# Impact of calcium and pH on ISG alteration at basic pH: Mechanism of formation and transport properties of the gel layer

Benjamin Cagnon, Stéphane Gin, Martiane Cabié, Damien Daval

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Benjamin Cagnon, Stéphane Gin, Martiane Cabié, Damien Daval. Impact of calcium and pH on ISG alteration at basic pH: Mechanism of formation and transport properties of the gel layer. Journal of Nuclear Materials, 2025, 610, pp.155796. 10.1016/j.jnucmat.2025.155796. hal-05344818

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# Impact of calcium and pH on ISG alteration at basic pH: Mechanism of formation and transport properties of the gel layer

Benjamin Cagnon<sup>a</sup>, Stéphane Gin<sup>b</sup>, Martiane Cabié<sup>c</sup>, Damien Daval<sup>a,*</sup>

## ARTICLE INFO

### Keywords:

ISG

Dissolution

Gel layer

Diffusion coefficients

Glass alteration

Dissolution mechanisms

## ABSTRACT

The dissolution of International Simple Glass (ISG) was investigated at 90 °C, elevated concentration of dissolved silica and in the presence of calcium, with a specific emphasis on basic pH conditions. The leaching solution was labelled with <sup>29</sup>Si, <sup>18</sup>O and <sup>44</sup>Ca in part of the experiments to elucidate the dissolution mechanisms. Based on the isotopic signatures of the gel layer analyzed using Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS), it was concluded that oxygen atoms mostly originate from the solution for all investigated conditions, while silicon atoms almost exclusively originate from the glass. A negative correlation was found between the initial concentration of calcium in solution and the gel layer thickness, suggesting either the formation of a passivating (Si, Ca)-rich layer, a catalytic effect of Ca on the gel densification or a combination of both. In addition, the pH-dependence of the diffusion coefficient of B within the gel was found to be stronger in the basic pH range than in the acidic pH range, which was suggested to originate from the change in coordination of B species at pH<sub>90</sub> ~ 8.5. Overall, these results suggest that in a (Ca, Si)-rich solution at basic pH, the durability of ISG is stronger than previously thought, as the diffusion coefficient of B under such conditions are lower than expected based on literature.

## 1. Introduction

Understanding the mechanisms that govern the aqueous reactivity of silicates is central to various concerns such as the biogeochemical cycle of elements [1], carbon dioxide sequestration [2] as well as vitrified nuclear waste disposal [3,4]. In the latter case, assessing the resistance of glass with respect to aqueous corrosion is essential to the evaluation of the geological repository long-term safety, over timescales extending up to several thousands of years.

In contact with water, the silicate matrix of the borosilicate glass is depolymerized via the hydrolysis of its network-forming elements [5]. This process results in the formation of a porous and hydrated layer (often referred to as gel layer [6,7]), which plays a key role in understanding glass dissolution kinetics [6,8–11]. The mechanism of gel formation is still debated. According to the so-called Coupled Interfacial Dissolution-Reprecipitation (CIDR) reaction, the gel results from the dissolution of all glass elements in an interfacial film of water, and the gel forms by precipitation of the less-soluble elements [12].

Alternatively, the gel was suggested to form by the preferential dissolution of B and alkalis without breaking all the bonds linking the other network formers [13]. This reaction is followed by recondensation of silanol groups. This process is referred to as incongruent dissolution and in situ reorganization of the silicate network.

Once the gel starts to form, the glass dissolution rate can drop by several orders of magnitude [14]. This decrease results from the transport-limiting properties of the growing gel layer [9,15,16] and the reduced affinity of the dissolution reaction with respect to the pristine glass and/or the gel layer [17,18]. This results in the release of B and Na in a congruent manner, proportional to the square root of time. This phenomenon has been deeply studied for ISG, and it was concluded that the dissolution of B and its diffusion in the gel limit the release of Na by interdiffusion [11]. Thus, it is possible to calculate apparent diffusion coefficients from the time evolution of the boron released in solution and to parameterize these coefficients as a function of temperature and pH. At higher reaction progress, the evolution of the thickness and porosity of the gel layer further impacts its transport properties (i.e., the

<footnote><sup>a</sup> Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IRD, Univ. G. Eiffel, ISTERRE, 38000, Grenoble, France</footnote>

<footnote><sup>b</sup> CEA, DES, DPME, SEME, University of Montpellier, Marcoule, France</footnote>

<footnote><sup>c</sup> Aix Marseille Univ, CNRS, Centrale Marseille, FSCM, CP2M, Marseille, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: damien.daval@univ-grenoble-alpes.fr (D. Daval).</footnote>
associated diffusivity of chemical species in the gel layer), which in turn further reduces the dissolution rate of the glass [19].

Regarding porosity, the gel layer formation should be considered as a dynamic process that may evolve over time [16,20]. The sensitivity of the gel to aqueous corrosion can be decreased by an in situ reorganization of its structure and the condensation of silanol groups into siloxane bonds [21,22]. This densification of the gel leads to the closure of the pores and a decrease of the rate of transport of species towards the bulk solution, [19]. The passivation properties of the gel layer may therefore spontaneously evolve, depending on external drivers (mechanical strength, pH...).

Additionally, the precipitation of secondary phases such as (alumino)phyllosilicates or zeolites on the surface of the gel layer can impact the apparent reactivity of the gel [23]. Under certain conditions, the low porosity and high density of the coating by secondary phases may prevent the exchange of species between the solution and the pristine glass [24]. Conversely, precipitates such as calcium silicate hydrates (CSH) or zeolites destabilize the gel layer by consuming aluminum from the solution, which eventually triggers gel dissolution [25-28]. The precipitation of such secondary phases can in turn trigger the resumption of the glass alteration [13,29-32].

The glass composition is another parameter that can greatly influence its dissolution mechanisms and rate [14,33-35]. Through 14-year long alteration experiments (90 °C, deionized water) of 10 simple borosilicate glasses with increasing composition complexity, and ultimately that of the 30-oxide nuclear glass SON68, Gin et al. [33] highlighted strong correlations between the glass composition and the long-term dissolution rates. As an example, as compared to CJ1 which contains only Si, B and Na, glasses containing Al and Ca or Zr and Ca (referred to as CJ3 and CJ9 in their study) exhibit a much lower dissolution rate due to the incorporation of those elements in the gel layer [11]. Conversely, the glass with Ca only (with a 5.5 wt. % for CaO) in addition to CJ1 (glass named CJ8) cannot form a stable passivating gel layer because of the precipitation of secondary phases. Overall, the impact of a given element on the chemical durability of glass strongly depends on the presence of other elements as well as on alteration conditions, such as pH, temperature, and solution composition.

