Temperature-dependent densification of sodium borosilicate glass

Abstract

Densified glasses recovered from a high-pressure state are of potential technological interest due to their modified physical and chemical properties. Here we investigate the temperature-dependent densification behavior of a sodium borosilicate glass in a gas pressure chamber at 1 GPa. The temperature is varied for a 30 min treatment between 0.6T_g and 1.15T_g, where T_g is the glass transition temperature, and the treatment duration is varied between 10 and 10 000 min for compression at 0.9T_g. Permanent densification occurs for temperatures above 0.7T_g and the degree of densification increases with increasing compression temperature and time, until attaining an approximately constant value for temperatures above T_g. The same temperature and time dependence is also found for the glass mechanical properties (hardness and brittleness) and the network structure, i.e., fraction of three-fold versus four-fold coordinated boron atoms and ring versus non-ring trigonal boron atoms, and the extent of mixing of Si and B. The results provide insights into the temperature-dependence of the network densification and the relative roles of viscous flow and more localized rearrangements.

---

1. Introduction

The behavior of silicate glasses and glass-forming liquids under pressure is of interest for understanding geochemical processes in the mantle and crust.^1,2 The densification mechanisms have been associated with reduction of the inter-tetrahedral bond angle,^3–5 decrease in network modifier-oxygen distances,^6–8 and increase in the network former-oxygen coordination number.^9,10 From the perspective of post-treating industrial glasses, there is also an interest in permanently densified glasses recovered from a high-pressure state,¹¹ but the changes in glass structure and properties depend on the utilized pressure route, such as compression temperature and static vs. dynamic compression.¹²

The permanent densification of glass occurs at significantly lower pressures for compression at elevated temperature compared to that at room temperature. That is, the extent of densification increases with increasing pressure at a given temperature and with increasing temperature at a given pressure.^13,14 At room temperature, where high pressures in excess of 10 GPa can easily be reached but only small sample specimens can be processed, most structural changes are reversible upon decompression at pressures below 5–10 GPa.^15,16 Freezing in the glass structure under pressure during quenching causes permanent densification at pressures even at 0.1 GPa (ref. 17) and enables the preparation of bulk sample specimens. However, while there have been numerous studies of glass structure as a function of pressure at room temperature, there are fewer examples of the effects of simultaneous pressure and temperature treatment on glass structure and even fewer extensions of this knowledge to the rationalization of post-compression glass properties.

In this work, we investigate the effect of compression temperature and time on the pressure-induced changes in structure, density, and mechanical properties of a sodium borosilicate glass. This will provide insights into the temperature and time dependence of the network densification, the role of viscous flow at temperatures near the glass transition, and the coupling between pressure-induced changes in microscopic structure and macroscopic properties. The pressure treatment is performed isostatically at 1 GPa using an internally heated nitrogen gas pressure chamber and the temperature is varied between 0.6T_g and 1.15T_g, where T_g is the glass transition temperature in Kelvin. The treatment duration at 1 GPa is also varied between 10 and 10 000 min for compression at 0.9T_g. The model borosilicate glass of composition 20Na₂O–22B₂O₃–58SiO₂ (in mol%) is studied due to its stability against crystallization even at prolonged treatment at 1.15T_g and because it forms the basis for various industrially relevant glasses. Moreover, B₂O₃-containing glasses are interesting objects for high-pressure studies, since they exhibit relatively high compressibilities and are capable of undergoing changes in short- and intermediate-range order, even at moderate pressures.^18,19

2. Experimental section

2.1 Sample preparation

The sodium borosilicate batch was melted at 1350 °C in a Pt₉₀Rh₁₀ crucible in air and poured onto a brass plate at room temperature. The obtained glass was transparent and confirmed to be amorphous by X-ray diffraction (XRD). By using inductively coupled plasma atomic emission and flame emission spectroscopy, the chemical composition was found to be 20.4Na₂O–21.7B₂O₃–57.8SiO₂. T_g was found to be 840 K, which was determined as the onset of the glass transition by differential scanning calorimetry (DSC 449C, Netzsch) at the heating rate of 10 K min⁻¹ (equal to the prior cooling rate). The glass was annealed at T_g + 25 K and individual samples (12 × 12 × 2 mm³) were cut and polished to an optical finish.

