# Impact of carbonate minerals on strontium and caesium reactivity in natural clay-rich materials

Jean Maillet, Clément Lynde, Sébastien Savoye, Christelle Latrille

► To cite this version:

Jean Maillet, Clément Lynde, Sébastien Savoye, Christelle Latrille. Impact of carbonate minerals on strontium and caesium reactivity in natural clay-rich materials. Environmental Science and Pollution Research, 2025, 32 (40), pp.23308-23328. 10.1007/s11356-025-36982-4. hal-05504658

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1 **Impact of carbonate minerals on strontium and caesium reactivity in natural clay-rich**
2 **materials**

3 Jean Maillet, Clément Lynde, Sébastien Savoye, Christelle Latrille.

4 Université Paris-Saclay, CEA, Service de Physico-Chimie, 91191 Gif-sur-Yvette, France

5 Corresponding author: Christelle Latrille: christelle.latrille@cea.fr; Phone: +33 (0) 1 69 08 34 24; Fax: +33 (0) 1 69 08 32 42

7

8 **Abstract**

Numerous databases and models have been developed to predict the behaviour of radio-contaminants (such as
⁹⁰Sr and ¹³⁷Cs) in the environment. Carbonate minerals found in surface environments, such as soils, sediments
and aquifers, significantly contribute to the chemical composition of pore water. The objective of this study is to
examine the potential influence of calcium (in solution) and carbonate (in solution or crystallized form) on the
retention of Sr and Cs on a multi-component alluvium. The isotherms acquired on the carbonate-free clay
fraction (less than 2 µm) were used to validate the ion-exchange process involved in the retention of Sr and Cs
on clay minerals. The concentration sorption isotherms of Sr and Cs at two Ca concentrations in solution clearly
show that there is a significant reduction of Cs and Sr retention as Ca increases in the background solution. Both
aforementioned conditions applied to the carbonated clay fraction indicate that the crystallized carbonates do not
limit accessibility to the solid sorption site for Sr and Cs. However, at the highest Sr and Ca concentrations, the
Sr retention increase suggests the formation of SrHCO₃⁺ and precipitation of strontianite (SrCO₃).

20 **Keywords:** Reactivity, Sr, Cs, Clay-rich materials, Carbonates, Ion-exchanger model, Retention, Adsorption

21

22 **1. Introduction**

Soil and groundwater contamination by radionuclides has been a growing concern since the advent of nuclear power generation in the 1950s, the use and tests of nuclear weapons after 1945 (Aarkrog et al. 1987; Hanson 2000) and more recently, subsequently to nuclear power plant accidents like Chernobyl or Fukushima (Bugai et al. 2020; Kasar et al. 2020). As fission products of uranium, ⁹⁰Sr and ¹³⁷Cs (Siegel and Bryan 2014) can induce serious health and ecological issues due to their high solubility and their long half-lives (28.8 and 30.0 years respectively). It is therefore essential to understand the physicochemical processes that govern the migration of these two radionuclides in soils and groundwater. In natural environments, Sr and Cs migration is mainly driven by solid-solution interactions. Clay mineral phases are mainly responsible for the surface retention of these elements. Previous studies have shown that Sr and Cs are primarily adsorbed by phyllosilicates (Comans et al. 1991; Gorgeon 1994; Latrille and Bildstein 2022; Nolin 1997; Reinoso-Maset and Ly 2016; Siroux et al. 2017; Wissocq et al. 2018). Phyllosilicates carry negative surface charges due to (i) isomorphic substitutions within their tetrahedral and octahedral layers and (ii) hydroxyl groups at the particle edges. In general, the free cations
present in natural fluids, such as Ca²⁺, Mg²⁺, K⁺ and Na⁺, and specifically Sr²⁺ and Cs⁺, can compensate for these surface charges (Gaucher 1998; Tournassat et al. 2004; Reinoso-Maset and Ly 2014; Siroux et al. 2017, 2018; Wissocq et al. 2018). Surface charges define the sorption sites, which vary depending on the type of mineral and can be distinguished by their structural origin or their chemical reactivity (Bradbury and Baeyens 2000; Missana et al. 2014; Wissocq et al. 2018). The affinity of cations for clay minerals depends on their selectivity for each type of sorption site type and on its speciation in solution.

Various models have been developed to describe these retention properties. Empirical models consider trace concentrations and different types of sites (Stumm and Sulzberger 1992). Therefore, they are not predictive and are unable to account for variations in the physicochemical conditions of the environment (pH and solution concentration). In natural environments, these physicochemical conditions vary greatly depending on the surrounding rock or soil. Consequently, these models are inadequate when predictions must account for (i) variations in the solution composition (El Aamrani et al. 2002; Tertre et al. 2010), and (ii) cation competition for adsorption on reactive sites (Poinssot et al. 1999; Reinoso-Maset and Ly 2014). For this reason, thermodynamic models (e.g. ion-exchange models) have been developed to explicitly account for this process involved in retention. Among these models, the multi-site ion exchanger model (MSIE) developed by Ly et al. (1991) was selected for this study. In this macroscopic model the solid reactive phases are ion exchangers characterized by negatively charged sites compensated by sorbed cations. This means that globally, the exchanger is electrically neutral, as well as the solution. The sorbed cations can be replaced by other cations from the solution by means of an ion exchange process. This choice takes into account the following points: (i) the proton is chosen as the reference cation because of its ability to exchange at all sorption sites and its ubiquitous occurrence in the environment, (ii) ion exchange is involved at all sites, and (iii) an extensive database of retention parameters for Ca, Sr and Cs taking into account the model formalism is used. Numerous studies on clay retention provided a robust database on clay minerals sorption properties (Savoye et al. 2012; Wissocq et al. 2018; Siroux et al. 2018, 2021). These studies allowed simplifying the description of the reactivity of a mineral assemblage, demonstrating the additivity of retention properties: the retention of a complex solid amounts the sum of the retentions due to each dominant reactive phase, weighted by their proportion in the assemblage. This approach has yielded very satisfactory results describing Sr and Cs retention in complex mineral assemblages (Savoye et al. 2012, 2015; Wissocq et al. 2018; Siroux et al. 2018, 2021).

Sedimentary and alluvial soils contain not only clay minerals but also significant amounts of carbonates, which can strongly influence pore water. Carbonate dissolution alters pH as well as calcium and bicarbonate concentrations in solutions. Because Ca and Sr exhibit similar chemical behavior, competition between Ca²⁺ and Sr²⁺ for phyllosilicate sorption sites must be considered. Sr also forms aqueous complexes with carbonate and can precipitate as strontianite (SrCO₃) under certain conditions (Sahai et al. 2000). In addition, adsorption, complexation and co-precipitation of Sr on carbonate phases (such as calcite or strontianite) in carbonated environments have been also evidenced by Jeong et al. (1996), Cole et al. (2000), Kamel (2010), Lerouge et al. (2017), Tertre et al. (2012). Finally, calcite can be closely associated with phyllosilicates, especially in natural materials. This raises two questions: can calcite physically limit the accessibility of phyllosilicate sorption sites for Cs and Sr? To what extent can calcite compete with phyllosilicates for Sr retention in carbonate clayey materials?
This study aims to investigate the influence of calcium (in solution) and carbonate (in solution or crystallized form) on the retention of Sr and Cs in a multi-component alluvium. To this end, three experimental and modelling steps of increasing complexity were performed. First, experimental Cs and Sr adsorption isotherms were performed on the carbonate-free clay fraction of the alluvium in the absence of bicarbonate in solution. Secondly, sorption experiments were carried out with two different Ca concentrations in the background solution to assess the influence of calcium in solution on Cs and Sr sorption. Thirdly, sorption experiments were carried out on the raw clay fraction isolated from the alluvium to assess the influence of bicarbonate in solution and crystallized carbonate minerals on Cs and Sr sorption. The multi-site ion exchange model (MSIE) was used to interpret the retention experiments. The behaviour of Cs and Sr was discussed by discriminating between adsorption, complexation in solution, complex adsorption and co-precipitation. The distribution of Ca, H, Sr and Cs on sorption sites can be used to calculate the individual cation contributions to charge balance on the sorption sites. This allows the cation competitive effect to be discussed as a function of the experimental conditions covered in the overall sorption isotherms acquired in the current study.

## 2. Modelling approach

### 2.1. Multi-site ion exchanger model

The multi-site ion exchanger model (MSIE) is based on the thermodynamics of chemical equilibria and considers the negatively charged phases compensated by cations as a neutral charged ion-exchanger. The ion-exchanger is described by several types of 'Xᵢ⁻' sites, each of one contributing to the global cation adsorption. These different sites are characterized by their exchange capacities ECᵢ and their selectivity coefficients K*ᵢ. The model is based on a macroscopic description and does not assume any structural site assignment (Jacquier et al. 2004). The proton is considered as the reference cation. Consequently, the cation selectivity coefficients are expressed with respect to H⁺ (Motellier et al. 2003). For more detail on the formalism of this model, readers can refer to Motellier et al. (2003) and Jacquier et al. (2004). The robustness of this approach has been demonstrated for describing the retention properties of clay minerals (Jacquier et al. 2004, 2001; Reinoso-Maset and Ly 2014, 2016; Tertre et al. 2009; Wissocq 2017; Wissocq et al. 2018; Siroux et al. 2017, 2018, 2021; Latrille and Bildstein 2022).

Considering a sorption site called 'Xᵢ⁻', the exchange equation between an H⁺ adsorbed on the Xᵢ⁻ site and a cation in solution M⁺ is expressed by Eq. 1.

$$m\{(X_i^-) - H^+\} + M^{m+}_{aq} \rightleftharpoons \{(X_i^-)_m - M^{m+}\} + mH^+_{aq} \quad (1)$$

With (Xᵢ⁻) - H⁺ and (Xᵢ⁻)ₘ - M⁺ representing the adsorbed species on the Xᵢ⁻ site, and m the valence of the cations M⁺.

The equilibrium constant K*<sub>H⁺/M⁺</sub><sup>Xᵢ</sup> is calculated with the activities of the cations in solution and adsorbed on the site Xᵢ⁻ (Eq. 2):
$$K_{H^+/M^{m+}}^{X_i} = ((X_i^-)_m - M^{m+})(H^+)^m/((X_i^-) - H^+)^m(M^{m+}) \quad (2)$$

The activity of species in solution is calculated from their concentrations and corresponding to ionic activity coefficients (Eq. 3).

$$(M^{m+}) = \gamma_{M^{m+}}[M^{m+}] \quad (3)$$

With $[M^{m+}]$ and $[H^+]$ representing the concentrations of $M^{m+}$ and $H^+$ in solution (mol·L⁻¹), and $\gamma_{M^{m+}}$ and $\gamma_{H^+}$ the activity coefficient of $M^{m+}$ and $H^+$ in solution (L·mol⁻¹) respectively.

In carbonate media, Sr can form complexes with carbonate species in solution such as $HCO_3^-$. The resulting $SrHCO_3^+$ complex can be adsorbed onto negatively charged surfaces. The Ringböm coefficient $\alpha$ is taken into account in such reaction (Eq. 4).

$$[M^{m+}] = [M]/\alpha_{M^{m+}} \quad (4)$$

The ionic activity coefficient is calculated by using the Davis relationship valid for the ionic strength of solution between $10^{-1}$ and $10^{-4}$ mol L⁻¹ as expressed in the PhreeqC speciation calculation code (Eq. 5).

$$-\log(\gamma) = Az^2\left(\left(I^{1/2}/(1 + I^{1/2})\right) - 0.3I\right) \quad (5)$$

With $z$ being the ion valency, $I$ the ionic strength of the solution, $A$ a constant dependent on the temperature, the density and the dielectric constant of the solvent (water) (Nordstrom and Munoz 1994).

