Disordered Crystal Structure and Anomalously High Solubility of Radium Carbonate

Abstract

Radium-226 carbonate was synthesized from radium–barium sulfate (²²⁶Ra_0.76Ba_0.24SO₄) 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 (log₁₀K_sp⁰) is −7.5(1) (2σ) (s = 0.05 g·L^–1). This is significantly higher than the log₁₀K_sp⁰ 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).

Short abstract

XRD measurements of RaCO₃ revealed that it is not isostructural with witherite, and direct-space ab initio modeling showed that the carbonate oxygens are highly disordered. It was found that the solubility of RaCO₃ is unexpectedly higher than the solubility of witherite (log₁₀K_sp⁰ = −7.5 and −8.56, respectively), supporting the disordered nature of RaCO₃. EXAFS data revealed an ionic radius of Ra²⁺ of 1.55 Å. Radium is the only alkaline-earth metal which forms disordered crystals in its carbonate phase.

1. Introduction

Radium is the heaviest alkaline-earth metal and has no stable isotopes. It occurs in the earth’s crust in only trace quantities (≈1 pg·g^–1)¹ as part of the ²³⁸U, ²³⁵U, and ²³²Th radioactive decay series. The most long-lived and abundant radium isotope is ²²⁶Ra with a half-life of 1600 years. Radium is among the most radiotoxic elements,² and if ingested, it follows similar pathways to calcium and concentrates mostly in bones and bone marrow and can cause bone sarcoma.³ The decay chain of ²²⁶Ra includes many alpha-, beta-, and gamma-emitting short-lived radionuclides, and dose rates even from milligram quantities of radium are significant. Moreover, ²²⁶Ra decays to the radioactive noble gas radon, ²²²Rn (t_1/2 = 3.82 days), which is also an alpha-emitter. Handling of volatile alpha emitters requires rigorous safety precautions, and as a result, experimental work even with small quantities of radium compounds is challenging, as is the case for other highly radioactive elements.^4,5

The high radiotoxicity of radium and its decay products requires an understanding of its migration in the environment from technologically enhanced naturally occurring radioactive materials. Moreover, in 2013, a ²²³Ra²⁺ (t_1/2 = 11.43 days) saline solution (trademark Xofigo^©) was approved by the U.S. Food and Drug Administration and later by the European Medicines Agency for treatment of patients with castration-resistant prostate carcinomas, symptomatic bone metastases, and no known visceral metastatic disease. To date, ²²³Ra²⁺ saline solution is the first and only approved radiopharmaceutical for targeted alpha therapy, but other radiopharmaceuticals with radium, for example, CaCO₃ microparticles radiolabeled with ²²⁴Ra (t_1/2 = 3.63 days), are under development for local therapy of disseminated cancers and are undergoing clinical trials.^6,7

Knowledge of the fundamental chemical properties of radium is required to understand its behavior in the environment and to exploit the therapeutic potential of radium in metastatic disease treatment. However, its chemistry remains unexplored compared with the other non-radioactive alkaline-earth metals due to the extreme rarity of radium as a laboratory material and its highly radioactive nature.⁸ For example, the paper by Shannon⁹ is considered one of the most comprehensive and accurate set of ionic radii; however, it includes ionic radii for radium only in 8- and 12-fold coordination but not in 9-fold. Moreover, all radium radii were estimated by Shannon⁹ from plots of ionic radii (r³) against unit cell volume (V) of isostructural series assuming that the relationship between r³ and V is linear. To the best of our knowledge, there are only two studies, where interatomic distances in radium compounds have been measured experimentally: Hedström and co-workers¹⁰ studied solid radium–barium sulfate using extended X-ray absorption fine structure (EXAFS) and recently Yamaguchi et al.¹¹ measured diluted HNO₃ with 2 MBq of ²²⁶Ra (≈4 mM) also using EXAFS. Therefore, experimental studies of radium will extend the knowledge of alkaline-earth metal chemistry applicable on both fundamental and applied levels.

Generally, it is assumed that radium chemistry is similar to that of barium due to their similar chemical and physical properties.⁸ For example, radium migration in natural waters is mainly controlled by its co-precipitation with other alkaline-earth metal sulfate minerals, mostly with barite (BaSO₄). However, radium mobility in some natural sulfate-free waters can be controlled by its co-precipitation with various carbonate minerals, moslty with witherite (BaCO₃).¹² The mechanism and degree of radium co-precipitation with witherite depends mainly on crystal structures and the solubilities of pure witherite and RaCO₃. The crystal structure and solubility of witherite and other non-radioactive alkaline-earth metal carbonates are well established, but little is known about the properties of RaCO₃. Only two papers deal with the crystal structure of RaCO₃. It was studied experimentally by Weigel and Trinkl¹³ in 1973 and by Butkalyuk and co-workers¹⁴ in 2013. In both papers, the RaCO₃ samples studied were obtained by calcination (3.5 h at 640 °C and 8 h at 800 °C, respectively) and characterized using the X-ray powder diffraction (XRPD) technique. The XRPD patterns obtained are in good agreement and reveal that calcined RaCO₃ is isostructural with strontianite (SrCO₃), witherite, and cerussite (PbCO₃), crystallizing in the space group Pnma (no. 62).

To the best of our knowledge, an experimentally determined RaCO₃ solubility product has never been reported in the literature, although an indication that the solubility of RaCO₃ is significantly higher than that of witherite was first given by Nikitin¹⁵ in 1937. Nikitin performed the following experiment: 100 mL of a solution containing 2 g of (NH₄)₂CO₃, 5 g of NH₄Cl, and 10 mL of concentrated NaOH was added to 40 mL of a pure concentrated radium solution. The formed precipitate was filtered and a mixture of HCl and H₂SO₄ was added to the filtrate to precipitate RaSO₄. Then, the mass of the precipitated RaSO₄ was measured. Nikitin did the same experiment with pure barium and found that the mass of precipitated RaSO₄ was approximately 10 times higher than the mass of precipitated BaSO₄, which means that the solubility product of RaCO₃ is approximately 10 times larger than that of BaCO₃ under the experimental conditions used. At that time, the theories for calculation of activity coefficients in such concentrated solutions (Specific ion Interaction Theory or Pitzer formalism) were not developed yet. Nowadays, there is evidence that Ra²⁺ and Ba²⁺ have similar activity coefficients in chloride and hydroxide media.^16,17 Therefore, it can be argued that the same difference (10 times) in solubilities of BaCO₃ and RaCO₃ can be expected at zero ionic strength. Moreover, recently Brown and co-workers¹⁸ used thermodynamic modeling to derive the solubility of pure radium carbonate and showed that the decimal logarithm of the solubility product of pure radium carbonate at zero ionic strength and 25 °C is log₁₀K_sp⁰ = −7.57 (s = 0.047 g·L^–1). This value is in good agreement with the experimental results obtained by Nikitin and is significantly different from the solubility product of witherite at zero ionic strength (log₁₀K_sp⁰ = −8.56).¹⁹ This may indicate that non-calcined RaCO₃ is not isostructural with witherite.

