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# Predominance of the alkaline earth (II) triscarbonatoactinyl (VI) complexes in different geochemical contexts: Review of existing data and estimation of potentially unidentified species

Pascal E. Reiller

► To cite this version:

Pascal E. Reiller. Predominance of the alkaline earth (II) triscarbonatoactinyl (VI) complexes in different geochemical contexts: Review of existing data and estimation of potentially unidentified species. Chemosphere, 2024, 350, pp.141049. 10.1016/j.chemosphere.2023.141049. hal-04394102

HAL Id: hal-04394102

https://hal.science/hal-04394102v1

Submitted on 18 Jan 2024

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Predominance of the alkaline earth(II) triscarbonatoactinyl(VI) complexes in different geochemical contexts: review of existing data and estimation of potentially unidentified species.

Pascal E. Reiller

Université Paris-Saclay, CEA, Service de Physico-Chimie (SPC), F-91191 Gif-sur-Yvette
CEDEX, France.

e-mail: pascal.reiller@cea.fr

keywords

uranium; actinides; carbonate complexes; alkaline earth metals
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**Abstract**

From the available thermodynamic data in the literature, a review of the impact of the
formation of complexes between triscarbonatoactinyl(VI) and alkaline earth(II) (Ae) is
estimated under varying conditions. First, using the ascertained thermodynamic data available
from the commissioned reviews from the Nuclear Energy Agency (Organization for the
Economic Cooperation and Development) Thermochemical DataBank Project on actinides
(An) U, Np, and Pu, and from recently determined Ae<sub>n</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(<sup>4-2n</sup>-) thermodynamic
functions, the formation of Ae<sub>n</sub>AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(<sup>4-2n</sup>-) complexes for Pu(VI) and Np(VI) are
estimated using linear free energy relationships (LFERs). The data are in good agreement with
the sole determination of AePuO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup> from Jo *et al*. (Dalton Trans. 49, 11605), which gives
a relative confidence in the LFERs, and allows the application to actual situations. From
existing uranium data, first, the impact of the origin of the data on the calculated predominance
is addressed under 0.1 M NaCl and atmospheric CO<sub>2</sub>(g); second, the influence of ionic strength
and salinity on predominance is estimated; and finally, the influence of temperature up to 50 °C
on the solubility of uraninite in a deep geological radioactive waste storage or disposal site is
calculated. For neptunium and plutonium, the impact of the potential
log<sub>10</sub>β°(Ae<sub>n</sub>AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(<sup>4-2n</sup>-)) on Pourbaix diagrams of Pu and Np in Mg-Ca-CO<sub>3</sub> media are
estimated from Jo *et al*. (Dalton Trans. 49, 11605) and LFERs. Finally, the application to the
speciation of Pu and Np in seawater is proposed.

**1. Introduction**

The complexes between triscarbonatouranyl(VI) and alkaline earth(II) — afterward noted
Ae(II) — have been the subject of several studies since their discovery in uranium mine seepage
waters (Bernhard *et al.*, 1996). The general stoichiometry Ae<sub>n</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(<sup>4-2n</sup>-) (n = {1,2}) have
been evidenced throughout the alkaline earth series from Mg to Ba (Bernhard *et al.*, 1996, 1998;
Bernhard *et al.*, 2001; Dong and Brooks, 2006, 2008; Endrizzi *et al.*, 2016; Geipel *et al.*, 2008;
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Jo *et al.*, 2019a; Jo *et al.*, 2019b; Kalmykov and Choppin, 2000; Lee *et al.*, 2017; Lee and Yun, 2013; Maia *et al.*, 2021; Shang and Reiller, 2020, 2021a, b; Shang *et al.*, 2020). These complexes represent the vast majority of the species in uranium-containing carbonated waters (Gardner *et al.*, 2022; Lartigue *et al.*, 2020; Reiller and Descostes, 2020; Shang *et al.*, 2023) even in reducing conditions such as envisaged underground radioactive waste storage sites (Grivé *et al.*, 2015; Montavon *et al.*, 2022; Montoya *et al.*, 2021; Reiller and Descostes, 2020; Tullborg *et al.*, 2017).

Up to very recently (Grenthe *et al.*, 2020), no thermochemical functions or constants of
formation for these species were selected by the widely recognized commissioned selection for
the Thermochemical Data Base (TDB) project of the Nuclear Energy Agency-Organization for
Economic Cooperation and Development (NEA-OECD https://www.oecd-
nea.org/jcms/pl_22166/thermochemical-database-tdb-project) in Guillaumont *et al.* (2003).
Despite the interest that these species have aroused, the data that allowed an extrapolation to
infinite dilution, necessary to estimate the thermochemical functions of formation, were
relatively scarce (Dong and Brooks, 2008; Kalmykov and Choppin, 2000; Shang and Reiller,
2020, 2021a; Shang *et al.*, 2020). Moreover, in the first years, only Ca₂UO₂(CO₃)₃(aq) was
evidenced (Bernhard *et al.*, 1996; Kalmykov and Choppin, 2000); CaUO₂(CO₃)₃²⁻ was first
suggested by Bernhard *et al.* (2001). This prevented the selection of specific ion-interaction
theory (SIT) coefficient ε for these species in Grenthe *et al.* (2020). Shang *et al.* (Shang and
Reiller, 2020, 2021a; Shang *et al.*, 2020) — who published their results after the cut-off date of
the latter NEA-OECD review (Grenthe *et al.*, 2020) —, proposed log₁₀β° and ε values for the
AeₙUO₂(CO₃)₃⁽⁴⁻²n⁾⁻ species in NaCl and NaClO₄. They also shown a good agreement between
all values in the literature.

The environmental importance of these species has been recognised in various fields of
research (Carvajal *et al.*, 2012; Crançon *et al.*, 2012; Doughman *et al.*, 2024; Liu *et al.*, 2007;
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Xie *et al.*, 2021). They have been evidenced spectroscopically *in situ* (Bernhard *et al.*, 1996; Maloubier *et al.*, 2015; Prat *et al.*, 2009; Shang *et al.*, 2023; Tullborg *et al.*, 2017). The structure of the AenUO2(CO3)3(4-2n)- complexes was ascertained in EXAFS (Bernhard *et al.*, 2001; Brooks *et al.*, 2003; Kelly *et al.*, 2007; Kelly *et al.*, 2005), and calculated in molecular dynamics and ab initio (Oher *et al.*, 2020; Priest *et al.*, 2016; Tirler and Hofer, 2016).

Knowing the similarities between the chemistry of the actinides (An) at their +VI redox state (Vercouter, 2021; Vitorge, 1999; Vitorge and Capdevila, 2003), the question of the formation of eventual AenAnO2(CO3)3(4-2n)- species for Np(VI) and Pu(VI) was pending. Very recently, Jo *et al.* (2020) evidenced the formation of MgPuO2(CO3)32- and CaPuO2(CO3)32- in visible-near-infrared absorption spectroscopy at 0.1 M H/NaClO4 ionic strength. These experiments allowed the authors to propose thermodynamic constants extrapolated to infinite dilution using the Davies (1962) equation. The general conditions under which these species can be dominant in geochemical media are somewhat difficult to apprehend as activities of Mg2+, Ca2+, HCO3-/CO32-, Na+, and H+ have a direct impact. For uranium, Reiller and Descostes (2020) proposed log10 a(SO42-)-pH at fixed -log10 a(Mg2+), -log10 a(Ca2+), and -log10 P(CO2). Shang *et al.* (2023) proposed representations of activity products log10(a(Ca2+)/a(H+)2)-log10(a(HCO3-)) a(H+)–log10(a(Na+)/a(H+)). For the corresponding solids, Lee *et al.* (2019) also proposed the activity product log10(a(Ca2+) a(HCO3-))2). Jo *et al.* (2022) proposed a Pourbaix diagram for Pu at [Ca]total = 1 mM and atmospheric P(CO2).

The influence of ionic strength on these species has been shown to be important, particularly
on the globally neutral Ca₂UO₂(CO₃)₃(aq) complex. Shang and Reiller (2020) determined a
non-nil value for ε(Ca₂UO₂(CO₃)₃(aq),Na⁺Cl⁻) = 0.66 kg_w mol⁻¹, contrary to generally accepted
nil value for neutral complex — even if several neutral complexes have non-nil values in the
literature (Ciavatta, 1980; Hummel *et al.*, 2005; Plyasunova *et al.*, 1998; Zhang and
Muhammed, 2001), or ε values which can be calculated from Δε values (Brown and Ekberg,
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2016; Powell *et al.*, 2009, 2011; Powell *et al.*, 2007). The like-charged hypothesis for
ε(AeₙUO₂(CO₃)₃²⁻,Na⁺) has also been questioned (Shang and Reiller, 2020, 2021a; Shang *et al.*,
2020).

It is known since long that commonalities between similar elements can be represented
through correlations (Irving and Rossotti, 1956) — namely linear free-energy relationships
(LFERs) —, which could be used to estimate missing constants (Grenthe *et al.*, 1997; Murphy
and Shock, 1999) with an inevitable high uncertainty. It could be possible then to propose
estimation of missing formation constants for AeₙAn(CO₃)₃*(4-2n)*, and to define their possible
prevalence domain.

The purpose of the study is first to compare the prevalence domains of
Ae<sub>n</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(<sup>4-2n</sup>) complexes in various relevant media based on selected values from NEA-
OECD (Grenthe *et al.*, 2020) and like-charged hypothesis for ε values (Lee and Yun, 2013),
and on recent constants, functions of reaction and formation, and ε proposed from extrapolation
to zero ionic strength of existing literature values. Second, based on these comparisons, LFERs
for U-Pu, U-Np, and Pu-Np from NEA-OECD selections (Grenthe *et al.*, 1992; Grenthe *et al.*,
2020; Guillaumont *et al.*, 2003; Lemire *et al.*, 2001) will be plotted to estimate missing
formation constants, and compare them to the sole existing determination (Jo *et al.*, 2020).
Finally, speciation (percent of species vs. pH or pe) and Pourbaix predominance diagram (E<sub>h</sub>
vs. pH) will be calculated to define the possible predominance domain and help orienting further
studies.
## 2. Methods

### 2.1. General description

The formation of species ML from reactants M and L is described by the equilibrium thermodynamic law. Following Sillén and Martell (1964), the reaction constants can be written as follows, omitting charges for the sake of simplicity.

$$ML_{n-1} + L \rightleftharpoons ML_n$$

$$M + nL \rightleftharpoons ML_n$$

$$K_n^\circ = \frac{[ML_n]}{[ML_{n-1}][L]} \quad (1)$$

$$\beta_n^\circ = \frac{[ML_n]}{[M][L]^n} \quad (2)$$

Here, $K_n^\circ$ is a stepwise reaction constant, and $\beta_n^\circ$ a cumulative reaction constant.

The free energy of reaction is written as,

$$\Delta_r G^\circ_m = -RT \ln K_n^\circ \quad (3)$$

There are numerous compilation of thermodynamic functions and constants (Chase, 1998; Cox et al., 1989; Cross and Ewart, 1991; Grenthe et al., 1992; Grenthe et al., 2020; Guillaumont et al., 2003; Lemire et al., 2001; Naumov et al., 1974; Robie and Hemingway, 1995; Wagman et al., 1982), all of which are not always traceable (Hummel et al., 2019, and references therein).

For the actinides U, Np, and Pu, data have been selected by reviews commissioned by the TDB project from NEA-OECD (Grenthe et al., 1992; Grenthe et al., 2020; Guillaumont et al., 2003; Lemire et al., 2001) for ligands of interest for radioactive waste management programs, e.g., $OH^-$, $F^-$, $SO_4^{2-}$, $PO_4^{3-}$, $CO_3^{2-}$, $H_4SiO_4(aq)$.

A general formation reaction of hydroxocarbonato complexes of uranyl(VI) is written as follows.
$$ \begin{gathered} n\text{UO}_2^{2+} + \text{mH}_2\text{O} + \text{pCO}_3^{2-} \rightleftharpoons (\text{UO}_2)_n(\text{OH})_m(\text{CO}_3)_p^{(2n-m-2p)} + \text{mH}^+ \\ \beta^\circ = \frac{a((\text{UO}_2)_n(\text{OH})_m(\text{CO}_3)_p^{(2n-m-2p)}) a(\text{H}^+)^m}{a(\text{UO}_2^{2+})^n a(\text{H}_2\text{O})^m a(\text{CO}_3^{2-})^p} \end{gathered} \quad (4) $$

The general stepwise formation of $A_e n\text{AnO}_2(\text{CO}_3)_3^{(4-2n)-}$ is written as follows,

$$ \begin{gathered} A_e^{2+} + A_{e-1}UO_2(CO_3)_3^{(4-2(n-1))-} \rightleftharpoons A_e n\text{UO}_2(CO_3)_3^{(4-2n)-} \\ K_{\text{n.1.3}}^{\circ} = \frac{a(A_e n\text{AnO}_2(CO_3)_3^{(4-2n)-})}{a(A_e^{2+}) a(A_{e-1} n\text{AnO}_2(CO_3)_3^{(4-2(n-1))-})} \end{gathered} \quad (5) $$

and the cumulative reaction is written as follows.

$$ \begin{gathered} nA_e^{2+} + UO_2^{2+} + 3CO_3^{2-} \rightleftharpoons A_e n\text{UO}_2(CO_3)_3^{(4-2n)-} \\ \beta_{\text{n.1.3}}^{\circ} = \frac{a((\text{UO}_2)_n(\text{OH})_m(\text{CO}_3)_p^{(2n-m-2p)})}{a(\text{UO}_2^{2+})^n a(A_e^{2+})^n a(CO_3^{2-})^p} \end{gathered} \quad (6) $$

The influence of ionic strength $I_m$ on $\log_{10}K$ values is accounted for in the NEA-OECD reviews (Grenthe et al., 1992; Grenthe et al., 2020; Guillaumont et al., 2003; Lemire et al., 2001) through the specific ion-interaction theory (SIT),

$$ \log_{10} K = \log_{10} K^{\circ} + \frac{A(T) \Delta z^2 \overline{I_m}}{1+1.5 \overline{I_m}} - \Delta \varepsilon I_m \quad (7) $$

where $A(289.15 \text{ K}) = 0.509 \text{ kgw}^{1/2} \text{ mol}^{-1/2}$.

$$ \Delta \varepsilon = \sum_i v_i \varepsilon_i \quad (8) $$

with $v_i$ the stoichiometric coefficient of species i — positive for products and negative for reactants —, and $\varepsilon_i$ the specific ion-interaction parameter of species i tabulated in NEA-OECD reviews (Grenthe et al., 1992; Grenthe et al., 2020; Guillaumont et al., 2003; Lemire et al., 2001).
However, due to their selective nature, these compilations are intrinsically incomplete. It means that either thermodynamic functions ($\Delta_r G^\circ_m$, $\Delta_r H^\circ_m$, $\Delta_r S^\circ_m$), or constants ($\log_{10}K^\circ$ or $\log_{10}\beta^\circ$), or $\varepsilon$ values are missing.