The activity of the adsorbed species remains unknown. The MSIE convention (Ly et al. 1991) assumes that the ratio of the activity coefficients (F) of the adsorbed species remains constant (Eq. 6). Consequently, the apparent coefficient, also called the selectivity coefficient of site ‘Xi⁻’ for the cation $M^{m+}$, $K_{H^+/M^{m+}}^{*X_i}$ is defined in Eq. 6:

$$K_{H^+/M^{m+}}^{*X_i} = \frac{[X_i^- - M^{m+}] [F_{X_i^- - M^{m+}} + [H^+]^m] \gamma_{H^+}}{[X_i^- - H^+]^m [F_{X_i^- - H^+} + [M^{m+}]^m] \gamma_{M^{m+}}} = \frac{[X_i^- - M^{m+}] [H^+]^m \gamma_{H^+}}{[X_i^- - H^+]^m [M^{m+}]^m \gamma_{M^{m+}}} \quad (6)$$

Using saturation curves and major cations (i.e. $Ca^{2+}$, $K^+$, $Na^+$, $Cs^+$) as a function of the pH, the exchange capacity (ECᵢ) of three major sites could be determined experimentally on homo-ionic illite and smectite (Gorgeon 1994; Peynet 2003; Wissocq et al. 2018). The methodology to study the saturation of an exchanger with a major cation is detailed elsewhere (Motellier et al. 2003; Reinoso Maset and Ly 2014; Stammose et al. 1992). A fourth type of site, a low exchange capacity and a high affinity site, is only effective at low concentrations (Missana et al. 2004). Consequently, its exchange capacity is usually determined from concentration isotherms (Latrille and Bildstein 2022). The sum of the site exchange capacities must be equal to the total exchange capacity (CEC) of the mineral.

The exchange capacity of a site ‘Xi⁻’ is the sum of the ion-adsorbed concentrations at this site (Eq. 7):

$$EC_i = [(X_i^-)_m - M^{m+}] + \cdots + [X_i^- - H^+] \quad (7)$$

Studies using this approach confirmed that ECᵢ is an inherent property of the solid, regardless of the competing cation (Wissocq 2017).
The concentration of an M⁺ cation adsorbed on the site 'Xi⁻' competing with the proton and a divalent D²⁺ cation is given in Eq. 8. Similarly, for an N²⁺ cation, the concentration is expressed by Eq. 9. These equations are derived from Eq. 2, Eq. 4 and Eq. 7 using the same approach as that described by Motellier et al. (2003).

$$ [X_i^- - M^+] = \frac{\left( -\frac{10^{-pH}}{K_{H^+/M^+}^{*i} + \frac{\gamma M^+ + [M^-]}{\alpha_{M^+}}} + 1 \right) + \left( \frac{10^{-pH}}{K_{H^+/M^+}^{*i} + \frac{\gamma M^+ + [M^-]}{\alpha_{M^+}}} + 1 \right) + 8EC_i \left( \left( \frac{10^{-pH}}{K_{H^+/M^+}^{*i} + \frac{\gamma M^+ + [M^-]}{\alpha_{M^+}}} \right)^2 \left( \frac{K_{2H^+/D^2+\gamma M^+}^{*i} + [D^-]}{10^{-2pH}} \right) \right)}{4 \left( \frac{10^{-pH}}{K_{H^+/M^+}^{*i} + \frac{\gamma M^+ + [M^-]}{\alpha_{M^+}}} \right)^2 \left( \frac{K_{2H^+/D^2+\gamma M^+}^{*i} + [D^-]}{10^{-2pH}} \right)} \quad (8) $$

$$ [X_i^- - N^{2+}] = \frac{\left( \sqrt{8EC_i \left( \left( \frac{K_{2H^+/D^2+\gamma M^+}^{*i} + [D^-]}{10^{-2pH}} \right) \left( \frac{10^{-2pH}}{K_{2H^+/N^2+\gamma M^+}^{*i} + \frac{[N^-]}{\alpha_{N^2+}}} \right) + 1 \right) + \left( \frac{10^{-2pH}}{K_{2H^+/N^2+\gamma M^+}^{*i} + \frac{[N^-]}{\alpha_{N^2+}}} \right) - \sqrt{\left( \frac{10^{-2pH}}{K_{2H^+/N^2+\gamma M^+}^{*i} + \frac{[N^-]}{\alpha_{N^2+}}} \right)^2} \right)}{\frac{1}{16} \left( \left( \frac{K_{2H^+/D^2+\gamma M^+}^{*i} + [D^-]}{10^{-2pH}} \right) \left( \frac{10^{-2pH}}{K_{2H^+/N^2+\gamma M^+}^{*i} + \frac{[N^-]}{\alpha_{N^2+}}} \right) + 1 \right)^2} \quad (9) $$

With $K_{H^+/M^+}^{*i}$, $K_{2H^+/D^2+\gamma M^+}^{*i}$ and $K_{2H^+/N^2+\gamma M^+}^{*i}$ representing the selectivity coefficients of cations M⁺, D²⁺ and N²⁺ towards H⁺, and ECᵢ representing the exchange capacity of site Xi⁻.

The selectivity coefficients $K_{H^+/M^+}^{*i}$ of each sorption site Xi⁻ were determined for major cations (Ca²⁺, Na⁺, etc.) and trace cations (Sr²⁺ and Cs⁺) by fitting Eq. 8 and Eq. 9 to saturation curves, the pH and concentration isotherms obtained on pure phases (illite and smectite).

An additive approach was used to simulate the adsorption properties of a multi-component material. This approach considers the site capacities of the mineral assemblage as the sum of the site capacities of each reactive mineral component, weighted by their relative abundance in the assemblage (Wissocq et al. 2018).

## 2.2. Model uncertainties

Sorption isotherms on multi-component material were simulated using the MSIE model. The modelled isotherm uncertainties were determined through a probabilistic Monte-Carlo method based on the law of large numbers (Kroese et al. 2011). Specifically, a large number of model input data sets (1618, to be precise) were randomly generated according to normal laws. The model input data set comprised experimental data and their uncertainties. It included the uncertainties associated with Ca, Cl, HCO₃⁻ and Sr or Cs concentrations and pH measurements. The modelled isotherm uncertainties also considered the ECᵢ and the selectivity coefficient, and their respective uncertainties for each site of the minerals constituting the assemblage and referenced in a database (Table 1). The Kd was calculated for each model input data set with the relationships described in Section 3.3, which are implemented in the geochemical calculation code PhreeqC (Parkhurst and Appelo 2013). The 1618 model input data sets were used to determine the distribution of the Kd values, which represents the dispersion domain of the model. A 90% confidence interval was then calculated from this dispersion domain.
## 2.3. Database

The primary parameters of the exchanger ($EC_i$ and $K_{2H^+/Ca^{2+}}^{*X_i}$) were determined by fitting the saturation curve of a homo-ionic Ca-exchanger at varying pH. This study uses the site capacities of major sites previously determined by Gorgeon (1994) and validated by Wissocq et al. (2018). To reduce the uncertainties of the selectivity coefficients, $K_{2H^+/Ca^{2+}}^{*X_i}$ determined by Wissocq et al. (2018), the Ca saturation curve on illite was reinterpreted within the framework of the multi-site ion exchanger model. This study applied the $EC_i$ of montmorillonite determined by Nolin (1997) and the $K_{2H^+/Ca^{2+}}^{*X_i}$ determined by Wissocq et al. (2018) based on the saturation curve and the Na/Ca concentration isotherms obtained by Peynet (2003) on montmorillonite; this was also the case for Tertre et al. (2009) and Robin et al. (2015).

A site of low capacity and high selectivity has been evidenced from Cs isotherms in Ca-illite (Latrille and Bildstein 2022). Thus, these $EC_i$ and $K_{H^+/Cs^+}^{*X_i}$ of illite were selected for this study. For the sake of consistency, Sr isotherms acquired on illite and smectite by Wissocq et al. (2018) were reinterpreted with four sites, considering the $EC_i$ determined by Latrille and Bildstein (2022) for illite. Likewise, the Cs isotherms on smectite by Wissocq et al. (2018) were reinterpreted with four sites, by refining the $EC_i$ of the low-capacity site and minimizing the selectivity coefficient uncertainties.

Once the data was retrieved, the MSIE model was applied to determine the selectivity coefficients by fitting the model to the data using the MS Excel Solver. The parameter uncertainties were finally determined using the SolverAid macro from De Levie (2004).

Table 1 lists the $EC_i$ and selectivity coefficients obtained for Ca-illite and Ca-smectite. It is worth noting that the $K_{2H^+/Ca^{2+}}^{*X_i}$ and $K_{2H^+/Sr^{2+}}^{*X_i}$ values obtained for Xb, Xd, Xg and Xh are comparable, which is consistent with the similar chemical behaviours of Ca and Sr. Moreover, the contribution of the Xh sites in Cs adsorption on smectite is too low to allow us to obtain an accurate estimation of the $LogK_{H^+/Cs^+}^{*Xh}$.

<table><caption>Table 1: Exchange capacity and selectivity coefficient of the four sites of illite and smectite for $2H^+/Ca^{2+}$, $2H^+/Sr^{2+}$ and $H^+/Cs^+$ used in this study</caption><thead><tr><th>Sites</th><th>ECi (eq·kg<sup>-1</sup>)</th><th>LogK<sup>*Xi</sup><sub>2H<sup>+</sup>/Ca<sup>2+</sup></sub></th><th>LogK<sup>*Xi</sup><sub>2H<sup>+</sup>/Sr<sup>2+</sup></sub></th><th>LogK<sup>*Xi</sup><sub>H<sup>+</sup>/Cs<sup>+</sup></sub></th></tr></thead><tbody><tr><td rowspan="4">Illite</td><td>Xa</td><td>3.03 10<sup>-4</sup> <sup>b</sup></td><td>-0.22 ± 0.57</td><td>2.28 ± 0.28</td><td>4.86 ± 0.07 <sup>b</sup></td></tr><tr><td>Xb</td><td>0.131 <sup>a</sup></td><td>-2.27 ± 0.27</td><td>-2.28 ± 0.24</td><td>-0.52 ± 0.27 <sup>b</sup></td></tr><tr><td>Xc</td><td>0.043 <sup>a</sup></td><td>-4.36 ± 0.13</td><td>-3.85 ± 0.17</td><td>-0.19 ± 0.12 <sup>b</sup></td></tr><tr><td>Xd</td><td>0.074 <sup>a</sup></td><td>-11.81 ± 0.08</td><td>-11.25 ± 0.06</td><td>-4.87 ± 0.63 <sup>b</sup></td></tr><tr><td rowspan="4">Smectite</td><td>Xe</td><td>2.02 10<sup>-4</sup></td><td>-0.22 ± 0.33 <sup>a</sup></td><td>2.96 ± 0.32</td><td>3.16 ± 0.34</td></tr><tr><td>Xf</td><td>0.387 <sup>a</sup></td><td>-0.49 ± 0.64 <sup>a</sup></td><td>-0.31 ± 0.13</td><td>0.62 ± 0.23</td></tr><tr><td>Xg</td><td>0.361 <sup>a</sup></td><td>-4.35 ± 7.80 <sup>a</sup></td><td>-4.74 ± 0.82</td><td>-2.27 ± 2.03</td></tr><tr><td>Xf</td><td>0.139 <sup>a</sup></td><td>-14.84 ± 13.50 <sup>a</sup></td><td>-14.99 ± 3.20</td><td>-6.63 ± 29632</td></tr></tbody></table>
In this study, the exchange capacity of the minor sites, Xa and Xe, was increased by a factor of 3 compared with previous studies (Wissocq et al. 2018; Latrille and Bildstein 2022). This increase is due to a significant difference in the observed grain-size between the reference materials used to build the database and those of the materials studied. The grain-size distribution of the infra 2 µm carbonate free fraction extracted from the studied alluvium shows a bimodal grain-size distribution in volume (Supplementary information 1), which has been attributed to the main clay minerals, illite and smectite. Compared with the grain-size distribution of pure illite and smectite used in the database, the studied material contains particles with smaller sizes than those of the pure phases. In this sense, the decrease in the particle size increases the reactive surface area (SI figure 2b), which can be extrapolated to the minor-site ECi values of pure illite and smectite. This factor 3 was simple to achieve at better sorption isotherm simulations whatever the cation and the experimental conditions, respecting the CEC samples. Nevertheless, the modified CEₓₐ values remain lower than those determined by Wissocq et al. (2018) at 1 10⁻³ eq·kg⁻¹ and Altmann et al. (2015) at 2 10⁻³ eq·kg⁻¹ on illite du Puy with divalent cations. In addition, the modified CEₓₑ remains close to that of 5 10⁻⁴ eq·kg⁻¹ determined during the Cs sorption experiments by Peynet (2003). Consequently, the CEₓₐ and CEₓₑ multiplied by 3 are consistent with values found in the literature.

Some uncertainties, in particular those of $\text{Log}K_{2\text{H}^+/\text{Ca}^{2+}}^{*\text{X}_i}$ for the Xa, Xe, Xf and Xg sites and of $\text{Log}K_{\text{H}^+/\text{Cs}^+}^{*\text{X}_i}$ for the Xh site, are greater than their nominal value (more than 100% of the selectivity value). For the sake of modelling convergence to simulate the isotherm uncertainties, their uncertainties were reduced to 10% of the nominal values. To this end, a 10% uncertainty was assigned to each ECi of the sorption sites in order to calculate the modelled isotherm uncertainty.

