Теория металлургических процессов: Theory of non-ferrous extractive metallurgy 9785763839791

Table of contents :
INTRODUCTION
1. PYROMETALLURGICAL PROCESSES
1.1. THERMODYNAMICS OF THERMAL DISSOCIATION
1.1.1. General Notions
1.1.2. Effect of Phase Transitions on Dissociation Process
1.1.3. Dissociation of Compounds with Different Oxidation Numbers
1.1.4. Dissociation of Oxides at Solution Formation
1.2. THERMODYNAMICS AND KINETICS OF SOME COMBUSTION REACTIONS
1.2.1. General Characteristic of Gaseous Atmospheres
1.2.2. Interaction of Carbon with Oxidant Gases
1.2.3. Kinetics of Carbon Combustion and the Boudouard-Bell Reaction
1.3. REDUCTION PROCESSES
1.3.1. Thermodynamics of Metal Oxide Reduction by Hydrogen and Carbon Monoxide
1.3.2. Reduction of Oxides of Volatile Metals
1.3.3. Reduction of Oxides in Systems with Solutions
1.3.4. Carbon Reduction of Oxide
1.3.5. Metallothermy
1.4. OXIDATION OF METALS AND SULFIDES. OXIDIZING REFINING
1.4.1. Theory of Oxidation of Metals
1.4.2. Thermodynamics of Oxidation of Sulfides and Interaction of Sulfides and Oxides
1.4.3. Kinetics of Oxidation of Sulfides
1.4.4. Thermodynamics of Oxidizing Refining
1.4.5. Oxidizing Refining of Metals with Introduction of Chemically Active Additions
1.4.6. Oxidizing Refining of Metals with Obtaining Gas Products (by the Example of Removal of Carbon from Iron)
1.4.7. Deoxidizing of Metals
1.5. PHYSICOCHEMICAL PROPERTIES OF METAL AND SLAG MELTS
1.5.1. Metallurgical Slags and Their Functions in Metallurgy
1.5.2. Composition and Structure of Molten Slags
1.5.3. Structure-Sensitive Properties of Metal and Slag Melts
1.5.4. Viscosity
1.5.5. Diffusion
1.5.6. Electrical Conductivity
1.5.7. Surface Tension
1.6. CRYSTALLIZATION REFINING METHODS
1.6.1. Liquation Refining
1.6.2. Fractional Recrystallization
1.7. PROCESSES OF EVAPORATION, SUBLIMATION AND CONDENSATION
Control Questions and Tasks
2. HYDROMETALLURGICAL PROCESSES
2.1. HYDROMETALLURGY
2.2. LEACHING
2.2.1. Gas – Liquid Solution Equilibrium in Binary Systems
2.2.2. Solubility of Solids
2.2.3. Thermodynamics of Simple Dissolution
2.2.4. Thermodynamics of Leaching Processes Followed by Chemical Reactions. Dissolution of Metals, Oxides and Sparingly Soluble Salts
2.2.5. Reagent Consumption and Equilibrium Constant
2.2.6. Dilution of the Solution
2.2.7. Pourbaix Diagrams
2.2.8. Kinetics of Leaching. Multi-Stage Nature of Leaching. Influence of Temperature
2.2.9. General Equation of Leaching Kinetics
2.2.10. Features of Leaching Involving Gaseous Reagent
2.2.11. Regularities of External and Internal Diffusion
2.2.12. The Regularities of the Process in the Kinetic Region
2.2.13. Influence of Surface Modification of Solid Phase
2.3. EXTRACTION AND ION EXCHANGE PROCESSES
2.3.1. Fundamentals of Extraction Processes. General Information
2.3.2. Extractional Equilibrium
2.3.3. Synergic Effect with the Use of Two Extragents
2.3.4. Kinetics of Extraction Processes
2.3.5. Fundamentals of Ion Exchange Processes. General Information
2.3.6. Equilibrium of Ion Exchange
2.3.7. Kinetics of Ion Exchange
2.3.8. Influence of Various Factors on the Process of Sorption
2.4. FUNDAMENTALS OF METAL OR THEIR COMPOUNDS ALLOCATION FROM WATER SOLUTIONS
2.4.1. Selection of Small-Solved Compounds
2.4.2. Factors Affecting Solubility of Salts
2.4.3. Conditions of Deposition of Hydroxides and Basic Salts
2.4.4. Deposition of Metal Sulfides
2.5. CEMENTATION
2.5.1. Thermodynamics of Cementation
2.5.2. Mechanism and Kinetics of Cemen
2.6. DEPOSITION OF METALS AND OXIDES FROM SOLUTIONS BY MEANS OF REDUCTION WITH HYDROGEN AND OTHER GASES
Control Questions and Tasks
3. ELECTROMETALLURGICAL PROCESSES
3.1. ELECTROCHEMICAL SYSTEMS AND THEIR BASIC ELEMENTS
3.2. EQUILIBRIUM IN SOLUTIONS OF ELECTROLYTES
3.2.1. Equilibrium of Electrolytic Dissociation
3.2.2. Criticism of the Arrenius Theory
3.2.3. Electrostatic Theory of Strong Electrolytes
3.3. NON-EQUILIBRIUM PHENOMENA IN ELECTROLYTE SOLUTIONS
3.3.1. Basic Concepts and Regulations
3.3.2. Number of Transfer
3.3.3. Faradey’s Laws
3.4. ELECTROCHEMICAL THERMODYNAMICS
3.4.1. Electrode Potential and Electromotive Force
3.4.2. Electrode Reactions and Electrochemical Chains
3.4.3. Thermodynamics of Reversible Electrochemical Systems
3.4.4. Classification of Reversible Electrodes
3.4.5. Electrochemical Circuits
3.5. ELECTROCHEMICAL KINETICS
3.5.1. Types of Transfer in Electrochemical Systems
3.5.2. Diffusional Overvoltage
3.5.3. Electrochemical Overvoltage
3.5.4. Chemical Reaction Overvoltage
3.5.5. Phase Overvoltage
3.6. REGULARITIES AND MECHANISM OF SOME ELECTRODE PROCESSES
3.6.1. Electrolytic Evolution of Hydrogen
3.6.2. Electrodeposition of Metals
3.6.3. Joint Reduction of Metal and Hydrogen Cations
3.6.4. Joint Reduction of Multiple Metals
3.6.5. Anodic Dissolution of Metals
3.7. MOLTEN SALTS ELECTROCHEMISTRY
3.7.1. General Characteristics of Molten Salts
3.7.2. Electrochemical Thermodynamics of Molten Salt Systems
3.7.3. Reference Electrodes and Rows of Potentials
3.7.4. Kinetics of Electrode Processes in Molten Salts
Control Questions and Tasks
CONCLUSION
BIBLIOGRAPHY

Citation preview

Теория металлургических процессов // Theory of Non-Ferrous Extractive Metallurgy

ISBN 978-5-7638-3979-1

Н.В. Белоусова, А.С. Ясинский

Изложен курс теории металлургических процессов, включающий три основных раздела, посвященных теоретическим вопросам пиро-, гидро- и электрометаллургии.

Н.В. Белоусова, А.С. Ясинский ТЕОРИЯ МЕТАЛЛУРГИЧЕСКИХ ПРОЦЕССОВ THEORY OF NON-FERROUS EXTRACTIVE METALLURGY УЧЕБНОЕ ПОСОБИЕ

ИНСТИТУТ ЦВЕТНЫХ МЕТАЛЛОВ И МАТЕРИАЛОВЕДЕНИЯ

Министерство науки и высшего образования Российской Федерации Сибирский федеральный университет

Н.В. Белоусова А.С. Ясинский ТЕОРИЯ МЕТАЛЛУРГИЧЕСКИХ ПРОЦЕССОВ THEORY OF NON-FERROUS EXTRACTIVE METALLURGY Учебное пособие

Красноярск СФУ 2019 1 | Theory of Non-Ferrous Extractive Metallurgy

УДК 669.2/8=111(07) ББК 34.33я73+81.432.1я73 Б438

Рецензенты: М.Я. Шестаков, доктор технических наук, профессор кафедры электронной техники и телекоммуникаций Института информатики и телекоммуникаций Сибирского государственного университета науки и технологий имени академика М.Ф. Решетнёва; А.М. Жижаев, кандидат технических наук, заведующий лабораторией рентгеновских и спектральных методов анализа Института химии и химической технологии Сибирского отделения Российской академии наук

Белоусова, Н.В. Б438 Теория металлургических процессов = Theory of Non-Ferrous Extractive Metallurgy : учеб. пособие / Н.В. Белоусова, А.С. Ясинский. – Красноярск : Сиб. федер. ун-т, 2019. – 216 с. ISBN 978-5-7638-3979-1 Изложен курс теории металлургических процессов, включающий три основных раздела, посвященных теоретическим вопросам пиро-, гидрои электрометаллургии. Предназначено студентам магистратуры направления подготовки 22.04.02 «Металлургия», программа 22.04.02.02 «Металлургия цветных металлов». УДК 669.2/8=111(07) ББК 34.33я73+81.432.1я73 Электронный вариант издания см.: http:/catalog.sfu-kras.ru ISBN 978-5-7638-3979-1 2 | Theory of Non-Ferrous Extractive Metallurgy

© Сибирский федеральный университет, 2019

CONTENT INTRODUCTION .................................................................................................................. 6 1. PYROMETALLURGICAL PROCESSES ..................................................................... 7 1.1. THERMODYNAMICS OF THERMAL DISSOCIATION ............................................ 8 1.1.1. General Notions ........................................................................................................... 8 1.1.2. Effect of Phase Transitions on Dissociation Process ................................................ 11 1.1.3. Dissociation of Compounds with Different Oxidation Numbers ............................. 14 1.1.4. Dissociation of Oxides at Solution Formation .......................................................... 15 1.2. THERMODYNAMICS AND KINETICS OF SOME COMBUSTION REACTIONS.......................................................................................................................... 17 1.2.1. General Characteristic of Gaseous Atmospheres ...................................................... 17 1.2.2. Interaction of Carbon with Oxidant Gases ............................................................... 18 1.2.3. Kinetics of Carbon Combustion and the Boudouard-Bell Reaction ......................... 20 1.3. REDUCTION PROCESSES ........................................................................................... 22 1.3.1. Thermodynamics of Metal Oxide Reduction by Hydrogen and Carbon Monoxide ............................................................................................................................. 22 1.3.2. Reduction of Oxides of Volatile Metals ................................................................... 25 1.3.3. Reduction of Oxides in Systems with Solutions ....................................................... 25 1.3.4. Carbon Reduction of Oxide ....................................................................................... 26 1.3.5. Metallothermy ............................................................................................................ 30 1.4. OXIDATION OF METALS AND SULFIDES. OXIDIZING REFINING................... 32 1.4.1. Theory of Oxidation of Metals .................................................................................. 32 1.4.2. Thermodynamics of Oxidation of Sulfides and Interaction of Sulfides and Oxides ........................................................................................................................... 36 1.4.3. Kinetics of Oxidation of Sulfides .............................................................................. 39 1.4.4. Thermodynamics of Oxidizing Refining ................................................................... 40 1.4.5. Oxidizing Refining of Metals with Introduction of Chemically Active Additions . 43 1.4.6. Oxidizing Refining of Metals with Obtaining Gas Products (by the Example of Removal of Carbon from Iron) ....................................................................................... 44 1.4.7. Deoxidizing of Metals................................................................................................ 45 1.5. PHYSICOCHEMICAL PROPERTIES OF METAL AND SLAG MELTS ................. 46 1.5.1. Metallurgical Slags and Their Functions in Metallurgy ........................................... 46 1.5.2. Composition and Structure of Molten Slags .............................................................. 46 1.5.3. Structure-Sensitive Properties of Metal and Slag Melts ........................................... 50 1.5.4. Viscosity .................................................................................................................... 50 1.5.5. Diffusion .................................................................................................................... 52 1.5.6. Electrical Conductivity .............................................................................................. 52 1.5.7. Surface Tension ......................................................................................................... 53 1.6. CRYSTALLIZATION METHODS REFINING ............................................................ 55 1.6.1. Liquation Refining ..................................................................................................... 55 1.6.2. Fractional Recrystallization ....................................................................................... 57 1.7. PROCESSES OF EVAPORATION, SUBLIMATION AND CONDENSATION ....... 60 Control Questions and Tasks .................................................................................................. 67 Content |3

2. HYDROMETALLURGICAL PROCESSES ................................................................ 67 2.1. HYDROMETALLUGY .................................................................................................. 68 2.2. LEACHING..................................................................................................................... 69 2.2.1. Gas – Liquid Solution Equilibrium in Binary Systems............................................. 69 2.2.2. Solubility of Solids .................................................................................................... 71 2.2.3. Thermodynamics of Simple Dissolution ................................................................... 72 2.2.4. Thermodynamics of Leaching Processes Followed by Chemical Reactions. Dissolution of Metals, Oxides and Sparingly Soluble Salts ............................................... 73 2.2.5. Reagent Consumption and Equilibrium Constant ..................................................... 76 2.2.6. Dilution of the Solution ............................................................................................. 78 2.2.7. Pourbaix Diagrams (-рН Diagrams) ........................................................................ 79 2.2.8. Kinetics of Leaching. Multi-Stage Nature of Leaching. Influence of Temperature .... 82 2.2.9. General Equation of Leaching Kinetics ..................................................................... 85 2.2.10. Features of Leaching Involving Gaseous Reagent .................................................. 89 2.2.11. Regularities of External and Internal Diffusion ....................................................... 90 2.2.12. The Regularities of the Process in the Kinetic Region ........................................... 92 2.2.13. Influence of Surface Modification of Solid Phase .................................................. 93 2.3. EXTRACTION AND ION EXCHANGE PROCESSES ................................................ 96 2.3.1. Fundamentals of Extraction Processes. General Information ................................... 96 2.3.2. Extractional Equilibrium ............................................................................................ 99 2.3.3. Synergic Effect with the Use of Two Extragents .................................................... 100 2.3.4. Kinetics of Extraction Processes .............................................................................. 100 2.3.5. Fundamentals of Ion Exchange Processes. General Information ........................... 102 2.3.6. Equilibrium of Ion Exchange ................................................................................... 104 2.3.7. Kinetics of Ion Exchange ......................................................................................... 105 2.3.8. Influence of Various Factors on the Process of Sorption ....................................... 106 2.4. FUNDAMENTALS OF METAL OR THEIR COMPOUNDS ALLOCATION FROM WATER SOLUTIONS ............................................................................................ 107 2.4.1. Selection of Small-Solved Compounds ................................................................... 107 2.4.2. Factors Affecting Solubility of Salts ........................................................................ 107 2.4.3. Conditions of Deposition of Hydroxides and Basic Salts ....................................... 109 2.4.4. Deposition of Metal Sulfides ................................................................................... 111 2.5. CEMENTATION .......................................................................................................... 111 2.5.1. Thermodynamics of Cementation ............................................................................ 111 2.5.2. Mechanism and Kinetics of Cementation ................................................................ 112 2.6. DEPOSITION OF METALS AND OXIDES FROM SOLUTIONS BY MEANS OF REDUCTION WITH HYDROGEN AND OTHER GASES ................. 114 Control Questions and Tasks ................................................................................................ 115 3. ELECTROMETALLURGICAL PROCESSES ......................................................... 117 3.1. ELECTROCHEMICAL SYSTEMS AND THEIR BASIC ELEMENTS .................... 118 3.2. EQUILIBRIUM IN SOLUTIONS OF ELECTROLYTES........................................... 120 3.2.1. Equilibrium of Electrolytic Dissociation ................................................................. 120 3.2.2. Criticism of the Arrenius Theory ............................................................................. 125 3.2.3. Electrostatic Theory of Strong Electrolytes ............................................................ 126 4 | Theory of Non-Ferrous Extractive Metallurgy

3.3. NON-EQUILIBRIUM PHENOMENA IN ELECTROLYTE SOLUTIONS .............. 132 3.3.1. Basic Concepts and Regulations .............................................................................. 132 3.3.2. Number of Transfer .................................................................................................. 138 3.3.3. Faradey’s Laws ........................................................................................................ 141 3.4. ELECTROCHEMICAL THERMODYNAMICS ......................................................... 143 3.4.1. Electrode Potential and Electromotive Force .......................................................... 143 3.4.2. Electrode Reactions and Electrochemical Chains .................................................... 147 3.4.3. Thermodynamics of Reversible Electrochemical Systems ..................................... 151 3.4.4. Classification of Reversible Electrodes ................................................................... 153 3.4.5. Electrochemical Circuits .......................................................................................... 159 3.5. ELECTROCHEMICAL KINETICS ............................................................................. 164 3.5.1. Types of Transfer in Electrochemical Systems........................................................ 168 3.5.2. Diffusional Overvoltage ........................................................................................... 169 3.5.3. Electrochemical Overvoltage ................................................................................... 172 3.5.4. Chemical Reaction Overvoltage .............................................................................. 174 3.5.5. Phase Overvoltage ................................................................................................... 175 3.6. REGULARITIES AND MECHANISM OF SOME ELECTRODE PROCESSES..... 176 3.6.1. Electrolytic Evolution of Hydrogen ......................................................................... 176 3.6.2. Electrodeposition of Metals ..................................................................................... 179 3.6.3. Joint Reduction of Metal and Hydrogen Cations .................................................... 185 3.6.4. Joint Reduction of Multiple Metals ......................................................................... 188 3.6.5. Anodic Dissolution of Metals .................................................................................. 191 3.7. MOLTEN SALTS ELECTROCHEMISTRY ............................................................... 196 3.7.1. General Characteristics of Molten Salts................................................................... 197 3.7.2. Electrochemical Thermodynamics of Molten Salt Systems ................................... 199 3.7.3. Reference Electrodes and Rows of Potentials.......................................................... 202 3.7.4. Kinetics of Electrode Processes in Molten Salts...................................................... 206 Control Questions and Tasks ................................................................................................ 211 CONСLUSION ................................................................................................................... 213 BIBLIOGRAPHY .............................................................................................................. 214

Content |5

INTRODUCTION

Extractive metallurgy is concerned with processes and methods of extraction of metals from natural raw materials or products of their dressing as well as with purifying the extracted metals. Ores often contain more than one valuable metal. Tailings of a previous process may be used as a feed in another process to extract a secondary product. In addition, a concentrate containing several valuable metals would be processed to separate them into individual constituents. The field of non-ferrous extractive metallurgy is traditionally divided into pyrometallurgy, hydrometallurgy, and electrometallurgy. Pyrometallurgical processes go at high temperatures in a medium involving often molten materials, solids and gases. Pyrometallurgical processes with gases and solids are typified by calcining and roasting operations. Processes with molten products are referred to as smelting operations. Hydrometallurgical processes involve chemical reactions in aqueous solutions, in specific cases with participation of organic solvents or sorbents, at normal or increased pressure and temperatures of 20–200 °С. Electrometallurgical processes take place in some form of electrolytic cell. They can proceed both in aqueous solutions and in salt melts at increased temperatures.