The samples were then isostatically compressed at elevated temperature in a nitrogen gas pressure chamber, which contains a multizone cylindrical furnace.²⁰ Each sample was subjected to an individual treatment at 1 GPa at the following compression temperatures (T_c): 0.6T_g (504 K), 0.7T_g (588 K), 0.8T_g (672 K), 0.9T_g (756 K), 0.95T_g (798 K), 1.0T_g (840 K), 1.05T_g (882 K), 1.1T_g (924 K), and 1.15T_g (966 K), where T_g is the glass transition temperature prior to compression. We note that T_g is a function of pressure, but the change is expected to be small within this pressure regime.^21,22 The system was in each case kept at the elevated temperature for 30 minutes, but for the treatment at 0.9T_g, the treatment duration (t_c) was also varied: 10, 20, 30, 120, 960, and 10 000 min. Afterwards the samples were first cooled, followed by decompression, at initial rates of 60 K min⁻¹ and 30 MPa min⁻¹, respectively. XRD analyses of the compressed samples showed no evidence of crystallization due to the pressure treatment.

2.2 Characterization

To study the structural changes around boron, ¹¹B magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy was conducted on selected samples at 16.4 T using a commercial spectrometer (VNMRS, Agilent) and MAS NMR probe. The resonance frequency for ¹¹B at this external magnetic field strength is 224.51 MHz. The samples were crushed using an agate mortar and pestle, packed into 1.6 mm zirconia rotors and spun at frequencies of nominally 25 kHz. The MAS NMR spectra were collected using short radio-frequency pulses (0.6 μs, equivalent to π/12 tip angles), relaxation delays of 5 s, and signal averaging of 400 acquisitions. Data was frequency referenced to aqueous boric acid at 19.6 ppm. ¹¹B triple quantum magic-angle spinning (3QMAS) NMR spectra were collected using a hypercomplex 3QMAS pulse sequence with a Z filter.²³ The solid π/2 and 3π/2 pulse widths were optimized to 0.8 and 2.3 μs, respectively. A lower power π/2 pulse width of 20.0 μs was used as the soft reading pulse of the Z filter. ¹¹B 3QMAS NMR data were typically collected using 24 acquisitions at each of 256 t₁ points, with a recycle delay of 5 s and sweep widths of 200 and 50 kHz in the MAS and isotropic dimensions, respectively. The ¹¹B 3QMAS NMR data were processed using commercial software and referenced to 1 M boric acid at 19.6 ppm.

To obtain additional structural information, we measured the Raman spectra on a Renishaw Invia Raman microscope with a 532 nm excitation source. Raman spectra were processed using an asymmetric least squares baseline correction and area normalization procedure.²⁴

The density values of all the glass samples before and after isostatic compression were determined by Archimedes' principle using ethanol as the immersion medium. Each measurement of sample weight was repeated ten times. Vickers hardness (H_V) and crack-to-indent size ratio (c/a) of the glass samples before and after isostatic compression were measured using a Vickers micro-indenter (Duramin 5, Struers A/S). The measurements were performed in air at room temperature. At least 30 indents were performed at a load of 4.91 N with a dwell time of 15 seconds.

3. Results

3.1 Density

The density measurements show that there is almost no permanent densification of the samples compressed at temperatures at or below 0.7T_g (Fig. 1a). For T_c ≥ 0.8T_g, the density increases approximately linearly with T_c and then assumes an approximately constant value for T_c > T_g. That is, the kinetic processes responsible for densification increase in frequency with increasing temperature up to the glass transition. For compression at or above the glass transition temperature, the structural relaxation time is well below the compression duration of 30 min and no further densification occurs. Our results are in agreement with those of Yamada et al. for compression of MgSiO₃ glass.²⁵ When the treatment duration increases for T_c = 0.9T_g, the density increases approximately linearly with log t_c (Fig. 2a). For t_c = 10 000 min (∼7 days), the density exhibits a value (∼2.58 g cm⁻³) similar to for 30 min treatments at T_c > T_g. At the lower compression temperature, longer time is required for the structure to equilibrate with the high-pressure environment.

Fig. 1 Effect of compression temperature (T_c) on glass structure and properties for the compression duration of 30 min at 1 GPa. (a) Density (ρ) and fraction of tetrahedral to total boron (N₄). (b) Vickers hardness (H_V) and crack-to-indent size ratio (c/a). The dashed lines represent the values of the as-prepared glass. The errors of density are smaller than the size of the symbols.

