Recrystallization and Uptake of 226 Ra into Ba-Rich (Ba,Sr)SO 4 Solid Solutions

: 226 Ra is an important contributor to naturally occurring radioactive materials (NORM) and also considered in safety cases related to the disposal of spent nuclear fuel in a deep geological repository. Recrystallization and solid solution formation with sulfates is regarded as an important retention mechanism for 226 Ra. In natural systems sulfates often occur as (Ba,Sr)SO 4 . Therefore, we have chosen this solid solution at the Ba-rich end for investigations of the 226 Ra uptake. The resulting 226 Ra-solubility in aqueous solution was assessed in comparison with a thermodynamic model of the solid solution-aqueous solution system (Ba,Sr,Ra)SO 4 + H 2 O. The temperature and composition of the initial (Ba,Sr)SO 4 solid solution were varied. Measurements of the solution composition were combined with microscopic observations of the solid and thermodynamic modeling. A complex recrystallization behavior of the solid was observed, including the dissolution of signiﬁcant amounts of the solid and formation of metastable phases. The re-equilibration of Ba-rich (Ba,Sr)SO 4 to (Ba,Sr,Ra)SO 4 leads to a major reconstruction of the solid. Already trace amounts of Sr in the solid solution can have a signiﬁcant impact on the 226 Ra solubility, depending on the temperature. The experimental ﬁndings conﬁrm the thermodynamic model, although not all solids reached equilibrium with respect to all cations.


Introduction
The fate of 226 Ra is relevant to a number of environmental questions, mainly due to the fact that it is one of the main contributors to naturally occurring radioactive materials (NORM). 226 Ra containing NORM appears in many raw material production processes e.g., phosphate industry, unconventional gas production, geothermal energy production, and oil extraction [1][2][3][4][5][6]. 226 Ra is also considered as a relevant radionuclide in safety cases that are prepared for the deep geological disposal of high-level nuclear waste [7][8][9]. There, it will occur as a fission product of the 238 U decay chain and may dominate the dose after about 100,000 years.
The migration of radionuclides in the geosphere is, to a large extent, controlled by sorption processes onto minerals and colloids. On a molecular level, sorption phenomena involve surface complexation, ion exchange as well as co-precipitation reactions. Co-precipitation can lead to the formation of solid solutions in which the radionuclides are structurally incorporated in a host structure [6,8,10]. Such solid solutions are ubiquitous in natural systems-most minerals in nature are mixtures of elements on the molecular scale rather than pure compounds. Recent studies [11][12][13][14][15][16][17][18] have shown that the formation of a (Ba,Ra)SO 4 solid solution significantly reduces the solubility of 226 Ra in aqueous systems. Rapid uptake via co-precipitation [11][12][13] as well as the slower recrystallization The grain size was adjusted to 20-63 µm by grinding and sieving. The chemical homogeneity and morphology of the initial solid solution particles is shown in the back-scatter electron (BSE) image of Figure 1. In order to allow for comparison, the preparation of the solids as well as the general set-up of the recrystallization experiments were adopted from earlier studies (e.g., [17,25]). 0.01 or 0.1 g of solid were added to 10 mL of a 0.2 mol/kg NaCl solution in 25 mL glass vessels. The particles were pre-equilibrated for four weeks at 23 ± 2 • C before the start of the actual experiments to avoid high energy surface sites and ultrafine particles. Long-term batch recrystallization experiments running 664 days were performed at 90 °C, 70 °C and ambient conditions (23 ± 2 °C). 10 mL of tracer solution were added to 10 mL of the pre-equilibrated suspension, resulting in solid/liquid ratios (S/L) of 0.5 g/kg and 5.0 g/kg, respectively, and an ionic strength I = 0.1 mol/kg NaCl. For the same type of glass vessels, in earlier Long-term batch recrystallization experiments running 664 days were performed at 90 • C, 70 • C and ambient conditions (23 ± 2 • C). 