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A Thermodynamic Model for ZrO2(am) Solubility at 25 °C in the Ca2+–Na+–H+–Cl−–OH−–H2O System: A Critical Review

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A Correction to this article was published on 08 June 2018

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Abstract

Zirconium is an important element in the nuclear fuel cycle. Thermodynamic data and models to reliably predict Zr–OH system behavior in various conditions including high ionic strengths are required and currently are unavailable. Most available experimental data are rather old, obtained using inadequate methodologies, and provide equilibrium constant values that differ by many orders of magnitude. Previous reviews have recommended values based on available data. These reviews used all of the available data, including poor quality data, in a global fit to determine these values. This has resulted in recommended thermodynamic models with a large number of polynuclear species and a number of mononuclear species with values of thermodynamic constants for the solubility product of ZrO2(am) and Zr–OH hydrolysis constants that are many orders of magnitude different from those for the reliable analogous Hf reactions. In this critical review, we have evaluated the quality of the available data, selected only those data that are of high quality, and reinterpreted all of the high quality data using SIT and Pitzer models for applications to high ionic strength solutions. Herein for 25 °C we (1) present formation constant values for ZrOH3+, \( {\text{Zr}}\left( {\text{OH}} \right)_{2}^{2 + } \), Zr(OH)4(aq), \( {\text{Zr}}\left( {\text{OH}} \right)_{5}^{ - } \), and \( {\text{Zr}}\left( {\text{OH}} \right)_{6}^{2 - } \), and the solubility product for ZrO2(am) which are consistent with the Hf system, (2) report a revised value for the formation constant of \( {\text{Ca}}_{3} {\text{Zr}}\left( {\text{OH}} \right)_{6}^{4 + } \), (3) show that several hypothetical polynuclear species (\( {\text{Zr}}_{3} \left( {\text{OH}} \right)_{9}^{3 + } \), Zr4(OH) +15 , and Zr4(OH)16(aq)) proposed in previous reviews are not needed, and (4) show that polynuclear species (\( {\text{Zr}}_{3} \left( {\text{OH}} \right)_{4}^{8 + } \) and \( {\text{Zr}}_{4} \left( {\text{OH}} \right)_{8}^{8 + } \)) are not important in a very extensive H+ concentration range (0.1–10−15.4 mol·kg−1). Our review has also resulted in SIT and Pitzer ion-interaction parameters applicable to as high ionic strength solutions as 5.6 mol·kg−1 in NaCl, 2.11 mol·kg−1 in CaCl2, and 23.5 mol·kg−1 in NaOH.

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Change history

  • 08 June 2018

    In the original publication of the article, there are errors in this document that pertain to a species that is reported as Zr2(OH) 2+2 . There is no such species; in each instance this species should have been reported as Zr(OH) 2+2 . Specifically this erroneous species, Zr2(OH) 2+2 , appears once in the heading of Sect. 5.2 on p. 873 and at nine different places including Eq. 7 in Sect. 5.2 on pp. 873 and 874, once in Sect. 5.6 on p. 880, once in the third equation of Table 7 on p. 881, and twice in Sect. 5.6 on p. 883. Wherever it occurs in the document it should be replaced with Zr(OH) 2+2

Notes

  1. We do not necessarily believe that the reported reactions or their equilibrium constant values (especially involving carbonate) reported in Table 1 are accurate. However, the important point we want to make here is that when the experimental data are obtained using similar techniques and the data are interpreted using a similar theory, the reported equilibrium constant values for Hf and Zr are similar, showing that they are excellent analogs of each other.

  2. The amorphic solid phase can be represented as either hydrous oxide or hydroxide; in this manuscript we chose to represent it as ZrO2(am).

  3. Brown and Ekberg [21], using the same method Brown et al. [1] used to interpret Zr data, reinterpreted HfO2(am) and ZrO2(am) solubility data of Larsen and Gammill [20], who reported unusually high solubilities for both Hf and Zr due most likely to the presence of unfiltered colloids and other experimental problems. Not surprisingly, the values Brown and Ekberg [21] report for the HfO2(am) solubility product and Hf–OH system are very similar to the values for the corresponding Zr reactions reported by Brown et al. [1]. These values cannot possibly be correct. Brown and Ekberg’s [21] review included publications prior to 1973. Apparently, they missed a much more recent, very comprehensive article of Rai et al. [4] dealing with the Hf-OH system and covering a wide range in H+ (0.1–10−15.3 mol·kg−1) and NaCl (ranging up to 5.6 mol·kg−1), and NaOH (ranging up to 21.7 mol·kg−1) concentrations. In the Rai et al. [4] publication a reliable thermodynamic model is presented, based on all high quality literature as well as their own experimental data.