Fig. 2 Effect of compression duration (t_c) on glass structure and properties for the compression temperature of 0.9T_g (756 K) at 1 GPa. (a) Density (ρ) and fraction of tetrahedral to total boron (N₄). (b) Vickers hardness (H_V) and crack-to-indent size ratio (c/a). The dashed lines represent the values of the as-prepared glass. The errors of density are smaller than the size of the symbols.

3.2 ¹¹B MAS NMR and Raman spectroscopy

Fig. 3 shows ¹¹B MAS NMR spectra of the as-prepared and compressed borosilicate glasses. These spectra are characterized by a broad peak centered around 15 ppm, corresponding to trigonal boron (B^III) sites, and a relatively narrow peak centered around 0 ppm, corresponding to tetrahedral boron (B^IV) sites. The ¹¹B MAS NMR data were fit using DMfit²⁶ to reproduce B^III and B^IV line shapes, and for both spectral regions, two distinct peaks were required to adequately reproduce the experimental data. The fraction of tetrahedral to total boron (N₄ = [B^IV]/([B^IV] + [B^III])) was determined from the integration of these resonances. As part of the N₄ determination, excess contributions from B^IV satellite transitions were subtracted from the total B^IV integrals.²⁷ For the as-prepared glass (R = [Na₂O]/[B₂O₃] = 0.94; K = [SiO₂]/[B₂O₃] = 2.66), we obtain N₄ ∼ 70 at%, which is close to the value predicted by the model of Dell and Bray.²⁸ The isostatic compression at 1 GPa causes an increase of N₄ in agreement with previous results.^17–19,29 The dependence of N₄ on compression temperature for t_c = 30 min is shown in Fig. 1a, whereas the dependence of N₄ on compression duration for T_c = 0.9T_g is shown in Fig. 2a. Cold compression of this glass at room temperature does not modify the boron speciation, but as the compression temperature increases, N₄ increases from 70 to 76 at% for T_c = T_g, with no further increase when T_c is increased from T_g to 1.1T_g (Fig. 1a). Increasing the compression duration also causes an increase in N₄ up to 74.5 at% for t_c = 960 min (Fig. 2a).

Fig. 3 ¹¹B MAS NMR spectra for the as-prepared (black dashed curve), glasses compressed at or below T_g (solid gray curves), and the glass compressed at 1.1T_g for 30 min (solid black line). The inset shows the fitted spectrum of the as-prepared glass based on contributions of different boron environments. From low to high frequencies these represent B^IV(0B, 4Si), B^IV(1B, 3Si), B^III(non-ring), and B^III(ring).

In Fig. 3, we observe a shift of the peak position of the B^IV resonance to smaller ppm values (corresponding to higher shielding) with increasing compression temperature. Fitting of the ¹¹B MAS NMR spectra using two B^IV peaks (see inset to Fig. 3) provides more detail on what types of B^IV sites are involved in the network structure, as well as their relative concentrations. The B^IV peak with highest shielding, found at −1.4 ppm, has been assigned to B^IV atoms with 0B and 4Si next-nearest neighbors (NNN). The other B^IV resonance detected in these glasses is at +0.2 ppm consistent with B^IV having 1B and 3Si NNN. These peak assignments and the types of B^IV environments found in this sodium borosilicate glass composition are in agreement with peak assignments for other sodium borosilicate glasses.^30–32 The changes in B^IV peaks with pressure (cf. Fig. 3) are simply due to a shift in the relative population of the two B^IV resonances, with more B^IV (0B, 4Si) being formed with compression. Such pressure-induced network ordering has previously been found by Du et al.²⁹ and is due to the avoidance of energetically unfavorable B^IV–O–B^IV linkages upon the conversion of B^III to B^IV.^33,34 Furthermore, the value of [B^IV(0B, 4Si)]/[B^IV(1B, 3Si)] exhibits a similar temperature dependence as density and N₄ (Fig. 4). This ratio also increases with increasing compression duration.

Fig. 4 Effect of compression temperature (T_c) on the fraction of B^IV and B^III in different environments for the compression duration of 30 min at 1 GPa. The relative intensities have been extracted from the deconvoluted ¹¹B MAS NMR spectra.