10 mL of tracer solution were added to 10 mL of the pre-equilibrated suspension, resulting in solid/liquid ratios (S/L) of 0.5 g/kg and 5.0 g/kg, respectively, and an ionic strength I = 0.1 mol/kg NaCl. For the same type of glass vessels, in earlier experiments no measurable wall adsorption of 226 Ra was detected. All recrystallization experiments were started from a concentration of c(Ra) = 5.5 ± 0.5 × 10 −6 mol/kg 226 RaBr 2 . A summary of the experiments is provided in Table 2.  After a settling time of 1 h, samples of 500 µL of the aqueous solution were taken at the same time intervals for all experiments. The settling time was required for cooling and handling of the radioactive solutions at 70 • C and 90 • C. Based on the experience of Klinkenberg et al., 2018 [25], this is a much shorter time than required for barite and 226 Ra to re-equilibrate to the lower temperature. The solution samples were filtered through Advantec ultrafilters (Molecular weight cut-off (MWCO) = 10,000 Da) to avoid possible colloids or fine particles without measurable adsorption of 226 Ra at the given filtered solution amount. This procedure was tested in earlier studies [14,15]. Parallel recrystallization experiments without 226 Ra were carried out as reference.
A N 2 cooled high-purity (HP) Ge-detector was used for the quantification of the 226 Ra concentration at the characteristic 186 keV γpeak of 226 Ra. The Sr and Ba concentrations in solution were quantified using an ICP-MS ELAN 6100 DRC (PerkinElmer SCIEX, Waltham, MA, USA) instrument. The filtered solution was diluted in 0.1 m HNO 3 by 1:1000 for Ba and 1:10,000 for Sr-measurements.
Small amounts of solid (10 µL of the suspension) were sampled at selected sampling times from the settled particles of the recrystallization experiments. The evolution of the crystal morphology and chemical composition were studied using SEM combined with EDX. In order to avoid artefacts due to precipitation of e.g., NaCl, SrSO 4 or RaSO 4 , the samples were separated from their solution by two washing steps in iso-propanol. The samples were then prepared as a suspension on a Cu holder and subsequently dried.
Thermodynamic calculations were carried out to compare theoretical predictions based on a thermodynamic model for the SS-AS system (Ba,Sr,Ra)SO 4 + H 2 O with the experimental results. The thermodynamic model derived in   [23] and refined in Klinkenberg (2019) [25] was used for the calculation of the total equilibrium between the solid and aqueous phase.
In the case of SS-AS systems, not only do the activities of ions in solution but also of the components of the solid need to be considered. In contrast to pure phases, in SS-AS systems the solution composition is not independent of the amount of solid. For SS-AS equilibria, the solution composition is also linked to the composition of the solid. Gibbs energy minimization approaches implemented in the GEMS3K solver (http://gems.web.psi.ch/GEMS3K) and described in Kulik et al. (2013) [28] were applied to calculate the solid solution composition as well as the aqueous solution equilibria at 23 • C, 70 • C and 90 • C. The equilibria were calculated assuming full equilibration of all (Ba,Sr)SO 4 with 226 Ra in solution. The activity coefficients for all dissolved species (γ j ) were calculated according to the extended Debye-Hückel equation [29]. Thermodynamic data for aqueous species were taken from the PSI-Nagra database [30] integrated in GEMS that inherits temperature and pressure dependencies for most aqueous ions and complexes from the Helgeson-Kirkham-flowers equation of state (HKF EoS) [29] as given in the SUPCRT92 database (http://gems.web.psi.ch/TDB). Interaction parameters for the ternary (Ba,Sr,Ra)SO 4 + H 2 O SS-AS system were taken from Klinkenberg et al. (2018) [25].

