Preface... xi Chapter 1. Metallurgical Thermochemistry... 1 1.1. Introduction... 1 1.2. Quantities characterizing the state of a system and its evolution... 3 1.2.1. The types of operations... 3 1.2.2. Stoichiometric description of a chemical system... 4 1.2.3. Evolution of a system s state: degree of advancement of a reaction... 6 1.2.4. Characteristic quantities of a phase s composition... 11 1.3. Thermodynamic fundamentals of reactions... 16 1.3.1. Reaction enthalpy... 16 1.3.2. Gibbs free energy of a system, affinity of a reaction and chemical potential of a component... 18 1.3.3. Expressions of the chemical potential and activities of a component... 21 1.3.4. Affinity of a reaction: law of mass action (thermodynamic modeling of a process)... 28 1.3.5. Applications... 32 1.4. Phase diagrams... 36 1.4.1. Binary phase diagrams... 36 1.4.2. Ternary phase diagrams... 36 1.5. Bibliography... 39 Chapter 2. Oxides, Sulfides, Chlorides and Carbides... 41 2.1. Introduction... 41 2.2. Metal-oxygen/metal-sulfur systems activities in the intermediate phases... 42
vi Extractive Metallurgy 1 2.2.1. Phase diagrams... 42 2.2.2. Component activities in the intermediate phases... 46 2.3. Standard Gibbs free energy: temperature diagrams for oxides Ellingham-Richardson diagrams... 51 2.3.1. Stoichiometric oxides... 51 2.3.2. Unstoichiometric compounds... 54 2.3.3. Thermodynamic data for the reduction of oxides by a reducing gas... 58 2.4. Thermodynamic data for sulfides and chlorides... 58 2.4.1. Ellingham-Richardson diagram for sulfides... 58 2.4.2. Stability diagrams for the (M-O-S) systems... 60 2.4.3. Ellingham-Richardson diagram for chlorides... 62 2.4.4. Stability diagrams of M-O 2 -Cl 2 systems... 62 2.5. Metal-carbon phase diagrams and the Ellingham-Richardson diagram for carbides... 63 2.6. Carbon and carbon oxide reactions... 67 2.6.1. Oxidation reactions... 67 2.6.2. Boudouard s reaction... 68 2.6.3. The different types of coal... 70 2.7. Bibliography... 71 Chapter 3. Metal Solutions, Slags and Mattes... 73 3.1. Introduction... 73 3.2. Metal solutions... 74 3.2.1. Phase diagrams and activities of liquid alloys components... 74 3.2.2. Activities and solubilities of metalloids in metal solutions... 83 3.2.3. Solubility and precipitation of oxide and sulfide compounds in metals... 92 3.3. Mattes... 93 3.3.1. Structure and physical properties of sulfide melts (mattes)... 93 3.3.2. Thermodynamic data for the binary Fe-S, Ni-S, Cu-S and Pb-S systems... 95 3.3.3. Thermodynamic data of ternary mattes... 97 3.3.4. Thermodynamic data for M-O-S systems... 99 3.4. Slags... 106 3.4.1. Structure and physical properties... 106 3.4.2. Phase diagrams and activities... 110 3.4.3. Phase diagrams and activities of oxide mixtures forming the basis of metallurgical slags CaO-SiO 2 -Al 2 O 3 -MgO... 111 3.4.4. Phase diagrams and activities of mixtures of CaO-SiO 2 -Al 2 O 3 -MgO oxides and reducible (iron, manganese and chrome) oxides... 115 3.5. Bibliography... 127
vii Chapter 4. Aqueous Electrolytic Solutions and Salt Melts... 131 4.1. Introduction... 131 4.2. Thermodynamics of aqueous electrolyte solutions... 131 4.2.1. Chemical potentials and activities of the components of electrolyte aqueous solutions... 132 4.2.2. Aqueous solutions of acids and bases... 138 4.2.3. Aqueous solutions of metallic salts: complexation and speciation... 148 4.2.4. Solubility of oxides and hydroxides... 156 4.2.5. Solubility of salts... 165 4.2.6. Solubility of gases in an aqueous solution... 171 4.3. Thermodynamics of salt melts (fluxes)... 173 4.3.1. Compositions and physical properties of fluxes... 174 4.3.2. Thermodynamic properties... 174 4.3.3. Solubility of oxides in halides... 177 4.4. Bibliography... 179 Chapter 5. Reaction Kinetics... 183 5.1. Introduction... 183 5.2. Rate of a chemical reaction... 184 5.2.1. Definitions... 184 5.2.2. Expressions of the rate of a chemical reaction... 186 5.3. Homogeneous precipitation... 189 5.3.1. Thermodynamics of primary nucleation... 190 5.3.2. Nucleation and primary particle formation processes... 191 5.3.3. Secondary nucleation... 193 5.4. Kinetics and mechanism of heterogeneous reactions... 194 5.4.1. Mechanism of heterogeneous chemical reactions... 