Thermodynamic and crystallographic model for anion uptake by hydrated calcium aluminate (AFm): an example of molybdenum

Amongst all cement phases, hydrated calcium aluminate (AFm) plays a major role in the retention of anionic species. Molybdenum (Mo), whose 93Mo isotope is considered a major steel activation product, will be released mainly under the form of MoO42− in a radioactive waste repository. Understanding its fate is of primary importance in a safety analysis of such disposal. This necessitates models that can both predict quantitatively the sorption of Mo by AFm and determine the nature of the sorption process (i.e., reversible adsorption or incorporation). This study investigated the Cl−/MoO42− exchange processes occurring in an AFm initially containing interlayer Cl in alkaline conditions using flow-through experiments. The evolution of the solid phase was characterized using an electron probe microanalyzer and synchrotron high-energy X-ray scattering. All data, together with their quantitative modeling, coherently indicated that Mo replaced Cl in the AFm interlayer. The structure of the interlayer is described with unprecedented atomic-scale detail based on a combination of real- and reciprocal-space analyses of total X-ray scattering data. In addition, modeling of several independent chemical experiments elucidated that Cl−/OH− exchange processes occur together with Cl−/MoO42− exchange. This competitive effect must be considered when determining the Cl−/MoO42− selectivity constant.

With more than seven billion cubic meters produced annually, cement is probably the most widely used material on Earth 1 . Cement-based materials are ubiquitous in construction, including in the design of access structures, galleries, vaults, and waste packages of deep underground radioactive waste disposal sites. In this context, cement-based materials are chosen primarily for their mechanical resistance. However, additional properties of interest are their low permeability, together with their strong chemical reactivity manifest via their cation and anion sorption properties [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] , which contribute to the concept of a multiple barrier system between the waste matrix and the biosphere 22 .
Amongst all cement phases, hydrated calcium aluminate (AFm) plays a major role in the retention of (radioactive) anions that enter into contact with cement-based materials. AFm is member of the layered double hydroxides (LDHs) group, meaning that its structure consists of stacked layers of positively charged atoms separated from each other by anion-containing hydrated interlayer spaces. The general structural formula of an AFm is [Ca 2+ 4 (Al 3+ x Fe 3+ (1−x) ) 2 (OH) 12 ]•A•nH 2 O, where the layered species are between the brackets and A•nH 2 O represents the hydrated exchangeable "interlayer anions. " These exchangeable interlayer anions compensate for the layer charge induced by the presence of the trivalent cations in the layers 8,9,[17][18][19][20][21][23][24][25] , providing AFm with an anion-exchange capacity (AEC). If monovalent, the stoichiometry of the interlayer anions is equal to that of trivalent layer cations.
Scientific REPORTS | (2018) 8:7943 | DOI: 10.1038/s41598-018-26211-z precipitation of calcite during the experiments (e.g. 50 ) and to avoid the presence of CO 3 2− in the interlayer 51 . Inlet solutions were injected through the reactors using a peristaltic pump (Watson Marlow, 205U) at a constant flow rate of about 2 mL min −1 . AFm-Cl particles were maintained in suspension using a magnetic stirrer rotated on an axle to prevent any grinding of the material between the bar and the bottom of the reactor.
The initial masses, flow rates, and experimental durations are presented in Table 1.
As schematized in Fig. 1, the outlet solutions were filtered through a 0.1-μm membrane before being collected. The fluid sampling allowed the monitoring of solution chemistries (Cl, Mo, Al, Ca, Al, Na, and K concentrations) and flow rates as a function of time. All monitored data are reported in the Supplementary Information (Tables S1-S3).
On completion of the experiment, the solid suspension was collected and it was then filtered using a 0.1-µm filter. Subsequently, the solid samples were freeze-dried and then stored in an N 2 -filled glove box, which was maintained at a relative humidity of c.a. 10% using a saturated LiCl solution.
Materials. AFm-Cl sample. AFm-Cl was synthetized following a previously described protocol 48 , which involves mixing stoichiometric amounts of tricalcium aluminate (C 3 A) and CaCl 2 ·2H 2 O (1:1 molar ratio 37 ) in water and at room temperature. All syntheses were performed in an N 2 -filled glove box using ultrapure water (resistivity = 18.2 MΩ cm), which was degassed prior to its introduction into the glove box. After 15 d maturation, the synthesized AFm-Cl was filtered, freeze-dried, and stored in an N 2 -filled glove box.