Finally, the passivating properties of the gel layer are correlated with the chemical composition of the aqueous fluid [7,25,36-39]. For instance, Collin et al. [7] investigated the influence of exogenous alkali ions such as Li⁺, Na⁺, K⁺ and Cs⁺ on the formation and passivation properties of the gel layer formed on the ISG. They observed little to no effect of Li⁺ and Na⁺ on the alteration kinetics. Conversely, the presence of K⁺ and Cs⁺ decreases the alteration rate due to their incorporation into the gel layer. These alkalis replace Ca in the gel layer structure as the new charge compensation for aluminum, and this exchange greatly affects the total quantity of water within the gel layer, providing another explanation for the decrease in glass dissolution. The impact of alkaline earth cations has also been studied. For example, Mercado-Depierre et al., 2013 [25] focused on the antagonist effect of calcium on the passivating properties of the gel layer according to the pH and the glass surface area to solution volume (SA/V) ratio. On one hand, calcium can bond with silicon atoms at the interface between the gel layer and the solution, weakening Si-O bonds and making them more susceptible to hydrolysis [40,41]. On the other hand, Ca can be adsorbed into the gel layer, resulting in an increase in the retention of elements that make up the glass. Furthermore, calcium can act synergistically with silica and form a (Si, Ca)-rich passivating layer. As such, Ca may actively participate in the densification of the gel layer as a catalyst [38]. The presence of other elements with low solubility such as Zr and Al can also increase the passivating properties of this (Si, Ca)-rich layer [42].

Refining our understanding of the role of Ca in ISG dissolution is essential because in certain geological disposal scenarios, the use of a buffer material could lead to glass alteration by a solution with high Ca concentration and high pH (cf [43] and references therein). In the scenario envisaged for the disposal of French vitrified nuclear waste,

oxidation of pyrite in the clayey formation where the nuclear glass will be stored is suggested to promote a transient drop in pH, resulting in the subsequent dissolution of carbonate minerals also contained in the clayey formation, and a transient increase in partial pressure of CO₂. Gradual neutralization of CO₂ is then supposed to occur through the carbonation of the cementitious backfilling material purposely placed between the host rock and the steel liner of the storage cells in which the vitrified nuclear waste is stored [44]. At the end of the corrosion of the stainless-steel container, the pH of the pore fluid is supposed to be basic, which emphasizes the need to better understand the reactivity of ISG in this pH domain. In a recent study, Cagnon et al. [43] showed that the dissolution of ISG at elevated concentrations of dissolved Ca and Si species at basic pH conditions (pH₉₀ °C ~ 10) results in the formation of calcium silicate hydrates (CSHs), which are responsible for the consumption of Si from the gel layer and a possible resumption of ISG dissolution. However, Cagnon et al. [43] also showed that when CO₂ is included in the system, the precipitation of calcium carbonates at the expense of CSHs occurs rapidly, so that the sink for Si represented by CSHs is suppressed. As such, the consumption of the gel layer stops, and ISG dissolution may essentially proceed in the so-called 'residual corrosion rate' regime (i.e., Stage II) over long timespans. Such a scenario strengthens the need to get insights into the mechanisms of ISG dissolution and transport properties of the gel layer at basic pH and elevated concentrations of dissolved Ca and Si species where the formation of secondary phases is limited, in order to get a more reliable picture of the durability of ISG.

In the present study, we thus combined dissolution experiments conducted with ISG powders and ISG coupons to investigate the impact of pH and aqueous Ca on the transport properties of the gel layer at 90 °C, with a particular focus on the basic pH domain. In all experiments, the concentration of aqueous silica in the solution was fixed at a threshold that exceeds that of the apparent solubility of the gel layer, while maintaining conditions under which the precipitation of secondary phases, such as CSHs, was slow enough to ensure that glass dissolution took place in the so-called 'residual corrosion rate' regime. The powder dissolution experiments were conducted without initial addition of Ca to the solution, aimed mainly to extend the relationships between pH and diffusion coefficient initially proposed by Gin et al. [11] in the pH₉₀ °C domain ranging from 3 ± 0.1 to 9 ± 0.1. The experiments using ISG coupons were performed at calcium concentrations increasing from 0 ppm to 240 ppm and pH₉₀ °C = 10.3. The alteration solution was labelled with ¹⁸O (¹⁸O/¹⁶O = 0.035 ± 0.001) and ²⁹Si (²⁹Si/²⁸Si = 0.74 ± 0.02) to investigate the gel layer formation mechanism based on the incorporation of those elements into the gel structure. Additionally, the role of calcium on the passivation properties of the gel layer was tackled. Taken together, those experiments were used to discuss the mechanisms and transport properties of the gel layer at basic pH and with variable Ca concentrations.

## 2. Material and methods

### 2.1. Sample preparation

International Simple Glass (wt % 56.2 SiO₂, 17.3 B₂O₃, 12.2 Na₂O, 6.1 Al₂O₃, 5.0 CaO, 3.3 ZrO₂; cf [45]) was prepared either as powders or monoliths. The powders were prepared by grinding ISG chunks, followed by sieving and washing in ethanol ultrasonic baths. The grain size selected for the experiments was 100–125 µm with a specific surface area (SSA) determined by the Brunauer Emmett and Teller (BET) method using Kr as the absorbent gas of 455 cm²/g; the estimated accuracy being 20 %. The monoliths were prepared as coupons with dimensions 2 × 2 × 0.1 cm³. They were polished by PrimeVerre, Montpellier, France, on all faces using suspensions of decreasing grain sizes and soft polishing cloths, and a 1/4 µm diamond grain paste in the final step. The specific ISG starting material used in this work, denoted as ISG-1, was elaborated as described in Ryan et al. [46]. On each corner,
top and bottom surfaces of ISG samples, a small part (<1 mm², on average <5 % of the polished surface) was protected with room-temperature-vulcanizing (RTV) glue spots to create a non-reacted reference surface used for subsequent topography analyses run with Vertical Scanning Interferometry (VSI; see Section 2.4.3).