194 5.4.2. Rates of heterogeneous reactions in fluid-solid systems... 195 5.4.3. Experimental rates of gasification reactions... 197 5.4.4. Experimental rates of oxide and sulfide dissolution by acid-base reactions... 202 5.4.5. Rates of heterogeneous chemical reactions in fluid-fluid systems... 206 5.4.6. Experimental rates of transfer processes... 207 5.4.7. Experimental rates of gas-liquid reactions... 209 5.5. Reaction rates for in situ conversion of a solid particle... 211 5.5.1. Reduction of an oxide in solid state by carbon monoxide or hydrogen... 211 5.5.2. Roasting of a zinc sulfide particle... 214 5.6. Heterogeneous precipitation... 215 5.6.1. Deposition mechanism... 216
viii Extractive Metallurgy 1 5.6.2. Silicon deposition by heterogeneous thermal decomposition of silane... 216 5.7. Bibliography... 217 Chapter 6. Transport Kinetics... 219 6.1. Introduction... 219 6.1.1. Identification of the rate-limiting step... 222 6.2. Equations of change and relationships between diffusion fluxes and driving forces... 223 6.2.1. Equations of change (in terms of the fluxes)... 223 6.2.2. Relationships between diffusion fluxes, driving forces and transport properties... 225 6.3. Interphase mass or heat transport (mass and heat transfer)... 227 6.3.1. Definitions of heat and mass transfer coefficients... 227 6.3.2. Kinetics of diffusion-controlled processes... 229 6.4. Mass and heat transfer coefficients... 236 6.4.1. Mass and heat transfer (across a phase boundary) between two semi-infinite and stagnant phases... 237 6.4.2. Heat and mass transfer between a flat wall and a fluid flowing along the flat surface in forced convection: boundary layer theory... 239 6.4.3. Heat and mass transfer between particles, drops or bubbles and a continuous fluid phase... 243 6.5. Overall kinetics of extraction processes under mixed control... 247 6.5.1. Extraction process-type gasification... 247 6.5.2. Transfer process-type solvent extraction... 249 6.5.3. Note on the rule of addition of resistances acting in series... 250 6.6. Bibliography... 251 Chapter 7. Particulate Kinetics... 253 7.1. Introduction... 253 7.2. Gasification/leaching of a particle... 254 7.2.1. Non-porous particles... 254 7.2.2. Porous particles (pellets)... 259 7.3. Heterogeneous precipitation: growth rate of the particles... 263 7.4. In situ conversion of a solid particle... 264 7.4.1. Non-porous particle: the shrinking unreacted core model... 265 7.4.2. In situ conversion of a porous particle: the grain pellet model... 269 7.5. Conversion of a particle undergoing strong exo- or endothermic chemical reactions... 270 7.5.1. Exothermic chemical reactions... 270 7.5.2. Endothermic chemical reactions... 275
ix 7.6. Transfer processes between two fluid phases, one phase being dispersed (as drops or bubbles) in the second phase... 276 7.6.1. Heat transfer... 276 7.6.2. Mass transfer... 277 7.6.3. Hydrogen removal from liquid steel bath by injection of inert gas bubbles... 278 7.7. Bibliography... 280 Chapter 8. Electrochemical Reactions... 283 8.1. Overview of electrochemical processes... 283 8.2. Equilibrium electric potential of an elementary electrochemical reaction... 285 8.2.1. Nernst equation... 285 8.2.2. Electrode potentials in aqueous solutions... 288 8.2.3. Equilibrium potential metal/ion E MM z+ in molten salts... 292 8.3. Electrochemical equilibria of metals and metalloids (Pourbaix diagrams)... 292 8.3.1. Diagram of electrochemical equilibria of water... 293 8.3.2. Pourbaix diagram for metal-water systems... 294 8.3.3. Pourbaix diagram for the Fe, Cu and Zn-Cl-H 2 O systems... 300 8.3.4. Pourbaix diagrams for the M-NH 3 -H 2 O systems... 302 8.3.5. Pourbaix diagrams for the M-HCN-H 2 O systems... 304 8.3.6. Pourbaix diagrams for the M-S-H 2 O systems... 305 8.4. Electrochemical kinetics... 306 8.4.1. Rate of an elementary electrochemical reaction: Tafel s Law... 307 8.4.2. Diffusion-controlled rate of an elementary electrochemical reaction... 312 8.4.3. Rate of a redox chemical reaction... 313 8.5. Redox electrochemical reactions... 314 8.5.1. Cementation or displacement reaction... 315 8.5.2. Leaching (dissolution) of metals... 319 8.6. Bibliography... 322 List of Symbols... 325 Index... 337 Summaries of Other Volumes... 345