Because the synthesis of AFm-Cl involved the use of CaCl 2 ·2H 2 O, and because the retrieved material was not washed after filtration, a weak presence of calcium chloride salt in the dried AFm could have been suspected. This was tested for by performing leaching experiments (Table 2). No linearity between the measured Cl and Ca concentrations as a function of the solid/liquid ratio was observed (S/L in g g −1 of water); thus, the presence of salts in the dried product was discounted.
Reacting solutions. Two types of solution were prepared for each flow-through experiment: (i) an "input solution" enriched in Mo, which was injected inside the reactor, and (ii) an "initial reactor solution", which initially filled the reactor. The solutions were prepared using MoO 3 , Ca(OH) 2 , NaCl, KCl, Al 2 O 3 , and ultrapure water. The fluids were bubbled with N 2 for about 20 h before the experiments.
The chemistry of the reacting solutions is presented in Table 3. Note that NaCl and KCl were used as tracers to constrain the modeling of the flow-through experiments. Relative uncertainties were estimated at 10% from the discrepancies between the measured Cl and K/Na concentrations (Table 3).
AFm precipitation was not expected from the reacting solutions because AFm-Cl, AFm-OH, and AFm-MoO 4 were undersaturated.

Results and Discussion
To constrain the mechanisms of Mo incorporation into the AFm with initially interlayer Cl, and thus to allow successful interpretation of the chemical data, the solids collected on completion of all flow-through experiments, as well as an aliquot of unreacted sample, were analyzed for their mineralogy to elucidate the changes that occurred during the flow-through experiments.

Mineralogical transformations. Chemical composition of initial and reacted samples. The unreacted
AFm had a stoichiometric Ca to Al ratio of 2, as expected for defect-free AFm (Table 4). Coherently, the Cl to Al ratio was, within the limit of uncertainties, 1. This suggests the only source of layer charge was Al. After the flow-through experiments, in comparison with the unreacted material, the samples were depleted in Cl and  (Table 4).
Although the ratio of Cl removed to Mo incorporated was close to 2, suggesting that MoO 4 2− replaced Cl − as the interlayer charge-compensating anion, a deficit of anions in the interlayer position was suspected because all samples verified, on average, the following relation: where n i is the number of moles of an anion i (Cl − or MoO 4 2− ) per mole of AFm, z i is the charge of that ion (1 for Cl − , 2 for MoO 4 2− ), and n Al is the number of moles of Al per mole of AFm. As the Ca to Al ratio in the solids collected on completion of all the experiments remained similar to that of the unreacted sample, a change in the density of the layer charge was excluded. Another anion that cannot be probed straightforwardly by an electron probe microanalyzer (EPMA) was thus incorporated in the AFm during the experiments. This anion was OH − , because it is unquantifiable by EPMA (i.e., the loss of weight is unquantifiable because the AFms are highly hydrated) and because it is present in large concentrations in the input solutions used for the flow-through experiments (i.e., pH > 12). Moreover, the opposite exchange process (i.e., Cl − sorption onto AFm-OH) has been reported by Suryavanshi et al. 52 .
Crystal structure. The X-ray diffraction (XRD) pattern of the unreacted material was typical of AFm-Cl, with the presence of an intense maximum at 3.19° 2θ (7.86 Å; Fig. 2a), assigned to the basal 002 reflection 53 . Upon exchange with Mo, the low angle region of the diffraction pattern underwent significant change (Fig. 2a). In the XRD pattern of the sample with the lowest Mo content (experiment 1), the 002 reflection of AFm-Cl was present, as were two new reflections at 2.52° 2θ and 2.91° 2θ (9.93 Å and 8.60 Å). These two new layer-to-layer distances were close to those of ~10.3 Å and ~9.1 Å observed previously during Mo incorporation into AFm-Cl 21 . The fact that the presently observed layer-to-layer distances were 5-6% smaller was certainly because the previous data were obtained on samples in suspension, which consequently incorporated more H 2 O in the interlayer 23 . The swelling from 7.86 Å to 8.60-9.93 Å was translated as a replacement of Cl − by MoO 4 2− . Two different layer-to-layer distances were observed for the Mo-exchanged structure (hereafter, referred to as AFm-Mo), indicating the presence of two different orderings of the MoO 4 2− tetrahedra in the interlayer. For a Mo-O distance of 1.78 Å for the interlayer Mo in the tetrahedral coordination (see below), the height of an interlayer MoO 4 2− polyhedron is 2.37 Å. The increase in the layer-to-layer distance from 8.60 Å to 9.93 Å possibly reflects the ordering of MoO 4 2− polyhedra, with part of the polyhedra pointing toward a given layer and the other part pointing toward the opposite layer. In this assumption, the interlayer mid-plane passes through the middle of each tetrahedron (Fig. 3).