It has been observed since long that for similar complexes of analogous elements linear relationships exist between $\log_{10}K$, or $\log_{10}\beta$, values (Irving and Rossotti, 1956, and references therein) that are related to free energy — $\Delta_r G^\circ_m/RT\ln(10)$, see eq. 3. These linear free energy relationships (LFERs) can be used to estimate missing data (Grenthe *et al.*, 1997).

## 2.2. Linear free energy relationships

### 2.2.1. General thermochemical data and SIT parameters

For the LFERs between complexation constants, as stressed in Grenthe *et al.* (1997) it is within classes of reactions that share some common characteristics that correlations are most precise. Nevertheless, as we will see it afterwards, a certain level of precision can be attained even if either the ligands or the redox states of the metals are not totally the same.

The logarithm of the thermodynamic constants of the common complexes between U, Np, and Pu, are reported in Table 1. The $\varepsilon$ parameters for the specific ion interaction theory (SIT), on which the effect of ionic strength on complexation constants is based (Grenthe *et al.*, 2013) in the NEA-OECD reviews (Grenthe *et al.*, 1992; Grenthe *et al.*, 2020; Guillaumont *et al.*, 2003; Lemire *et al.*, 2001; Silva *et al.*, 1995), are regrouped in Table 2. The value of $PuO_2(OH)(aq)$ in Grenthe *et al.* (2020) was not included in Table 1, as it is an upper estimated value. The recent determination by Aupiais *et al.* (2023) was used instead, even if this estimation was done using like-charged analogy between $\varepsilon(NpO_2^+,Cl^-)$ and $\varepsilon(PuO_2^+,Cl^-)$, and $\varepsilon(PuO_2(OH)(aq),Na^+Cl^-) = 0$, the low 0.1 M ionic strength was inducing a low influence of $\Delta\varepsilon I_m$ in equation 7 — an estimation using equation from Davies (1962) gives the same value.
The LFERs $\log_{10}\beta^\circ(\text{U}) = f(\log_{10}\beta^\circ(\text{An}))$ are plotted in Figure 1 and Figure 2, for Pu and Np, respectively. The LFER $\log_{10}\beta^\circ(\text{Pu}) = f(\log_{10}\beta^\circ(\text{Np}))$ is plotted in Figure 3. The regression parameters presented in Table 3 are used to draw the uncertainty hyperboles. It can be noted that: (i) the slopes between the $\log_{10}\beta^\circ$ values are not significantly different from unity and y-intercepts are not different from nil according to $2\sigma_y$; and (ii) that the values for the cumulative formations constants of $(\text{AnO}_2)_3(\text{OH})_5^+$, $\text{An}(\text{CO}_3)_4^{4+}$, $\text{An}(\text{CO}_3)_5^{6-}$, and $(\text{AnO}_2)_3(\text{CO}_3)_6^{6-}$ are importantly driving the values of the slopes. The main difference between these elements is the redox potential values of the free ions (Vercouter, 2021; Vitorge, 1999) that are not accounted for in the LFERs.
<table><caption>Table 1. Selected thermodynamic constants $log_{10}\beta^{\circ}(An)$ of common inorganic species of $An = \{U; Np; Pu\}$.</caption><thead><tr><th>Equilibrium</th><th>log<sub>10</sub>β°(U)</th><th>log<sub>10</sub>β°(Np)</th><th>log<sub>10</sub>β°(Pu)</th></tr></thead><tbody><tr><td>An<sup>4+</sup> + H<sub>2</sub>O ⇌ An(OH)<sup>3+</sup> + H<sup>+</sup></td><td>-0.54 ± 0.06<sup>a</sup></td><td>0.55 ± 0.20<sup>d</sup></td><td>0.60 ± 0.20<sup>b</sup></td></tr><tr><td>An<sup>4+</sup> + 2H<sub>2</sub>O ⇌ An(OH)<sup>2+</sup> + 2H<sup>+</sup></td><td>-1.90 ± 0.20<sup>e</sup></td><td>0.35 ± 0.30<sup>d</sup></td><td>0.60 ± 0.30<sup>b</sup></td></tr><tr><td>An<sup>4+</sup> + 3H<sub>2</sub>O ⇌ An(OH)<sup>3+</sup> + 3H<sup>+</sup></td><td>-5.20 ± 0.40<sup>e</sup></td><td>—</td><td>-2.30 ± 0.40<sup>b</sup></td></tr><tr><td>An<sup>4+</sup> + 4H<sub>2</sub>O ⇌ An(OH)<sub>4</sub>(aq) + 4H<sup>+</sup></td><td>-10.01 ± 1.40<sup>d</sup></td><td>-8.31 ± 1.10<sup>d</sup></td><td>-8.50 ± 0.50<sup>b</sup></td></tr><tr><td>AnO<sub>2</sub><sup>+</sup> + H<sub>2</sub>O ⇌ AnO<sub>2</sub>(OH)(aq) + H<sup>+</sup></td><td>—</td><td>-11.30 ± 0.70<sup>d</sup></td><td>-11.50 ± 0.12<sup>e</sup></td></tr><tr><td>AnO<sub>2</sub><sup>2+</sup> + H<sub>2</sub>O ⇌ AnO<sub>2</sub>(OH)<sup>+</sup> + H<sup>+</sup></td><td>-5.25 ± 0.24<sup>e</sup></td><td>-5.10 ± 0.40<sup>d</sup></td><td>-5.50 ± 0.50<sup>d</sup></td></tr><tr><td>AnO<sub>2</sub><sup>2+</sup> + 2H<sub>2</sub>O ⇌ AnO<sub>2</sub>(OH)<sub>2</sub>(aq) + 2H<sup>+</sup></td><td>-12.15 ± 0.07<sup>d</sup></td><td>—</td><td>-13.20 ± 1.50<sup>b</sup></td></tr><tr><td>2AnO<sub>2</sub><sup>2+</sup> + 2H<sub>2</sub>O ⇌ (AnO<sub>2</sub>)<sub>2</sub>(OH)<sub>2</sub><sup>+</sup> + 2H<sup>+</sup></td><td>-5.62 ± 0.08<sup>e</sup></td><td>-6.27 ± 0.21<sup>d</sup></td><td>-7.50 ± 1.00<sup>b</sup></td></tr><tr><td>3AnO<sub>2</sub><sup>2+</sup> + 5H<sub>2</sub>O ⇌ (AnO<sub>2</sub>)<sub>3</sub>(OH)<sub>5</sub><sup>+</sup> + 5H<sup>+</sup></td><td>-15.55 ± 0.12<sup>e</sup></td><td>-17.12 ± 0.22<sup>d</sup></td><td>—</td></tr><tr><td>An<sup>4+</sup> + F<sup>-</sup> ⇌ AnF<sup>3+</sup></td><td>9.42 ± 0.51<sup>d</sup></td><td>8.96 ± 0.14<sup>d</sup></td><td>8.84 ± 0.10<sup>b</sup></td></tr><tr><td>An<sup>4+</sup> + 2F<sup>-</sup> ⇌ AnF<sup>2</sup><sup>2+</sup></td><td>16.56 ± 0.71<sup>d</sup></td><td>15.70 ± 0.30<sup>d</sup></td><td>15.70 ± 0.20<sup>b</sup></td></tr><tr><td>AnO<sub>2</sub><sup>2+</sup> + F<sup>-</sup> ⇌ AnO<sub>2</sub>F<sup>+</sup></td><td>5.16 ± 0.06<sup>e</sup></td><td>4.57 ± 0.07<sup>d</sup></td><td>4.56 ± 0.20<sup>b</sup></td></tr><tr><td>AnO<sub>2</sub><sup>2+</sup> + 2F<sup>-</sup> ⇌ AnO<sub>2</sub>F<sub>2</sub>(aq)</td><td>8.83 ± 0.08<sup>e</sup></td><td>7.60 ± 0.08<sup>d</sup></td><td>7.25 ± 0.45<sup>b</sup></td></tr><tr><td>An<sup>4+</sup> + Cl<sup>-</sup> ⇌ AnCl<sup>3+</sup></td><td>1.72 ± 0.13<sup>d</sup></td><td>1.50 ± 0.30<sup>d</sup></td><td>1.80 ± 0.30<sup>b</sup></td></tr><tr><td>AnO<sub>2</sub><sup>2+</sup> + Cl<sup>-</sup> ⇌ AnO<sub>2</sub>Cl<sup>+</sup></td><td>0.17 ± 0.02<sup>c</sup></td><td>0.40 ± 0.17<sup>d</sup></td><td>0.23 ± 0.03<sup>d</sup></td></tr><tr><td>AnO<sub>2</sub><sup>2+</sup> + 2Cl<sup>-</sup> ⇌ AnO<sub>2</sub>Cl<sub>2</sub>(aq)</td><td>-1.10 ± 0.40<sup>d</sup></td><td>—</td><td>-1.15 ± 0.30<sup>d</sup></td></tr><tr><td>An<sup>4+</sup> + Br<sup>-</sup> ⇌ AnBr<sup>3+</sup></td><td>1.46 ± 0.20<sup>d</sup></td><td>—</td><td>1.60 ± 0.30<sup>d</sup></td></tr><tr><td>An<sup>4+</sup> + I<sup>-</sup> ⇌ AnI<sup>3+</sup></td><td>1.25 ± 0.30<sup>d</sup></td><td>1.50 ± 0.40<sup>d</sup></td><td>—</td></tr><tr><td>AnO<sub>2</sub><sup>2+</sup> + IO<sub>3</sub><sup>-</sup> ⇌ AnO<sub>2</sub>(IO<sub>3</sub>)<sup>2+</sup></td><td>2.00 ± 0.02<sup>d</sup></td><td>1.20 ± 0.30<sup>d</sup></td><td>—</td></tr><tr><td>An<sup>4+</sup> + NO<sub>3</sub><sup>-</sup> ⇌ AnNO<sub>3</sub><sup>3+</sup></td><td>1.47 ± 0.13<sup>d</sup></td><td>1.90 ± 0.15<sup>d</sup></td><td>—</td></tr><tr><td>An<sup>4+</sup> + SO<sub>4</sub><sup>2-</sup> ⇌ An(SO<sub>4</sub>)<sup>2+</sup></td><td>6.58 ± 0.19<sup>a</sup></td><td>6.85 ± 0.27<sup>d</sup></td><td>6.89 ± 0.31<sup>d</sup></td></tr><tr><td>An<sup>4+</sup> + 2SO<sub>4</sub><sup>2-</sup> ⇌ An(SO<sub>4</sub>)<sub>2</sub>(aq)</td><td>10.51 ± 0.20<sup>d</sup></td><td>11.05 ± 0.51<sup>d</sup></td><td>11.14 ± 0.55<sup>d</sup></td></tr><tr><td>AnO<sub>2</sub><sup>2+</sup> + SO<sub>4</sub><sup>2-</sup> ⇌ AnO<sub>2</sub>(SO<sub>4</sub>)(aq)</td><td>3.15 ± 0.10<sup>e</sup></td><td>3.28 ± 0.06<sup>d</sup></td><td>3.38 ± 0.20<sup>d</sup></td></tr><tr><td>AnO<sub>2</sub><sup>2+</sup> + 2SO<sub>4</sub><sup>2-</sup> ⇌ AnO<sub>2</sub>(SO<sub>4</sub>)<sub>2</sub><sup>2-</sup></td><td>4.14 ± 0.15<sup>e</sup></td><td>4.70 ± 0.10<sup>d</sup></td><td>4.40 ± 0.20<sup>d</sup></td></tr><tr><td>An<sup>4+</sup> + SCN<sup>-</sup> ⇌ AnSCN<sup>3+</sup></td><td>2.97 ± 0.06<sup>d</sup></td><td>3.00 ± 0.30<sup>d</sup></td><td>—</td></tr><tr><td>An<sup>4+</sup> + 2SCN<sup>-</sup> ⇌ An(SCN)<sub>2</sub><sup>2+</sup></td><td>4.26 ± 0.18<sup>d</sup></td><td>4.10 ± 0.50<sup>d</sup></td><td>—</td></tr><tr><td>An<sup>4+</sup> + 4CO<sub>3</sub><sup>2-</sup> ⇌ An(CO<sub>3</sub>)<sub>4</sub><sup>4-</sup></td><td>35.12 ± 0.96<sup>d</sup></td><td>36.69 ± 1.03<sup>b</sup></td><td>37.00 ± 1.10<sup>d</sup></td></tr><tr><td>An<sup>4+</sup> + 5CO<sub>3</sub><sup>2-</sup> ⇌ An(CO<sub>3</sub>)<sub>5</sub><sup>6-</sup></td><td>34.00 ± 0.90<sup>d</sup></td><td>35.62 ± 1.05<sup>b</sup></td><td>35.65 ± 1.13<sup>d</sup></td></tr><tr><td>AnO<sub>2</sub><sup>+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>5-</sup></td><td>6.95 ± 0.36<sup>d</sup></td><td>5.50 ± 0.07<sup>d</sup></td><td>5.61 ± 0.24<sup>e</sup></td></tr><tr><td>AnO<sub>2</sub><sup>2+</sup> + CO<sub>3</sub><sup>2-</sup> ⇌ AnO<sub>2</sub>(CO<sub>3</sub>)(aq)</td><td>9.94 ± 0.03<sup>d</sup></td><td>9.86 ± 0.10<sup>e</sup></td><td>9.50 ± 0.50<sup>d</sup></td></tr><tr><td>AnO<sub>2</sub><sup>2+</sup> + 2CO<sub>3</sub><sup>2-</sup> ⇌ AnO<sub>2</sub>(CO<sub>3</sub>)<sub>2</sub><sup>2-</sup></td><td>16.61 ± 0.09<sup>d</sup></td><td>16.52 ± 0.73<sup>e</sup></td><td>14.70 ± 0.50<sup>d</sup></td></tr><tr><td>AnO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ AnO<sub>2</sub>(CO<sub>3</sub>)<sub>4</sub><sup>4-</sup></td><td>21.84 ± 0.04<sup>d</sup></td><td>19.90 ± 0.50<sup>e</sup></td><td>18.00 ± 0.50<sup>d</sup></td></tr><tr><td>2AnO<sub>2</sub><sup>2+</sup> + CO<sub>3</sub><sup>2-</sup> + 3H<sub>2</sub>O ⇌ (AnO<sub>2</sub>)<sub>2</sub>CO<sub>3</sub>(OH)<sub>3</sub><sup>-</sup> + 3H<sup>+</sup></td><td>-0.86 ± 0.50<sup>d</sup></td><td>-1.79 ± 1.92<sup>e</sup></td><td>—</td></tr><tr><td>3AnO<sub>2</sub><sup>2+</sup> + 6CO<sub>3</sub><sup>2-</sup> ⇌ (AnO<sub>2</sub>)<sub>3</sub>(CO<sub>3</sub>)<sub>6</sub><sup>6-</sup></td><td>54.00 ± 1.00<sup>d</sup></td><td>51.43 ± 2.14<sup>e</sup></td><td>—</td></tr></tbody></table>

a Grenthe et al. (1992); b Lemire et al. (2001); c Aupiais et al. (2023); d Guillaumont et al. (2003); e Grenthe et al. (2020).
<figure><img src="image_2.png" /></figure>

