THEORIES OF SOLUTIONS
PART I: Extended summary 1 I1 Introduction: scope, objectives and the audience of guidelines 1 I11 Motivation 1 I12 Objectives3 I13 Audience3 I14 Scope4 I2 Definitions4 I3 From Aqueous to Solid Solutions 7 I4 Basic Thermodynamics of Solid Solutions 12 I41 The enthalpy of mixing 13 I42 The entropy of mixing 13 I43 Regular, subregular and generalised mixing models 14 I44 Dilute solid solutions 14 I45 On the relevance of non-ideality 14 I46 Solid solution versus other uptake modes 16 I47 Concepts and approximations in geochemical modelling of Aq-SS systems 17 I471 Lippmann diagrams, a tool to visualise binary Aq-SS systems 18 I48 Kinetic and thermodynamic approximations to Aq-SS in geochemical reactive transport modelling 18 I5 Experimental and analytical aspects 19 I51 Synthesis procedures 20 I52 Characterization of the solid solution 20 I53 Solubility measurements in aqueous solutions 22 I54 Partition/distribution experiments 22 I55 Direct measurements of thermodynamic and mixing properties of solids in Aq-SS systems 23 I551 Retrieval of excess Gibbs energy from electrochemical measurements 23 I552 Calorimetry 23 I6 Testing the Aq-SS concepts and methods in nuclear waste management relevant systems 25 I61 Radium and its incorporation into the barite solid solution family: environmental implications 25 I611 The radium-barite relationship in natural and anthropogenic environments 25 I612 Numerical modelling involving (Ba,Ra)SO4 solid solutions 26 I613 Conclusions27 I62 Cement phases – Solubility of calcium silicate hydrates (C-S-H) 27 I621 Relevance of cement phases in radioactive waste management 27 I622 Thermodynamic modelling of C-S-H and its limitations 27 I623 Geochemical modelling of C-S-H systems of interest in radioactive waste management 28 I624 Conclusions29 I63 Structural incorporation of trivalent actinides/lanthanides into calcite 29 I631 The relevance of calcite for radioactive waste management 29 I632 Macroscopic information related to the sorption of f-elements into calcite 30 I633 Spectroscopic information on the incorporation of f-elements into the calcite structure 30 I634 Thermodynamic modelling of the Eu(III)/calcite system 31 I635 Conclusions31 I64 Solid solutions in the nuclear fuel cycle 31 I641 The applicability of Aq-SS thermodynamics to spent nuclear fuel 31 I642 Main results from the characterisation of UO2 spent nuclear fuel 32 I643 Application of Aq-SS thermodynamics to spent fuel dissolution data 32 I644 Conclusions33 I7 Report conclusions 33 PART II: Theory, experimental aspects and cases for study 35 II1 Theoretical aspects of solid solutions and their solubility 35 II11 Theory of solid solutions 35 II111 Introduction35 II112 Thermodynamic formalism37 II113 The entropy of mixing 40 II114 Regular, subregular and generalised mixing models 44 II1141 Dilute solid solutions 49 II115 Phases with different structures 51 II116 Order-disorder phenomena 55 II1161 General comments 55 II1162 An example: carbonates with calcite and dolomite structure 56 II12 Methods and tools for thermodynamic description of aqueous-solid solution (Aq-SS) equilibria 60 II121 Definitions and basic thermodynamics relations 62 II1211 Mole fraction scale 64 II1212 Molality scale 65 II1213 Aqueous activity coefficients 66 II12131 SIT Model 69 II12132 Pitzer Model70 II12133 Extended UNIQUAC Model 70 II1214 Gas mixtures and gas solubility 71 II1215 Solid solubility72 II1216 Unified theory of ionic solid solution solubilities 74 II1217 Multicomponent ionic Aq-SS system 76 II122 Lippmann diagrams, a tool to visualise binary Aq-SS systems 77 II1221 Example of the use of Lippmann diagrams 80 II123 Law of mass action (LMA) method for computing equilibrium speciation 86 II124 Gibbs energy minimisation (GEM) method 94 II1241 GEM IPM algorithm 97 II1242 GEM dual-thermodynamic calculations in forward modelling 101 II1243 Multiple solid solutions and miscibility gaps 103 II13 Methods of retrieval of stoichiometry, stability of solid solution end-members, and parameters of non-ideal mixing (inverse modelling) 105 II131 The “activity ratios” technique 105 II132 Dual Thermodynamic retrieval calculations 109 II1321 Algorithm of the single Dual-Th calculation at equilibrium 110 II1322 Retrieval of activity coefficients and mixing parameters 110 II1323 Retrieval of end-member standard Gibbs energy and solubility product at equilibrium 112 II1324 Retrieval of apparent molar Gibbs energy for a trace end-member 113 II1325 Dual-Th retrieval calculations at minimum stoichiometric saturation 113 II1326 Statistical Dual-Th calculations 115 II1327 Example: EuIII in calcite 116 II133 Graphical fitting and regression methods 120 II1331 Weighted least-squares and Bayesian estimation techniques 121 II134 Retrieval of excess Gibbs energy from electrochemical measurements 122 II135 Estimation of interaction parameters from the position of miscibility gaps 125 II1351 Miscibility gap data 126 II1352 Critical mixing-point data 127 II136 Estimation of interaction parameters from distribution coefficients 129 II2 Experimental and analytical aspects 130 II21 Co-precipitation experiments in aqueous solution 131 II211 Limitations and points to notice 131 II2111 Synthesis procedures 134 II22 Solubility measurements in aqueous solutions 136 II221 Thermodynamic equilibrium solubility137 II222 Stoichiometric saturation 139 II23 Solid phase characterisation 142 II3 Cases of specific interest in relevant systems155 II31 Sulphates: the barite isostructural family and the incorporation of radioactive isotopes of Ra 155 II311 Introduction to the barite isostructural family 155 II312 The radium and its incorporation into the barite solid solution family: environmental implications 158 II3121 The radium-barium relationship in natural and anthropogenic environments 158 II3122 Numerical modelling involving (Ba,Ra)SO4 solid solutions 160 II313 Conclusions168 II32 Cases study/Cement phases – Solubility of calcium silicate hydrates (C-S-H) 169 II33 Structural incorporation of trivalent actinides/lanthanides into calcite 184 II34 Solid solutions in the nuclear fuel cycle 193 II341 Introduction 193 II342 Solid solution in nuclear materials 194 II3421 Uraninite and non irradiated fuel 194 II3422 Irradiated UO2 195 II3423 Mixed oxide (MOX) and Rock-like oxide (ROX) 196 II343 Application of Aq-SS thermodynamics to spent fuel dissolution experimental data 196 II3431 Strontium 197 II3432 Barium 199 II3433 Neptunium 200 II3434 Plutonium 201 II3435 Lanthanides202 II344 Final remarks 203