6 | Theory of Non-Ferrous Extractive Metallurgy

1 PYROMETALLURGICAL PROCESSES

Content |7

1.1. THERMODYNAMICS OF THERMAL DISSOCIATION

1.1.1. General Notions At high temperatures of pyrometallurgical processes, compounds of metals stable under normal conditions can dissociate into constituent elements. This process is determined by the external factors (P, T) and the nature of the matters. The reaction of dissociation may be written in a generalized form as АВ = А + В, (1) where АВ can be oxide, sulfide, carbonate or another compound. А can be metal, oxide or sulfide of metal which are gaseous or condensed. В is most commonly gas. If В is a gas, the equilibrium constant may be written as а Р К А В. (2) а АВ The equilibrium pressure of the gas (РВ) is said to be its dissociation pressure (dissociation tension). It is taken to be a measure of the thermal stability of the given compound. Let us suppose that a reaction of dissociation of an oxide of a bivalent metal takes place: 2МО(s) = 2М(s) + О2. (3) If the oxide and metal form the pure condensed phases, i.e. they are not part of solutions, the equilibrium constant is given by K Р  РО2 (МО) . (4) The greater the dissociation pressure, the lower is the stability of the oxide. Another criterion of the thermal stability is the Gibbs energy change in this reaction, G. The more positive (or less negative) is G, the higher is the stability of the oxide. In other words, the less negative is the standard energy of formation of the given oxide, the lower is its stability. During oxide dissociation, the first portions of the metal go to the gas state, and as soon as the vapor pressure of the metal reaches the equilibrium value (the saturation vapor pressure), condensation of this metal begins. If the vapor pressure of the metal formed in dissociation doesn’t reach the equilibrium pressure, the metal remains gaseous. 8 | Theory of Non-Ferrous Extractive Metallurgy

Depending on the coexisting phases and temperature, three cases can be observed at dissociation (using oxide as an example): 1. The metal and its oxide belong to condensed phases and the compositions of these phases don’t change in reaction. 2. The metal and its oxide form solutions with varying compositions. 3. Both components dissolve into a solvent inert to the oxygen. We consider the first case. For the equation (3), the equilibrium constant has the form of the equation (4). On the other hand, according to the Van’t Hoff equation, d ln K P H , (5)  dT RT 2 where H is the reaction enthalpy and R is the gas constant. The temperature dependence of the enthalpy is described by the Kirchhoff’s law: T

HT  H 298 

 CPdT .

(6)

298

Here, CP is the change of the heat capacity at constant pressure in the reaction. The heat capacity depends on the temperature also, and this goes to a subsequent complication of the equations. However for practical aims, we may sometimes neglect the dependence of H and CP on temperature and in this case

H  const . (7) RT A dependence of PO2  f (T ) will plot as a logarithmic curve and a ln PO2  

ln PO2  1/T plot yields a straight line whose slope is H/R (Fig. 1).

Fig. 1. A temperature dependence of oxide dissociation pressure Pyrometallurgical Processes |9

An example of such a plot for 2Ags + 1/2 O2 = Ag2Os reaction is shown in Fig. 21. Let us consider a temperature dependence of РВ ( PO2 ) on the PO2  T coordinates (Fig. 3). The field of the diagram is divided by the curve into two parts. This curve is formed by an aggregate of points characterizing equilibrium pressures. If, in the initial state at a temperature of Т1 (point a), the oxygen pressure in the closed system was higher than the equilibrium pressure

 РО (in)  PO (MO)  then the trend of this system to the equilibrium would re2

2

sult in the interaction of the oxygen and metal. Thus the field I will be the region of oxide existence. The Gibbs energy change in the dissociation process is described by the following equation: G   RT (ln PO2 (MO)  ln PO2 (in) ). (8) Because РО2 (in)  PO2 (MO) , G > 0. Therefore a counterreaction, namely, the oxidation of the metal by oxygen must go.

Fig. 2. Plot of the equilibrium dissociation pressure for Ag2Os versus temperature in Van’t Hoff format. The top line is experimental data for bulk Ag2Os. The two lower lines are predicted for thin films of Ag2Os of thickness 2 and 1 nm covering Ags 1

Charles T. Campbell. Transition Metal Oxides: Extra Thermodynamic Stability as Thin Films // Phys. Rev. Lett. 2006. № 96. Р. 66–106. 2 A disproportionation reaction of carbon monoxide into carbon dioxide and carbon black was investi10 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

The transition of the system to the equilibrium state is shown by the аа' straight line in the case of isothermal conditions and by the аа'' line under isobaric ones. If neither the temperature nor the pressure remain constant then the transition of the system to the equilibrium state will go along the аа''' trajectory.

Fig. 3. Diagram "the oxide dissociation pressure – the temperature"

When the partial pressure of oxygen in closed systems is lower than the equilibrium pressure, РО2 (in)  PO2 (MO) (point b at a temperature of T2), then G < 0 and the oxide dissociation takes place. Depending on the conditions, the transition to the equilibrium state will be represented on the plot by the bb', bb'' or bb''' line. The field II is the region of the stability of the metal. Similarly in Fig 2, at O2 pressures above such an equilibrium line, the bulk oxide is the only bulk solid phase that is stable, whereas below this line, the bulk metal is the only stable bulk solid. The most of metals are thermodynamically unstable in air at standard ambient temperature and change to oxides. The exceptions are the noble metals, for which РО2 (oxide)  PO2 (system) . The dissociation of other compounds (carbonates, sulfides, halogenides and others) is governed by the above-said regularities demonstrated with oxides.

1.1.2. Effect of Phase Transitions on Dissociation Process This effect can be estimated by the analysis of the change of Н for a reaction АВcond = Аcond + В.

(9)

P y r o m e t a l l u r g i c a l P r o c e s s e s | 11

If the dissociation takes place at low temperatures, then AB and A can be solids. In this case, ∆Н = ∆НB + ∆НА – ∆НАВ. (10) m At elevated temperatures, if TAm  TAB (Tm is a melting point) and A goes to a liquid state,

∆Н = ∆НВ + ∆НА + H Am – ∆НАВ,

(11)

where H Am is the enthalpy of fusion of A. At higher temperature, when AB melts, m АВl = Аl + В; ∆Н = ∆НВ + ∆НА + H Am – ∆НАВ – H AB ,

(12)

m where H AB is the enthalpy of fusion of AB. Thus at melting points, the change of the enthalpy occurs in discrete steps. It results in inflections in the temperature dependences of dissociation pressure (Fig. 4) and the Gibbs energy change.

Fig. 4. Schematic view of the dissociation pressure change in two cases corresponding to the metal fusion at lower and higher temperatures, respectively, than oxide melting point.

The cause of these inflections is explained in studies of the temperature dependence of the enthalpy of dissociation: d ln K P d ln PO2 H    tgα1 , (13) dT dT RT 2 where Н is the enthalpy of reaction when the oxide and the metal formed at its dissociation are solids. 12 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

After melting, the slope of the line varies: d ln PO2 H  Н Мm   tgα 2 ; Ml : (14) dT RT 2 m d ln PO2 H  Н М xОy MxOy(l) : (15)   tgα3 . dT RT 2 At high temperatures, the dissociation can be accompanied with the sublimation of compounds or their constituents. As this takes place, further inflections appear in the ln PO2  1/T plot. If the enthalpy of dissociation is appreciably less than the enthalpy of sublimation, then a complete or partial dissociation of compounds will proceed simultaneously with their sublimation. 2 When Н diss  H subl , the given compound goes to gaseous state with3 out dissociation. In spite of rather high number of works devoted to the investigation of evaporation and dissociation of different oxides, many questions are not completely understood. An example of the development of conceptions on mechanisms of these processes is the study of reactions going on in the zinc oxide dissociation. This oxide is characterized by a relatively high vaporization coefficient. There is a paper concerning its decomposition. It is the author’s opinion that this process cannot be explained by simple conventional equilibria, i.e. ZnOg = Zng + ½ O2, g, ZnOs = ZnOg.

(16) (17)

The basis of the reasoning were the facts that (i) ZnO sublimed only by dissociation into Zn g and O2,g, (ii) there was an apparent oxygen dissociation pressure of zinc oxide, which was many orders of magnitude greater than that deduced theoretically from the thermodynamic data, (iii) equilibrium dissociation constant was greater than that calculated from the standard free energy data by a factor of ca. l0 8. It has been proposed the existence of an unstable superficial suboxide such as Zn 2O and Zn4O3. According to the author, if the surface of the ZnO becomes covered with an impervious layer of the suboxide so as to isolate the oxide, the dissociation reaction is essentially that of the solid suboxide. In more recent times, B.V. L’vov et al proved the mechanism of evaporation of ZnO and HgO with releasing of atomic oxygen (O) as a primary product P y r o m e t a l l u r g i c a l P r o c e s s e s | 13

of decomposition and the mechanism of evaporation of CdO with releasing of molecular oxygen (O2). From the analysis of crystal structure for 12 different oxides, which evaporate with releasing of atomic oxygen, and for 13 compounds, which evaporate with releasing of molecular oxygen, it was revealed that (i) the first mechanism is observed for all oxides with the cubic crystal structure and (ii) the difference in mechanisms is not related with interatomic O–O distances in these oxides. It was proposed that a decisive role here belongs to a local symmetry in the position of O atoms.

1.1.3. Dissociation of Compounds with Different Oxidation Numbers According to the A.A. Baikov’s principle, when metal has more than one possible oxidation state, the process of dissociation of its compounds proceeds stepwise with the formation of all compounds which can exist in the given system. In the analysis of such processes, the thermodynamic stability of the concrete compounds must be taken into account. The stability of many oxides with the lowest oxidation number is limited for the lower temperatures; therefore there are two schemes of transformations: low-temperature and hightemperature ones. For example, the scheme of oxide iron transformation at T > 843 K can be presented as follows: (18) Fe2O3  Fe3O4  FeO  Fe , i.e. in dissociation of Fe2O3, reactions go consistently: (19) 6Fe2O3  4Fe3O4  2 , (20) 2Fe3O4  6FeO  O2 , (21) 2FeO  2Fe  O2 . When T < 843 K, the scheme of the transformations appears as (22) Fe2O3  Fe3O4  Fe , and the following reactions take place: (23) 6Fe2O3  4Fe3O4  O2 , (24) Fe3O4  3Fe  2O2 . Fig. 5 shows the respective regions of existence of iron oxides (I – Fe2O3, II – Fe3O4, III – FeO) and iron (IV) bounded by the equilibrium curves relating to the above mentioned reactions. 14 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

Fig. 5. Effect of temperature on the dissociation pressure of iron oxides

The more rigorous analysis of dissociation processes calls for taking into account possibilities of formation of phases with changing compositions.

1.1.4. Dissociation of Oxides at Solution Formation Ores of non-ferrous metals are complex in compositions. In smelting, as a rule, metal oxides dissolve in the slag phase while metals become the components of liquid metal alloy. In this case the equation of dissociation of an oxide of a bivalent metal may be written as 2(МО) = 2[M] + O2, (25) where parentheses show that the given compound is in the slag phase and square brackets point to the fact that the component is in the metal one. The equilibrium constant is given by

KP 

2 РM РО2

, (26) 2 PMO where РМ and РМО are the equilibrium partial pressures of vapor of the metal and oxide, respectively. Then РО2 

2 K P PMO

PM2

.

(27)

P y r o m e t a l l u r g i c a l P r o c e s s e s | 15

Let us assume that the solubility of the metal and its oxide is limited. Their concentrations in saturated solutions will be written as [M]s.s. and (МО)s.s, respectively. According to the Henry's law, the equilibrium pressure of substance's vapor over the solution is proportional to the mole fraction of the given substance in this solution. The pressure of substance's vapor over the saturated so0 0 , РМО lution is equal to the saturation vapor pressure ( РМ ). And then  РM Р [M] (MО) ; MО   0  0 (MО) s.s.  PM [M]s.s. PMО   Р  P 0 [M] ; Р  P 0 (MО) M МО MО  М [M]s.s. (MО) s.s.  Substitution of the expressions for PM and PMO into Eq. (27) gives

РО2 

0 K P ( РМО )2 (МО)2[M]2s.s. 0 2 ( РМ ) (МО)2s.s.[M]2

(28)

(29)

This equation defines oxide dissociation pressure when a metal and its oxide dissolve in some solutions.



0 With K0 to denote K P PMO

  PM0  2

2

2

, we obtain 2

2 [M]s.s.   (MO)  аМО РО2  K0  (30)     K0 2 , аМ  [M]   (MO) s.s.  where аМО and аМ are activities of metal and oxide in solutions. When M forms a pure phase while MO is a component of a solution, Eq. (30) is simplified. Since [M]s.s./[M] = 1, so

2

 (MO)  РО2  K 0  (31)  . (MO) s.s.   From this expression it follows that the equilibrium dissociation tension of oxide depends on its concentration in the solution. The lower is this concentration, the lower is the dissociation pressure and the more stable is the given oxide. As a result, difficulties emerge when we try to reduce this oxide to metal. When the concentration increases, the equilibrium pressure grows only up to a value corresponding to РО2 for the undissolved oxide (Fig. 6, a). 16 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

а b Fig. 6. Dependence of oxide dissociation pressure in a system with solutions on the concentration of MO in the slag solution (a) and of M in the metal one (b)

When MO forms a pure phase while M is a component of a solution, we obtain 2

[ M ]s.s.  РО2  K0  (32)  . [ M ]   Hence it follows that the dissociation pressure of oxide, when the resultant metal dissolve in some inert solvent, is greater than, or equal to, the oxide dissociation pressure in the case that the metal is in the pure condensed phase (Fig. 6, b). Removal of obtained metal in a solution provides the more complete reduction of oxides. It can be used in the case of the difficult-to-reduce compounds.

1.2. THERMODYNAMICS AND KINETICS OF SOME COMBUSTION REACTIONS

1.2.1. General Characteristic of Gaseous Atmospheres Almost all pyrometallurgical processes involve a gaseous atmosphere as one of the phases. It can be inert but, for the most part, is reacting, i.e. interacts with the main metallurgical phases. The composition of gaseous atmospheres can include three kinds of constituents: P y r o m e t a l l u r g i c a l P r o c e s s e s | 17

1. Products of complete interaction with oxygen: СО2, Н2О, SO3; 2. Products of incomplete interaction with oxygen, of thermal dissociation and degasification of metals: СО, Н2, СН4, SO2, O2; 3. Inert constituents: inert gases and others. The composition and properties of metallurgical gaseous atmospheres can define the direction of important reactions. In addition, the reactions of combustion of fuel are the heat source required for obtaining high temperatures. Specifically, of great importance are the reactions of combustion of hydrogen and carbon monoxide: 2Н2 + О2 = Н2О(steam) G = –494490 + 111,6T, (J); 2СО + О2 = 2СО2 G = –561380 + 170,294T, (J).

(33) (34)

G has large negative values up to temperatures of 2000 К. This gives an indication of shifting the position of equilibrium to the right and of the thermodynamic stability of the products. Completeness of these reactions falls with a rise in temperature. This is connected with a temperature coefficient of G which is determined by the entropy change:

 G     S .  T  P

(35)

These reactions go with decreasing the number of moles of gas, so S < 0.

1.2.2. Interaction of Carbon with Oxidant Gases On interaction of carbon with oxidant gases (O2, H2O), following reactions can go simultaneously: 2С + О2 = 2СО (reaction of incomplete combustion), С + О2 = СО2 (reaction of complete combustion), С + Н2О = СО + Н2 (coal gasification by water to CO), С + 2Н2О = СО2 + 2Н2 (coal gasification by water to СО2).

(36) (37) (38) (39)

At low temperature, the combustion of carbon produces CO2. At high temperature it produces CO. Both reactions are exothermic. The reaction (36) occurs with an increase in the number of gas molecules and the standard affinity of this reaction increases with the increasing temperature. 18 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

There is no change in the number of gas mole of the reaction (37) and the variation of standard affinity of formation of CO2 with temperature is very low. Unlike two first reactions having small probability of proceeding in reverse direction at temperatures of pyrometallurgical processes, two last reactions are thermodynamically probable both in the forward direction and the opposite one. To define compositions and properties of a gaseous atmosphere in the presence of carbon, overall reactions (36)–(37) and (38)–(39) are convenient to use. As a result of the summation, we can obtain the following reactions: С + СО2 = 2СО (reaction of carbon gasification by CO), 2СО + О2 = 2СО2 (reaction of СО after-burning), СО + Н2О = Н2 + СО2 (water-gas shift reaction).

