# The effect of pressure on the aluminoborosilicate glass optical basicity

Gabin Haryouli, Sami Soudani, Stéphane Grolleau, Michael Paris, Yann Morizet

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Gabin Haryouli, Sami Soudani, Stéphane Grolleau, Michael Paris, Yann Morizet. The effect of pressure on the aluminoborosilicate glass optical basicity. Journal of the American Ceramic Society, In press, 10.1111/jace.20359. hal-04861285

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Submitted on 2 Jan 2025

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THE EFFECT OF PRESSURE ON THE ALUMINOBOROSILICATE GLASS

OPTICAL BASICITY

Gabin HARYOULIª, Sami SOUDANIª,ᵇ, Stéphane GROLLEAUᵇ, Michael PARISᵇ, Yann MORIZETª,ᵇ*,

<footnote>ªNantes Université, Université Angers, Le Mans Université, CNRS, UMR 6112, Laboratoire de Planétologie et Géosciences, F-44000 Nantes, France</footnote>

<footnote>ᵇNantes Université, CNRS, Institut des Matériaux de Nantes Jean Rouxel, IMN, F-44000 Nantes, France</footnote>
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*Corresponding author: Yann Morizet

Postal address:

Laboratoire de Planétologie et Géosciences (LPG), UMR 6112, Nantes Université.

2 rue de la Houssinière, 44322 Nantes Cedex (FRANCE)

phone: +33 (0) 2 5112 5491

fax: +33 (0) 2 5112 5268

*E-mail: yann.morizet@univ-nantes.fr
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## Abstract

The glass optical basicity ($Λ$) is an adequate way of representing a glass composition that has been successfully applied for glasses made under ambient pressure conditions. However, we do not know if the proposed calculation based on the glass structure and the proposed measurement involving the determination of glass refractive index can apply to glasses made under high-pressure conditions.

We studied several aluminoborosilicate glass compositions synthesized under high-pressure conditions up to 3 GPa and 1250°C. Recovered glasses were characterized to determine the refractive index ($n_D$) and the density ($ρ$). The glass structure was determined using $^{11}$B and $^{27}$Al Nuclear Magnetic Resonance. Increasing pressure up to 3 GPa increases $n_D$ and $ρ$ for the studied glasses. Change in the glass structure is consistent with previous studies showing an increase in Al coordination, especially for Ca-bearing glass composition; and an increase in the proportion of $BO_4$ species. The glass optical basicity decreases with increasing pressure. From the structural changes, $Λ$ decreases by ~2% from ambient to 1 GPa in pressure for the investigated glass compositions.

## Introduction

Glass physical and chemical properties are governed by glass structure.$^{1-5}$ However, it is often difficult to describe in a simple way the glass structure and to extract the glass macroscopic properties. It is currently assumed that glass structure is a combination of structural units interconnected together forming a long range random distribution network with ordering of these units at short to medium range distances.$^{6-8}$ The structure of the glass can be deciphered using advanced analytical techniques such as Nuclear Magnetic Resonance (NMR) spectroscopy.$^{9-12}$ In aluminoborosilicate glasses, the situation is rather complex as there is a mixing between three subnetworks: silicate, borate and aluminate networks; coexisting with
cations (i.e. alkaline and/or alkaline-earth) playing the role of charge compensators or network modifying agents. In such complex glass compositions, it is often complicated to express the glass degree of polymerization corresponding to the connectivity in between the network units. To do so, it requires accessing the distribution in silicate network species (i.e. Qn species),⁶ the distribution in the boron species (i.e. BO3 and BO4)¹³⁻¹⁵ and the distribution of aluminum species (i.e. AlO4, AlO5 and AlO6).¹⁶⁻¹⁸ Hence, expressing a glass composition by a single parameter is not straightforward.

The glass optical basicity (Λ) concept has been employed for describing the physics and chemistry of glasses.¹⁹⁻²⁴ The glass optical basicity is an interesting feature as it takes into consideration the type of oxygen atoms involved into the glass structure and how they react to the presence of a nearby cation. It witnesses the capacity for oxygen atoms to donate some of their negative charges to the nearby cation.²⁰ Measurement of the glass optical basicity is not straightforward. The first method that has been developed involves the study of the absorption spectrum of element such as Pb²⁺ in the glass as an indicator.¹⁹ The absorption band of the used element is strongly influenced by the change in the glass optical basicity. However, this method supposes that the addition of the indicating element changes the glass structure, which is not preferred. Alternative methods have been employed that all relies on the application of the Lorentz-Lorenz equation that determines the glass total molar polarizability (αm in Å³):

$$ \alpha_m (\AA^3) = \frac{3}{4\pi \rho N_A} \left( \frac{n^2-1}{n^2+2} \right) \quad (1) $$

In Eq. (1), M stands for the molecular weight, N<sub>A</sub> is the Avogadro's number, ρ is the density and n is the glass refractive index. As shown in Rodriguez et al.²², the total molar polarizability can be decomposed into the contribution of the cations (α<sub>m,cat</sub>) and the oxygen atoms (α<sub>m,ox</sub>) such as:

$$ \alpha_m (\AA^3) = \sum_i (x_i q_{ox,i} \alpha_{ox,i} + x_i p_{cat,i} \alpha_{cat,i}) = F_{ox} \alpha_{ox} + \alpha_{m,cat} = \alpha_{m,ox} + \alpha_{m,cat} \quad (2) $$
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Where $x_i$ is the molar fraction of oxides, p and q are the number of cations and oxygen atoms per oxide. Hence, the average oxygen polarizability ($\alpha_{ox}$) can be extracted with division by $F_{ox}$, the fractional oxygen atoms in the glass. Once the $\alpha_{ox}$ is obtained, the glass optical basicity can be determined through the following equation:

$$ \Lambda_n = 1.67 \left( 1 - \frac{1}{\alpha_{ox}} \right) \quad (3) $$

In Eq. (3), the subscript n indicates that for determining the glass optical basicity, only the glass density and refractive index are required according to Eq. (1). Previous works$^{20,21}$ also proposed a general equation to calculate the glass optical basicity ($\Lambda_{th}$) such as:

$$ \Lambda_{th} = \sum_i X_i \Lambda_i \quad (4) $$

Where $X_i$ is the equivalent fraction based on the amount of oxygen in each oxide and $\Lambda_i$ is the basicity parameter that can be found in the literature for each oxide.$^{22,24}$ The glass optical basicity can be calculated with the sole knowledge of the glass composition. However, implementations can be added to the present calculation to obtain a more accurate value of the glass optical basicity. For instance, the landmark work by Dimitrov et al.$^{25}$ clearly states that consideration of the different network units distribution (i.e. $Q^n$ species; $BO_3$ and $BO_4$; $AlO_4$, $AlO_5$ and $AlO_6$) within the glass structure is required to obtain a calculated value that is closer to the true value of the glass optical basicity. Whereas the $BO_3$ and $BO_4$ distribution and the $AlO_4$, $AlO_5$ and $AlO_6$ distribution can be easily obtained from $^{11}$B and $^{27}$Al NMR, the quantitative determination of $Q^n$ species distribution within the glass is much more challenging and, for the low amount of glass produced under high-pressure conditions, requires the $^{29}$Si enrichment of the glass to achieve NMR acquisition.$^{13,14,26-29}$

Optical basicity parameters are available in the literature for $BO_3$, $BO_4$, $AlO_4$ and $AlO_6$ species; to our knowledge, optical basicity parameter for $AlO_5$ and different $Q^n$ species is not
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available. For instance, Dimitrov et al.²⁵ mentioned values of 0.42 and 0.24 for ΛBO₃ and ΛBO₄, respectively. Komatsu et al.³⁰ mentioned values of 0.60 and 0.40 for ΛAlO₄ and ΛAlO₆, respectively. Considering 1) the large range in BO₃/BO₄ distribution in aluminoborosilicate glasses as a function of chemical composition, 2) the possible change in Al speciation as a function of glass composition and 3) the non-negligible difference in the optical basicity parameters, it implies that the true glass optical basicity is difficult to obtain.³¹⁻³³

It should be emphasized that the notion of glass optical basicity has been developed for glasses made at ambient pressure conditions; previous equations and calculations might not apply for glasses made under conditions different from 1 bar. In fact, it has been recently demonstrated that high-pressure conditions strongly influence the glass structure for aluminoborosilicate glass composition and especially the distribution in between BO₃ and BO₄ species. All studies point towards the conversion of BO₃ species into BO₄ species with increasing pressure, which would induce a major change in the glass optical basicity.³⁴⁻⁴¹ Allwardt et al.²⁷ showed that increasing pressure induces an increase in the proportion of highly coordinated Al species (i.e. AlO₅ and AlO₆), which would also induce a change in the glass optical basicity. To our knowledge, the impact of pressure has never been taken into account for calculating a glass optical basicity for glasses synthesized under high-pressure conditions. However, obtaining a well-approached value for glass optical basicity is a prerequisite for various chemical processes such as the modelling of volatile species incorporation into the glass structure. Recent work by Morizet et al.⁴² showed that iodine solubility in aluminoborosilicate glasses synthesized at 1.5 GPa is positively correlated with the increase in glass optical basicity. However, they pointed out that glass optical basicity could only be partially approached due to the fact that the network units speciation was not taken into account. Clearly, this lack of information is detrimental for building up reliable models for volatile solubilities in glasses of various compositions.
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We have attempted to tackle this problem and to determine if a substantial correction is required for glass optical basicity synthesized under high-pressure conditions. We synthesized several high-pressure glass series up to 3.0 GPa. The recovered glasses were investigated optically for determining the glass refractive index and density as a function of pressure conditions. The glass structure was also studied by ¹¹B and ²⁷Al NMR to determine the element speciation as a function of pressure. We calculated the glass optical basicity as a function of pressure using the different methods and compared the obtained values together.

A discussion on the effect of pressure on glass optical basicity is also proposed.

## Experimental syntheses

### Starting materials

The investigated glass compositions were studied in previous works and an additional glass composition was also prepared.⁴³⁻⁴⁵ All the investigated glasses have compositions in the $SiO_2-B_2O_3-Al_2O_3-CaO-Na_2O$ system (see Table 1; i.e. $ZrO_2$ is also present in ISG). The first glass composition is the International Simple Glass (ISG) that corresponds to a standardized, highly polymerized nuclear waste glass defined by Gin et al.⁴⁶ and a surrogate of the French SON68 glass for immobilizing high-activity nuclear waste. This glass composition has been widely studied, even under high-pressure conditions.⁵,⁴⁴,⁴⁷ The second glass (NH) is a typical Low Activity Waste (LAW) that has been studied for the incorporation of iodine by Jolivet et al.⁴⁴. This glass composition is less polymerized than ISG considering the lower $SiO_2$ content (~45 mol.%) and higher $Na_2O$ content (~23 mol.%). The third glass (SHM) is a Ca-rich, Na-free glass composition. This glass composition is targeted as we expect large changes in the glass structure upon pressure: 1) change in B speciation and 2) change in the Al-speciation; as suggested in recent works.⁴⁰,⁴¹
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Except from ISG that is coming from an industrial batch provided by Dr. S. Gin, the other
glasses were prepared from a mixture of spec pure oxides (SiO2, B2O3, Al2O3 and CaO) and
carbonate (Na2CO3). The oxide mixtures were melted at 1200°C for 1 hour in a Pt crucible in
a box furnace. The melt was quenched to a glass by pouring the bottom of the Pt crucible in a
bowl of water. The recovered glasses were characterized for major element concentration (see
Table 1) and were used to conduct the high-pressure experiment. It should be pointed out that
the SHM glass experienced a major B2O3 loss during the ambient pressure synthesis; a
phenomenon that is currently well-known. We targeted a composition with 30 mol.% and
only 15 mol.% remained in the glass (see Table 1). However, this does not have any impact
on the scientific message considering that ambient pressure glass was used for the high-
pressure experiments.