The expected layer-to-layer distance for an AFm containing interlayer OH − is 7.9 Å 24 , i.e., identical to that of AFm-Cl. Consequently, the analysis of the XRD patterns could not provide information on the presence of OH − in the interlayer.  Table 3. Solution compositions of reacting solutions. *PHREEQC calculation considering addition of Ca(OH) 2 with respect to measured Ca concentrations.   Using the intensities of the peaks at 3.19° 2θ (7.86 Å) and 2.91° 2θ (8.60 Å) as indicators of the abundances of the interlayer Cl − and MoO 4 2− , respectively, the degree of Cl/Mo exchange increased in the order: unreacted sample, experiment 1, experiment 3, and experiment 2, which also agreed with the EPMA data ( Table 4). Note that the presence of synthetic powellite (CaMoO 4 ) was not detected here, although it was detected in a previous study 21 of a closed system, at Mo concentration over 1 mM. The lower Mo concentrations used here (i.e., <1 mM), together with the continuous renewing of reacting solutions that limited the increase of Ca concentration, prevented powellite precipitation.
All peaks attributable to 00 l reflections of AFm-Mo were asymmetric (Fig. 2a) and the peak at 7.86 Å was shifted towards low angles, which is indicative of interstratified structure. Given the high degree of asymmetry, the Reichweite parameter, describing how many neighbors influence the position of a given layer 54,55 , was probably S = 0 (random interstratification). This type of stacking defect has been described repeatedly for AFm during SO 4 2− /I − exchange 8 , for C-S-H (the main cement phase) 43,56 , and more generally for several types of layered materials, including LDH and clay minerals 54,57,58 .
To provide further structural constraints on the mechanisms of Mo sorption, and to constrain better the Mo sorption sites, high-energy X-ray scattering data were converted to pair-distribution functions (PDFs). These data are therefore represented as interatomic distances in real space (Fig. 2b-d). To assign atomic pairs to the observed correlations, data from the unreacted sample were fitted using the AFm model proposed by Renaudin et al. 53 ( Figure S1 and Table S4). This analysis revealed that the unreacted sample was pure AFm and that the overall PDF signal was dominated by the signal from Ca-Ca and Ca-Al atomic pairs, while the low r part of the signal contained correlations from the first oxygen shells of Al and Ca (Al-O 1 and Ca-O 1 , with respective distances of 1.89 Å and 2.42 Å).
