbols), and BMP-harm (red symbols) potentials. Linear regression has been made on data of each potential, giving the following linear equations and correlation coefficient ($R^2$) for the angles: $Y_{\mathrm{PMMCS}}\left(x\right)=0.969x+10.308$, $R^2=0.718$; $Y_{\mathrm{BMP}\text{−}\mathrm{shrm}}\left(x\right)=0.866x+19.608$, $R^2=0.870$; $Y_{\mathrm{BMP}\text{−}\mathrm{harm}}\left(x\right)=0.905x+14.130$, $R^2=0.909$. The same procedure has been applied to the density data, giving the following equations and correlation coefficients ($R^2$): $Y_{\mathrm{PMMCS}}\left(x\right)=0.812x+0.527$, $R^2=0.883$; $Y_{\mathrm{BMP}\text{−}\mathrm{shrm}}\left(x\right)=0.759x+0.603$, $R^2=0.897$; $Y_{\mathrm{BMP}\text{−}\mathrm{harm}}\left(x\right)=0.795x+0.513$, $R^2=0.914$.

Figure 2

Correlation plot between the experimental and calculated densities of the glasses investigated using the different potentials. Linear regression has been made on data obtained with each potential, giving the following straight line equations and correlation coefficients ($R^2$): $Y_{\mathrm{PMMCS}}\left(x\right)=0.988x+0.015$, $R^2=0.569$; $Y_{\mathrm{SHIK}}\left(x\right)=0.964x+0.099$, $R^2=0.795$; $Y_{\mathrm{Coreshell}}\left(x\right)=0.684x+0.584$, $R^2=0.433$; $Y_{\mathrm{BMP}\text{−}\mathrm{harm}}\left(x\right)=0.857x+0.353$, $R^2=0.848$; $Y_{\mathrm{BMP}\text{−}\mathrm{shrm}}\left(x\right)=0.820x+0.435$, $R^2=0.830$.

Figure 3

Simulated and experimental total neutron distribution functions of the binary alkali silicate LS33, NS30, and KS33 glasses and sodium, calcium phosphate NP, NCP, and CP glasses.

Figure 4

Si-O, M-O ($M=\mathrm{Li}$, Na, and K), and Al-O pair distribution functions of the LS33, NS33, and KS33 glasses and of the NASR series for the aluminosilicate glasses.

Figure 5

Si-O-Si, Si-O-Al, P-O-P bond angle distributions in (a) $v$-silica, (b) binary alkali silicate NS30, (c) aluminosilicate NASR-1, and (d) sodium calcium phosphate NCP glasses.

Figure 6

Computed and experimental trends of the $Q^n$ species in the alkali silicate glasses investigated.

Figure 7

(a) Phosphorous $Q^n$ distributions in NP, NCP, and CP glasses; (b) trends of the $Q^0$ species for phosphorous in phosphosilicate glasses for BMP-harm, BMP-shrm, PMMCS, and two core-shell model (CSM) parameterizations.

Figure 8

(a) Percentage of NBO bonded to aluminum atoms and (b) total percentage of NBO in the NASR and NAST glasses calculated with all studied potentials.

Figure 9

Percentage of $T_1\text{−}\mathrm{O}\text{−}{T}_2$ bridges (where $T_1$ and $T_2=\mathrm{Si}$, Al) in the simulated NASR glasses. The cyan and black horizontal lines highlight the values computed, assuming a random distribution of Al/Si species, and the one determined experimentally, respectively [6].

Figure 10

Simulated and experimental MAS NMR spectra of (a) ${}^{29}\mathrm{Si}$ of NS33, (b) ${}^{27}\mathrm{Al}$ of NASR-1, (c) ${}^{17}\mathrm{O}$ of NS33, and (d) ${}^{31}\mathrm{P}$ of NCPS_2.11 glasses.

Figure 11

Elastic constants (Young's modulus, shear modulus, and bulk modulus) of the binary alkali silicates and sodium aluminosilicate NAST glasses computed with the different potentials. The mean absolute error (MAE) has been calculated for all properties. They are $\mathrm{MA}{\mathrm{E}}_{\mathrm{PMMCS}}=2.53$, $\mathrm{MA}{\mathrm{E}}_{\mathrm{BMP}\text{−}\mathrm{harm}}=3.42$, and $\mathrm{MA}{\mathrm{E}}_{\mathrm{BMP}\text{−}\mathrm{shrm}}=3.74$ for the bulk modulus, and $\mathrm{MA}{\mathrm{E}}_{\mathrm{PMMCS}}=3.96$, $\mathrm{MA}{\mathrm{E}}_{\mathrm{BMP}\text{−}\mathrm{harm}}=5.60$, and $\mathrm{MA}{\mathrm{E}}_{\mathrm{BMP}\text{−}\mathrm{shrm}}=5.86$ for the Young modulus.

Figure 12

Logarithm of resistivity obtained for the three glasses studied at variable temperature by different interatomic potentials.