(40) (41) (42)

The reaction (40) is exothermic and goes with a decrease in the number of gas moles. The standard affinity of formation CO2 decreases as the temperature increases. The shift reaction (42) is reversible, mildly exothermic reaction that has the tendency to increase the amount of H2 compared to CO in the product gas. The direction of the reaction depends on the conditions: if the temperature is high enough the reverse reaction takes place. Though all the participating chemical species are in the form of a gas, It is believed that this reaction predominantly takes place at the heterogeneous surfaces of coal and also that the reaction is catalyzed by carbon surfaces. The most important relation in a gaseous atmosphere in the presence of carbon is the РСО / РСО2 ratio determined by the reaction of carbon gasification (40) which is called Boudouard-Bell reaction2. It can be evaluated with the equilibrium diagram of this reaction (Fig. 7). The standard affinity of this reaction becomes positive above 938 K. A sharp change in the equilibrium composition of the gas phase from CO 2 to CO takes place in the temperature interval of 800–1200 K. Increasing the temperature causes the equilibrium to shift to the right toward a higher concentration of CO, because this reaction is endothermic. Increased pressure decreases the volume available to this equilibrium and, ac2

A disproportionation reaction of carbon monoxide into carbon dioxide and carbon black was investigated at the end of XIX century, first by Sainte-Claire Deville in 1864 and then from 1869–1871 by the English metallurgist Sir Isaac Lothian Bell. As late as July 23rd, 1900, at a Paris conference, Octave Boudouard described and discussed his earlier published work on the progress of the endothermic and reversible reaction С + СО2 = 2СО. (ref. by: The Boudouard-Bell reaction analysis under high pressure conditions / A. Mianowski [et al.] // J. Therm. Anal. Calorim. 2012. № 110. Р. 93–102). P y r o m e t a l l u r g i c a l P r o c e s s e s | 19

cording to the Le Chatelier's principle, favors the reverse reaction, because it decreases the number of gaseous molecules.

Fig. 7. Isobars of equilibrium compositions of gas for the Boudouard-Bell reaction

1.2.3. Kinetics of Carbon Combustion and the Boudouard-Bell Reaction The interaction of carbon with oxygen as well as with other oxidant gases is a heterogeneous process which can be presented by the following stages: 1. Diffusion of oxidizer from gas stream to the phase boundary; 2. Adsorption of the oxidizer on the carbon surface; 3. Surface reaction; 4. Desorption of products from the carbon surface; 5. Diffusion of the products to the gas phase. The stages 2, 3 and 4 are characterized as chemical ones and the stages 1, 5 are diffusive. The rate of diffusion is determined by the equation of diffusion transfer: С  Со rdif  D surf    Со  Сsurf  , (43)  where D is the diffusion coefficient,  is the depth of the diffusion layer, Со and Сsurf are the concentrations of oxidizer in the gas phase and at the carbon surface, respectively;   D /  . The acceleration of molecular diffusion due to the increasing temperature is relatively small and appears by the action of temperature on the diffusion coefficient:

D / Dо  (Т / Т о )n . 20 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

(44)

In the field of high temperatures, the value of n for real gases and vapors in metallurgical system is in the range from 1,7 to 2. Going to the chemical stages of process, we can write the following equation for the rate per unit surface: (45) r  k  Csurf . Here the reaction order with respect to a given oxidizer is taken equal to 1. The chemical stages of process are characterized by an exponential increase in the rate of reaction with rise in temperature: (46) k  ko exp( Ea / RT ) and by a considerable value of apparent activation energy, Ea, being in the range of 100–400 kJ/mole. Therefore with increasing temperature, the rate of chemical stages increases faster than of diffusive ones. The total rate of a heterogeneous process depends on the rates of the individual steps. If the rate of one of sequential stages is considerably lower than remaining ones, then the rate of a multi-step reaction is determined by this slowest step (the rate-determining step). When the rates of sequential steps become equal, then stationary conditions are attained. In this case we can equate the rate of diffusion of oxidizer and the rate of its interaction with carbon: r  rdif , (47)

Со  Сsurf    Со  Сsurf  , (48)   Сsurf  Со , (49) k  С k Со r о or r  . (50) 1 1 k   k Rewriting the last equation in terms of the temperature dependences of diffusive and chemical steps, we obtain: Со r . (51) 1 n 1  ko exp( Ea / RT )    (Т / Т о )  At low temperatures, k is so small that the numerical value of the denominator in this equation is practically independent of the second summand. This corresponds to the realization of a kinetic reaction regime. With increasing temperature, the value of the second summand becomes more and more considerable. The process changes to a diffusive regime, new factors influencing on the rate (effect of the gas stream, slight influence of temperature) appear. k  Csurf  D

P y r o m e t a l l u r g i c a l P r o c e s s e s | 21

The rate of the Boudouard-Bell reaction in the absence of external mass transfer control and at conditions not close to equilibrium, according to the Langmuir-Hinshelwood (L–H) mechanism, is described by an equation of the form b1  CO2  , (52) r 1  b2 CO  b3 CO2  where [CO] and [CO2] are concentrations of CO and CO2; b1, b2, b3 are coefficients connected to the kinetic rate constants of the elementary steps comprising the reaction mechanism. This equation depends on the conventions of the L–H mechanism; however, in the general equation, it is assumed that [CO2]  PCO and [CO]  PCO 2 ( PCO and PCO 2 are the ambient partial pressures of CO and CO2, respectively). Combustion or oxidation of coal is much more complex in its nature than oxidation of carbon. Coal is not a pure chemical species; rather, it is a multifunctional, multispecies, heterogeneous macromolecule that occurs in a highly porous form with a very large available internal surface area. The internal surface area of coal is usually expressed in terms of specific surface area that is a measure of the internal surface area available per unit mass. The reaction phenomenon is complicated by transport processes of simultaneous heat and mass transfer. The overall rate of coal oxidation, both complete and partial, is affected by a number of factors and operating parameters, including the reaction temperature, O2 partial pressure, coal porosity and its distribution, coal particle size, types of coal, types and contents of specific mineral matter, heat and mass transfer conditions in the reactor, etc.

1.3. REDUCTION PROCESSES

1.3.1. Thermodynamics of Metal Oxide Reduction by Hydrogen and Carbon Monoxide In the general form, the reaction of metal oxide reduction with the use of hydrogen and CO can be written as МО + Н2(СО) = М + Н2О(СО2). (53) Let us assume that the metal and its oxide form solid interinsoluble phases. 22 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

At designated pressure and temperature conditions, the composition of the gas mixture being in equilibrium with these phases is determined by the solution of the following equations: РН2  РН2О  Рtotal or РСО  РСО2  Рtotal . (54)

KP 

РН2О(СО2 ) РН2 (СО)

 ехр(G / RT )

(55)

According to the Le Chatelier's principle, increasing the pressure has no effect on the position of the equilibrium of this reaction, because the number of moles of gas is the same on each side of the chemical equation. Thus at given temperature we obtain a rigorous ratio of РН2 / РН2О or РСО / РСО2 . Fig. 8 shows the equilibrium compositions of gas phase (CO + CO2) for the reduction of some oxides depending on temperature. Equilibrium lines for the reduction of oxides of metals with low affinity with respect to the oxygen (for example, Pb) lie in the bottom part of the diagram. Lines for oxides of metals with high affinity with respect to the oxygen (Zn, Si) are localized within the upper part of this diagram. In the case of the former, the equilibrium content of CO in gas phase doesn’t exceed several percent while the latter are reduced by gas consisting of practically pure CO.

Fig. 8. Dependence of the content of equilibrium gas phase on temperature for some reactions of reduction of oxide by carbon monoxide

P y r o m e t a l l u r g i c a l P r o c e s s e s | 23

The field of the diagram above the equilibrium curve for the given oxide is the field of reducing compositions for this oxide. The field of the diagram under a curve shows oxidizing compositions of the gas for this oxide. According to this diagram, the gas with a defined composition is oxidative for some oxides and reducing for others. The gas reduction process can be considered as a combination of oxide dissociation and interaction of gaseous reducer with oxygen. Such presentation doesn’t connect with a mechanism of the process but is a mathematical technique: 2МО = 2М + О2 (56)  2Н2О = 2Н2 + О2 (57) (or 2СО2 = 2СО + О2) (58) 2МО + 2Н2(СО) = 2М + 2Н2О (СО2) (59) The equilibrium constants of these reactions are (60) K Р56  РО' 2 ; K P57 

PH22 (CO) PO'' 2

(61)

;

PH22O(CO2 )

K Р56  РО' 2 ;

(62)

The equilibrium condition for these reactions is an equality of partial pressure of oxygen at oxide dissociation and at dissociation of water steam or CO2: (63) РО' 2  PO'' 2 . Then РО' 2

 K P56

PH22O(CO2 ) PH22 (CO)

.

(64)

Hence it follows that the equilibrium constant of the reaction of oxide reduction can be expressed as

K P57 

PH2O(CO2 ) PH2 (CO)



PO' 2 K P15



K P14 K P15

.

(65)

PO' 2 depends on the nature of the oxide and temperature. The lower is PO' 2 , the lower is the equilibrium constant and the higher is the stability of the

oxide and, as a result, the harder the oxide is to reduce.

24 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

1.3.2. Reduction of Oxides of Volatile Metals Many of the non-ferrous metals (Hg, Cd, Zn, Pb et al.) at temperatures of pyrometallurgical processes exhibit high vapor tension. Therefore the equation for the equilibrium constant of the reduction of oxides of such metals should involve the equilibrium pressure of metal vapor also. For example, the reaction of zinc oxide reduction at temperatures above 1180 K can be written as ZnOs + CO (H2) = Znv + СО2 (Н2О), (66) PZn  PCO PZn  PH O 2 2 KP  or K p  . (67) PCO PH2 Since

PZn  PCO and

 P  PZn  PCO

2

2

 PCO

or PZn  PH or

2

(68)

O

 P  PZn  PH O  PH 2

,

(69)

2

then simultaneous solution of these equations will result in the following expression:

PZn   K p 

 P  K p  K p2 .

(70)

A decrease in total pressure favors the reduction of zinc oxide.

1.3.3. Reduction of Oxides in Systems with Solutions In the case of real metallurgical processes, we deal with oxides being in dissolved state (for example, in a slag). Obtained metals are enough often in a solution with other metals or sulfides. Then the reaction of reduction should be written so: (МО) + СО = [M] + CO2 or (МО) + Н2 = [M] + Н2О (71) (here the parentheses imply the slag phase, the square brackets imply the metal one), РСО2 (Н2О) аМ К . (72) РСО(Н2 ) аМО P y r o m e t a l l u r g i c a l P r o c e s s e s | 25

It follows that the equilibrium ratio of РСО2 / РСО in a gas phase РСО

аМО (73) РСО аМ increases with increasing oxide (and/or metal) activity in melt. The reduction of oxides from a slag melt, as their concentration (activity) is decreasing, requires more and more reducing gas phase. Attempts to completely reduce the oxide therewith are not necessarily successful. With decreasing concentration of reduceable oxide, the equilibrium content of СО(Н2) can increase to the point where an undesirable reduction of accompanying oxides begin (for example, of iron oxides to metal at the reduction of lead or copper). On the contrary, the decreasing activity (concentration) of metal in solution allows using the less reducing atmosphere. This is employed at the reduction of hard-reducible metals. For the same reason it is in essence unfeasible to produce a pure metal at reduction of an oxide mixture. The lower will be the concentration of metal impurities dissolved in a main metal; the higher will be the РСО2 / РСО ratio for their reduction. 2

K

To increase the activity of oxides, special addition agents are introduced in solutions (for example, calcium oxide in slags). Sometimes metals which cannot be produced in the appointed interval of temperatures with the use of accepted reducers are obtained in alloy form. In particular, a process of Al2O3 reduction with obtaining silumin (silicoaluminium alloy) is based on this property of solutions.

1.3.4. Carbon Reduction of Oxide To predict the conditions of reduction of metal oxides and sulphides, Ellingham diagrams are used. They are plots of ΔG versus temperature as a series of straight lines, where dΔG / dT = − ΔS is the slope and ΔH is the y-intercept. A specific example of such diagram for some oxidation reactions is shown in Fig. 93. The slope of the plots is positive for all metals, with ΔG always becoming more negative with lower temperature The reaction 2C + O2 = CO2, (74) 3

Randhawa N.S., Jana R.K., Das N.N. Manganese Nodules Residue: Potential Raw Material for FeSiMn Production // Int. J. Metallurg. Eng. 2012. № 1(2). Р. 22–27. 26 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

as indicated above, is characterized by the increasing standard affinity with the increasing temperature and the line slopes rather sharply downward. The position of the line for a given reaction on the Ellingham diagram shows the stability of the oxide depending on temperature. The closer to the bottom of the diagram is lines for the metals, the more progressively reactive these metals are and the harder their oxides are to reduce. The intersection of two lines implies oxidation-reduction equilibrium. Since the 2C + O2 = 2CO line is downward-sloping, it cuts across the lines for many of the other metals. As soon as the carbon oxidation line goes below a metal oxidation line, the carbon can then reduce the metal oxide to metal. So, for example, solid carbon can reduce FeO once the temperature exceeds approximately 980 K, and can even reduce highly-stable compounds like silicon dioxide at temperatures above about 1890 K. The analysis with the use of Ellingham diagrams is thermodynamic in nature, and ignores reaction kinetics. As for the carbothermal reactions, they are heterogeneous and their rates, among other things, are determined by the point contact area of condensed phases. For this reason, at the reduction of oxides in the presence of solid carbon, the Boudouard-Bell reaction is of the utmost significance.

Fig. 9. Ellingham diagram for carbothermic reduction of Si, Mn and Fe oxides

Several mechanisms have been proposed to explain the reaction of carbothermal reduction. According to one of them, the process of oxide reduction includes two steps: P y r o m e t a l l u r g i c a l P r o c e s s e s | 27

МОs + СО = Мs + СО2, СО2 + Сs = 2СО МОs + Сs = Мs + СО.

(75) (76) (77)

In this case we deal with the combined equilibrium of two reactions. Reduction (75) is possible when Р'СО of gaseous phase is higher than the equilibrium РСО for a given oxide. At the same time for the Boudouard-Bell reaction, Р'СО of gaseous phase should be lower than the equilibrium РСО of this reaction. The joint reaction is possible from some temperature characteristic of each oxide. Fig. 10 shows temperature dependences of equilibrium compositions of gaseous phase for reduction of some oxides and the Boudouard-Bell reaction.

Fig. 10. Combination of equilibrium curves of monoxide reduction of metal oxide and the Boudouard-Bell reaction depending on temperature: 1 – 1 atm.; 2 – 0,5 atm.; 3 – 0,2 atm.

The equilibrium of reaction (77) can be reached only in the case if the equilibriums of (75) and (76) reactions have established. The joint equilibrium of М-С-СО-СО2 system is graphycally determined by the intersection of equilibrium curves for the reactions of reduction and carbon gasification. Reduction is possible at temperatures above the intersection point where the carbon gasification line is higher on the diagram than that of the metallic oxide to be reduced. For example, reduction of FeO begins from temperature t0 and the equilibrium composition of gaseous phase is determined by the point O. At a higher temperature (t1), the point corresponding to the equilibrium composition of gas for the Boudouard-Bell reaction (O1) is higher than that for the reduction of FeO (a). Thus the FeO + CO = Fe + CO2 reaction will go. 28 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

The composition of the gaseous phase will trend to the point a. Two combined reactions will proceed until FeO or C will be consumed. With excess carbon, oxide will be completely reduced and the final composition of gas phase will correspond to the point O. If carbon is lacking the oxide remains unreduced and the final composition of gas corresponds to the point a. At a temperature of t2, FeO will be not reduced as the equilibrium content of CO on the Boudouard-Bell reaction is lower (the point O2) then that for the reduction reaction (the point b). When there are several oxides in a system, then at first more easily reducible oxides will be reduced. Reduction in the presence of solid carbon goes with changing gas volume. Therefore the system responds to the change of ambient pressure. According to the Le Chatelier's principle, at decreasing pressure, the carbon gasification increases in importance. In this case, reduction of oxides begins at lower temperatures. On closer examination it is emerged that the mechanism described by the equations (75)–(77) is inconsistent with some facts. One of them is a slow and thermodynamically limited restoration of CO at low temperatures. Because of this, alternative mechanisms have been proposed4. Based on a critical analysis of literature data and their comparison with theoretical calculations, B.V. L'vov concluded that the process of carbothermal reduction of iron, cobalt, nickel and copper oxides could be described in the framework on the mechanism of dissociative evaporation of oxide with the simultaneous condensation of metal at the oxide/metal interface. The function of carbon in this process, in his opinion, is to react with oxygen liberated from the decomposition of the oxide, thus maintaining a low partial pressure of oxygen in the system: MOs = Ms + 1/2O2, (78) Cs + O2 = CO2. (79) A similar process is expected to occur for oxides of some other metals like those of platinum group, silver and gold. The oxides of these metals are not stable and the volatility of these metals at temperatures below 1000 K is very low. At the same time, this mechanism does not work, if the metal is in the gaseous phase at the temperature of oxide reduction. This is true for the oxides of Al, Cr, Mg, Mn, Sn, Zn, etc. Their carbothermal reduction occurs most probably via the gaseous carbide mechanism: 2MOs + MC2 g = 3Mg + 2CO, (80) 2Cs + Mg = MC2 g. (81) 4

L'vov B.V. Mechanism of carbothermal reduction of iron, cobalt, nickel and copper oxides // Thermochim. 2000. Acta 360. Р. 109–120. P y r o m e t a l l u r g i c a l P r o c e s s e s | 29

1.3.5. Metallothermy Carbothermal reactions being endothermic require the energy supply in order to proceed. In addition, carbon can react with some metals metal to form carbides. It is evident from Ellingham diagrams that a given metal can reduce the oxides of all other metals whose lines lie above theirs on the diagram. In this case metallothermic reduction characterized by exothermicity takes place: МО + М' = М'О + М. (82) Aluminium, magnesium, sodium and calcium are used as the reducing agents (M'). Two groups of the reactions are possible from the viewpoint of purity of phases. One of them involves processes in which reactants and products of reactions are "pure" phases. One such example is the magnesium reduction of titanium tetrachloride, a major process for the commercial-scale production of titanium metal: TiCl4(g) + 2Mg(l) = Ti(s) + 2MgCl2(l). (83) Mutual solubility of the components of this reaction doesn’t exceed 0,25 %. In this connection the equilibrium constant can be written as 1 . (84) K РTiCl4 Special features of the metallothermic reduction with participation of "pure" condensed phases are the production of commercially pure metal and its total-lot extraction from an initial raw. The second group of metallothermic processes involves reaction with the formation of solution. When the reductant and the reduced metals have high mutual solubility or chemical affinity, the production of pure reduced metal will not be possible as it will be contaminated by the reductant. An example is the aluminothermic reduction of chromium: (Cr2O3) + 2[Al] = 2[Cr] + (Al2O3). (85) Alumimium and chromium oxides exhibits a complete mutual solubility at temperatures above 1570 K. Below this temperature, an asymmetric miscibility gap exists on the alumina-rich side of the phase diagram. Chromium, which has a low solid-state solubility in binary aluminium alloy, reacts with the aluminium and form several compounds. As for the liquid state, the higher the concentration of aluminium in the Al-Cr system, the higher the solubility chromium in melts. 30 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

Therefore the equilibrium constant takes the form: K

2 aCr aAl2O3 2 aAl aCr2O3

.