Goldschmidt²⁰ was the first to show that radium can co-precipitate with strontianite, witherite, and cerussite in aqueous solution and determined its partition coefficients in these phases. Co-precipitation of trace radium with witherite, aragonite, calcite, and other minerals has been recently studied by other researchers²¹⁻²⁵ and has also been reviewed.^26,27 All reported partition (crystallization) coefficients of radium in witherite are below unity, which means that most of the radium stays in the aqueous phase and that pure RaCO₃ is more soluble than pure witherite. The limited co-precipitation of radium with aragonite and witherite also indicates that RaCO₃ may have a different crystal structure than these minerals.

However, the commonly accepted solubility product of RaCO₃ in the literature is from Langmuir and Riese.¹² They assumed that RaCO₃ is isostructural with witherite and plotted logarithms of the solubility products of strontianite, witherite, and RaCO₃ as functions of the effective ionic radii of Sr²⁺, Ba²⁺, and Ra²⁺ in 8-fold coordination and estimated a log₁₀K_sp⁰ for RaCO₃ of −8.3 (s = 0.02 g·L^–1) at ambient conditions and zero ionic strength.

The present study attempted to refine the crystal structure parameters of radium carbonate and gain a better understanding of the radium co-precipitation mechanism with witherite and other carbonate phases. For this purpose, a radium–barium carbonate co-precipitate was synthesized, characterized by XRPD and EXAFS techniques, and modeled using direct space methods. The solubility of RaCO₃ was experimentally studied as a function of ionic strength at 25.1 °C, and the apparent solubility products of RaCO₃ determined were extrapolated to zero ionic strength to obtain the thermodynamic value for the solubility product of RaCO₃.

2. Methods

Warning: Radium sources used in this work are highly radioactive and emit the short-lived α-emitting gas—radon. The experimental work described requires rigorous safety precautions including working in radiological fume hoods, gloveboxes, and hot cells equipped with a Rn capture system.

2.1. Chemicals

All experimental work with radium powder samples was performed in gloveboxes or hot cells at negative pressure and equipped with a radon capture system to avoid contamination, inhalation of radon, and ingestion of radium. All solutions were prepared using an analytical balance (Sartorius Quintix125D-1S). All chemicals used in this work are listed in Table 1.

Table 1. Chemicals Used^a.

chemical	source	purity
226Ra(Ba)CO3 powder	synthesized in house from radium sulfate22	mole fractions: Ra = 0.756 ± 0.010, Ba = 0.244 ± 0.006, Pb = 0.00228
226Ra stock solution in 2.77 mol·L–1 HCl	synthesized in house from radium sulfate22 using HCl from Merck (Suprapur)	mole fractions: Ra = 0.756 ± 0.005, Ba = 0.244 ± 0.003, Pb = 0.00228
BaSO4	Sigma-Aldrich	99.998% trace metals basis
Na2CO3	Sigma-Aldrich	99.999% trace metals basis
NaOH	Sigma-Aldrich (Fluka) standard solution	99.9%
Na2EDTA·2H2O	Sigma-Aldrich	99% molecular biology grade
HCl	Sigma-Aldrich	99.999% trace metals basis
H2O	Type 1 Merck Milli-Q	18.2 MΩ·cm at 25 °C, total organic content <5 mg·L–1
ethanol	Solveco	Aa grade, 99.7%

^aUncertainties of Ra and Ba mole fractions are 2σ standard deviations.

2.2. Synthesis of Radium Carbonate

The initial source of radium for this work was used for brachytherapy in the 1940s to 1960s and was in the form of a steel flat plaque with five platinum-gold cylinders sealed inside the plaque. Each cylinder contained 20 mg of radium–barium sulfate powder. Disassembly of the radium source and synthesis of the radium–barium carbonate from radium–barium sulfate powder was performed as previously described²²—the radium–barium sulfate powder was heated in 1.5 mol·L^–1 aqueous solution of Na₂CO₃ up to ca. 85 °C using a heating mantle. After about 90 min of heating, the solution was cooled, and the supernatant was removed. The procedure was repeated twice more. Pure BaCO₃ was synthesized from BaSO₄ using the same procedure and chemicals as used for the radium–barium carbonate synthesis. Small portions of the initial radium–barium sulfate and synthesized radium–barium carbonate were dissolved in 0.1 mol·L^–1 Na₂EDTA solution and in 0.1 mol·L^–1 hydrochloric acid solution, respectively, and their purities were measured using a sector field inductively coupled plasma mass spectrometer.²⁸

2.3. XRPD and EXAFS Data Collection

The sample for the XRPD study was prepared using a similar procedure to that previously described.²⁸ The whole batch of synthesized radium–barium carbonate powder was heated for 4 h at 200–250 °C using a heating mantel. After cooling, approximately 0.5 mg of radium–barium carbonate powder was placed on a low background silicon air-tight sample holder, and several drops of ethanol were added to evenly distribute the powder on the sample holder. After ethanol evaporation, the sample holder with the radium–barium carbonate powder was closed using a screw dome and transferred to another glovebox with the X-ray powder diffractometer inside. The sample holder was then placed in the measuring position, fixed in place, and the dome was removed.

The XRPD measurements of radium–barium carbonate and pure synthesized BaCO₃ were collected using the same procedure as described previously.²⁸ Both samples were approximately of the same size and were measured at 25 °C in Bragg–Brentano reflection geometry using a Bruker D2 Phaser XRPD system with Cu Kα radiation (λ = 1.5418 Å) equipped with a LynxEye detector. A standard reference material (NIST 640c) was measured to verify the positions of the diffraction lines and no significant deviation was found. The data were obtained by step scanning in the angle range 10° ≤ 2θ ≤ 80° with a step increment of 0.006° (2θ) and a dwell of 0.25 s per step. A 1 mm slit was used for the measurements.

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 (sample photo is shown in the Supporting Information, Figure S1).