## High-pressure syntheses

The ambient pressure glasses were crushed into powder and loaded into a 5.0-5.4 mm
diameter Pt capsule for the high-pressure experiments up to 2.0 GPa. For the 3.0 GPa pressure
experiment on SHM, we used 4.0-4.4 mm diameter Pt capsule. The Pt capsule is welded shut
by arc welding. We conducted the high-pressure experiments in an Oxford-type end-load
piston-cylinder apparatus. We used a ¾ inch pressure plate for reaching pressures between 0.5
and 2.0 GPa; and we used a ½ inch for the experiment at 3.0 GPa. The prepared Pt capsule is
then loaded into a ¾ and ½ inch talc-Pyrex assemblies for the experiments. The high-pressure
assembly consists in an outer talc sleeve, intercalated Pyrex sleeve and a graphite furnace with
straight walls. The Pt capsule is placed inside a Magnorite© ceramic piece. The experimental
protocol for the high-pressure experiments has been described in previous works.⁴⁰ We kept
run duration short (1h). Even with the observed precautions, we could not avoid graphite to be
present after the experiments in the recovered glasses. During the experiment, the temperature
is monitored by a Eurotherm accurate to ±1°C that is connected to a type S thermocouple (Pt-
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PtRh₁₀). We applied a +10% correction to the pressure to account for internal frictions involved in talc compression. The samples are quenched isobarically so as to prevent from the glass structure to record a fictive pressure structure lower than the experimental pressure as inferred in previous works.⁴⁸,⁴⁹ For ¾ inch pressure plate, the quench rate has been estimated to ~100°C/s; for ½ inch pressure plate, the quench rate is much higher and estimated to ~150°C/s in the first 500°C.

The recovered glasses are colored in black due to graphite presence in most of the case. For instance, the high-pressure ISG and SHM glasses are colored in black whereas the NH glasses are totally transparent after the high-pressure experiments. Previous work documented the high-pressure sample blackening, however, in the case of Brooker et al.⁵⁰ the blackening was due to the possible diffusion of hydrogen coming from the talc dehydration; diffusing through the Pt capsule walls and reducing the CO₂ into graphite. The blackening of our samples cannot result from the same process and we suggest that organic impurity (either in the glass powder or the capsule inside wall) or even the CO₂ present in the entrapped atmosphere could be responsible from the presence of graphite at the end of the high-pressure experiment.

Currently, we do not know the influence of the dissolved graphite in glass on the present results; however, the NMR characterization is insensitive to the presence of graphite.

Although the graphite concentration has not been quantified, we suspect its quantity is relatively small (on the order of a few ppm) because the glass is not entirely tainted in black.

The problem of graphite dissolution in glass structure has never been clearly addressed.

Although, the presence of graphite is not supposed to affect the structure of glass as C atoms do not interact with the aluminoborosilicate network; recent work suggested that C could exchange with O atoms from the silicate network under moderately reducing atmosphere conditions (i.e. Ar gas).⁵¹ Considering that graphite colors the glass, we suspect that the
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presence of graphite affects the refractive index measurements. Therefore, the presence of
graphite and its impact on aluminoborosilicate glass properties is still to be deciphered.

For the remaining of the manuscript, we adopted the following sample nomenclature: Name
of the composition followed by the pressure condition. For example, the NH-2.0 stands for the
glass of NH composition synthesized at 2.0 GPa.

**Analytical methods**

*Glass major element concentration*

We used a JEOL JSM 5800LV Scanning Electron Microscope coupled to an SSD SAMx
Energy Dispersive Spectrometer (SEM-EDS) to characterize the ambient pressure glass for
major element concentrations (except for B₂O₃, Table 1). The glass chips were embedded into
epoxy plugs and polished down to 1 µm before carbon coating (25 nm thick). The analytical
conditions were 15 kV for voltage and 0.5 nA for current. The spot size was set to
approximatively 20 µm to avoid Na loss under the electron beam. Each sample has been
analyzed 5 to 10 times with a measurement time of 1 min. We used the internal standards for
the element quantification: corundum for Al₂O₃, wollastonite for SiO₂ and CaO and NaCl for
Na₂O. We measured a standard deviation from 0.1 to 0.9 mol.% from the replicated
measurements that is considered to represent the homogeneity in the element distribution
within the glass.

We used Laser Ablation-Inductively Coupled Plasma-Mass Spectroscopy (LA-ICP-MS) for the quantification of B₂O₃ in SHM and NH glasses. The measurements were conducted on a Quadrupole ICP-MS (Varian Bruker 820-MS) with ablation by an ArF excimer laser (193 nm, Analyte G2, Photon Machines) in an HelEx II 2-Volume Cell with He as carrier gas. The laser energy density is 4.54 J.cm⁻² with a repetition rate of 10 Hz. The spot size is set to 110 µm and the acquisitions are performed on 30 s with points collected every 0.25 s (120 pts per
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analysis), preceded and followed by a 30 s blank acquisition. We conducted 5 analyses on glass samples. We used the protocol described in previous works for the quantification.<sup>40,52</sup> The standard deviation on the measured B<sub>2</sub>O<sub>3</sub> is better than 0.1 mol.%.

## Refractometry

The glass refractive index ($n_D$) has been measured using a NAR 1T Solid© Abbe refractometer from Atago® fitted with a light operating at 589 nm corresponding to the Na D-line. We used monobromo-naphtalene with refractive index of 1.6570 as a contact liquid between the Abbe refractometer prism and the glass sample. The measurement accuracy from the refractometer is on the order of ±0.001 for $n_D$ value.

Acquisitions are conducted on glass polished wafers. On one side, we polished down to 1 µm and a coarse polishing (~8 µm) was done on the other side to avoid multiple internal interferences. In most of the case, the size of the wafer is below 4x4 mm² (i.e. lower than the capsule diameter), which is small for conducting refractive index measurements using Abbe refractometer (usually 8x8 mm²). Several high-pressure glass samples could not be analyzed due to their small size. In order to test the reproducibility and correctness of the measurements, at least 12 measurements were performed for all glass chips during different day-to-day sessions (i.e. one glass chip has been analyzed several times). The standard deviation derived from the replicated measurements is better than ±0.007 for SHM and ISG glasses, whereas for NH glasses, the standard deviation appears higher at ±0.02. Although this later value appears higher than expected, the derived standard deviation for most of the high-pressure glasses is lower than the observed $n_D$ variation (see Table 1). We tried, as much as possible; to select glass wafers showing the less graphite evidence; however, this pollutant cannot be entirely avoided.