## 2.2. Experimental procedure

Two series of experiments were conducted to isolate the respective impacts of pH and Ca concentration on ISG dissolution rates, and infer the corresponding transport properties of the gel.

The first series of experiments was carried out using ISG powders, with targeted pHs of 3, 9 and 9.5. Experiments were similar to Experiment 3 described in Gin et al. [11]. In brief, glass powders were altered in PFA Savillex® vessels for short duration (1 h for pH 3 and 13 days for pH 9 and 9.5) in static mode at 90 °C in solutions close to saturation with respect to amorphous silica at the target pH (C₀(Si) = 150 ppm, 330 ppm and 615 ppm for experiments conducted at pH 3, pH 9 and pH 9.5, respectively). The pH 3 was fixed with suprapur HNO₃ solution, whereas the basic pHs were fixed with M LiOH solution (99.5 % purity). Uncertainty on the pH is 0.1 unit. S/V ratio was 1 cm⁻¹, 1 cm⁻¹ and 2 cm⁻¹ for pH 3, pH 9 and pH 9.5, respectively. The solutions were stirred with a magnetic bar, and were sampled at several durations for B concentration determination (2 mL taken at each sampling from a starting volume of 100 mL), using UV-Visible spectrophotometry.

The second series of experiments was carried out using ISG coupons immersed in PFA Savillex® vessels. The experiments were conducted at fixed pH (10.3) and elevated concentration of SiO₂(aq), with increasing concentrations of dissolved calcium from 0 ppm to 240 ppm (experiments referred to as G0 to G4 in [43], see Table 1 below). Note that, in contrast to powder dissolution experiments, the solutions were not equilibrated with respect to SiO₂(am), as such conditions would have promoted the continuous formation of secondary (Ca, Si)-rich phases during the experiments, which could have ultimately destabilized the gel layer, resulting in its breakdown, and preventing the estimation of its transport properties [43]. On average, the total Si concentration in solution was adjusted to ~50 % of the equilibrium value with respect to amorphous silica (SiO₂(am)). Such a value was chosen as it was shown to be much above the apparent solubility of the gel layer (< 12 % of the equilibrium value with respect to SiO₂(am) at 90 °C and pH ~ 10, [43]). These concentrations were achieved using nanopowder silica (specific surface area 175 – 225 m²·g⁻¹, 99.8 % trace metals basis) and ²⁹SiO₂(am) powder (Eurisotop, 99.35 % purity of ²⁹Si), so that the ²⁹Si/²⁸Si ratio in solution was 0.74 ± 0.02. The solution was also labelled with ¹⁸O (Eurisotop, 99.7 % purity of ¹⁸O) in a ¹⁸O/¹⁶O ratio of 0.035 ± 0.001. The pH of the stock solution was measured at high temperature (90 °C) and adjusted to 10.3 ± 0.1 by addition of LiOH (Prolabo) on a daily basis. Once the pH of the solution stopped evolving (within approximately 10 days), the CO₂ in the solution was removed through degassing

<caption>**Table 1**</caption>

Summary of the initial conditions for the experiments conducted with ISG coupons. The first column refers to the name of the experiment. The second, third, fourth and fifth columns refer to the concentration of Si (ppm) in the solution, measured by ICP-OES, the [SiO₂(aq)]/[SiO₂(aq)eq] ratio (which is the saturation state of the solution with respect to amorphous silica), the ²⁹Si/²⁸Si ratio, measured by ICP-MS, and the concentration of Ca (ppm) in the solution, measured by ICP-OES, respectively. Note that the concentration of Ca reported with (*) corresponds to the theoretical value based on weighing, as the ICP-OES analyses failed for the corresponding samples.

<table><thead><tr><th>Experiment</th><th>[Si] (ppm)</th><th>[SiO<sub>2</sub>(aq)]/[SiO<sub>2</sub>(aq)eq]</th><th>2<sup>9</sup>Si/2<sup>8</sup>Si</th><th>[Ca] (ppm)</th></tr></thead><tbody><tr><td>G0</td><td>1740</td><td>35 %</td><td>73 %</td><td>2.50</td></tr><tr><td>G1</td><td>2680</td><td>54 %</td><td>73 %</td><td>1.72</td></tr><tr><td>G2</td><td>2760</td><td>55 %</td><td>75 %</td><td>73.9</td></tr><tr><td>G3</td><td>2860</td><td>57 %</td><td>76 %</td><td>117</td></tr><tr><td>G4</td><td>2820</td><td>56 %</td><td>75 %</td><td>240*</td></tr></tbody></table>

with N₂ (0.15 L·min⁻¹) at high temperature (near water ebullition, T > 90 °C) during 30 min for 500 mL of solution. PFA Savillex® vessels, containing a Teflon® basket, were filled with approximately 35 mL of solution and placed in a N₂ atmosphere-controlled glove box to prevent the precipitation of calcium carbonates that would consume calcium in the solution. The appropriate amount of Ca was added to G0, G1 and G2 reactors by sampling 1 mL or 2 mL aliquots from a stock solution prepared with dissolved CaCl₂ (ACS reagent, ≥99 %). G3 and G4 reactors were 100 % spiked with calcium carbonate powder in the form of ⁴⁴CaCO₃ (Eurisotop, 99.2 % purity of ⁴⁴Ca) to determine whether the Ca present in the gel layer and/or secondary phases at the end of the experiments (i.e., after 21 days) originated from the glass or from the solution.

After the addition of calcium, each reactor was placed in an oven at 90 °C for an incubation time of 24 h as the chemical composition of the solution has been shown in our previous study [42] to evolve spontaneously over the first day of solution preparation. Next, the glass monoliths were introduced into each reactor and placed on a tripod, while the solutions were continuously stirred with magnetic bars. To collect aqueous samples, reactors were briefly removed from the oven and placed in a glovebox at the start of the experiments, after a 13-day period, and at the conclusion of the experiments (21 days). All collected aqueous samples were 2 mL in volume, and were filtered using a 0.45 µm pore size filter before dilution (5x, 150x, and 1500x) with ultrapure water (18.2 MΩ·cm).

At the end of the experiments, the reactors were quenched, and ISG coupons were recovered and then dipped three seconds in ultrapure water (18.2 MΩ·cm) before being dipped in ethanol for three seconds. The coupons were then dried overnight at room temperature and stored in the glove box at room temperature until being cut into smaller pieces using a diamond saw in order to perform various surface analyses detailed hereafter.

