Chemical Metallurgy Second Edition J.J. MOORE, PhD, BSc, CEng, MIM Professor and Head, Department of Metallurgical and Materials Engineering, Colorado School of Mines, Golden, Colorado, USA Co-authors E.A. Boyce, CChem, FRSC MJ. Brooks, BSc B. Perry, PhD, BSc, CEng, MIM P.J. Sheridan, PhD, BSc, CChem, MRSC Lecturing staff in the Materials Technology Division at Sandwell College of Further and Higher Education FachbereicM^aiBriaivvisssnschaft derTechn.KochschuieD3mstaol Inv.-Nr.: Butterworths London Boston Singapore Sydney Toronto Wellington Contents Preface v Units and symbols xv 1 BONDING AND PERIODICITY 1 (E.A. Boyce) 1.1 The Atomic Structure of Elements 1 1.1.1 The Nucleus 1 1.1.2 Atomic Spectra 2 1.1.2.1 Bohr theory 2 1.1.2.2 Quantum numbers 3 1.1.2.3 Electronic configuration of the elements 4 1.2 The Periodic Table of the Elements 7 1.3 Chemical Bonds 7 1.3.1 The Ionic Bond (Electrovalency) 9 1.3.1.1 Size of atoms 9 1.3.1.2 Ionisation energy 10 1.3.1.3 Electron affinity 11 1.3.1.4 Electronegativity value 12 1.3.1.5 Structures of ionic solids 13 1.3.1.6 Applications of ionic compounds 15 1.3.2 The Covalent Bond 15 1.3.2.1 Shapes of covalent molecules 16 1.3.2.2 Multiple bonds 18 1.3.2.3 Intermolecular forces 18 1.3.2.4 Covalent giant structures of industrial importance 18 1.3.3 The Metallic Bond 20 1.4 A More Detailed Study of the Periodic Table of the Elements 22 1.4.1 The s-Block elements 22 1.4.1.1 Oxides 22 1.4.1.2 Chlorides 22 1.4.2 Transition Elements (d-Block) 22 1.4.2.1 Magnetic properties 25 1.4.2.2 Colour 26 1.4.2.3 Catalytic properties 26 1.4.2.4 Interstitial compound formation 26 1.4.2.5 Variable oxidation states 26 1.4.2.6 Complexes 26 1.4.2.7 The first transition series (Sc to Zn) 27 1.4.3 The p-Block Elements 29 s I viii Contents . I 2 METALLURGICAL THERMODYNAMICS 32 (M.J. Brooks) 2.1 Thermochemistry 32 2.1.1 Exothermic and endothermic reactions 32 2.1.1.1 Standard enthalpy change for a reaction 33 2.1.2 Calculating enthalpies and enthalpy changes 37 f 2.1.2.1 Further calculations 38 2.1.2.2 Hess's Law (of constant heat summation, 1840) 39 2.1.3 Measurement of enthalpy changes of reactions 41 2.1.4 Enthalpy Changes: The effect of temperature 42 2.1.4.1 Heat capacity (C) I 2.1.4.2 Kirchoff's Equation 43 I 2.2 Thermodynamics 48 1 2.2.1 Energy: The driving force for chemical change 48 f 2.2.1.1 The First Law of Thermodynamics 48 I 2.2.1.2 Entropy: The second factor governing energy changes 53 | 2.2.2 Free Energy: The driving force of a chemical reaction 59 2.2.2.1 The Gibbs-Helmholtz (Second Law) Equation 59 2.2.2.2 The effect of temperature on the feasibility of a reaction 61 2.2.2.3 Calculating AG° for reactions 62 2.2.2.4 Calculations of free energy 65 2.2.3 Chemical Equilibrium 66 2.2.3.1 Law of mass action 67 2.2.3.2 Reactions in progress 69 2.2.3.3 Activities: the effective concentrations of solutions 69 2.2.3.4 Factors affecting the position of equilibrium 70 2.2.3.5 Questions on equilibrium 72 2.2.3.6 Relationship between free energy and equilibrium constant 72 Calculations 75 2.2.3.7 Equilibria in metallurgical processes 76 Calculations 77 2.2.3.8 The effect of temperature on equilibrium 77 I 2.2.3.9 Variation of vapour pressure with temperature ' 80 n Calculations 82 2.2.3.10 Standard free energy - temperature diagrams: application to metal extraction 82 Construction of AG° - T diagrams 83 UseofAG" - T diagrams 86 Nomographic scales on AG° - T diagrams 89 Disadvantages of AG° - T diagrams 92 Calculations 92 3 REACTION KINETICS 95 . (PJ. Sheridan) 3.1 Rate of reaction 96 3.1.1 Effect of conditions on rate of reaction 96 3.1.1.1 Surface area 96 3.1.1.2 Catalysts 97 3.1.2 Concentration—time graphs 97 3.1.3 Kinetics and mechanism 97 3.2 Experimental Rate Laws 98 3.2.1 Order of reaction 99 3.2.2 The rate constant 99 3.2.3 Molecularity 100 3.2.4 Stoichiometry 100 3.2.5 Integrated equations 100 Contents ix 3.2.5.1 Zero order 100 3.2.5.2 First order 101 3.2.5.3 Second order 103 3.2.5.4 Reversible reactions 104 3.2.5.5 Consecutive reactions 106 3.3 Determination of Order of Reaction 107 3.3.1 Integral method 107 3.3.2 Differential method 108 3.3.2.1 Initial rate method 109 3.3.3 Half-life method 110 3.4 Experimental Techniques 111 3.4.1 General considerations 111 3.4.2 Techniques - in general 111 3.4.3 Techniques - in detail 111 3.4.3.1 Weight 111 3.4.3.2 Volume of gas 112 3.4.3.3 Pressure 112 3.4.3.4 Analysis 112 3.4.3.5 Radioactivity 112 3.4.3.6 Dilatometric method 112 3.4.3.7 Absorbance 113. 