The EXAFS measurements of radium–barium carbonate were performed using the radium L₃ absorption edge. The data were collected at the wiggler beam line I811 at MAX-lab (Lund University, Sweden), which operated at 1.5 GeV and a maximum current of 180 mA. The EXAFS station was equipped with a Si[111] double-crystal monochromator for the data collection. Higher order harmonics were reduced by detuning the second monochromator crystal to reflect 70% of maximum intensity at the end of the scans. The measurement was performed in transmission and fluorescence modes simultaneously. Ten continuous scans of 10 min each were averaged. The energy calibration was performed by measuring the position of the Pb L₂ edge of metallic lead before and after the measurement of the radium–barium carbonate sample; the first inflection point of the Pb L₂ edge of metallic lead was assigned to 15,200 eV.²⁹

2.4. Solubility Data Collection

The solubility of RaCO₃ was studied from under- (one sample) and oversaturation (five samples) as a function of ionic strength using NaCl (0.01, 1.3, 1.9, 2.5, 4, and 5 mol·L^–1) as a background electrolyte. For the undersaturation study, a small sample (approximately 0.5 mg), which was previously measured via XRPD, was transferred from the XRPD sample holder to the test-tube containing 0.5 mL of 0.01 mol·L^–1 NaCl. For the oversaturation studies, a previously prepared radium stock solution in the form of 2.77 mol·L^–1 HCl and with a ²²⁶Ra concentration of 0.40 ± 0.02 mmol·L^–1 was added to a solution containing Na₂CO₃ and NaCl. For all oversaturation samples, the sample volume was 2 mL, the concentration of ²²⁶Ra was 0.13 mmol·L^–1 and the concentration of Na₂CO₃ was 0.1 mol·L^–1. Preliminary experiments showed that radium sorption losses on polypropylene at such high radium concentrations were negligible. According to the literature,³⁰ the recommended value for the second dissociation constant (pK_a2) of H₂CO₃ at 25 °C and zero ionic strength is 10.239. Complete dissociation of H₂CO₃ in NaCl media will occur at a lower pH due to activity coefficient changes.³¹ Therefore, the pH was increased by the addition of a small amount of 2 mol·L^–1 NaOH to both the under- and oversaturation samples.

All polypropylene tubes used for the solubility experiments were pre-washed first with ethanol and then with type 1 Milli-Q water to remove any residues. All samples were gently shaken under a constant temperature of 25.1 ± 0.1 °C using a shaking machine (IKA VXR basic Vibrax) coupled with a heated circulating water bath (Grant Optima T100-P12). After 39 (the undersaturation sample) and 230 (oversaturation samples) days, at least two 100 μL samples were taken and centrifuged in polypropylene tubes at 5 ·10⁴g at a constant temperature of 25 °C for 60 min (Beckman Coulter Allegra 64R refrigerated centrifuge with F2402H rotor). The pH of all samples was measured after the last sampling and was always above 12. Radium hydrolysis at this pH is very weak and can be neglected.¹⁶

After centrifugation, two 10 μL samples were taken and the concentration of ²²⁶Ra was measured using a High Purity Germanium Detector (Ortec GEM-C5060 coaxial high purity germanium detector 50.5 mm diameter, 68.3 mm length, and 0.9 mm carbon epoxy entrance window coupled to a digital spectrum analyzer Ortec DSPEC50). The detector was calibrated for the same geometry (1 mL of 4 mol·L^–1 HCl in polypropylene tube) using a mixed radionuclide reference solution (NIST traceable from Eckert and Ziegler, USA). Dead time was always kept below 10%. All gamma spectra obtained were evaluated using the Gamma Vision 7.01.03 software. Radium-226 was measured using its gamma emission peak at 186.2 keV and its half-life, gamma emission energies, and photon emission probabilities were taken from the Decay Data Evaluation Project.³²

2.5. Data Analysis

Refinement of the witherite and radium–barium carbonate XRPD patterns obtained was performed using the Rietveld method³³ in the Fullprof2k³⁴ software package, using both TREOR³⁵ and DICVOL-06.³⁶ Available witherite unit cell parameters,³⁷⁻⁴³ corrected for the difference in ionic radius between barium and radium,⁹ were used as a starting estimate.

The EXAFS oscillations were extracted from averaged raw data using standard procedures for pre-edge subtraction, spline removal, and data normalization. To obtain quantitative information for the coordination structure of the radium ion, the experimental k³-weighted EXAFS oscillations were analyzed by non-linear least-squares fits of the data to the EXAFS equation, refining the model parameters: number of backscattering atoms (N), mean interatomic distances (R), Debye–Waller factor coefficients (σ²), and threshold energy (E₀). Data analysis was performed using the EXAFSPAK program package.⁴⁴ Model fitting was performed with theoretical phase and amplitude functions including both single and multiple scattering paths using the ab initio FEFF7 code (version 7.02).⁴⁵ Diamond software⁴⁶ was used to visualize the Ra²⁺ surroundings.

The apparent solubilities of RaCO₃ were derived as follows—first, the free Ra²⁺ concentrations were calculated using values of the measured total Ra²⁺ concentrations, the value of the RaCO₃ solubility product constant at zero ionic strength obtained from experimental data (undersaturation point at 0.01 mol·L^–1 was extrapolated to zero ionic strength using the Davies equation), and the value of the estimated stability constant of the RaCO₃(aq) complex at zero ionic strength taken from the literature (log₁₀K₀ = 2.5).¹² The value of RaCO₃(aq) stability constant had a very small contribution to the calculated free Ra²⁺ concentration. Then, the free CO₃^2– concentrations were calculated using the value of the total added concentrations of CO₃^2– and the values of the NaCO₃^– stability constants. The values of the NaCO₃^– stability constants were derived via non-linear curve fitting. The derived values were in good agreement with the literature values.⁴⁷⁻⁵⁹ Subsequently, the RaCO₃ solubility product constants were computed as a product of the free Ra²⁺ and free CO₃^2– concentrations and then extrapolated to zero ionic strength using the extended specific ion interaction theory (ESIT). Non-linear curve fitting was performed using a Levenberg–Marquardt iteration algorithm, and the experimental apparent solubility constants of RaCO₃ were weighted using their standard deviations (ω_i = 1/σ²). Models for activity coefficients computation and adaptation of the ESIT can be found in the Supporting Information.

2.6. Uncertainty Assessment

The standard deviations (2σ) of the gamma spectrometric measurements of total Ra²⁺ concentrations were approximately 6%. To the best of our knowledge, the stability constant of RaCO₃(aq) has never been measured experimentally, and therefore, the standard deviation (2σ) of the stability constant of RaCO₃(aq) at zero strength was estimated to be 50%. The standard deviation (2σ) of the values of the NaCO₃^– stability constants were estimated based on the fitting results and an extensive literature review.⁴⁷⁻⁵⁹ Estimation of uncertainties of stability constants of weak ion pairs including NaCO₃^– is the only reliable method because in this case systematic uncertainties are much greater than stochastic.¹⁶ The standard deviations (2σ) of the gamma spectrometric measurements, estimated RaCO₃(aq), and NaCO₃^– stability constants were first propagated to the 2σ standard deviation of free Ra²⁺ and free CO₃^2– concentrations and then to the apparent solubility product constant of RaCO₃ using standard uncertainty propagation. The value for the RaCO₃ solubility is subject to some systematic uncertainties due to the probable presence of barium impurities. As a result, the uncertainty (1σ standard deviation of the fit) obtained for the RaCO₃ solubility at zero ionic strength was increased to reflect possible systematic effects from 0.02 to 0.04 log₁₀ units.

The uncertainties reported for the EXAFS refined parameters obtained are 2σ standard deviations related to the least-squares refinements. Variations in the refined parameters obtained using different models and data ranges indicate that the accuracy of the distances given for the separate complexes is within an interval of 0.005–0.02 Å, which is typical for well-defined interactions.

