4urn:lsid:arphahub.com:pub:27D7DBB2BDE15A1FB26F1372106F69DBBioRiskBR1313264413132652Pensoft Publishers10.3897/biorisk.17.7752377523Research ArticleAnimaliaPlantaeData analysis & ModellingEcology & Environmental sciencesLandscape ecologyWaste management & remediationWorldDevelopment of accurate chemical thermodynamic database for geochemical storage of nuclear waste. Part III: Models for predicting solution properties and solidliquid equilibrium in cesium binary and mixed systemsTsenovTsvetan1InvestigationDonchevStanislav1InvestigationChristovChristomirch.christov@shu.bg1ConceptualizationMethodologySupervisionDepartment Chemistry, Faculty of Natural Sciences, Shumen University “Konstantin Preslavski”, Shumen, BulgariaShumen University “Konstantin Preslavski”ShumenBulgaria
2022210420221740742276F9D6896AD251D3A3C28971268D1E9B64788810211202108122021Tsvetan Tsenov, Stanislav Donchev, Christomir ChristovThis is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The models described in this study are of high importance in the development of thermodynamic database needed for nuclear waste geochemical storage as well as for technology for extracting cesium resources from saline waters. In this study we developed new not concentration restricted thermodynamic models for solution behavior and solidliquid equilibrium in CsFH_{2}O CsOHH_{2}O and Cs_{2}SO_{4}H_{2}O systems at 25 °C. To parameterize models we used all available experimental osmotic coefficients data for whole concentration range of solutions and up to saturation point. The new models are developed on the basis of Pitzer ion interactions approach. The predictions of new developed here models are in excellent agreement with experimental osmotic coefficients data (ϕ) in binary solutions from low to extremely high concentration (up to 21.8 mol.kg^{1} for CsOHH_{2}O and up to 35.6 mol.kg^{1} for CsFH_{2}O). The previously developed by Christov by Christov and coauthors and by other authors Pitzer approach based thermodynamic models for five (5) cesium binary systems (CsClH_{2}O CsBr H_{2}O CsIH_{2}O CsNO_{3}H_{2}O and Cs_{2}SeO_{4} H_{2}O) are tested by comparison with experimental osmotic coefficients data and with recommendations on activity coefficients (γ_{±}) in binary solutions. The models which give the best agreement with (ϕ) and (γ_{±}) data from low to high concentration up to m(sat) are accepted as correct models which can be used for solubility calculations in binary and mixed systems and determination of thermodynamic properties of precipitating cesium solid phases. The thermodynamic solubility products (ln K^{o}_{sp}) and the Deliquescence Relative Humidity (DRH) of solid phases precipitating from saturated cesium binary solutions (CsF(cr) CsCl(cr) CsBr(cr) CsI(cr) CsOH(cr) CsNO_{3}(cr) Cs_{2}SO_{4}(cr) and Cs_{2}SeO_{4}(cr)) have been determined on the basis of evaluated and accepted binary parameters and using experimental solubility data. The reported mixing parameters [θ(Cs M^{2+}) and ψ(Cs M^{2+} X)] evaluated by solubility approach for 15 cesium mixed ternary systems (CsClMgCl_{2}H_{2}O CsBrMgBr_{2}H_{2}O CsClNiCl_{2}H_{2}O CsBrNiBr_{2}H_{2}O CsClMnCl_{2}H_{2}O CsClCoCl_{2}H_{2}O CsClCuCl_{2}H_{2}O CsClCsBrH_{2}O CsClRbClH_{2}O Cs_{2}SO_{4}CoSO_{4}H_{2}O Cs_{2}SeO_{4}CoSeO_{4}H_{2}O Cs_{2}SO_{4}NiSO_{4}H_{2}O Cs_{2}SeO_{4}NiSeO_{4}H_{2}O Cs_{2}SO_{4}ZnSO_{4}H_{2}O and Cs_{2}SeO_{4}ZnSeO_{4}H_{2}O) are tabulated.
Cesium binary and mixed systemscomputer thermodynamic modelinggeochemical nuclear waste sequestrationPitzer approachThe work was supported by the European Regional Development Fund, Project BG05M2OP0011.0010004, and by Shumen University Research Program, Project No. RD08131/04.02.2021Citation
Tsenov T, Donchev S, Christov C (2022) Development of accurate chemical thermodynamic database for geochemical storage of nuclear waste. Part III: Models for predicting solution properties and solidliquid equilibrium in cesium binary and mixed systems. In: Chankova S, Peneva V, Metcheva R, Beltcheva M, Vassilev K, Radeva G, Danova K (Eds) Current trends of ecology. BioRisk 17: 407–422. https://doi.org/10.3897/biorisk.17.77523
Introduction
Radioactive waste is a byproduct of the nuclear fuel cycle and the production of weapons and medical radioisotopes. As nuclear technologies become more widespread, so does the production of waste materials. In Europe, nuclear waste is classified into 1) highlevel; 2) intermediate level; 3) lowlevel, and 4) transitional radioactive waste. The longterm storage of highlevel waste is still experimental. Radiocesium isotopes, particularly ^{137}Cs, form part of the highlevel nuclear waste group. Crucially, the storage of highlevel waste in liquid form poses serious risks. On 29 September 1957 a liquid storage tank exploded at the Mayak facility (Chelyabinsk40), contaminating more than 52,000 square kilometers with ^{137}Cs and ^{90}Sr (Kostyuchenko and Krestinina 1994). This is known as the Kyshtym accident and is the second most serious radiation disaster after Chernobyl at 1986. On 1987 a release of ^{137}Cs occurred as a result of improper disposal of radiotherapy source (Rosenthal et al. 1991). This is known as Goiânia accident in Brazil. According to Scharge et al. (2012) among the more common fission products from spent nuclear fuels, the radionuclide ^{137}Cs with halflives of 30.17 years, is mostly critical for the design of the nuclear waste repository because of the intense γ and β radiation and the heat generated by the decay process, as well as the high solubilities of cesium halides. Thus, modelling the properties of cesium atoms in salts and solutions is a current, pertinent question in theoretical chemistry.