The Evolution of the 226 Ra Concentration over Time
Distinct differences with respect to the evolution of the 226 Ra concentrations in solution were observed, depending on the composition of the original solid solution ( Figure 2). Qualitatively, all experiments follow the trend predicted by the thermodynamic modelling, i.e., the highest uptake of 226 Ra is observed at X SrSO4 = 29 mol% in the initial solid solution. The kinetics of the 226 Ra uptake also follow a trend according to X SrSO4 of the initial solid solution, with a slower uptake at low initial X SrSO4 and an increasing uptake rate from 17 mol% to 29 mol%.
In particular, the combination of low temperature (23 • C) and a low initial X SrSO4 keeps the 226 Ra concentration in solution almost on the original level for more than 100 days. Compared to pure BaSO 4, the 226 Ra uptake is slightly slower in the case of X SrSO4 = 5 mol% and faster at higher X SrSO4 of the original solid solution (Figure 2). At 70 • C and 90 • C, the 226 Ra concentration in solution has a minimum below the predicted equilibrium concentration before equilibrium is approached at later stages of the experiment. This is likely to be a kinetic effect which leads to the metastable "entrapment" of a surplus of 226 Ra due to a relatively high uptake rate. This effect was also observed with 226 Ra uptake into pure barite in earlier studies [31]. In addition to temperature, the S/L has an effect on the uptake kinetics, resulting in higher 226 Ra uptake rate at 90 • C and S/L = 5 g/kg ( Figure 3) in comparison to 0.5 g/kg.
Minerals 2020, 10, x FOR PEER REVIEW 5 of 29 effect on the uptake kinetics, resulting in higher 226 Ra uptake rate at 90 °C and S/L = 5 g/kg ( Figure 3) in comparison to 0.5 g/kg. Within 100 days, the majority of the recrystallization experiments reach a plateau of the 226 Ra concentrations which is close to the predicted equilibrium (lines in Figure 2). At 23 °C and S/L = 0.5 g/kg, the effect of Sr added to the SS-AS system results in a significant decrease of the Ra solubility.  [24,31]. The grey dotted line in the c(Sr) vs. time plot refer to the solubility of pure SrSO 4 , and to pure BaSO 4 in the other two plots. Data are given in the Appendix A Tables A1-A20. The thermodynamic predictions (lines) are based on [23,25]. 226 Ra-solubilities for the respective experiments become more similar with increasing temperatures of 70 °C and 90 °C. This is also experimentally observed for the final 226 Ra concentrations in this study. At 90 °C, the observed and predicted differences of the 226 Ra solubility between the different solid solutions and pure BaSO4 are small and within the experimental error (Figure 2). At 90 °C and S/L = 5 g/kg, the predicted results of the 226 Ra solubility as well as the experimental results are almost independent from the original XSrSO4 of the solid solution ( Figure 3).

The Evolution of Ba and Sr Concentrations over Time
As shown in Figure 2, the presence of 226 Ra has a rather small impact on the calculated equilibrium concentrations of Ba and Sr in solution. The predicted Ba-solubility at all temperatures decreases in the order from Ba-rich to Ba-poor original solid solutions whereas the Sr-solubility increases from Sr-rich to Sr-poor original solid solutions. Therefore, the final predicted solids are much more similar to each other in composition than the original solid solutions before re-equilibration (Table 3). Due to the high proportion of total (Ba + Sr) compared to the amount of 226 Ra added to the respective experiment, the predictions for the Ba and Sr solubility after recrystallization are very similar for corresponding 226 Ra-free reference experiments and the 226 Ra-recystallization experiments.