## 3. Material and method

### 3.1. Materials

The studied material was an alluvial deposit collected at a depth of two meters below a calcosol at the CEA Cadarache site (southern France). A raw sample was crumbled and air dried for 7 to 14 days-then sieved at 2 mm and the < 2 mm fraction was dry-stored at 20°C. The < 2 mm raw material contained 35% carbonates, 20 % clay minerals, < 3% organic matter, and 42 % quartz. Bulk-chemical analyses indicated-traces of Sr and Cs at levels of 300 and 3.2 µg g⁻¹ respectively. These natural Sr and Cs contents were shown to be neither soluble nor exchangeable.

Grain-size fractionation was performed on the raw < 2 mm sample by wet sieving and sedimentation according to AFNOR NF X31-107 standard. For this purpose, the < 2 mm fraction was dispersed in Milli-Q water (Millipore®, 18.2 MΩ cm⁻¹) with a solid/water ratio of 1.5/100 (g·mL⁻¹), shaken end-over-end overnight and sieved with nylon sieves at 200 µm, 50 µm and 20 µm. The < 2 µm fraction was separated from the 20 - 2 µm by sedimentation. The < 2 µm suspension was centrifuged 40 minutes at 33617 g then air dried during 3 to 5 days. Wet particle-size analysis showed 3% of coarse sand (2 mm - 200 µm) and 17% of fine sand (200 - 50 µm), 23% of coarse silt (50 - 20 µm) and 37% of fine silt (20 - 2 µm), and 20% of clay (< 2 µm).
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In order to focus on the chemical reactivity of the alluvium clay fraction, the carbonated clay fraction was collected after the wet fractionation process. The carbonate free clay fraction was extracted from the < 2 mm fraction decarbonated before wet fractionation. Carbonate dissolution was achieved by successively adding small amounts of 0.1 mol·L⁻¹ HCl in the < 2 mm suspension until pH stabilization at pH 5. The decarbonated sample was rinsed with ultrapure water five times before grain-size fractioning. The decarbonation process was controlled by XRD measurement of the clay fraction, by indicating the absence of (hkl) peaks of calcite. Finally, the carbonate and carbonate free clay fractions were conditioned by equilibration with solutions of different compositions listed in Table 2. The samples were preconditioned by dispersing the solids in their respective background solutions (see Table 2) at a solid/liquid ratio of 1:10 (g mL⁻¹). The suspensions were shaken for 5 days. Around 3 and 5 cycles were performed to ensure optimal conditioning. The suspensions were then centrifuged at 27670 g for 40 minutes. Sludges were rinsed with ethanol and air dried.

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The clay mineral composition was identified on the carbonate-free clay fraction using a PANalytical X'Pert diffractometer at Cu Kα radiation (λ = 1.54 Å) equipped with a X'Celerator detector. The samples were prepared as oriented deposits of air dried or ethylene glycol treated clay fractions on glass plates (see e.g., Kinter and Diamond, 1956; Reynolds, 1992). Preparations were scanned between 4 and 40°, with a step size of 0.013 and a counting time of around 60 minutes. The clay minerals identified by XRD were kaolinite, illite, smectite, illite/smectite mixed layers and chlorite. Clay minerals were quantified by modelling the X-ray diffraction pattern in both air-dried and ethylene-glycol-solvated states (SI 2), acquired on the carbonate-free clay fraction, with the Sybilla© software developed by Chevron™ (Aplin et al. 2006). The assemblage consisted of kaolinite (29.8wt%), discrete illite (26.4wt%), mixed layers illite/smectite (IS) with 29.3% IS (94wt%/6wt%), 9% IS (77wt%/23wt%) and 3.5wt% IS (82%/18%), discrete chlorite (1.4wt%) and discrete smectite (0.5wt%). The quantification uncertainty was evaluated at 5wt% from the difference of XRD spectra between air-dried and ethylene glycol treated clay fractions. This uncertainty was then used to calculate the model uncertainty.

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The cation exchange capacity (CEC) of the carbonate-free clay fraction was determined by Sr/Cs exchange. Firstly, 0.1 g of air-dried solid was dispersed in 5 mL of 0.05 mol·L⁻¹ SrCl₂ solution with 50 µL of 10¹ mol·L⁻¹ Sr(OH)₂ in order to achieve a pH of around 8. The suspension was orbitally shaken for 7 days; this contact time is sufficient to ensure chemical balance as previously shown by Latrille and Bildstein (2022) and Wissocq et al. (2018). It was then centrifuged for 40 minutes at 33617 g and the supernatant was replaced by ethanol for 1 h to eliminate the excess salt and finally air dried for 2 days. The adsorbed Sr²⁺ was then extracted with Cs by dispersing the solid in 5 mL of 0.1 mol·L⁻¹ CsCl solution with 50 µL of 10⁻¹ mol·L⁻¹ CsOH solution. The suspension was orbitally shaken for 7 days, and centrifuged for 40 minutes at 33617 g. The supernatant was separated and analyzed by ion chromatography. The CEC of the carbonate-free clay fraction was estimated at 29.7 ± 2.9 meq·100g⁻¹. Potential contributions of iron and aluminium oxides to CEC were negligible due to their very low amount in the solid (not identified by XRD) and their charge at pH 8 (Villalobos et Leckie 2000, Kasprzyk-Hordern 2004). Similarly, the contribution of organic matter from this clay fraction was estimated at 1 meq·100g⁻¹. This is below the uncertainty of the CEC measurement.
For sorption modelling, the mineral composition of the clay-size fraction was estimated to 93% of illite and 7% of smectite (detailed in Supplementary information 2). This simplified mineral composition is consistent with the XRD quantification and the CEC of the carbonate-free clay fraction.

## 3.2. Solutions

### 3.2.1. Chemical composition

The composition of the solutions used in this study was defined according to the mineral composition of the clay fractions at equilibrium: carbonate or carbonate-free clay fraction. Two concentrations of $CaCl_2$ at $10^{-3}$ and $10^{-2}$ mol·L$^{-1}$ (respectively condition 1 and 2, Table 2) were chosen to perform the experiments with the carbonate-free clay fraction. In carbonate media, the prepared solutions must be equilibrated with calcite. A water solution was then equilibrated with calcite by adding 4 g L$^{-1}$ of calcite to a vessel open to the atmosphere. The solution was stirred for at least 10 days, then filtered at 0.45 µm and stored at 20°C open to the atmosphere with a sample of calcite trapped in a dialysis tube to maintain solid contact and thus calcite equilibrium. This solution was used to achieve experimental condition 3. The solution containing both $CaCl_2$ and $HCO_3^-$ (condition 4) was prepared by equilibrating a $10^{-2}$ mol·L$^{-1}$ $CaCl_2$ solution with calcite. The chemical conditions are given in Table 2. Complementary information on the different compositions described below is available in Supporting Information 2.

<table><caption>Table 2: Theoretical compositions of the solutions used to perform the retention experiments on the alluvium clay-fractions</caption><thead><tr><th>Experimental condition</th><th>Solid clay fraction</th><th>[Ca<sup>2+</sup>]<br>(mol·L<sup>-1</sup>)</th><th>[Cl<sup>-</sup>]<br>(mol·L<sup>-1</sup>)</th><th>[HCO<sub>3</sub><sup>-</sup>]<br>(mol·L<sup>-1</sup>)</th><th>pH</th><th>I<br>(mol·L<sup>-1</sup>)</th></tr></thead><tbody><tr><td>1</td><td>Carbonate-free</td><td>1 10<sup>-3</sup></td><td>2.00 10<sup>-3</sup></td><td>0</td><td>7.50</td><td>3.0 10<sup>-3</sup></td></tr><tr><td>2</td><td>Carbonate-free</td><td>1 10<sup>-2</sup></td><td>2.00 10<sup>-2</sup></td><td>0</td><td>8.00</td><td>3.0 10<sup>-2</sup></td></tr><tr><td>3</td><td>Raw</td><td>5 10<sup>-4</sup></td><td>0</td><td>1 10<sup>-3</sup></td><td>8.15</td><td>1.5 10<sup>-3</sup></td></tr><tr><td>4</td><td>Raw</td><td>1 10<sup>-2</sup></td><td>1.95 10<sup>-2</sup></td><td>5 10<sup>-4</sup></td><td>7.00</td><td>3.0 10<sup>-2</sup></td></tr></tbody></table>

### 3.2.2. Cs and Sr speciation in the operating conditions and equilibrium phases

The speciation of Cs and Sr in the studied solutions was calculated with the PhreeqC software using phreeqc.dat and the ThermochimieV10 database (Figure 1). The results indicate that Sr and Cs are present in their free cationic form at over 95% and 98% respectively under all the experimental conditions. In solution, the other forms were: $SrHCO_3^+$ and $CsCl$, followed by $SrCl^-$ in negligible concentrations. The saturation index (SI) of strontianite ($SrCO_3$) calculated for solutions 3 and 4 (Table 2) indicates undersaturation until the Sr concentrations in solution reach $10^{-4}$ mol·L$^{-1}$ and $10^{-3}$ mol·L$^{-1}$ (I at $1.5 10^{-3}$ and $3 10^{-2}$ mol·L$^{-1}$, respectively). At $10^{-2}$ mol·L$^{-1}$ Ca concentration in solution, the strontianite saturation index decreases due to the decrease in the activity coefficient. No carbonate phase of Cs was expected according to the database used in this study.
<figure><img src="image_2.png" /><figcaption>**Fig. 1** Speciation of Sr (blue circle), Cs (red circle), SrHCO₃⁺ (blue square) and CsCl (red square) calculated under experimental retention conditions within the measured Sr and Cs concentration range. The domain of the strontianite saturation index (SI) upper to 0 is delimited in blue</figcaption></figure>

**3.3. Acquisition of Cs and Sr adsorption/desorption isotherms**

Sr and Cs sorption isotherms were acquired with 14 to 18 batches according to the experimental approach previously detailed by Wissocq et al. (2018), Siroux et al. (2021), Dubus et al. (2023). Experiments were carried out at room temperature (20 ± 2°C). All solutions and suspensions were prepared by weighing. The Sr and Cs sorption isotherms in carbonate or carbonate-free media were performed with the mass/volume ratio reported in Table 3. The different values of the m/v ratio were adjusted to introduce a range of Sr moles comparable to the carbonate-free condition (Table 2) at both tested carbonate conditions (Table 2), considering radioactive decay and optimizing the measurement accuracy of the ¹³⁷Cs radiotracer. The solids were dispersed in 7 mL or 30 mL Nalgene polycarbonate centrifuge tubes depending on the background solution volume (Table 3): 0.05 g to 0.1 g of air-dry solid was dispersed in 5 to 15 mL of background solution and equilibrated for 18 to 24 hours with end-over-end stirring. SrCl₂ (or CsCl) solutions (containing only stable isotopes) spiked with 50 µL of ¹³⁷CsCl or ⁸⁵SrCl₂ solutions were then added to the suspensions to cover a concentration range from 10⁻².⁵ to 10⁻⁷ mol·L⁻¹ Sr and from 10⁻².⁵ to 10⁻⁹ mol·L⁻¹ Cs. The lowest concentration of Sr or Cs corresponded to conditions without stable Sr or Cs in solution. The 50 µL of ¹³⁷CsCl or ⁸⁵SrCl₂ solutions diluted in 0.015 mol·L⁻¹ HCl contained an activity about 5000 Bq (corresponding to 10⁻⁶ and 10⁻⁸ mol·L⁻¹ of Cs and Sr per batch respectively). A Ca(OH)₂ solution at 0.05 mol·L⁻¹ was added to stabilize the pH between 7.5 and 8.2. This was done to maintain a calcite equilibrium and/or restrict pH variations between the different conditions (carbonate-free and carbonate media), and to neutralize the acidity introduced by the radiotracer solution. The suspensions were then orbital-stirred for 7 days and centrifuged at 27670 g for 45 min (Beckman Optima LE-80 K, Beckman Ultracentrifuge). ¹³⁷Cs (30.02 years decays to ¹³⁷barium) and ⁸⁵Sr (64.8 days decays to ⁸⁵rubidium) activities were measured on the supernatants by gamma counting (2480Wizard², NaI detector, Revvity); Ca and Cl concentrations were
measured by ion chromatography (Metrohm 850 professional IC; 0.8 and 0.9 mL min⁻¹ flow rate; C4 and ASUP7 column; HNO₃ 3.10⁻³ mol·L⁻¹ (diluted from 75%HNO₃, N°CAS 7697-37-2) and Na₂CO₃ 3.6·10⁻³ mol·L⁻¹ (N°CAS 497-19-8) eluent for cation and anion analysis respectively); bicarbonate concentration as HCO₃⁻ was measured by visible UV (Sarazin *et al.* 1999) (BBp (N°CAS 85-68-7) and CH₂O₂ (N°CAS 64-18-6) with CaCl₂ (N°CAS 10043-52-4) at background solution, adsorption wave at 591 nm, Cory 60 UV-VIS Agilent technologies) and pH was checked (InLab® Micro METTLER TOLEDO, at 22°C with pH buffer at 4.01, 7.0 and 12.0 Certipur®, Supelco®).