A long term safety assessment of a repository for radioactive waste requires evidence that all relevant processes are known and understood, which might have a significant positive or negative impact on its safety (Altmaier et al. 2011a, b; Lach et al. 2018; Donchev and Christov 2020; Donchev et al. 2021b). It has to be demonstrated, that the initiated chemical reactions don’t lead to an undue release of radionuclides into the environmental geo, hydro, and biosphere. One key parameter to assess the propagation of a radionuclide is its solubility in solutions interacting with the waste. Solubility estimations can either be based on experimental data determined at conditions close to those in the repository or on thermodynamic calculations. The thermodynamic database created from experimental data is the basis for thermodynamic model calculations. Since the disposal of radioactive waste is a task encompassing decades, the database is projected to operate on a longterm basis. Chemical models that predict equilibrium involving mineral, gas and aqueous phases over a broad range of solution compositions and temperatures are useful for studying the interactions between used nuclear fuel waste and its surroundings. The reliability of such predictions depends largely on the thermodynamic database. An accurate description of highly concentrated waters should be required for modeling of chemical interactions in and around nuclear repositories. The modeling of dissolution and precipitation processes in concentrated solutions requires an adequate thermodynamic model for the prediction of activities and solubilities (Lach et al. 2018; Donchev and Christov 2020; Donchev et al. 2021b). This requirement is fulfilled by the ion interaction model of Pitzer (Pitzer 1973). Extensive thermodynamic databases, which are based on the Pitzer ion interaction model, were developed within the Yucca Mountain Project (YMTDB: data0.ypf.r2) (Sandia National Laboratories (2005, 2007), Thereda project (THermodynamic REference DAtabase, THEREDAFinal Report) (Altmaier et al. 2011a, b), and ANDRA project (Lach et al. 2018). However, the subject of longterm radioactive waste storage still has many questions left for scientists to solve. Unfortunately, many of the Pitzer models introduced in YMTDB and in THEREDA databases for cesium binary and mixed systems are concentration restricted and cannot describe correctly the solidliquid equilibrium in geochemical and industrial systems of interest for nuclear waste programs.
This paper presents a comprehensive analysis and evaluation of existent thermodynamic database for cesium binary and mixed systems. It should be noted, that the thermodynamic properties, solubility isotherms and their simulation by thermodynamic model of the cesium binary and mixed brine type systems (s.a. CsX−MgX_{2}−H_{2}O (X =Cl,Br,I) ternary systems) are also of significant importance for extracting cesium resources from brine type solutions (Balarew et al. 1993; Christov et al. 1994; Christov 1995a, b, 1996a, 2005; Guo et al. 2017). According to Baranauskaite et al. (2021) carnalite type minerals of the type MX.MgX_{2}.6H_{2}O (cr) (M=Li, K,NH_{4},Rb,Cs) (Christov and Balarew 1995; Christov 2012; Lassin et al. 2015) “are interesting not only as natural sources of chemical compounds, but also they can be made use of in renewable thermochemical energy storage since their hydration reactions are exothermic”.
In this study we developed new, not concentration restricted thermodynamic models for solution behavior and solidliquid equilibrium in CsFH_{2}O, CsOHH_{2}O and Cs_{2}SO_{4} H_{2}O systems at 25 °C. The new models are developed on the basis of Pitzer ion interactions approach. The previously developed by Christov (2003a, 2005), and Christov and coauthors (Balarew et al. 1993; Barkov et al. 2001; Donchev and Christov 2020) and by other authors (Pitzer and Mayorga 1973; Scharge et al. 2012; Palmer et al. 2002) Pitzer approach based thermodynamic models for five (5) cesium binary systems (CsClH_{2}O, CsBr H_{2}O, CsIH_{2}O, CsNO_{3}H_{2}O, and Cs_{2}SeO_{4} H_{2}O) are tested by comparison with experimental osmotic coefficients data and with recommendations on activity coefficients (γ_{±}) in binary solutions. The models that give the best agreement with (ϕ), and (γ_{±}) data from low to high concentration, up to m(sat), are accepted as correct models, which can be used for solubility calculations in binary and mixed systems. We also summarized the previously established by the main author (C. Christov) solidliquid equilibrium model for 15 cesium mixed ternary systems at 25 °C. The evaluated mixing parameters [θ(Cs,M^{2+}) and ψ(Cs,M^{2+},X)], determined by solubility approach are tabulated.