3. Results

3.1. Crystal Structure of Radium–Barium Carbonate and Its Ab Initio Modeling

Rietveld refinement of the XRPD pattern of synthesized BaCO₃ shows that it is orthorhombic witherite and crystallizes in the Pnma (no. 62) space group. The unit cell parameters obtained are in good agreement with the literature values.³⁷⁻⁴³ A comparison of the XRPD patterns of witherite and radium–barium carbonate synthesized using the same method is shown in Figure 1. As can be observed in Figure 1, the diffraction peaks in the radium–barium carbonate XRPD pattern (red) at 23.5 and 23.8° (2θ) have the same shape as the diffraction peaks in the witherite XRPD pattern (blue), but they are slightly shifted to lower angles. Similar observations can be seen for the diffraction peaks in the radium–barium carbonate XRPD pattern at 27.0, 33.6, and 34.2° (Figure 1). The intensity of these diffraction peaks is much lower than the intensities of the other diffraction peaks at 18.6, 21.5, 30.7 36.2, and 37.9° (Figure 1). Thus, it can be concluded that the synthesized radium–barium carbonate contains two phases—a dominating major phase represented by ten diffraction peaks and a minor phase represented by five diffraction peaks. The small systematic shift of the five diffraction peaks in the radium–barium XRPD pattern at 23.5, 23.8, 27.0, 33.6, and 34.2° in comparison to the diffraction peaks of pure witherite shows that the minor phase is isostructural with witherite. The small systematic shift of these peaks to lower angles also shows that the minor orthorhombic Ba(Ra)CO₃ phase has slightly larger unit cell dimensions than witherite. This is consistent with the fact that the effective ionic radius of radium is 0.06–0.09 Å larger than that of barium, depending on the coordination number.⁹ Similar differences are observed for barite and RaSO₄.²⁸

Figure 1.

Comparison of the measured XRPD patterns of radium–barium carbonate (upper red line) and witherite (lower blue line) synthesized using the same method.

The limited number of weak diffraction lines makes it impossible to refine any unit cell dimensions for the orthorhombic witherite-type minor phase but it can be concluded that the minor orthorhombic Ba(Ra)CO₃ phase is isostructural with witherite and crystallizes in the space group Pnma (no. 62) with slightly larger unit cell dimensions. Furthermore, it is not possible to determine precisely the barium and radium content in this minor orthorhombic phase, but integration and comparison of the two most intense witherite peaks (blue) at 24.1 and 24.4° (2θ) in Figure 1 with those from the radium–barium carbonate XRPD pattern (red) at 23.5 and 23.8° shows that the peak areas at 23.5, 23.8 and 24.1, 24.4° are equal to 36, 22 and 116, 59, respectively. Taking into account that sample sizes of radium–barium carbonate and pure witherite were similar and that the initial Ra/Ba molar ratio was 0.76:0.24, it can be concluded that almost all barium present in the radium–barium carbonate sample precipitated in the orthorhombic witherite phase. Moreover, the significant displacement (0.6°) of the 23.5 and 23.8° peaks and their relatively high intensity indicates that the minor witherite phase contains a significant amount of Ra. Based on the fact that the intensities of the 23.5 and 23.8° peaks from the radium–barium XRPD pattern are approximately equal to one-third of the intensities of the 24.1 and 24.4° peaks from the pure witherite XRPD pattern, it can be assumed that the approximate stoichiometry of the minor phase is Ba_0.7Ra_0.3CO₃ and that the major phase is almost pure radium carbonate.

The major Ra(Ba)CO₃ phase is represented by the high-intensity diffraction peaks at 18.6, 21.5, 30.7, 36.2, and 37.9° (Figure 1). The only two sparingly soluble metal ion carbonates in the system used in the synthesis are witherite and RaCO₃. The radium concentration in the initial system was significantly higher than that of barium (the Ra/Ba molar ratio was 0.76:0.24 for the mixture) and taking into account that almost all Ba precipitated in the minor orthorhombic witherite phase, it can be concluded that the major Ra(Ba)CO₃ phase is almost pure RaCO₃ with a Ba/Ra molar ratio of 0.1 or less.

The limited number of reflections did not allow for a direct Rietveld refinement of the major Ra(Ba)CO₃ phase structure. Attempts to solve the major Ra(Ba)CO₃ phase by direct space methods were made using the FOX software.⁶⁰ The model consisted of one radium atom and a carbonate ion modeled with the Avogadro software⁶¹ and fed into FOX 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 modeling the close contact and overlap of different atoms. The resulting final model showed enormous disorder features. Structural disorder in the major 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 modeled acceptably using the cubic F23 space group. Further details of the attempts to solve the crystal structure of Ra(Ba)CO₃ are given in the Supporting Information.

3.2. Interatomic Distances in Radium–Barium Carbonate

The quality of the EXAFS data for the mixture of the major Ra(Ba)CO₃ and minor Ba(Ra)CO₃ is very good despite the small amount of non-homogenized sample. Based on the XRPD pattern, it can be inferred that the derived Ra–O bond distance in the sample is dominated by the major Ra(Ba)CO₃ phase and that the influence of the minor Ba(Ra)CO₃ phase is limited. The results of the EXAFS data refinement are listed in Table 2 and the fits are shown in Figure 2.

Table 2. EXAFS Refinement Parameters for the Ra L₃ EXAFS of the Major Ra(Ba)CO₃ Phase^a.

	number of backscattering atoms	mean interatomic distance for single scattering paths, R (Å)	Debye–Waller factor, σ2 (Å2)	threshold energy, E0 (eV)	amplitude reduction factor, (S02)
Ra–O	9	2.885(5)	0.0144(9)	15,452.8(3)	0.80(6)
Ra–C	6	3.283(3)	0.0090(6)
Ra–OII	6	4.26(1)	0.014(1)
Ra–OIII	12	4.94(4)	0.016(2)

^aAll uncertainties are 1σ standard deviations related to the least-squares refinements.

Figure 2.

Fit (left) and Fourier transform (right) of raw EXAFS data of the major Ra(Ba)CO₃ phase. Dashed line—experimental and solid line—calculated.

The EXAFS data reveal a mean Ra–O bond distance of 2.885(5) Å (1σ), which indicates that radium is surrounded by nine oxygen atoms from the carbonate ions in a broad bond distance distribution in solid Ra(Ba)CO₃. This is in good agreement with the corresponding mean metal–oxygen distances in strontianite, witherite, and cerussite, as shown in Table 3. The effective ionic radius of Ra²⁺ in a 9-fold coordination can be calculated using the mean Ra–O distance from this work and an atomic radius of the carbonate oxygen of 1.34 Å from Beattie and co-workers⁶² with an estimated 1σ of 0.005 Å and compared with the effective ionic radii of Sr²⁺, Pb²⁺, and Ba²⁺ (Table 3).