To test the reversibility of the Cs⁺ and Sr²⁺ adsorption, desorption experiments were carried out on the slurry obtained after the adsorption step. For this desorption step, the background solutions (free of Cs or Sr) were used to exchange the adsorbed Cs⁺ or Sr²⁺ with Ca²⁺ and H⁺ in solutions, respecting the pH, the solid-solution ratio and the contact time used in the adsorption step. Like for the adsorption step, suspensions were orbital-shaken for 7 days and centrifuged at 27670 g for 45 min. ¹³⁷Cs, ⁸⁵Sr, Ca²⁺ and H⁺ were analysed by gamma counting and ion chromatography. pH was checked for each supernatant.

<table><caption>Table 3: Experimental solid-liquid ratio used for batch experiments</caption><thead><tr><th>Experimental condition</th><th>Tracer</th><th>Solid mass (g)</th><th>Solution volume (mL)</th><th>m/v (g·mL<sup>-1</sup>)</th></tr></thead><tbody><tr><td rowspan="2">1</td><td>Sr</td><td>0.10</td><td>7</td><td>1.4·10<sup>2</sup></td></tr><tr><td>Cs</td><td>0.05</td><td>5</td><td>1.0·10<sup>2</sup></td></tr><tr><td rowspan="2">2</td><td>Sr</td><td>0.10</td><td>15</td><td>6.7·10<sup>3</sup></td></tr><tr><td>Cs</td><td>0.05</td><td>6</td><td>8.0·10<sup>3</sup></td></tr><tr><td rowspan="2">3</td><td>Sr</td><td>0.10</td><td>7</td><td>1.4·10<sup>2</sup></td></tr><tr><td>Cs</td><td>0.05</td><td>5</td><td>1.0·10<sup>2</sup></td></tr><tr><td rowspan="2">4</td><td>Sr</td><td>0.10</td><td>15</td><td>6.7·10<sup>3</sup></td></tr><tr><td>Cs</td><td>0.05</td><td>5</td><td>1.0·10<sup>2</sup></td></tr></tbody></table>

The adsorption and desorption results were expressed in terms of the partitioning coefficients Kd (ADS and DES) (L·Kg⁻¹), which is defined by the ratio of the adsorbed species M concentration (|M| in mol·Kg⁻¹) divided by the M⁺ concentration in solution (|M⁺|sol,eq in mol·L⁻¹). By means of the radioisotopes, the Kd was also estimated using the activity initially introduced and the activity in solution at equilibrium.

Kd(ADS) and Kd (DES) were calculated using Eq. 10 and Eq. 11:

$$K_d(ADS) = \frac{[M]_{ads}}{[M^{m+}]_{sol,eq}} = \left( \frac{A_{ini}}{A_{sol,eq}} - 1 \right) \frac{V}{m} \qquad (10)$$

$$K_d(DES) = \frac{[M]_{des}}{[M^{m+}]_{sol,eq}} = \left( \frac{A_{ini,DES}}{A_{sol,eq}} - 1 \right) \frac{V}{m} \qquad (11)$$

With Aₗₗᵢ (Bq) and Aₗₗₐₐ (Bq) representing the initial and equilibrium activities of the solutions, V the total volume of the solution (L), m the introduced mass of solid (kg), and Aₗₗᵢ,DES the initial activity for the desorption experiment calculated according to Eq. 12.
$$A_{ini,DES} = A_{sorbed} + A_{sol,eq,ADS} * V_{residual,ADS} \qquad (12)$$

With $A_{sorbed}$ representing the sorbed activity during adsorption step, $A_{sol,eq,ADS}$ the activity concentration measured in solution during the adsorption step (Bq.mL⁻¹), and $V_{residual,ADS}$, the volume remaining in the batch after removing the supernatant from the adsorption step.

The initial activities $A_{ini}$ introduced into the batch for the adsorption step were determined using experimental blanks, i.e., solid-free batches receiving the same spike. Equilibrium concentrations (Eq. 13) were calculated from the moles introduced and from the initial and equilibrated activity ratios, assuming that there was no isotopic fractionation:

$$[M^{m+}]_{sol,eq} = M_{introduced} \left(\frac{A_{sol,eq}}{A_{ini}}\right) \qquad (13)$$

With $A_{ini}$ and $A_{sol,eq}$ being the initial and equilibrium activities of the solutions, and $M_{introduced}$ the quantities of M element introduced (mole).

The adsorbed concentrations were calculated from the equilibrium concentrations and the partition coefficient (Eq. 10 or Eq. 11). The activity of the residual adsorption solution, not recoverable from the slurry, was considered to define the initial activity of ¹³⁷Cs or ⁸⁵Sr adsorbed on the solids for the desorption step.

### 3.4. Experimental uncertainties

The experimental uncertainties of the equilibrium concentration and the Kd were calculated by propagating the estimated measurement errors. Each measured parameter (weighing, gamma counting) had a defined standard deviation (Ku 1966). The errors estimated for mass and volume (m and v in Eq. 10 or Eq. 11) were derived from the measuring devices. The error on gamma counting (A on Eq. 10 or Eq. 11) was calculated using a Poisson distribution. A Python implementation of the uncertainty module, created by Lebigot (2009), was used to calculate the standard deviation (σ). The experimental error bar for each batch experiment data was shown as ± 2σ.

## 4. Results and discussion

To understand the influence of crystallized carbonate, carbonate and calcium in solution on the ion exchange process involved in strontium and caesium retention, various retention experiments (see Section 3.3) were carried out under increasingly complex experimental conditions. In this section, the conditions are presented from the simplest to the most complex: (1) the sorption of Sr and Cs on the carbonate-free clay fraction, (2) the effect of the increasing calcium concentration in solution on the retention of Sr and Cs in the carbonate-free clay fraction, and, (3) the effect of carbonate content of both the solid and the solution on Sr and Cs retention as a function of the high ionic strength of the solution. All experimental isotherms presented later were interpreted using the multisite ion exchanger model (MSIE).

### 4.1. Sr and Cs retention on the carbonate-free clay fraction

#### 4.1.1. Strontium sorption on the carbonate-free clay fraction
The results of the strontium sorption experiments with the carbonate-free clay fraction under test condition 1 (Table 2) are shown in Figure 2. The isotherm is based on 14 experimental batches with Sr concentrations ranging from $10^{-2.5}$ to $10^{-8}$ mol·L$^{-1}$. The measured pH values for the adsorption and desorption were 7.2 ± 0.2 and 7.22 ± 0.2 respectively. The average calcium concentration at equilibrium was 6.4 $10^4$ mol·L$^{-1}$ for both steps. Dissolved carbonate ($HCO_3^-$) was not detected in either the background or the equilibrium solutions.

In agreement with Cherif (2017), the highest retention was obtained at the lowest concentrations ($< 10^{-5}$ mol·L$^{-1}$) with a log Kd = 2.9 L·Kg$^{-1}$. Considering the measurement uncertainties, the Kd values below $10^{-5}$ mol·L$^{-1}$ Sr concentrations at equilibrium did not vary significantly (Figure 2). This flat-shaped isotherm shows constant adsorption with the increase in the Sr concentration. For Sr concentrations above $10^{-5}$ mol·L$^{-1}$, the distribution coefficients decrease from log Kd = 2.9 to log Kd = 1.23 L·Kg$^{-1}$ at a maximum Sr concentration of $10^{-2.5}$ mol·L$^{-1}$. This decrease in the distribution coefficient indicates a gradual saturation of the sorption sites with increasing concentration. The shape of the isotherm is in agreement with those previously described in the literature for strontium on a natural sediment (Hsu et al. 1994; Koss and Kim 1990), on soils (Siroux et al. 2021), on an illite/smectite clay mixture (Missana et al. 2008), on illite and sedimentary rock (Wissocq et al. 2018), and on bentonite MX80 (Siroux et al. 2017).

Sr desorption experiments on the carbonate-free clay fraction carried out under comparable physical and chemical conditions as those used for the adsorption experiments show no significant difference with the adsorption Kd values. This demonstrates the reversibility of the adsorption process (Figure 2) at chemical equilibrium. At equilibrium, the number of moles of calcium in solution is equal to the sum of the moles of calcium introduced into the batch added to the moles of calcium desorbed by the exchange with strontium (in moles), thus respecting the calcium mass balance (Supporting Information 3). This corroborates the fact that Sr retention on this complex material is controlled by an ion exchange process between the strontium in solution and the calcium adsorbed on the solid.

<figure><img src="image_3.png" /><figcaption>**Fig 2** Sr isotherm on the carbonate-free clay fraction as a function of the Sr concentration at equilibrium at $I \approx 3 \times 10^{-3}$ mol·L$^{-1}$: adsorption and desorption Kd values in black and grey points respectively with a 2 σ uncertainty. The red line indicates the MSIE direct modelling, and the 90% confidence interval of the model is shown by the light and dark grey shading for the adsorption and desorption models respectively. The dashed lines and the</figcaption></figure>
dotted lines show the high capacity/ low selectivity (Xa and Xe) and the low-capacity/ high-selectivity (Xb, Xc, Xd, Xf, Xg and Xh) sites respectively. Purple and orange colours indicate illite and smectite respectively.

The simulation of the Sr retention isotherm using the MSIE model uses the database (Table 1) and the modelling approach described in Section 2. The reactivity of the carbonate-free clay fraction is assimilated to that of a mixture of 93% illite and 7% smectite. The reactivity of illite and smectite is described by three high capacity/low selectivity sites and one low-capacity/high-selectivity site each. Figure 2 displays the modelling results of direct simulation, highlighting the discrimination between the sorption sites of illite and smectite. The direct simulation (red line) agrees with the experimental data, especially for Sr concentrations below 10⁻⁵.⁵ mol·L⁻¹ and above 10⁻³.⁵ mol·L⁻¹. The simulation slightly under-estimates the retention in this concentration ranges. However, given the model uncertainties discussed in Section 2.3, the model adequately reproduces Sr retention on the carbonate-free clay fraction. Sr²⁺ sorbs selectively on three sorption sites corresponding to the high-capacity sites (Xb and Xc) and the low-capacity site (Xa) of illite. Only the low-selectivity high-capacity site of smectite (Xf) mostly contributes to Sr sorption. The remaining three sorption sites of smectite contributed only very slightly. At the lowest Sr equilibrium concentrations, the plateau records the contribution of overall sites as none of them are saturated with Sr. Log Kd decreases at the highest Sr concentrations, indicating the saturation of both illite and smectite sorption sites. This saturation begins with the low-capacity sites Xa and Xe ([Sr]eq = 10⁻⁷ mol·L⁻¹), followed by Xb and Xf, and finally Xc ([Sr]eq = 10⁻⁴ mol·L⁻¹). The lowest selective sites with the largest exchange capacities are saturated at last. It is important to note that the site Xf of smectite contributes to 1/3 of the Sr retention on the exchanger, despite representing less than 10% of the total exchanger CEC (Table 4). Therefore, it would be inaccurate to base the retention of reactive phases solely on the site exchange capacities, as the selectivity of the sites appears to be equally important.

<table><caption>Table 4: Contribution of each reactive site ECi compared with the total CEC of the exchanger</caption><thead><tr><th colspan="2">Site</th><th>ECi / CEC</th><th colspan="2">Site</th><th>ECi / CEC</th></tr></thead><tbody><tr><td rowspan="4">Illite</td><td>Xa</td><td>0.1%</td><td rowspan="4">Smectite</td><td>Xe</td><td>0.003%</td></tr><tr><td>Xb</td><td>41%</td><td>Xf</td><td>9.7%</td></tr><tr><td>Xc</td><td>13%</td><td>Xg</td><td>9.1%</td></tr><tr><td>Xd</td><td>23%</td><td>Xh</td><td>3.5%</td></tr></tbody></table>

This modelling result confirms that Sr sorption is satisfactorily described by both the illite and smectite contributions and controlled by an ion exchange process alone.