Figure 1. Linear free energy relationship between uranium and plutonium inorganic species selected by the NEA-OECD TDB reviews (blue circles from Table 1, LFER blue line, uncertainty hyperboles short-dashed blue line); estimation of $log_{10}K^°_{CaPuO_2(CO_3)_3^2^-}$ (red dash-dotted line) and $log_{10}K^°_{Ca_2PuO_2(CO_3)_3(aq)}$ (purple long-dashed line) and $log_{10}K^°_{MgPuO_2(CO_3)_3^{2-}}$ (green double dot dashed line) from the LFER using $log_{10}K^°$ from Shang and Reiller (2020) for $Ca^{2+}$, and Shang and Reiller (2021a) for $Mg^{2+}$; experimental value for $log_{10}K^°_{AePuO_2(CO_3)_3^{2-}}$ (Mg green diamond, Ca red square) from Jo et al. (2020).
<table><caption>Table 2. Specific ion-interaction theory parameters used in this study.</caption><thead><tr><th>Species</th><th>Counter-ion</th><th>U</th><th>Np</th><th>Pu</th></tr></thead><tbody><tr><td>H<sup>+</sup></td><td>Cl<sup>-</sup></td><td></td><td>0.12 ± 0.01<sup>a</sup></td><td></td></tr><tr><td>Na<sup>+</sup></td><td>Cl<sup>-</sup></td><td></td><td>0.03 ± 0.01<sup>a</sup></td><td></td></tr><tr><td>HCO<sub>3</sub><sup>-</sup></td><td>Na<sup>+</sup></td><td></td><td>0.00 ± 0.02<sup>a</sup></td><td></td></tr><tr><td>CO<sub>3</sub><sup>2-</sup></td><td>Na<sup>+</sup></td><td></td><td>-0.08 ± 0.03<sup>a</sup></td><td></td></tr><tr><td>An<sup>4+</sup></td><td>Cl<sup>-</sup></td><td>-</td><td>-</td><td>-</td></tr><tr><td>AnO<sub>2</sub><sup>+</sup></td><td>Cl<sup>-</sup></td><td>-</td><td>0.09 ± 0.05<sup>b</sup></td><td>-</td></tr><tr><td>AnO<sub>2</sub><sup>2+</sup></td><td>Cl<sup>-</sup></td><td>0.21 ± 0.02<sup>a</sup></td><td>-</td><td>-</td></tr><tr><td>An(OH)<sub>4</sub>(aq)</td><td>Na<sup>+</sup>(Cl<sup>-</sup>)</td><td>0<sup>h</sup></td><td>0<sup>h</sup></td><td>0<sup>h</sup></td></tr><tr><td>An(CO<sub>3</sub>)<sub>4</sub><sup>4-</sup></td><td>Na<sup>+</sup></td><td>-0.09 ± 0.10<sup>c</sup></td><td>-</td><td>-</td></tr><tr><td>An(CO<sub>3</sub>)<sub>5</sub><sup>6-</sup></td><td>Na<sup>+</sup></td><td>-0.30 ± 0.15<sup>c</sup></td><td>-</td><td>-</td></tr><tr><td>AnO<sub>2</sub>(CO<sub>3</sub>)(aq)</td><td>Na<sup>+</sup>(Cl<sup>-</sup>)</td><td>0<sup>h</sup></td><td>0<sup>h</sup></td><td>0<sup>h</sup></td></tr><tr><td>AnO<sub>2</sub>(CO<sub>3</sub>)<sub>2</sub><sup>2-</sup></td><td>Na<sup>+</sup></td><td>-0.02 ± 0.09<sup>c</sup></td><td>-0.02 ± 0.14<sup>c</sup></td><td>-0.7 ± 0.2<sup>b</sup></td></tr><tr><td>AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4-</sup></td><td>Na<sup>+</sup></td><td>-0.01 ± 0.11<sup>c</sup></td><td>-0.40 ± 0.19<sup>c</sup></td><td>-0.2 ± 0.3<sup>b</sup></td></tr><tr><td>(AnO<sub>2</sub>)<sub>3</sub>(CO<sub>3</sub>)<sub>6</sub><sup>6-</sup></td><td>Na<sup>+</sup></td><td>0.37 ± 0.01<sup>c</sup></td><td>-0.46 ± 0.73<sup>c</sup></td><td>-</td></tr><tr><td>(AnO<sub>2</sub>)<sub>2</sub>CO<sub>3</sub>(OH)<sub>3</sub><sup>-</sup></td><td>Na<sup>+</sup></td><td>0.00 ± 0.05<sup>c</sup></td><td>-</td><td>-</td></tr><tr><td>CaUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td>Na<sup>+</sup>(Cl<sup>-</sup>)</td><td>0.29 ± 0.11<sup>d</sup><br>0.12 ± 0.25<sup>e</sup></td><td>-</td><td>-</td></tr><tr><td>CaUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>Na<sup>+</sup>(Cl<sup>-</sup>)</td><td>-0.02 ± 0.09<sup>f</sup></td><td>-</td><td>-</td></tr><tr><td>MgUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td>Na<sup>+</sup>(Cl<sup>-</sup>)</td><td>0.66 ± 0.12<sup>d</sup><br>0.50 ± 0.38<sup>e</sup></td><td>-</td><td>-</td></tr></tbody></table>

<footnote>a Grenthe *et al.* (1992), b Lemire *et al.* (2001), c Guillaumont *et al.* (2003), d Shang and Reiller (2020); e This study; f like-charged analogy to ε(UO<sub>2</sub>(CO<sub>3</sub>)<sub>2</sub><sup>2-</sup>,Na<sup>+</sup>) = -0.02 ± 0.09 kg<sub>w</sub> mol<sup>-1</sup> in Lee and Yun (2013) and in Thermochimie 11a, g Shang and Reiller (2021a), h by default.</footnote>
<table><caption>Table 3. Regression parameters of the $log_{10}\beta^{\circ}(U) = f(log_{10}\beta^{\circ}(An))$</caption><thead><tr><th></th><th>log<sub>10</sub>β<sup>°</sup><sub>U</sub> = f(log<sub>10</sub>β<sup>°</sup><sub>Np</sub>)</th><th>log<sub>10</sub>β<sup>°</sup><sub>U</sub> = f(log<sub>10</sub>β<sup>°</sup><sub>Pu</sub>)</th><th>log<sub>10</sub>β<sup>°</sup><sub>Pu</sub> = f(log<sub>10</sub>β<sup>°</sup><sub>Np</sub>)</th></tr></thead><tbody><tr><td>slope</td><td>1.008 ± 0.015</td><td>0.995 ± 0.026</td><td>0.998 ± 0.011</td></tr><tr><td>y-intercept</td><td>0.035 ± 0.238</td><td>0.073 ± 0.365</td><td>-0.248 ± 0.156</td></tr><tr><td>S<sub>x/y</sub></td><td>1.1283</td><td>1.5326</td><td>0.6251</td></tr><tr><td>r<sup>2</sup></td><td>0.9939</td><td>0.9840</td><td>0.9975</td></tr><tr><td>Degrees of freedom</td><td>27</td><td>23</td><td>20</td></tr><tr><td>y&#773; = log<sub>10</sub>β<sup>°</sup>(U)</td><td>7.480</td><td>6.016</td><td>6.948</td></tr><tr><td>SSR(log<sub>10</sub>β<sup>°</sup>(An))</td><td>5549.05</td><td>3356.64</td><td>3139.87</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>Figure 2. Linear free energy relationship between uranium and neptunium inorganic species selected by the NEA-OECD TDB reviews (blue circles) from Table 1, LFER (blue line), uncertainty hyperboles (dashed blue line); estimation of $log_{10}K^{\circ}_{CaNpO_2(CO_3)_3}$ (red dash-dotted line) and $log_{10}K^{\circ}_{Ca_2NpO_2(CO_3)_3(aq)}$ (purple dashed line) and $log_{10}K^{\circ}_{MgNpO_2(CO_3)_3}$ (green double dash dotted line) from the LFER using $log_{10}K^{\circ}_{Ae_nUO_2(CO_3)_3}$ from Shang and Reiller (2020, 2021a).</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Figure 3. Linear free energy relationship between plutonium and neptunium inorganic species selected by the NEA-OECD TDB reviews (blue circles) from Table 1, LFER (blue line), uncertainty hyperboles (dashed blue line); estimation of $log_{10}K^{\circ}_{CaNpO_2(CO_3)_3^{-}}$ (red dash-dotted line) and $log_{10}K^{\circ}_{MgNpO_2(CO_3)_3^{-}}$ (green double dash-dotted line) from the LFER using $log_{10}K^{\circ}_{AePuO_2(CO_3)_3^{-}}$ from Jo et al. (2020).</figcaption></figure>

The common enthalpy of reaction values for U-Pu and U-Np are too scarce to obtain a satisfying correlation: 2 values for U-Pu(IV), 5 for U-Pu(VI), 5 for U-Np(IV), 2 for U-Np(VI) in addition to the 4 pairs of redox species. If the enthalpies of formation are fairly well aligned (Figure S1a of the SI), the $\Delta_r H^\circ_m(Ae_nUO_2(CO_3)_3^{4-2n-})$ values are lower than the available values of the correlation and the uncertainties of $\Delta_r H^\circ_m$ correlations for Pu(VI) are too high (Figure S1b of the SI).

### 2.2.2. Reinterpretation of $Ae_nUO_2(CO_3)_3^{(4-2n)-}$ data from literature

Since the seminal work from Bernhard *et al.* (1996), there have been several determinations of the formation constants of the $Ae_nUO_2(CO_3)_3^{(4-2n)-}$ complexes (Amayri, 2002; Bernhard *et al.*, 2001; Dong and Brooks, 2006, 2008; Endrizzi and Rao, 2014; Geipel *et al.*, 2008; Jo *et al.*, 2001;
2019a; Jo et al., 2019b; Kalmykov and Choppin, 2000; Lee et al., 2017; Lee and Yun, 2013; Maia et al., 2021). Among them, some only identified the Ca₂UO₂(CO₃)₂(aq) complex (Bernhard et al., 1996; Kalmykov and Choppin, 2000) or only suggested the formation of CaUO₂(CO₃)₃²⁻ (Bernhard et al., 2001). The effect of ionic strength on the repartition of species is important for these voluminous species, but the effect of this parameter was not studied often (Dong and Brooks, 2008; Kalmykov and Choppin, 2000; Shang and Reiller, 2020, 2021a, b; Shang et al., 2020), or only postulated from like-charge comportment (Endrizzi and Rao, 2014; Lee and Yun, 2013). Following the original work from Bernhard et al. (1996), a large part of these studies were performed using the strong luminescence increase of UO₂(CO₃)₃⁴⁻ with Ae²⁺ concentration in time-resolved laser-induced fluorescence spectroscopy (TRLFS). The luminescence of AeₙUO₂(CO₃)₃⁽⁴⁻n²⁾⁻ species, with n = {0,1,2}, have a distinctive blue shift relative to the free uranyl ion and slight shift between Mg and Ca species (Oher et al., 2020; Shang and Reiller, 2021a). Ion-exchange resins (Dong and Brooks, 2006, 2008; Maia et al., 2021), UV-Visible spectroscopy (Jo et al., 2019a; Jo et al., 2019b), Ca-selective electrode (Endrizzi and Rao, 2014; Jo et al., 2019b), or calorimetry (Endrizzi and Rao, 2014) were also used. A critical analysis of the data published before the cut-off date (2017) has been done in Grenthe et al. (2020). The different values of log₁₀K values are reported in Table S1 of the SI.

The interpretation in the framework of the SIT are shown in Figure 4. The extrapolation of
log₁₀K<sub>AeUO₂(CO₃)₃⁽⁴⁻n²⁾⁻</sub> - Δz²D values were obtained in NaCl and NaClO₄ using multilinear fittings.
The case of NaNO₃ was not treated with the NaCl and NaClO₄ media, because: (i) only data for
MgUO₂(CO₃)₃²⁻ vs. I⁻ are available; and (ii) the variation of values of log₁₀K<sub>MgUO₂(CO₃)₃²⁻</sub> vs. ionic
strength of Dong and Brooks (2008) are quite important as seen in Figure 4a, even compared
to log₁₀K<sub>CaUO₂(CO₃)₃²⁻</sub> in NaClO₄ (Shang et al., 2020) and even to the value at 0.1 M (Dong and
Brooks, 2006). As differences of comportment were evidenced between NaCl and NaClO₄
media (Shang and Reiller, 2020, 2021a; Shang et al., 2020), further works are needed to
elucidate this comportment in NaNO₃ — particularly in view of the comments in Grenthe *et al.*
(2020) that led to the non-selection of these data by the critical review.

<figure><img src="image_5.png" /><figcaption>Figure 4. SIT plot of the NaCl (green lines and circles), NaClO₄ (orange lines and diamonds) and NaNO₃ (blue squares) of the formation constant of MgUO₂(CO₃)₃²⁻ (a), CaUO₂(CO₃)₃²⁻ (b), and Ca₂UO₂(CO₃)₃ (c) from Table S1 of the SI; plain lines are the linear fits and dashed lines are the propagations of errors (green for NaCl, orange for NaClO₄).</figcaption></figure>