As also shown in Fig. 3, two distinct B^III resonances were necessary to fit this part of the ¹¹B MAS NMR spectra. Based on the measured value of N₄ for the as-prepared glass and the content of Na₂O, we estimate that only 5.2% of the oxygens are non-bridging oxygen (NBO) and the Dell and Bray²⁸ model predicts that all of these NBOs should be associated with Si for the present composition. Therefore, the two types of B^III sites are likely not due to symmetric and asymmetric sites found for some borosilicate compositions,^28,35 since the asymmetric sites are connected to one or two NBO. This is also consistent with the fitted NMR parameters for the two B^III resonances. In particular, the quadrupolar asymmetry parameter (η) exhibits a value around 0.30 for the two peaks, regardless of temperature or time of compression. This η value is perhaps slightly higher than normally observed for symmetric BO₃ sites (i.e., all bridging oxygen), but is also too small to unambiguously attribute to asymmetric BO₃ sites. Instead, and consistent with other studies of similar sodium borosilicate glass compositions, the two components can be attributed to B^III in ring and non-ring sites.^36–38 This accounts for the smaller η values for both peaks, and also the significant isotropic chemical shift difference between them (18 ppm for the ring B^III and 15 ppm for the non-ring B^III). Furthermore, ¹¹B 3QMAS NMR spectra can also be used to characterize the two B^III peaks, as shown in Fig. 5. Here, the isotropic dimension exhibits pronounced asymmetry, indicating the presence of multiple B^III peaks. Slices at the isotropic shifts corresponding to two B^III peaks allow for closer inspection of their individual MAS NMR lineshape, shown to the right of the 3QMAS NMR data in Fig. 5. DMfit simulation of these two slices are consistent with the deconvoluted MAS NMR data in Fig. 3, with two very similar B^III peaks (nearly identical η and quadrupolar coupling constant (C_q)) distinguished only by a difference in isotropic chemical shift.

Fig. 5 ¹¹B 3QMAS NMR spectrum of the as-prepared sodium borosilicate glass showing the B^III shift region. Spectra to the right are MAS slices at isotropic shifts corresponding to B^III peaks at 20 and 17.5 ppm, as described in the text.

The Raman spectrum of the as-prepared glass (Fig. 6) also seems to indicate the presence of ring B^III. The band representing boroxol rings (three corner-sharing B^III triangles) is typically found around 800 cm⁻¹,^39–42 but here it is weak and overlaps with a peak near 770 cm⁻¹ in borosilicates,⁴³ which has been assigned to ring structures containing both B^III and B^IV (pentaborate, triborate, and tetraborate).^44–46 Based on the assignment of the B^III peaks in the ¹¹B MAS NMR spectra, we find that the fraction of B^III in non-ring sites increases with increasing compression temperature as shown in Fig. 4, similar to the pressure-induced conversion of ring into non-ring found for vitreous B₂O₃ at room⁴⁷ or elevated temperature.^48,49 This is also in agreement with the Raman spectroscopy data as the intensity in the region around 750 to 800 cm⁻¹ decreases upon compression (Fig. 6). The population of B^III in ring and non-ring environments was determined by deconvolution of the MAS NMR data in Fig. 3 (e.g., Fig. 3 inset), but also confirmed by fitting of the isotropic projections from ¹¹B 3QMAS NMR, as shown in Fig. 7. Here, two Gaussian curves adequately reproduce the data and there is a clear change in the relative peak intensities with compression. As was evident in the MAS NMR spectra, the upfield B^III resonance (non-ring B^III) increases in intensity with compression temperature. The same overall trend is found for increasing compression duration.

Fig. 6 Raman spectrum of the as-prepared glass (black dashed curve) and the glass compressed at T_g for 30 min (solid gray curve).

Fig. 7 ¹¹B 3QMAS NMR isotropic projections for the B^III frequency region. Dashed black lines denote as-prepared sodium borosilicate glass with two peaks fit (filled Gaussians). All glasses compressed at or below T_g are shown with solid gray curves, and the glass compressed at 1.1T_g is shown by a solid black line.