## 2.3. Characterization of aqueous solutions and ISG alteration

### 2.3.1. Characterization of aqueous solutions

For both series of experiments conducted with powders and monoliths, the concentration of dissolved elements (B, Si, and Ca) was determined from diluted aliquots by Inductively Coupled Plasma Optical Emission Spectrometer (ICP-OES) (Varian 720-ES). Relative error on concentration is ~5 %. The aqueous ²⁹Si/²⁸Si ratio of the solution was measured with Inductively Coupled Plasma Mass Spectroscopy (ICP-MS) (ICAP RQ, Thermo Scientific).

### 2.3.2. Determination of the glass alteration layer thickness ($E_{th}(B)$) and boron diffusion coefficient

For both series of experiments, $E_{th}(B)$ (nm), was calculated following Eq. (1):

$$E_{th}(B) = \frac{[B]_t \times V_t}{SA \times \rho \times x(B)} \quad (1)$$

where $[B]_t$ is the B concentrations (ppm) at time t, $V_t$ is the volume (L) of the solution in the reactor just before collection, SA is the sample surface area (m²) (determined by either by BET for experiments conducted with powder, or from the dimensions of the monolith measured by electron microscopy), ρ is the specific volume of ISG glass (ρ = 2.498 g·cm⁻³) and x(B) is the mass proportion of B in ISG (x(B) = 0.0537). Note that if the alteration is isovolumetric, $E_{th}(B)$ is equal to the gel layer thickness. Following this assumption, the concentration of B can thus be used to determine the position of the ‘internal interface’, which represents the boundary between the gel layer and the pristine glass, as detailed by Wild et al. [47].

The diffusion coefficient of B is derived from the second Fick's law, assuming that the glass is a semi-infinite medium from which B, once hydrolyzed by protons, diffuses towards the bulk solution. D(B) (m²·s⁻¹)
is calculated following Eq. (2), making sure that B release follows a square root dependency:

$$D(B) = \frac{\pi}{4 \Delta t} E_{th}(B)^2 \qquad (2)$$

with $E_{th}(B)$ expressed in m and $\Delta t$ is time difference between consecutive aliquots, in s.

## 2.4. Solid characterizations

### 2.4.1. FIB-TEM analyses

Scanning electron microscopy analyses were carried out using a FEI Helios 600 Nanolab dual beam at CP2M (Marseille, France). The reacted samples were first carbon-coated, and ultrathin electron-transparent cross-sections were then prepared with focused ion beam (FIB) milling, using an FEI Helios 600 Nanolab dual-beam at CP2M (Marseille, France), following methods previously described by Daval et al. [48]. In summary, FIB Ga⁺ ion milling was conducted at an ion beam voltage of 30 kV, with beam currents varying from 9 nA to 90 pA in the final stages. Micrometer-thick sections were gently lifted out in situ using an Omniprobe 200 micromanipulator and subsequently transferred to a half copper grid for the final ion milling process to achieve electron transparency, resulting in a final thickness of approximately 100 nm. This milling procedure was executed at a reduced acceleration voltage of 5 kV to mitigate beam damage. Similarly, the final cleaning steps were carried out at 2 and 1 kV for the same reasons.

Transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) observations were performed on FIB foils using a FEI Tecnai G2 microscope operated at CP2M (Marseille, France) with a LaB6 electron source operating at 200 kV. Energy dispersive X-ray (EDX) spectra were acquired in STEM mode to probe the chemical composition of the interface between the gel layer and the pristine glass, with an EDX Detector (Oxford XMax 80). The analyses were conducted on two FIB thin sections (G0 and G4).

### 2.4.2. ToF-SIMS analyses

ISG coupons were analyzed by an IONTOF GmbH® TOF 5 spectrometer from TESCAN Analytics (Fuveau, France). The external surface was abraded on an area of 200 × 200 µm² for an analyzed area of 50 × 50 µm². The ToF-SIMS device operated as cycles of abrasion and analysis. After each cycle, the surface charge was neutralized by a low energy electron beam (<20 eV) in order to prepare the area for the next cycle. The depth of the crater ($h_{crater}$, in nm) created by ion milling after a given number of abrasion cycles ($N_{cycles}$) was measured using a 3D profilometer. The depth associated to one cycle of abrasion ($z_{cycle}$, in nm) is then assumed to be simply given by:

$$z_{cycle} = h_{crater}/N_{cycles} \qquad (3)$$

Uncertainties at $2\sigma$ are approximately 15 % of the result value. Depth profiles of positive ions were recorded thanks to a 25 keV, 1.5 pA $Bi_1^+$ beam for the analyses and a 1 keV, 210 nA $O_2^-$ beams for the ablation. Depth profiles of negative ions were recorded thanks to $Bi_3^+$ 25 keV, 0.5 pA beams for the analysis and $Cs^+$ 2 keV, 185 nA beams for the ablation.

### 2.4.3. VSI analyses

For each coupon, an RTV glue mask was used to create a non-reactive reference area on the glass surface to measure its retreat resulting from dissolution. Topography analyses were conducted using VSI (Zygo Newview 7300). For all samples, the images were taken at 10x-magnification, corresponding to a lateral resolution of 1.7 µm, while the vertical resolution was of the order of 1 nm.

## 3. Results

### 3.1. Time-resolved release of boron from powder dissolution experiments

The evolution of the equivalent thickness ($E_{th}(B)$) was calculated according to Eq. (1) for the 3 powder experiments conducted in this study at pH = 3.0, 9.0 and 9.5, in a solution close to saturation with respect to $SiO_2(am)$. Whatever the pH of the experiment, the increase in equivalent thickness showed a linear trend as a function of the square root of time, reflecting a diffusion-controlled dissolution regime (Fig. 1). Note that such a conclusion can be extended up to pH 10.3 by including the data obtained by Fournier et al. [10] (experiment S2-sat-10.3), corresponding to dissolution experiments under conditions where the gel layer was stable as well.

From these profiles, diffusion coefficients were calculated according to Eq. (2) and are reported in Table 2.