## Pycnometry
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The measurement of the glass density was carried out on a Micromeritics© AccuPyc II 1340 operating under helium gas. Owing to the small size of the high-pressure glass samples (i.e. few tenths of mg), an Al metal insert was placed to reduce the chamber size (0.1 µL) and allows a better measurement of the helium gas volume. More than 10 replicated cycle measurements were conducted on each glass sample for obtaining a standard deviation value on the density measurements. On average, the observed deviation on density is ±0.01 (see Table 1) suggesting a good consistency in the replicated measurements. For ISG-1.5, we determined a standard deviation at ±0.053 that is ascribed to the lower mass that has been used for measuring the density (0.009 g).

Density measurements were conducted on the standardized ISG glass (i.e. ISG-0). We measured the ISG density on a glass fragment of 245 mg (30 measurements). The density obtained was 2.495, respectively. This value is in good agreement with previous reported data suggesting a density on the order of 2.5.⁵,⁴⁷ For SHM-3.0 and ISG-1.0, we could not obtain a reliable density measurement possibly due to polluting particles (Pt from the capsule) incorporated into the glass sample during the capsule opening. However, considering that the SHM density data are reliable at the lower pressure, we extrapolated the density for SHM-3.0 using linear regression of the data at 3.154 (see Table 1).

### ¹¹B and ²⁷Al MAS NMR spectroscopy

For most of the synthesized high-pressure glasses, we acquired ¹¹B and ²⁷Al NMR data on a Bruker Avance III 500 MHz (11.7 T, IMN Jean-Rouxel) spectrometer with a 2.5 mm Magic Angle Spinning (MAS) probe at Larmor frequency of 160.46, 132.29 and 130.32 MHz, respectively. The finely crushed glass powder was loaded into ZrO₂ rotor with Teflon caps. The ¹¹B and ²⁷Al acquisitions were performed at MAS frequency of 20 kHz with a single π/12 excitation pulse and a radio frequency field strength of 20 kHz. The spectra were referenced
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against H₃BO₃ (19.6 ppm) and Al(NO₃)₃ (0 ppm) solutions for ¹¹B and ²⁷Al, respectively. For ¹¹B and ²⁷Al, 512 and 2048 scans were collected, respectively.

For aluminoborosilicate glasses, the ¹¹B spectra consist in the contribution of two main spectroscopic bands: the asymmetric 3B (i.e. BO₃) and the Gaussian 4B (i.e. BO₄) bands. We followed the protocol described in Angeli et al.²⁸ and Soudani et al.⁴¹ for treating the ¹¹B NMR spectra that consists in two main steps: 1) the subtraction of the probe signal using a reference spectrum of an empty rotor acquired in the same conditions, 2) the subtraction of the central transition by subtracting the same spectra shifted by 20 kHz.

## Results

*Refractive index and density change as a function of pressure*

We show in Figure 1A the change in n<sub>D</sub> as a function of pressure for the three investigated glass compositions: ISG, NH and SHM. The corresponding data are provided in Table 1 along with the standard deviation calculated from the replicated measurements. We added linear trend for each series in Figure 1A. At ambient pressure, the n<sub>D</sub> value is 1.532, 1.534 and 1.544 for ISG-0, NH-0 and SHM-0, respectively. Whereas we do not have any reference for the refractive index for NH and SHM glass compositions, the refractive index for ISG has been determined in previous studies. Guerette and Huang<sup>47</sup> determined n = 1.5315 at 532 nm using a prism coupler, which is in good agreement with the present determination using the Abbe refractometer at 589 nm. Kaspar et al.<sup>5</sup> found similar results using ellipsometric measurements.

We observe that the n<sub>D</sub> values are very close for ISG-0 and NH-0 despite the difference in glass composition: 1.532 and 1.534, respectively. On the contrary, the n<sub>D</sub> value for SHM-0 is slightly different: 1.544. Recent work by Wu et al.<sup>53</sup> observed a slight decrease (0.001) in the refractive index with increasing B<sub>2</sub>O<sub>3</sub> from 5 to 25 mol.%; therefore, we do not believe that
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change in n<sub>D</sub> from 1.532 to 1.544 could be due to the change in B<sub>2</sub>O<sub>3</sub> content between NH (16.5 mol.%) and SHM glasses (13.9 mol.%). One possible explanation that requires to be further investigated is the fact that NH and ISG glass compositions are both Na<sub>2</sub>O and CaO bearing whereas the SHM glass composition is only CaO bearing and Na<sub>2</sub>O free.

As a function of pressure, there is a systematic increase in the n<sub>D</sub> value from ambient pressure to 3.0 GPa, regardless of the glass composition. The n<sub>D</sub> behavior as a function of pressure has been documented on different type of glass compositions and using different methods.<sup>36,47</sup>

The change in n<sub>D</sub> for SHM glass composition appears less important than for NH and ISG between ambient pressure and 2.0 GPa. For instance, the n<sub>D</sub> changes from 1.544 to 1.567 between SHM-0 and SHM-2.0 whereas the n<sub>D</sub> change is from 1.532 to 1.565 between ISG-0 and ISG-1.5 and from 1.534 to 1.577 between NH-0 and NH-2.0. We explain this different behavior by the difference in the glass compositions. We also observe that the n<sub>D</sub> change for SHM is progressive between 1 bar and 2.0 GPa whereas there is an abrupt change in the n<sub>D</sub> for ISG and NH located at 1.0 GPa. Currently, this inflection is not clearly explained.

According to the Lorentz-Lorenz equation the increase in the refractive index will induce a change in the glass optical basicity value calculated from glass density and refractive index (A<sub>n</sub>).

We have reported the change in the glass density as a function of pressure in Figure 1B; linear trend were added. The obtained glass density at ambient pressure is on the order of 2.5 and is increasing with increasing pressure. The increase in glass density as a function of pressure has been documented previously;<sup>54,55</sup> hence, the results shown in Figure 1B are in good consistency. The density increase seems more important for ISG and SHM than for NH. For NH, there is an increase in density of ~10% from 2.514 to 2.738 between 1 bar and 2.0 GPa. For ISG, there is an increase in density of ~20% from 2.495 to 2.935 between 1 bar and 1.5 GPa. Considering that in the Lorentz-Lorenz equation the oxygen polarizability (α<sub>O2</sub-)</sub>
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inversely correlated to the partial molar volume of the glass (i.e. to the density), therefore, the
results point towards a decrease in the optical basicity calculated from the nD and ρ values.