  4. As for example, the pH dependence of ZrO2(am) solubility reaction [4ZrO2(am) +  8H2O ⇌ Zr4((OH)16(aq)] involving Zr4((OH)16(aq) is identical to the pH dependence of [ZrO2(am) +  2H2O ⇌ Zr((OH)4(aq)] involving Zr((OH)4(aq). Similar ZrO2(am) solubility reactions involving (\( {\text{Zr}}_{4} \left( {\text{OH}} \right)_{15}^{ + } \) and \( {\text{Zr}}\left( {\text{OH}} \right)_{3}^{ + } \)) or (\( {\text{Zr}}_{3} \left( {\text{OH}} \right)_{9}^{3 + } \) and ZrOH3+) can be written to show that the pH dependence of each set of species is identical.

  5. Data reported in these studies are fraught with the possible presence of colloids, poor detection limits, and other uncertainties, making these studies unsuitable for use in developing a reliable Zr–OH model.

  6. For examples (1) Rai and Swanson [31] report that polymeric Pu suspensions are stable for 6 months at pH = 2, and (2) Cho et al. [22] report that Zr colloids, which are stable for several months, are formed within a few minutes after the solubility limit is exceeded.

  7. All of the calculations performed in this document involve (either originally reported or calculated by us) concentrations of species in mol·kg−1, even though the original authors may have reported concentrations in mol·dm−3.

  8. Because Kovalenko and Bagdasarov [27] conducted their study in very dilute solutions, both the NONLINT-SIT and NONLINT can be used to accurately interpret the data and they will provide very similar fitted values.

  9. Here ΔZ2 is the sum of the valence squared of ions weighted by the stoichiometric coefficients of products minus the reactants, Im is the ionic strength in mol·kg−1, D = {0.509(Im)1/2}/{1 + 1.5(Im)1/2} at 25 °C, and Δε is the difference between the sum of ion interaction parameters (kg·mol−1) weighted by the stoichiometric coefficients of the products minus the reactants.

  10. We understand Ekberg et al.’s [26] rationale in attempting to minimize the potential adsorption of aqueous Zr by autopipette. However, we are very surprised that they chose to do this by treating the autopipette with an alkaline solution, because the solubility in the acidic region decreases approximately three orders of magnitude with a unit increase in pH, and treating the autopipette with an alkaline solution will have the effect of increasing the pH, thereby decreasing the equilibrated aqueous Zr concentration. It is essential to minimize adsorption and changes in pH value of equilibrated samples during the process of preparing samples for analyses. Rai [30] reported that the untreated filters he was using to filter aqueous Pu(IV) suspensions increased the pH values of the samples significantly enough that PuO2(am) precipitated on the filter surfaces. As a result, to avoid adsorption of metals and potential changes in pH during sample processing, Rai and coworkers (e.g., see [3, 30]) have demonstrated that these problems can be mitigated by equilibrating the filters and filtration equipment with pH solutions (without the presence of the metal of interest) adjusted to the exact pH value of the sample to be processed and then passing a portion of the sample through the equipment and discarding this filtrate before collecting the sample for analyses.

  11. This uncertainty is so high one wonders whether it might be a typo; however there are similarly high uncertainties in several ion interaction parameters reported by these authors.

  12. Equivalently log10 K0 of \( { \lesssim } \) 25.7 for the reaction \( {\text{Zr}}^{ 4+ } + 2 {\text{OH}}^{ - } \rightleftharpoons {\text{Zr}} \left( {\text{OH}} \right)_{2}^{2 + } \).

  13. Bilinski et al. [6], Ekberg et al. [26], and Cho et al. [22] did not filter their samples through membrane filters to eliminate colloids. Sasaki et al. [23] specifically note that their results are affected by the presence of colloids even though they filtered their samples through fine membrane filters.

  14. Zr and NaOH concentrations reported by the authors in molarity units were converted to molality units by using the NaOH data reported in Weast [41] for these conversions. The data in Weast [41] are for NaOH molarities ranging from 0.125 to 14.295. Therefore the converted values for NaOH molality of < 14.295 are based on interpolations and are much more reliable than the values for NaOH molality of > 14.295 based on extrapolations.

  15. Poor detection limits and uncertainties in these data could have been avoided had the studies been conducted in the absence of NaCl solutions.

  16. Based on analogy to known interaction coefficients of doubly charged anionic species with alkali ions reported in Lemire et al. [42].

  17. Assuming that the entire uncertainty in the equilibrium constant for the formation of \( {\text{Zr}}\left( {\text{OH}} \right)_{6}^{- } \) results from the uncertainty in the ε(Na+, \( {\text{Zr}}\left( {\text{OH}} \right)_{6}^{- } \)) value.