### 3.2. VSI characterizations of the coupons

At the end of the experiments, all coupons were analyzed with VSI to measure the height difference (also called surface retreat) between a portion of the surface that was masked (and therefore, not exposed to the solution) during the experiment and the part of the coupon that was subjected to aqueous alteration. Apart from the coupon recovered from experiment G0, which exhibited a negligible surface retreat of ~7 nm, it was impossible to detect any surface retreat for coupons recovered from experiments G1-G4. These results demonstrate that the Si-enriched solutions prevented dissolution of the gel layer. Hence, the solubility of the gel is less than that of $SiO_2(am)$ under the investigated conditions ($T = 90$ °C, and $pH_{90}$ °C = 10.3). These observations also support that estimating reliable diffusion coefficients of boron can be achieved through the measurement of the thickness of the gel layer after a given duration. Such measurements are detailed in the next section.

### 3.3. ToF-SIMS characterizations of the coupons

Each ISG coupon was analyzed using Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS) and the results for the major elements of the glass are depicted in Fig. 2. Note that each elemental profile was normalized to the $X/^{28}$Si ratio ($X = Al, Ca, B$, and Na) of the pristine glass, so that $X/^{28}$Si = 1 in the pristine glass.

As a first observation, the depletion fronts of the Ca, B and Na profiles are consistent (Fig. 2a-d), as they position the transition between the gel layer and the pristine glass at the same depth. In addition, a slight retention of B and Ca within the gel is observed, which, in the case of boron, is characteristic of the formation of a passivating gel [32]. Indeed, recent studies demonstrated that the retention of B and Ca in the gel strongly reduced the dissolution and release of Na from the glass [11, 42]. Conversely, the Al/²⁸Si ratio is constant throughout the gel layer and identical to that of the pristine glass. Only the first 5–10 nm of the gel are depleted in Al. Similar observations were made regarding the $Zr/^{28}$Si profiles.

The thickness of the gel, defined as the depth from the surface at which the normalized $X/^{28}$Si ratio reaches 0.5, shows the following trend: G0 > G1 > G2 > G3 > G4, and is negatively correlated ($R^2 = 0.93$) with the calcium concentration in solution (Fig. 2e). Based on the observation that under conditions where the solution is supersaturated with respect to the gel layer over the pH range 3.0–10.3, the dissolution of ISG is consistent with a diffusion-like behavior (see Section 3.1), the diffusion coefficient of B in any $Gi$ experiment ($D_{Gi}^{ToF}(B)$) can be calculated according to Eq. (2), using the position of the interface between the gel layer and the pristine glass as the value for $Eth(B)$.

Following the work of Gin et al. [11], the same formula was used to calculate diffusion coefficients from the release of B into solution. Table 3 presents the results obtained with ToF-SIMS depth profiling and
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Evolution of equivalent thickness of B release as a function of the square root of time for the 3 powder dissolution experiments conducted in the present study (pH 3.0 – 9.5), including also experiment S2-sat-10.3 from Fournier et al. [10]. Note that all experiments were carried out with a starting solution devoid of dissolved calcium but close to saturation with respect to SiO₂(am) to prevent the chemical breakdown of the gel layer.</figcaption></figure>

**Table 2**

Calculated diffusion coefficients of B during ISG dissolution in an aqueous medium saturated with respect to SiO₂(am). Note that for the experiment taken from [10], the data were regressed only on the period prior to the potential resumption of glass dissolution following the precipitation of Si-rich secondary phases.

<table><thead><tr><th>Reference</th><th>pH<sub>90</sub> °C</th><th>D(B) (m<sup>2</sup>.s<sup>-1</sup>)</th><th>log(D(B))</th></tr></thead><tbody><tr><td>This study</td><td>3.0</td><td>7.5E-17</td><td>-16.1</td></tr><tr><td>This study</td><td>9.0</td><td>4.3E-20</td><td>-19.4</td></tr><tr><td>This study</td><td>9.5</td><td>5.9E-21</td><td>-20.2</td></tr><tr><td>Fournier et al. (2019): S2-sat-10.3</td><td>10.3</td><td>4.0E-22</td><td>-21.4</td></tr></tbody></table>

solution analyses. A reasonable agreement is obtained for the 5 experiments. However, it is worth noting that, due to the low ratio of coupon surface area to solution volume in these experiments, the concentration of B remained very low (in the ppb range), so that the diffusion coefficients determined following this approach are also fraught with a high uncertainty (which can be as high as 50 % (2σ), as D(B) varies with the square of [B]; see Eq. (2)). Therefore, only $D_{G_i}^{ToF}(B)$ are considered in the following section to discuss the impact of Ca on the transport properties of the gel layer.

Spiking the solution with ²⁹Si and ¹⁸O provides further information on the mechanisms of gel layer formation. Regarding Si, only the first 5–10 nm of gel layer are found to be enriched in ²⁹Si (supplied by the

solution), with the ²⁹Si/²⁸Si ratio returning to the natural abundance in the glass for depth exceeding ~20–30 nm (Fig. 3a). Conversely, the O isotopic signature of the gel layer corresponds, within analytical uncertainties, to that of the aqueous solution for coupons from all experiments (Fig. 3b). This indicates that the entire gel is enriched in ¹⁸O. In addition, the enrichment front extends to a depth that corresponds reasonably well to the Na and B depletion fronts reported above (Fig. 2), demonstrating that water does not diffuse into the glass without reacting with its elements. Finally, the calcium cations that remained trapped within the gel mainly have the isotopic signature of the solution. The ⁴⁴Ca from the solution penetrated up to the alteration front, and the ⁴⁴Ca/(⁴⁴Ca + ⁴⁰Ca) ratio stabilized at around 0.8 for G3 and G4 experiments (Fig. 3c).

