Probing and modeling of pressure-induced coordination transformation in borate glasses: Inelastic x-ray scattering study at high pressure

Here, we report on the in situ synchrotron inelastic x-ray scattering spectra of Na-borate glasses at high pressure up to 25 GPa. The pressure-induced boron coordination transformation from ${}^{\left[3\right]}\text{B}$ to ${}^{\left[4\right]}\text{B}$ is linear with pressure characterized by a single value of ${\left(\partial {}^{\left[3\right]}\text{B}/\partial P\right)}_T$. Previous studies of Li-borate and pure-borate glasses show a nonlinear transformation with multiple ${\left(\partial {}^{\left[3\right]}\text{B}/\partial P\right)}_T$ values for different pressure ranges, revealing the important role cation field strength plays in densification and pressure-induced structural changes. Considering the distribution of the energy difference between low- and high-pressure states $\left(\Delta \epsilon \right)$ in the energy landscape and the variance of the ratio $\Delta \epsilon$ to its pressure gradient ${\left(\partial \Delta \epsilon /\partial P\right)}_T$ as a measure of network flexibility with pressure, an amorphous system with a large variance in $\Delta \epsilon$ at 1 atm and/or a small ${\left(\partial \Delta \epsilon /\partial P\right)}_T$ may undergo a gradual coordination transformation (e.g., Na borates). In contrast, a system with the opposite behavior (e.g., Li borates) undergoes an abrupt coordination transformation. The results and concepts of this study thus can shed light on opportunities to study the effect of composition on the nature of densification in low-$z$ oxide and other archetypal glasses and melts.

Figure 1

(Color online) Boron $K$-edge inelastic IXS spectra of Na-diborate $\left({\text{Na}}_2{\text{B}}_4{\text{O}}_7\right)$ glasses with varying pressure, as labeled. The IXS spectra of Li-borate (red) and pure-borate glasses (blue) at 1 bar have been reported previously and are shown here for comparison purposes (Refs. 2, 31). The spectra are plotted as the normalized scattered intensity vs the energy loss (incident energy-elastic energy).

Figure 2

(Color online) (a) Pressure dependence of the ${}^{\left[3\right]}\text{B}$ fraction for ${\text{Na}}_2{\text{B}}_4{\text{O}}_7$ glass (red) and ${\text{Li}}_2{\text{B}}_4{\text{O}}_7$ glass (blue). The red dashed curve shows the Li-borate data that are shifted to correct for pressure gradients of 4 GPa at 25 GPa. Here we assume that the pressure difference between edge and center increases linearly with pressure. The black dashed lines for I, II, and III represent distinct pressure ranges with varying ${\left(\partial {}^{\left[4\right]}\text{B}/\partial P\right)}_T$ values. There are two distinct pressure ranges of densification: above and below the crossover pressure. (b) Normalized ${}^{\left[3\right]}\text{B}$ fraction in borate glasses. The ${}^{\left[3\right]}\text{B}$ fraction in pure-borate glasses is 100% and that in alkali-diborate glasses is approximately 50%; however, these fractions are normalized to the total fraction of ${}^{\left[3\right]}\text{B}$ at 1 atm.

Figure 3

(Color online) Variation in mole fraction $X_{\alpha }\left(P\right)$ of low-pressure coordination state $\left(\alpha \right)$ as a function of pressure and the variation ${\sigma }_p$ with $P_{\text{tr}}=6\text{GPa}$ and ${\sigma }_p^0=0.3\text{GPa}$. The transition zone is the pressure range for a rapid coordination transformation. The distribution $G\left(P_{\text{tr}}\right)$ of $P_{\text{tr}}$ as a function of pressure is shown in the inset.