(86)

Physicochemical regularities of such processes could be considered for a reaction written in general form (82). The expression for the equilibrium constant of this reaction a a K  M M'O (87) aM'aMO allows obtaining aM ' аМ'О  exp(G / RT ) . (88) аМ аМО

aM ' ratio, the higher the аМ completeness of reduction (extraction of metal M). The decrease of this ratio is favoured by maximal negative values of Gibbs energy change, i.e. chemical affinity of reductants for oxygen should be much higher than that of reduced metals. The presence of a compound which reacts with product compound in metallothermic reaction facilitates the reaction in the forward direction by decreasing the activity of the product compound. Thus lime can be used in aluminothermic reactions to decrease the activity of alumina at the expense of interaction of Al2O3 and CaO. The equilibrium of reaction (82) is characterized by an equal affinity of reductant and reduced metal for oxygen. It can be described by the following equations: PO/2 ( MO)  PO/2 ( Me ' O) , (89) From this relation it follows that the lower the

PO/2 ( MO ) PO/2 ( M ' O )

 PO2 ( MO )  PO2 ( M ' O )

2 aMO 2 , aM 2 aM 'O , 2 aM '

(90)

(91)

/ where PO2 is dissociation pressure in the case of occurrence of solution.

Solving these equations in combination, we can determine a residual concentration (activity) of reductant in reduced metal:

aM '

PO2 ( M ' O ) aM ' O  aM   PO2 ( MO ) aMO .

(92)

P y r o m e t a l l u r g i c a l P r o c e s s e s | 31

It follows herefrom that the residual activity of reductant in reduced metal depends on dissociation pressures of reductant oxide  PO2 ( M ' O )  and reduced metal oxide  PO2 ( MO )  as well as activity of components in slag phase and reduced metal activity. To obtain more pure metals, reductants with minimal dissociation pressures of their oxides need to be selected. Introduction of reductant metal in excess of what is needed by following a stoichiometric course shifts the equilibrium of reaction (82) to the right, i.e. results in a more complete of reduction, but the excess of reductant remains in reduced metal and lowers the quality of a product. When reductants are introduced in reaction in amounts less than according to stoichiometry, the degree of extraction decreases but the reduced metal has to be more pure.

1.4. OXIDATION OF METALS AND SULFIDES. OXIDIZING REFINING

1.4.1. Theory of Oxidation of Metals When ambient pressure of oxygen over a metal is higher than the dissociation pressure of its oxide, an oxidation reaction occurs: 2M + O2 = 2MO. (93) This process is the reverse of dissociation, thus thermodynamics of dissociation considered previously can be used in understanding the oxidation too. Consider the kinetics of this process. It is heterogeneous and involves at the least the following stages: 1. Diffusion of oxygen from gas stream to the gas-metal interface; 2. Adsorption of the oxygen on the metal surface; 3. Diffusion of reactants through a scale layer; 4. Crystal-chemical transformations connected with structural changes in solids. It is considered that there are two types of oxide scales varying in structure, namely, non-protective and protective layers. The former as opposed 32 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

to the latter doesn’t prevent the further penetration of oxygen to the metal surface. This determines kinetics of oxidation of a given metal. The development of a protective oxide barrier is connected with the ability of a metal (or an alloy) to reform a protective scale, if stress-induced spalling or cracking occurs. These are growth stresses, which develop during the isothermal formation of the scale, and thermal stresses, which arise from differential thermal expansion or contraction between the metal substrate and the scale. We will discuss only one cause of the growth stresses which is conditioned by volume differences between the oxide and the metal from which it forms. To explain the formation of protective or non-protective scale, in this case the Pilling–Bedworth ratio (PBR) is used: PBR = Vox / Vm . (94) If PBR < 1, the oxide is assumed to be in tension and the scale should be porous. If PBR > 1 (this is the case for most metals), the oxide is compression and the scale should be compact5. For example, Fe, Al, Cr, W, for which the last situation is observed, are covered by dense, tightly adhering oxide films. Na, K, Mg can not form protective scales (PBR > 1) and then the oxide film grows at a constant rate not depending on the scale thickness (L). Such oxidation is said to obey the "linear rate law", i.e., Eq. (95) Q  k1t ,

(95) where Q is the mass of oxide layer per unit area of the metal surface; k1  dL/dt is the linear rate constant. The corresponding dependence is reflected by the line 1 in Fig. 11.

Fig. 11. Kinetics of formation of oxide scales at different oxidation laws 5

However, this mechanism of the development of stresses would only seem to be feasible if the oxide were growing at the scale-metal interface by inward migration of oxygen ions. Scales forming at the oxide-gas interface on a planar specimen should not develop stresses. P y r o m e t a l l u r g i c a l P r o c e s s e s | 33

The linear rate law is usually observed under conditions where a phaseboundary process or diffusion of molecules of oxygen diluted by an inactive or inert gases to the metal surface is the rate-determining step for the reaction. The growth of formed compact, protective layer is determined by two stages: (i) reactions at the scale-metal and oxide-gas interfaces; (ii) the migration of reactants through the scale. Diffusion through the scale is unlikely to be rate limiting when the scale is thin, i.e., in the initial stages of the process. With increasing scale thickness, on the contrary, this process becomes the ratedetermining step. Then the further oxidation proceeds according to the parabolic rate law: 1

(96) Q  k2t 2 (or Q 2  k ' t ) , where k2 is the parabolic rate constant (Fig. 11, line 2). Sometimes the protective properties of the scale can be partially or totally lost during later stages. Such oxidation is said to obey the “paralinear rate law”. In this case parabolic rate law describes the early stages of oxidation, becoming linear at longer times. Paralinear oxidation is observed during thermal cycling if the thermal expansion coefficient of the oxide is much less or greater than unity. The special case of parabolic oxide growth with simultaneous vaporization of the protective oxide was treated by Tedmon6 who showed that if the rate of vaporization is constant and if the rate of oxidation is inversely dependent on oxide thickness, oxide growth is described by Eq.: dx kd   ks , (97) dt x where x is oxide thickness, kd is the parabolic rate constant in terms of thickness (cm2 s-1) and ks is the evaporation rate constant (cms-1). Paralinear kinetics has been considered by Tedmon for oxidation of Fe-Cr alloys. In that system, parabolic oxidation results in solid Cr2O3 formation, with concurrent reaction of the oxide with O2 to form volatile CrO3(g). Sometimes the dependence of Q = f() for paralinear oxidation is presented as k kp , (98) Q  p ln kl k p  kl (Q  kl t ) where kp and kl are the parabolic and linear rate constants, respectively. An inverse logarithmic law is observed at formation of very thin films: 6

Tedmon C.S., Jr. The Effect of Oxide Volatilization on the Oxidation Kinetics of Cr and Fe-Cr Alloys // J. Electrochem. 1966. Soc. 113 (8). Р. 766–768. 34 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

k4  A  ln t (Fig. 11, curve 4). (99) Q Oxidation of some metals is described by a direct logarithmic law: (100) Q  k3 ln t or Q  k ln( Bt  1) (Fig. 11, curve 3). Compared to pure metals, alloy oxidation is generally much more complex for a number of reasons: – The metals in the alloy have different affinities for oxygen. – Ternary and higher oxides may be formed. – Solid solutions may be formed between the oxides. – The various metal ions have different mobilities in the oxide phases. – The various metals have different diffusivities in the alloy. As a result, the oxide scales on the alloys don’t contain the same relative amounts of the alloy constituents as does the alloy. – Dissolution of oxygen into the alloy may result in sub-surface precipitation of oxides of one or more alloying elements (internal oxidation). The difference of PBR between oxidation of a metal and an alloy relates to the volume change of the alloy, which is affected by the crystal structure and cell constants. Supposing that for a binary alloy A-B consisting of a noble7 metal A and a base metal B, only B will oxidize to form oxide during oxidation (or, in other words, the B oxide is more stable than the A oxide), C. Xu and W. Gao8 suggested PBR for alloys: PBRAlloy 

Volume of a mole of BxOy

. (101) Volume of x moles of B in alloy When liquid oxide phases are formed as a part of a multi-component system, a phenomenon called catastrophic oxidation of metals ("hot corrosion") may occur. Two stages of this process are recognized: fast, whose rate depends on diffusion process, and super-fast, whose rate depends on dissolution of a protective oxide film. The kinetics, thermodynamics, and mechanisms of the two stages of accelerated oxidation of metals, namely, fast and super-fast stages, are considered by V.V. Belousov9 with the copper-bismuth oxide system as an example. It is shown that the fast stage is caused by the formation of a liquid-channel grain boundary structure in the corrosion product, while the super-fast stage is caused by the high rate of dissolution of the oxide layer. 7

According to the Wagner’s classification, alloys can be grouped as (i) a noble parent with base alloying elements, and (ii) a base parent with base alloying elements. 8 Xu C., Gao W. Pilling-Bedworth ratio for oxidation of alloys // Mat. Res. Innovat. 2000. № 3. P. 231–235. 9 Belousov V.V. Catastrophic oxidation of metals // Russ. Chem. Rev. 1998. V. 67, № 7. P. 563. P y r o m e t a l l u r g i c a l P r o c e s s e s | 35

1.4.2. Thermodynamics of Oxidation of Sulfides and Interaction of Sulfides and Oxides The most of nonferrous metal ores contains valuable components in sulfide form. Concentrates produced by ore dressing contain from 5 to 40 per cent of sulfur. Desulphurization, as a rule, is realized by the use of the simplest procedure: oxidation of sulfides by atmospheric oxygen at elevated temperatures. Sulfur is withdrawn in this case in the form of oxides (SO2, SO3) or other compounds, or else in the elementary form. Oxidation of sulfides by atmospheric oxygen occurs in accordance with the following reactions: MS + 2O2 = MSO4, (102) MS + 1,5O2 = MO + SO2, (103) MS + O2 = M + SO2. (104) Besides the reaction of SO2 after-burning may take place: SO2 + 0,5O2 = SO3. (105) To analyze equilibriums in ternary systems M-S-O, thermodynamic phase diagrams presented in a plot of log PO2 versus log PS2 (Fig. 12) are convenient to use. Ii can be seen that if PO2 is increased the oxide phase will become stable, as PS2 is of no effect, until it is high enough for the sulfide to be stable.

Fig. 12. Schematic thermodynamic diagram of the M-S-O system at constant P and T

PSO3

Stability ranges for different phases can be considered depending on the / PSO ratio and temperature. As an illustration, Fig. 13 shows thermodynam2

ic diagram of the Cu-S-O system as a PSO3 / PSO2  1/T plot. According to con36 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

ditions, the products of oxidation of sulfides are sulfates, oxides or metal. As the PSO / PSO ratio increases, phases containing oxygen become more stable. 3

2

The stability range of sulfides is largely determined by the partial pressure of oxygen, since the PSO / PSO ratio depends on PO2 . At elevated temperatures 3

2

and high partial pressure of oxygen, the most stable phase in the ternary systems M-S-O is oxides. Besides mentioned processes, the following reactions may occur in these systems: MS + 2MO = 3M + SO2, (106) MS + MSO4 = 2M + 2SO2, (107) MS + 2SO3 = M + 3SO2. (108) In metallurgy, oxidation of sulfides in liquid state is of great practical importance. At temperatures above 1400 K the most of sulfates are thermodynamically unstable and oxidation of liquid sulfides should proceed according to the reactions (103), (104) to form either oxides or metals. The probability of the formation of metal can be evaluated with the use of the thermodynamic method.

Fig. 13. Thermodynamic diagram of the Cu-S-O system

Let us assume that matte converting process is conducted, and oxygen or air is blown into molten sulfides. If the partial pressure of oxygen in the air stream entering in melt equals 0,21 atm., and at the output it approaches zero, then the average value of oxygen pressure in the system is characterized by an insignificant magnitude. One can concede that under these conditions the formed metal can interact with the melted sulfide according to the reaction (106). P y r o m e t a l l u r g i c a l P r o c e s s e s | 37

Taking the simplifying assumption on the insolubility of condensed phases, we obtain K102  PSO2 . (109) The equilibrium of the reaction (106) may be considered as a combination of three equilibriums: reactions of dissociation of sulfide, oxide and SO 2. The first equilibrium is characterized by a certain pressure of sulfur; the second one is determined by the oxygen pressure. The equilibrium constant of reaction SO2 = 1/2S2 + O2 (110) is expressed by Eq.:

K106

P   ' S2

1/2

PSO' 2

PO' 2

.

(111)

At equilibrium, the pressure of sulfur vapor resulting from MS dissociation ' must be equal to that from SO2 dissociation ( PS2  PS2 ), as well as the oxygen ' pressures at dissociation of the oxide and SO2 ( PO2  PO2 ) must be identical.

Solving these equations in combination, we obtain PS'2  PO2 . (112) PSO2  K106 With knowledge of K106 and thermodynamic characteristics of the components of the reaction (106), it is possible to evaluate the thermodynamic probability of the realization of the reaction (106). For each metal there is a temperature beginning from which the reaction of the metal formation becomes probable. Metal oxides and sulfides react rather readily when the corresponding metal has a relatively low value of sum of affinities for oxygen and sulfur (Cu, Pb, Bi, Sb). High values of dissociation tension define an elevated pressure of SO2 even at low temperatures. For example, the reaction Cu2S + 2Cu2O = 6Cu + SO2 (113) becomes probable at 1020 K. The reaction PbS + 2PbO = 3Pb + SO2 (114) proceed relatively readily also. Unlike these examples, the interaction Ni3S2 + 4NiO = 7Ni + 2SO2 (115) can be realized only at high temperatures (1870 С). 38 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

1.4.3. Kinetics of Oxidation of Sulfides Oxidation of sulfides is a heterogeneous, highly exothermal process with the release of high amount of heat at the gas/solid (liquid) sulfide interface. The ability of sulfides to liberate heat is used in pyrometallurgical processes. Sometimes oxidation of sulfides and burden smelting are conducted in an autogenous or semi-autogeneous regime, i.e., without using the external heating or with a minimal expenditure of carbonic fuel. Oxidation of sulfides in converters, roasting of sulfide ores, and oxygen flash smelting are grouped with such technological processes. The amount of heat releasing in a unit time is determined by the rate of the chemical reaction. That withdrawn from a reaction zone depends on heattransfer conditions. The rate of heat transfer (q) is proportional to the difference between the temperature of sulfide surface (t1) and the temperature in a centre of gas stream t2:

q  a(t1  t 2 )1, 25  b(t14  t 24 ) ,

(116)

where а and b are constants. Under certain conditions, the amount of heat releasing in a unit time (Q 1) becomes more than the withdrawn heat (Q2). Q1 > Q2 inequality meets conditions of sulfide combustion. The ignition temperature of sulfides depends on a number of factors: the sulfide structure; the degree of its disorder; the number of dislocations and other defects on the surface; the sizes of the sulfide grains; heat capacity, thermal conductivity and density of initial material and formed films of oxidation products. The defect structure of sulfides favors its interaction with oxygen. The reaction rate depends on the value of the sulfide/gas interface area. The smaller grains of sulfides ignite at lower temperatures. The higher are the heat capacity and the density of a sulfide, the higher is the temperature of its ignition. Ambient conditions effect on the ignition temperature also. A moistening of air results in some decrease of its value. The dilution of air by the sulfur dioxide, on the contrary, increases the ignition temperature. Higher sulfides having more defect structure (for example, pyrite) ignite at lower temperatures than lower ones (pyrrhotite). Oxidation depending on ambient conditions and the structure of sulfides and formed oxides can occur in the diffusion-controlled, kinetic or mixed regime. If the process proceeds in the kinetic regime, then the effect of concentration of oxygen in a gas stream on the solid sulfide oxidation rate is described by the Eq.: P y r o m e t a l l u r g i c a l P r o c e s s e s | 39

v  ke



E RT

PO2 .