Data for the formation of AeₙUO₂(CO₃)₃⁽⁴⁻²n⁾⁻ complexes and ε values either proposed in the literature, selected in the latter selection from the NEA-OECD (Grenthe *et al.*, 2020), or determined here are reported in Table 2 and Table 4. It can be seen that the obtained values are in agreement with estimation available otherwise. It is also noteworthy that even rejected in
Grenthe *et al.* (2020), the data from Dong and Brooks (2006) are described satisfactorily by the extrapolations. The general comportment in ionic strength is inevitably mainly driven by the data from Shang *et al.* (Shang and Reiller, 2020, 2021a; Shang *et al.*, 2020). Accounting for the other data is increasing the uncertainties, particularly the ones for $\Delta\epsilon$ and $\epsilon(A_eUO_2(CO_3)_3^{(4-2n)-},Na^+X^-)$. Interestingly enough, given the large uncertainties on $\epsilon(MgUO_2(CO_3)_3^{2-},Na^+Cl^-)$, the value determined here is not significantly different from the like-charged hypothesis value with $\epsilon(UO_2(CO_3)_2^{2-},Na^+)$.
<table><caption>Table 4. Thermodynamic constants of AenAnO2(CO3)3(4-2n)- complexes, for An(VI) = {U(VI), Np(VI), Pu(VI)}; values in italic are from LFERs (Table 3).</caption><thead><tr><th rowspan="2">Equilibrium</th><th colspan="3">log<sub>10</sub>K°<sub>n.1n3</sub> or log<sub>10</sub>β°<sub>n.1.3</sub></th></tr><tr><th>U</th><th>Np</th><th>Pu</th></tr></thead><tbody><tr><td rowspan="3">Mg<sup>2+</sup> + AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4-</sup> ⇌ MgAnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td>4.56 ± 0.09<sup>a</sup></td><td>4.5 ± 1.1</td><td>4.5 ± 1.6</td></tr><tr><td>4.36 ± 0.20<sup>b</sup></td><td>4.3 ± 1.1</td><td>4.3 ± 1.6</td></tr><tr><td>4.41 ± 0.11<sup>c</sup></td><td>4.3 ± 1.1</td><td>4.4 ± 1.6</td></tr><tr><td rowspan="4">Mg<sup>2+</sup> + AnO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ MgAnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td></td><td>4.5 ± 0.6</td><td>4.29 ± 0.18<sup>d</sup></td></tr><tr><td>26.40 ± 0.09<sup>a</sup></td><td>24.4 ± 1.1*</td><td>22.5 ± 1.6</td></tr><tr><td>26.20 ± 0.20<sup>b</sup></td><td>24.2 ± 1.1*</td><td>22.3 ± 1.6</td></tr><tr><td>26.25 ± 0.12<sup>c,*</sup></td><td>24.2 ± 1.1*</td><td>22.4 ± 1.6</td></tr><tr><td></td><td></td><td>24.4 ± 0.8*</td><td>22.29 ± 1.61<sup>d,*</sup></td></tr><tr><td>Mg<sup>2+</sup> + MgAnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup> ⇌ Mg<sub>2</sub>AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>0.9 ± 0.6<sup>b</sup></td><td>0.9 ± 1.1</td><td>0.9 ± 1.6</td></tr><tr><td rowspan="2">2Mg<sup>2+</sup> + AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4-</sup> ⇌ Mg<sub>2</sub>AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>n.d.<sup>a</sup></td><td></td><td></td></tr><tr><td>5.26 ± 0.60<sup>b</sup></td><td>5.2 ± 1.1</td><td>5.1 ± 1.6</td></tr><tr><td rowspan="2">2Mg<sup>2+</sup> + AnO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ Mg<sub>2</sub>AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>n.d.<sup>a</sup></td><td></td><td></td></tr><tr><td>27.10 ± 0.60<sup>b</sup></td><td>25.1 ± 1.1*</td><td>23.1 ± 1.6</td></tr><tr><td rowspan="4">Ca<sup>2+</sup> + AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4-</sup> ⇌ CaAnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td>5.36 ± 0.01<sup>e</sup></td><td>5.3 ± 1.1</td><td>5.3 ± 1.6</td></tr><tr><td>5.16 ± 0.20<sup>b</sup></td><td>5.1 ± 1.1</td><td>5.1 ± 1.6</td></tr><tr><td>5.25 ± 0.08<sup>c</sup></td><td>5.2 ± 1.1</td><td>5.2 ± 1.6</td></tr><tr><td></td><td>6.3 ± 0.6</td><td>6.05 ± 0.50<sup>d</sup></td></tr><tr><td rowspan="3">Ca<sup>2+</sup> + AnO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ CaAnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td>27.20 ± 0.01<sup>e,*</sup></td><td>25.2 ± 1.1*</td><td>23.3 ± 1.6*</td></tr><tr><td>27.00 ± 0.20<sup>b,*</sup></td><td>25.0 ± 1.1*</td><td>23.1 ± 1.6*</td></tr><tr><td>27.09 ± 0.09<sup>c,*</sup></td><td>26.2 ± 0.8</td><td>23.2 ± 1.6*</td><td>24.05 ± 0.50<sup>d</sup></td></tr><tr><td rowspan="3">Ca<sup>2+</sup> + CaAnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup> ⇌ Ca<sub>2</sub>AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>3.29 ± 0.03<sup>e</sup></td><td>3.2 ± 1.1</td><td>3.2 ± 1.6</td></tr><tr><td>3.80 ± 0.35<sup>b</sup></td><td>3.7 ± 1.1</td><td>3.7 ± 1.6</td></tr><tr><td>3.33 ± 0.12<sup>c</sup></td><td>3.3 ± 1.1</td><td>3.3 ± 1.6</td></tr><tr><td rowspan="3">2Ca<sup>2+</sup> + AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4-</sup> ⇌ Ca<sub>2</sub>AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>n.d.<sup>d</sup></td><td></td><td></td></tr><tr><td>8.65 ± 0.03<sup>e</sup></td><td>8.5 ± 1.1</td><td>8.6 ± 1.6</td></tr><tr><td>8.96 ± 0.40<sup>b</sup></td><td>8.9 ± 1.1</td><td>8.9 ± 1.6</td></tr><tr><td></td><td>8.58 ± 0.14<sup>c</sup></td><td>8.5 ± 1.1</td><td>8.5 ± 1.6</td></tr><tr><td rowspan="3">2Ca<sup>2+</sup> + AnO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ Ca<sub>2</sub>AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>n.d.<sup>d</sup></td><td></td><td></td></tr><tr><td>30.49 ± 0.03<sup>e,*</sup></td><td>28.4 ± 1.1*</td><td>26.6 ± 1.6*</td></tr><tr><td>30.80 ± 0.40<sup>b,*</sup></td><td>28.8 ± 1.1*</td><td>26.9 ± 1.6*</td></tr><tr><td></td><td>30.42 ± 0.15<sup>c</sup></td><td>28.4 ± 1.1*</td><td>26.5 ± 1.6*</td></tr><tr><td rowspan="2">Sr<sup>2+</sup> + AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4-</sup> ⇌ SrAnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td>4.06 ± 0.20<sup>b</sup></td><td>4.0 ± 1.1</td><td>4.0 ± 1.6</td></tr><tr><td>5.02 ± 0.01<sup>f</sup></td><td></td><td></td></tr><tr><td rowspan="2">Sr<sup>2+</sup> + AnO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ SrAnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td>25.90 ± 0.20<sup>b,*</sup></td><td>23.9 ± 1.1*</td><td>22.0 ± 1.6*</td></tr><tr><td>26.86 ± 0.04<sup>f</sup></td><td></td><td></td></tr><tr><td>2Sr<sup>2+</sup> + AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4-</sup> ⇌ Sr<sub>2</sub>AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>7.86 ± 0.50<sup>b</sup></td><td>7.8 ± 1.1</td><td>7.8 ± 1.6</td></tr><tr><td>2Sr<sup>2+</sup> + AnO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ Sr<sub>2</sub>AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</td><td>29.70 ± 0.50<sup>*</sup></td><td>27.7 ± 1.1*</td><td>25.8 ± 1.6*</td></tr><tr><td rowspan="2">Ba<sup>2+</sup> + AnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>4-</sup> ⇌ BaAnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td>3.76 ± 0.30<sup>b</sup></td><td>3.7 ± 1.1</td><td>3.7 ± 1.6</td></tr><tr><td>4.84 ± 0.02<sup>f</sup></td><td></td><td></td></tr><tr><td rowspan="2">Ba<sup>2+</sup> + AnO<sub>2</sub><sup>2+</sup> + 3CO<sub>3</sub><sup>2-</sup> ⇌ BaAnO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>2-</sup></td><td>25.60 ± 0.30<sup>b,*</sup></td><td>23.6 ± 1.1*</td><td>21.7 ± 1.6*</td></tr><tr><td>26.68 ± 0.04<sup>f,*</sup></td><td></td><td></td></tr></tbody></table>

a Shang and Reiller (2021a); b Grenthe *et al.* (2020); c This study; d Jo *et al.* (2020); e Shang and Reiller (2020); f Dong and Brooks (2006); *log₁₀β° = log₁₀K° + log₁₀β°AnO₂(CO₃)₃⁺; n.d. not detected.
An estimation of the differences between the different values can be seen in Figure S1 of the SI. The speciation of a 1 nmol kg<sub>w</sub><sup>-1</sup> uranium solution at pH 8 containing 0.38 mol kg<sub>w</sub><sup>-1</sup> NaCl, 0.01 mol kg<sub>w</sub><sup>-1</sup> CaCl<sub>2</sub>, and 0.05 mol kg<sub>w</sub><sup>-1</sup> MgCl<sub>2</sub>, and 2 mmol kg<sub>w</sub><sup>-1</sup> NaHCO<sub>3</sub> — *I*<sub>m</sub> = 0.54 mol kg<sub>w</sub><sup>-1</sup> — gives a marked difference between results from Thermochimie 11a on the one hand, and Shang and Reiller (2020, 2021a) or estimation in Table 2 and Table 4 on the other hand. This difference can be mainly attributed to the highest value of log<sub>10</sub>β°<sub>Ca<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub></sub> in Grenthe *et al.* (2020). The influence of the ε values will be evidenced in the following.

From the very small differences between the values from Shang and Reiller (2020, 2021a)
or estimation in Table 2 and Table 4, and for the sake of coherency in the data, the former values
will be used in the following.

2.2.3. $log_{10}K^\circ$ over ionic radius relationship

An interesting and complementary way to represent the variation of log₁₀K° values for
common charged central ion is vs. the charge over the distance between the metal and the ligand
(z/r) (Grenthe et al., 1997; Kossiakoff and Harker, 1938). For the same metal type and charge,
and ligand, it can be plotted vs. the inverse of effective ionic radii IR<sub>CN</sub> (Shannon, 1976)
(Figure 5 and Table S2of the SI), where the coordination numbers (CN) are taken from Kerisit
and Liu (2010) for Mg²⁺ (IR<sub>VI</sub> = 0.72 Å), Ca²⁺ (IR<sub>VII</sub> = 1.06 Å), and Sr²⁺ (IR<sub>VIII</sub> = 1.26 Å), and
IR<sub>IX</sub> = 1.47 Å from Ba²⁺ coordination in halides (Brackett et al., 1963). It appears that the
log₁₀K°<sub>Ae₂UO₂(CO₃)₃</sub>²⁻ values for Ca²⁺, Sr²⁺, and Ba²⁺ from Dong and Brooks (2006) and Shang and
Reiller (2020) are following a linear relationship, and that octaedral Mg²⁺ is out of this trend
for symmetry reasons hypothesized in details in Shang and Reiller (2021a). The
log₁₀K°<sub>Ae₂UO₂(CO₃)₃</sub> values for Ca²⁺ and Ba²⁺ from Dong and Brooks (2006) and Shang and Reiller
(2021a) seem to follow a linear relationship as well, with the log₁₀K°<sub>Mg₂UO₂(CO₃)₃</sub> value form Lee
et al. (2017) out of the trend, for the same reasons — see discussions in Shang and Reiller
(2021a). The selected data from Grenthe et al. (2020), also plotted in Figure 5, seem to follow
the same trend but with Ca, Sr, and Ba having a different slope. It is noteworthy that the values
of Sr and Ba used to obtain the selection, in addition to the values from Dong and Brooks
(2006), are linked to values obtained in NaClO₄ where the KCl electrode filling of the pH-
electrode seemed not to have been replaced — see Shang *et al.* (2020) and Shang and Reiller
(2021a).

A linear regression 1/IR<sub>CN</sub> vs. log<sub>10</sub>K<sup>O</sup><sub>1.1.3</sub> (Neuilly, 1998) — and not log<sub>10</sub>K<sup>O</sup><sub>1.1.3</sub> vs. 1/IR<sub>CN</sub> as classically plotted in Figure 5 — allows estimating a potential log<sub>10</sub>K<sup>O</sup><sub>RaUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>-2</sup> (Table S3 of the SI). The CN value of Ra is not straightforwardly estimated. Knowing the propensity of Ra<sup>2+</sup> to form homogeneous solid solution with Ba<sup>2+</sup> in sulphate medium (Curti *et al.*, 2010; Lestini *et al.*, 2019), the values for Ra<sub>IX</sub> could be seen as more likely. A calculation using IR<sub>IX</sub> = 1.70 Å for Ra<sup>2+</sup> turn into log<sub>10</sub>K<sup>O</sup><sub>RaUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>-2</sup> = 4.6 ± 0.9 or log<sub>10</sub>β<sup>O</sup><sub>RaUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub><sup>-2</sup> = 26.5 ± 1.0 (Table S2 of the SI).

A conservative similar estimation for a potential Ra<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq) complex from the only
log<sub>10</sub>K<sup>O</sup><sub>Ca<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</sub> and log<sub>10</sub>K<sup>O</sup><sub>Ba<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</sub> values from Table S3 of the SI
— Mg<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq) is not taken into account (*vide supra*) — gives log<sub>10</sub>K<sup>O</sup><sub>Ra<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</sub> =
3.0, or log<sub>10</sub>β<sup>O</sup><sub>Ra<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq)</sub> = 29.5 (Table S2 of the SI) — no standard deviation can be
calculated.

From the usual radium concentration in natural waters, or even in water related to mining activities, the formation of the Ra<sub>n</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(4-2n)- complexes is not likely to impact the speciation of both uranium(VI) and radium(II).
<figure><img src="image_6.png" /></figure>

**Figure 5.** $\log_{10}K^{\circ}_{Ae_nUO_2(CO_3)_3(4-2n-)}$ vs. $1/IR_{CN}$ (Brackett *et al.*, 1963; Kerisit and Liu, 2010) — n = 1 (circles), and n = 2 (squares, diamond, and triangles) — from Dong and Brooks (2006) (filled circles and squares), Grenthe *et al.* (2020) (filled triangles), Shang and Reiller (Shang and Reiller, 2020, 2021a) (empty circles and squares), and Jo *et al.* (2019a) (filled diamond): plain blue line is the linear relationship $1/IR_{CN} = f(\log_{10}K^{\circ}_{n.1.3})$ for Ca, Sr, and Ba from Dong and Brooks (2006); green dotted line is the linear relationship between Ca and Ba from Dong and Brooks (2006); the blue dotted and dash-dot lines are the estimation of a potential $\log_{10}K^{\circ}_{RaUO_2(CO_3)_3^{2-}}$ complex considering $IR_{VIII}$ or $IR_{IX}$, respectively; the green long dash-dot and dash-dot-dot lines are the estimation of a potential $\log_{10}K^{\circ}_{Ra_2UO_2(CO_3)_3}$ complex considering $IR_{VIII}$ or $IR_{IX}$, respectively.
## 2.3. Speciation

All speciation calculations in the following were done using PhreeqC 3.5.7-15968 (Parkhurst and Appelo, 1999, 2013) or Phreeplot (Kinniburgh and Cooper, 2011). Database files used were the Thermochimie 11a (Giffaut et al., 2014; Grivé et al., 2015) (https://www.thermochimie-tdb.com/), and the Prodata 1.5.3.1 extractions (Reiller, 2022; Reiller and Descostes, 2020) — it can be noted that Thermochimie 12a issued October 4, 2023, is not changing anything for Ca-U(VI)-CO₃ species. Both are centred on NEA-OECD selected data for uranium, but the latter does not include transuranium elements. In both database extraction files, actinide data are mostly based on the NEA-OECD selected data (Grenthe et al., 1992; Grenthe et al., 2020; Guillaumont et al., 2003; Lemire et al., 2001; Silva et al., 1995). Some complementary data are to be noted straightforwardly, as the inclusion of An(OH)₂(CO₃)₂²⁻ (Rai et al., 1999a; Rai et al., 1999b) in Thermochimie 11a to represent the increase of AnO₂ solubility vs. carbonate concentration — Yamaguchi et al. (1994) also proposed Pu(OH)₄(CO₃)₂⁴⁺. The solubility of AnO₂ amorphous hydrated phases, noted AnO₂(am,hyd) in Grenthe et al. (2020), are written in Thermochimie 11a,

$$AnO_2:2H_2O + 4H^+ \rightleftharpoons An^{4+} + 4H_2O$$

which does not change $log_{10}K_s°$ values, but maybe submitted to a stronger influence of water activity with increasing ionic strength.