### 3.4. FIB-TEM characterizations

The characterizations of the two FIB foils prepared on G0 and G4 ISG coupons show alteration thicknesses and values of B and Ca retention in the gel layer similar to those obtained by ToF-SIMS (Fig. 4). However, as opposed to ToF-SIMS characterizations, the interface between the gel layer and the pristine glass is sharp. The gel thickness is approximately 122 nm for G0 and 89 nm for G4. The electron density increases from the pristine glass to the outer part of the gel. The zone located at the interface between the gel and the solution exhibits the highest electron
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Normalized element depth profiles of a) Na, b) B, c) Ca, d) Al, collected by ToF-SIMS for experiments G0 to G4. Each profile was collected using positive ion detection mode, and was normalized to ²⁸Si prior to being normalized with respect to the X/²⁸Si ratio (X = Na, B, Ca and Al) of the pristine glass. Of note, z = 0 corresponds to the outer surface of the alteration layer (in contact with the solution). The position of the interface between the alteration layer and the pristine glass, which is used to approximate the thickness of the gel layer, is defined as the z value for which X/²⁸Si = 0.5. e) Plot representing the gel layer thickness (nm) as a function of the final concentration of calcium (ppm) in the solution.</figcaption></figure>

**Table 3**

Diffusion coefficients calculated at 90 °C from the gel layer thickness measured by ToF-SIMS and from the release of B during the alteration, measured by ICP-OES. The first column refers to the name of the experiment. The second and third columns refer to the gel layer thickness (nm) measured by ToF-SIMS and the diffusion coefficient, $D_{G_i}^{\text{ToF}}(B)$ (m²·s⁻¹), calculated from Eq. (2), respectively. The last columns refer to the gel layer thickness (nm) estimated by ICP-OES measurements and corresponding diffusion coefficient, $D_{G_i}^{\text{ICP}}(B)$ (m²·s⁻¹), calculated from Eq. (2), respectively. Note that failure with the ICP-OES analyses prevented the measurement of [B] after 21 days, so that $E_{th}(B)$ and $D_{G_i}^{\text{ICP}}(B)$ were estimated at 13 days only.

<table><thead><tr><th rowspan="2">Experiment</th><th colspan="2">ToF-SIMS analysis</th><th colspan="2">ICP-OES analysis</th></tr><tr><th>Eth(B) (nm) 21 days</th><th>D<sub>G_i</sub><sup>ToF</sup> (B)</th><th>Eth(B) (nm) 13 days</th><th>D<sub>G_i</sub><sup>ICP</sup> (B)</th></tr></thead><tbody><tr><td>G0</td><td>122</td><td>6.4E-21</td><td>77</td><td>4.2E-21</td></tr><tr><td>G1</td><td>116</td><td>5.8E-21</td><td>35</td><td>8.4E-22</td></tr><tr><td>G2</td><td>103</td><td>4.6E-21</td><td>35</td><td>8.5E-22</td></tr><tr><td>G3</td><td>91</td><td>3.6E-21</td><td>57</td><td>2.2E-21</td></tr><tr><td>G4</td><td>82</td><td>2.9E-21</td><td>98</td><td>6.7E-21</td></tr></tbody></table>

density, extending over 22–26 nm for G0 and 15–17 nm for G4, respectively.

The STEM-EDX spectra collected on G0 and G4 FIB foils are similar: they both show incorporation of K (coming from the pH electrode)

within the gel, while the gel is depleted in Ca and Na. Note that the proportion of Ca incorporated into the gel increases with the initial concentration of Ca in the aqueous solution, since $(\frac{Ca}{Si})_{\text{gel}} / (\frac{Ca}{Si})_{\text{pristine glass}}$ amounts to ~5 % ± 1 % for G0, while it reaches up to 21 % ± 2 % for G4.

# 4. Discussion

## 4.1. Impact of pH on the transport properties of the gel layer

The diffusion coefficient of B calculated at 90 °C and 4 different pH values from either powder or monolith dissolution experiments in the present study are reported together with the data collected by Gin et al. [11] and Fournier et al. [10], to extend the pH range investigated to 3.0–10.3 (Fig. 5). Overall, the diffusion coefficient of boron decreases with increasing pH, which is consistent with the results previously reported by Gin et al. [11]. Two specific observations can however be made:

- First, the trend described by the values determined from powder dissolution experiments based on the monitoring of the aqueous release of B with time does not overlap with that determined from ToF-SIMS measurement of the thickness of the gel layer after a given duration. Instead, the values derived from time-resolved release of B into the so-

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Normalized element depth profiles of (a) ²⁹Si/²⁸Si, (b) ¹⁸O/¹⁶O and (c) ⁴⁴Ca/⁴⁴Ca+⁴⁰Ca) collected by ToF-SIMS. Each element profile was collected using positive ion detection mode except b) which was collected using negative ion detection mode. For ²⁹Si/²⁸Si ratio, only the first 25 nm are displayed, the rest of the gel has the signature of the natural abundance. ⁴⁴Ca profile was normalized to the total calcium, i.e. ⁴⁴Ca + ⁴⁰Ca. Of note, depth at z = 0 corresponds to the outer surface of the alteration layer.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** FIB-TEM characterizations of a) G0 and b) G4 ISG coupons. The composition of the gel layer and the pristine glass was obtained by STEM-EDX. For each part of the panels (a) and (b), the top left image is a TEM bright field image where the gel layer thickness is indicated in red. The red dashed line corresponds to the interface between the gel layer and the pristine glass and the yellow dashed line corresponds to the limit between the gel layer with an intermediate electron density and the outer surface, which has a higher electron density. The bottom left panel represents a STEM dark field image where EDX spectra were collected. EDX maps for the Si(K) and Ca(K) are also displayed in the upper right part of each panel.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** (a) Diffusion coefficients of boron in the gel layer as a function of pH. Note that the observed trends were divided into two, depending on whether the dissolution experiments were conducted with powders or monoliths (see text for details). The trends show an inflexion point at a pH ranging between 8 and 9. (b) Aqueous speciation of B at 90 °C as a function of pH, calculated with the CHESS code. The change in the dominant species occurs at a pH of ~8.5, which in turn may be linked to the inflexion point observed in (a).</figcaption></figure>

lution seem to systematically underestimate the values derived from the direct measurement of the gel layer thickness at the same pH by a 5- to 7x-fold factor. Three explanations may contribute to the observed discrepancies:

(i) As shown by Fournier et al. [49], powder dissolution rates normalized to BET surface area should be multiplied by 1.9 in order to match the corresponding rates measured on monolith dissolution experiments, both estimated from B release into the solution. A likely explanation for such a difference is that the BET surface area does not provide an accurate measurement of the reactive surface area of powders, resulting in an underestimation of the corresponding dissolution rates normalized to BET surface area. Accordingly, this would increase the calculated diffusion coefficients ($D_{G_i}^{ICP}(B)$) by a ~4x-factor.

(ii) As shown in Fig. 2b, a slight retention of B in the gel layer is observed, so that calculating an equivalent thickness from the release of B into the solution underestimates the actual gel layer thickness. However, based on the profiles shown in Fig. 2b, this contribution remains weak, of the order of 10 % at most.