(117)

At constant temperature, the rate of this process is directly proportional to the partial pressure of oxygen in the gas phase:

v  k ' PO2 .

(118)

Oxidation of sulfides coved by a compact film of oxide shares a number of traits with oxidation of metal in the diffusion regime. However the formation of dense oxide films at the surface of sulfides occurs not always. In many instances, liberation of SO2 at the sulfide/oxide interface can take place. Formed sulfur dioxide volatilizes along the grain boundaries or breaks the oxide film in some places. Therefore the formation of compact films on sulfides is less probable than on metals though it is not ruled out fully. The generation of porous scales is caused not only with gas liberations but also with the difference in molar volumes of oxides and sulfides. Oxidation of liquid sulfides has a number of distinctive characteristics: – There is a considerable mutual solubility of liquid sulfides and liquid oxides. – Many of M-S-O systems have large miscibility gaps. – Liquid sulfides have higher rates of oxidation and higher diffusion coefficients of components as compared with solid sulfides. – The gas liberation occurs easier in the case of the liquid-phase oxidation.

1.4.4. Thermodynamics of Oxidizing Refining The metals produced from ores and concentrates are crude ones, i.e. contain more than ten elements besides a base metal. The crude metals are subject to refine. Sometimes metal impurities are of great value, for example, Au, Ag, Pt and others. Oxidizing refining is most often realized by introducing an oxidizing gas, such as air, oxygen enriched air, or commercially pure oxygen into a tank to remove elements less noble than the base metals. In some cases, a feeding of oxides easily releasing of their oxygen is applied. Oxidized impurities emerge in the form of free or slagged oxides to the surface of the metal bath. A portion of formed oxides having high vapor pressure at the process temperature volatilizes either totally or partially (As2O3, Sb2O3, SnO and etc.). 40 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

Thus, oxidizing refining involves two key steps: (a) oxidation of impurities, (b) separation of formed oxides from the metal bath by liquation or volatilization. Oxidizing refining is based on the higher affinity of some impurities to oxygen as compared to a refinable metal. For example, when a stream of air is forced through molten copper, oxides are formed by admixtures of Fe, Ni, Zn, Pb, Sb, As, and Sn, since the admixtures have a greater tendency to react with oxygen than copper; the oxides rise to the surface of the tank and are removed. However the only difference in affinity is insufficient; an oxidized impurity can remain in molten refinable metal. It can be attributable to the solubility of some oxides in metals, reactions between oxides of impurities and of refinable metal to form compounds soluble in the bath, and to a small difference in dense of oxides of impurities and of refinable metal which obstructs the separation of phases. During oxidation of metal bath, the refinable metal is oxidized at first to form MO oxide which dissolves in the bath and gives its oxygen to impurities (M') those exhibit the higher affinity to oxygen. Thus, this process occurs according to the following equations: 2M + O2 = 2MO, MO → [MO], [MO] + [M'] = (M'O) + [M].

(119) (120) (121)

The direct oxidation of impurities by atmospheric oxygen by the equation 2M' + O2 = 2M'O

(122)

proceeds to only a small extent in proportion to the concentration of impurities in the refined metal. The fundamental reaction of oxidizing refining of metals (reaction (121)) is reversible. The concentration of refined metal acting as a solvent for impurities varies insignificantly and can be taken as a constant. Therefore, at аМ = const a K  M'O . (123) aMO aM' Hence it follows that the activity of an impurity remaining in the bath is equal to a aM'  M'O . (124) KaMO Thus, the higher is the activity of oxide of refinable metal in the metal itself and the lower is the activity of impurity metal oxide in a slag; the more effective will be the oxidizing refining. P y r o m e t a l l u r g i c a l P r o c e s s e s | 41

The reaction of (121) will be in equilibrium when P   P



 



,

(125)

i.e. when the affinity of M to oxygen will be equal to that of M'. If P )  P

 





,

(126)

then the impurity is being oxidized; and on the contrary, if P   P

 





,

(127)

then the impurity is being reduced from oxide and is passing in the metal bath. From expressions for dissociation pressure of the oxides

P 

P

2 ( Me

/

O)

2 aMO K 2 , aM

K

2 aMe / O

, 2 aMe /

(128)

(129)

it follows that the lower is the activity of an impurity metal in the bath; the higher is the dissociation pressure of the impurity oxide, and the lower it the affinity of the given impurity to oxygen. At the beginning of the process, the M' activity is high, the change in the Gibbs energy of the reaction is negative, so oxidation of the impurity must occur. As the reaction of oxidizing refining develops, the MO activity in the bath decreases, while the affinity of the refinable oxide to oxygen increases. The activity of impurity oxide, on the contrary, shows a rise, the concentration of the impurity in the metal bath diminishes, therefore dissociation pressure of the impurity oxide increases and the affinity of impurity to oxygen decreases. As a result, there comes a point where PO2 (MO)  PO (M/ O) , (130) 2

and an equilibrium is established. In the case that P   P

 





,

(131)

the reaction will go in the reverse direction. Thus, it may be concluded that, for the most complete oxidation of impurities, a sufficiently high activity of oxide of refinable metal should be maintained in the bath throughout the oxidation process. Of a number of impurities presenting in a bath, impurities with lower dissociation pressure should be oxidized first. If out of two impurities M' and 42 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

M'' the oxide of the former is characterized by a higher dissociation pressure as compared to that of the latter but just the first impurity was oxidized, then the following reaction must go from left to right: [M'O] + [M''] = (M''O) + [M']. (132) The most complete removal of impurities is achieved by a disturbance of equilibrium owing to the removal of formed slag from the bath surface. The reaction of oxidizing refining is exothermic process, so the increase of temperature shifts the equilibrium to left, i.e., has an adverse effect on the results of refining.

1.4.5. Oxidizing Refining of Metals with Introduction of Chemically Active Additions Sometimes the decrease of a residual content of an impurity in the bath is achieved owing to a conversion of formed impurity oxides to a more complex, stable compound. An illustrative example is the removal of lead from copper by oxidizing refining. Lead exhibits a grater affinity for oxygen in comparison with copper but the difference is small: 

[Pb] + [Cu2O] = (PbO) + 2[Cu], G°1420 = –21820 J, K = 6,35.

(133) (134)

Obtained lead oxide is of higher density than liquid copper and doesn’t emerge to the melt surface. The more complete removal of lead is accomplished by the introduction of silica as a flux. The acidic silicon dioxide interacts with the lead oxide to form lead metasilicate and orthosilicate:  

[Pb] + [Cu2O] + (SiO2)= (PbO SiO2) + 2[Cu], G°1420 = –45195 J, K = 46,1; [Pb] + [Cu2O] + 0,5(SiO2)= 0,5(2PbO  SiO2) + 2[Cu], G°1420 = –43270 J, K = 39,1.

(135) (136) (137) (138)

The formation of silicates increases the equilibrium constant of the lead oxidation reaction 6–7 times, resulting practically in the decrease of the residual concentration of lead in copper as many times. In addition, the lead silicates have lower densities than liquid copper, which facilitates their floating and transfer into a slag phase.

P y r o m e t a l l u r g i c a l P r o c e s s e s | 43

1.4.6. Oxidizing Refining of Metals with Obtaining Gas Products (by the Example of Removal of Carbon from Iron) After reducing the iron oxide the resultant material is pig or cast iron. Carbon is distributed throughout the molten cast iron as cementite (iron carbide, Fe3C) and graphite. Iron carbide dissociates in part according to the reaction [Fe3C] = 3[Fe] + [C], (139) so the activity of carbon in the molten cast iron doesn’t equal to its total concentration. The cast iron must be further refined to reduce the carbon content and the other undesirable elements before the material can be categorised as particular steel. Refining iron into steel requires the remelting of the iron in a steelmaking furnace with a large oxygen input. The reaction of carbon burning is expressed by the equation [FeO] + [C]= [Fe] + CO. (140) with the equilibrium constant K

PCO  aFe . aFeO  ac

(141)

PCO . aFeO  ac

(142)

Taking aFe = const, we obtain K

Hence PCO  K  aFeO  ac .

(143) The residual concentration of carbon will be minimal in the case of saturated solution of FeO in steel: [C ]min 

PCO 1 . K [FeO]saturated

(144)

This reaction is exothermic. According to the Le Chatelier's principle, with increasing temperature the CO equilibrium pressure increases and the residual concentration of carbon decreases correspondingly.

44 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

1.4.7. Deoxidizing of Metals During oxidizing refining a part of the refinable metal is oxidized along with the impurities and this part increases with the purity to which the metal must be refined. Therefore the refined metal contains soluted oxygen. Oxygen impurity affects the physicochemical properties of metals, and for this reason after oxidizing refining various deoxidizers are employed, chiefly manganese, silicon, aluminum and titanium, or alloys thereof. All elements which have a greater affinity for oxygen than the refined metal can be theoretically used as deoxidizers. Deoxidizing of metals is the reverse of oxidizing refining. The reaction of deoxidizing can be written in a general form as [MO] + [R] = [M] + (RO), (145) where [R] is a deoxidizer. If activity of the metal is taken to be constant, we obtain the following expression for the residual activity of MO: a aMO  RO . (146) KaR One can see from this equation that the lower is the RO activity in a bath and the higher is the activity of the deoxidizer, the more complete is the process of deoxidizing. However the high concentration (activity) of the deoxidizer in the metal is impermissible in practice because the residual deoxidizer affects the properties of the metal. A good deoxidizer must satisfy the following requirements: (i) To have a high affinity for oxygen; (ii) To have no harmful effect on the quality of the metal in those concentrations which are requirements for deoxidizing; (iii) Oxide of the deoxidizer must exhibit a minimal solubility in the metal; (iv) Oxide of the deoxidizer must be capable of interacting with other oxides to form fusible compounds being of low density and insoluble in the bath; (v) Deoxidizer must be low in cost and available.

P y r o m e t a l l u r g i c a l P r o c e s s e s | 45

1.5. PHYSICOCHEMICAL PROPERTIES OF METAL AND SLAG MELTS

1.5.1. Metallurgical Slags and Their Functions in Metallurgy Slag is usually a mixture of metal oxides and silicon dioxide. In addition, slags can contain metal sulfides (or other salts; for example, CaF2, NaCl) and elemental metals. Slags play an important role in many processes in metal production and refining. They are used for removing impurity elements and undesirable nonmetallic inclusions (oxides and sulphides) from metal in order to achieve required composition. Other functions of slags: (i) Usually a liquid slag layer covers the molten metal and protects it from oxidizing atmosphere. (ii) Slag is often a medium, where reactions take place. (iii) It acts as thermal insulation layer on molten metal, reduces the heat losses from the metal surface and prevents the “skull formation”. (iv) The composition of slag determines that maximal or minimal temperature which can be obtained in each specific case in furnaces of shaft type. (v) Slags are a binder at agglomeration of ores and concentrates. (vi) Sometimes slags are not wastes but a main product of smelting which contains valuable metals. The various processes and different purposes in which slags are involved, each obviously demands particular properties of slag, and thus a certain composition.

1.5.2. Composition and Structure of Molten Slags The main constituents of metallurgical slags are CaO, Al2O3 and SiO2. Oxides entering into the composition of slags can be grouped as (i) acidic ones that absorb O2- ions in reactions with basic oxides to form corresponding salts (an example is silicon dioxide, which reacts with basic oxides to form silicates); 46 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

(ii) basic ones like as Na2O, CaO, MgO, FeO, Cu2O, BaO that are donors of oxygen ions in reactions with acidic oxides; (iii) amphoteric ones which are metallic oxides showig both basic as well as acidic properties (For example, Al2O3 reacts with basic oxides to form aluminates and with silica to form silicates). The bonding between cations and anions in acidic oxides like SiO2 is strong, and these simple ions form complex ions. The silicate structural unit SiO44 consists of one Si4+ ion surrounded tetrahedrally by four O2- ions (Fig. 14). In silicate slags, the unit tetrahedra may form more complicated structures (Fig. 15) as Si 2O76 , cyclic polymers (for example, Si3O96 ) and even three-dimensional network of bridged silica tetrahedra.

Fig. 14. Silicate structural unit

Such oxides which tend to form a three-dimensional network of anion complexes are called network formers. Basic oxides are called network breakers (network modifiers), since they destroy the hexagonal network of silica by reacting with it10. An example is the reaction between an alkaline oxide, e.g. Na2O, and SiO2: Increasing content of basic oxides in silicate slags results in breaking down silicate polymers into smaller units. Thus, slags contain two forms of bonds: (i) covalent Si-O bonds that form into chains, rings etc., and (ii) ionic bonds involving cations such as Na + or Ca2+. Oxygen ions can connect to either another O- ion and thereby add to the network (named bridging oxygen) or to a cation, thereby breaking the chain 10

At the same time, amphoteric oxides like Al2O3 added to the silicate slags contribute to the chain structure. P y r o m e t a l l u r g i c a l P r o c e s s e s | 47

(named non-bridging oxygen). Oxygen ions that are not associated with silicon ions are called free oxygen.

Fig. 15. Examples of different types of polymeric silicate structures

The degree of polymerization of slag can be presented by the ratio of non- bridging oxygen to tetrahedrally coordinated cation (NBO/T). The understanding of slag structures is of great importance, as the formation of structures is widely reflected in the physicochemical properties of these melts. A quantitative measure of the basicity of the slag system is a basicity index which is used as a parameter with which the chemical behavior and the physicochemical properties of slags can be correlated. There are several approaches to definitions of basicity indices leaning upon the three theories: 1) theory of undissociated oxides, 2) ionic theory and 3) theory of Lewis base11. Various definitions of basicity indices of oxide systems put forward by researchers may be grouped under the following three theories: 1) theory of undissociated oxides (molecular theory), 2) ionic theory and 3) theory of Lewis base. It is now generally accepted that slags are ionic in nature, although they have an occasion been viewed as having a molecular structure. According to the molecular theory, liquid slags consist of individual oxides, sulfides, or fluorides, the molecules of which interact to form more complex compounds, for 11

Datta I., Parekh M. Filler Metal Flux Basicity Determination Using the Optical Basicity Index. Welding J. 1989. № 2. Р. 68–74. 48 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

example, CaO.2SiO2, existing in dissociated equilibrium with the corresponding components. As noted by I. Datta and M. Parekh, the earliest form of a basicity index proposed in the contex of this theory, was expressed as a basic-to-acidic oxide ratio sum of basic oxides Basicity index  . (147) sum of acidic oxides There are also other expressions taking into account, particularly, the presence in slags not only oxides but fluorides as well. According to the ionic theory of oxide melts, basic oxides dissociate into metal cations and oxygen anions, while acidic oxides consumes O2- to form more complex anions as discussed above by the example of silicate structures. Within the framework of this theory, a basicity index is given by





pO   log aO2 ,

(148)

where aO2 is the activity of the oxygen anions, and pO is the potential of oxygen. This expression is noted to have two drawbacks: 1) it was derived by applying the theory of ideal oxide mixture; and 2) it is not possible to determine aO2 . A Lewis base is defined as a substance that is an electron-pair acceptor and therefore able to react with a Lewis base to form a Lewis adduct, by sharing the electron pair furnished by the Lewis base. Then, a Lewis base is a substance that donates a pair of electrons to a Lewis acid. The affinity of cations for the negative charge is evaluated by Pauling’s electronegativity. The oxygen atoms of network systems formed by highly polarizing cations such as Si4+ bear charges which are between those of their parent oxides. The negative charge can be estimated using the optical (ultraviolet) spectra of certain probe ions and is represented by the optical basicity, Λ. The optical basicity is shown to be dependent upon the stoichiometry of the medium or compound, the oxidation numbers of the cations and upon a newly defined "basicity moderating" parameter, γ, which is related to the Pauling electronegativity, x12: x   c ,  = 1,36(x – 0.26), (149)  where xc is the cation fraction. In order to evaluate the average optical basicity of a multicomponent system, the following expression can be used: 12

Duffy J. A Review of Optical Basicity and its Applications to Oxidic Systems // Geochimica et Cosmochimica Acta. 1993. № 57. Р. 3961–3970; Duffy J., Ingram M. Establishement of an Optical Scale for Lewis Basicity in Inorganic Oxyacids, Molten Salts, and Glasses // J. Amer. Chem. Soc. 1971. Р. 6448–6454. P y r o m e t a l l u r g i c a l P r o c e s s e s | 49

  xa a  xb b  ...

(150)

Here a(b) is the optical basicity of oxide a and b, xa(b) is the corresponding cation fraction.

1.5.3. Structure-Sensitive Properties of Metal and Slag Melts It is known that some properties of melts depend on microstructure and vary greatly with the heat treatment: These are the structure-sensitive properties: viscosity, diffusivity, thermal and electrical conductivity, surface tension. These parameters, determining particle mobility, are related each other. For example, according to the Stokes-Einstein equation, the diffusion constant, D, is inversely proportional to dynamic viscosity, :

D

k BT 6r .

(151)

Here kB is Boltzmann’s constant, T is the absolute temperature, r ie the radius of the spherical particle. Electrical conductivity is related with viscosity by the following empirical relation: (152) æn = const, where n > 1.

1.5.4. Viscosity Viscosity is one of the most important properties in the case of metallurgical melts, in view of its direct effect on the kinetic conditions of the processes. The mass and heat transfer, the solubility of slag formers and additions, the separation of metal and slag are improved by the low viscosities. But on the other hand a low viscosity of aggressive slags increases the corrosion of the refractory material of metallurgical vessels. Viscosity13 is a measure of the internal friction of a fluid when a layer of a fluid is made to move in relation to another layer: 13

The SI-unit for the dynamic viscosity is Pa·s (Nm-2s).