Table 3. Comparison of Experimental, Mean Metal–Oxygen Distances in Cerussite, Strontianite, Witherite, Ra(Ba)CO₃, and RaSO₄ and Effective Ionic Radii of Sr²⁺, Pb²⁺, Ba²⁺, and Ra²⁺ in 9-fold and 12-Fold Coordination.

compound	formula	mean metal–oxygen distancea (Å)	metal coordination number	effective ionic radiusb (Å)	effective ionic radiusc (Å)9	references
cerussite	PbCO3	2.696	9	1.356	1.35	(38,39, 43, 63,–66)
strontianite	SrCO3	2.645	9	1.305	1.31	(38,41,43,67,–69)
witherite	BaCO3	2.807	9	1.467	1.47	(37–43)
radium carbonate	Ra(Ba)CO3	2.885(3)	9	1.545(6)		EXAFS study, this work
radium nitrate solution	Ra(NO3)2	2.87(6)	9.2(1.9)	1.53(6)		EXAFS study11
radium–barium sulfate	Ra0.76Ba0.24SO4	2.96(2)	12	1.62(2)	1.7	EXAFS study10
radium sulfate	RaSO4	3.02	12	1.68	1.7	XRPD and DFT study28

^aCalculated mean metal–oxygen bond distance from the crystal structures in the references.

^bIonic radius of the metal ion calculated by subtracting 1.34 Å⁶² from the mean metal–oxygen bond distance in the reported compounds.

^cIonic radii proposed by Shannon.⁹ Uncertainties are 1σ standard deviations.

As shown in Table 3, the mean metal–oxygen distances in strontianite, witherite, cerussite, and Ra(Ba)CO₃ are in excellent agreement with the ionic radii for the corresponding metal ions in 9-fold coordination proposed by Shannon,⁹ as well as with the atomic radius of the carbonate oxygen (1.34 Å)proposed by Beattie and co-workers.⁶² Moreover, the ionic radius of Ra²⁺ with the coordination number of 9(2) measured in 0.001 mol·L^–1 of HNO₃ via EXAFS¹¹ is also in good agreement with the ionic radius of Ra²⁺ in 9-fold coordination measured in this work (1.53 and 1.545 Å, respectively).

The other experimental EXAFS study of a radium compound was conducted by Hedström and co-workers,¹⁰ who studied a RaSO₄ sample via XRPD and EXAFS. Hedström et al.¹⁰ assumed that the studied RaSO₄ sample was pure but later Matyskin et al.²⁸ showed that there was a barium impurity, and the actual stoichiometry of the studied sample was Ra_0.76Ba_0.24SO₄. EXAFS measurements give distances only between the absorbing atom (Ra) and the surrounding atoms (O), therefore the presence of the barium impurity did not affect the derived mean Ra–O bond distance.

As shown in Table 3, the mean Ra–O distance and effective ionic radius of Ra²⁺ in 12-fold coordination, obtained by Hedström et al.,¹⁰ are slightly larger, as expected, and are in good agreement with the Ra–O distance and with the effective ionic radius of Ra²⁺ in 9-fold coordination obtained in this work. Later, in 2017, Matyskin et al.²⁸ studied the crystal structure of a radium sulfate sample of the same origin as Hedström et al.¹⁰ also via XRPD and the derived unit cell parameters from both studies were the same. However, Matyskin et al.²⁸ showed that the actual stoichiometry of the studied sample was Ra_0.76Ba_0.24SO₄; therefore, the obtained unit cell parameters were extrapolated to the unit cell parameters of pure RaSO₄ using Vegard’s law, and density functional theory (DFT) was used to derive the atomic coordinates and Ra–O distances in pure RaSO₄.²⁸ The derived mean Ra–O bond distance and effective ionic radius of Ra²⁺ in 12-fold coordination are also in good agreement with the data obtained in this work and with the effective ionic radius estimated by Shannon⁹ but is slightly larger than the data obtained by Hedström et al.¹⁰ (Table 3). The most likely reason for the slightly shorter Ra–O bond distance derived from the EXAFS study is a possible asymmetric bond distance distribution causing the peak in the Fourier transform to be at a slightly shorter distance than the half-height center of the peak. However, the quality of the EXAFS data was not sufficient to perform detailed analysis. Moreover, the quality of the EXAFS data obtained by Hedström et al.¹⁰ permitted only derivation of the mean Ra–O distance in RaSO₄, while the EXAFS data obtained in this work were of a significantly higher quality, allowing accurate extraction of longer Ra–O, Ra–C, Ra–O_II, and Ra–O_III distances (Table 2).

The effective ionic radius of Ra²⁺ in 9-fold coordination derived in this work (1.545(6) Å) is also in very good agreement with the radius of Ra²⁺ in 8-fold coordination theoretically estimated by Shannon⁹ (1.48 Å). Moreover, the measured mean Ra–O distance (2.885(3) Å with coordination number 9) can be compared with the Ra–O distance in the first hydration shell obtained via molecular dynamics simulations (2.93 Å with coordination number 9.8⁷⁰ and 2.85 Å with coordination number 8.1⁷¹).

The effective ionic radius of Ra²⁺ in 9-fold coordination can be also estimated using the effective ionic radii of Ba²⁺ (Figure 3). As shown in the figure, the ionic radius of Sr²⁺ at each coordination number correlates very well with the corresponding ionic radius of Ba²⁺ at the same coordination number (black, lower line) and this linear correlation is observed over a large range of coordination numbers (from 6 to 12). The same methodology can be applied to derive the effective ionic radius of Ra²⁺ in 9-fold coordination using the available literature data for the ionic radii of Ba²⁺ and Ra²⁺ from Shannon⁹ and the ionic radius of Ra²⁺ in 6-fold coordination from Ahrens,⁷² as listed by Shannon and Prewitt.⁷³ The correlation of Ba²⁺ and Ra²⁺ ionic radii result in an effective ionic radius of Ra²⁺ in 9-fold coordination of 1.547 Å, which is within the 1σ standard deviation of the value measured in this work (1.545(6) Å as listed in Table 3).

Figure 3.

Correlation of effective ionic radii of Ba²⁺ with ionic radii of Sr²⁺ and Ra²⁺ using the literature data.^9,72,73

3.3. Solubility of Radium–Barium Carbonate

In determining the solubility, thirty-one solutions were sampled and on every occasion a few samples (3–6) were taken from the solution at each ionic strength. The activity of ²²⁶Ra at each ionic strength was always within 10% with only one outlier. Most of the samples were centrifuged at 5·10⁴g, and the activity of ²²⁶Ra was similar (within 10%) for both centrifuged and non-centrifuged samples. This indicates that Ra(Ba)CO₃ does not form colloids. The measured and computed concentrations of total and free Ra²⁺, respectively, are listed in Table 4 (more experimental details and details about extrapolation to zero ionic strength are given in the Supporting Information).