$^{11}$B and $^{27}$Al MAS NMR spectra

$^{11}$B MAS NMR spectra obtained for glasses synthesized at different pressures (1 bar, 1.0 and 2.0 GPa) are shown in Figure 2: A, ISG; B, NH and C, SHM glasses. The $^{11}$B NMR spectra are composed of two main signals: one intense peak with peak maximum centered at 0 ppm and one broad less intense asymmetric peak centered at 12 ppm. The first peak is assigned to boron atom in tetrahedral configuration ($BO_4$) and the second is assigned to boron atom in planar trigonal configuration ($BO_3$) as determined by previous studies.$^{14,28,30,43}$ We observe that the distribution of the $BO_3$ and $BO_4$ species is a function of the glass composition. For instance, ISG glass composition has a more intense $BO_4$ peak than the other glass compositions. On the other hand, the SHM glass spectra show a reduced $BO_4$ peak as compared to the $BO_3$. The distribution of the boron species is often described by the $N_4$ value corresponding to the proportion of $BO_4$ species and calculated as follows: $[BO_4] / [BO_3] + [BO_2]$.

From Figure 2, we observe that there is a change in the $^{11}$B spectra for each glass composition
as a function of pressure. Invariably, increasing the glass synthesis pressure induces an
increase in the $BO_4$ peak intensity (i.e. $BO_4$ proportion). The change in the $BO_4$ and $BO_3$ peak
intensity does not seem monotonic with increasing pressure for a given glass composition.
Actually, the same observation has been recently made by Soudani et al.$^{41}$. Between 1 bar and
2.0 GPa, there is a gradual decrease in the $BO_3$ peak and a corresponding increase in the $BO_4$
peak for NH glasses. For ISG, there is also an increase in the $BO_4$ peak intensity and a
decrease in the $BO_3$ peak intensity, however, this change appears to occur only above 1.0
GPa; in other words, the $^{11}$B NMR spectrum obtained at 1.0 GPa is almost identical to the $^{11}$B
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<figure><img src="image_31.png" /></figure>

NMR spectrum obtained at 1 bar. There is also a change in the peak line shape at 2.0 GPa on the BO₄ peak. The BO₄ peak maximum appears to be shifted to a lower ppm value indicating that there is a change in the distribution of the different BO₄ units as suggested in previous works.<sup>12,56</sup>

Typical <sup>27</sup>Al NMR spectra are shown in Figure 3. The spectra exhibit a broad asymmetric line shape with a peak maximum around 60 ppm and extending to negative ppm values. Due to the quadrupolar nature of the <sup>27</sup>Al nuclei, the distribution of the electric field gradient is partly responsible for this broadening and peak asymmetry. However, there is a distribution in the different Al species that is currently well-known:<sup>16,27,37,38,57</sup> 4-, 5- and 6-fold coordinated Al species located at ~60, ~30 and 0 ppm, respectively. The distribution of the different Al species is a function of the glass composition. For instance, for Na-bearing glass compositions (i.e. ISG and NH), Al species are mostly AlO₄; whereas in Na-free SHM glass, there is a non-negligible contribution of the AlO₅ and AlO₆ species. The pressure increase induces an increase in the proportion of the highly coordinated Al species as seen in Figure 3. For ISG and NH, there is a slight increase in the AlO₅ peak intensity between 1 bar and 2.0 GPa and accompanied by a decrease in the AlO₄ peak intensity. For SHM, the same mechanism occurs, however, there is also an increase in the AlO₆ peak along with the decrease in the AlO₄ with increasing pressure between 1 bar and 3.0 GPa. Such behavior of the Al species with increasing pressure has been documented in previous studies for various types of glass composition. It has been shown that the increase in pressure induces an increase in the Al coordination number in glass and that this increase is much more exacerbated in glass compositions with alkaline-earth cations rather than alkaline cations.<sup>49,58,59</sup>

We have calculated the BO₃ and BO₄ proportions and the AlO₄, AlO₅ and AlO₆ proportions using the subsequent <sup>11</sup>B and <sup>27</sup>Al NMR spectrum simulations produced by DMFit software, respectively.<sup>60</sup> Typical simulations are shown in Figure 4 for two selected NMR spectra (<sup>11</sup>B,
<figure><img src="image_32.png" /></figure>

<figure><img src="image_33.png" /></figure>

Figure 4A and <sup>27</sup>Al, Figure 4B) for NH glasses at 1 bar (NH-0) and 2.0 GPa (NH-2.0). We provide the entire set of spectrum simulations in Suppl. Mat., along with the entire set of derived parameters from the fits. The error on each derived parameter has been obtained from the software package. The <sup>11</sup>B NMR spectra are simulated using two Gaussian lines for BO<sub>4</sub> species with different next nearest neighbors.<sup>61,62</sup> In NH-0, the peaks with δ<sub>iso</sub> at 1 and -0.5 ppm have been assigned to BO<sub>4</sub> unit surrounded by 3 silicon and 1 boron units (BO<sub>4</sub>(1B,3Si)) and to BO<sub>4</sub> unit surrounded by 4 silicon and 0 boron units (BO<sub>4</sub>(0B,4Si)), respectively. The BO<sub>3</sub> broad peak has been simulated by two asymmetric lines that could be assigned to BO<sub>3</sub> units (the so-called ring and non-ring configurations).<sup>14,28,41,61</sup> The δ<sub>iso</sub> for those BO<sub>3</sub> units is determined at 19 and 16 ppm for ring and non-ring units, respectively.

The <sup>27</sup>Al NMR spectra have been simulated with 2 to 3 peaks depending on the presence of the presence of highly coordinated AlO<sub>6</sub> species. We used Czjzek spectral line that is the typical line shape used for the simulation of <sup>27</sup>Al NMR spectra.<sup>41</sup> For instance, in Figure 4B, there is the clear presence of AlO<sub>4</sub> and AlO<sub>5</sub> but AlO<sub>6</sub> is almost absent or close to 0 in intensity. The derived peak δ<sub>iso</sub> is consistent with previous studies on the local environment of Al in glasses with δ<sub>iso</sub> of ~65, 30 and 3 ppm for AlO<sub>4</sub>, AlO<sub>5</sub> and AlO<sub>6</sub> units.<sup>16</sup> As expected and demonstrated in previous works, there is an increase in the proportion of highly coordinated Al species with increasing pressure.<sup>26,37</sup> This increase appears much more pronounced for SHM glass composition than ISG and NH glass compositions.