The same remark applies to PuO₂(OH)₂:H₂O(am), noted PuO₂(OH)₂(am,hyd) in Grenthe et al. (2020).

Other complexes are included in Thermochimie 11a such as Np(OH)₂⁺ (Allard et al., 1980) and Pu(OH)₂⁺ in analogy to Am(III). These species will be of very little importance here.
In Thermochimie 11a, the ε(AeUO₂(CO₃)₃²⁻,Na⁺) values were from the like-charged hypothesis (Lee and Yun, 2013). In Prodata 1.5.3.1, log₁₀β°, ΔrH°m, and ε(AeₙUO₂(CO₃)₃(⁴-2n)⁻,Na⁺Cl⁻) from Shang and Reiller (2020, 2021a, b) were included.

# 3. Results and Discussions

## 3.1. Uranium

Thermodynamic functions in Grenthe et al. (2020) allows calculating the oxidation potential diagram in Figure 6 — it can be noted that U(OH)³⁺ is ca. 2% at pH = 0 in HClO₄.

<figure><img src="image_7.png" /><figcaption>**Figure 6.** The formal oxidation potential (V) diagram of uranium in acidic aqueous solutions (Grenthe et al., 2020).</figcaption></figure>

### 3.1.1. *Impact of the origin of the data of Ae<sub>n</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(<sup>4-2n</sup>-)

#### 3.1.1.1 Case of Mg<sup>2+</sup> and Ca<sup>2+</sup>

Pourbaix (Eh vs. pH) predominance diagrams in Figure 7 are obtained using either: (i) data from Grenthe *et al.* (2020) (Figure 7a); (ii) log₁₀β°AeₙUO₂(CO₃)₃(⁴-2n)⁻ from Grenthe *et al.* (2020) (Figure 7b,c plain line) and ε(AeUO₂(CO₃)₃²⁻,Na⁺) from like-charged analogy (Lee and Yun, 2013) in Thermochimie 11a; and (iii) using log₁₀β°AeₙUO₂(CO₃)₃(⁴-2n)⁻ and ε(AeₙUO₂(CO₃)₃(⁴-2n)⁻,Na⁺Cl⁻) from Shang and Reiller (2020, 2021a) (Figure 7b,c, dashed line).
One can also note that no precipitation was required during calculation. Oversaturation of calcite (CaCO₃), magnesite (MgCO₃) or dolomite (MgCa(CO₃)₂) would reduce the predominance domains of the AeₙUO₂(CO₃)₃(⁴-2n)⁻ complexes. The differences between the log₁₀β°AeₙUO₂(CO₃)₃²⁻ are evidenced in Figure 7b,c. The lower log₁₀β°Ca₂UO₂(CO₃)₃ value for Shang and Reiller (2020) induces a slightly larger prevalence domain of UO₂(CO₃)(aq) complex and
slightly greater prevalence domain of Ca₂UO₂(CO₃)₃(aq). The higher values of log₁₀β° and ε for Mg explains the larger predominance domain using the data from Shang and Reiller (2021a). The main difference comes from the values log₁₀β° and ε from Shang and Reiller (2020) that induce the predominance of CaUO₂(CO₃)₃²⁻ at pH > 8.87, due to the increase of Na⁺ concentration, and thus ionic strength, during calculation in Phreeplot.
<figure><img src="image_8.png" /><figcaption>Figure 7. Pourbaix diagrams (Kinniburgh and Cooper, 2011) of [U] = 0.1 nmol kg⁻¹, I_m = 0.1 mol kg⁻¹ NaCl, and P(CO₂) = 10⁻³.₅ atm (Grenthe et al., 2020); considering no AenUO₂(CO₃)₃⁽⁴-2n)⁻ complexes (a), only the CanUO₂(CO₃)₃⁽⁴-2n)⁻ (b) or only MgUO₂(CO₃)₃²⁻ (c) complexes from NEA-OECD (plain line) or from Shang and Reiller (2020, 2021a) (b, c, dashed line); [Ae] = 5 mmol kg⁻¹ — Ae is Ca (b) or Mg (c) —; no precipitation required.</figcaption></figure>

### 3.1.1.2 Case of Sr²⁺, Ba²⁺, and Ra²⁺

The eventual impact of the other AenUO₂(CO₃)₃⁽⁴-2n)⁻ complexes, i.e., Sr²⁺, Ba²⁺, and Ra²⁺, can be done using the solution ES-85 from Bellezane, France, which PHREEQC script is
available in the Supplementary Information. It presented the highest carbonate concentration — or highest activity product a(HCO₃⁻) a(H⁺) = 10⁻⁸.⁴¹ mol² kg⁻² — of the tested radium containing waters in Reiller and Descostes (2020). The speciation are reported in Table S4 of the SI, using only the Prodata 1.5.3.1 file — containing SrUO₂(CO₃)₃²⁻, BaUO₂(CO₃)₃²⁻, and Ba₂UO₂(CO₃)₃ from Dong and Brooks (2006) —, and implementing the log₁₀β°RaₐUO₂(CO₃)₃⁽⁴⁻²n⁻⁾ in the PhreeqC input file.

It can be seen that only a mere fraction of total Ba, Ca, Mg, Sr, and Ra is engaged in a complexation with AeₐUO₂(CO₃)₃⁽⁴⁻²n⁻⁾. As already reported, uranium is controlled by CaₐUO₂(CO₃)₃⁽⁴⁻²n⁻⁾, but the calculated amount of MgUO₂(CO₃)₃²⁻ is higher than in Reiller and Descostes (2020) (Figure S3 of the SI), due to the implementation of the log₁₀β° and ε from Shang et al. (Shang and Reiller, 2020, 2021a, b; Shang et al., 2020).

Due to the differences in log₁₀β° between Ca²⁺ and the other Ae²⁺ cations, higher total concentrations of Ae — or rather higher Ae²⁺ activities — are needed as underlined in Shang et al. (2023)

Even if potentially existing, the constant between the Ca and other Ae species can be calculated as follows.

$$CaUO_2(CO_3)_3^{2-} + Ae^{2+} \rightleftharpoons AeUO_2(CO_3)_3^{2-} + Ca^{2+}$$

$$K^{\circ} = \frac{K^{\circ}_{AeUO_2(CO_3)_3^{2-}}}{K^{\circ}_{CaUO_2(CO_3)_3^{2-}}} = \frac{a(AeUO_2(CO_3)_3^{2-}) a(Ca^{2+})}{a(CaUO_2(CO_3)_3^{2-}) a(Ae^{2+})} = \frac{10^{\log_{10} K^{\circ}_{1.n.3}}}{10^{5.36}} \quad (9)$$

As all log₁₀K°AeₐUO₂(CO₃)₃²⁻ or log₁₀β°AeₐUO₂(CO₃)₃²⁻ other than Ca²⁺ are either lower, or awaited to be lower, than CaUO₂(CO₃)₃²⁻, it comes out that a higher Ae concentration than Ca — or rather a higher Ae²⁺ activity than Ca²⁺ — is needed in natural waters, which can occur for Mg²⁺ (vide post) but is not likely for Sr²⁺, Ba²⁺, and Ra²⁺.
### 3.1.2. Ionic strength evolution

#### 3.1.2.1 NaCl concentration

In recent studies (Shang and Reiller, 2020, 2021a; Shang et al., 2020) it was shown that the like-charged comportment in ionic strength for the $A_e n UO_2(CO_3)_3^{(4-2n)-}$ complexes did not fully apply. The differences in speciation are shown for Thermochimie 11a (Figure 8a), and implemented in the input file with $log_{10} \beta^o C_a n UO_2(CO_3)_3^{(4-2n)-}$ and $\varepsilon(C_a n UO_2(CO_3)_3^{(4-2n)-}, Na^+Cl^-)$ from Shang and Reiller (2020) (Figure 8b). In the validity domain of the Davies (1962) equation, the speciation is different because the $log_{10} \beta^o$ value are favouring $Ca_2UO_2(CO_3)_3(aq)$ for NEA-OECD (see Table 1). In both cases, the Davies (1962) equation deviates from the SIT speciation above 0.1 $mol kg_w^{-1}$, and speciation is substantially different: $CaUO_2(CO_3)_3^{2-}$ and $UO_2(CO_3)_3^{4-}$ are equally important with $Ca_2UO_2(CO_3)_3(aq)$ as secondary species using NEA-OECD data in Thermochimie 11a $ca$. 0.3 $mol kg_w^{-1}$, when $CaUO_2(CO_3)_3^{2-}$ is dominant with Shang and Reiller (2020); $UO_2(CO_3)_3^{4-}$ is dominating the SIT calculation in both cases at $I_m > 0.3$ $mol kg_w^{-1}$.

It can thus be seen that, in general and for these complexes in particular, using an ionic strength correction beyond its validity domain is leading to important differences in calculated speciation. It also shows the importance of $\varepsilon$ values in these cases. This was already cited as a limiting factor of speciation calculation by Nordstrom et al. (1979).
<figure><img src="image_9.png" /><figcaption>Figure 8. Influence of NaCl concentration on 1 nmol kg<sup>-1</sup> uranium speciation at pH = 8.1, [Ca]<sub>tot</sub> = 1 mmol kg<sup>-1</sup>, and P(CO<sub>2</sub>) = 10<sup>-3.5</sup> atm using thermochemical data in Table 1, and the log<sub>10</sub>β°<sub>Ca<sub>n</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(<sup>4-2n</sup>) values in Table 4 from NEA-OECD (used in Thermochimie 11a) (a) and Shang and Reiller (2020) (b): ionic strength corrections are Davies (1962) equation in the validity domain (plain line) and up to sea water domain (dotted line), and using the SIT ε(<i>Ca<sub>n</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(<sup>4-2n</sup>),Na<sup>+</sup>Cl<sup>-</sup>) parameters (Table 2) from Lee and Yun (2013) in Thermochimie 11a (a) and Shang and Reiller (2020) (b) (dashed line).</figcaption></figure>

3.1.2.2 Case of sea water

A particular application of the ionic strength influence is the seawater. One must keep in
mind the opening remarks in the discussion paragraph of Nordstrom *et al*. (1979). Even if the
specific interaction theory has brought many advances, many comments are still true today.

The predominance of Ca₂UO₂(CO₃)₃(aq) was proposed based on either like-charged
hypothesis for ε(CaUO₂(CO₃)₃²⁻,Na⁺) = ε(UO₂(CO₃)₂²⁻,Na⁺) and ε(Ca₂UO₂(CO₃)₃(aq),Na⁺Cl⁻) = 0, or application of an ionic strength out of its domain — see Shang and Reiller (2020) Shang and Reiller (2021a) and references therein. Reiller and Descostes (2020) evidenced the need of further determination based on pre-existing values, to which the works from Shang *et al*. (Shang and Reiller, 2020, 2021a; Shang *et al.*, 2020) answered. To further exemplify this, the calculated
speciation of $A_{n}UO_{2}(CO_{3})_{3}^{(4-2n)-}$ in solution adapted from seawater composition from Millero et al. (2008), also analysed in Reiller and Descostes (2020), is presented in Figure 9 — one must note that boron chemistry is not included in Prodata 1.5.3.1. The $[Na]_{total}$ is varied from 0 to 1 mol $kg_{w}^{-1}$ starting from pH = 8.1, $[Ca]_{total} = 10.6$ mmol $kg_{w}^{-1}$, $[Mg]_{total} = 54.7$ mmol $kg_{w}^{-1}$, $[CO_{3}]_{total} = 2$ mmol $kg_{w}^{-1}$, and $[Cl]_{total}$ concentration adjusted to charge balance, i.e., from 0.13 to 1.13 mol $kg_{w}^{-1}$. The $[U]_{total}$ is fixed at 1 nmol $kg_{w}^{-1}$. Ionic strength is then varied between $I_{m} = 0.19$ to 1.18 mol $kg_{w}^{-1}$. The differences between the speciation from thermodynamic data and SIT parameters in Thermochimie 11a and Shang and Reiller (2020, 2021a) for $A_{n}UO_{2}(CO_{3})_{3}^{(4-2n)-}$ are coming from: (i) the $log_{10}\beta^{o}$ values favouring $Ca_{2}UO_{2}(CO_{3})_{3}(aq)$ using NEA-OECD (Thermochimie 11a) (Figure 9a); and (ii) from the $\epsilon$ values gradually favouring $A_{n}UO_{2}(CO_{3})_{3}^{2-}$ using Shang and Reiller (2020, 2021a). The influence of the inclusion of $Na(HCO_{3})_{3}(aq)$ and $Na(CO_{3})^{-}$ in Thermochimie 11a — even using the SIT extraction of the database in which they should not be present — on the proportion of $MgUO_{2}(CO_{3})_{3}^{2-}$ vs. $Ca_{n}UO_{2}(CO_{3})_{3}^{2-}$ is shown by comparison with the same calculation using the Prodata 1.5.3.1 database (Reiller, 2022; Reiller and Descostes, 2020).