### 4.1.2. Caesium sorption on carbonate-free clay fraction

The Cs adsorption and desorption isotherms performed on the carbonate-free clay fraction in experimental condition 1 (Table 2) comprised 16 experimental batches with Cs concentrations ranging between 10⁻².⁵ and 10⁻⁹.⁵ mol·L⁻¹ (Figure 3). Both isotherms were acquired putting a background solution at equilibrium containing Ca²⁺ and pH at 7.4 10⁴ mol·L⁻¹ and 7.6 ± 0.2 respectively. The highest retention was reached for Cs concentrations below 10⁻⁸.⁵ mol·L⁻¹, with a plateau of log Kd equal to 5.0 L·Kg⁻¹. This result is in accordance
with that obtained by Latrille and Bildstein (2022) on illite du Puy at an ionic strength of 0.02 mol L⁻¹, taking into account the impact of the ionic strength on Cs sorption (difference of one logKd unit). Between a Cs concentration of 10⁻⁸ and 10⁻⁶ mol·L⁻¹ at equilibrium, the Kd values sharply decrease and reach log Kd = 3 L·Kg⁻¹. For Cs concentrations ranging from 10⁻⁶ to 10⁻⁴ mol·L⁻¹, there is a second plateau at log Kd = 2.7 L·Kg⁻¹ followed by a decrease in the log Kd values for Cs concentrations lower than 10⁻⁴ mol·L⁻¹. This successive plateau shape, characteristic of Cs retention on illite and smectite, has been extensively described in the literature (Torstenfelt et al. 1982; Savoye et al. 2012; Durrant et al. 2018; Latrille and Bildstein 2022; Wissocq et al. 2018).

There is no consensus in the literature on the reversibility of caesium sorption on clay minerals. Recently, Durrant *et al.* (2018) showed that the apparent irreversibility of Cs sorption is linked to slower desorption kinetics, particularly in the high-selectivity/ low-capacity sites of illite, based on the very high selectivity of these types of sites for Cs. However, Wissocq *et al.* (2018) and Latrille and Bildstein (2022) showed that Cs can be reversibly adsorbed on illite and smectite, regardless of the Cs concentration in solution. Similarly, our results indicate similar values for Kd obtained from adsorption and desorption experiments, suggesting reversible Cs adsorption on the illite and smectite mixture (Figure 3). Using the same approach as that used for Sr, the present study demonstrates that an ion exchange process between Ca and Cs is responsible for Cs retention (See Supplementary Information 4 for a detailed account of the calcium balance).

<figure><img src="image_4.png" /><figcaption>**Fig. 3** Cs isotherm on the carbonate-free clay fraction as a function of the Cs concentration at equilibrium at I ≈ 3·10⁻³ mol·L⁻¹: adsorption and desorption Kd values correspond to black and grey points respectively, with 2 σ of uncertainty. The red line expresses the MSIE direct modelling, and the 90% confidence interval of the model is shown by the light and dark grey shading for the adsorption and desorption models respectively. The dashed and dotted lines represent the high-capacity/ low-selectivity (Xa and Xe) and low-capacity/ high-selectivity (Xb, Xc, Xd, Xf, Xg and Xh) sites of illite (purple) and smectite (orange) respectively</figcaption></figure>

Direct simulations were carried out using the same input parameters as for Sr to describe the exchange of Cs on the carbonate-free clay fraction (CEC, illite and smectite proportion) and the K*<sup>Xi</sup><sub>H/Cs</sub> selectivity coefficients of the database (Table 1). The physical and chemical parameters used for modelling are those that were measured experimentally. The direct simulation (red line) reproduces the experimental data satisfactorily. The modelling
results show that Cs is preferentially sorbed on the illite sites (Figure 3). For Cs concentrations below 10⁵ mol·L⁻¹, the site of high selectivity and low capacity is the primary driver of Cs sorption. Although smectite is present in a minor proportion in the mixture, the high-selectivity site, Xe, is effective over a concentration range of 10⁻⁷ to 10⁻⁵ mol·L⁻¹. Despite its low capacity (either ECi Xa = 0.0009 eq/kg, or 0.01 % of total CEC (Table 4)), the Xa site contribution is not negligible. For concentrations greater than 10⁻⁵ mol·L⁻¹, the low-selectivity/high-capacity site Xc drives the Cs sorption. Despite their low selectivity towards Cs, the sites Xb, Xd and Xf contribute to Cs retention. For the highest concentrations tested, these sites were not saturated with Cs (Figure 6). Their low Cs saturation rate is due to their higher Ca selectivity, resulting in low Cs sorption.

These modelling results indicate that illite is primarily responsible for Cs sorption in this mineral assemblage. However, for concentrations ranging from 10⁻⁷ to 10⁻⁵ mol·L⁻¹, taking smectite into account is necessary to accurately describe the experimental data. Selectivity also controls retention in the case of Cs. In fact, the order of the sites contributing to Cs retention (site Xa > site Xc > site Xb) is the same as their selectivity value (K*Xa*Cs/H > K*Xc*Cs/H > K*Xb*Cs/H).

## 4.2. Effect of competition between Ca and Sr or Cs for sorption sites

### 4.2.1. Competition between calcium and strontium

The effect of the ionic strength on the sorption properties of clay minerals has been extensively studied. The consensus is that an increase in the ionic strength reduces the retention of sorbed elements. Missana *et al.* (2008) compared the Sr sorption on Na-smectite in NaClO₄ solutions at different ionic strengths (between 10⁻² and 10⁻¹ mol·L⁻¹ Na) at a constant pH of 6.5. It has been shown that the amount of Sr sorbed decreased by a factor of 10 with an increase in the Na concentration by the same factor. Figure 4(a) shows the Sr adsorption isotherm on the carbonate-free clay fraction in a background solution with an ionic strength (3 10⁻² mol·L⁻¹) (experimental condition 2, Table 2) ten times higher than the previous one (I = 3 10⁻³ mol·L⁻¹). The mean pH is 8.1 ± 0.2 and the Sr concentration ranges from 10⁻².⁵ to 10⁻⁸.⁵ mol·L⁻¹. At I = 3 10⁻² mol·L⁻¹, the adsorption isotherm shows a log Kd plateau of 1.6 L·Kg⁻¹ up to an equilibrium Sr concentration of 10⁻⁵ mol·L⁻¹. At higher Sr concentrations, the log Kd decreases until it reaches a Kd of 1.26 L·Kg⁻¹ at the highest Sr concentrations of 10⁻².⁵ mol·L⁻¹. The experimental data (empty black dots and squares of Figure 4 (a) and (b)) for desorption are more widely scattered than those for adsorption. Nevertheless, the calcium balance is maintained, and the Kd values are close enough to confirm a reversible adsorption process, supporting an ion exchange process.
<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 4** (a) Strontium and (b) caesium adsorption (black) and desorption (empty black) isotherms on the carbonate-free clay fraction at $I \approx 3 \cdot 10^{-3}$ mol·L$^{-1}$ (dot) and $I \approx 3 \cdot 10^{-2}$ mol·L$^{-1}$ (square) with uncertainty at $2 \sigma$. The blue dots correspond to the adsorption isotherm from Wissocq *et al.* (2018). The red lines represent the MSIE direct modelling for $I \approx 3 \cdot 10^{-3}$ mol·L$^{-1}$ (dashed line) and for $I \approx 3 \cdot 10^{-2}$ mol·L$^{-1}$ (straight lined). The 90% confidence intervals of the adsorption model are represented by the light and dark grey shading for $I \approx 3 \cdot 10^{-3}$ mol·L$^{-1}$ and $I \approx 3 \cdot 10^{-2}$ mol·L$^{-1}$ respectively</figcaption></figure>

Comparing the two adsorption isotherms ($I \approx 3 \cdot 10^{-3}$ and $3 \cdot 10^{-2}$ mol·L$^{-1}$), an increase in the ionic strength leads to a significant decrease in retention. At the lowest Sr concentrations, the log Kd is reduced from $2.7 \cdot 10^{-1}$ at $I = 3 \cdot 10^{-3}$ mol·L$^{-1}$ to $1.6 \cdot 10^{-1}$ at $I = 3 \cdot 10^{-2}$ mol·L$^{-1}$. The presence of a higher amount of Ca in solution leads to stronger competition with Sr for each sorption site. This competition effect is reduced when the saturation of the sorption sites is reached, at the highest Sr concentrations.

These results are slightly higher than those obtained by Wissocq *et al.* (2018) on a sandy clay sediment collected at 32 m below the here studied alluvium. In fact, their isotherm shows a log Kd plateau with a nearly constant Kd of $1.3 \cdot 10^{-1}$ at pH 6.0 in $10^{-2}$ mol·L$^{-1}$ CaCl$_2$ solution. The difference between these two isotherms at
502 I = 3·10⁻² mol·L⁻¹ and that of Wissocq *et al.* (2018) (Figure 4a) can be explained by a lower pH in Wissocq *et al.*
503 (2018) than in this study (pH 6 and 8 respectively) and a difference in the relative proportions of illite and
504 smectite in the two composite materials.

505 The MSIE model run in direct-simulation mode, reproduced experimental data without any adjustments,
506 demonstrating its robustness in handling variations in chemical conditions.

507
4.2.2. Competition between calcium and caesium

508
Figure 4(b) shows the Cs sorption isotherm on the carbonate-free clay fraction using a CaCl₂ background
509
solution with the highest ionic strength (experimental condition 2, see Table 2). The mean pH is 7.4 ± 0.2, and
510
the Cs concentration ranges from 10⁻².⁵ to 10⁻⁹.⁵ mol·L⁻¹ at equilibrium. The maximum log Kd value at 3·10⁻
511
³ mol·L⁻¹ ionic strength is 5 ± 1.7 L·Kg⁻¹, whereas it is 4.6 ± 1.2 L·Kg⁻¹ for I = 3·10⁻² mol·L⁻¹. The isotherm
512
shape remains the same independently of the ionic strength. The log Kd values vary significantly, only at the
513
lowest Cs concentrations (< 10⁻⁸.⁵ mol·L⁻¹). At these concentrations, the low-capacity site (Xa) mainly drives the
514
retention. Sufficient competition of Ca for Cs limits Cs retention on this sorption site. Adding calcium to the
515
solution slightly reduces the Cs sorption due to the high Cs selectivity for sorption sites. This conclusion is
516
consistent with that of Staunton and Roubaud (1997). These authors showed a slight decrease in Cs sorption on
517
illite and smectite by increasing the ionic strength of a CaCl₂ solution.

518
4.3. Effects of Ca and H competition with Sr or Cs on the sorption site occupancy

519
To improve the understanding of the exchange process involved in Sr and Cs adsorption on carbonate-free clay
520
fractions at both ionic strengths, Figures 5 and 6 display the species occupancy on each reactive site of illite and
521
smectite, resulting from the modelling of the ion exchange reactions at equilibrium.

522
In Figure 5, the percentages of each cation (Ca²⁺, Sr²⁺ and H⁺) adsorbed on each site type indicate that the
523
sorption sites Xa, Xb, Xc, Xe, Xf and Xg remain saturated with Ca below 10⁻⁸ mol·L⁻¹ Sr concentration. This
524
results from calcium conditioning before the sorption experiment. Nevertheless, the sites Xd and Xh are
525
saturated with H⁺. Two Sr behaviours could be underlined, depending on the type of site. For sites with high
526
selectivity (Xa and Xe), strontium slightly replaces calcium due to its low amount in solution. As the Sr
527
concentration increases, it progressively replaces Ca on the sites. The sites Xe and Xa become saturated with Sr
528
at concentrations of 10⁻⁵ mol·L⁻¹ and 10⁻⁴ mol·L⁻¹ respectively. The site Xe is saturated by Sr before Xa due to
529
its lower exchange capacity. For sites with low selectivity (Xb, Xc, Xd, Xf and Xg), the proportion of calcium
530
remains high (approximately 100%) up to an Sr concentration of less than 10⁻⁵ mol·L⁻¹. As the Sr concentration
531
in the solution increases, Sr can still be adsorbed until the site exchange capacity is reached, despite the much
532
lower selectivity.
<figure><img src="image_7.png" /><figcaption>**Fig. 5** Illite and smectite sites occupancies with Sr (blue), Ca (red) and H (green) at high ionic strength (solid line) and low ionic strength (dashed line). The coloured scale (right) corresponds to element colour and the black scale (left) corresponds to the other elements.</figcaption></figure>

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534

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537

Even under slightly basic conditions (pH ≈ 8), protons remain adsorbed on the solid as a small but significant fraction (< 0.1%) on the sites mentioned above, but as a much larger one (≈ 80 – 100 %) on the sites Xd and Xh due to their very high selectivity towards the proton (i.e. lowest log K<sup>*Xi</sup><sub>2H</sub><sup>+</sup>/Ca<sup>2+</sup> and K<sup>*Xi</sup><sub>2H</sub><sup>+</sup>/Sr<sup>2+</sup>).