3.3 Hardness and brittleness

Hardness is a measure of the resistance to elastoplastic deformation and crack-to-indent size ratio is a measure of the brittleness.⁵⁰ As shown in Fig. 1b, the effect of compression temperature on H_V and c/a is qualitatively similar to that on density (Fig. 1a). The onset of increase in H_V and c/a occurs for T_c > 0.9T_g and levels off around T_c = 1.05T_g. The increase in hardness and brittleness upon isostatic compression has been found previously for other glass systems.^19,51 This effect is due to a decrease in the contribution of densification to the indentation deformation.⁵² That is, when the glass network has already been compacted at elevated temperature prior to indentation, there is a larger resistance to densification when subjected to sharp-contact loading at room temperature. H_V and c/a also increase with increasing treatment duration (Fig. 2b), following the trend of the overall network compaction.

Fig. 8 shows the dependence of hardness on density for both series of compressed glasses (temperature and time variation). The data points appear to follow a common trend, suggesting that a certain critical increase in density is required before the increase in hardness occurs. Hardness is governed by the rigidity of bond length and angles,^53,54 which may not scale with the overall network compaction.¹⁷

Fig. 8 Vickers hardness (H_V) as a function of density (ρ) for the glasses compressed for 30 min at different temperatures (T_c) and at 0.9T_g (756 K) for different durations (t_c). The dashed line is a guide for the eye.

4. Discussion

Our results have shown a pronounced temperature and time dependence of the pressure-induced changes in structure, density, and properties. At the glass transition temperature, the relaxation time towards thermodynamic equilibrium is ∼100 s and for t_c = 30 min there is thus sufficient time for the glass to structurally equilibrate to the high pressure environment. Therefore, the finding that no further change in density, boron speciation, and indentation mechanics occurs for T_c > T_g implies that viscous flow plays a dominant role in the permanent densification in this temperatures range. Breakage and sequential reformation of, e.g., Si–O bonds is an important structural control of viscous flow at and above T_g,^55,56 which should thus also be responsible for the densification. When comparing the degree of densification in different glass compositions subjected to isostatic compression, it should therefore be done at constant isokom temperature (e.g., T_g) instead of constant absolute temperature (e.g., 800 K).

As the temperature is lowered below T_g, the viscosity and relaxation time increase markedly, exceeding the laboratory timescale by several orders of magnitude in glassy state. For t_c = 30 min, the relaxation times associated with viscous flow are thus much too long to solely explain the densification of the glass below T_g. At room temperature, densification under high stress can proceed through a process involving modification of bond angles and the dihedral angle of glass network, since this requires less energy than bond breakage.⁵⁷ For T_c < T_g, more localized rearrangements are thus expected to be responsible for the permanent densification, such as rotations about bonds and local slip.⁵⁶ The increased degree of densification with increasing t_c at T_c = 0.9T_g could thus reflect that a distribution of relaxation times are involved in the densification process. These sub-T_g rearrangements may be more readily relieved upon decompression, resulting in smaller permanent density increase. However, we note that sufficient energy is available for T_c < T_g to, e.g., partially change the boron coordination number from three to four. This indicates a formation mechanism of four-fold coordinated boron without long-range motion of atoms. We therefore suggest that inelastic changes in the configuration of large structural segments by bond breaking and reformation of the links among the large structural units are responsible for densification at temperature close to T_g, whereas these links remain intact during low-temperature compression.

5. Conclusions

We have shown that isostatic compression at 1 GPa of a sodium borosilicate glass results in temperature-dependent structural reorganization and densification. Samples recovered from the high-pressure/high-temperature condition are up to 2.5% denser than the as-prepared glasses and permanent densification occurs for all temperatures above 0.7T_g. The degree of densification increases with increasing compression temperature and time, until attaining an approximately constant value for temperatures above T_g. Significant temperature-dependent changes in the network topology occur and accompany the formation of four-fold coordinated boron. We also find clear correlations between these structural changes in the oxide network, the density of the compressed glasses, and their mechanical properties (hardness and brittleness).

Acknowledgements

M. N. S. and M. M. S. acknowledge the financial support from the Danish Council for Independent Research under Sapere Aude: DFF-Starting Grant (1335-00051A). S. J. R. acknowledges the support from the National Science Center of Poland under Grant No. UMO-2011/03/B/ST3/02352.