Methodology
The models for cesium binary systems have been developed and tested on the basis of Pitzer’s semiempirical equations (Pitzer 1973). The specific interaction approach for describing electrolyte solutions to high concentration introduced by Pitzer (1973) represents a significant advance in physical chemistry that has facilitated the construction of accurate computer thermodynamic models. Pitzer approach has found extensive use in the modeling of the thermodynamic properties of aqueous electrolyte solutions. It was shown that this approach could be expanded to accurately calculate solubilities in binary and complex systems, and to predict the behavior of natural and industrial fluids from very low to very high concentration at standard temperature of 25 °C (Harvie et al. 1984; Christov et al. 1994, 1998; Christov 1995a, 1996a, 1998, 1999, 2002, 2003a, b, 2005, 2007, 2009, 2012, 2020; Barkov et al. 2001; Park et al. 2009; Lach et al. 2018; Donchev and Christov 2020; Donchev et al. 2021a, b), and from 0 to 290 °C (Christov and Moller 2004; Moller et al. 2006; Lassin et al. 2015). Several extensive parameter databases have been reported. These include: 25 °C database of Pitzer and Mayorga (1973, 1974), of Kim and Frederick (1988), the most widely used database of Chemical Modelling Group at UCSD [(University California San Diego) at 25 °C (Harvie et al. 1984; Park et al. 2009), and Tvariation (from 0 to 300 °C) (Christov and Moller 2004; Moller et al. 2006; Christov 2009)], YMTDB (Sandia National Laboratories 2005, 2007), and THEREDA (2011a, b).
According to Pitzer theory, electrolytes are completely dissociated and in the solution there are only ions interacting with one another (Pitzer 1973; Pitzer and Mayorga 1973). Two kinds of interactions are observed: (i) specific Coulomb interaction between distant ions of different signs, and (ii) nonspecific shortrange interaction between two and three ions. The first kind of interaction is described by an equation of the type of the DebyeHueckel equations. Shortrange interactions in a binary system (MX(aq)) are determined by Pitzer using the binary parameters of ionic interactions (β^{(0)},β^{(1)}, C^{ϕ}). The Pitzer’s equations are described and widely discussed in the literature (Harvie et al. 1984; Christov and Moller 2004; Christov 2005; Moller et al. 2006; Donchev et al. 2021b). Therefore, these equations are not given here. According to the basic Pitzer equations, at constant temperature and pressure, the solution model parameters to be evaluated for mixed ternary system are: 1) pure electrolyte β^{(0)}, β^{(1)}, and C^{ϕ} for each cationanion pair; 2) mixing θ for each unlike cationcation or anionanion pair; 3) mixing ψ for each triple ion interaction where the ions are all not of the same sign (Christov 2003a, b, 2005; Donchev et al. 2021b).
Pitzer and Mayorga (1973) did not present analysis for any 22 (e.g. MgSO_{4}H_{2}O) or higher {e.g. 32: Al_{2}(SO_{4})_{3}H_{2}O} electrolytes. In their next study (Pitzer and Mayorga 1974) modify the original equations for the description of 22 binary solutions: parameter β^{(2)}(M,X), and an associated α_{2} term are added to the original expression. Pitzer presented these parameterizations assuming that the form of the functions (i.e. 3 or 4 β and C ^{ϕ} values, as well as the values of the α terms) vary with electrolyte type. For binary electrolyte solutions in which either the cationic or anionic species are univalent (e.g. NaCl, Na_{2}SO_{4}, or MgCl_{2}), the standard Pitzer approach use 3 parameters (i.e. omit the β^{(2)} term) and α_{1} is equal to 2.0. For 22 type of electrolytes the model includes the β^{(2)} parameter and α_{1} equals to 1.4 and α_{2} equals to 12. This approach provides accurate models for many 22 binary sulfate (Pitzer and Mayorga 1974; Christov 1999, 2003a) and selenate (Christov et al. 1998; Barkov et al. 2001; Christov 2003a) electrolytes, giving excellent representation of activity data covering the entire concentration range from low molality up to saturation and beyond.
To describe the high concentration solution behaviour of systems showing a “smooth” maximum on γ_{±} vs. m dependence, and to account for strong association reactions at high molality, Christov (1996b, 1998a, b, 1999, 2005) used a very simple modelling technology: introducing into a model a fourth ion interaction parameter from basic Pitzer theory {β^{(2)} }, and varying the values of α_{1} and α_{2} terms (see Eqns. (3) and (3A) in Donchev et al. 2021b). According to previous studies of Christov, an approach with 4 ion interaction parameters (β^{(0)},β^{(1)}, β^{(2)},and C^{ϕ}), and accepting α_{1} = 2, and varying in α_{2} values can be used for solutions for which ion association occurs in high molality region. This approach was used for binary electrolyte systems of different type: 11 type {such as HNO_{3}H_{2}O, LiNO_{3}H_{2}O (Donchev and Christov 2020), and LiClH_{2}O (Lassin et al. 2015)}, 21 {such as NiCl_{2}H_{2}O, CuCl_{2}H_{2}O, MnCl_{2}H_{2}O, CoCl_{2}H_{2}O: (Christov and Petrenko 1996; Christov 1996b, 1999); Ca(NO_{3})_{2}H_{2}O: (Lach et al. 2018); 12 {such as K_{2}Cr_{2}O_{7}H_{2}O: (Christov 1998)}, 31 {such as FeCl_{3}H_{2}O: (Christov 2005), and 32 {such as Al_{2}(SO_{4})_{3}H_{2}O, Cr_{2}(SO_{4})_{3}H_{2}O, and Fe_{2}(SO_{4})_{3}H_{2}O: (Christov 2002, 2005)}. The resulting models reduce the sigma values of fit of experimental activity data, and extend the application range of models for binary systems to the highest molality, close or equal to molality of saturation {m(sat)}, and in case of data availability: up to supersaturation.