A comparison of the experimental results and predicted equilibrium indicates Ba to be supersaturated in the aqueous solution at the beginning of all experiments. The concentration of Sr in solution starts from values well below the predicted equilibrium and usually approaches equilibrium later than Ba. After 200 to 400 days, in most of the experiments the concentrations of Sr and Ba are close to or at the predicted equilibrium ( Figure 2). The kinetic behavior of the (Ba,Sr)SO4 recrystallization is more or less independent of the presence of 226 Ra. In the series of 226 Ra free reference experiments, the experiment with XSrO4 = 5 mol% is an exception because the concentration of Sr in solution in particular stays well below the predicted equilibrium, and at 23 °C the Ba concentration stays higher than predicted-similar to the corresponding 226 Ra recrystallization experiment. Within 100 days, the majority of the recrystallization experiments reach a plateau of the 226 Ra concentrations which is close to the predicted equilibrium (lines in Figure 2). At 23 • C and S/L = 0.5 g/kg, the effect of Sr added to the SS-AS system results in a significant decrease of the Ra solubility. Compared to pure BaSO 4 this decrease can be up to one order of magnitude. The predicted 226 Ra-solubilities for the respective experiments become more similar with increasing temperatures of 70 • C and 90 • C. This is also experimentally observed for the final 226 Ra concentrations in this study. At 90 • C, the observed and predicted differences of the 226 Ra solubility between the different solid solutions and pure BaSO 4 are small and within the experimental error ( Figure 2). At 90 • C and S/L = 5 g/kg, the predicted results of the 226 Ra solubility as well as the experimental results are almost independent from the original X SrSO4 of the solid solution ( Figure 3).

The Evolution of Ba and Sr Concentrations over Time
As shown in Figure 2, the presence of 226 Ra has a rather small impact on the calculated equilibrium concentrations of Ba and Sr in solution. The predicted Ba-solubility at all temperatures decreases in the order from Ba-rich to Ba-poor original solid solutions whereas the Sr-solubility increases from Sr-rich to Sr-poor original solid solutions. Therefore, the final predicted solids are much more similar to each other in composition than the original solid solutions before re-equilibration (Table 3). Due to the high proportion of total (Ba + Sr) compared to the amount of 226 Ra added to the respective experiment, the predictions for the Ba and Sr solubility after recrystallization are very similar for corresponding 226 Ra-free reference experiments and the 226 Ra-recystallization experiments.
A comparison of the experimental results and predicted equilibrium indicates Ba to be supersaturated in the aqueous solution at the beginning of all experiments. The concentration of Sr in solution starts from values well below the predicted equilibrium and usually approaches equilibrium later than Ba. After 200 to 400 days, in most of the experiments the concentrations of Sr and Ba are close to or at the predicted equilibrium ( Figure 2). The kinetic behavior of the (Ba,Sr)SO 4 recrystallization is more or less independent of the presence of 226 Ra. In the series of 226 Ra free reference experiments, the experiment with X SrO4 = 5 mol% is an exception because the concentration of Sr in solution in particular stays well below the predicted equilibrium, and at 23 • C the Ba concentration stays higher than predicted-similar to the corresponding 226 Ra recrystallization experiment. Table 3. Calculated equilibrium compositions of solid solutions after total equilibration of the system (X for mole fraction).

Chemical and Microstructural Evolution of the Solid
The solid composition corresponding to the respective aqueous solution of each experiment at a given time is accessible in two independent ways, (1) via mass balance between original solid composition and solution at a given time and (2) via microchemical (SEM-EDX) analyses of individual particles. While (1) indicates the general evolution of the system, (2) can be used to evaluate the variation of particle morphology, composition and homogeneity during the approach to equilibrium. Based on the results in 3.2, three extreme examples are discussed here: (1) X SrSO4 = 5 mol%, 23 • C, S/L = 0.5 g/kg, slow macroscopic recrystallization kinetics; (2) X SrSO4 = 29 mol%, 23 • C, S/L = 0.5 g/kg, fast macroscopic recrystallization kinetics and 226 Ra entrapment; (3) X SrSO4 = 5 mol%, 90 • C, 5 g/kg, fast macroscopic recrystallization kinetics, no entrapment of 226 Ra.