(iii) The diffusion coefficient based on time-resolved analyses of the solution are calculated through the estimation of the equivalent thickness of glass alteration, where the boron concentration is divided by the glass density (see Eq. (1)). Note that such an equivalent alteration thickness corresponds to the actual thickness of the gel layer measured by ToF-SIMS only if the density of the gel layer is the same as that of the glass: a gel layer with a lower density would occupy a larger volume (and would therefore have a greater thickness), and vice versa. In practice, the density of the gel layer is generally lower than that of ISG and is close to 2.3 vs. 2.5 for ISG [7]. Regarding the data collected in the present study, if the thicknesses estimated by ToF-SIMS are corrected by a (2.3/2.5)²-fold factor to account for the difference between the density of the gel and that of ISG, this would decrease accordingly the calculated diffusion coefficients ($D_{G_i}^{ToF}(B)$) by a 0.8x-factor.

Combining these three explanations bridges most of the gap (up to a 5x-factor) that we highlighted between diffusion coefficients estimated on the basis of boron release into solution and diffusion coefficients
estimated by ToF-SIMS. More importantly, the main lesson to be drawn from the observations reported above is that it is preferable to compare separately the diffusion coefficients determined on the basis of B release from powder dissolution experiments and those determined on the basis of gel thickness measurements from monolith dissolution experiments. In any case, such small discrepancies (which do not exceed a factor of two at most, if we take into account the corrections discussed above) do not question the general trend revealed in this study, which extends over more than 6 orders of magnitude (see Fig. 5), and which we discuss in more detail below.

- The second point of discussion deals with the general trend observed for D(B) as a function of pH. While Gin et al. [11] showed that the diffusion coefficient of boron could be reasonably described following a linear relation between D(B) and pH for pH ranging between 3 and 9, extending this linear relation to pH up to 10.3 seems questionable. When the dataset is considered over the 3.0–10.3 pH range, a clear inflexion is observed at a pH value around 8.5. The general trend may be better described as two distinct linear trends from pH 3.0 to pH 8.5, and from pH 8.5 to pH 10.3, respectively (Fig. 5a). Interestingly, the inflexion in the trend occurs at a pH close to that at which the aqueous speciation of boron changes from B(OH)₃ to B(OH)₄ at 90 °C (Fig. 5b). One may hypothesize that the diffusion of B(OH)₄ is slower than that of B(OH)₃ because of the larger radius and/or negative charge of this ion and a higher bonding strength for BIV bonds than for BIII bonds [50], which would in turn result in an increase in the slope of the diffusion coefficient-pH relationship, as observed experimentally.

## 4.2. Impact of calcium on the transport properties of the gel layer

A negative correlation between the aqueous concentration of calcium and the gel layer thickness (R² = 0.93) is noticed from the ToF-SIMS results. Based on such a trend, an empirical relation between boron diffusion coefficient and calcium concentration can be proposed (R² = 0.9):

$$ \log(D(B)) = -1.39 \times 10^{-21} \log([Ca^{2+}]) + 6.59 \times 10^{-21} \quad (4) $$

with [Ca²⁺] expressed in ppm, and D(B) in m²·s⁻¹.

Note that the impact of calcium on the kinetics of the gel layer formation was previously documented in several studies. For instance, Damodaran et al. [42] described that the alteration depth of ISG in a SiO₂(aq)-saturated solution enriched in B, Ca and Na could be 50 times thinner compared to solution saturated in SiO₂(aq) only, free of the other elements. However, if either B or Ca was removed from the solution, the ISG alteration depth was only about 3 times thinner. Since the alteration decreases when the concentration of B and Ca increases, it was concluded that these elements limit the dissolution rate of the glass. Several mechanisms may account for such a trend:

(i) The first mechanism is based on the work of Mercado-Depierre et al. [25]: Caaq was described to be adsorbed into the growing gel layer, creating a Ca enriched layer that increases the retention of glass constituents in the gel layer. In our study, the FIB-TEM data (Fig. 4) highlight a higher concentration of Ca in experiment G4 (21 %) than in experiment G0 (5 %), which is consistent with the higher concentration of Caaq in G4 compared to G0. This (Si, Ca)-rich layer may decrease the transport properties of the gel layer and, consequently, its growth rate [36,42].

(ii) A second mechanism based on the work of Chave et al. [38] can be proposed. The authors hypothesized that calcium could play a catalytic role in the recondensation reaction of the gel, according to the following reactions:

$$ \equiv \mathrm{Si}-\mathrm{OH} + \mathrm{Ca}^{2+} + \mathrm{HO}-\mathrm{Si} \equiv \rightarrow \equiv \mathrm{Si}-\mathrm{O}-\mathrm{Ca}-\mathrm{O}-\mathrm{Si} \equiv +2\mathrm{H}^{+} \quad (5) $$

$$ \equiv \mathrm{Si}-\mathrm{O}-\mathrm{Ca}-\mathrm{O}-\mathrm{Si} \equiv +2\mathrm{H}^{+} \rightarrow \equiv \mathrm{Si}-\mathrm{O}-\mathrm{Si} \equiv +\mathrm{Ca}^{2+} + \mathrm{H}_{2}\mathrm{O} \quad (6) $$

Based on FIB-TEM images (Fig. 4), a densification of the gel layer occurs at the surface: the normalized intensity of the TEM bright field images (see Fig. 4a and 4b) was measured to decrease gradually from 1 in the pristine glass to ~0.4 and ~0.6 at the outermost past of the gel layer for samples G0 and G4, respectively. Considering the negative correlation between gel layer thickness and the calcium concentration in solution, the recondensation reaction seems to become more dominant with the Ca increase. However, the densification of the gel was also observed in G0 (Fig. 4a) where no Ca was initially added in the leaching solution, challenging this hypothesis. Ultimately, in the context of a catalytic role of Ca, it is possible that the low quantity of calcium in ISG, along with a 5 % retention, is sufficient for the calcium to efficiently contribute to the gel layer densification.