Results and discussionsModel parameterization for cesium binary CsFH<sub>2</sub>O, CsOHH<sub>2</sub>O and Cs<sub>2</sub>SO<sub>4</sub>H<sub>2</sub>O systems at 25 °C
In this study we developed new, not concentration restricted thermodynamic models for solution behavior and solidliquid equilibrium in CsFH_{2}O, CsOHH_{2}O and Cs_{2}SO_{4} H_{2}O systems at 25 °C. The new models are developed on the basis of Pitzer ion interactions approach. To parameterize models for cesium binary systems we used all available experimental osmotic coefficients data for whole concentration range of solutions, and up to saturation point. Raw data at low molality from Hamer and Wu (1972) and Mikulin (1968), and extrapolated data from Mikulin (1968) are used to parameterize the model for CsFH_{2}O system. The model for CsOHH_{2}O has been constructed using low molality data from Hamer and Wu (1972) and Mikulin (1968), and osmotic coefficients datapoint at saturation from Mikulin (1968). The new model for Cs_{2}SO_{4} H_{2}O system has been developed using low molality data from Palmer at al. (2002) and Mikulin (1968), and extrapolated osmotic coefficients dataup to saturation from Mikulin (1968). To construct the models, we used different versions of standard molalitybased Pitzer approach. It was established that for CsFH_{2}O system application of extended approach with 4 parameters (β^{(0)}, β^{(1)}, β^{(2)} and C^{ϕ}) and variation of α_{1} and α_{2} terms in fundamental Pitzer equations leads to the lowest values of standard modelexperiment deviation. For CsOHH_{2}O and Cs_{2}SO_{4} H_{2}O system a standard approach with 3 interaction parameters was used. The predictions of new developed here models are in excellent agreement with experimental osmotic coefficients data (ϕ) in binary solutions from low to extremely high concentration (up to 21.8 mol.kg^{1} for CsOHH_{2}O, and up to 35.6 mol.kg^{1} for CsFH_{2}O) (see Fig. 1a, b, g, h, k). As it is shown on Fig. 1 for CsFH_{2}O, CsOHH_{2}O systems the new models are in pure agreement at high concentration with the low molality models of Pitzer and Mayorga (1973). For Cs_{2}SO_{4} H_{2}O system the new model is again in pure agreement at high concentration with the low molality models of Palmer et al. (2002) and Scharge et al. (2012). New activity data are needed to validate the model for this binary.
D345807E9E285D29A3171828BF6D3CD0
(a,b,c,d,e,f,g,h,i,j,k). Comparison of model calculated (lines) for activity coefficients (Fig.i) and for osmotic coefficients (ϕ) in cesium binary solutions (CsFH_{2}O, CsClH_{2}O, CsBr H_{2}O, CsIH_{2}O, CsOHH_{2}O, CsNO_{3}H_{2}O, Cs_{2}SO_{4} H_{2}O, and Cs_{2}SeO_{4} H_{2}O) against molality at T = 298.15 K with recommendations in literature (symbols). For CsFH_{2}O (Fig. b) and CsOHH_{2}O (Fig. h) systems an enlargement of the low molality corner is also given. Heavy solid lines represent the predictions of the developed in this study (for CsFH_{2}O, CsOHH_{2}O, and Cs_{2}SO_{4} H_{2}O systems) and previously reported and accepted models constructed by Christov and coauthors (Christov 2003a, 2005; Balarew et al. 1993; Barkov et al. 2001; Donchev and Christov 2020) and by Pitzer and Mayorga (1973) (for CsIH_{2}O). Dasheddotted, dashed and light solid lines represent the predictions of the reference models of Pitzer and Mayorga (1973) (as P&M on Fig. a,b,c,f, g and h), of Scharge et al. (2012) (for CsClH_{2}O and for Cs_{2}SO_{4} H_{2}O (Fig. c, d and k)), and of Palmer et al. (2002) (for Cs_{2}SO_{4} H_{2}O (Fig. k)) and of YMTB (given as YM on Fig. c and g) (Sandia National Laboratories (2005). Experimental data (symbols) are from Hamer and Wu (1972) (for 11 systems), Robinson and Stokes (1959), Mikulin (1968), Palmer et al. (2002) (for Cs_{2}SO_{4} H_{2}O), Partanen (2010) (recommended values for CsIH_{2}O) and from Barkov et al. (2001) (for Cs_{2}SeO_{4} H_{2}O). The molality of stable crystallization of solid cesium phases is given on all figures by vertical lines (see Table 1 for m(sat) sources).
https://binary.pensoft.net/fig/675650Validation of models for cesium binary systems CsClH<sub>2</sub>O, CsBr H<sub>2</sub>O, CsIH<sub>2</sub>O, CsNO<sub>3</sub>H<sub>2</sub>O, and Cs<sub>2</sub>SeO<sub>4</sub> H<sub>2</sub>O
The previously developed by Christov (2003a, 2005), and Christov and coauthors (Balarew et al. 1993; Barkov et al. 2001; Donchev and Christov 2020) and by other authors (Pitzer and Mayorga 1973; Kim and Frederick 1988; Sharge et al. 2012) Pitzer approach based thermodynamic models for five (5) cesium binary systems (CsClH_{2}O, CsBrH_{2}O, CsIH_{2}O, CsNO_{3}H_{2}O, and Cs_{2}SeO_{4} H_{2}O) are tested in this study by comparison with experimental osmotic coefficients data and with recommendations on activity coefficients (γ_{±}) (for CsNO_{3}H_{2}O) in binary solutions (Fig. 1). The models which give the best agreement with (ϕ), and (γ_{±})  data from low to high concentration, up to m(sat), are accepted as correct models, which can be used for solubility calculations in binary and mixed systems and determination of thermodynamic characteristics of precipitating cesium solid phases. The following models are accepted as correct models: model of Balarew et al. (1993) and Christov et al. (1994) for CsClH_{2}O, and CsBrH_{2}O systems (see heavy solid line on Fig. 1c,d,e); model of Pitzer and Mayorga (1973) for CsIH_{2}O (see heavy solid line on Fig. 1f); model of Donchev and Christov (2020) for CsNO_{3}H_{2}O (see heavy solid line on Fig. 1i), and the model of Barkov et al. (2001) for Cs_{2}SeO_{4} H_{2}O system (see heavy solid line on Fig. 1j).