The evolution of the average particle composition (mass balance) versus the 226 Ra concentration in solution for the three examples is depicted in Figure 4. Starting at the initial 226 Ra concentration of ca. 5.5 × 10 −6 mol/kg (broken line in Figure 4), 226 Ra in solution drops up to three orders of magnitude while X SrSO4 stays more or less constant. At 23 • C, the calculated average X SrSO4 stays constant for the (Ba 0.95 Sr 0.05 )SO 4 solid solution during the complete experiment, and more than 42 days for (Ba 0.71 Sr 0.29 )SO 4 (arrows in Figure 4a). In the recrystallization experiment with 5 g/kg (Ba 0.95 Sr 0.05 )SO 4 and 90 • C, already after 42 days the concentration of 226   For the solids of this study, mainly Sr and Ba can be quantified by EDX whereas 226 Ra can only be quantified with this method at local concentrations of more than 0.5 at%. Depending on the chemical and morphological variability, between 5 and 25 EDX spot measurements were carried out on each powder sample. The best match between the average compositions obtained via EDX and mass balance for a given sampling time were observed at the end of the experiments. Here, the average XSrSO4 and XBaSO4 obtained by both methods agree within experimental error (Table 4). However, the XSrSO4 still deviates significantly from the calculated equilibrium. A trend in the temporal evolution towards the equilibrium composition is visible in Table 4 and Figure 4 and discussed in more detail in Section 4.
The XSrSO4 of individual particles as well as their morphology were analyzed as a function of time. For experiment (Ba0.95Sr0.05)SO4_0.5 g/kg_RT, during the first 98 days the grain morphology remained almost unchanged. Steps on the surface due to cleavage during sample preparation were still visible at day 98 ( Figure 5). The chemical composition of the particles at a given sampling time in this series was quite variable until the end of this experiment, with a range of XSrSO4 between 0.4 and 9.8 mol% (Table A21).
The morphology of the particles taken from experiment (Ba0.71Sr0.29)SO4_0.5 g/kg_RT changed after day 1 as large cavities occurred. At day 42 and 98, new smooth surfaces were visible in some areas whereas the cavities appeared to become smaller ( Figure 5). Coatings were typical on some surfaces whereas other surfaces were interrupted by cavities. Some particles still contained almost 2/3 of the original SrSO4. The early morphological evolution over time of the particles taken from experiment (Ba0.71Sr0.29)SO4_5 g/kg_90 was similar to (Ba0.71Sr0.29)SO4_0.5 g/kg_RT, just faster. The grains lost their cavities and developed smooth, well defined surfaces with time. Simultaneously to the morphological evolution, the XSrSO4 shifted towards lower values. However, even at the end of the experiments, the particles were not homogeneous but Sr-rich and Sr-poor zones in individual particles were observed ( Figure 5, spots 4 and 5). For the solids of this study, mainly Sr and Ba can be quantified by EDX whereas 226 Ra can only be quantified with this method at local concentrations of more than 0.5 at%. Depending on the chemical and morphological variability, between 5 and 25 EDX spot measurements were carried out on each powder sample. The best match between the average compositions obtained via EDX and mass balance for a given sampling time were observed at the end of the experiments. Here, the average X SrSO4 and X BaSO4 obtained by both methods agree within experimental error (Table 4). However, the X SrSO4 still deviates significantly from the calculated equilibrium. A trend in the temporal evolution towards the equilibrium composition is visible in Table 4 and Figure 4 and discussed in more detail in Section 4.
The X SrSO4 of individual particles as well as their morphology were analyzed as a function of time. For experiment (Ba 0.95 Sr 0.05 )SO 4 _0.5 g/kg_RT, during the first 98 days the grain morphology remained almost unchanged. Steps on the surface due to cleavage during sample preparation were still visible at day 98 ( Figure 5). The chemical composition of the particles at a given sampling time in this series was quite variable until the end of this experiment, with a range of X SrSO4 between 0.4 and 9.8 mol% (Table A21).