In conclusion, the concentration of calcium initially introduced into the solution moderately impacts the gel layer formation, either (i) by being incorporated into the growing gel to form a passivating (Si, Ca)-rich layer, or (ii) by playing a catalytic role in the gel layer recondensation and densification, or (iii) both being incorporated into the gel to form a passivating layer and participating in its densification. However, it should also be noted that the incorporation of Ca into the gel layer has only a modest impact on the diffusivity of B in the gel layer (which decreases by a factor of ~3 for aqueous Ca concentrations ranging between 0 and ~ 200 ppm; see Fig. 2e), and remains of second order compared to the impact of pH (see Fig. 5a).

## 4.3. Mechanisms of gel layer formation

As mentioned above, the aqueous solution was labeled with ²⁹Si and ¹⁸O isotopes to study their incorporation into the gel. The measured ²⁹Si/²⁸Si ratio of the starting solution was around 0.74 ± 0.02. An enrichment in ²⁹Si is noticed only at the outermost surface of the reacted coupons (thickness ranging between 5 and 10 nm depending on the samples) (Fig. 3a). This outermost part is also depleted in Al and Ca (Fig. 2a and c) and can thus be interpreted as precipitates of pure SiO₂(am), which might have originated from the quenching phase of the experiment, as the solubility of SiO₂(am) decreases with decreasing temperature.

Conversely, the gel layer located beneath these precipitates mostly forms without incorporating ²⁹Si from the solution. This observation highlights either that the hydrolysis of all Si-O-X (X standing for Si, Ca, Na, B, Al or Zr) bonds that link Si atoms to the glass occurs sequentially (i.e., Si atoms are never fully hydrolyzed, and always remain bonded to the structure of the solid via at least one of their four Si-O-X bonds), or that the diffusion of Si within the gel is seemingly non-existent over the duration of the experiments. Supporting the latter assertion, the outer part of the gel layer, with thickness ranging from around 16 ± 1 nm (G4) to 24 ± 2 nm (G0), shows a higher electron density compared to the rest of the layer (Fig. 4). This higher electron density suggests a densification, which may gradually limit the transport of species, as suggested by Cailleteau et al. [21]. In their work, they demonstrated that this densification mechanism resulted from the recondensation of silanols and in situ reorganization of network-forming elements. The present study suggests that this mechanism remains favored in alkaline conditions and at elevated Si concentrations, whatever the Ca concentration in the solution, and significantly prevents exchange of Si atoms between the solution and the transforming glass.

Finally, we note that all aqueous species are not equally impacted by this process: despite its densification, the gel remains permeable to certain elements of the solution. For instance, the ⁴⁴Ca/(⁴⁰Ca+⁴⁴Ca) ratio within the gel demonstrates that most Ca actually originates from
the solution (Fig. 3c). Therefore, the diffusivity differs from one chemical species to another. In particular, exchange with the solution remains possible and apparently not limited by diffusion for Ca. Similarly, the isotopic signature of oxygen within the gel suggests an exchange between the oxygen atoms from water molecules and those from the glass throughout the gel (Fig. 3b). For all experiments, the measured ¹⁸O/¹⁶O ratio of the gel observes a plateau that corresponds to that of the solution, within analytical uncertainties. This observation suggests that after the breaking of Si–O–Si bonds to form silanol groups, H₂¹⁸O molecules from the solution interact and exchange O atoms with silanols prior to the recondensation reaction. Hence, densification of the outer surface does not prevent diffusion of water molecules within the gel layer, and the ¹⁸O/¹⁶O profile demonstrates that most of (if not all) Si–O–Si bond of the glass have been eventually hydrolyzed, at least once, by the end of the experiments.

To conclude, in agreement with previous studies [11,13,16,51,52], TOF-SIMS characterizations suggest that the ISG gel layer is formed through an in situ hydrolysis–recondensation mechanism, with limited transport of Si across the gel. Overall, siloxane bond breaking and recondensation allow the exchange between ¹⁸O and ¹⁶O. Conversely, the measured ²⁹Si/²⁸Si ratio in the gel suggests either that Si atoms are mostly not released to the pore space of the gel layer (as a result of the sequential hydrolysis of Si-O-X bonds) or that the diffusion coefficient of Si in the gel is significantly lower than that of other species, such as water or calcium.

## 5. Conclusion

In conclusion, this study provides new insights into the understanding of the evolution of diffusivity within gel layers developed on ISG substrates at alkaline pH and elevated concentrations of dissolved Ca and Si species. The isotopic signature of the gel has revealed both the presence of an outermost layer of secondary phases and that of a gel layer with contrasted properties. While the gel layer does not act as a diffusion barrier for Ca and O from the solution over the durations of the experiments (up to 3 weeks), Si is found to be mainly inherited from the glass, with minor contribution of Si coming from the fluid. These observations prompted us to suggest that the gel layer is mainly formed by hydrolysis – recondensation, with the sequential hydrolysis of Si-O-X bonds. A negative correlation is found between the concentration of calcium in the solution and the gel layer thickness at the end of the experiments. This correlation might be explained by i) the formation of a (Si, Ca)-rich layer that limits the transport of species within the gel, ii) the catalytic role of calcium in the recondensation reactions of the gel layer, thus promoting its densification or iii) a combination of both previous hypotheses. The impact of Ca on the decrease of the transport properties remains weak, especially when compared to the impact of pH, which was found to be even greater than expected from previous studies in the basic pH domain. Altogether, this study suggests that under the investigated conditions, ISG is more durable than what could be expected using data that were available so far, as long as no (Ca, Si)-rich secondary phases such as CSHs form.

### CRediT authorship contribution statement

**Benjamin Cagnon:** Writing – original draft, Visualization, Investigation, Formal analysis, Data curation. **Stéphane Gin:** Writing – original draft, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. **Martiane Cabié:** Writing – review & editing, Investigation. **Damien Daval:** Writing – original draft, Visualization, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

The authors thank Simona Denti (ISTerre), Delphine Tisserand (ISTerre), Sylvain Campillo (ISTerre) and Sabine Santenac (ISTerre) for helping and providing advice with the ICP-OES analysis. The authors are also grateful to Loan Lai, Elodie Chauvet, Amandine David, Florian Cousy and Yves Depuydt from Tescan Analytics for performing TOF-SIMS analyses. Nicolas Michau and Christelle Martin from Andra, and Theo Montaigne from EDF are thanked for their inputs on an earlier version of this manuscript. Finally, two anonymous reviewers are acknowledged for their numerous constructive comments that improved the present manuscript. This work was funded by CEA, Andra and EDF.

### Data availability

Data will be made available on request.

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