The PDF data of the samples that were interacted with MoO 4 2− revealed several changes compared with the PDF data of the unreacted sample (Fig. 2b). The most obvious change was an increase in the intensity of the correlations attributed, in the PDF of the unreacted sample, to Cl-Cl pairs from a given interlayer (Figs 2b, 4). For example, between the PDFs of the unreacted sample and of that issued from experiment 2, the intensity of the first six of these correlations (up to ~20 Å) increased by a mean value of 85%. The study of possible changes in the intensity of the correlations involving Cl atoms from successive interlayers (along c*) was hampered by the changes in and multiplicity of the layer-to-layer distance upon Mo sorption. The increase in the intensity of the correlation attributed to Cl-Cl pairs in the unreacted sample was interpreted as an increase in the electron density at the Cl sites upon incorporation of MoO 4 2− . The occupancy of the Cl site in the unreacted sample was 1 and the atomic scattering factor of Mo is ~3-4 times higher than that of Cl over the diffraction angles investigated 59,60 . Therefore, such an increase was explained by the incorporation of MoO 4 2− in the AFm structure that occurred through replacement of Cl − at the same crystallographic position. Interestingly, the increase in intensity depended on the Mo-Mo pair considered (Mo-Mo x , where x is the rank of the pair, i.e., the numbers printed in Fig. 4a). More precisely, the Mo-Mo 4 correlation (at 15.2 Å) remained of constant intensity, while for all other pairs up to Mo-Mo 6 (at 19.9 Å), it increased in intensity (Fig. 2b). This suggests a long-range ordering of MoO 4 2− in the interlayer, possibly related to the regular alternation along b (Fig. 4a) of "rows" preferentially filled with MoO 4 2− and of "rows" depleted in MoO 4 2− . However, it could not be assessed quantitatively through data modeling because of the mineralogical heterogeneity of the finals solids (i.e., the presence of interlayer Cl − , MoO 4 2− , and OH − ) and their complexity (i.e., interstratification). More generally, the fact that Mo-Mo pairs were observed at the same distance as the Cl-Cl pairs, up to the separation distance of 2 nm, is remarkable support for the hypothesis that Mo sorption by AFm proceeds through anion exchange. However, it does not give the exchange stoichiometry, which was obtained through modeling of the chemical data (see below).
A second important modification of the PDF data upon Mo exchange occurred in the Al-O 1 correlation (Fig. 2c). The intensity of this correlation increased with an increasing degree of Mo incorporation, and the maximum of the correlation was displaced toward low r values. Given Al is located in the AFm layer, no significant change to its coordination environment was expected upon modification of the interlayer composition. To investigate the origin of this modification further, the PDF data from the unreacted sample were subtracted from that of the reacted samples. This provided differential PDF (d-PDF) data where it could be observed that the apparent modification of the Al-O 1 correlation was in fact due to the presence of a peak at 1.78 Å (Fig. 2d), which increased in intensity with an increasing degree of Mo incorporation within the structure. This 1.78 Å distance is fully coherent with the presence of interlayer MoO 4 2− , as the same distance was observed by extended X-ray absorption fine structure spectroscopy for the Mo-O distance in tetrahedral MoO 4 2− 21 . Finally, the d-PDF data showed the presence of a broad correlation at ~3.75-4.30 Å (Fig. 2d), which was certainly because of correlations involving Mo and the closest layer of O, Al, and Ca atoms when the layer-to-layer distance was 8.60 Å.
To sum up, both the analysis of high-energy X-ray scattering and the EPMA data evidence that the degree of Mo for Cl exchange increased in the order: unreacted sample, experiment 1, experiment 3, experiment 2. Mo was incorporated in the AFm interlayer under the form of tetrahedral MoO 4 2− , taking the same crystallographic position as Cl − in the unreacted sample, supporting the idea that Mo incorporation results mainly from an exchange reaction involving Cl − . All these data were then used for interpreting the chemical data collected during the flow-through experiments.

Evolution of Mo and Cl concentration during flow-through experiments.
As discussed above, the three flow-through experiments allowed the different stages of Mo sorption by AFm-Cl to be investigated. The evolution of Mo and Cl concentrations at the outlet of the reactor reflects these different stages (Fig. 5). In experiment 1, the release of Mo started after about 1 h of the flow-through experiment (>fluid residence time, i.e., 42 min) and a steady state could be observed, while in experiment 2, Mo was released after 3 h. In both experiments, the initial release of Cl was high. Analysis of experiment 3 provides greater insight into this high release of Cl.  Figure S2). No preferential release of Ca was observed at the beginning of the flow-through experiments, confirming the absence of CaCl 2 impurities mixed with the synthesized AFm-Cl. Output Al concentrations were scattered but they remained close to the input concentrations (except for the first hour of experiment 1, see Supplementary Information: Figure S2). Because no significant releases of Ca and Al were observed, AFm dissolution during the flow-through experiments was negligible. The pH values remained constant over time ( Supplementary Information: Figure S3). Because of the continuous renewing of the reacting solutions, AFm-Cl, AFm-OH, and AFm-MoO 4 were undersaturated (Supplementary Information: Figure S3); thus, precipitation reactions were not expected (except for two samplings of experiment 1 where SI AFm-MoO4 ~ 0).  . White and red polyhedra show the layered Ca and Al coordination spheres, respectively, and yellow dots are the interlayer anions (Cl or Mo). The concentric white circles highlight the presence of several shells of interlayer anions around a given interlayer anion. The shell to which a given interlayer anion belongs is noted with a number. (b) Number of atoms involved in each shell schematized in (a) as a function of the distance between the central atom and those forming the shell. Note that the interatomic distances match those increasing in intensity in Fig. 2b. Analysis arbitrarily restricted to distances r < 20 Å.