50 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y



F dx  , S dv

(153)

where dv/dx is the velocity gradient, i.e. the difference in velocity between adjacent layers of a fluid, F/S is the force per unit area required to produced shearing action "shear stress". Viscosity is determined for the most part by large, low-mobility particles, specifically by anions, the state of them depends substantially on the temperature. Increasing temperature leads to either anion dissociation or a change of bonding character inside complex ions. It tells on a decrease of viscosity with temperature. The most of experimental data on the temperature dependence of the viscosity of both metal and slags is approximated by the Arrhenius relationship:  = A exp(E/RT), (154) where A is the pre-exponential factor depending on the melt nature, R is the gas constant, E is the activation energy. The validity of this equation for a relatively narrow temperature interval is supported by a linear relationship of ln to 1/Т. A sharp change in slope (at the break temperature) can point to structural rearrangements in melt. In addition, in the case of slags, increasing temperature can result in Е because the activation energy is closely related to the type of ions and ionic complexes present in molten slags as well as the interionic forces they give rise to. In order to account for these changes, the temperature dependence of the viscosity is sometimes expressed in the form of the Frenkel relationship which is known also as the Wayman equation:  = AWT exp(E/RT), (155) where AW and E are similar to the A and E parameters in the previous equation but will have different values. Pure silica has very high viscosity at the melting point. Addition of basic oxides decreases the viscosity by breaking the hexagonal network of silica. The magnitude of the effect is strongly dependent on the components and their proportions present in the slag. Amphoteric oxides, like Al2O3, Fe2O3, may act either network former or breaker following the composition of the slag. In the case of transition metals (e.g. Fe, Cr) it is important to know the oxidation state (Fe2+/Fe3+, Cr2+/Cr3+) since they have different effect on the vis2+

3+

cosity14. It has been found15, particularly, that the ratio of Fe to Fe in silicate 14

Kondratiev A., Jak E., Hayes P.C. Predicting Slag Viscosities in Metallurgical Systems // J. Met. 2002, November. P. 41–45. P y r o m e t a l l u r g i c a l P r o c e s s e s | 51

melts decreased with increasing the oxygen partial pressure in all the samples. 2+

In parallel, the viscosity of the melts decreased with increasing the ratio of Fe 3+

2+

to Fe . The increase of Fe ion that behaves as a network modifier, would result in depolymerisation of the silicate anions. It should be also noted that the viscosity of the melts was decreased in the order of alkali cationic radius 2+

3+

(K > Na > Li) when the ratio of Fe to Fe in the melts was comparable; it would 3+

be due to the change in the coordination structure of Fe in these melts. The oxidation states depend critically on oxygen partial pressure, temperature and bulk composition of the slag, and any of these changes can lead to significant changes in phase equilibria and to variations of the slag viscosity.

1.5.5. Diffusion The temperature dependence of the diffusion coefficient is usually expressed in the form of the following equation: D = D0exp(–ED/RT), (156) where ЕD is the activation energy, D0 is the pre-exponential factor characterizing the value of diffusivity at 1/Т  0. Unlike metal melts, the diffusion in ionic systems such as slags is determined by not only the gradient of chemical potential but also electrostatic forces. According to the Nernst-Einstein equation, the diffusion coefficient in ionic melts is proportional to the limiting molar ionic conductivity, : RT , (157) D zF where z is an ion charge, F is Faraday’s constant.

1.5.6. Electrical Conductivity In metals, the charge carriers are valence electrons. Electron mobility in metals is generally determined by a mean free path of electrons which is in15

Effect of Oxidation State of Iron Ions on the Viscosity of Alkali Silicate Melt / T. Ohsugi, S. Sukenaga, Y. Inatomi [et al.] // ISIJ International, 2013. V. 53, № 2. 52 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

versely proportional to absolute temperature. Thus the electron mobility in molten metals and consequently the electric conduction are also inversely proportional to absolute temperature. Electrical conductance of liquid slags increases with temperature. The temperature dependence of the specific conductivity is approximated by the following equation: æ   Ai (  Ei / RT ) , (158) i where Аi is a coefficient of proportionality for ith ions, Ei is the activation energy. When cations and anions differ greatly in activation energy, a movement of ions of the mere sort with the lowest value of Ei is taken into account. Then the dependence of æ = f(Т) is expressed by the equation æ = æ 0exp(–Eæ / RT). (159) According to this formula, an ln æ  1/Т plot must yield a straight line. As in the case of viscosity, the breaks of lines can point to structural changes in melts. The total value of the specific conductivity is composed of ionic and electron-hole conductivities: æ = æ i + æ e/h. (160) In the case of oxides, the second summand depends on the partial pressure of oxygen: m æ = kPO2 .

(161)

m æ = æ i + kPO2 .

(162)

Hence, Since the electrical conductivity is dependent upon the number of ions available, it follows that the electrical conductivity of æNa2O > æCaO. The electrical conductivity is also dependent upon the mobility of the cations; thus the conductivity is greater for smaller cations such as Li+, Na+, and K+, but the reverse trend can be seen with Ba2+, Ca2+, and Mg2+.

1.5.7. Surface Tension Surface tension of molten slags and metals is one of the most important parameters for metallurgy processes, on account of which is closely related to the phenomena such as inclusion formation and removing in metal melt, slag foaming, slag-metal emulsification and slag-metal reaction. P y r o m e t a l l u r g i c a l P r o c e s s e s | 53

Surface tension is a thermodynamic property closely related to the bulk thermodynamic properties of the liquid. The free surface of a multicomponent liquid contains higher concentrations of the constituents with lower surface tension. These components tending to occupy the surface layer (e.g. Na2O, K2O and CaF2 in slags) are called surfactants. The surface concentration of a component depends upon both its surface tension and the chemical activity. When there are two or more surface-active components in the slag (e.g Na2O and CaF2), they compete for the surface sites. The surface tension of the molten slag system can be calculated from the Butler’s equation16: RT aisurf (163)   ipure  ln bulk , Ai ai where ipure is the surface tension of the pure molten component i; aisurf and

aibulk are the activities of the component i at the surface phase and at the bulk phase, respectively; superscripts surf and bulk indicate the surface and bulk phase, respectively. Ai is the molar surface area in a monolayer of pure molten component i, which can be determined by the following equation: 2/3 Ai  L  N 1/3 (164) A  Vi . Here NA is Avogadro’s number, Vi is the molar volume of the pure molten component i, L is a correction factor resulting from the surface structure and usually set to be 1 for the molten salts and ionic oxide mixtures. Surface tension of an oxide system can be also estimated from the (molar) weighted average surface tensions of its components: slag   i xi . (165) i

The surface tension of slags increases with decreasing SiO2 content, and with increasing CaO and Al2O3 concentrations. Addition of basic oxides (e.g. CaO) to the tetrahedral silica network structure rupture the bonds, creating free oxygen atoms that positively contribute to the surface tension. Surface tension of liquids decreases usually with increasing temperature as molecules become less tightly bound to the surface with increasing kinetic energy. Surface tension of a liquid as a function of temperature can be characd terised through a temperature coefficient, : dT 16

Chengchuan Wu, Guoguang Cheng, Qiqi Ma. Calculating Models on the Surface tension of CaOFeO-SiO2 Molten Slags // Research of materials Science. 2014. V. 3, Is. 1. P. 10–16. 54 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

d (166) T  Tm  , dT where Tm is melting temperature and m is surface tension at the melting temperature. Liquid metals and basic slags have negative temperature coefficients. In some cases temperature coefficients are positive, including slags with high SiO2 contents. This is related to the fact that silica has a relatively low surface tension value. For liquid iron containing surface active elements, when temperature increases, the surfactants gradually desorb from the surface, restoring a higher value of surface tension. The surface tension of molten metals is considerably influenced by oxygen partial pressure because oxygen which acts as surfactant is adsorbed to a melt surface from the atmosphere gas. When PO2 is low, the surface tension of T  m 

molten metal generally shows a negative temperature coefficient. However, the temperature coefficient of surface tension increases with increasing PO2 .

1.6. CRYSTALLIZATION REFINING METHODS

1.6.1. Liquation Refining Liquation refining is a method for removal of impurities from metals, based on differences in the melting temperatures and densities of alloy constituents and on the low level of mutual solubility of the constituents. For example, when molten crude lead is cooled, copper crystals (dross) separate out at established temperatures and, because of their low density, float to the surface and can be removed. This method is used to remove Cu, Ag, Au, and Bi from crude lead, to remove Fe, Cu, and Pb from crude zinc, and to refine tin and other metals. Liquation processes occur when crude metals are heated (melting) or cooled (crystallization); among these are some processes taking place at constant temperature. In the last case the formation of a second phase in molten metal and the liquation are associated with an admixture of other metals which react with impurities to form refractory compounds undissolving into refinable metal. P y r o m e t a l l u r g i c a l P r o c e s s e s | 55

Liquation on cooling is a result of nonsimultaneous crystallization of different constituent parts of an alloy; and the wider is the interval between upper and end point of solidification of a metal, the more effective is the l iquation. Liquation processes involve two steps: 1) The formation of a heterogeneous system with solid and liquid phases. It is realized by one of the listed techniques (heating, cooling, addition of admixtures). 2) The separation of two substances obtained at first step. This is achieved by the liquation of separable substances having different densities or by applying special facilities (for example, filters) allowing separating crystals from a liquid. The ability of realizing of one or another liquation process is determined by features of equilibrium diagrams “refinable metal – impurity”. Based on an equilibrium diagram, we can reveal temperature conditions providing sufficient completeness of removal of an impurity as well as the relative amounts of phases obtained by liquation refining. As an illustration we will consider refining of the lead. Crude lead contains up to 2,4 % of Cu. Consider refining of alloy containing about 1 % of copper. In the first stage, temperature is decreased to 450–500 С (Fig. 16, the point Tb). Since it results in the decrease of copper solubility, then, already from the temperature of Та, copper crystals separate out from the melt. Two phases is in equilibrium at Tb: molten lead with small copper concentration (the point b') and crystals of solid solution based on copper with small lead content. According to the lever rule, the amount of the solid phase is equal to: bb ' ms  ml . (167) bb '' As the density of copper is lower than the density of lead, so arisen crystals float up to the surface and form so-called “dry dross”. The decrease of temperature below 450–500 С results in better refining of lead, but it is not used in the first stage, because, with decreasing temperature, viscosity of the melt increases and conditions of phase separation become worse. The temperature is decreased to 330–340 С in the second stage, after removal of dry dross. At this temperature (Тс) the further segregation of copper takes place, and now crystals is in equilibrium with liquid lead containing a smaller amount of copper (the point c') compared to that at temperature of Tb. 56 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

Fig. 16. Cu-Pb phase diagram

Floating copper crystals form a surface layer (so-called "rich dross") containing a lot of mechanically trapped lead (80–90 %) due to its high viscosity at this temperature. The content of copper in lead is decreased after this stage up to 0,1 %. A fine drossing process is conducted with the use of sulfur to scavenge residual copper. Copper sulfides are characterized by relatively high melting temperatures, low densities and very low solubility in crude lead. They float up to the surface and, as a result, the content of copper in the melt is decreased to 0,0005–0,005 %.

1.6.2. Fractional Recrystallization These methods are used in the production of semiconductor materials and in the preparation of high-purity metals. Fractional recrystallization utilizes the difference in the solubilities of a metallic admixture in solid and liquid phases and the slow diffusion of impurities in the solid phase. The refining effects of these melting methods are controlled by crystallization processes on the crystal-melt boundary (normal freezing, zone melting, directional crystallization etc.). This boundary forms the crystallization front. P y r o m e t a l l u r g i c a l P r o c e s s e s | 57

The distribution coefficient, K, is a quantitative thermodynamic characteristic of distribution of an admixture between solid and liquid phases in equilibrium conditions. It is defined as an isothermal ratio of admixture concentration on the solidus curve ( CBs , Fig. 17) and on the liquidus curve ( СВl ) in binary element-admixture system: Cs (168) K  Bl . СВ

Fig. 17. Graphical determination of the equilibrium concentrations of an admixture B in solid and liquid phases and of the distribution coefficient: a – K < 1; b – K > 1

The equilibrium distribution coefficient takes the values K < 1 for systems, in which the admixture causes a temperature drop of the basic component (Fig. 17, a), and the values K > 1 for those admixtures causing a temperature rise of the basic component (Fig. 17, b). Equilibrium distribution coefficients characterize the behavior of admixtures during crystallization at the solidus-liquidus interface and refining processes. They provide reliable information about the distributing ability of individual admixture elements in the host in crystallization processes during which the admixture with K > 1 are enriched on the axes of crystallizing dendrites, and on the contrary, the admixtures with K < 1 are enriched in interdendritic spaces and in the finally solidifying host melts during the dendritic segregation which always accompanies solidification of substances in reality. In selective refining metallurgical crystallization processes such as zone melting or normal freezing used to prepare high purity metals, an effective distribution of admixtures occurs, so that admixtures with K > 1 accumulate at the beginning and admixtures with K < 1 at the end of the refined ingot. Deep refining of materials by crystallization methods is more effective if K is considerably different from 1. 58 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

Generally, K depends on concentration, with the exception of very dilute solutions. The final distribution of components in crystallized ingot depends not only on the equilibrium distribution coefficient but also on crystallization conditions. When equilibrium crystallization takes place, the diffusion rate of an admixture is commensurate with the solidification rate; and at each moment only crystals which are in equilibrium with the melt exist. At increasing crystallization rate, crystals are not in equilibrium with the melt existing at the given moment. Thus the ingot parts crystallized at different times will vary in composition. The actual process is characterized by an effective distribution coefficient, Keff, which must be determined experimentally. It expressed through the distribution coefficient K by the well-known Burton-Prim-Slichter equation: 1 K eff  , (169) 1   v  1    1 exp    К   D where v is the growth rate of the solidification front; D is the diffusion coefficient of the solute (impurity) in the melt;  is the thickness of the diffusion layer (a narrow layer of the melt adjacent to the interface; inside this layer the solute in the melt is transported by diffusion only). At v  , impurity concentration are equal in the melt and in the crystal, and Keff = 1 (i.e. refining doesn’t occur), while under equilibrium conditions, where v = 0, Keff = K. This equation can be presented in a form convenient to determine the /D ratio:  1  1  v ln   1  ln   1  . (170) K  K D    eff  It follows that the determination of K and /D involves the conduction of a series of directional crystallizations with different rates but under identical convection conditions. The deviation of effective distribution coefficients from the equilibrium one is explained by many causes. It depends to a large measure on the form of the solidification front. In order for the effective coefficient to approach K, a flat solidification front must be maintained in the process. The shape of the solid-liquid interface can strongly be influenced, for example, by the convective heat transport in the melt. The most-used crystallization methods of metal refining from impurities include the Bridgman method of normal directional crystallization, the method P y r o m e t a l l u r g i c a l P r o c e s s e s | 59

of pulling a crystal from the melt proposed by Czochralski, and the zone recrystallization by Pfann. There are several variants of the Bridgman method. One of these supposes solidification of molten metal in a graphite mould in the form of a boat. The melt is cooled at one end, where the growth of the crystal becomes in the direction opposite to the heat removal. The Czochralski method is implemented by the following way. Crystalseed is brought into contact with the melt surface and then is slowly lifted at constant slow rotation around its axis. The growing crystal entrains, due to the wetting, new portions of the molten metal. The fundamental difference between this method and the Bridgman one is that the interaction between the solid and liquid phases in the Czochralski method is limited and is possible only across the boundary at the solidification front. Zone recrystallization (or zone refining or zone melting) is a group of methods of purifying crystals, in which a narrow region of an ingot is molten, and this molten zone is moved along the ingot with a definite constant velocity. The movement of the melted zone along a solid ingot is technologically realized by two ways: (i) by the motion of a solid ingot with the molten zone relative to a heater and (ii) by the motion of the heat source along the stationary ingot. In zone refining, a number of molten zones are passed through the charge in one direction. The actual efficiency of this process depends upon the distribution coefficient, the number of zone passes, the zone velocity and the sample length to zone length ratio.

1.7. PROCESSES OF EVAPORATION, SUBLIMATION AND CONDENSATION The principle of refining of metals by evaporation or sublimation is that the vapor pressures of various metals at the same temperature are different. As a result, the metal with high vapor pressure and low boiling point can be separated from other metals through distillation, and then it can be recycled through condensation under a certain condition. The thermodynamic characteristic of volatility is saturation vapor pressure Pi 0 depending on the nature of the substance and temperature. The de60 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

pendence of Pi 0 = f(T) is described by the Clausius-Clapeyron equation which, with enthalpy of the respective transition (vaporization or sublimation; Htrans) taken as constant over the temperature range of interest, has the form: H trans (171) ln Pi 0   C, RT where C is a constant. Liquid-vapor equilibrium in binary systems depends on pressure, temperature and compositions of the phases. If P or T is constant, the equation of state f(P, T, x) = 0 becomes simpler and we obtain either an isotherm P = f(x)T or an isobar T = f(x)P. In the case of a binary system formed by components A and B, the composition of liquid phase in equilibrium with vapor can be determined by the use of Raoult’s law: PA  PA0  xlA , PB  PB0  xBl , (172) l l Ptotal  PA  PB , xB  1  xA ,

Ptotal  PA0  xlA  PB0 1  xlA  .