Deliquescence Relative Humidity (<abbrev xlink:title="Deliquescence Relative Humidity" id="ABBRID0EQSAE">DRH</abbrev> (%)) and thermodynamic solubility product (ln K<sup>o</sup><sub>sp</sub>) of cesium solid phases
On the basis of evaluated previously and accepted models (see previous paragraph) and evaluated in this study binary parameters we determine water activity (a_{w}) and Deliquescence Relative Humidity (DRH (%)) of solid phases crystallizing from saturated binary solutions. According to Christov (2009, 2012), Donchev and Christov (2020) and Donchev et al. (2021b): DRH (%) = a_{w} (sat) × 100; where a_{w} (sat) is activity of water at saturation. The results of DRH calculations are given in Table 1. The DRH predictions of new and accepted models are in excellent agreement with the experimental data determined using isopiestic method, and given in Mikulin (1968). According to model calculations the solidliquid phase change of CsF(s), occurs at extremely low relative humidity of environment. As a next step, using the accepted and new developed parameterizations, and experimentally determined molalities (m(sat)) of the saturated binary solutions (Mikulin 1968; Balarew et al. 1993; Barkov et al. 2001; Palmer et al. 2002) we calculate the logarithm of the thermodynamic solubility product (ln K^{o}_{sp}) of cesium solid phases crystallizing from saturated binary solutions at 25 °C. The calculation approach is the same as in Christov (1995a, 1996a, 2005, 2009, 2012), in Donchev and Christov (2020), and in Donchev et al. (2021b). The model calculations are given in Table 1.
Model calculated logarithm of the thermodynamic solubility product (as lnK^{o}_{sp}), and model calculated and recommended values of the Deliquescence Relative Humidity (DRH) of the of cesium solid phases crystallizing from saturated binary solutions at T = 25 °C.
Salt composition
m (sat) (exp) (mol.kg^{1})
Calculated lnK^{o}_{sp}
DRH(%)
Calculated
Experimental data^{a}
CsF (cr)
35.6^{a}
14.74
2.46
4.0
CsCl (cr)
11.37^{b}
3.49
65.69
65.80
CsBr(cr)
5.79^{b}
1.905
82.62
82.6
CsI(cr)
3.305^{a}
0.675
90.71
90.60
CsOH(cr)
21.8^{a}
6.067
66.57

CsNO_{3}(cr)
1.40^{a}
1.328^{e}
96.54^{e}
96.50
Cs_{2}SO_{4}(cr)
5.0^{c}
0.9424^{f}
80.60^{f}
80.40
1.971^{g}
74.59 ^{g}
1.486^{h}
76.74^{h}
Cs_{2}SeO_{4}(cr)
6.34^{d}
1.45
72.86

aExperimental data of Mikulin (1968); bExperimental data of Balarew et al. (1993) and Christov (2005); cExperimental data of Palmer et al. (2002) and Christov (2003,2005); dExperimental data of Barkov et al. (2001) and Christov (2003); eFrom Donchev and Christov (2020);
^{f}Calculated using binary parameters determinate in this study (heavy solid line on Fig. 1k);
^{g}Calculated using binary parameters from Palmer et al. (2002) (dashed line on Fig. 1k);
^{h}Calculated using 4 parameters model of Sharge et al. (2012) (light solid line on Fig. 1k).
Models for cesium ternary systems
In previous studies of Christov (1996bc, 2003a, 2005) and Christov and coauthors (Balarew et al. 1993; Christov et al. 1994; Christov and Petrenko 1996; Barkov et al. 2001), a solidliquid equilibrium Pitzer approach models for 15 cesium mixed ternary (CsClMgCl_{2}H_{2}O, CsBrMgBr_{2}H_{2}O, CsClNiCl_{2}H_{2}O, CsBrNiBr_{2}H_{2}O, CsClMnCl_{2}H_{2}O, CsClCoCl_{2}H_{2}O, CsClCuCl_{2}H_{2}O, CsClCsBrH_{2}O, CsClRbClH_{2}O, Cs_{2}SO_{4}CoSO_{4}H_{2}O, Cs_{2}SeO_{4}CoSeO_{4}H_{2}O, Cs_{2}SO_{4}NiSO_{4}H_{2}O, Cs_{2}SeO_{4}NiSeO_{4}H_{2}O, Cs_{2}SO_{4}ZnSO_{4}H_{2}O, and Cs_{2}SeO_{4}ZnSeO_{4}H_{2}O) systems at 25 °C are reported. The validated here parameterization for binary systems CsClH_{2}O, CsBr H_{2}O, and Cs_{2}SeO_{4} H_{2}O have been used without adjustment to develop a model for mixed systems. The Pitzer mixing ion interaction parameters (θ(Cs,M^{2+}) and ψ(Cs,M^{2+},X) for the cesium common anion ternary systems have been evaluated on the basis of the experimental data on the compositions of the saturated ternary solutions, i.e. using “ solubility approach” (Harvie et al. 1984; Christov 1995a, 1996a, b, 1998, 1999, 2005, 2012).