The morphology of the particles taken from experiment (Ba 0.71 Sr 0.29 )SO 4 _0.5 g/kg_RT changed after day 1 as large cavities occurred. At day 42 and 98, new smooth surfaces were visible in some areas whereas the cavities appeared to become smaller ( Figure 5). Coatings were typical on some surfaces whereas other surfaces were interrupted by cavities. Some particles still contained almost 2/3 of the original SrSO 4 . The early morphological evolution over time of the particles taken from experiment (Ba 0.71 Sr 0.29 )SO 4 _5 g/kg_90 was similar to (Ba 0.71 Sr 0.29 )SO 4 _0.5 g/kg_RT, just faster. The grains lost their cavities and developed smooth, well defined surfaces with time. Simultaneously to the morphological evolution, the X SrSO4 shifted towards lower values. However, even at the end of the experiments, the particles were not homogeneous but Sr-rich and Sr-poor zones in individual particles were observed ( Figure 5, spots 4 and 5). In addition to the differences in the morphological evolution with time, also the chemical homogeneity and local enrichment of 226 Ra varied among the experimental series. The 226 Ra uptake for experiment (Ba 0.95 Sr 0.05 )SO 4 _0.5 g/kg_RT was mainly homogenous-only a small number of EDX spectra detected an enrichment of 226 Ra. Only at the end of this experiment, some areas showed a significant 226 Ra enrichment (spot 1 of Figure 5, Table A21). 226 Ra-rich areas were detected on some particles, often small particles associated with the surfaces of larger particles. At higher X SrSO4 and 23 • C, already at the beginning 226 Ra-rich areas in some particles were observed (Table A22; spot 2 in Figure 5). The surfaces appeared to be covered by Ba-Ra-rich coatings (spot 3 in Figure 5). In experiment (Ba 0.71 Sr 0.29 )SO 4 _5 g/kg_90, between day 1 and day 98 226 Ra was detected in significant amounts in the solid phase, usually associated with higher X BaSO4 as well. A complete homogenization of the solid was not observed in any experiment.

Effect of XSrSO4 upon the Solubility of 226 Ra
The theoretically derived thermodynamic model for the SS-AS system (Ba,Sr,Ra)SO4 of Vinograd et al. (2018) [23] predicts a significant impact of the mole fraction XSrSO4 upon the solubility of 226 Ra. Depending on temperature, the 226 Ra solubility is expected to vary up to several orders of magnitude in the range of XSrSO4 between 0 and 10 mol%. According to the model, the re-equilibration of Ba-rich (Ba,Sr)SO4 to (Ba,Sr,Ra)SO4 requires a major reconstruction of the solid. In order to reach equilibrium, a large fraction of more than 95 mol% of the Sr formerly present in the Figure 5. SEM micrographs of representative particles taken from recrystallization experiments with X SrSO4 = 5 mol%, 23 • C, 0.5 g/kg, X SrSO4 = 29 mol%, 23 • C, 0.5 g/kg, and X SrSO4 = 5 mol%, 90 • C, 5 g/kg. The numbered spots marked with (*1, *2, *3, *4, *5) represent the areas where EDX analyses were taken (Tables A21-A23).

Effect of X SrSO4 upon the Solubility of 226 Ra
The theoretically derived thermodynamic model for the SS-AS system (Ba,Sr,Ra)SO 4 of Vinograd et al. (2018) [23] predicts a significant impact of the mole fraction X SrSO4 upon the solubility of 226 Ra. Depending on temperature, the 226 Ra solubility is expected to vary up to several orders of magnitude in the range of X SrSO4 between 0 and 10 mol%. According to the model, the re-equilibration of Ba-rich (Ba,Sr)SO 4 to (Ba,Sr,Ra)SO 4 requires a major reconstruction of the solid. In order to reach equilibrium, a large fraction of more than 95 mol% of the Sr formerly present in the solid needs to be released into the aqueous solution while 226 Ra is taken up. At the same time they indicate that already trace amounts of Sr in the solid solution can have a significant impact on the 226 Ra solubility if the solid solution is in full equilibrium with the aqueous solution. According to these calculations, this impact depends on temperature as well, i.e., at 23 • C the differences between the 226 Ra solubilities are more pronounced than at 70 • C or 90 • C.