Table 4. Measured Total and Computed Free Ra²⁺ Concentrations^a.

ionic strength (mol·kg–1)	measured concentration of total Ra2+ (mol·L–1)	concentration of free Ra2+ (mol·L–1)
0.01 ± 0.001	(2.65 ± 0.13) × 10–4	(2.65 ± 0.13) × 10–4
1.34 ± 0.01	(1.19 ± 0.06) × 10–4	(1.09 ± 0.08) × 10–4
1.98 ± 0.01	(1.23 ± 0.06) × 10–4	(1.13 ± 0.08) × 10–4
2.65 ± 0.01	(1.14 ± 0.06) × 10–4	(1.05 ± 0.08) × 10–4
4.38 ± 0.01	(1.22 ± 0.06) × 10–4	(1.12 ± 0.08) × 10–4
5.59 ± 0.01	(1.19 ± 0.12) × 10–4	(1.10 ± 0.13) × 10–4

^aAll uncertainties are 2σ standard deviations. The pH of all samples was measured after the last sampling and was always above 12. The ionic strength of NaCl was recalculated from molar to molal units using the densities and relevant conversion factors.⁷⁵

A comparison of the total and free Ra²⁺ concentrations listed in Table 4 shows that the difference between the two values is less than 1·10^–5 mol·L^–1, which means that the formation of the RaCO₃(aq) complex does not significantly decrease the concentration of total Ra²⁺. As also shown in Table 4, the concentrations of Ra²⁺ (total and free) are within 2σ standard deviations for all ionic strengths above and equal to 1.34 mol·kg^–1. Similar behavior is observed in the case of the solubility of aragonite (CaCO₃), strontianite, and witherite in NaCl media.⁷⁴

There is ample evidence in the literature that a weak NaCO₃^– ion pair is formed in aqueous media.⁴⁷⁻⁵⁹ According to Marcus and Hefter,⁷⁶ dielectric relaxation spectroscopy has unusual capabilities for studying ion pairing phenomena. The method is particularly sensitive to very weakly associated ion pairs (log₁₀K° < 1) and can be used to distinguish between various types of ion pairs (solvent separated, solvent shared, and contact ion pairs). Dielectric relaxation spectroscopy was used by Capewell and co-workers⁴⁸ to determine weak NaCO₃^– ion pairing in aqueous CsCl media. It was shown that the apparent stability constant of the NaCO₃^– ion pair in aqueous chloride media is equal to approximately 0.3 at 1 mol·L^–1 (i.e., K_A ≈ 0.3) and then decreases with increasing ionic strength. The same trends and similar values for the NaCO₃^– stability constants were obtained in potentiometric^49,58 and spectroscopic⁵⁶⁻⁵⁹ studies. However, weak ion pairing is always subject to some uncertainties, mostly systematic, due to various effects: ion pair formation between components of the background medium, separation of short-range ion interaction, and weak ion pairing, among others.¹⁶ Therefore, relatively high uncertainties were assigned to all values of the NaCO₃^– stability constant obtained by numerical fitting, despite good agreement between the values obtained in this work and the literature values. The values of the apparent NaCO₃^– stability constant and associated uncertainties obtained in this work and reported by Capewell and co-workers,⁴⁸ who studied NaCO₃^– ion pairing by dielectric relaxation spectroscopy (also in chloride media), are listed in Table 5.

Table 5. Stability Constants of the NaCO₃^– Ion Pair from This Work and the Literature and Computed Free CO₃^2– Concentration^a.

ionic strength (mol·kg–1)	stability constant of NaCO3– ion pair	stability constant of NaCO3– ion pair from Capewell et al.48	concentration of free CO32– (mol·L–1)
1.34 ± 0.01	0.4 ± 0.2	0.3	0.066 ± 0.035
1.98 ± 0.01	0.1 ± 0.05	0.1	0.081 ± 0.034
2.65 ± 0.01	0.04 ± 0.02	0.05	0.091 ± 0.047
4.38 ± 0.01	0.002 ± 0.001	<0.01	0.010 ± 0.044
5.59 ± 0.01	0.0003 ± 0.0002	<0.01	0.010 ± 0.062

^aAll uncertainties are 2σ standard deviations. The pH values of all samples were measured after the last sampling and were always above 12. The ionic strength of NaCl was recalculated from molar to molal units using the densities and relevant conversion factors.⁷⁵

As shown in Table 5, NaCO₃^– ion pairing will only affect the concentration of free CO₃^2– at the first three ionic strengths and the NaCO₃^– stability constants at ionic strengths above 4 mol·kg^–1 are too small to decrease the concentration of free CO₃^2– in its complex formation with Na⁺. The apparent solubility product constants of Ra(Ba)CO₃ were calculated as the product of the free Ra²⁺ and free CO₃^2– concentrations (Tables 4 and 5, respectively) and extrapolation of the Ra(Ba)CO₃ apparent solubility product constant to zero ionic strength using the ESIT is shown in Figure 4. All parameters obtained in the regression analysis are listed in Table 6.

Figure 4.

Extrapolation of experimental log₁₀K_sp of Ra(Ba)CO₃ to zero ionic strength using the ESIT. Error bars are 2σ standard deviations.

Table 6. Solubility Product of Ra(Ba)CO₃ and Ra²⁺–Cl^– Ion Interaction Coefficients (ε) at 25 °C and Zero Ionic Strength^a.

constant	value	references
log10 Ksp0 of Ra(Ba)CO3	–7.52 ± 0.02	this work—Davies equation
log10 Ksp0	–7.52 ± 0.02	this work—ESIT
ε1 (Ra2+, Cl–)	–0.49 ± 0.05
ε2 (Ra2+, Cl–)	0.56 ± 0.07

^aAll uncertainties are 1σ standard deviations.

As shown in Table 6, extrapolation of the Ra(Ba)CO₃ apparent solubility product constant using the Davies equation and ESIT leads to the same value for the Ra(Ba)CO₃ solubility product at zero ionic strength.

Millero and co-workers⁷⁴ studied the solubility of witherite in NaCl media as a function of ionic strength, and these experimental data were used to derive ε₁ (Ba²⁺, Cl^–) and ε₂ (Ba²⁺, Cl^–) ESIT ion interaction coefficients. The derived ESIT coefficients were used to plot the witherite solubility product as a function of NaCl ionic strength and the increase of its solubility product with an increase of the NaCl concentration is compared with that of Ra(Ba)CO₃ in Figure 5.

Figure 5.

Comparison of the logarithm of the apparent RaCO₃ (this work) and BaCO₃ (witherite, from Millero et al.⁷⁴) solubility products at different ionic strengths of aqueous NaCl media at 25 °C.