The values of evaluated mixing parameter are summarized in Table 2. The mixed solution models are developed using our own solubility data (Balarew et al. 1993; Barkov et al. 2001), or the reference data from Zdanovskii et al. (2003), and Silcock (1979). The choice of the mixing parameters is based on the minimum deviation of the logarithm of the solubility product (lnK^{o}_{sp}) for the whole crystallization curve of the component from its value for the binary solution. See Table 1 for lnK^{o}_{sp} values for cesium simple salts. In addition, the lnK^{o}_{sp} value for the cesium double salts crystallizing from the saturated ternary solutions has to be constant along the whole crystallization branch of the double salt. Since the parameters θ(M,M’) take into account only the ionic interactions of the type MM’ in mixing solutions, their values have to be constant for the chloride, bromide, sulfate and selenate solutions with the same cations (M^{+} and M^{2+}). Therefore, for common cation systems in constructing the mixing model, we keep the same value of θ(M,M’), and only the ψ(M,M’,X) have been varied. In our θ and ψ evaluation the unsymmetrical mixing terms (^{E}θ and ^{E}θ’) have been included (2003a, b, 2005). Mixing solution parameters for systems with precipitation of solid solutions (CsClCsBrH_{2}O and CsClRbClH_{2}O) calculated by using the Zdanovskii rule (Christov et al. 1994; Christov 1996c, 2005) are also given in Table 2.
Solutions mixing parameters [q(Cs,M^{2+}) and y(Cs,M^{2+},X)] evaluated on the basis of the m (sat) molality in cesium common anion ternary systems at 25 °C.
System
q(Cs,M^{2+})
y(Cs,M^{2+},X)
Reference
CsClMgCl2H2O
0.1260
0.0000
Balarew et al. (1993)
CsBrMgBr2H2O
0.1260
0.0367
Balarew et al. (1993)
CsClMnCl2H2O
0.00
0.00
Christov and Petrenko (1996)
CsClCoCl2H2O
0.00
0.00
Christov and Petrenko (1996)
Cs_{2}SO_{4}CoSO_{4}H_{2}O^{a}
(I) 0.00
(I)0.09
Christov (2003a, 2005)
(II) 0.05
(II) 0.04
Cs_{2}SeO_{4}CoSeO_{4}H_{2}O^{a}
(I) 0.00
(I) 0.04
Christov (2003a, 2005)
(II) 0.05
(II) 0.02
CsClNiCl2H2O
0.23
0.0000
Christov (1996b)
CsBrNiBr2H2O
0.23
0.0199
Christov (1996b)
Cs_{2}SeO_{4}NiSO_{4}H_{2}O^{a}
(I) – 0.23
(I) 0.015
Christov (2003a, 2005)
(II) 0.05
(II) 0.05
Cs_{2}SeO_{4}NiSeO_{4}H_{2}O^{a}
(I) – 0.23
(I) 0.015
Barkov et al. (2001)
(II) 0.05
(II) 0.13
Christov (2003a, 2005)
Cs_{2}SO_{4}ZnSO_{4}H_{2}O
0.05
0.05
Christov (2003a)
Cs_{2}SeO_{4}ZnSeO_{4}H_{2}O
0.05
0.08
Christov (2003a)
CsClCuCl2H2O
0.00
0.050
Christov and Petrenko (1996)
CsClCsBrH_{2}O^{b}
0.0001
0.00001
Christov (1996c, 2005)
CsClRbClH_{2}O^{b}
0.00025
0.00060
Christov et al. (1994)
^{a} Two sets of mixing parameters (I and II) are evaluated in Christov (2003, 2005); ^{b}Mixing solution parameters calculated by using the Zdanovskii rule (Christov et al. (1994); Christov (1996c, 2005)).
Summary and conclusions
In this study we developed new, not concentration restricted thermodynamic models for solution behavior and solidliquid equilibrium in CsFH_{2}O, CsOHH_{2}O and Cs_{2}SO_{4} H_{2}O systems at 25 °C. To parameterize models for cesium binary systems we used all available experimental osmotic coefficients data for whole concentration range of solutions, and up to saturation point. The new models are developed on the basis of Pitzer ion interactions approach. To construct the models, we used different versions of standard molalitybased Pitzer approach. It was established that for CsFH_{2}O system application of extended approach with 4 parameters (β^{(0)}, β^{(1)}, β^{(2)} and C^{ϕ}) and variation of α_{1} and α_{2} terms in fundamental Pitzer equations leads to the lowest values of standard modelexperiment deviation. The predictions of new developed here models are in excellent agreement with experimental osmotic coefficients data (ϕ) in binary solutions from low to extremely high concentration (up to 21.8 mol.kg^{1} for CsOHH_{2}O, and up to 35.6 mol.kg^{1} for CsFH_{2}O). The previously developed Pitzer approach based thermodynamic models for five (5) cesium binary systems (CsClH_{2}O, CsBr H_{2}O, CsIH_{2}O, CsNO_{3}H_{2}O, and Cs_{2}SeO_{4} H_{2}O) are tested by comparison with experimental osmotic coefficients data and with recommendations on activity coefficients (γ_{±}) in binary solutions. The models which give the best agreement with (ϕ), and (γ_{±}) data from low to high concentration, up to m(sat), are accepted as correct models, which can be used for solubility calculations in binary and mixed systems and determination of thermodynamic characteristics of cesium solid phases. The thermodynamic solubility products (ln K^{o}_{sp}), and the Deliquescence Relative Humidity (DRH) of solid phases, precipitating from saturated cesium binary solutions (CsF(cr), CsCl(cr), CsBr(cr), CsI(cr), CsOH(cr), CsNO_{3}(cr), Cs_{2}SO_{4}(cr), and Cs_{2}SeO_{4}(cr)) have been determined on the basis of evaluated binary parameters and using experimental solubility data. The previously established and validated here parameterization for binary systems CsClH_{2}O, CsBr H_{2}O, Cs_{2}SO_{4} H_{2}O, and Cs_{2}SeO_{4} H_{2}O have been used without adjustment to develop a solidliquid equilibrium model for 15 cesium mixed ternary (CsClMgCl_{2}H_{2}O, CsBrMgBr_{2}H_{2}O, CsClNiCl_{2}H_{2}O, CsBrNiBr_{2}H_{2}O, CsClMnCl_{2}H_{2}O, CsClCoCl_{2}H_{2}O, CsClCuCl_{2}H_{2}O, CsClCsBrH_{2}O, CsClRbClH_{2}O Cs_{2}SO_{4}CoSO_{4}H_{2}O, Cs_{2}SeO_{4}CoSeO_{4}H_{2}O, Cs_{2}SO_{4}NiSO_{4}H_{2}O, Cs_{2}SeO_{4}NiSeO_{4}H_{2}O, Cs_{2}SO_{4}ZnSO_{4}H_{2}O, and Cs_{2}SeO_{4}ZnSeO_{4}H_{2}O) systems at 25 °C. The evaluated previously mixing parameters [θ(Cs,M^{2+}) and ψ(Cs,M^{2+},X)], determined by solubility approach are tabulated. The models described in this study are of high importance in development of thermodynamic database needed for nuclear waste geochemical storage. The models are also of significant importance for extracting cesium resources from saline waters.