  18. For example ΔZ2D − ΔεIm = − 0.022 at 23 molal ionic strength.

  19. For these highly charged species, the equilibrium constant value for the formation of \( {\text{Ca}}_{3} {\text{Zr}}\left( {\text{OH}} \right)_{6}^{4 + } \) and the values for the ion-interaction parameters are interdependent and thus it is not possible to determine unique values for these parameters. The values for the formation constant of \( {\text{Ca}}_{3} {\text{Zr}}\left( {\text{OH}} \right)_{6}^{4 + } \) determined in this study are obtained by using/fitting reasonable values of the SIT and Pitzer ion-interaction parameters that provide close agreement with the ZrO2(am) solubility data in all CaCl2 solutions. It is possible to fit these data using both \( {\text{Ca}}_{2} {\text{Zr}}\left( {\text{OH}} \right)_{6}^{2 + } \) (log10 K0 of ~ − 27.1 ± 0.3 determined from SIT or Pitzer modeling of data using reasonable values of ion-interaction parameters (kg·mol−1) for \( {\text{Ca}}_{2} {\text{Zr}}\left( {\text{OH}} \right)_{6}^{2 + } \) with Cl− of ε = 0.1, and β(0) = 0.3159, β(1) = 1.614, Cϕ = − 0.00034) and \( {\text{Ca}}_{3} {\text{Zr}}\left( {\text{OH}} \right)_{6}^{4 + } \). However, the inclusion of \( {\text{Ca}}_{2} {\text{Zr}}\left( {\text{OH}} \right)_{6}^{2 + } \) in modeling only marginally improved the fit to the ZrO2(am) solubility data in the lowest concentration of CaCl2 solutions investigated (0.1 mol·kg−1) and these species are not dominant in most of the samples. The overall standard deviations in fitting all of these data with either \( {\text{Ca}}_{3} {\text{Zr}}\left( {\text{OH}} \right)_{6}^{4 + } \) or both \( {\text{Ca}}_{3} {\text{Zr}}\left( {\text{OH}} \right)_{6}^{4 + } \) and \( {\text{Ca}}_{2} {\text{Zr}}\left( {\text{OH}} \right)_{6}^{2 + } \) are identical. In order to obtain a reliable equilibrium constant value for the formation of \( {\text{Ca}}_{2} {\text{Zr}}\left( {\text{OH}} \right)_{6}^{2 + } \), ZrO2(am) solubility studies need to be conducted at CaCl2 concentrations < 0.1 mol·kg−1. For these reasons we recommend using only \( {\text{Ca}}_{3} {\text{Zr}}\left( {\text{OH}} \right)_{6}^{4 + } \) to explain ZrO2(am) solubility data in the presence of Ca.

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Acknowledgements

We thank Japan Atomic Energy Agency for funding this research. Kevin Rosso acknowledges support from the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division through its Geosciences Program at Pacific Northwest National Laboratory.

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Authors and Affiliations

  1. Rai Enviro-Chem, LLC, Yachats, OR, USA

    Dhanpat Rai

  2. Japan Atomic Energy Agency, Tokai-mura, Ibaraki, Japan

    Akira Kitamura

  3. Karlsruhe Institute of Technology, Institute for Nuclear Waste Disposal, Karlsruhe, Germany

    Marcus Altmaier

  4. Pacific Northwest National Laboratory, Richland, WA, USA

    Kevin M. Rosso

  5. Kyoto University, Kyoto, Japan

    Takayuki Sasaki & Taishi Kobayashi

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  1. Dhanpat Rai
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  2. Akira Kitamura
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Correspondence to Dhanpat Rai.

Appendix: Computational Methods

Appendix: Computational Methods

Ab initio molecular orbital calculations were performed to evaluate the energy required to construct the polynuclear \( {\text{Zr}}_{4} \left( {\text{OH}} \right)_{8}^{8 + } \) ion from its equivalent monomeric subunits of \( {\text{Zr}}\left( {\text{OH}} \right)_{2}^{2 + } \). To do this, total energy minimizations were performed on the \( {\text{Zr}}_{4} \left( {\text{OH}} \right)_{8}^{8 + } \) ion, modeled as a doubly μ-hydroxy bridged square planar Zr tetramer, and the \( {\text{Zr}}\left( {\text{OH}} \right)_{2}^{2 + } \) ion in the gas-phase at 0 K at the density functional level of theory. Energy minimizations were performed without symmetry constraint first at the spin-restricted Hartree–Fock (RHF) level of theory as a pre-optimization step, and then using the hybrid functional B3LYP [54] starting from the RHF result. The 3-21G basis set was used for all atoms (Zr, O, H) throughout [55, 56]. Water ligands were systematically added to available inner-shell coordination sites on each Zr atom in the tetramer as well as the dihydroxo monomer as long as the computed total energy of hydration remained negative. This yielded final stoichiometries of \( {\text{Zr}}_{4} \left( {\text{OH}} \right)_{8} \left( {{\text{H}}_{2} {\text{O}}} \right)_{12}^{8 + } \) and \( {\text{Zr}}\left( {\text{OH}} \right)_{2} \left( {{\text{H}}_{2} {\text{O}}} \right)_{4}^{2 + } \), respectively. All calculations were performed using the software NWChem version 6.1.1 [57].

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Rai, D., Kitamura, A., Altmaier, M. et al. A Thermodynamic Model for ZrO2(am) Solubility at 25 °C in the Ca2+–Na+–H+–Cl−–OH−–H2O System: A Critical Review. J Solution Chem 47, 855–891 (2018). https://doi.org/10.1007/s10953-018-0766-4

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