As shown in Figure 5, the shape of the solubility product curves of Ra(Ba)CO₃ and witherite in aqueous NaCl media are very similar, which means that Ra²⁺ and Ba²⁺ have similar activity coefficients and undergo similar short-range ion interactions in aqueous NaCl media. The same conclusion was obtained by Matyskin and co-workers who studied the hydrolysis of Ra²⁺ and Ba²⁺ in aqueous NaClO₄–NaOH media,¹⁶ the complex formation of these metal ions with ethylenediaminetetraacetic acid (EDTA) also in aqueous NaCl media,¹⁷ and the solubility product of RaSO₄ in aqueous NaCl media.⁷⁷

4. Discussion

The results obtained in the crystallographic study of this work are different to the results obtained by Weigel and Trinkl¹³ and Butkalyuk and co-workers,¹⁴ who studied RaCO₃ by XRPD and reported that it is isostructural with witherite. Weigel and Trinkl¹³ precipitated RaCO₃ by addition of (NH₄)₂CO₃ (p.a. grade, Merck) to approximately 65 μg of RaCl₂ dissolved in aqueous solution (obtained from RaBr₂ with 98–99% purity), while Butkalyuk and co-workers¹⁴ synthesized RaCO₃ by long heating of Ra(NO₃)₂ (with a metallic purity of 99% analyzed by inductively coupled plasma-optical emission spectroscopy) in a Ni crucible (99.99% purity). In both papers, the RaCO₃ sample was prepared by calcination (3.5 h at 640 °C, and 8 h at 800 °C, respectively), and the purity of the synthesized samples was not measured. In the case of BaCO₃ and SrCO₃, a phase transformation from the space group Pnma (orthorhombic, no. 62) to R3m (trigonal, no. 160) occurs at approximately 811³⁷ and 912 °C,⁷⁸ respectively, and this difference may be explained by a possible phase transformation. A similar transformation may occur for RaCO₃ at temperatures above 250 °C.

Another possible explanation is that the Ra(Ba)CO₃ co-precipitate crystallizes in a space group different from the space group of pure RaCO₃ or witherite due to Ba²⁺ or SO₄^2– doping. In many cases, doping can result in the formation of a compound with a crystal structure different from the crystal structure of the pure end members and can also decrease the phase transformation temperatures. An example of SO₄^2– doping was described by Nishino and co-workers.⁷⁹ They reported that mixing witherite doped with up to 10 mol % of barite (BaSO₄) and heating to 820 °C for 30 min results in the formation of monoclinic BaCO₃ that is stable at room temperature and atmospheric pressure. However, in this work, witherite was synthesized using the same method as Ra(Ba)CO₃ and a typical orthorhombic witherite crystal structure was obtained. This indicates that the possible presence of small amounts of SO₄^2– had a negligible influence on the crystal structure of the obtained Ra(Ba)CO₃ phase. Moreover, it can be shown that the synthesis of non-orthorhombic BaCO₃,^37,38,40,42 SrCO₃,⁴² and PbCO₃^65,80 requires high pressures and temperatures, far above 250 °C.

An example of witherite doping with Ca²⁺ and Sr²⁺ has been reported in a study by Lander,⁷⁸ who synthesized barium (46 wt %), strontium (46 wt %), and calcium (8 wt %) carbonate by co-precipitation from a solution and measured the triple carbonate obtained using XRPD. Lander found that the synthesized co-precipitate was orthorhombic with a crystal structure similar to aragonite. A systematic study of the crystal structures of Ba_1–xSr_xCO₃ co-precipitates was performed by Weinbruch and co-workers.⁸¹ They synthesized Ba_1–xSr_xCO₃ co-precipitates of different compositions (14 samples in total) by grinding and mixing pure witherite and strontianite and reported that all co-precipitates had orthorhombic crystal structures at room temperature. This implies that co-precipitation of Ca²⁺, Sr²⁺, and Ba²⁺ results in the formation of stable orthorhombic phases that are isostructural with the pure end-members aragonite, strontianite, and witherite.

In summary, there is evidence in the literature that temperatures far above 250 °C are required to synthesize pure or doped BaCO₃ with a crystal structure different to witherite.³⁷⁻⁴³ Furthermore, both methods of Ra(Ba)CO₃ synthesis used in the present work (three cycles of Ra_0.76Ba_0.24SO₄ heating in 1.5 mol·L^–1 Na₂CO₃ to 85 °C, cooling, and subsequent removal of the supernatant and precipitation of Ra(Ba)CO₃ by the addition of RaCl₂ solution to highly alkaline Na₂CO₃ solution) results in the same values of solubility product, which is approximately 10 times higher than the solubility product of witherite. This shows that the synthesis route of Ra(Ba)CO₃ has no influence on its solubility product or crystal structure.

The difference in the crystal structure between witherite and the major Ra(Ba)CO₃ phase obtained in this work can be explained by the fact that both pure RaCO₃ and the major Ra(Ba)CO₃ phase crystallize in the same space group (presumably cubic F-centered) with exceptional disorder. In this case, the possible barium impurity in the major Ra(Ba)CO₃ phase obtained would co-precipitate as a minor component and would adopt the crystal structure of pure RaCO₃. This hypothesis is supported by the significantly higher solubility of the major Ra(Ba)CO₃ phase determined in this work compared with the solubility of witherite. The decimal logarithm of the witherite solubility product at infinite dilution (log₁₀K_sp⁰) is equal to −8.56,¹⁸ and extrapolation of this value to the solubility product of RaCO₃ using an electrostatic model and assuming that it is isostructural with witherite (Pnma no. 62) gives a value of −8.3.¹² The larger solubility product of Ra(Ba)CO₃ obtained in this work (log₁₀K_sp⁰ = −7.5) compared to the solubility product of witherite shows that the major Ra(Ba)CO₃ phase dominates and indicates that this phase is disordered because such phases usually have higher solubilities than the equivalent crystalline phases. The fact that the solubility product of Ra(Ba)CO₃ in NaCl media obtained from undersaturation (1 sample) and oversaturation (5 samples) is almost one order of magnitude higher than the solubility product of witherite shows that the same disordered Ra(Ba)CO₃ phase is systematically formed at all ionic strengths. Moreover, the solubility studies of Ra(Ba)CO₃ performed in this work are in a very good agreement with the findings of Nikitin,¹⁵ who experimentally studied and compared solubilities of pure RaCO₃ and BaCO₃. Nikitin’s experiments were very similar to experiments preformed in this work—he precipitated RaCO₃ inNH₄Cl media by the addition of (NH₄)₂CO₃ and NaOH to RaCl₂ solution (total I ≈ 2.7 mol·L^–1) and then measured the concentration of radium in the aqueous phase. The same experiments were carried out with BaCO₃, and it was found that the solubility of RaCO₃ in grams per liter was approximately 10 times higher than the solubility of BaCO₃ at the experimental conditions used (total I ≈ 2.7 mol·L^–1). Thermodynamic modeling performed by Brown and co-workers,¹⁸ who assumed that the solubility of each alkaline-earth metal carbonate is a function of the inverse of absolute temperature with a constant, but non-zero, heat capacity change, determined a solubility product for pure RaCO₃ of log₁₀K_sp⁰ = −7.57 (s = 0.047 g·L^–1). Thus, the value of the Ra(Ba)CO₃ solubility product determined in this work is in excellent agreement with experimental results for pure RaCO₃ solubility from Nikitin¹⁵ and the thermodynamic modeling by Brown et al.¹⁸ and the crystallographic and solubility studies of RaCO₃ complement each other. Additionally, according to the literature,⁸² the solubility of Ra(NO₃)₂ is higher than the solubility of Ba(NO₃)₂ which is not within the trend of the solubilities of alkaline-earth metal nitrates. This indicates that a similar phenomenon may occur in Ra(NO₃)₂ synthesized at room temperature as was found for RaCO₃, and both phases have disordered oxygen atoms around the nitrogen and carbon, respectively. Another argument that RaCO₃ is not isostructural with witherite is the limited co-precipitation of trace Ra²⁺ within witherite. To the best of our knowledge, all reported partition (crystallization) coefficients of radium in witherite are below unity,^26,27 which means that most of the radium does not co-precipitate with witherite but stays in the aqueous phase.