References

1. E. M. Stolper and T. J. Ahrens, Geophys. Res. Lett., 1987, 14, 1231–1233.
2. B. T. Poe, P. F. McMillan, D. C. Rubie, S. Chakraborty, J. Yarger and J. Diefenbacher, Science, 1997, 276, 1245–1248.
3. S. K. Sharma, D. Virgo and B. O. Mysen, Am. Mineral., 1979, 64, 779–787.
4. D. Sykes, B. T. Poe, P. F. McMillan, R. W. Luth and R. K. Sato, Geochim. Cosmochim. Acta, 1993, 57, 1753–1759.
5. N. Li, R. Sakidja, S. Aryal and W.-Y. Ching, Phys. Chem. Chem. Phys., 2014, 16, 1500–1514.
6. S. K. Lee, G. D. Cody, Y. Fei and B. O. Mysen, Chem. Geol., 2006, 229, 162–172.
7. J. S. Wu, J. Deubener, J. F. Stebbins, L. Grygarova, H. Behrens, L. Wondraczek and Y. Z. Yue, J. Chem. Phys., 2009, 131, 104504.
8. S. J. Gaudio, T. G. Edwards and S. Sen, Am. Mineral., 2015, 100, 326–329.
9. J. Diefenbacher and P. F. McMillan, J. Phys. Chem. A, 2001, 105, 7973–7978.
10. J. L. Yarger, K. H. Smith, R. A. Nieman, J. Diefenbacher, G. H. Wolf, B. T. Poe and P. F. McMillan, Science, 1995, 270, 1964–1967.
11. J. C. Mauro, Front. Mater., 2014, 1, 20.
12. P. S. Salmon and A. Zeidler, J. Phys.: Condens. Matter, 2015, 27, 13320.
13. D. R. Uhlmann, J. Non-Cryst. Solids, 1973, 13, 89–99.
14. S. J. Gaudio, S. Sen and C. E. Lesher, Geochim. Cosmochim. Acta, 2008, 72, 1222.
15. S. K. Lee, P. J. Eng, H. Mao, Y. Meng, M. Newville, M. Y. Hu and J. Shu, Nat. Mater., 2005, 4, 851–854.
16. R. J. Hemley, H. K. Mao, P. M. Bell and B. O. Mysen, Phys. Rev. Lett., 1986, 57, 747–750.
17. M. M. Smedskjaer, R. E. Youngman, S. Striepe, M. Potuzak, U. Bauer, J. Deubener, H. Behrens, J. C. Mauro and Y. Z. Yue, Sci. Rep., 2014, 4, 3770.
18. L. Wondraczek, S. Sen, H. Behrens and R. E. Youngman, Phys. Rev. B, 2007, 76, 014202.
19. M. N. Svenson, T. B. Bechgaard, S. D. Fuglsang, R. H. Pedersen, A. Ø. Tjell, M. B. Østergaard, R. E. Youngman, J. C. Mauro, S. J. Rzoska, M. Bockowski and M. M. Smedskjaer, Phys. Rev. Appl., 2014, 2, 024006.
20. M. M. Smedskjaer, S. J. Rzoska, M. Bockowski and J. C. Mauro, J. Chem. Phys., 2014, 140, 054511.
21. N. Bagdassar, J. Maumus, B. Poe, A. B. Slutskiy and V. K. Bulatov, Phys. Chem. Glasses, 2004, 45, 197–214.
22. A. Drozd-Rzoska, S. J. Rzoska, M. Paluch, A. R. Imre and C. M. Roland, J. Chem. Phys., 2007, 126, 164504.
23. J. P. Amoureux, C. Fernandez and S. J. Steuernagel, J. Magn. Reson., Ser. A, 1996, 123, 116–118.
24. J. Felten, H. Hall, J. Jaumot, R. Tauler, A. D. Juan and A. Gorzsás, Nat. Protoc., 2015, 10, 217–240.
25. A. Yamada, S. J. Gaudio and C. E. Lesher, J. Phys.: Conf. Ser., 2010, 215, 012085.
26. D. Massiot, F. Fayon, M. Capron, I. King, B. Le Calve, J. O. Alonso, B. Durand, Z. Bujoli and G. Hoatson, Magn. Reson. Chem., 2002, 40, 70–76.
27. D. Massiot, C. Bessada, J. P. Coutures and F. Taulelle, J. Magn. Reson., 1990, 90, 231–242.
28. W. J. Dell, P. J. Bray and S. Z. Xiao, J. Non-Cryst. Solids, 1983, 58, 1–16.