(173) (174)

Thus, Ptotal  PB0 , (175) x  0 PA  PB0 where PA and PB are the partial equilibrium vapor pressures of A and B, respecl A

tively; PA0 and PB0 are the saturation vapor pressures of the pure components; Ptotal is the total vapor pressure; x lA and xBl are the mole fractions of A and B in the melt. Hence, so that the composition of liquid in equilibrium with vapor will be determined at distillation of a binary system, we must know values of the saturation vapor pressures of the components and the total vapor pressure. For distillation, both vapor and liquid compositions are of interest. For finding the composition of vapor in equilibrium with liquid phase, we can use the combination of Raoult's law with Dalton's law: P P 0  xl (176) x Av  A  A A . Ptotal Ptotal Here x Av is the mole fraction of the component A in equilibrium vapor phase. In actual practice, distillation is used for real, non-ideal solutions for which positive and negative deviations from the Raoult's law are observed. In P y r o m e t a l l u r g i c a l P r o c e s s e s | 61

this case the activity coefficient accounting for the interactions between molecules of different substances would be incorporated instead of the mole fraction in the corresponding equations. The relative amounts of two phases in equilibrium can be determined with the use of the phase diagram according to the lever rule. Distillation is used for purifying metals that have high vapor pressure at moderate temperature, e.g., mercury and zinc. Single stage distillation of a metal containing another metal as an impurity yields good results only when the difference in vapor pressure of both metals is large. However, when this difference is small, the vapors will be contaminated by the impurity metals, and therefore for achieving acceptable purification use is made of the rectification technique, also called fractional distillation. As we heat the mixture overall composition is indicated by x1 in Fig. 18, the first vapor is formed at T1 and has the composition y1* . This vapor is enriched in B; if it is condensed, the resulting liquid will have the composition x2. If we will heat this liquid at a temperature of T1 and will condense the formed vapor, we will obtain the condensate having the composition х3 = y2* . As may be seen from the diagram, x3 > x2 > x1. The fraction may be redistilled one or more times until the liquid with the lowest boiling point is pure. Fractional distillation is conducted in a continuous countercurrent fashion in which volatilization and condensation of the fraction being separated are repeated many times: the stream of a liquid (condensed vapors) move against the rising stream of vapors. In metallurgy, it is challenging engineering problem because of the high temperature involved, the high specific gravity of the molten metals, and the choice of the materials of construction

Fig. 18. The T–x phase diagram of a binary system at P = const 62 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

Rectification may be accelerated considerably if it is performed in a vacuum. This method has applications in the removal of Cd from Zn or Zn from Pb, in the separation of Al and Mg, and in Ti metallurgy.

Control Questions and Tasks 1. Determine partial pressure of oxygen in C-O system at 1 500 K. Carbon interacts with oxygen to yield CO and CO2. The composition of gaseous phase is determined by the equilibrium of the Boudouard-Bell reaction: C + CO2 = 2CO, G  166 410  170,837  T , J . 2. One of the reactions taking place at refining of secondary aluminum is the following: 2 2  Mg   AlF3    Al   MgF2  . 3 3 Determine the equilibrium concentration of Mg in Al at 1 030 K. aAlF3  0,2; aMgF2  0,1; aAl  1;  Mg  0,3 . The changes in the Gibbs energy of the formation of the reaction participants are described by the following equations: G  1 041 780  120,3  T , MgF2

GAlF3  1506 300  257,65  T . 3. Al-Mg alloys are obtained at 1100 K. Al can interact with brickwork material according to the reaction 3MgOsolid  2[Al]  3Mg vapour  Al2O3 solid . Determine the magnesium pressure at equilibrium. aAl  0,9 . The changes in the Gibbs energy of the formation of the reaction participants are described by the following equations: G  728 900  203,85  T , MgO

GAl2O3  1 685 630  326,5  T .

P y r o m e t a l l u r g i c a l P r o c e s s e s | 63

4. Chromium is reduced from chromium oxide with the use of aluminium. A burden is prepared according to the stoichiometry of the reaction (Cr2O3) + 2[Al] = 2[Cr] + (Al2O3). Chromium melts at 1 875 C, and the reduction process is realized at 2 000 C. Alumimium and chromium oxides have high melting points (2 100 and 2 050C, respectively). To decrease slag melting temperature, a flux (CaO) is introduced into the system. Assume that the weight ratio of mAl2O3 / mCaO equals 1. Determine the residual concentration of Al (wt. %) in reduced chromium at 2 000 C. There is CrO oxide in the Cr-O system. According to the A.A. Baikov’s principle, the reduction of chromium is described by the scheme: Cr2O3  CrO  Cr , and, as a result, the following reaction takes place: 3(CrO) + 2[Al] = 3[Cr] + (Al2O3). The changes in the Gibbs energy of the reactions of oxide metal formation are determined by the equations GAl2O3  1 685 630  326,5  T , J , GCrO  333 900  63,75  T , J .

Assume aCr  xCr , aAl  xAl ,  Al2O3  0,6,  CaO  1 ( is an activity coefficient). 5. Oxidizing refining of Cu from Ni results in the formation of Cu 2O. It reacts with nickel: Cu 2O   Ni  2Cu    NiO . Determine the residual concentration of Ni in Cu at 1420 K, if metal contains 0,5 wt. % of oxygen.  Cu2O  21, aNiO  0,2, aCu  1, aNi  xNi . The changes in the Gibbs energy of the formation of the reaction participants are described by the following equations: GNiO  253 500  95,1  T , GCu 2O  147 000  60  T .

6. Dissociation of ZnO goes at 1 100 K: 2ZnO = 2Zn + O2. Temperature dependence of the change in the Gibbs energy for this reaction is described by the following equation: GT  683 600  195,95  T , J / mol O2 . 64 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

Determine the state of Zn (gaseous or condensed matter) which is generated in this process. Take into consideration that temperature dependence of the saturated vapor pressure of zinc is given by the equation: 6 670 lg PZn0    9,12  1,126 lg T . T Assume that the activity of ZnO is equal to 1. 7. Using the following experimental data for the specific conductivity of the Bi2O3-TiO2 system, calculate the activation energy and conclude about the validity of the equation æ = æ0 exp(–Eæ / RT) in the given temperature range. æ, Cm/m T, K

205 1 240

223 1 280

260 1 320

310 1 360

390 1 380

425 1 400

8. The viscosity of alloys of the Bi-Zn system containing 44,4 at. % of Zn was determined at different temperatures: T, K ·103, Pa·s

790 1,178

823 1,122

873 1,047

923 0,981

Estimate the validity of the equation  = A exp(E / RT). 9. How can the equilibrium of the reaction ZnOs + CO = Zng + CO2 be shifted to the right? Explain the answer. 10. Using Fig. 8, write down what reactions involving iron oxides occur in the system if the CO content in the gas mixture is 60 % and the temperature is 800 ° C.

P y r o m e t a l l u r g i c a l P r o c e s s e s | 65

66 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

2 HYDROMETALLURGICAL PROCESSES

H y d r o m e t a l l u r g i c a l P r o c e s s e s | 67

2.1. HYDROMETALLURGY

Hydrometallurgy is concerned with processes of metals extraction from ores, concentrates, intermediate materials and wastes of production with the use of aqueous solutions.

Fig. 19. A generalized flow diagram of processing resources in hydrometallurgy

Advantages of hydrometallurgy over pyrometallurgy are the following: (i) Selective extraction of metals from lean and difficult ores; (ii) Complex processing of mineral raw materials with a high degree of extraction of valuable components; (iii) Much less environmental pollution; 68 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

(iv) Higher cost-effectiveness of complex raw material processing and smaller production scale. The main disadvantages of hydrometallurgy are as follows: (i) Large volumes of solutions requiring considerable amount of handling as well as space; (ii) Lower reaction rates at lower temperatures and, as a result, lower tonnage capacity of a plant. Pyrometallurgical and hydrometallurgical processes are very often combined in practice to exploit the best features of both. Basic unit processes in hydrometallurgy is shown in Fig. 19.

2.2. LEACHING

2.2.1. Gas – Liquid Solution Equilibrium in Binary Systems Solutions of gases in liquids can be considered as systems with the equilibrium between a liquid phase containing a solvent and a dissolved gas, and a gas phase containing the given gas and the vapor of the solvent. If this solvent is relatively low-volatile, then the equilibrium can be represented as that between the solution and the practically pure soluble gas. The solubility of a substance is determined by its concentration in the saturated solution. The solubility of gases depends on the nature of the gas and the solvent, gas pressure, temperature and the presence of other components in the solution, especially electrolytes. The solubility of gases increases at chemical interaction of a soluble gas with a solvent, while it is decreased in the presence of electrolytes. The decrease of gas solubility in electrolyte solutions is known as salting-out effect. It increases with the size and decreases with the polarity of the solute molecule. Salting-out action of an ion increases with the charge and decreases with the size of this ion. This effect derives from the fact that ions attract polar molecules of water but don’t attract nonpolar and lowpolarizable molecules of gases; owing to this the volatility of soluted gas increases. H y d r o m e t a l l u r g i c a l P r o c e s s e s | 69

The effect of molar salt concentration C can be described in the form of the Sechenov equation: s lg 0  KC C , (177) s where s0, s are the gas solubility in pure water and in an electrolyte solution, respectively; КС is the Sechenov constant which depends on the salt, the gas and the temperature. When a gas doesn’t interact chemically with a solvent, the dependence of gas solubility in the liquid on pressure is expressed by Henry’s law which has the following form for nonideal solutions: (178) P2  K H x2 , where P2 is the partial pressure of the gas over the solution, x2 is its mole fraction in the solution, KH is the Henry’s law constant being a constant characteristic of the dissolved component and the solvent at a given temperature. This equation holds valid only for dilute-gas-liquid solutions (that is, liquids with a small concentration of dissolved gas) and at not high pressures. The value of the Henry's law constant is found to be temperature dependent. It generally increases with increasing temperature. As a consequence, the solubility of gases generally decreases with increasing temperature. But this statement is not universally true. For aqueous solutions, the Henry's law constant usually goes through a maximum (i.e., the solubility goes through a minimum). For the most gases, the minimum is below 120 °C. Often, the smaller the gas molecule (and the lower the gas solubility in water), the lower the temperature of the maximum of the Henry's law constant. The dependence of the gas solubility in liquid on the temperature is described by the following equation: d ln x2 H 2( s )  H 2( g )  , (179) dT RT 2 where H 2( s )  H 2( g ) is the enthalpy change at the transition of 1 mole of the gas from the gaseous state to the state of a component of saturated solution. At low d ln x2 temperatures, usually, H 2( p )  H 2( г ) and < 0, i.e., the solubility of gases dT d ln x2 decreases with increasing temperature. At high temperatures, > 0, i.e., dT increasing the temperature leads to increasing the solubility. 70 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

2.2.2. Solubility of Solids The ability of a solid substance to dissolve in one or another solvent depends on its nature and temperature. On close examination of solubility of solids it should be distinguished between ionic and nonionic solutions. The formers are also called electrolytes. Let us consider a saturated solution of slightly soluble electrolyte AgCl: AgCls ⇾ Ag+ + Cl–. (180) In equilibrium, AgCl  Ag+  Cl . (181) Here I is the chemical potentials of the i-th substance (ion). The chemical potentials of individual ions can't be measured independently because solutions must be electrically neutral. However we can determine a mean chemical potential 1 (182)   Ag  Cl 2 to give (183) AgCl  2 .





In the general case, Ax By

xAz   yB z  ,

(184)

and

x  y salt  . (185) x y x y If, as usual, the molal scale of concentration is employed then the equilibrium in a solution saturated with AgCl can be described by the following equation:  





AgCl  RT ln aAgCl  2  RT ln  2 mAg mCl ,

(186)

where ± is the mean ionic activity coefficient; mAg and mCl are the molal concentrations of the respective ions. The equilibrium constant for this process can be written as:

 AgCl  2   aAg aCl  exp  . (187) RT   Since the equilibrium constant refers to the product of the concentration of the ions that are present in a saturated solution of an ionic compound, it is K m   2 mAg mCl

H y d r o m e t a l l u r g i c a l P r o c e s s e s | 71

given the name solubility product constant, and given also the symbol Ksp. Solids are not included when calculating equilibrium constant expressions, because their concentrations do not change the expression; any change in their concentrations are insignificant, and therefore omitted. In the case of slightly soluble electrolytes such as AgCl, even saturated solutions remain very dilute,    1 , and the solubility product constant can be calculated as the product of the concentrations of the ions, with each concentration raised to a power equal to the coefficient of that ion in the balanced equation for the solubility equilibrium. Specifically, for AgCl: K sp  mAg mCl . (188)

2.2.3. Thermodynamics of Simple Dissolution Leaching boils down to operations which result in the transition of a valuable component in an aqueous solution. In raw materials, valuable components are as usual in form of sparingly soluble compounds; therefore simple dissolution is preceded by prestarting procedures (sintering, fusion, sulfation roasting etc.) for conversion of a metal to some soluble form. Enthalpy of solubility of solids is defined from the equation: s H  1 1  (189) ln 2    , s1 R  T1 T2  where s1 and s2 are the solubility of a substance at temperatures of Т1 and Т2, respectively. The simple dissolution goes, as a rule, with the participation of substances having ionic crystal lattice in the solid state. Polar molecules of water interact with ions of the solid and pull these ions, one by one, away from the crystal. As a result, the dissolution with dissociation takes place. The change of Gibbs energy in this process is determined by the lattice energy and the hydration energy of ions:  ± Gdissolution  Ghydration  Gcr. lattice ;

(190)

± ± ± Gdissolution  Нdissolution  Т Sdissolution ;

(191)

± ± H dissolution  Н hydration  Н cr. lattice ;

(192)

±  Sdissolution  Shydration  Scr. lattice .

(193)

72 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

When the values of entropy and enthalpy are not available, empirical equations are used to estimate them. The Gibbs energy of dissolution of a substance is connected with the activity of the compound in a saturated solution: ± Gdissolution  RT ln a ,

(194)

where  is the number of ions forming the molecule of the soluble salt. The calculation of the solubility with the use of thermodynamic data according to this equation is possible for the poorly soluble compounds. In addition to salts, gases and organic liquids restrictedly soluble in water belong to the group of substances characterized by the simple dissolution in aqueous phase.

2.2.4. Thermodynamics of Leaching Processes Followed by Chemical Reactions. Dissolution of Metals, Oxides and Sparingly Soluble Salts Dissolution of metals can be carried out in acidic, neutral and alkaline aqueous solutions, in the presence of a specially introduced oxidizer or without its, at ordinary or elevated temperatures. Zinc provides an example of a metal soluble without a special oxidizer. In acidic solutions, the following reaction goes: Zn + 2H+ = Zn2+ + H2; G= –147,22 kJ. (195) In alkaline medium at moderate concentrations, the dissolution of zinc is described by the equation _

Zn + 2H2O + OH- = Zn(OH)3 + H2; G = –63,74 kJ, while in more concentrated solutions another process takes place: _

(196)

2_

Zn + 2H2O + 2OH = Zn(OH)4 + H2; G = –64,55 kJ. (197) Reactions (196) and (197) are characterized by close values of the Gibbs energy change and of the equilibrium constants, but as is evident from the equation (197), when the concentration of alkali is increased, zinc is in a solution in the form of the higher complex. Let us consider the dissolution of copper. Without addition of a special oxidizer, copper doesn’t dissolve in acids: Cu + 2H+ = Cu2+ + H2; G= +65,65 kJ. (198) H y d r o m e t a l l u r g i c a l P r o c e s s e s | 73

The dissolution with the formation of univalent copper is still less probable. This metal passes into solution only with the availability of sufficiently strong oxidizer (O2, Fe3+, K2Cr2O7 etc.): Cu + 2H+ + ½ O2 = Cu2+ + H2O; G=–179,79 kJ. (199) However, despite the very large decrease in Gibbs energy, this reaction proceeds with considerable kinetic difficulties. Some electropositive metals cannot be transferred into solution even with the addition of strong oxidants. For their oxidation, it is necessary to additionally introduce into the solution a reagent that forms a sufficiently strong complex with the ion of the dissolved metal. For example, if during the interaction of gold with chlorine – one of the most powerful oxidants – there is no complexation, then the change in the Gibbs energy of the reaction Au + 1,5Cl2(dis) = Au3+ + 3Cl– (200) will be + 53.22 kJ. However, gold forms a fairly strong complex with chlorine ions, and the chlorination reaction proceeds according to another equation: –

_

Au + 1,5Cl2(dis) + Cl = AuCl4 ; G= –116,12 kJ. (201) Use of complexing process is especially needed in the case of weaker oxidants. As we have already pointed out, in many processes raw materials before the hydrometallurgical leaching is subjected to calcination. During further dissolution depending on the acidity of the solution one can obtain solution, which contains valuable component or more or less contaminated by undesirable impurities one. In some cases, thermodynamic calculation allows to optimize the process mode. Let us consider leaching of zinc and iron from zinc calcine: ZnO + 2H+ = Zn2+ + H2O; K = 1,45·1011; (202) + 3+ 3 Fe(OH)3 + 3H = Fe + 3H2O; K = 2,44·10 . (203) Comparison of equilibrium constants for these reactions shows that iron hydroxide dissolves considerably worse over zinc oxide. Equilibrium constant of the reaction of iron (III) ions deposition by zinc oxide is in the order of 1027. Consequently, iron Fe 3 + must be precipitated completely. However, the process of purifying zinc electrolyte from iron in neutral cycle is highly complicated: one part of iron is in bivalent form, another one is in 

2

2

the form of complex ions Fe(OH)2 , FeOH , FeSO4 etc, but the main complication is kinetics: the more reduces the concentration of iron compounds in solution, the smaller the precipitation rate becomes, i.e., equilibrium is not reached in the process. 74 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

In the process of insoluble compounds dissolution reagents that give strong enough cation complex compounds (anionic or cationic) or transfer it in less-dissociated molecular form is typically used. The example is the dissolution of heavy metals sulfides. Most heavy metals sulfides are virtually insoluble in water. Active dissolution of many of them in acidic medium becomes possible due to the fact that the resulting hydrogen sulfide is a very weak acid and in alkaline medium – thanks to sulfide cation binding into strong complex connection. In acidified solutions may appear the reaction MeS + 2H+ = Me2+ +H2S(dis). (204) Calculations and experiment show that manganese, iron, thallium (I) indium, zinc, cadmium sulfides, and more active nickel and cobalt sulfides modifications can be dissolved in weak or moderately concentrated solutions of inorganic acids. Sulfides of copper, silver, mercury and other electropositive metals virtually are not dissolved in acidic solutions without oxidation, but they can be dissolved in the presence of active complexing agent. For example, copper (I) sulfide can be dissolved in cyanide solution: –

_

Cu2S + 4CN = 2Cu(CN)2 +S2-. At higher concentrations of cyanide there is the reaction

(205)

Cu 2S  6CN  2Cu(CN)32  S 2 .