In summary, the following evidence confirms that the major Ra(Ba)CO₃ phase obtained in this work behaves as pure RaCO₃ and presumably crystallizes in an F-centered cubic space group with exceptional disorder of the carbonate ion oxygen atoms:

• 1.High temperatures and pressures are required to obtain pure or doped non-orthorhombic BaCO₃, and BaCO₃ synthesized using the same method as Ra(Ba)CO₃ always crystallizes in the orthorhombic space group.
• 2.The solubility product of Ra(Ba)CO₃ measured from both under- and oversaturation (6 measurements) shows that it is 10 times higher than witherite solubility product at zero ionic strength, and this result is consistent with literature data¹⁵ where the solubility of pure RaCO₃ was measured and also with thermodynamic modeling.¹⁸
• 3.Radium co-precipitation with barium into witherite (orthorhombic BaCO₃) is very limited, in complete contrast to the almost complete radium co-precipitation with barium into barite (orthorhombic BaSO₄).
• 4.The effective ionic radius of Ra²⁺ in 9-fold coordination determined from the EXAFS data (1.545(6) Å) is in excellent agreement with the predicted value (1.547 Å) demonstrating that the major dominant phase is almost pure RaCO₃.

Table 7 shows the influence of the effective ionic radii of the metal ion on the crystal structure of metal carbonates. The table shows that radium carbonate is the only carbonate which forms disordered crystals at ambient conditions. Possibly, the ionic radius of Ra²⁺ is too large to fit into an ordered orthorhombic crystal system with carbonate ions. Moreover, the ionic radii of Ba²⁺ and Ra²⁺, even though close in magnitude, differ by too much to fit into their respective crystal structures, confirmed by experimental data of limited Ba²⁺ co-precipitation in the major RaCO₃ phase and limited co-precipitation of Ra²⁺ within witherite.^26,27 Differences in the crystal structure of RaCO₃ and witherite and limited Ra²⁺ co-precipitation within witherite suggests that Ra²⁺ is mostly physically absorbed during the crystal growth or at the surface of witherite.

Table 7. Influence of Effective Ionic Radii of the Metal Ion on the Crystal Structure of Metal Carbonates at Ambient Conditions.

compound	coordination number	effective ionic radii (Å)9	crystal system and space group
MgCO3	6	0.72	trigonal calcite type, R3̅c (no. 167)
ZnCO3	6	0.74
CoCO3	6	0.745
FeCO3	6	0.78
MnCO3	6	0.83
CdCO3	6	0.95
CaCO3 (calcite)	6	1.0
CaCO3 (aragonite)	9	1.18	orthorhombic aragonite type, Pnma (no. 62)
SrCO3	9	1.31
PbCO3	9	1.35
BaCO3	9	1.47
RaCO3	9	1.545(6)a	disordered, presumably F-centered cubic F23 (no. 196)

^aEffective ionic radius of Ra was measured in this work, and its uncertainty is 1σ standard deviation.

5. Conclusions

In this work, a mixture of major Ra(Ba)CO₃ and minor orthorhombic Ba(Ra)CO₃ phases, dominated by the former, was synthesized at atmospheric pressure and low temperatures (below 250 °C) and measured by XRPD and EXAFS techniques. It was found that the minor orthorhombic Ba(Ra)CO₃ phase is isostructural with witherite and crystallizes in the space group Pnma (no. 62), with slightly larger unit cell dimensions due to the larger ionic radius of Ra²⁺. Presumably, the major Ra(Ba)CO₃ phase crystallizes in the F-centered cubic space group with exceptional structural disorder of the carbonate ions. The derived bond distance from the EXAFS data reveals that radium is surrounded by nine oxygens from the carbonate ions in a broad bond distance distribution in solid Ra(Ba)CO₃ with a mean Ra–O bond distance of 2.885(3) Å. The mean Ra–O bond distance is consistent with the literature and gives an effective ionic radius of Ra²⁺ in 9-fold coordination of 1.545(6) Å (1σ). The apparent solubility of RaCO₃ was experimentally determined as a function of ionic strength over a wide range of NaCl concentrations. It was shown that the RaCO₃ solubility product is one order of magnitude higher than the solubility product of witherite at all ionic strengths, which confirms that RaCO₃ synthesized at room temperature is not isostructural with witherite.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.inorgchem.3c01513.

• Methods used to prepare RaCO₃ sample for the EXAFS measurements including photo of the measured sample, details of RaCO₃ solubility computations including adaptation of the extended interaction theory, and results of the attempt to solve RaCO₃ crystal structure using Rietveld refinement combined with direct-space ab initio modeling (PDF)

Author Present Address

^# Radiation Science and Engineering Center, College of Engineering, Pennsylvania State University, 135 Breazeale Nuclear Reactor, University Park, Pennsylvania, 16802, United States of America

Author Present Address

^¶ Talga AB, Södra Kungsgatan 5 B, SE-972 35 Luleå, Sweden.

Author Contributions

A.V.M. and S.A. synthesized the samples. A.V.M., B.E., and S.A. designed the experiment and collected XRPD data. A.V.M., S.A, N.T., and I.P. designed the experiment and collected EXAFS data. A.V.M. and L.E. analyzed XRPD data. N.T. and I.P. analyzed EXAFS data. L.E. carried out direct space modeling. A.V.M. designed the experiment, collected solubility data, did γ-spectrometry, and analyzed the obtained γ-ray spectra. A.V.M., P.L.B., and C.E. analyzed solubility data. A.V.M. wrote the first manuscript draft, L.E. added direct space modeling, and N.T. and I.P. added EXAFS analysis. A.V.M., P.L.B., I.P., and C.E. finalized the manuscript. C.E. conceived the original idea for the manuscript. All authors discussed and commented on the manuscript.

The authors declare no competing financial interest.

Notes

All data are available in the paper. Additional data and measured XRD patterns are available on request to the corresponding author.