29. L.-S. Du, J. R. Allwardt, B. C. Schmidt and J. F. Stebbins, J. Non-Cryst. Solids, 2004, 337, 196–200.
30. L.-S. Du and J. F. Stebbins, J. Non-Cryst. Solids, 2003, 315, 239–255.
31. L.-S. Du and J. F. Stebbins, J. Phys. Chem. B, 2003, 107, 10063–10076.
32. X. W. Wu, R. E. Youngman and R. Dieckmann, J. Non-Cryst. Solids, 2013, 378, 168–176.
33. T. Abe, J. Am. Ceram. Soc., 1952, 35, 284–299.
34. S. Wang and J. F. Stebbins, J. Am. Ceram. Soc., 1999, 82, 1519–1528.
35. S. Sen, Z. Xu and J. F. Stebbins, J. Non-Cryst. Solids, 1998, 226, 29–40.
36. R. E. Youngman, S. T. Haubrich, J. W. Zwanziger, M. T. Janicke and B. F. Chmelka, Science, 1995, 269, 1416–1420.
37. R. E. Youngman and J. W. Zwanziger, J. Phys. Chem., 1996, 100, 16720–16728.
38. S. K. Lee and J. F. Stebbins, Geochim. Cosmochim. Acta, 2001, 66, 303–309.
39. R. L. Mozzi and B. E. Warren, J. Appl. Crystallogr., 1970, 3, 251–257.
40. C. F. Windisch and W. M. Risen, J. Non-Cryst. Solids, 1982, 48, 307–323.
41. G. Ferlat, T. Charpentier, A. P. Seitsonen, A. Takada, M. Lazzeri, L. Cormier, G. Calas and F. Mauri, Phys. Rev. Lett., 2008, 101, 065504.
42. A. K. Yadav and P. Singh, RSC Adv., 2015, 5, 67583.
43. M. Lenoir, A. Grandjean, Y. Linard, B. Cochain and D. R. Neuville, Chem. Geol., 2008, 256, 316–325.
44. B. N. Meera and J. Ramakrishna, J. Non-Cryst. Solids, 1993, 159, 1–21.
45. E. I. Kamitsos and G. D. Chryssikos, J. Mol. Struct., 1991, 247, 1–16.
46. D. Maniu, T. Illiescu, I. Ardelean, S. Cinta, N. Tarcea and W. Kiefer, J. Mol. Struct., 2003, 651, 485–488.
47. A. C. Wright, C. E. Stone, R. N. Sinclair, N. Umesaki, N. Kitamura, K. Ura, N. Ohtori and A. C. Hannon, Phys. Chem. Glasses, 2000, 41, 296–299.
48. S. K. Lee, K. Mibe, Y. W. Fei, G. D. Cody and B. O. Mysen, Phys. Rev. Lett., 2005, 94, 165507.
49. V. V. Brazhkin, I. Farnan, K. Funakoshi, M. Kanzaki, Y. Katayama, A. G. Lyapin and H. Saitoh, Phys. Rev. Lett., 2010, 105, 115701.
50. J. Sehgal, Y. Nakao, H. Takahashi and S. Ito, J. Mater. Sci. Lett., 1995, 14, 167–169.
51. K. Hirao, Z. Zhang, H. Morita and N. Soga, J. Soc. Mater. Sci. Jpn., 1991, 40, 400–404.
52. K. G. Aakermann, K. Januchta, J. A. L. Pedersen, M. N. Svenson, S. J. Rzoska, M. Bockowski, J. C. Mauro, M. Guerette, L. Huang and M. M. Smedskjaer, J. Non-Cryst. Solids, 2015, 426, 175–183.
53. M. M. Smedskjaer, J. C. Mauro and Y. Z. Yue, Phys. Rev. Lett., 2010, 105, 115503.
54. M. Bauchy, M. J. A. Qomi, C. Bichara, F.-J. Ulm and R. J.-M. Pellenq, Phys. Rev. Lett., 2015, 114, 125502.
55. B. O. Mysen and P. Richet, Silicate Glasses and Melts – Properties and Structure, Elsevier, Amsterdam, 2005.
56. M. Naji, D. D. S. Meneses, G. Guimbretiere and Y. Vaills, J. Phys. Chem. C, 2015, 119, 8838–8848.
57. Y. Kato, H. Yamazaki, S. Itakura, S. Yoshida and J. Matsuoka, J. Ceram. Soc. Jpn., 2011, 119, 110–115.

---