The N<sub>4</sub> and CNA<sub>1</sub> values are given in Table 1. We clearly observe that increasing the pressure induces an increase in the N<sub>4</sub> value, regardless of the glass composition. Between 1 bar and 2.0 GPa, N<sub>4</sub> increases from 0.31 to 0.44, from 0.48 to 0.54 and from 0.19 to 0.36 for NH, ISG and SHM, respectively. Owing to the various types of glass compositions, it is difficult to compare those results with previous studies investigating the effect of pressure on the N<sub>4</sub> value; however, the derived N<sub>4</sub> values for ambient pressure ISG-0 and NH-0 glasses is
<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>

consistent with previous studies: ~0.5 for ISG63 and 0.37 for NH44. The error on the N4 and CNAl values are small, on the order of 5-10% in relative to the value.

A discussion on the detailed change in the boron and aluminum species with respect to the glass structure (i.e. the degree of polymerization) is beyond the scope of this work and we have considered these changes on a more global view and on the prism of optical basicity change. Without exception, increasing pressure induces an increase in the coordination of the Al and B species: AlO4 to AlO5 and AlO6, BO3 to BO4. Dimitrov and Komatsu64 described how the distribution of boron and aluminum species should be taken into account for calculating the glass optical basicity. Hence, the observed change in the 11B and 27Al NMR spectra as a function of pressure will be accompanied by a change in the value of the glass optical basicity.

Discussion

*Consistent changes in B and Al speciation in glass as a function of pressure*

Boron speciation is usually represented by the proportion of BO4 units expressed as the N4 parameter. Aluminum speciation is on the other hand represented by the average coordination number defined as $CN_{Al} = 4 \times [AlO_4] + 5 \times [AlO_5] + 6 \times [AlO_6]$. We have represented those parameters as a function of pressure in Figure 5. As mentioned earlier, the error on each data point has been determined from error propagation using the standard deviation obtained on the species proportions and is within the size of the point. For clarity, we provide in Table 1 the N4 and CNAl values and not the proportion of the different species (i.e. BO3, BO4, AlO4, AlO5 and AlO6) that will be used to calculate glass optical basicity; however, those data can be found in the Suppl. Mat.. The observed trends for N4 (Figure 5A) and CNAl (Figure 5B) are consistent with results reported in previous studies. First of all, the N4 values are in agreement with current knowledge. For instance, the ISG-0 N4 is 0.48 that is close to previously reported
<figure><img src="image_36.png" /></figure>

<figure><img src="image_37.png" /></figure>

values for the same glass composition: 0.58 in Charpentier et al.⁶⁵; 0.52 in Collin et al.⁶⁶; 0.45 in Jolivet et al.⁴³; 0.50 in Jolivet et al.⁴⁴. We obtained a lower N₄ value for NH-0 (0.31) and SHM-0 (0.19) glasses that is expected owing to the lower K' values for those glass compositions, which would lead to a lower N₄ value according to B speciation model.¹⁴,⁴³,⁵⁷

The increase in N₄ with increasing pressure has been shown in several works.²,³⁴⁻³⁷,⁵⁸ For NH and SHM glasses, the increase in N₄ is monotonic with pressure. The most important change in N₄ is observed for SHM with N₄ changing from 0.19 to 0.36 between SHM-0 and SHM-2.0. Both NH and SHM glasses have depolymerized structures and it is commonly assumed that increasing pressure for depolymerized glass will result in an increase in the glass polymerization. It is consistent with the increase in the B and Si intermixing and the associated increase in the BO₄(4Si) with pressure. On the contrary, ISG glass is optimized to be polymerized;⁴⁶ therefore pressure increase could result in almost no effect on the glass polymerization at first (up to 1.0 GPa) then followed by the conversion of BO₃ into BO₄ units above 1.0 GPa.

The change in CN<sub>Al</sub> as a function of pressure in Figure 5B is also consistent with previous studies.<sup>16,26,35</sup> It has been shown that Na-rich glass compositions do not favor the formation of highly coordinated Al species. On the contrary, alkaline-earth bearing glass compositions will strongly enhance the conversion of AlO<sub>4</sub> into AlO<sub>5</sub> and AlO<sub>6</sub> units, therefore increasing the CN<sub>Al</sub> value even at ambient pressure. We derived a higher CN<sub>Al</sub> for SHM-0 (4.23, Na-free) as compared to the CN<sub>Al</sub> derived for NH-0 and ISG-0 (4.00, Na-bearing). The observed pressure effect on CN<sub>Al</sub> was also expected. The CN<sub>Al</sub> for ISG is not affected, the CN<sub>Al</sub> is slightly affected for NH and the CN<sub>Al</sub> is strongly affected for SHM. For this latter glass composition, the CN<sub>Al</sub> changes from 4.23 to 4.54 between ambient and 2.0 GPa pressure.

*Changes in glass optical basicity as a function of pressure: from optical and from structure measurements*
We calculated the glass optical basicity from the refractive index ($\Lambda_n$) using the Lorentz-Lorenz equation (Eq. 1) and subsequent equations. The results are provided in Table 1 and shown in Figure 6 as a function of pressure. The ambient pressure $\Lambda_n$ determined is compared to the optical basicity calculated from theoretical chemical composition ($\Lambda_{th}$). Using the optical basicity parameters from Rodriguez et al.²², we calculated $\Lambda_{th}$ at 0.523, 0.574 and 0.570 for ISG-0, NH-0 and SHM-0, respectively. The respective $\Lambda_n$ is 0.566, 0.631 and 0.599 for ISG-0, NH-0 and SHM-0. As a function of pressure in Figure 6, we see a clear distinct behavior in between the glass compositions. We observe a strong decrease in the $\Lambda_n$ for ISG and SHM glasses whereas the $\Lambda_n$ for NH only slightly decreases: $\Lambda_n$ for SHM changes from 0.599 to 0.420 between ambient and 3.0 GPa; $\Lambda_n$ for ISG changes from 0.566 to 0.433 between ambient and 1.5 GPa; $\Lambda_n$ for NH changes from 0.631 to 0.607 between ambient and 2.0 GPa. The error bar on $\Lambda_n$ is difficult to extract; however, in most of the reported works,²⁰,²¹,⁶⁷ the optical basicity is given with two significant digits. Hence, the change observed in Figure 6 for ISG and SHM glasses is above any possible error bars.