Shang et al. (2023) identified that the proportion $x$ of the sum of activities of $Mg^{2+}$ and $Ca^{2+}$ is directly impacting the predominance of $Ca_{n}UO_{2}(CO_{3})_{3}^{(4-2n)-}$ and $MgUO_{2}(CO_{3})_{3}^{2-}$ — and potentially $Mg_{2}UO_{2}(CO_{3})_{3}(aq)$.

$$x = \frac{a(Mg^{2+})}{a(Mg^{2+}) + a(Ca^{2+})} \qquad (10)$$

It can be seen on the second x-axis in Figure 9 that the activity product $a(Mg^{2+})^{n} a(Ca^{2+})^{1-n} a(HCO_{3})^{2}$ is lower using Thermochimie 11a database for the same $[Na]_{total}$ in the solution — mostly due to the gradual increase of $Na(HCO_{3})_{3}(aq)$ concentrations —, which gradually favours $CaUO_{2}(CO_{3})_{3}^{2-}$ vs. $MgUO_{2}(CO_{3})_{3}^{2-}$ using Prodata 1.5.3.1 (Reiller, 2022; Shang and Reiller, 2020).
Here again, it can be seen that the speciation of uranium is changed from a dominating
neutral species (Figure 9a) to the shared predominance with AeUO₂(CO₃)₃²⁻ (Figure 9b,c)
depending on the ε(AeUO₂(CO₃)₃²⁻,Na⁺) values.
<figure><img src="image_10.png" /><figcaption>Figure 9. Influence of Na⁺ concentration on 1 nmol kg_w⁻¹ uranium speciation at pH = 8.1 t = 25 °C, [Mg]tot = 54.7 mmol kg_w⁻¹, [Ca]tot = 10.6 mmol kg_w⁻¹, [CO₃]total = 2 mmol kg_w⁻¹ — adapted from Millero *et al.* (2008) —, and [Cl⁻] from charge balance; thermochemical data are from Table 1 (in Thermochimie 11a) (a) implemented by the log₁₀β°AenUO₂(CO₃)₃(4-2n)- values from Shang and Reiller (Shang and Reiller, 2020, 2021a) (b), and Prodata 1.5.3.1 (Reiller, 2022) (c): ionic strength corrections using the SIT with ε(AenUO₂(CO₃)₃(4-2n)-, Na⁺Cl⁻) parameters from Thermochimie 11a (a), implemented with Shang and Reiller (2020, 2021a) (b), and Prodata 1.5.3.1 (Reiller, 2022) (c).</figcaption></figure>
3.1.2.3 Case of an estuary

A further interesting application of these data is the representation of the uranium speciation
in an estuary where salinity S and concentration of carbonate, magnesium and calcium are
gradually changing. Very recently, Smolíková et al. (2022) reported the evolution of the
uranium speciation in the Scheldt Estuary (border between Belgium and The Netherlands).
Uranium concentration was followed between Antwerp and the North Sea-ward. The authors
calculated the speciation using Visual Minteq (https://vminteq.lwr.kth.se/) including the
Ca<sub>n</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(4-2n)- data from Dong and Brooks (2006) — i.e. with no SIT parameters, and
MgUO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>2- apparently not included —, and the very minor natural organic matter
influence. The speciation was suggesting that Ca<sub>2</sub>UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>(aq) was dominating whatever the
salinity S — increasing from Antwerp to the sea-ward — and that UO<sub>2</sub>(CO<sub>3</sub>)<sub>3</sub>4- percentage was
increasing with S (Figure 10a) — Fig. 6 and Table S3 in Smolíková et al. (2022). Calculation
of speciation can be done using the physico-chemical data in Table S3 in Smolíková et al.
(2022) — ignoring the influence of natural organic matter — with the data from Grenthe et al.
(2020) in Thermochimie 11a (Figure 10b), implemented with Shang and Reiller (2020, 2021a,
b) (Figure 10c), and Prodata 1.5.3.1 (Figure 10d). Values of dissolved O<sub>2</sub> (Table S3 in
Smolíková et al., 2022) assures the predominance of uranium(VI).

As the ratio of concentration of [Mg]/[Ca] — or proportion of activity ratio x, see equation
(10) — increases from Antwerp (S ca. 1 mg L⁻¹) to the sea-ward (S ca. 24 mg L⁻¹), it can be
seen in Figure 10b,c,d that the MgUO₂(CO₃)₃²⁻ complex must be implemented in the database
— it was not implemented in the calculation in Smolíková et al. (2022) (Figure 10a) — as it
increases with S (and concentration of Mg outlined by the value of x) for the three other cases
(Figure 10b,c,d). Furthermore, the values of ε(AeₙUO₂(CO₃)₃(4⁻2n)⁻,Na⁺) are strongly impacting
the speciation results (*vide ante*), particularly when closing the sea-ward, at the highest S value.
This is closely reminiscent of the analysis of a Canadian aquitard (Reiller and Descostes, 2020; Reiller *et al.*, 2012).

<figure><img src="image_11.png" /><figcaption>Figure 10. Evolution of uranium speciation vs. salinity in the Scheldt estuary digitized from Fig. 6 and Table S3 in Smolíková *et al.* (2022) (a), calculated using NEA-OECD data (Grenthe *et al.*, 2020, in Thermochimie 11a) (b), implemented with data from Shang and Reiller (2020, 2021a, b) (c), and using Prodata 1.5.3.1 database (d).</figcaption></figure>

### 3.1.3. *Particular case of temperature in radioactive waste management sites*

In the deep underground envisaged laboratories for the management of radioactive waste, the speciation of uranium in solution is under many conditions around the limit between $U(OH)_4(aq)$ and $Ca_nUO_2(CO_3)_3^{(4-2n-)}$ (Grivé *et al.*, 2015; Reiller and Descostes, 2020). The differences in pH, $E_h$ (or pe), and activities of $Ca^{2+}$, $Mg^{2+}$, $HCO_3^-$, and $Na^+$ are driving the
proportions of species (Reiller and Descostes, 2020). The activity products can also be usefully employed: pH + pe, $log_{10}(a(Ae^{2+}) a(H^{+})^{-2})$, $log_{10}(a(HCO_3^-) a(H^{+}))$, $log_{10}(a(Na^{+}) a(H^{+})^{-1})$, and $log_{10}(a(Ae^{2+}) a(HCO_3^-)^2)$ (Lee *et al.*, 2019; Shang *et al.*, 2023).

In Shang and Reiller (2021b), speciation calculations of uranium have been proposed in waters representative of radioactive waste management laboratory sites in Belgium (De Craen *et al.*, 2004) and France (Gaucher *et al.*, 2009) at temperature between 10 and 80 °C. These calculations were done in absence of mineral buffer, and using amorphous $UO_2$ with no $\Delta_r H^\circ_m$ values selected in the Thermochimie 9b database file used then — taken from Guillaumont *et al.* (2003) —, which induced the reduction of U(VI) to U(IV), but also of S(VI) to S(-II), and C(IV) to C(-IV). Even if it was specified that the absence of mineralogical buffer could lead to a biased view of the actual situation, a more complete calculation could be proposed to further clarify the situation of the $Ae_nUO_2(CO_3)_3^{(4-2n)-}$ complexes under these conditions.

The $E_h$ value of the *in situ* pore-water proposed by Gaucher *et al.* (2009) — i.e. $E_h = -199$ mV at pH = 7.2 and t = 25 °C — or by De Craen *et al.* (2004) — i.e. $E_h = -274$ mV at pH = 8.5 and t = 16 °C — can be represented by an equimolar mixture of $FeS_2/FeCO_3$ (pyrite/siderite) — siderite has been found slightly oversaturated in the Mol aquifer (Beaucaire *et al.*, 2000). The thermodynamic functions in Table 5 (Grenthe *et al.*, 2020; Lemire *et al.*, 2013; Lemire *et al.*, 2020) can be used to calculate the $log_{10}K^\circ$ values (Table 6).
<table><caption>**Table 5.** Thermodynamic function of formation for species implied in the pyrite/siderite (FeS<sub>2</sub>/FeCO<sub>3</sub>) redox buffer.</caption><thead><tr><th>Species</th><th>ΔfG°<sub>m</sub><br>(kJ mol<sup>-1</sup>)</th><th>ΔfH°<sub>m</sub><br>(kJ mol<sup>-1</sup>)</th><th>Reference</th></tr></thead><tbody><tr><td>O<sub>2</sub>(g)</td><td>0</td><td>0</td><td>Grenthe et al. (2020)</td></tr><tr><td>H<sub>2</sub>(g)</td><td>0</td><td>0</td><td>Grenthe et al. (2020)</td></tr><tr><td>H<sup>+</sup></td><td>0</td><td>0</td><td>Grenthe et al. (2020)</td></tr><tr><td>H<sub>2</sub>O</td><td>-237.140 ± 0.041</td><td>-285.830 ± 0.040</td><td>Grenthe et al. (2020)</td></tr><tr><td>SO<sub>4</sub><sup>2-</sup></td><td>-744.004 ± 0.418</td><td>-909.340 ± 0.400</td><td>Grenthe et al. (2020)</td></tr><tr><td>CO<sub>2</sub>(g)</td><td>-394.373 ± 0.133</td><td>-393.510 ± 0.130</td><td>Grenthe et al. (2020)</td></tr><tr><td>CO<sub>3</sub><sup>2-</sup></td><td>-527.900 ± 0.390</td><td>-675.230 ± 0.250</td><td>Grenthe et al. (2020)</td></tr><tr><td>FeS<sub>2</sub>-pyrite(cr)</td><td>-162.219 ± 2.361</td><td>-173.630 ± 2.360</td><td>Lemire et al. (2013)</td></tr><tr><td>FeCO<sub>3</sub>(cr)</td><td>-679.557 ± 0.917</td><td>-752.609 ± 0.895</td><td>Lemire et al. (2020)</td></tr></tbody></table>

<table><caption>**Table 6.** Gibbs energies and enthalpies of reaction, log<sub>10</sub>K° and redox potentials calculated from functions of formation in Table 5, unless noted otherwise.</caption><thead><tr><th>Reaction</th><th>ΔfG°<sub>m</sub><br>(kJ mol<sup>-1</sup>)</th><th>ΔfH°<sub>m</sub><br>(kJ mol<sup>-1</sup>)</th><th>log<sub>10</sub>K°</th><th>E°<br>(V)</th></tr></thead><tbody><tr><td>FeS<sub>2</sub>(cr) + 9H<sub>2</sub>O + CO<sub>2</sub>(g) ⇌ FeCO<sub>3</sub>(cr) + 18H<sup>+</sup> + 2SO<sub>4</sub><sup>2-</sup> + 14e<sup>-</sup></td><td>523.287 ± 2.047</td><td>568.321 ± 2.068</td><td>-91.66 ± 0.36</td><td>0.387</td></tr><tr><td>FeS<sub>2</sub>(cr) + 9H<sub>2</sub>O + CO<sub>2</sub>(g) ⇌ FeCO<sub>3</sub>(cr) + 4H<sup>+</sup> + 2SO<sub>4</sub><sup>2-</sup> + 7H<sub>2</sub>(g)</td><td>-1136.693 ± 2.015</td><td>-1432.489 ± 2.036</td><td>199.11 ± 0.35</td><td>—</td></tr><tr><td>FeS<sub>2</sub>(cr) + 3.5O<sub>2</sub>(g) + CO<sub>2</sub>(g) + 2H<sub>2</sub>O ⇌ FeCO<sub>3</sub>(cr) + 4H<sup>+</sup> + 2SO<sub>4</sub><sup>2-</sup></td><td>429.674 ± 2.072</td><td>564.211 ± 2.072</td><td>-75.26 ± 0.36</td><td>0.318</td></tr><tr><td>FeS<sub>2</sub>(cr) + 8H<sub>2</sub>O + CO<sub>3</sub><sup>2-</sup> ⇌ FeCO<sub>3</sub>(cr) + 16H<sup>+</sup> + 2SO<sub>4</sub><sup>2-</sup> + 14e<sup>-</sup></td><td>-1240.306 ± 2.047</td><td>-1436.599 ± 2.048</td><td>217.26 ± 0.36</td><td>—</td></tr><tr><td>FeS<sub>2</sub>(cr) + 8H<sub>2</sub>O + CO<sub>3</sub><sup>2-</sup> ⇌ FeCO<sub>3</sub>(cr) + 2H<sup>+</sup> + 2SO<sub>4</sub><sup>2-</sup> + 7H<sub>2</sub>(g)</td><td>-97.757</td><td>-35.96<sup>a</sup></td><td>-17.13<sup>a</sup></td><td>—</td></tr><tr><td>FeS<sub>2</sub>(cr) + 3.5O<sub>2</sub>(g) + CO<sub>3</sub><sup>2-</sup> + H<sub>2</sub>O ⇌ FeCO<sub>3</sub>(cr) + 2H<sup>+</sup> + 2SO<sub>4</sub><sup>2-</sup></td><td>-64.9</td><td>-12.859<sup>b</sup></td><td>11.37<sup>b</sup></td><td>—</td></tr><tr><td>MgCa(CO<sub>3</sub>)<sub>2</sub>(cr) ⇌ Mg<sup>2+</sup> + Ca<sup>2+</sup> + 2CO<sub>3</sub><sup>2-</sup></td><td>-17.01</td><td>8.804<sup>c</sup></td><td>2.98<sup>c</sup></td><td>—</td></tr><tr><td>Mg<sup>2+</sup> + H<sup>+</sup> + CO<sub>3</sub><sup>2-</sup> ⇌ MgHCO<sub>3</sub><sup>+</sup></td><td>-48.408</td><td>-10.62<sup>d</sup></td><td>-8.48<sup>d</sup></td><td>—</td></tr><tr><td>Mg<sup>2+</sup> + CO<sub>3</sub><sup>2-</sup> ⇌ MgCO<sub>3</sub>(aq)</td><td>-65.243</td><td>-23.595<sup>e</sup></td><td>11.43<sup>e</sup></td><td>—</td></tr><tr><td>CaCO<sub>3</sub>(cr) ⇌ Ca<sup>2+</sup> + CO<sub>3</sub><sup>2-</sup></td><td>-18.38</td><td>14.83<sup>e</sup></td><td>3.22<sup>e</sup></td><td>—</td></tr><tr><td>Ca<sup>2+</sup> + CO<sub>3</sub><sup>2-</sup> ⇌ CaCO<sub>3</sub>(aq)</td><td>-18.38</td><td>14.83<sup>e</sup></td><td>3.22<sup>e</sup></td><td>—</td></tr></tbody></table>

a Robie and Hemingway (1995), b Shock and Koretsky (1995), c Sverjensky et al. (1997), and d Plummer and Busenberg (1982) from Thermochimie 11a database file; e Thermochimie 11a database file.

A PhreeqC calculation at pH 7.2 and 25 °C using the data from Table 6 gives $pH = -2.905$ ($E_h = -171.9$ mV, $t = 25$ °C). Using the composition in Table 1 from Gaucher et al. (2009).

Concerning Ca and Mg buffering, the use of calcite and dolomite is widespread (Beaucaire et al., 2000). From a thermodynamic point of view (Table 6), calcium is slightly more supersaturated relative to dolomite than to calcite both for Mol — as already evidenced by Beaucaire et al. (2000) using slightly different log<sub>10</sub>K° values — and Callovo-Oxfordian formations. Hence, a calculation for Mol using De Craen et al. (2004) gives SI = 0.11 and 0.53
for calcite and dolomite, respectively; the calculation for Callovo-Oxfordian using Gaucher *et al.* (2009) gives SI = 0.14 and 0.33 for calcite and dolomite, respectively.