538

539

540

Cation occupancy of illite and smectite sites (Figure 5) clearly shows competition with Ca. This is illustrated by the decreasing occupancy rate of Ca on the sorption sites as the Sr occupancy rate increases. Furthermore, by considering the sites Xa, Xb, Xc, Xe, Xf, Xg, the site occupancy rate exceeds 99% with only Ca and Sr. At the highest ionic strength, competition with Ca due to the elevated Ca concentration results in a decrease in Sr<sup>2+</sup> and H<sup>+</sup> sorption which affects all reactive sites (Figure 5). The sequence of site saturation and total amount of sorbed cations remain unchanged. By increasing the amount of Ca in the solution, only the equilibrium points corresponding to 50% saturation shift towards higher strontium concentrations (Figure 5). This shift is more significant when the selectivity coefficients between 2H<sup>+</sup>/Ca<sup>2+</sup> and 2H<sup>+</sup>/Sr<sup>2+</sup> are close (Table 1). Sites occupancy of Xd and Xh shows no extensive change due to the increase of Ca<sup>2+</sup> in the solution: the proton occupancy rate is reduced by 10% and less than 1% respectively.

541

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543

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545

546

547

548

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550

Figure 6 illustrates the percentage of each cation (Ca²⁺, Cs⁺ and H⁺) adsorbed on each site type of illite and smectite considering their relative proportion in the carbonate-free clay fraction. For sites with high selectivity (Xa and Xe), caesium only slightly replaces calcium due to its low content in solution. As the Cs concentration increases, Cs progressively replaces Ca on the sites. The sites Xa and Xe become saturated with Cs at concentrations of 10⁻⁷ mol·L⁻¹ and 10⁻⁶ mol·L⁻¹ respectively. The Xa site is saturated by Cs before the Xe site due to its higher selectivity for Cs. For sites with low selectivity (Xb, and Xf), the proportion of Ca remains high (approximately 100%) up to a Cs concentration of less than 10⁻⁵.⁵ and 10⁻⁴ mol·L⁻¹ respectively. As Cs concentration increases, Cs continues to be adsorbed until the exchange site capacity is reached, despite its much lower selectivity. Regarding the Xc and Xg sites, it can be observed that they remain saturated by Ca²⁺ regardless of the Cs concentration. The occupancy rates of these sites by H⁺ are only 0.17 to 0.15% and 0.06 to 0.05% respectively, as the Cs concentration increases, the Ca concentration in solution remaining constant. The sites Xd and Xh remain saturated by H⁺ independently of the Cs⁺ or Ca²⁺ concentration in solution due to their very high selectivity towards H⁺.

551

552

553

554

555

556

557

558

559

560

561

562

563

The sorption behaviour of Cs⁺, H⁺ and Ca²⁺ on all sorption sites remains unchanged with the Ca concentration in solution. The occupancy rate of H⁺ is higher at low ionic strength than at high ionic strength on sites Xe, Xf, Xg, Xb and Xa at a Cs concentration lower than 10⁻⁷ mol·L⁻¹. Conversely, Ca²⁺ loading increases on Xh, although the Ca quantity involved is insufficient to be considered significant. It can be observed that there is small discrepancy between the Cs sorption isotherms at both ionic strengths. Due to the significant difference in their respective selectivity (Table 1), it can be concluded that Cs⁺ is less prone to compete with Ca²⁺. In fact, the selectivity of Cs⁺ with respect to Ca²⁺ is so high that increasing Ca²⁺ concentration in the solution has no effect on its adsorption, especially at trace concentrations (sites Xa and Xe, Figure 6). For sites Xb, Xc, Xf and Xg, the lower Cs selectivity leads to a decay in the saturation ratio of Cs as the Ca concentration in solution rises (see dotted line, Figure 6).

564

565

566

567

568

569

570

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572
<figure><img src="image_8.png" /><figcaption>Fig. 6 Illite and smectite site occupancies with Cs (blue), Ca (red) and H (green) for high ionic strength (solid line) and low ionic strength (dash line). The coloured scale (right) corresponds to the element colour and the black scale (left) corresponds to the other elements.</figcaption></figure>

4.4. Effect of carbonate on the retention of Sr and Cs in the alluvium clay fraction
Crystallized carbonate minerals are suspected to potentially impede access to the sorption sites for ion exchange processes, and bicarbonate in solution may complex strontium in solution or allow co-precipitation in solid phase. The effect of carbonates on Sr and Cs retention is investigated by comparing the isotherms obtained on the carbonate-free and carbonate clay fractions. All solutions used were in equilibrium with calcite prior to contact with the solid in the carbonated state. Again, two different concentrations of calcium in the solution were also tested.

### 4.4.1. Effect of carbonate on the retention of caesium

Figure 7 shows the Cs sorption results on the carbonated clay fraction using a background solution with low (experimental condition 3) or high (experimental condition 4, Table 2) ionic strength. The mean pH is 7.6 ± 0.2, and the Cs concentration at equilibrium ranges from 10⁻⁹.⁵ to 10⁻².⁵ mol·L⁻¹. The bicarbonate and calcium concentrations in the background solutions are of 10⁻³ and 5·10⁻⁴ mol·L⁻¹ respectively at I = 1.5·10⁻³ mol·L⁻¹ and of 5·10⁻⁴ and 10⁻² mol·L⁻¹ respectively at I = 3·10⁻² mol·L⁻¹, respecting an equilibrium with calcite (see Supplementary Information 3). The maximum log Kd is 4.8 ± 1.7 L·Kg⁻¹ at the lowest ionic strength (1.5·10⁻³ mol·L⁻¹), whereas it is equal to 4.6 ± 1.2 L·Kg⁻¹ at I = 3·10⁻² mol·L⁻¹. The isotherm shape remains unchanged from the isotherm with the carbonate-free solid: the Kd values are similar over the entire concentration range. There is no significant difference in Cs adsorption behaviour between the carbonate and carbonate-free environments. The apparent shift between the two isotherms (less than the model uncertainty) is due to the lower initial Ca concentration imposed by the calcite equilibrium in carbonate media, increasing it slightly from 5·10⁻⁴ mol·L⁻¹ Ca (carbonate-free media) to 10⁻³ mol·L⁻¹ Ca (carbonate media).

<figure><img src="image_9.png" /></figure>

**Fig. 7** Cs adsorption isotherm on the carbonate (green) and carbonate-free (black) clay fraction as a function of the Cs concentration at equilibrium at I ≈ 1.5·10⁻³ mol·L⁻¹ (green circle), I ≈ 3·10⁻³ mol·L⁻¹ (black circle) and I ≈ 3·10⁻² mol·L⁻¹ (black and green square) with uncertainty at 2 σ. The red and green lines represent the MSIE direct modelling. The 90% confidence intervals of the model are shown by the green and grey shading for carbonate and carbonate-free condition respectively.
These results support the assumption that crystallized carbonates do not limit Cs access to sorption sites.
Crystallized carbonate minerals and bicarbonate primarily control the solution chemistry mainly affecting Ca²⁺ and HCO₃⁻ concentrations.

#### 4.4.2. Effect of carbonate on the retention of strontium

As shown for Cs, carbonates in crystalline form are not able to impede access to the reactive sites of the solid. It would be beneficial to consider the effect of these compounds on the chemistry of the media and the potential formation of complexes with Sr observed in carbonate media.

The isotherms performed with Sr on the carbonated clay fraction for both ionic strength $I = 1.5 \cdot 10^{-3} \text{ mol} \cdot \text{L}^{-1}$ (experimental condition 3) and $I = 3 \cdot 10^{-2} \text{ mol} \cdot \text{L}^{-1}$ (experimental condition 4, Table 2) are shown in Figure 8. The mean pH is $7.6 \pm 0.2$ and the Sr concentration at equilibrium ranges from $10^{-2.5}$ to $10^{-8} \text{ mol} \cdot \text{L}^{-1}$. The bicarbonate and calcium concentrations are of $10^{-3}$ and $5 \cdot 10^{-4} \text{ mol} \cdot \text{L}^{-1}$ respectively at $I = 1.5 \cdot 10^{-3} \text{ mol} \cdot \text{L}^{-1}$ and of $5 \cdot 10^{-4}$ and $10^{-2} \text{ mol} \cdot \text{L}^{-1}$ respectively at $I = 3 \cdot 10^{-2} \text{ mol} \cdot \text{L}^{-1}$, according to the equilibrium with calcite in all conditions. The Sr isotherm at $I = 1.5 \cdot 10^{-3} \text{ mol} \cdot \text{L}^{-1}$ is very similar (mean log Kd plateau of $2.6 \text{ L} \cdot \text{Kg}^{-1}$ for Sr) to that shown in carbonate-free media (black circle in Figure 8). The simulation result obtained on carbonate media (green dashed line) overlaps the one obtained on carbonate-free media (black dashed line) by considering the model uncertainty. The small difference between the two direct simulations is only due to the Ca concentration discrepancy between the two conditions. It can be concluded that crystallized carbonates do not limit accessibility to the sorption sites. For Sr concentrations lower than $10^{-4} \text{ mol} \cdot \text{L}^{-1}$, the calcium unbalance, established on Ca concentration in solution, is greater than 20% (Supplementary Information 4). This indicates a significant loss of Ca from the solution. Moreover, there is a significant decrease in the bicarbonate content in solution and the Sr sorption is comparable to that in carbonate-free media. Consequently, the loss of Ca can be attributed to the precipitation of calcite. For Sr concentrations higher than $10^{-4} \text{ mol} \cdot \text{L}^{-1}$, the experimental data on carbonate media are significantly higher than the model confidence interval. This is consistent with the increase in concentration of the $\text{SrHCO}_3^+$ complex and strontianite oversaturation (see Supporting Information 5), as shown in Figure 1.

The adsorption and desorption Kd values are not significantly different in the carbonate media at low ionic strength (see Supporting Information 6). This indicates that Sr adsorption in carbonate media is reversible at Sr concentrations below $10^{-4} \text{ mol} \cdot \text{L}^{-1}$. Above this concentration, the $\text{SrHCO}_3^+$ complex increases in solution (Figure 1) and is also reversibly adsorbed. Concerning the experimental data at $[\text{Sr}]_{\text{eq}} = 10^{-6.9} \text{ mol} \cdot \text{L}^{-1}$, the low Kd ($\text{Log Kd} = 2.3 \text{ L} \cdot \text{Kg}^{-1}$) is an abnormal result, probably due to physicochemical instability or to heterogeneous samples.
<figure><img src="image_10.png" /><figcaption>**Fig. 8** Sr adsorption isotherms on the carbonate clay fraction (green), carbonate-free clay fraction (black) as a function of the Sr concentration at equilibrium. The Log Kd are at I ≈ 1.5·10⁻³ mol·L⁻¹ (green circle), I ≈ 3·10⁻³ mol·L⁻¹ (black circle) and I ≈ 3·10⁻² mol·L⁻¹ (black and green square) with uncertainty at 2 σ. The red and green lines represent the MSIE direct modelling and the 90% confidence interval of the model is shown by the green and grey shading for carbonate and carbonate-free conditions respectively.</figcaption></figure>

The difference between the Sr sorption isotherms on the carbonate (green) and carbonate-free (black) clay fractions at high ionic strength I = 3·10⁻² mol·L¹ (square), shows two relevant behaviours. The experimental Sr adsorption isotherm (green square) indicates an almost constant log Kd of 1.8 L·Kg⁻¹ over all Sr concentrations (Figure 8). This value is significantly higher than that for carbonate-free conditions (log Kd = 1.6 L·Kg⁻¹). The balance of bicarbonate and calcium (Supplementary Information 4, condition 4) indicates a significant deficit of these components in solution. This is explained by a consumption of HCO₃⁻ and Ca²⁺ throughout the carbonate formation. Furthermore, the log Kd values of desorption (grey point in Figure 9) are higher than those of adsorption (black points in Figure 9) and increase at Sr concentrations higher than 10⁻⁵ mol·L⁻¹. This behaviour is characteristic of an equilibrium process with a mineral phase. These equilibrium solution compositions are slightly oversaturated towards calcite (CaCO₃) across the entire concentration ranges and towards strontianite (SrCO₃) for Sr concentrations higher than 10⁻⁵ mol·L⁻¹ (see Supplementary Information 5).
<figure><img src="image_11.png" /><figcaption>**Fig. 9** Sr isotherm on the carbonate clay fraction as a function of the Sr concentration at equilibrium at I ≈ 3·10⁻⁷² mol·L⁻¹: adsorption and desorption Kd values indicated as black and grey points respectively with uncertainty at 2 σ. The red line represents the MSIE direct modelling, and the 90% confidence interval of the model is shown by the light and dark grey shading for the adsorption and desorption models respectively. The dashed and dotted lines are for high-capacity/low-selectivity and low-capacity/high-selectivity sites respectively. Illite and smectite are indicated in purple and orange respectively</figcaption></figure>

The increase in desorption Kd data and the constant adsorption behaviour are consistent with strontianite precipitation at Sr concentrations higher than 10⁻⁵ mol·L⁻¹ and to the incorporation or co-precipitation of Sr and Ca with calcite (for all Sr concentration ranges), in addition to ion exchange on clay solid. Both processes are highlighted by the MSIE model. Since this model only simulates ion exchange and is not sufficient to accurately describe the retention isotherms obtained in carbonate media, that implies that other processes besides ion exchange takes place.