Acknowledgement
We wish to thank the reviewers (Dr. Krasimir Kostov, Dr. Francisca Justel and anonymous reviewer) for their constructive suggestions and helpful comments. The manuscript was improved considerably through their comments. The work was supported by the European Regional Development Fund, Project BG05M2OP0011.0010004, and by Shumen University Research Program, Project No. RD08131/04.02.2021.
ReferencesAltmaierMBrendlerVBubeCMarquardtCMoogHCRichterASchargeTVoigtWWilhelmS (2011a) THEREDA: Thermodynamic Reference Database. Final Report (short version), 63 pp.AltmaierMBrendlerVBubeCNeckVMarquardtCMoogHCRichterASchargeTVoigtWWilhelmSWilmsTWollmannG (2011b) THEREDAThermodynamische Referenzdatenbasis. Report GRS 265. [In German]BalarewCChristovCPetrenkoSValyashkoV (1993) Thermodynamics of formation of carnallite type double salts.BaranauskaiteVBelyshevaMPestovaOAnufrikovYSkripkinMKondratievYKhripunV (2021) Thermodynamic Description of Dilution and Dissolution Processes in the MgCl2CsClH2O Ternary System. Materials (Basel) 14(14): e4047. https://doi.org/10.3390/ma14144047BarkovDChristovCOjkovaT (2001) Thermodynamic study of (m_{1}Cs_{2}SeO_{4} + m_{2}NiSeO_{4})(aq), where m denotes molality, at the temperature 298.15 K.ChristovC (1995a) Thermodynamic study of (b_{1}LiBr + b_{2}MgBr_{2})(aq), where b denotes molality, at the temperature 348.15 K.ChristovC (1995b) Discontinuities in the mixed crystal series of isostructural carnallite type double salts.ChristovC (1996a) Thermodynamics of the aqueous sodium and magnesium bromide system at the temperatures 273.15 K and 298.15 K.ChristovC (1996b) Pitzer model based study of CsX  NiX_{2}  H_{2}O (X = Cl, Br) systems at 298.15 K.ChristovC (1996c) A simplified model for calculation of the Gibbs energy of mixing in crystals: Thermodynamic theory, restrictions and applicability.ChristovC (1998) Thermodynamic study of the KClK_{2}SO_{4}K_{2}Cr_{2}O_{7}H_{2}O system at the temperature 298.15 K.ChristovC (1999) Study of (m_{1}KCl + m_{2}MeCl_{2})(aq), and (m_{1}K_{2}SO_{4} + m_{2}MeSO_{4})(aq) where m denotes molality and Me denotes Cu or Ni, at the temperature 298.15 K.ChristovC (2002) Thermodynamics of formation of ammonium, sodium, and potassium alums and chromium alums.ChristovC (2003a) Thermodynamics of formation of double salts M_{2}SO_{4}.MeSO_{4}.6H_{2}O and M_{2}SeO_{4}.MeSeO_{4}.6H_{2}O where M denotes Rb, or Cs, and Me denotes Co, Ni or Zn.ChristovC (2003b) Thermodynamic study of aqueous sodium, potassium and chromium chloride systems at the temperature 298.15 K.ChristovC (2005) Thermodynamics of formation of double salts and solid solutions from aqueous solutions.ChristovC (2007) An isopiestic study of aqueous NaBr and KBr at 50°C. Chemical Equilibrium model of solution behavior and solubility in the NaBrH_{2}O, KBrH_{2}O and NaKBrH_{2}O systems to high concentration and temperature.ChristovC (2009) Chemical equilibrium model of solution behavior and solubility in the MgCl_{2}H_{2}O, and HClMgCl_{2}H_{2}O systems to high concentration from 0°C to 100°C.ChristovC (2012) Study of bromide salts solubility in the (m_{1}KBr + m_{2}CaBr_{2})(aq) system at T = 323.15 K. Thermodynamic model of solution behavior and solidliquid equilibria in the ternary (m_{1}KBr + m_{2}CaBr_{2})(aq), and (m_{1}MgBr_{2} + m_{2}CaBr_{2})(aq), and in quinary {Na+K+Mg+Ca+Br+H_{2}O} systems to high concentration and temperature.ChristovC (2020) Thermodynamic models for solidliquid equilibrium of aluminum, and aluminumsilicate minerals in natural fluids. Current state and perspectives.ChristovCBalarewC (1995) Effect of temperature on the solubility diagrams of carnallite type double salts.ChristovCMollerN (2004) A chemical equilibrium model of solution behavior and solubility in the HNaKCaClOHHSO_{4}SO_{4}H_{2}O system to high concentration and temperature.ChristovCPetrenkoS (1996) Thermodynamics of formation of double salts in the systems CsClMCl_{2}H_{2}O where M denotes Mn, Co or