On the macroscopic side, the experimental findings are coherent with the thermodynamic model. In particular, the plateau of the final c( 226 Ra) in solution was close to the predicted equilibrium. The final Ba and Sr concentrations in solution approached equilibrium, but especially Sr in solution deviated significantly from the prediction in some of the experiments, indicating that these were still not at equilibrium ( Figure 6). Within the duration of the experiments at 23 • C, X SrSO4 was not completely adjusted to equilibrium in any solid. In particular, the experiments with only 5 mol% SrSO 4 in the initial solid solution didn't reach equilibrium, but at high temperature and high S/L the deviation for the same initial solid solution composition became small, close to the experimental error (Figure 6b). On the macroscopic side, the experimental findings are coherent with the thermodynamic model. In particular, the plateau of the final c( 226 Ra) in solution was close to the predicted equilibrium. The final Ba and Sr concentrations in solution approached equilibrium, but especially Sr in solution deviated significantly from the prediction in some of the experiments, indicating that these were still not at equilibrium (Figure 6). Within the duration of the experiments at 23 °C, XSrSO4 was not completely adjusted to equilibrium in any solid. In particular, the experiments with only 5 mol% SrSO4 in the initial solid solution didn't reach equilibrium, but at high temperature and high S/L the deviation for the same initial solid solution composition became small, close to the experimental error (Figure 6b).

Kinetics of the Recrystallization from (Ba,Sr)SO4 to (Ba,Sr,Ra)SO4
The SS-AS system is dominated by the re-equilibration of (Ba,Sr)SO4. All three original (Ba,Sr)SO4 solid solutions need to release only a very low proportion of total BaSO4 from the solid to reach the predicted equilibrium solution composition, i.e., dissolution at the surface is sufficient to fulfill this condition. On the other hand, more than 97 mol% of the SrSO4 originally present in the solid solutions of this study would need to be released from the solid into the aqueous solution in order to reach equilibrium. Taking into account the amount to be released from the solid, SrSO4 may be more accessible to dissolution at the particle surfaces in the case of higher XSrSO4, and therefore equilibrium may be reached earlier. Brandt et al., 2018 [32] have shown that in certain combinations of S/L and temperature, Sraq can inhibit the recrystallization of BaSO4 and the uptake of 226 Ra. Therefore, at 23 °C and low XSrSO4 the system may behave similar to pure BaSO4, and the presence of Sr in solution may thus slow down the kinetics of recrystallization. The solid solution with initially only XSrSO4 = 5%, recrystallized at 23 °C, appeared to undergo very little change of XSrSO4 with time (Figure 6a). A higher XSrSO4 of the original solid solution lead to faster 226 Ra uptake kinetics, and in some cases even to a minimum of the 226 Ra concentration, which was attributed to a kinetic "entrapment" effect. The faster re-equilibration correlated with the higher solubility of SrSO4 compared to the other two sulfates.
For a given composition, 226 Ra appeared to be adjusted more or less independent of Sr. As soon as 226 Ra was structurally taken up, the concentration in solution dropped by several orders of magnitude whereas the re-structuring of the solid towards a full equilibrium required several steps

Kinetics of the Recrystallization from (Ba,Sr)SO 4 to (Ba,Sr,Ra)SO 4
The SS-AS system is dominated by the re-equilibration of (Ba,Sr)SO 4 . All three original (Ba,Sr)SO 4 solid solutions need to release only a very low proportion of total BaSO 4 from the solid to reach the predicted equilibrium solution composition, i.e., dissolution at the surface is sufficient to fulfill this condition. On the other hand, more than 97 mol% of the SrSO 4 originally present in the solid solutions of this study would need to be released from the solid into the aqueous solution in order to reach equilibrium. Taking into account the amount to be released from the solid, SrSO 4 may be more accessible to dissolution at the particle surfaces in the case of higher X SrSO4 , and therefore equilibrium may be reached earlier. Brandt et al., 2018 [32] have shown that in certain combinations of S/L and temperature, Sr aq can inhibit the recrystallization of BaSO 4 and the uptake of 226 Ra. Therefore, at 23 • C and low X SrSO4 the system may behave similar to pure BaSO 4 , and the presence of Sr in solution may thus slow down the kinetics of recrystallization. The solid solution with initially only X SrSO4 = 5%, recrystallized at 23 • C, appeared to undergo very little change of X SrSO4 with time (Figure 6a). A higher X SrSO4 of the original solid solution lead to faster 226 Ra uptake kinetics, and in some cases even to a minimum of the 226 Ra concentration, which was attributed to a kinetic "entrapment" effect. The faster re-equilibration correlated with the higher solubility of SrSO 4 compared to the other two sulfates.