Modeling of flow-through experiments and determination of exchange parameters.
As the dissolution of AFm can be neglected (see above), the amount of exchanger remained constant. The best fit of the experimental data, performed after modeling of the transport parameters (Supplementary Information: Figure S4), was obtained by considering two exchangeable sites. Cl − , MoO 4 2− , and OH − were allowed to compete for adsorption on site 1, while only monovalent anions could compete for adsorption on site 2 (i.e., Cl − /OH − exchange only). The total amount of exchanger adhered to the following relation: theoretical s ite s ite 1 2 Figure 5. Evolutions of experimental and modeled Mo and Cl concentrations as a function of time. "Best fit" models were obtained using different AEC (Table 5), while "average" models considered the same AEC site 1 (230 meq. 100 g −1 ) and AEC site 2 (126.3 meq. 100 g −1 ) for all experiments (see text). Gray shading represents estimated error on experimental data (i.e., 10%). where AEC theoretical is calculated from the ideal mineral formula of the AFm (i.e., 356.3 meq. 100 g −1 AFm or 2 eq mol −1 AFm), AEC site 1 is the AEC fitted for OH − /Cl − /MoO 4 2− exchange reactions, and AEC site 2 is the AEC for which only the OH − /Cl − exchange reaction occurs.
The best fit to the experimental data ( Fig. 5) was obtained using identical selectivity constants in all experiments (log K OH = −0.8 both for sites 1 and 2 and log K Mo = 1.3 for site 1, Table 5). In contrast, various AECs were fitted: AEC site 1 was in the range 178-260 meq. 100 g −1 , while AEC site 2 was in the range 120-178 meq. 100 g −1 ( Table 5). Qiu et al. 61 reported a collapse of the AFm interlayer in the presence of interlayer OH − that inhibited the adsorption of B(OH) 4 − . In our experiments, the fitted AEC site 1 increased from experiment 1 to 3 to 2, consistent with the measured pH of the "initial reactor solution" decreasing from experiments 1 to 3 to 2 (Table 3). Nonetheless, despite these expected AEC variations, a reasonable fit of all experiments was obtained with fixed values of 230 and 126.3 meq. 100 g −1 for sites 1 and 2, respectively (Fig. 5).
The estimated AECs for site 1 were systematically lower than the theoretical AEC (i.e., 356.3 meq. 100 g −1 ) irrespective of the modeling assumptions and considered experiments. Therefore, monovalent anions (i.e., Cl − and to a lesser extent, OH − ) in the interlayer position were not fully exchangeable with MoO 4 2− . This could result from partial accessibility of exchangeable sites, as reported previously for boron 61 , and/or because of high thermodynamic stability of the interstratified AFm containing Mo and monovalent anions, as reported by Mesbah et al. 62 for Kuzel's salt. To validate the modeling procedure, the chemical composition of the solid at the end of the experiment was calculated (Table 5) and found consistent with the EPMA data (Table 4); thus, confirming the robustness of the proposed geochemical model.

Evidence of Cl/OH exchange reactions.
Modeling of the leaching experiment was performed to validate the proposed Cl − /OH − exchange. In these experiments, solutions were slightly undersaturated and oversaturated with respect to AFm-Cl and gibbsite, respectively (SI AFm-Cl ~ −0.49 and SI Gibbsite ~ 0.86, Table 2).