In order to support the occurrence of such additional Sr retention processes under carbonate media, Sr amounts (in mole) extracted from solution were compared to those of Sr²⁺ adsorbed by ion exchange and calculated by the MSIE model. As shown in supporting information 7, Table 3, at I = 1.5·10⁻³ mol·L⁻¹, the other Sr retention processes would contribute to 20 to 70% of Sr retained on solid phases for Sr concentration in solution above 10⁻⁴ mol·L⁻¹. Below 10⁻⁵ mol·L⁻¹, these other processes are not significant anymore. At I = 3·10⁻² mol·L⁻¹, these processes are predominant compared to ion exchange independently of the Sr concentration in solution, arising more than 70% for Sr concentration above 10⁻⁴ mol·L⁻¹.

The differences between the results at the two ionic strengths can be explained as follows: ion exchange mainly determines the Sr concentration in solution, since the adsorption kinetics are instantaneous (Galamboš *et al.* 2013). At the highest ionic strength (I ≈ 3·10⁻² mol·L⁻¹), due to lower Sr adsorption by ion exchange the Sr concentrations in solution at equilibrium are sufficiently high to allow precipitation or incorporation of Sr within
carbonate phases. At lower ionic strengths, Sr and Ca equilibrium concentrations in solution only allow
complexation as SrHCO₃⁺ and CaHCO₃⁺.

## Conclusion

To accurately predict Sr and Cs retention in natural environments, it is essential to consider the effect of carbonates on retention capacity. To investigate this issue, Sr and Cs retention isotherm experiment were performed on the clay fraction extracted from raw carbonate alluvium. The reactivity of this complex material was simplified to an illite/smectite assemblage and calcite. Three experimental and modelling steps of increasing complexity were carried out involving both carbonate and carbonate-free clay fractions reacting with solutions at two ionic strengths. Carbonates were introduced both in solutions equilibrated with calcite and in the crystalline form inherent to the raw material. The ion exchange model, implemented as the multi-site ion-exchanger (MSIE) configuration, successfully simulated Sr and Cs adsorption isotherms under carbonate-free conditions, demonstrating that ion exchange is the primary process controlling Sr and Cs retention under all experimental conditions. Significant competition between Ca and Sr or Cs observed when varying Ca concentration generally reducing Sr or Cs retention as Ca concentration increases. Cation occupancy ratios on illite and smectite sites revealed that Sr and Cs sorption occurs through first order exchanges Ca²⁺/Sr²⁺ and Ca²⁺/2Cs⁺ and second-order exchanges 2H⁺/Sr²⁺ and H⁺/Cs⁺ at equilibrium. Cs adsorption isotherms on raw clay fraction showed that crystallized carbonate does not impede Cs access to sorption sites. Similarly, Sr adsorption on the carbonate clay fraction at low ionic strength was unaffected. Conversely, carbonate in solution enhances Sr retention at Sr concentrations above 10⁻⁵ mol·L⁻¹, due to SrHCO₃⁺ complex formation and strontianite (SrCO₃) precipitation. This effect is enhanced at high ionic strength in the presence of carbonate. Reduced Sr retention caused by competition with Ca resulted in higher Sr concentration, facilitating its incorporation or precipitation with carbonates.

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## Acknowledgments

The authors would like to acknowledge the French Alternative Energies and Atomic Energy Commission for their financial support. The authors would like to thank Hélène Isnard and Nathalie Coreau for their analytical support in ICP/MS and ion chromatography.

## Author contributions

Jean Maillet: Conceptualization, Methodology, Investigation, Writing—Original draft, Visualization. Clément Lynde: Software, Formal analysis, Data curation. Sébastien Savoye: Validation, Writing—Review & Editing. Christelle Latrille: Conceptualization, Validation, Resources, Writing—Review & Editing, Visualization, Supervision

## Funding

The authors received financial support from the French Alternative Energies and Atomic Energy Commission.

**Availability of data and material** Not applicable.

**Code availability** Not applicable.

## 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.

**Ethics approval and consent to participate** Not applicable.

**Consent for publication** Not applicable
Supplementary information

Impact of carbonate minerals on the strontium and caesium reactivity on natural clay-
rich materials

Jean Maillet, Clément Lynde, Sébastien Savoye, Christelle Latrille.

French Alternative Energies and Atomic Energy Commission Saclay, Service de Physico-Chimie, 91191 Gif-
sur-Yvette, France

Corresponding author: Christelle Latrille: christelle.latrille@cea.fr; Phone: +33 (0) 1 69 08 34 24; Fax: +33 (0) 1 69 08 32 42

Supplementary Information 1: The grain-size distributions were analyzed by laser diffraction particle-size analysis (PSA1190 L/D Anton Paar) and expressed as a volume (a) and surface (b) (SI Fig. 1 a and b). Grain-size distributions of the infra 2 µm carbonate free fraction extracted from the studied alluvium were compared with those of Ca-illite and Ca-smectite.

<figure><img src="image_12.png" /></figure>

The grain-size distribution of the infra 2 µm carbonate free fraction extracted from the studied alluvium shows a bimodal grain-size distribution in volume (SI Fig.1a), attributed to the main clay minerals, i.e. illite and smectite. Compared to the grain-size distribution of pure illite and pure smectite used in the database, the studied material contains particles with smaller sizes than those of the pure phases. In this sense, the decrease in the particle-size increases the reactive surface area (SI Fig.1b), which is extrapolated to the minor site ECi values of pure illite and smectite.

Supplementary Information 2: Mineral assemblage of the clay fraction simplification

Quantification of the clay's mineral composition performed by modelling the carbonate and decarbonate clay-fraction X-ray diffraction patterns with the Sybilla© software developed by Chevron™ (Aplin et al. 2006)
indicates an assemblage containing kaolinite (29.8%), discrete illite (26.4%), mixed layers illite/smectite (IS) with 29.3% IS (94%/6%), 9% IS (77%/23%) and 3.5% IS (82%/18%), discrete chlorite (1.4%) and discrete smectite (0.5%). The quantification uncertainty was assessed at 5%.

<figure><img src="image_13.png" /></figure>

SI Fig. 1: Sybilla treatment result on the clay fraction XRD pattern at Ethyl Glycol solvated. Pure illite (Illite 1 et Illite 2), kaolinite (Kaolinite 1 et Kaolinite 2), illite/smectite mixed layers: I/S (94% / 6%) (IS R0 GLY 1), I/S (77% / 23%) (IS R0 GLY 2), I/S (82% / 18%) (IS R0 GLY 3), pure smectite (SS di-GLY 1 et 2), chlorite/smectite mixed layer (99% / 1%)(Ch/ GLY di-R0)

Based on this result, the main reactive phyllosilicates in this clay fraction are illite and smectite. Indeed, the exchanges capacities of kaolinite and chlorite are usually around 3 and 10 meq/100g respectively whereas illite and montmorillonite are 25 and 89 meq·100g⁻¹ respectively. In order to simplify the modelling task, the mineral composition was restricted to the most reactive phases of this system, i.e. a mixture of illite and smectite. For this purpose, the illite and smectite proportions were revised from their initial contents, by maintaining their relative proportion according to the measured clay fraction CEC. The initial phyllosilicate mixture contained 63.7% illite and 5.2% smectite. The CEC of this illite and smectite mixture was calculated with respect to the CEC of pure illite and smectite (24.89 and 88.76 meq·100g⁻¹ respectively) and their relative proportions in the clay fraction (SI Eq 1).

$$CEC_{I+S} = \%illite_{XRD} \times CEC_{pure illite} + \%smectite_{XRD} \times CEC_{pure smectite} \quad (SI Eq 1)$$

With; %illite<sub>XRD</sub> and %smectite<sub>XRD</sub> representing the proportion of illite and smectite determined by XRD, and CEC<sub>I+S</sub> the CEC of only the illite and smectite components from the mineral composition determined by XRD.

The proportions of illite and smectite in this simplified assemblage (%illite<sub>AC</sub> and %smectite<sub>AC</sub>) were calculated by weighing the illite and smectite proportions, determined by XRD quantification, by the ratio between the measured CEC of the carbonate-free clay fraction (29.7 meq·100g⁻¹) and the calculated CEC<sub>I+S</sub> at 20.27 meq·100g⁻¹ (SI Eq 2).
922 $%illite_{AC} = \frac{%illite_{XRD} \times CEC_{MES}}{CEC_{I+S}}$ and $%smectite_{AC} = \frac{%smectite_{XRD} \times CEC_{MES}}{CEC_{I+S}}$ (SI Eq 2)

923 With; %illite<sub>AC</sub> and %smectite<sub>AC</sub> being the proportion of illite and smectite in the assimilated mineral composi-

924 tion, and CEC<sub>MES</sub> the measured CEC of the carbonate-free clay fraction.

925
926 Supplementary Information 3: Solution composition and calcite equilibrium

927 The solution composition details (see Section 3.2.1) were defined according to the Sillén diagram (SI Fig. 2)
928 which describes the chemical species in solution as a function of the pH. This diagram shows the equilibrium of
929 the carbonate system CO₃²⁻/HCO₃⁻/H₂CO₃ (violet curve) in solution open to the atmosphere at a pCO₂ of 4.17 10⁻⁴
930 atm and the calcium (blue curve) and the chlorides (violet dotted curve) concentrations with respect to the
931 experimental conditions. The “I = 3 10⁻² mol·L⁻¹” condition (vertical green line) corresponds to that obtained in
932 the field, i.e. the point of electro-neutrality between Ca²⁺ and HCO₃⁻ (condition 4). This condition is well known
933 in carbonate environments, as it corresponds to calcite equilibrium in environments open to the atmosphere. By
934 introducing chloride into the solution such as 10⁻² mol·L⁻¹ (yellow vertical line), the solution becomes more
935 acidic (pH 7.75 instead of 8.2) with a lower bicarbonate concentration (5 10⁻⁴ mol·L⁻¹). In this case, the calcium
936 concentration was fixed by addition of CaCl₂. These variations in pH and HCO₃⁻ concentration result from the
937 chloride concentration which increases the alkalinity reserve, the sum of the charges for inactive species
938 (Michard 1989). The carbonate equilibrium considers the addition of anions to the solution. The equilibrium
939 point is therefore between calcium and the sum of bicarbonates and chlorides. Below 10⁻³ mol·L⁻¹ chloride,
940 HCO₃⁻ dominates and Cl⁻ becomes negligible in the ionic balance. As the chloride concentration increases, this
941 anion controls the equilibrium with the calcite and thus the composition of the solution.

<figure><img src="image_14.png" /></figure>

942
943 SI Fig. 2 Sillén diagram showing the theoretical compositions of solutions in equilibrium with calcite with a background solution of 10⁻³ mol·L⁻¹ (green) and 10⁻² mol·L⁻¹ (yellow) calcium chloride. The Ca, Cl and HCO₃⁻ concentration values of these compositions are given as conditions 3 and 4 in Table 2
944
945
946

946
Supplementary Information 4:

Ca balances of the retention experiments on Sr and Cs for carbonate and carbonate-free conditions with two ionic strength conditions. The conditions names 1, 2, 3 and 4 refer to Table 2.