In Figure 6, we have reported the $\Lambda_n$ calculated from the refractive index and glass density from the high-pressure experimental studies of Kuryaeva et al.⁵⁴ and Kuryaeva⁵⁵. We observe that the derived $\Lambda_n$ follows a similar to our NH glasses. Kuryaeva et al.⁵⁴ and Kuryaeva⁵⁵ performed the high-pressure experiment using diamond anvil cells up to 6.0 GPa and at ambient temperature. Hence, their data did not suffer from the presence of polluting graphite impurities with this experimental protocol. Our synthesized NH glasses did not show evidence of graphite impurities on the contrary to ISG and SHM glasses. As a result, we suggest that the strong decrease observed in the $\Lambda_n$ for ISG and SHM glasses is possibly due to the presence of graphite. It implies that the evolution in $n_D$ value with pressure shown in Figure 1 is probably erroneous for graphite bearing glasses. In addition, it suggests that determining the glass refractive index will require a more advanced approach. We have pointed out the fact

<figure><img src="image_38.png" /></figure>

<figure><img src="image_39.png" /></figure>
that the measurement of n<sub>D</sub> value is subject to caution considering the size of high-pressure glasses that is too small to allow adequate measurement for n<sub>D</sub>. Nevertheless, the trends shown in Figure 6 all point towards a decrease in the glass optical basicity with increasing pressure.

We calculated optical basicity based on glass structure with an implemented version of Eq. (4) that integrates the proportion of the structural units: BO<sub>3</sub>, BO<sub>4</sub>, AlO<sub>4</sub>, AlO<sub>5</sub> and AlO<sub>6</sub>; such as Λ<sub>N4+CNAI</sub>:

$$ \Lambda_{N4+CNAI} = X_{SiO2}\Lambda_{SiO2} + X_{CaO}\Lambda_{CaO} + X_{Na2O}\Lambda_{Na2O} + X_{B2O3}[N4\Lambda_{BO4} + N3\Lambda_{BO3}] + X_{Al2O3}[[AlO4]\Lambda_{AlO4} + [AlO5]\Lambda_{AlO5} + [AlO6]\Lambda_{AlO6}] \quad (5) $$

In Eq. (5), N<sub>3</sub> corresponds to the proportion of BO<sub>3</sub> species and therefore is equal to 1-N<sub>4</sub>. We used the Λ<sub>BO4</sub> and Λ<sub>BO3</sub> of 0.24 and 0.42 mentioned in Dimitrov et al.<sup>25</sup>, respectively. We used the values of 0.60 and 0.40 for Λ<sub>AlO4</sub> and Λ<sub>AlO6</sub> reported in Komatsu et al.<sup>30</sup>. Since there is no value for Λ<sub>AlO5</sub> in the literature, we choose to use an average value of 0.50 between the Λ<sub>AlO4</sub> and the Λ<sub>AlO6</sub> values. The data are provided in Table 1. In Figure 7, we plot the Λ<sub>N4+CNAI</sub> as a function of pressure for the investigated glass compositions. We also added the data from Soudani et al.<sup>41</sup> for various Ca- and Na-bearing glass compositions recently published. Invariably, there is a decrease in the glass optical basicity with increasing pressure. The observed change is similar to the change in Λ<sub>n</sub> for NH glass in Figure 6. The most important change in the Λ<sub>N4+CNAI</sub> is determined for SHM with 0.562 for SHM-0 at ambient pressure and decreasing to 0.549 for SHM-3.0 at 3.0 GPa.

The change with pressure is on the order of ~2% in relative to the value. It is not clear if such a low variation in the optical basicity could have major implication in model building using optical basicity. Considering a typical error of ±0.01 on the optical basicity value suggests that the effect of pressure is relatively limited. Nonetheless, we can observe that the ambient
<figure><img src="image_40.png" /></figure>

<figure><img src="image_41.png" /></figure>

pressure $\Lambda_{N4+CNAI}$ is not identical to the $\Lambda_{th}$ and the glass structure consideration (i.e. element speciation) has a non-negligible impact on optical basicity value. Considering B and Al species distribution into the calculation induces a slight decrease in the optical basicity, which we believe is required to approach the true glass optical basicity. Nevertheless, to a first approximation, one can employ the theoretical glass optical basicity as defined by Duffy and Ingram¹⁹ for high-pressure glasses without having to apply a correction.

## Summary

We have synthesized several aluminoborosilicate glass compositions at pressure up to 3.0 GPa to investigate the change in glass optical basicity. We determined the glass optical basicity from glass refractive index and density measurements. We also approached the glass optical basicity from glass structure analysis. All results indicate a decrease in the glass optical basicity with increasing pressure. We also showed that it appears difficult to determine in an adequate way the glass optical basicity using refractive index due to multiple factors: small size of high-pressure samples and the presence of graphite impurities. Other micrometric techniques such as ellipsometry could represent an adequate solution to determine at micrometer scale the glass refractive index. Alternatively, the determination of the network unit distribution within the glass structure is probably the most appropriate method to approach the true value of the glass optical basicity even under pressure.

## Acknowledgments

The authors are grateful to the Agence Nationale de la Recherche, which financed the current work through the ANR project "Iodine-CLEAN-UP" (ANR-20-CE08-0018). The authors thank the Région Pays de la Loire for financing the present research through the "Trajectoire nationale de la recherche ligérienne" program. The authors thank the Laboratoire de Planétologie et Géosciences, Nantes Université and the CNRS for providing access to the
<figure><img src="image_42.png" /></figure>

<figure><img src="image_43.png" /></figure>

analytical facilities. SEM-EDS and NMR measurements were performed using the IMN's
characterization platform, PLASSMAT, Nantes, France. We thank José Ferreira for handling
our manuscript and the two anonymous reviewer for helping us to greatly improve the present
manuscript.

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Figure caption

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Figure 1: A) Change in glass refractive index ($n_D$) as a function of pressure in GPa. B)

Change in glass density ($\rho$ in kg.m$^{-3}$) as a function of pressure. The open symbols correspond to density data that have been calculated and not measured. The error bars on $n$ and $\rho$ were determined from replicated measurements.