For a given composition, 226 Ra appeared to be adjusted more or less independent of Sr. As soon as 226 Ra was structurally taken up, the concentration in solution dropped by several orders of magnitude whereas the re-structuring of the solid towards a full equilibrium required several steps of dissolution and re-precipitation as microscopically observed. Microscopically, the recrystallization of the binary (Ba,Sr)SO 4 solid solution to (Ba,Sr,Ra)SO 4 is a complex process that is clearly different from the replacement reaction observed for the formation of (Ba,Ra)SO 4 from barite [31]. Instead, the re-equilibration lead to similar features as observed in earlier studies on the reaction of SrSO 4 with Ba in solution [33] and on the recrystallization of Sr-rich (Sr,Ba)SO 4 in the presence of 226 Ra [25]. Rims of newly formed phases were observed on the original particles. The original particles dissolved partially, leaving large cavities in the original grains of some experiments presented here. Already, at the beginning of the experiments with high X SrSO4 in the original solid solution, or at high temperature and solid/liquid ratio, theses cavities indicate a significant dissolution. Later on, the particles of the experiment with higher X SrSO4 changed in their morphology and new smooth surfaces became visible in some areas whereas the cavities appeared to become smaller. In some areas, an idiomorphic habitus occurred. However, even at day 664 the morphology and also X SrSO4 were still not at equilibrium ( Figure 6). In many cases, the particles remained chemically heterogeneous. Simultaneously to the morphological evolution, the X SrSO4 changed, with X SrSO4 in some measurements even below the predicted equilibrium. Therefore, the grain morphology apparently followed the macroscopically observed recrystallization kinetics.
At slow recrystallization rates as observed for experiment (Ba 0.95 Sr 0.05 )SO 4 _0.5 g/kg_RT, during the first 98 days the grain morphology remained almost unchanged. Here, the cavities which were observed early on in the other experiments occurred at the end of the experiment.

Conclusions
The newly derived thermodynamic model for the SS-AS system (Ba,Sr,Ra)SO 4 + H 2 O [23,25] was tested in recrystallization experiments at the Ba-rich corner. In contrast to pure barite, in the ternary system significant dissolution and neo-formation of particles with a more ideal particle morphology occurs. A simultaneous evolution of the grain morphology and the X SrSO4 was observed. After 664 days, many experiments reach a partial equilibrium with c( 226 Ra) already close to the predicted values. Most experiments approach the predicted equilibrium concentrations of Ba and Sr, but only the experiments with high X SrSO4 in the original solid reached the predicted equilibrium within the duration of the experiments.
In conclusion, the trends predicted by the thermodynamic model of

Funding:
The research leading to these results has received partial funding from the German Federal Ministry of Education and Research (BMBF) ThermAc3 project (project number 02NUK039D).   Table A21. Temporal evolution of the solid composition analyzed by EDX of (Ba 0.95 Sr 0.05 )SO 4 _0.5 g/kg_RT. Superscript numbers indicate spot measurements in Figure 5.   Table A23. Temporal evolution of the solid composition analyzed by EDX of (Ba 0.95 Sr 0.05 )SO 4 _5 g/kg_90. Superscript numbers indicate spot measurements in Figure 5.