Disordered Crystal Structure and Anomalously High Solubility of Radium Carbonate

Radium-226 carbonate was synthesized from radium–barium sulfate (226Ra0.76Ba0.24SO4) at room temperature and characterized by X-ray powder diffraction (XRPD) and extended X-ray absorption fine structure (EXAFS) techniques. XRPD revealed that fractional crystallization occurred and that two phases were formed—the major Ra-rich phase, Ra(Ba)CO3, and a minor Ba-rich phase, Ba(Ra)CO3, crystallizing in the orthorhombic space group Pnma (no. 62) that is isostructural with witherite (BaCO3) but with slightly larger unit cell dimensions. Direct-space ab initio modeling shows that the carbonate oxygens in the major Ra(Ba)CO3 phase are highly disordered. The solubility of the synthesized major Ra(Ba)CO3 phase was studied from under- and oversaturation at 25.1 °C as a function of ionic strength using NaCl as the supporting electrolyte. It was found that the decimal logarithm of the solubility product of Ra(Ba)CO3 at zero ionic strength (log10Ksp0) is −7.5(1) (2σ) (s = 0.05 g·L–1). This is significantly higher than the log10Ksp0 of witherite of −8.56 (s = 0.01 g·L–1), supporting the disordered nature of the major Ra(Ba)CO3 phase. The limited co-precipitation of Ra2+ within witherite, the significantly higher solubility of pure RaCO3 compared to witherite, and thermodynamic modeling show that the results obtained in this work for the major Ra(Ba)CO3 phase are also applicable to pure RaCO3. The refinement of the EXAFS data reveals that radium is coordinated by nine oxygens in a broad bond distance distribution with a mean Ra–O bond distance of 2.885(3) Å (1σ). The Ra–O bond distance gives an ionic radius of Ra2+ in a 9-fold coordination of 1.545(6) Å (1σ).


Methods
For the EXAFS study, approximately 0.2 mg of the synthesized radium-barium carbonate, in the form of a number of crystals clustered together, were placed between a few Kapton tape layers and carefully sealed ( Figure S1). Figure S1. Radium-barium carbonate sample measured via EXAFS

Models for activity coefficients computation
The Davies equation 1 can be used to calculate activity coefficients of an individual ion i at an ionic strength below approximately 0.3 mol·kg -1 : where zi is the charge of ion i, A is a temperature and solvent permittivity dependent constant which is equal to 0.5093 mol -0.5 ·L 0.5 for aqueous solutions at 25 °C and Im is the ionic strength in mol·kg -1 .
The specific ion interaction theory (SIT) developed by Brønsted 2-3 , Scatchard 4 and Guggenheim and Turgeon 5 can be used to calculate activity coefficients of an individual ion i at ionic strengths below approximately 3.5 mol·kg -1 : where DH is the Debye-Hückel term, ε(i, j, Im) is the interaction coefficient of ion i with all oppositely charged ions j and mj is the molal concentration of ion j. The Debye-Hückel term is defined as: where B is the temperature and solvent permittivity dependent constant and a is the distance of closest approach, which is the minimal distance at which two ions can approach each other. The where ε1(i, j, Im) and ε2(i, j, Im) are the first and second interaction coefficient of ion i with all oppositely charged ions j respectively.

Adaptation of the extended ion interaction theory
The solubility reaction for solid RaCO3 is given by the equilibrium reaction: The equilibrium solubility product constant at infinite dilution for reaction (5) can be calculated using the following equation: The concentration of Na2CO3 was 100 mM·L -1 for all oversaturation samples and was much lower compared to the total ionic strength of the NaCl electrolyte. Therefore, it can be assumed that Na2CO3 had a small contribution to the ionic medium and ion interactions of the carbonate ion with all positively charged ions was minimal [8][9][10] . There is agreement in the literature that the alkaline-earth metal ions form complexes with carbonate ions in aqueous media [11][12] : Therefore, in the case of the oversaturation samples, the total measured Ra 2+ concentration will be equal to the sum of the free Ra 2+ and RaCO3(aq). The equilibrium constant at infinite dilution for the reaction (7) is: Combination of Eqs 6 and 8 gives: assuming that RaCO 3 is equal to unity.
As is shown in Eq. 9 and in the literature 13  Therefore, the total measured radium concentration was corrected for RaCO3(aq) using the following equation: There is evidence that the sodium ion forms a weak ion pair with the carbonate ion in aqueous media 15-27 : Consequently, in the case of the oversaturation samples, the total CO3 2concentration will be equal to the sum of the free CO3 2and NaCO3 -. The equilibrium constant at infinite dilution for reaction (11) is: As shown in Eq. 12, the concentration of NaCO3can be expressed as a product of its apparent stability constant and free sodium and carbonate concentrations. The concentration of the free carbonate ion can be calculated as: The concentration of Na + (background electrolyte) was much higher (more than 90 % of all ionic strength) than the concentration of Na2CO3 in all oversaturation samples. Therefore, it can be assumed that the concentration of the free Na + is constant and equal to the ionic strength.
The apparent stability constant for the NaCO3ion pair can be obtained both from the literature and in a non-linear regression: S4 where ∆ε1 (or ∆ε2) is equal to: The solubility product constant of RaCO3 at zero ionic strength (Eq. 6) and associated ion interaction coefficients can be obtained via non-linear regression: where Ksp apparent is the product of the free radium (Eq. 10) and free carbonate (Eq. 13) concentrations and ∆εn (∆ε1 or ∆ε2) are equal to: with n equal to 1 or 2.

Attempt to solve the crystal structure of Ra(Ba)CO3
The best outcome of the attempts to solve the crystal structure of the major cubic Ra(Ba)CO3 phase was a model consisting of one radium atom and a carbonate ion modelled with the Avogadro software 28 and fed into FOX software 29 as a rigid molecular unit. These two objects were randomly placed and adjusted in a Monte Carlo procedure to obtain an optimal fit between the observed data and the data calculated from the present model. A dynamic occupancy correction was used for modelling the close contact and overlap of different atoms. The resulting final model showed enormous disorder features. Structural disorder in the major cubic Ra(Ba)CO3 phase results in a higher symmetry of the unit. A low symmetry cubic space group, F23 (no. 196), was used to not impose any additional restraints than cubic symmetry. It must be emphasized that it is hardly possible to estimate the space group with complete certainty for a sample with as few peaks as the phase investigated because of the small sample size and also the small unit cell size. However, only four formula units are required to fill the unit cell, thus it can be modelled acceptably using the cubic F23 space group.
Rietveld refinement of the major cubic Ra(Ba)CO3 crystal structure modelled in FOX was made using the Fullprof software package 30 . Soft constraints were applied to the carbonate ion to approximately maintain its triangular shape. An overall isotropic displacement parameter was used, and the occupation parameters were allowed to be refined. Rietveld refinement profile and parameters are shown in Fig. S2 and Table S1, respectively.  The final (best) RBragg value was 9.7 %, calculated from the part of the pattern close to the calculated peaks. Including all peaks gives slightly higher residual values. As can be seen from the Rietveld profile ( Figure S2), several weak peaks are present in the pattern, except for those derived from the cubic unit cell. These are most likely related to witherite, or similar structures but this conclusion cannot be easily reached. The arrangement of carbonate ions around radium(II) in radium carbonate and its electron density map are shown in Figures S3 and S4, respectively.