Figure 2: $^{11}$B MAS NMR spectra acquired on ISG (A), NH (B) and SHM (C). The spectra are shown as a function of pressure. We observe an increase in the $BO_4$ peak intensity and a decrease in the $BO_3$ peak intensity with increasing pressure.

Figure 3: $^{27}$Al MAS NMR spectra acquired on ISG (A), NH (B) and SHM (C). The spectra are shown as a function of pressure and have been scaled to the same area. Increasing pressure induces a change in Al speciation with appearance of Al species with higher coordination: $AlO_5$ and $AlO_6$.

Figure 4: Typical fit of NMR spectrum for $^{11}$B (A) and $^{27}$Al (B). The $BO_3$ broad peak has been fitted with two non-symmetric lines corresponding to ring and non-ring configurations. The $BO_4$ intense peak has been fitted with two Gaussian lines standing for $BO_4$ units with different second neighbor. The $^{27}$Al NMR peak has been fitted with asymmetric lines depending on the presence of $AlO_4$, $AlO_5$ and $AlO_6$ species.

Figure 5: Change in the $N_4$ (A) and Average $CN_{Al}$ (B) as a function of pressure conditions. The error bars are calculated from error propagation.

Figure 6: Calculated optical basicity from $n$ values ($\Lambda_n$) as a function of pressure for the investigated glass compositions. We also plotted the optical basicity calculated from the $n$ data of Kuryaeva et al.⁵⁴ and Kuryaeva⁵⁵ obtained on three different glass composition in the CaO-Al₂O₃-SiO₂ system.
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Figure 7: Change in the optical basicity calculated from the structural changes ($\Lambda_{N4+CNAI}$): N₄ and CNₐ. We also integrated the recent structural data provided in the Soudani et al.⁴¹ for Na- and Ca-bearing aluminoborosilicate glasses synthesized under pressure.
<table><caption>Table 1: High-pressure aluminoborosilicate optical and structural properties.</caption><thead><tr><th>Sample</th><th>SiO<sub>2</sub></th><th>B<sub>2</sub>O<sub>3</sub></th><th>Al<sub>2</sub>O<sub>3</sub></th><th>CaO</th><th>Na<sub>2</sub>O</th><th>R'</th><th>K'</th><th>N<sub>4</sub><sup>NMR</sup></th><th>CN<sub>Al</sub><sup>NMR</sup></th><th>n<sub>D</sub></th><th>ρ</th><th>Λ<sub>th</sub></th><th>Λ<sub>N4+CNAI</sub></th><th>Λ<sub>n</sub></th></tr></thead><tbody><tr><td colspan="14" style="text-align: center; font-weight: bold;">ISG</td></tr><tr><td>-0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.48</td><td>4.00</td><td>1.532(6)</td><td>2.495(7)</td><td>0.507</td><td>0.566</td></tr><tr><td>-0.5</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.44</td><td>4.00</td><td>n.d.</td><td>2.621</td><td>0.509</td><td>n.d.</td></tr><tr><td>-1.0</td><td>60.2</td><td>16.0</td><td>3.8</td><td>5.7</td><td>12.6</td><td>0.924</td><td>3.040</td><td>0.49</td><td>4.00</td><td>1.558(3)</td><td>2.715(11)</td><td>0.523</td><td>0.507</td></tr><tr><td>-1.5</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.52</td><td>4.00</td><td>1.565(3)</td><td>2.935(53)</td><td>0.505</td><td>0.433</td></tr><tr><td>-2.0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.54</td><td>4.00</td><td>n.d.</td><td>n.d.</td><td>0.504</td><td>n.d.</td></tr><tr><td colspan="14" style="text-align: center; font-weight: bold;">NH</td></tr><tr><td>-0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.31</td><td>4.00</td><td>1.534(19)</td><td>2.514(1)</td><td>0.565</td><td>0.631</td></tr><tr><td>-0.5</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.34</td><td>4.00</td><td>n.d.</td><td>n.d.</td><td>0.564</td><td>n.d.</td></tr><tr><td>-1.0</td><td>43.0(7)</td><td>16.5(7)</td><td>9.4(4)</td><td>8.1(1)</td><td>22.9(5)</td><td>1.197</td><td>1.660</td><td>0.36</td><td>4.00</td><td>1.540(19)</td><td>2.585(8)</td><td>0.574</td><td>0.563</td></tr><tr><td>-1.5</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.40</td><td>4.03</td><td>1.565(15)</td><td>2.686(17)</td><td>0.560</td><td>0.610</td></tr><tr><td>-2.0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.44</td><td>4.06</td><td>1.577(1)</td><td>2.738(12)</td><td>0.558</td><td>0.607</td></tr><tr><td colspan="14" style="text-align: center; font-weight: bold;">SHM</td></tr><tr><td>-0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.19</td><td>4.23</td><td>1.544(2)</td><td>2.575(4)</td><td>0.562</td><td>0.599</td></tr><tr><td>-1.0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.21</td><td>4.27</td><td>1.549(2)</td><td>2.711(10)</td><td>0.560</td><td>0.549</td></tr><tr><td>-2.0</td><td>43.1(9)</td><td>13.9(1)</td><td>12.1(1)</td><td>30.9(7)</td><td></td><td>1.190</td><td>1.656</td><td>0.30</td><td>4.40</td><td>1.567(3)</td><td>2.975(20)</td><td>0.555</td><td>0.468</td></tr><tr><td>-3.0</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.36</td><td>4.54</td><td>1.581(7)</td><td>3.154</td><td>0.549</td><td>0.420</td></tr></tbody></table>
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<figure><img src="image_63.png" /><figcaption>Figure 1</figcaption></figure>
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<figure><img src="image_66.png" /><figcaption>Figure 2</figcaption></figure>
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<figure><img src="image_69.png" /><figcaption>Figure 3</figcaption></figure>
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<figure><img src="image_73.png" /><figcaption>Figure 4</figcaption></figure>
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<figure><img src="image_76.png" /><figcaption>Figure 5</figcaption></figure>
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<figure><img src="image_79.png" /><figcaption>Figure 6</figcaption></figure>
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<figure><img src="image_82.png" /><figcaption>Figure 7</figcaption></figure>