The speciation of uranium vs. temperature was done using two strategies: (i) $6 \le \text{pH} \le 9$ speciation was done at 25 and 50 °C at equilibrium with pyrite, siderite, and dolomite; and (ii) the varying temperature allowing pH to equilibrate with pyrite siderite, and dolomite — it can be noted that the increase in temperature from 25 to 50 °C decreases pH from 7.20 (pE = -3.36) to 7.06 (pE = -3.12) for Callovo-Oxfordian water, and from pH 8.5 (pE = -4.36) to pH 8.17 (pE = -5.05) for the Mol water composition. Uranium was equilibrated with mineral uraninite (crystalline UO₂) in order to avoid the bias of the absence of $\Delta_r H^\circ_m$ for amorphous UO₂ identified in Shang and Reiller (2021b). Figure 11 and Figure 12 are showing the solubility and speciation diagrams at varying pH — and $\log_{10}(a(Mg^{2+})^x a(Ca^{2+})^{1-x} a(HCO_3^-)^2)$ — at 25 °C (Figure 11a,c and Figure 12a,c), and 50 °C (Figure 11b,d and Figure 12b,d) implementing (dashed lines) or not (plain lines) the thermochemical data and SIT parameters from Shang and Reiller (2020, 2021a, b). As awaited from the ionic strength evolution (Figure 8) the differences of solubility and speciation between Thermochimie 11a and Shang and Reiller (2020, 2021a, b) are limited, but significant nonetheless. The general comportment of uranium at 25 °C in Callovo-Oxfordian pore-water calculated in previous studies (Shang and Reiller, 2020, 2021a, b), is again evidenced here. At lower pH and higher $\log_{10}(a(Mg^{2+})^x a(Ca^{2+})^{1-x} a(HCO_3^-)^2)$, the increasing dolomite solubility is favouring the formation of $Ca_nUO_2(CO_3)_3^{(4-2n)-}$ in both cases, but the higher carbonate, or $\log_{10}(a(Mg^{2+})^x a(Ca^{2+})^{1-x} a(HCO_3^-)^2)$, in Mol is favouring the predominance of UO₂(CO₃)₃⁺ at high pH at the expenses of U(OH)₄(aq), which dominates the speciation under Callovo-Oxfordian conditions. The situation is slightly different at 50 °C as the predominance of $Ca_nUO_2(CO_3)_3^{(4-2n)-}$ is narrowed to lower pH values. In Mol water the situations are comparable — yet slightly shifted to lower pH, or higher $\log_{10}(a(Mg^{2+})^x a(Ca^{2+})^{1-x} a(HCO_3^-)^2)$. In Callovo-Oxfordian conditions, if $Ca_2UO_2(CO_3)_3(aq)$ is
still predominant at lower pH or higher $log_{10}(a(Mg^{2+})^x a(Ca^{2+})^{1-x} a(HCO_3^-)^2)$ — due to the higher $[Ca]_{total}$ —, as the predominance of $U(OH)_4(aq)$ occurs at lower pH or higher $log_{10}(a(Mg^{2+})^x a(Ca^{2+})^{1-x} a(HCO_3^-)^2)$ values, $CaUO_2(CO_3)_{3/2}$ is slightly predominant over a narrow pH or $log_{10}(a(Mg^{2+})^x a(Ca^{2+})^{1-x} a(HCO_3^-)^2)$ range. The decreasing $log_{10} a(Ca^{2+})$ and $log_{10}(a(Ca^{2+})/a(H^+)^2)$ values compared to 25 °C is monitoring and explaining the lower solubility increase of uraninite and lower predominance of $Ca_2UO_2(CO_3)_3(aq)$.

Figure 13 is showing the variation of speciation of dissolved uranium from uraninite at equilibrium with pyrite, siderite, and dolomite, at varying temperature, and the accompanying $log_{10}(a(Mg^{2+})^x a(Ca^{2+})^{1-x} a(HCO_3^-)^2)$ decrease for Mol (Figure 13a) and Callovo-Oxfordian (Figure 13b). It shows that with decreasing pH — and accompanying decrease in $log_{10}(a(Ca^{2+}) a(H^+)^2)$ values —, the predominance of $Ca_2UO_2(CO_3)_3(aq)$ is lowered to the benefit of $CaUO_2(CO_3)_3^{2-}$, leaving only a small amount of $U(OH)_4(aq)$. These calculations mitigate the calculations in Shang and Reiller (2021b), and are giving a more complete vision of the importance of these complexes.
<figure><img src="image_12.png" /><figcaption>**Figure 11.** Solubility of uraninite (a,b) and solution speciation of uranium (c,d) vs. pH — and $log_{10}(a(Mg^{2+}) \times a(Ca^{2+})^{1-x} a(HCO_3^-)^2)$ — at equilibrium with pyrite, siderite, and dolomite at 25 (a,c) and 50 °C (b,d), from the composition of pore-water from the Mol pore-water (De Craen *et al.*, 2004), using Thermochimie 11a database and thermodynamic functions and SIT parameters for $A_{e,}UO_2(CO_3)_3^{(4-2n)-}$ from Shang and Reiller (2020, 2021a, b). Only species with concentration permanently higher than 5% or higher than $U(OH)_4(aq)$ are plotted.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Figure 12. Solubility of uraninite (a,b) and speciation of dissolved uranium (c,d) vs. pH — and $log_{10}(a(Mg^{2+}) \times a(Ca^{2+})^{1-x} a(HCO_3^-)^2)$ — at equilibrium with pyrite, siderite, and dolomite at 25 (a,c) and 50 °C (b,d), from the composition of pore-water from the Callovo-Oxfordian formation (Gaucher et al., 2009), using Thermochimie 11a database (plain) and thermodynamic functions and SIT parameters for $A_{e,n}UO_2(CO_3)_3^{(4-2n)-}$ from Shang and Reiller (2020, 2021a, b) (dashed). Only species higher than 5% are plotted.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Figure 13. Solubility of uraninite (a,b) and speciation of dissolved uranium (c,d) vs. temperature — and $log_{10}(a(Mg^{2+})^x a(Ca^{2+})^{1-x} a(HCO_3^-)^2)$ — calculated at equilibrium with pyrite, siderite, and dolomite allowing pH to equilibrate, from the initial composition of pore-water from the Mol (De Craen et al., 2004) (a,c) and Callovo-Oxfordian (Gaucher et al., 2009) (b,d) formations, using Thermochimie 11a database (plain) and $log_{10}\beta^°(A_{en}UO_2(CO_3)_3^{(4-2n)-})$ and $\varepsilon(A_{en}UO_2(CO_3)_3^{(4-2n)-},Na^+,Cl^-)$ from Shang and Reiller (2020, 2021b) (dashed).</figcaption></figure>
## 3.2. Plutonium

The formal oxidation potentials of the free ions of plutonium calculated from the Gibbs energies in Grenthe et al. (2020) are reported in Figure 14 — it can be noted that extensive hydrolysis of Pu(IV) induces that Pu⁴⁺ represent ca. 72% at pH = 0 in HClO₄.

<figure><img src="image_15.png" /><figcaption>**Figure 14.** The formal oxidation potential (V) diagram of plutonium in acidic aqueous solutions (Grenthe et al., 2020).</figcaption></figure>

Recently, Jo et al. (2020) studied the formation of MgPuO₂(CO₃)₃²⁻ and CaPuO₂(CO₃)₃²⁻ complexes; no formation of Ae₂PuO₂(CO₃)₃(aq) was evidenced. The formation of the AePuO₂(CO₃)₃²⁻ complexes are thought to principally impact the equilibrium between Pu(V) and Pu(VI) in oxic carbonated media, viz. pe > 8, and 8 < pH < 9.25 (Jo et al., 2022). Nevertheless, further estimation or determination of the log₁₀β° and ε values are still desirable for the reasons seen for uranium (vide supra).

### 3.2.1. Experiment vs. LFER estimation

The formation of the AeₙPuO₂(CO₃)₃⁽⁴⁻²n⁾ complexes could have been estimated from the LFER in Figure 1 between inorganic ligand log₁₀β° using thermochemical data selection for U, Np, and Pu (Grenthe et al., 1992; Grenthe et al., 2020; Guillaumont et al., 2003; Lemire et al., 2001).

The regression uncertainty calculated using the parameters in Table 3 cannot be better than 1.6 logarithmic unit for estimated log₁₀β°Pu values. As the log₁₀β°AeₙAnO₂(CO₃)₃⁽⁴⁻²n⁾ are deeply dependent on the log₁₀β°AnO₂(CO₃)₃⁺ values, which are different for U, Np, and Pu (Table 1), the estimation via the LFERs will be done using the successive experimental constants log₁₀K°.
The estimated $log_{10}K^\circ$ values for eventual $MgPuO_2(CO_3)_3^{2-}$, $CaPuO_2(CO_3)_3^{2-}$, and $Ca_2PuO_2(CO_3)_3(aq)$ are plotted in Figure 1, and reported in Table 4, together with the values determined experimentally by Jo *et al.* (2020). There is a very good agreement between the experimental ($log_{10}K^\circ = 4.29 \pm 0.18$) and the estimated values for the stepwise reaction, either using the experimental data of $MgUO_2(CO_3)_3^{2-}$ from Shang and Reiller (2021a) ($log_{10}K^\circ = 4.5 \pm 1.6$) or from the selected value in Grenthe *et al.* (2020) or determined in Figure 4 ($log_{10}K^\circ = 4.4 \pm 1.6$). The $Mg_2PuO_2(CO_3)_3(aq)$ species have not been detected by Jo *et al.* (2020) and should be regarded with caution.

There is a fairly good agreement between the experimental ($log_{10}K^\circ = 6.05 \pm 0.50$) and the estimated values for the stepwise reaction, either using the experimental data of $CaUO_2(CO_3)_3^{2-}$ from Shang and Reiller (2020) ($log_{10}K^\circ = 5.3 \pm 1.6$) or from the selected value in Grenthe *et al.* (2020) ($log_{10}K^\circ = 5.1 \pm 1.6$) or determined in Figure 4 ($log_{10}K^\circ = 5.2 \pm 1.6$). Because of the value of the stepwise reaction constant between $CaUO_2(CO_3)_3^{2-}$ and $Ca_2UO_2(CO_3)_3(aq)$, the $Ca_2PuO_2(CO_3)_3(aq)$ complex may have been difficult to evidence under the conditions used by Jo *et al.* (2020). Applying $log_{10}K^\circ CaPuO_2(CO_3)_3^{2-} = 6.05$ from Jo *et al.* (2020) and $log_{10}K^\circ Ca_2PuO_2(CO_3)_3(aq) = 3.2$ (Table 4), then $Ca_2PuO_2(CO_3)_3(aq)$ would only account for ca. 6% at the highest calcium concentration used (Figure S4 of the SI).

The cumulative constants $log_{10}\beta^\circ$ for the $MgPuO_2(CO_3)_3^{2-}$ and $CaPuO_2(CO_3)_3^{2-}$ complexes can be estimated using $log_{10}\beta^\circ_{PuO_2(CO_3)_3^4}$ in Table 1. In both cases the estimated $log_{10}\beta^\circ_{AePuO_2(CO_3)_3^{2-}}$ values are in agreement with the one obtained from the determination of Jo *et al.* (2020). The estimation of the potential $Sr^{2+}$ and $Ba^{2+}$ complexes for $PuO_2^{2+}$, using the U-selected values by Grenthe *et al.* (2020) are also given in Table 4 for scoping calculation.

It can also be noted that the $log_{10}K^\circ$ values obtained by Jo *et al.* (2020) after extrapolation to infinite dilution using Davies (1962) equation are no different than the ones that could be
obtained using the ε(AeUO₂(CO₃)₃⁽⁴⁻²n⁾,Na⁺Cl⁻) values in Shang and Reiller (2020, 2021a) in analogy (Table 2), i.e. log₁₀K°CaUO₂(CO₃)₃²⁻,Na⁺Cl⁻ = 6.05 ± 0.50 and log₁₀K°MgUO₂(CO₃)₃²⁻,Na⁺Cl⁻ = 4.32 ± 0.18

The values of Mg and Ca complexes from Jo *et al.* (2020) and from the LFER — only estimation from Shang and Reiller (2020, 2021a) — are used to draw the Pourbaix diagrams at I_m = 0.1 mol kg_w⁻¹ NaCl, and P(CO₂) = 10⁻³.₅ atm (Figure 15a), [Ca] = 5 mmol kg_w⁻¹ (Figure 15b), and [Mg] = 5 mmol kg_w⁻¹ (Figure 15c) using the Thermochimie 11a database — one can note the importance of Pu(OH)₂(CO₃)₂²⁻ that was not selected in Grenthe *et al.* (2020). The SIT parameters from Shang and Reiller (2020, 2021a) are used in analogy. It can be seen that the MgPuO₂(CO₃)₃²⁻ and CaPuO₂(CO₃)₃²⁻ complexes are not awaited to have any influence on the chemistry of Pu under the conditions of the underground research laboratories in Belgium (De Craen *et al.*, 2004; Honty *et al.*, 2022; Wang *et al.*, 2023), France (Gaucher *et al.*, 2009; Vinsot *et al.*, 2008), Sweden (Emrén *et al.*, 1999), or Switzerland (Courdouan Merz, 2008; Montoya *et al.*, 2021; Thury and Bossart, 1999), where equivalent P(CO₂) is ca. 10⁻² atm. The Pu speciation calculated for the Callovo-Oxfordian water (Gaucher *et al.*, 2009) at varying pH and constant P(O₂) = 10⁻⁶⁵.₇ atm corresponding to the pe is shown in Figure S5a of the SI suggesting a Pu(III)/Pu(IV) mixture. The speciation at constant pH = 7.1, and varying pe from the site value to atmospheric O₂(g), not accounting (Figure S5b of the SI) and accounting (Figure S5c of the SI) for the AePuO₂(CO₃)₃²⁻ complexes from Jo *et al.* (2020). The CaPuO₂(CO₃)₃²⁻ complex nevertheless extends significantly the Pu(VI) domain in oxidized mildly alkaline media, particularly in carbonated calcium and magnesium media, more at the expenses of Pu(V) than of Pu(IV).

The question of the potential importance of these complexes in seawater should then be addressed directly.
<figure><img src="image_16.png" /><figcaption>Figure 15. Pourbaix diagrams (Kinniburgh and Cooper, 2011) of [Pu] = 0.1 nmol kg⁻¹ (a,b,c), I_m = 0.1 mol kg⁻¹ NaCl, and P(CO₂) = 10⁻³.⁵ atm (Grenthe et al., 2020); not considering (a) and considering the CaPuO₂(CO₃)₃²⁻ (b) or MgPuO₂(CO₃)₃²⁻ (c) complexes from Jo et al. (2020) (plain line) or from LFER (dashed line); [Ae] = 5 mmol kg⁻¹ (Ae is Ca (b) or Mg (c)), and considering ε(AePuO₂(CO₃)₃²⁻,Na⁺Cl⁻) = ε(AeUO₂(CO₃)₃²⁻,Na⁺Cl⁻) from Shang and Reiller (2020) (b) and Shang and Reiller (2021a) (c); no precipitation required.</figcaption></figure>
### 3.2.2. Application to standard seawater

The most striking parameter affecting the chemistry of Pu in seawater is the redox potential. The $E_h$ varies with depth (McManus *et al.*, 2005) with the dissolved oxygen concentration. However, measurements did not seem to follow the $O_2/H_2O$ equilibrium but other oxygen equilibria (Meyer *et al.*, 2014). Particularly, the equilibria including superoxide radical $O_2^{\cdot -}/H_2O_2$ and $O_2/O_2^{\cdot -}$ have been proposed to control the redox with depth.

In sea and ocean waters, speciation of plutonium seem to be driven by $Pu(VI+V)/Pu(IV)$, as suggested by Figure 15: Nelson and Lovett (1978) seemed to favour $Pu(VI)/Pu(IV)$. Aston (1980) estimated that dissolved Pu in seawater should likely be under the form of $Pu(VI)$ species with $Pu(IV)$ as colloidal form. The complex $PuO_2OHCO_3^{\cdot -}$ proposed then was disregarded in the first NEA-OECD commissioned review for Pu (Lemire *et al.*, 2001).