The calcium balance is calculated by subtracting the sum of the desorbed Ca and the Ca in solution at equilibrium from the amount of introduced calcium (in mole) (SI Eq. 3). The percentage represents the ratio between the ΔCa calculated above and the number of moles of introduced Ca (SI Eq. 4). A positive balance indicates a calcium deficiency at equilibrium, which is interpreted as a consumption of cations by precipitation or co-precipitation reactions. A negative balance indicates a calcium excess at equilibrium, which is interpreted as calcite dissolution. A Ca balance below 10% is assumed insignificant, i.e. below the error propagation of analytical uncertainty. Batches 1 to 15 were ranked from the highest to the lowest tracer (Cs or Sr) concentrations.

$$ \Delta_{Ca} = ca_{ini} - (ca_{DES} + ca_{sol,eq}) \qquad (\text{SI Eq. 3}) $$

$$ Ca\ balance = \frac{\Delta ca}{ca_{ini}} \cdot 100 \qquad (\text{SI Eq 4}) $$

With ΔCa representing the calculated difference of Ca (mol); Ca<sub>DES</sub> and Ca<sub>sol,eq</sub> the quantity of Ca desorbed and at equilibrium respectively (mole)

<table><thead><tr><th>Sample number</th><th>Sr Condition 1</th><th>Sr Condition 2</th><th>Sr Condition 3</th><th>Sr Condition 4</th><th>Cs Condition 1</th><th>Cs Condition 2</th><th>Cs Condition 3</th><th>Cs Condition 4</th></tr></thead><tbody><tr><td>1</td><td>5%</td><td>-24%</td><td>14%</td><td>-11%</td><td>-3%</td><td>-7%</td><td>-23%</td><td>-5%</td></tr><tr><td>2</td><td>8%</td><td>-8%</td><td>15%</td><td>-11%</td><td>-2%</td><td>-2%</td><td>5%</td><td>9%</td></tr><tr><td>3</td><td>1%</td><td>-1%</td><td>0%</td><td>0%</td><td>-5%</td><td>-9%</td><td>5%</td><td>-5%</td></tr><tr><td>4</td><td>5%</td><td>15%</td><td>1%</td><td>8%</td><td>-14%</td><td>15%</td><td>-4%</td><td>3%</td></tr><tr><td>5</td><td>3%</td><td>7%</td><td>18%</td><td>-4%</td><td>-5%</td><td>11%</td><td>-1%</td><td>11%</td></tr><tr><td>6</td><td>6%</td><td>16%</td><td>19%</td><td>6%</td><td>6%</td><td>-8%</td><td>4%</td><td>14%</td></tr><tr><td>7</td><td>-1%</td><td>12%</td><td>3%</td><td>18%</td><td>2%</td><td>18%</td><td>2%</td><td>17%</td></tr><tr><td>8</td><td>-4%</td><td>-4%</td><td>19%</td><td>20%</td><td>3%</td><td>7%</td><td>4%</td><td>-5%</td></tr><tr><td>9</td><td>-4%</td><td>6%</td><td>18%</td><td>20%</td><td>3%</td><td>-13%</td><td>8%</td><td>-6%</td></tr><tr><td>10</td><td>-4%</td><td>1%</td><td>20%</td><td>15%</td><td>-3%</td><td>-5%</td><td>7%</td><td>-7%</td></tr><tr><td>11</td><td>3%</td><td>5%</td><td>21%</td><td>19%</td><td>2%</td><td>13%</td><td>6%</td><td>-17%</td></tr><tr><td>12</td><td>-2%</td><td>6%</td><td>18%</td><td>8%</td><td>-11%</td><td>-3%</td><td>6%</td><td>-16%</td></tr><tr><td>13</td><td>0%</td><td>6%</td><td>16%</td><td>19%</td><td>0%</td><td>3%</td><td>7%</td><td>-8%</td></tr><tr><td>14</td><td>-3%</td><td>5%</td><td>3%</td><td>21%</td><td>3%</td><td>12%</td><td>6%</td><td>-8%</td></tr><tr><td>15</td><td></td><td></td><td></td><td></td><td></td><td>8%</td><td>3%</td><td>-6%</td></tr></tbody></table>
962 SI, Table 1: Calcium balance of Sr and Cs retention experiments on carbonate (conditions 3 and 4) and

963 carbonate-free (conditions 1 and 2) clay fractions at two ionic strength conditions
<table><thead><tr><th rowspan="2">[Sr]<sub>eq</sub><br>mol·L<sup>-1</sup></th><th colspan="2">Sr experimental condition 3</th><th rowspan="2">[Sr]<sub>eq</sub><br>mol·L<sup>-1</sup></th><th colspan="2">Sr experimental condition 4</th></tr><tr><th>SI Calcite</th><th>SI Strontianite</th><th>SI Calcite</th><th>SI Strontianite</th></tr></thead><tbody><tr><td>2.0 10<sup>-3</sup></td><td>1.76</td><td>1.98</td><td>3.4 10<sup>-3</sup></td><td>0.58</td><td>2.21</td></tr><tr><td>6.5 10<sup>-4</sup></td><td>1.56</td><td>1.30</td><td>3.6 10<sup>-3</sup></td><td>0.60</td><td>2.26</td></tr><tr><td>5.0 10<sup>-4</sup></td><td>1.83</td><td>1.38</td><td>2.7 10<sup>-4</sup></td><td>0.00</td><td>0.53</td></tr><tr><td>3.2 10<sup>-4</sup></td><td>1.79</td><td>1.16</td><td>2.4 10<sup>-4</sup></td><td>-0.02</td><td>0.45</td></tr><tr><td>1.6 10<sup>-4</sup></td><td>1.27</td><td>0.41</td><td>1.1 10<sup>-4</sup></td><td>-0.10</td><td>0.03</td></tr><tr><td>6.8 10<sup>-5</sup></td><td>1.12</td><td>-0.12</td><td>4.2 10<sup>-5</sup></td><td>-0.16</td><td>-0.44</td></tr><tr><td>4.6 10<sup>-5</sup></td><td>1.70</td><td>0.25</td><td>1.4 10<sup>-5</sup></td><td>-0.18</td><td>-0.95</td></tr><tr><td>3.4 10<sup>-5</sup></td><td>1.10</td><td>-0.45</td><td>1.2 10<sup>-5</sup></td><td>-0.19</td><td>-1.03</td></tr><tr><td>1.6 10<sup>-5</sup></td><td>1.19</td><td>-0.70</td><td>7.4 10<sup>-6</sup></td><td>-0.19</td><td>-1.23</td></tr><tr><td>6.1 10<sup>-6</sup></td><td>1.01</td><td>-1.24</td><td>1.5 10<sup>-6</sup></td><td>-0.20</td><td>-1.93</td></tr><tr><td>4.4 10<sup>-6</sup></td><td>0.94</td><td>-1.46</td><td>7.7 10<sup>-7</sup></td><td>-0.20</td><td>-2.22</td></tr><tr><td>2.8 10<sup>-6</sup></td><td>1.18</td><td>-1.42</td><td>1.4 10<sup>-7</sup></td><td>-0.20</td><td>-2.94</td></tr><tr><td>1.2 10<sup>-6</sup></td><td>1.27</td><td>-1.75</td><td>1.2 10<sup>-7</sup></td><td>-0.20</td><td>-3.01</td></tr><tr><td>9.0 10<sup>-7</sup></td><td>1.72</td><td>-1.47</td><td>1.9 10<sup>-8</sup></td><td>-0.20</td><td>-3.83</td></tr></tbody></table>

966 SI, Table 2: Saturation index of calcite and strontianite in carbonated experimental conditions calculated from

968 the solution composition at equilibrium
969
970
971

Supplementary Information 6: Sr isotherm on the carbonate clay fraction as a function of the Sr concentration at equilibrium at I ≈ 3 10⁻² mol·L⁻¹: adsorption and desorption Kd values (black and grey points respectively) with uncertainty at 2 σ

<figure><img src="image_15.png" /></figure>

972
973
974
975
976

SI Fig. 3 Sr isotherm on the carbonate clay fraction as a function of the Sr concentration at equilibrium at I ≈ 3 10⁻² mol·L⁻¹: adsorption and desorption Kd values (black and grey points respectively) with uncertainty at 2 σ
Supplementary Information 7: Contribution relative of additional Sr retention process under carbonate media in percentage.

$$ \Delta = \frac{\text{mole of Sr extracted from solution} - \text{mole of Sr adsorbed}}{\text{mole of Sr extracted from solution}} \times 100 $$

<table><caption>I = 1.5 10<sup>-3</sup> mol·L<sup>-1</sup></caption><thead><tr><th>[Sr]<sub>eq</sub> exp</th><th>Sorbed Sr exp</th><th>Sorbed Sr model</th><th>Δ</th></tr><tr><th>mol·L<sup>-1</sup></th><th>mol</th><th>mol</th><th>%</th></tr></thead><tbody><tr><td>3.40E-03</td><td>1.71E-04</td><td>8.02E-05</td><td>53</td></tr><tr><td>3.62E-03</td><td>1.51E-04</td><td>4.46E-05</td><td>70</td></tr><tr><td>2.72E-04</td><td>5.22E-05</td><td>3.76E-05</td><td>28</td></tr><tr><td>2.37E-04</td><td>3.40E-05</td><td>2.72E-05</td><td>20</td></tr><tr><td>1.11E-04</td><td>2.79E-05</td><td>1.58E-05</td><td>43</td></tr><tr><td>4.19E-05</td><td>1.26E-05</td><td>7.18E-06</td><td>43</td></tr><tr><td>1.39E-05</td><td>6.11E-06</td><td>4.95E-06</td><td>19</td></tr><tr><td>1.16E-05</td><td>4.38E-06</td><td>3.77E-06</td><td>14</td></tr><tr><td>7.35E-06</td><td>1.79E-06</td><td>1.78E-06</td><td>0</td></tr><tr><td>1.47E-06</td><td>5.97E-07</td><td>6.86E-07</td><td>-15</td></tr><tr><td>7.71E-07</td><td>4.25E-07</td><td>4.99E-07</td><td>-17</td></tr><tr><td>1.44E-07</td><td>2.58E-07</td><td>3.20E-07</td><td>-24</td></tr><tr><td>1.24E-07</td><td>9.31E-08</td><td>1.38E-07</td><td>-48</td></tr><tr><td>1.87E-08</td><td>8.50E-08</td><td>1.02E-07</td><td>-20</td></tr></tbody></table>

<table><caption>I = 3 10<sup>-2</sup> mol·L<sup>-1</sup></caption><thead><tr><th>[Sr]<sub>eq</sub> exp</th><th>Sorbed Sr exp</th><th>Sorbed Sr model</th><th>Δ</th></tr><tr><th>mol·L<sup>-1</sup></th><th>mol</th><th>mol</th><th>%</th></tr></thead><tbody><tr><td>1.98E-03</td><td>4.87E-05</td><td>1.48E-05</td><td>70</td></tr><tr><td>6.52E-04</td><td>2.55E-05</td><td>5.85E-06</td><td>77</td></tr><tr><td>5.01E-04</td><td>2.07E-05</td><td>5.26E-06</td><td>75</td></tr><tr><td>3.20E-04</td><td>1.41E-05</td><td>3.25E-06</td><td>77</td></tr><tr><td>1.64E-04</td><td>6.23E-06</td><td>2.20E-06</td><td>65</td></tr><tr><td>6.79E-05</td><td>2.47E-06</td><td>8.30E-07</td><td>66</td></tr><tr><td>4.57E-05</td><td>2.25E-06</td><td>8.85E-07</td><td>61</td></tr><tr><td>3.44E-05</td><td>1.11E-06</td><td>4.88E-07</td><td>56</td></tr><tr><td>1.60E-05</td><td>5.41E-07</td><td>3.84E-07</td><td>29</td></tr><tr><td>6.06E-06</td><td>1.67E-07</td><td>1.02E-07</td><td>39</td></tr><tr><td>4.41E-06</td><td>1.36E-07</td><td>1.33E-07</td><td>2</td></tr><tr><td>2.82E-06</td><td>8.92E-08</td><td>4.91E-08</td><td>45</td></tr><tr><td>1.22E-06</td><td>7.42E-08</td><td>6.03E-08</td><td>19</td></tr><tr><td>8.99E-07</td><td>2.59E-08</td><td>1.62E-08</td><td>37</td></tr></tbody></table>

SI. Table 3: Percentage of mole of Sr extracted from the solution by an additional process to ion exchange. under two different ionic strengths in carbonate media.