Research Article 
Corresponding author: Christomir Christov ( ch.christov@shu.bg ) Academic editor: Michaela Beltcheva
© 2022 Tsvetan Tsenov, Stanislav Donchev, Christomir Christov.
This 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.
Citation:
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: 407422. https://doi.org/10.3897/biorisk.17.77523

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 systems, computer thermodynamic modeling, geochemical nuclear waste sequestration, Pitzer approach
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 (
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 (
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 (
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
The models for cesium binary systems have been developed and tested on the basis of Pitzer’s semiempirical equations (
According to Pitzer theory, electrolytes are completely dissociated and in the solution there are only ions interacting with one another (
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,
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
(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 (
The previously developed by
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
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   
In previous studies of
The values of evaluated mixing parameter are summarized in Table
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 

CsBrMgBr2H2O  0.1260  0.0367 

CsClMnCl2H2O  0.00  0.00 

CsClCoCl2H2O  0.00  0.00 

Cs_{2}SO_{4}CoSO_{4}H_{2}O^{a}  (I) 0.00  (I)0.09 

(II) 0.05  (II) 0.04  
Cs_{2}SeO_{4}CoSeO_{4}H_{2}O^{a}  (I) 0.00  (I) 0.04 

(II) 0.05  (II) 0.02  
CsClNiCl2H2O  0.23  0.0000 

CsBrNiBr2H2O  0.23  0.0199 

Cs_{2}SeO_{4}NiSO_{4}H_{2}O^{a}  (I) – 0.23  (I) 0.015 

(II) 0.05  (II) 0.05  
Cs_{2}SeO_{4}NiSeO_{4}H_{2}O^{a}  (I) – 0.23  (I) 0.015 

(II) 0.05  (II) 0.13 


Cs_{2}SO_{4}ZnSO_{4}H_{2}O  0.05  0.05 

Cs_{2}SeO_{4}ZnSeO_{4}H_{2}O  0.05  0.08 

CsClCuCl2H2O  0.00  0.050 

CsClCsBrH_{2}O^{b}  0.0001  0.00001 

CsClRbClH_{2}O^{b}  0.00025  0.00060 

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.
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.