Data were modeled in a first step assuming congruent AFm-Cl dissolution until undersaturation of −0.49, while allowing gibbsite to precipitate at an oversaturation index of 0.86. This model was unable to reproduce the experimental data (Fig. 6). In a second step, the K OH selectivity constant, fitted from the flow-through experiments, was implemented and the same AEC was used. The modeled Cl concentrations then increased with the solid concentration (Fig. 6). Modeled Ca and Al concentrations, as well as the pH, were also in agreement with the experimental data over the entire range of investigated S/L ratios. More specifically, the highest amount of exchanger led to increases in both OH − uptake and Cl − release capacities. Therefore, the Cl − concentration increased concomitantly with pH decrease, leading to the highest AFm dissolution (i.e., AFm solubility vs. pH) and explaining the Ca behavior. Finally, the lowest pH favored the stability of gibbsite (i.e., gibbsite solubility vs. pH), consistent with the observed evolution of Al concentration. Such modeling validated the proposed Cl − / OH − exchange process.

Conclusions
The objective of the present study was to describe quantitatively the mechanisms of Mo uptake by AFm, and to provide a geochemical model valid at both macroscopic (chemical) and molecular (crystallographic) scales. It was demonstrated that Mo, under the form of a tetrahedral MoO 4 2− complex, binds to AFm by replacing 2 Cl − in the interlayer mid-plane. The affinity constant was evaluated to K Mo = 10 1.3 . In addition, OH − competes with MoO 4 2− for sorption at the same sorption site, which also prevents MoO 4 2− accessing part of the AEC. Both these effects reduce the AFm sorption capacity toward Mo; thus, lowering the capacity of cement-based materials to buffer Mo.
Although this study focused on AFm, it should be remembered that this phase belongs to the LDH group of materials, which have been investigated intensively with regard to numerous applications that include depollution, industrial, and pharmacological processes. Batch and flow-through experiments, combined with geochemical data modeling and crystallographic characterization, appear powerful tools with which to investigate the exchange reactions occurring in layered materials. It is proposed that the present methodology could be generalized and extended to investigate other LDHs and/or exchangeable anions, which would enhance the understanding of the involved mechanisms and allow the determination of selectivity constants.

Methods
Analytical procedure. Solution analysis. The pH was monitored continuously (Fig. 1) using a Metrohm electrode connected to a Mettler Toledo pH meter, which was calibrated before each experiment. The solution collected at the output was divided in three aliquots. The first was used for Cl analysis using ion chromatography (Thermo-Dionex ICS3000; detection limits -dl = 0.5 mg L −1 ). The second and third aliquots were acidified using nitric acid (65% Suprapur ® ) and used respectively for determination of Ca, Na, and K concentrations using an ICP-AES (OPTIMA 5300 DV, Perkin Elmer; dl = 0.5 mg L −1 for all elements) and Al and Mo concentrations using an ICP-MS (NEXION 350X, Perkin Elmer; dl = 0.5 and 0.05 µg L −1 for Al and Mo, respectively).
Solid analysis. The leaching experiment was performed in an N 2 -filled glove box using various masses of synthesized AFm-Cl and ultrapure water (resistivity = 18.2 MΩ cm). The experiment lasted 10 min and the obtained solutions were then filtered using a 0.1-µm filter prior to analysis. An electron probe microanalyzer (EPMA) was used to determine the chemical composition after the flow-through experiments (CAMECA SX FIVE). Matrix corrections were performed using a ZAF program 63 .
High-energy X-ray diffraction data were collected at station CRISTAL from SOLEIL synchrotron (Orsay, France). The energy of the incident X-rays was 28 keV (λ = 0.4367 Å). Data were collected using an XPad hybrid pixel detector in the 1.5-130° 2θ range and processed using specific software 64 to obtain diffraction patterns. After subtraction of signal arising from the empty capillary, these patterns were processed further to produce X-ray pair-distribution function (PDF) data using PDFGetX3 65 and a q-range of 0.4-17 Å −1 . PDF data simulation was performed using PDFGui 66   Exchange reactions were implemented following the convention of Gaines and Thomas 69 . The exchange between the macroscopic sorption site (hereafter, AFm + ) and Cl − was assumed as a reference (arbitrary choice). Therefore, the logarithm of the selectivity constant (K Cl ) was set to zero: where Afm + is the exchanger and Cl − refers to the exchangeable anion. In addition, the exchange reaction between OH − and AFm + was also taken into account: Estimation of the logarithm of the selectivity constant (log K OH ) was obtained from the fitting of experimental data.
Finally, the exchange reaction between AFm + and MoO 4 2− was implemented as follows: The value of the selectivity constant (log K Mo ) was also fitted using experimental data.