Cu.ChristovCPetrenkoSBalarewCValyashkoV (1994) Thermodynamic simulation of fourcomponent carnallite type systems.ChristovCOjkovaTMihovD (1998) Thermodynamic study of (m_{1}Na_{2}SeO_{4} + m_{2}NiSeO_{4})(aq), where m denotes molality, at the temperature 298.15 K.DonchevSChristovC (2020) Development of Accurate Chemical Thermodynamic Database for Geochemical Storage of Nuclear Waste. Part I: Models for Predicting Solution Properties and SolidLiquid Equilibrium in Binary Nitrate Systems of the Type 11, Ecologia Balkanica, Special Edition 3: 195–210. http://eb.bio.uniplovdiv.bgDonchevSTsenovTChristovC (2021a) Chemical and geochemical modeling. Thermodynamic models for binary fluoride systems from low to very high concentration (> 35 m) at 298.15 K.DonchevSTsenovTChristovC (2022) Development of accurate chemical thermodynamic database for geochemical storage of nuclear waste. Part II: Models for predicting solution properties and solidliquid equilibrium in binary nitrate systems. In: ChankovaSPenevaVMetchevaRBeltchevaMVassilevKRadevaGDanovaK (Eds) Current trends of ecology.GuoLWangYTuLLiJ (2017) Thermodynamics and Phase Equilibrium of the System CsCl−MgCl_{2}−H_{2}O at 298.15 K.HamerWJWuYC (1972) Osmotic coefficients and mean activity coefficients of uniunivalent electrolytes in water at 25°C.HarvieCMollerNWeareJ (1984) The prediction of mineral solubilities in natural waters: The NaKMgCaHClSO_{4}OHHCO_{3}CO_{3}CO2H_{2}O system from zero to high concentration at 25°C.KimHTFrederickW (1988) Evaluation of Pitzer ion interaction parameters of aqueous electrolytes at 25°C. 1. Single salt parameters.KostyuchenkoVKrestininaL (1994) Longterm irradiation effects in the population evacuated from the eastUrals radioactive trace area.LachAAndréLGuignotSChristovCHenocqPLassinA (2018) A Pitzer parameterization to predict solution properties and salt solubility in the HNaKCaMgNO_{3}H_{2}O system at 298.15 K.LassinAChristovCAndréLAzaroualM (2015) A thermodynamic model of aqueous electrolyte solution behavior and solidliquid equilibrium in the LiHNaKClOHH_{2}O system to very high concentrations (40 Molal) and from 0 to 250°C.MikulinG (1968) MollerNChristovCWeareJ (2006) PalmerDRardJCleggS (2002) Isopiestic determination of the osmotic and activity coefficients of Rb_{2}SO_{4}(aq) and Cs_{2}SO_{4}(aq) at T = (298.15 and 323.15) K, and representation with an extended ioninteraction (Pitzer) model.ParkJHChristovCIvanovAMolinaM (2009) On OH uptake by sea salt under humid conditions. Geophysical Research Letters 36(2): LO2802. https://doi.org/10.1029/2008GL036160PartanenJ (2010) Reevaluation of the Thermodynamic Activity Quantities in Aqueous Alkali Metal Iodide Solutions at 25 °C.PitzerKS (1973) Thermodynamics of Electrolytes. I. Theoretical Basis and General Equations.PitzerKSMayorgaG (1973) Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one or both ions univalent.PitzerKSMayorgaG (1974) Thermodynamics of electrolytes. III. Activity and osmotic coefficients for 22 electrolytes.RobinsonRStokesR (1959) Electrolyte Solutions, 2^{nd} edn. Butterworths, London.RosenthalJJde AlmeidaCEMendonçaAH (1991) The radiological accident in Goiania: The initial remedial actions.Sandia National Laboratories (2005) Pitzer database expansion to include actinides and transition metal species (data0.ypf.R1) U.S. Department of Energy, ANLWISGS000001 REV 00.Sandia National Laboratories (2007) Qualification of thermodynamic data for geochemical modeling of mineralwater interactions in dilute systems (data0.ypf.R2) U.S. Department of Energy, ANLWISGS000003 REV 01.SchargeTMunozAMoogH (2012) Activity Coefficients of Fission Products in Highly Salinary Solutions of Na^{+}, K^{+}, Mg^{2+}, Ca^{2+}, Cl^{−}, and SO4 ^{2−}: Cs^{+}.SilcockH (1979) Solubilities of Inorganic and Organic Compounds, Pergamon Press.ZdanovskiiASolovevaELiahovskaiaEShestakovNShleimovichPAbutkovaLCheremnihLKulikovaT (2003) Experimentalnie Dannie po rastvorimosti. vols. I1, I2, II1 and II2. Khimizdat, St. Petersburg.