McManus *et al.* (2005) proposed dissolved oxygen concentrations in deep Pacific Ocean samples that would suggest the predominance of $Pu(VI)$ in solution, even if redox in sea and ocean waters is more complicated (Meyer *et al.*, 2014).

A speciation calculation using the data from Jo *et al.* (2020), and $\varepsilon$ values from Shang and Reiller (2020, 2021a) in analogy, and the seawater composition from Millero *et al.* (2008) is drawn in Figure 16 at $P(O_2) = 0.2095$ atm and varying pH — the carbonate concentration is not equilibrated either with atmospheric $CO_2$ ($SI = -3.29$) or alkaline earth carbonate phases such as calcite ($CaCO_3$, $SI = 0.35$), magnesite ($MgCO_3$, $SI = 0.81$), nesquehonite ($MgCO_3:3H_2O$, $SI = -2.15$), or dolomite ($MgCa(CO_3)_2$, $SI = 1.77$, or $Mg_{0.5}Ca_{0.5}CO_3$, $SI = 0.89$). At pH = 8.1 of the standard seawater proposed by Millero *et al.* (2008), it can be seen that $CaPuO_2(CO_3)_3^{2-}$ is calculated to be ca. 72% and $MgPuO_2(CO_3)_3^{2-}$ ca. 8% and are the major and fourth major species, respectively — $PuO_2(CO_3)_2^{2-}$ ca. 11%, and $PuO_2(CO_3)_3^{4-}$ ca. 8%. It is then evident that the $log_{10}K^\circ$ values from Jo *et al.* (2020) need to be confirmed further and $\varepsilon$ values determined instead of being estimated by analogy.
These theoretical calculations could be compared to the laboratory experiments from Dumas
et al. (2018) where the precipitation of colloidal Pu(IV) was observed after an addition of 50
µmol$_{Pu}$ kg$_{w}^{-1}$ in a natural seawater sample. The authors measured E$_{h}$ = 210 mV at pH = 7.8(8)
(pe = 3.54 at 25 °C), which does allow anticipating any influence of CaPuO$_{2}$(CO$_{3}$)$_{3}^{2-}$ — cf.
Figure 15b, Figure 17, and Figure S6 of the SI. This also indicates that the redox potential is
not controlled by dissolved oxygen — E$_{h}$ = 210 mV/NHE at 25 °C would correspond to P(O$_{2}$)
= 10$^{-37.4}$ atm, or as low as 1.6 10$^{-36}$ mg kg$_{w}^{-1}$ O$_{2}$ — but by another redox couple. This total
concentration of Pu would allow the formation of either phases contained in Thermochimie 11a
database file: amorphous PuO$_{2}$:2H$_{2}$O(am) or colloidal PuO$_{2}$(coll) (taken from Neck et al.,
2007), up to the formation of PuO$_{2}$(OH)$_{2}$:H$_{2}$O(am). At pH 7.88, for PuO$_{2}$(coll), pe = 11.23, E$_{h}$
= 0.665 V, 8.9 10$^{-6}$ mg L$^{-1}$ O$_{2}$ (Figure 17), and for PuO$_{2}$:2H$_{2}$O(am), pe = 12.48, E$_{h}$ = 738 mV,
0.85 mg kg$_{w}^{-1}$ O$_{2}$ (Figure S7 of the SI). It can be noted that Pu(OH)$_{2}$(CO$_{3}$)$_{3}^{2-}$ from Rai et al.
(1999b), which was not selected in Grenthe et al. (2020), strongly dominates the Pu(IV)
speciation at the measured E$_{h}$ value.

Meyer *et al.* (2014) measured E*h* values in the Gotland Deep (Baltic Sea) from -55 to 167 mV at temperature varying from 3 to 8 °C, *i.e.* pe from -0.99 to 2.99, which would correspond to Pu(IV) predominance.
<figure><img src="image_17.png" /><figcaption>Figure 16. Speciation of [Pu] = 0.1 nmol kg_w⁻¹ in standard seawater (Millero *et al.*, 2008), at P(O₂) = 0.2095 atm, using Jo *et al.* (2020) constants for MgPuO₂(CO₃)₃²⁻ and CaPuO₂(CO₃)₃²⁻, and ε values from Shang & Reiller (2020, 2021a) in analogy.</figcaption></figure>
<figure><img src="image_18.png" /></figure>

Figure 17. Solubility (a) and speciation in solution (b,c) of Pu from Dumas *et al.* (2018) including precipitation of PuO₂:2H₂O(am) (a) or PuO₂(coll) (a,b,c), and PuO₂(OH)₂:H₂O(cr) using Thermochimie 11a (b), and implemented with the AePuO₂(CO₃)₃²⁻ complex (Jo *et al.*, 2020) and ε(AeUO₂(CO₃)₃(4-2n)⁻,Na⁺Cl⁻) (Shang and Reiller, 2020, 2021a) in analogy, at pH 7.88 and varying pe: green thick plain line and shaded red domain indicate the measured Eₕ value from Dumas *et al.* (2018) and Meyer *et al.* (2014), respectively.

### 3.3. Neptunium

The formal oxidation potentials of the free ions of neptunium calculated from the Gibbs energies in Grenthe *et al.* (2020) are reported in Figure 18 it can be noted that extensive hydrolysis of Np(IV) induces that Np⁴⁺ represent ca. 48% at pH = 0 in HClO₄.
<figure><img src="image_19.png" /><figcaption>**Figure 18.** The formal oxidation potential (V) diagram of neptunium in acidic aqueous solutions (Grenthe *et al.*, 2020).</figcaption></figure>

### 3.3.1. Estimation by LFER

Up to now, no determination of the formation of $Ae_nNpO_2(CO_3)_3^{(4-2n)-}$ has been reported. From the general agreement between estimated and measured $log_{10}\beta^{\circ}_{AePuO_2(CO_3)_3^{2-}}$ values, a comparable exercise can be proposed for $Np$. The LFER uncertainty for estimated $log_{10}\beta^{\circ}_{Np}$ values cannot be better than 1.1 and 0.7 logarithmic unit from $log_{10}\beta^{\circ}_{U}$ and $log_{10}\beta^{\circ}_{Pu}$, respectively. The estimated $log_{10}K^{\circ}$ values for eventual $MgNpO_2(CO_3)_3^{2-}$, $CaNpO_2(CO_3)_3^{2-}$, and $Ca_2NpO_2(CO_3)_3(\text{aq})$ are plotted in Figure 2, and reported in Table 4. Here again, $Ca_2NpO_2(CO_3)_3(\text{aq})$ has to be regarded with caution as long as the hypothesis on plutonium is not verified (vide ante). The values for $MgNpO_2(CO_3)_3^{2-}$, estimated either from $log_{10}\beta^{\circ}_{U}$ and $log_{10}\beta^{\circ}_{Pu}$ LFERs are in excellent agreement whatever the origin of the constants and LFER used, i.e. $log_{10}K^{\circ} = 4.5 \pm 1.1$ from Shang and Reiller (2021a) (Table 4, Figure 2), and $log_{10}K^{\circ} = 4.3 \pm 1.1$ from Grenthe *et al.* (2020) (Table 4) using $log_{10}\beta^{\circ}_{U} = f(log_{10}\beta^{\circ}_{Np})$, and $log_{10}K^{\circ} = 4.5 \pm 0.7$ from Jo *et al.* (2020) using $log_{10}\beta^{\circ}_{Pu} = f(log_{10}\beta^{\circ}_{Np})$ (Table 4, Figure 3).

In the case of $CaNpO_2(CO_3)_3^{2-}$, the agreement is fair considering the uncertainties. Using the $log_{10}\beta^{\circ}_{U} = f(log_{10}\beta^{\circ}_{Np})$ LFER, a $log_{10}K^{\circ}_{CaNpO_2(CO_3)_3^{2-}} = 5.3 \pm 1.1$ from Shang and Reiller (2020) (Table 4, Figure 2), and $log_{10}K^{\circ}_{CaNpO_2(CO_3)_3^{2-}} = 5.1 \pm 1.1$ from Grenthe *et al.* (2020), whereas $log_{10}K^{\circ}_{CaNpO_2(CO_3)_3^{2-}} = 6.3 \pm 0.7$ is obtained from Jo *et al.* (2020) using $log_{10}\beta^{\circ}_{Pu} = f(log_{10}\beta^{\circ}_{Np})$ (Table 4, Figure 3). The value for $Ca_2NpO_2(CO_3)_3(\text{aq})$ can only be estimated using $log_{10}\beta^{\circ}_{U} = f(log_{10}\beta^{\circ}_{Np})$ LFER: a $log_{10}K^{\circ}_{Ca_2NpO_2(CO_3)_3} = 3.2 \pm 1.1$ from Shang and Reiller (2020) (Table 4, Figure 2), and $log_{10}K^{\circ}_{Ca_2NpO_2(CO_3)_3} = 3.7 \pm 1.1$ from Grenthe *et al.* (2020). Here again, as Jo *et al.*
(2020) did not evidenced the formation of Ca₂PuO₂(CO₃)₃(aq), this latter value should regarded
with caution. The cumulative constants in Table 4 are calculated accounted for the formation
of NpO₂(CO₃)₃⁴⁻ (Table 1).

The values of Mg and Ca complexes in Table 4 are used to draw the Pourbaix diagrams at
I_m = 0.1 mol kg_w⁻¹ NaCl, and P(CO₂) = 10⁻³.₅ atm (Figure 19a), [Ca] = 5 mmol kg_w⁻¹
— Figure 19b using Shang and Reiller (2020) and Jo et al. (2020) —, and [Mg] = 5 mmol kg_w⁻¹
— Figure 19c using Shang and Reiller (2021a) — implemented in the input file using the
Thermochimie 11a database — one can note that the selection of Np(OH)₂(CO₃)₂²⁻ from Rai et
al. (1999a) strongly impacts the speciation of Np(IV). The SIT parameters from Shang and
Reiller (2020, 2021a) are used in analogy. As in the case of Pu, It can be seen that the
Ae_nNpO₂(CO₃)₃⁽⁴⁻²n⁾⁻ complexes are not awaited to have any influence on the chemistry of Np
under the conditions of the underground research laboratories in Belgium, France, Sweden, or
Switzerland for the same reasons explained beforehand. The Ca_nNpO₂(CO₃)₃⁽⁴⁻²n⁾⁻ complexes
nevertheless extend significantly the Np(VI) domain in oxidized alkaline media — particularly
in carbonated calcium and magnesium media —, more at the expenses of NpO₂⁺ than of
NpO₂CO₃⁻. The question of the potential importance of these complexes in shallow seawater
should also then be addressed.
<figure><img src="image_20.png" /><figcaption>Figure 19. Pourbaix diagram (Kinniburgh and Cooper, 2011) of [Np] = 0.1 nmol kg⁻¹, I_m = 0.1 mol kg_w⁻¹ NaCl, and P(CO₂) = 10⁻³.₅ atm (Grenthe et al., 2020); not considering (a) and considering the AenPuO₂(CO₃)₃(⁴⁻²n)⁻ complexes in Table 4 (b,c); [Ae] = 5 mmol kg_w⁻¹ — Ae = Ca (b), Ae = Mg (c) —, log₁₀β°Ca_nPuO₂(CO₃)₃(⁴⁻²n)⁻ estimated from LFER (Table 4) from Shang and Reiller (2020) (b, dashed lines) and Jo et al. (2020) (b, plain lines) and considering ε(AeNpO₂(CO₃)₃²⁻,Na⁺Cl⁻) = ε(AeUO₂(CO₃)₃²⁻,Na⁺Cl⁻) from Shang and Reiller (2020) (b) and Shang and Reiller (2021a) (c); no precipitation required.</figcaption></figure>
### 3.3.2. Application to standard seawater (Millero et al., 2008)

The calculated speciation of Np in standard seawater from Millero *et al.* (2008) in Figure 20 using data in Table 4, and $\varepsilon(A_{e_n}UO_2(CO_3)_3^{(4-2n)-},Na^+Cl^-)$ from Shang & Reiller (2020, 2021a) in analogy suggests that the sum of $A_{e_n}NpO_2(CO_3)_3^{(4-2n)-}$ could be major in seawater. It seems then desirable to determine both $\log_{10}\beta^{\circ}_{A_{e_n}NpO_2(CO_3)_3^{(4-2n)-}}$ and $\varepsilon(A_{e_n}NpO_2(CO_3)_3^{(4-2n)-},Na^+Cl^-)$ values.

<figure><img src="image_21.png" /><figcaption>Figure 20. Speciation of [Np] = 0.1 nmol kg⁻¹ in standard seawater (Millero *et al.*, 2008), at P(O₂) = 0.2095 atm, using $\log_{10}\beta^{\circ}_{A_{e_n}NpO_2(CO_3)_3^{(4-2n)-}}$ in Table 4, and $\varepsilon$ values from Shang & Reiller (2020, 2021a) in analogy.</figcaption></figure>

## 4. Conclusion

This study stresses the need to accurately determine the thermochemical constants ($\log_{10}K^{\circ}$ and $\log_{10}\beta^{\circ}$) and functions ($\Delta_fG^{\circ}_m$, $\Delta_fH^{\circ}_m$, and $S_f^{\circ}_m$), of the $A_{e_n}AnO_2(CO_3)_3^{(4-2n)-}$ complexes, as well as the specific ion-interaction coefficients $\varepsilon$ in relevant ionic media, i.e. NaCl or NaNO₃,
of the nuclear fuel cycle. The comparisons of calculations using different thermochemical
databases showed that implementation of these data are needed for a trustworthy evaluation of
the impact of $Ae_nAnO_2(CO_3)_3^{(4-2n)-}$ in slightly alkaline and carbonated media.

With the use of recent data, this study has ascertained the predominance domains of the
$Ae_nUO_2(CO_3)_3^{(4-2n)-}$ complexes in terms pH, activities of $HCO_3^-$, $Ca^{2+}$ and $Mg^{2+}$, redox
potentials (pe, E_h, or dissolved O_2), salinity, and temperature. Linear free energy relationships,
based on widely accepted thermochemical data, have been used to estimate the potential
predominance of $Ae_nAnO_2(CO_3)_3^{(4-2n)-}$ for Pu and Np. The estimated value for
$CaPuO_2(CO_3)_3^{2-}$ is in fair agreement with a recent experimental determination, which allows
better defining the predominance of the complex at the expenses of Pu(V) and slightly to
Pu(IV). In the case of neptunium, where no experimental evidence has been published at the
time of submission, the estimated constant also allows estimating the potential predominance
of $AeNpO_2(CO_3)_3^{2-}$ at the expense of Np(V) ($NpO_2^+$ and $NpO_2(CO_3)^-$).

Hence, the determination of the thermochemical constants and functions, and $\varepsilon$ values of
$Ae_nPuO_2(CO_3)_3^{(4-2)-}$ and $Ae_nNpO_2(CO_3)_3^{(4-2)-}$ in NaCl (at least) are needed for a better
evaluation of their predominance in oxidizing to slightly reducing media.

## Acknowledgement

ONDRAF-NIRAS is acknowledged for its support through contract (DEN4857-CCHO
2018-0456/00/00).

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