3.5 Kinetics and Temperature 113 3.5.1 The Arrhenius equation 113 3.5.2 Determination of activation energy 114 3.5.3 Potential energy profiles 115 3.5.4 Effect of temperature 116 3.5.5 Catalysis 117 3.6 Mechanism 118 3.6.1 Rate determining step 119 3.6.1.1 Diffusion control 119 Mass transfer coefficient 120 3.6.2 Elucidation of mechanism 121 3.7 Theories of Reaction Rates 122 3.7.1 Collision theory 122 3.7.1.1 Collision frequency (Z) 122 3.7.2 Potential energy surfaces 123 3.7.3 Transition state theory 124 LIQUID METAL SOLUTIONS 127 (J.J. Moore) 4.1 Solution and Composition 127 4.2 Surface and Interfacial Energy 128 4.3 Thermodynamics of Solutions 129 4.3.1 Partial and integral quantities 130 4.3.2 Ideal solutions and activity 131 4.3.3 Raoult'slaw 132 4.3.4 Non-ideal or real solutions 134 4.3.5 The Gibbs—Duhem equation 136 4.3.6 Henry's Law and dilute solutions 138 4.3.7 Multicomponent solution and interaction coefficients 139 4.3.8 Thermodynamics of mixing solutions 140 4.3.9 Excess thermodynamic quantities 141 x Contents 4.3.10 Construction of equilibrium phase diagram from integral free energy—composition curves 143 4.3.11 Free energy of nucleation 146 4.4 Gases in Metals 148 5 SLAG CHEMISTRY 152 (J.J. Moore) 5.1 Functions and Properties of a Slag 152 5.2 Slag Metal Reactions 154 5.3 Structure of Liquid Slags 154 5.3.1 The cation-O2" bond 154 5.3.2 Aluminate and phosphate structures 160 5.4 Liquid Immiscibility 161 5.4.1 Binary silicate melts 161 5.4.2 Ternary silicate 165 5.4.3 Phosphate melts 165 5.5 The Transition from Ionic to Covalent Bonding and Polarisation 166 5.5.1 Thermodynamic properties-effect of non-ionic bonding 167 5.5.1.1 Thermodynamics and mixing of silicates 168 5.6 Physical Properties of Slags 169 5.6.1 Electrical and thermal conductivities 169 5.6.2 Viscosity of slags 169 5.7 Slag Theories 173 5.7.1 Ionic slag theories 173 i 5.7.1.1 Temkin's theory 173 \ 5.7.1.2 Electrical equivalent ion fraction 177 V 5.7.1.3 Flood's theory 179 5.7.1.4 Masson'stheory, 184 5.7.2 Molecular theory 187 5.7.3 Summary of slag theories 191 6 AQUEOUS METAL SOLUTIONS AND ELECTROCHEMISTRY 193 (P.J. Sheridan and B. Perry) 6.1 Ionics I: Ions in solution 193 6.1.1 Electrolytes 193 6.1.2 Aqueous solutions of electrolytes 193 6.1.3 Ionic activity 194 6.1.4 Mean ionic activity 194 6.1.5 Debye-Hiickel theory 196 6.1.6 Measurement of mean ionic activity 197 6.1.7 Acids and bases 198 6.1.8 The pH scale 199 6.1.9 Buffer solutions 200 6.1.10 pH measurement 200 6.2 Ionics II: Electrolytic conduction 201 6.2.1 Measurement of conductivity 201 6.2.2 Molar conductivity 201 Contents xi 6.2.3 Variation of molar conductivity with concentration 202 6.2.4 Kohlrausch's law of independent migration 204 6.2.5 Transport numbers 204 - 6.2.6 Conduction in fused salts 206 6.3 Electrodics I 206 6.3.1 Electrode potentials 206 6.3.2 The metal electrode 207 6.3.3 Comparison of electrode potentials-electrochemical series 208 6.3.4 Diagrammatic representation of cells 209 6.3.5 The standard electrode potential 209 6.3.6 Reference electrodes 210 6.3.7 Indicator electrodes 211 6.3.8 Cell mechanism 212 6.3.9 Concentration cell 213 6.3.10 Redox potentials 213 6.3.11 Cell thermodynamics 214 6.3.12 The Nernst equation 215 6.3.13 Calculation of emf (cell potential) 215 6.3.14 Concentration cell potentials 216 6.3.15 Application of the Redox Series 217 6.3.16 Kinetic considerations 218 6.3.17 Variation of Redox Potential with pH 218 6.4 Electrolysis 219 6.4.1 Basic considerations 219 6.4.2 Faraday's Laws of electrolysis 221 6.4.3 Current efficiency 221 6.4.4 Energy efficiency 222 6.4.5 Current density 223 6.4.6 Theoretical cell voltage 223 6.4.7 Polarisation and overpotential 224 6.4.8 Decomposition voltage 225 6.4.9 Discharge potential 227 6.4.10 Electroplating 228 6.5 Partition (Distribution) — of solutes between immiscible phases 232 6.5.1 Extraction 233 6.6 Ion Exchange 234 6.7 Adsorption 235 6.7.1 Gibbs Adsorption Isotherm 235 6.7.2 Adsorption of gases 239 7 METAL EXTRACTION PROCESSES 243 (J.J.