(206) Even the most insoluble of heavy metal sulfides – gold (I) sulfide – can be dissolved in cyanide solutions. Dissolution of heavy metals sulfides significantly more active in the presence of oxidants, but often this process is multi-stage, accompanied by kinetic constraints and preference for one or another stage cannot be resolved by thermodynamic analysis. The positive role of oxidant can be evaluated using three sphalerite dissolution reactions in acidic medium: ZnS  2 H   Zn 2  H 2S(dis) , G  25,94 kJ; ZnS  2H   1 2 O2(dis)  Zn 2  H 2O  S, G  191,38 kJ;

(207)

ZnS  2O2(dis)  Zn 2  SO42 , G  724,59 kJ.

At normal temperature and oxygen concentration in the solution first reaction almost does not occur. Second and third reactions are competitive, but one can assume that at low temperatures the second one is preferable. In the process of sphalerite oxidation in alkaline medium there are also three competitive reactions: H y d r o m e t a l l u r g i c a l P r o c e s s e s | 75

2ZnS  2O2(dis)  H 2O  2OH   2Zn(OH) 2  S2O32 ,

1

2 G

 358,95 kJ;

ZnS  1,5O2(dis)  2OH   Zn(OH) 2  SO32 , G  546,05 kJ,

(208)

ZnS  2O2(dis)  2OH   Zn(OH)2  SO42 , G  813,18 kJ.

At 298 K reaction almost does not go. In low alkalinity solution the thiosulfate ion dominates, while the Gibbs energy change to 1 mole of sphalerite in the first reaction is much smaller than in the other two. At higher alkalinity solution there is preferably the second reaction.

2.2.5. Reagent Consumption and Equilibrium Constant One of the leaching effectiveness indicators is the specific reagent consumption, the reagent consumption per unit mass of the reduced metal. This indicator depends on the phase composition of raw materials, solvent regeneration indicators at the stage of metal deposition from solution and the organization closed on solvent schemes. Minimal reagent consumption, necessary for full extraction of metal from solution, is associated with concentration equilibrium constants. In General, the leaching reaction can be represented as the equation (209) aAsolid  bBdis  dDdis  lLdis  mM dis  nNsolid , where A is the connection of a leached metal in the initial material; B – basic reagent; D – solution component, taking part in the leaching reaction: L is the main reaction product, connection of leached metal, transferring into the solution; M and N –soluble and solid substances formed during leaching. If solids are present in the form of separate phases, an expression for the equilibrium constant concentration has the form

KC 

m CLl CM

CBb CDd

.

(210)

We introduce the notation: rB – specific consumption in moles per mole; rD – specific consumption of D; x – equilibrium degree transferring of A into L, i.e. the degree of reaction. If the initial amount of A is 1 mole, then after equilibration there will remain: 76 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

Substance

Number of moles

B

rB  x

b a

D

rD  x

d a

L

x

l a

M

x

m a

To go from the quantities of substances to their concentrations, one should take into account the volume of solution. The result will be l m xl / a   xm / a   KC  V b  d l  m , b d  rB  xb / a   rD  xd / a 

(211)

where V is specific volume of solution, l/mol A. This expression corresponds to the case when all soluble reagents and reaction products concentrations change during the reaction. Actually a gaseous reagent with constant pressure can participate in the reaction. In addition, the reaction can proceed involving ions H+ or OH-, and since medium pH tend to maintain a constant, the concentration of these ions does not depend on the degree of leaching. In such cases, an expression of concentration equilibrium constant instead of the number of the relevant substance put its pressure or concentration, and appropriate term is excluded from exponent V. Expression (211) can be used to calculate the minimum specific consumption of the primary reagent В. Denote the minimum consumption of B for the condition х = 1, rminB, then l m l / a m / a  KC  V b  d l  m . b d  rmin B  b / a   rD  d / a 

(212)

To reduce the records of equilibrium constant concentration, combining with constant and preset values, we introduce the notation: KC'

d rD  d / a    KC V l  m b  d . l m l / a   m / a 

(213)

H y d r o m e t a l l u r g i c a l P r o c e s s e s | 77

Then 1 KC'

  rmin B  b / a  . b

(214)

From which 1/ b

 1  rmin B  b / a   '  . (215) K   C Unlike the stoichiometrically required amount of reagent b/a , one can consider value rminB as thermodynamically necessary amount, and value  1  '  KC

1/ b

  

– thermodynamic reagent B excess, unlike kinetic excess, which goes 1/ b

 1  beyond the value  '  and used to rate up the process.  KC  If KС  , i.e. the reaction is almost irreversible, thermodynamic reagent excess is not needed, if KС  0, for a full transfer of the metal into the solution an infinitely large reagent consumption is required.

2.2.6. Dilution of the Solution If the number of particles during the reaction does not change, then the completeness of its course and the equilibrium constant does not depend on the degree of dilution of the solution or the initial concentration (some effect may have ionic strength of the solution). An example of a reaction of this type can be exchange chemical reaction:

 A2  . MeA  B 2  MeB  A2 ; KC   (216) 2  B    If the number of ions or moles in the solution increases, dilution of the solution or a decrease in the initial concentration contributes to a more complete course of the process. Such are the reactions of dissociation of weak electrolytes, the hydrolysis reaction, the decomposition of complexes, some dissolution reactions of metals or their sulfides, for example,

78 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

HCN p  H   CN  , S2   H 2O  SH   OH  , Me(CN) 2  Me   2CN  ,

(217)

Me  Fe3  Me  Fe 2 , MeS  2Fe3  Me2   2Fe 2  . Since the expression for the equilibrium constant includes a different number of ions with different valence, the completeness of the reaction will depend on the dilution of the solution and on the ionic strength to a much greater extent than in the case of reactions without changing the number of ions or molecules. If, during the course of the reaction, the number of moles or ions decreases, the completeness of the reaction becomes larger in more concentrated solutions. Such reactions include dissolution of precipitates with formation of complexes, dissolution of metal oxides in acid solutions, and a number of others.

2.2.7. Pourbaix Diagrams (-рН Diagrams) Potential-pH diagrams are used to graphically represent equilibria in systems containing solid phases and aqueous solutions. They allow to present thermodynamically stable states depending on the magnitude of the potential and pH in a visual form. The ordinate axis is the scale (–2,6 ... + 1,4 V), the axis of x – is the scale of pH. The calculation of these diagrams is based on the Nernst equation. With a lower potential, the corresponding form can be restored to the underlying (if it exists), with a higher – oxidized to the overlying one (if it exists). The boundaries between the solution-solid or solution-gas forms of existence usually depend on the concentration of dissolved forms; the boundaries between the forms of existence of dissolved forms usually do not depend on their concentration. Pourbaix diagram often mark the boundaries of the existence of water (Fig. 20). Upper of them ( = 1,23–0,059 pH) corresponds to the oxygen evolution (i.e. at higher potentials possible oxidation of water to oxygen): 4H2O – 4e- = 4H+ + O2 (pH < 7), (218) – 4OH – 4e = 2H2O + O2 (pH > 7). (219) H y d r o m e t a l l u r g i c a l P r o c e s s e s | 79

Fig. 20. The diagram of electrode potential on pH dependence for water and its dissociation products (Pourbaix diagram)

Lower boundary ( = –0,059 pH) corresponds to the hydrogen evolution (i.e. at lower potentials water may be reduced to hydrogen): 2H+ + 2e– = H2 (pH < 7), (220) – – 2H2O + 2e = H2 + 2OH (pH > 7). (221) Given the overvoltage of hydrogen and oxygen, the water stability region expands. The distance between the solid lines corresponds to the theoretical value of the decomposition potential of water. Overvoltage in the separation of hydrogen and oxygen depends on the nature of the electrode. So, when using platinum electrodes, hydrogen overvoltage is 0.09 V, and oxygen 0.45 V. In Fig. 21 Pourbaix diagrams for iron-water system are shown. In Fig. 22 the Pourbaix diagram is shown where the shaded area refers to insoluble iron compounds. From the diagram it can be seen that when the value of the рН 4,5 Fe2+ oxidized to Fe3+ with the formation of Fe(OH)3. In the pres80 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

ence of sulfides at values  < – 0,2 В, рН > 4,5, formation of FeS in the form of precipitate is possible. In the presence of carbonates at рН > 8,4 formation of FeCO3 is observed, and at рН > 10,3 – the formation of Fe(OH)2. The Pourbaix diagram displays only thermodynamically stable forms. Kinetically stable (also known as metastable) forms are not displayed on it. Therefore, it is inapplicable for predicting the formation of metastable forms. For example, a form such as hypochlorite-ion OCl- is metastable (unstable thermodynamically, but disproportionates extremely slowly). Therefore, in the Pourbaix diagram for chlorine it is not available and it is impossible to predict its formation (in particular, with the disproportionation of chlorine) in the Pourbaix diagram: Cl2 + 2OH– = Cl– + ClO– + H2O. (222) In addition, not all processes, predicted by Pourbaix diagram, have large enough rate to be visible.

Fig. 21. Pourbaix diagram for iron-water system: non-hydrated (a) and hydrated (b) forms of oxides H y d r o m e t a l l u r g i c a l P r o c e s s e s | 81

Fig. 22. Pourbaix diagram for iron compounds in the water

2.2.8. Kinetics of Leaching. Multi-Stage Nature of Leaching. Influence of Temperature

С2

С1



х0 Fig. 23. Schematic representation of the diffusion process

Leaching is a complex heterogeneous process consisting of three main stages: 1) transfer of reacting substances to the phase interface, 2) chemical reaction, and 3) transport of soluble reaction products from the surface to the solution volume. Each of these stages can consist of several more. For example, the transfer steps may include diffusion of the reactants to the surface of the solid phase through the adjacent solution layer and diffusion through the reaction product film or through the porous residual layer of the non-alkaline material. If the rate constant of the diffusion is much greater than the rate constant of the chemical reaction, then the rate of the whole process will be determined by the rate of chemical transformation, and then it is said that the process proceeds in the kinetic re-

82 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

gion (or in the kinetic regime). The order of the reaction will depend on the nature of the reactants. For the reaction occurring in the transition region, the rate constants of diffusion and chemical transformation are commensurable. The diffusion region differs from the kinetic one by: a) small values of the activation energy of the process, b) the effect of mixing on the reaction rate in the diffusion region and the absence of this influence in the kinetic. In addition, if the rate of the stationary process is determined by the rate of diffusion, then the reaction will always follow the first order, regardless of the true one. The order of the majority of heterogeneous reactions with respect to solvent reactants and oxidants is rarely more than one (oxygen order in the diffusion regime is equal to unity, and in the kinetic regime it is 0,5). As we have already noted, in many hydrometallurgical processes three components are involved: a solid phase, a solvent reagent and an oxidizing agent. Depending on the initial ratio of reagent concentrations, two areas can be distinguished: 1) the region in which the oxidizer predominates and the dissolution rate is directly proportional to the concentration of the solvent reagent; and 2) the region in which the solvent reagent predominates, and the process rate is determined by the concentration of the oxidant reagent in fractional power or equal to 1 depending on the process regime (kinetic or diffusion). If the process proceeds in a diffusion mode, the temperature affects the increase in the diffusion rate of the solvent reagent from the volume of the solution to the reaction surface. The calculated value of the experimental activation energy, equal to 13-17 kJ / mol, is very close to the values that can be calculated from the temperature dependence of the diffusion coefficients of the same solvent. The temperature diffusion coefficient, which is the ratio of diffusion coefD ficients at two temperatures, differing by 10 degrees, T 10 , varies in the range DT 1,5–1,1; the smaller the diffusion coefficient of substance D, the greater is the temperature diffusion coefficient. Assuming that the thickness of the diffusion layer does not depend on temperature, for the temperature coefficient of the rate constant we obtain dln kэ dln D ED   . (223) dT dT RT 2 H y d r o m e t a l l u r g i c a l P r o c e s s e s | 83

According to this equation, the value of the activation energy of diffusion can be determined graphically, by analyzing the dependence of the logarithm of the diffusion coefficient on the reciprocal temperature. If the process proceeds in the kinetic region, then two cases are possible: 1. in the absence of film formation on the reaction surface, the Van't Hoff empirical rule is satisfied, according to which, with a temperature increase of 10 degrees in the region of moderate temperatures, the reaction rate increases by a factor of 2 to 4. In a narrow temperature range, the effect of temperature on the reaction rate can be quantitatively characterized by the value of the temperature coefficient of the rate constant of the reaction, which is the ratio of the reaction rate constants at two temperatures differing by 10 degrees: k   T 10 kT . (224) According to the Arrhenius equation, the dependence of the rate constants from temperature in differential form can be expressed by the equation E d ln k (225)  a2 , dT RT where Еа – the activation energy of a reaction. If Еа = const, the integration gives:  E  k  A  exp  a  , (226)  RT  where А – pre-exponential multiplier. To calculate the activation energy from the experimental data, the linear form of the Arrhenius equation obtained after the logarithm of the last equation is used:

Fig. 24. Graphical determination of constants in the Arrhenius equation

ln k  ln A –

Ea . RT

84 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

(227)

The activation energy is found from the tangent of the straight line slope (Fig. 24): Ea   R tg  . (228) pre-exponential multiplier А is determined by the length, either direct to the yaxis when 1/Т = 0. If the data is available at two temperatures, the Ea can be calculated analytically: R  T1  T2 k Ea   ln 2 , (229) T2  T1 k1 where k1 and k2 – rate constants at Т1 and Т2. The activation energy of the process occurring in the kinetic region is much higher than the process controlled by diffusion, and the reaction rate in the kinetic region is lower than in the diffusion process, that result in fact, that with increasing temperature both these rates can be equalized and the process goes to the diffusion region; reaction will be determined by the amount of the reagent supplied due to its diffusion). For example, the dissolution of copper in sulfuric acid at 298 K proceeds in the kinetic region, at 303 K – in mixed, and at 348 K – in diffusion. 2. If the process proceeds in the kinetic region and its rate is determined by the chemical act, but it is complicated by the formation of films on the reaction surface, then the temperature increase will affect the nature of the change in the process rate in different ways. In most cases, an increase in temperature is accompanied by an increase in the rate of the process – the films become either thinner or more permeable, and the rate of diffusion of the reagent through the films to the reaction surface increases, which is ambiguously connected with the activation. However, there are cases when an increase in temperature leads to a decrease in the process rate, which corresponds to apparent negative activation energy (for example, the dissolution of silver telluride in a cyanide solution). The explanation is that in this case, an increase in temperature leads to a sharp increase in the rate of formation of the surface film that inhibits the leaching process.

2.2.9. General Equation of Leaching Kinetics Since in the leaching the chemical reaction proceeds at the phase interface, the kinetics of this process is characterized by the specific rate, j, which is H y d r o m e t a l l u r g i c a l P r o c e s s e s | 85

the amount of leachate that passes into the solution per unit time from a unit surface of the solid phase: dQ j , (230) sdt where Q – the amount of dissolved solids, s – its surface. Parameter j is also called leaching flux. Consider the scheme of the leaching model (Fig. 25), in which it is assumed that the reaction between the liquid reagent and the solid develops from the surface of solid particles to their center, and until the leaching is complete, the unreacted core remains in the center, and the solid product at the periphery. The flow diffusion of reagent through the layer of mortar, adjacent to the solid phase, i.e. through the external diffusion layer is defined by the Fick's first law: dC j   D1 , (231) dx dC where D1 – diffusion coefficient of reagent in solution, – concentration dx gradient in the direction of diffusion. Considering that within the external diffusion layer concentration reagent changes from С0 to С1 linearly, after integrating this equation we get (232) j1  D1(C0  C1) / 1 .

Fig. 25. Leaching model diagram: I – a solution layer with thickness 1, adjacent to the surface of solid particles, II – a layer of solid reaction product with thickness 2, III – unreacted part (core) of leached substance, С0 and С0’, – accordingly, the concentration of the reactant and product of reaction in solution, С1 and С1’ – the concentration of the reactant and product of reaction on the border between the solid phase and solution, С2 and С2’ – the concentration of the reactant and product of reaction at the surface of the nucleus 86 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

Similar expression is determined by the flow of reagent through reaction product layer, i.e. through internal diffusion layer: (233) j2  D2 (C1  C2 ) / 2 , where D2 – the diffusion coefficient of reactant in a layer of the reaction solid product. Suppose that the dissolution process is based on a reversible reaction (234) aAsol  bBdis lLdis  mM sol . Reversible reaction rate is equal to the difference between the rates of the forward and reverse reactions. Then applied to the equation (234) expression to determine stream leaching on reagent, i.e. the amount of reagent per unit of time consumed on a unit surface, can be written as

j3  kCBnB  kCLnL ,

(235)

where k and k – rate constants of forward and backward reactions, СВ and СL – concentrations of regent В and dissolved product L on the surface of leaching substances, nB and nL – accordingly, the order of the direct reaction on substance В and order of backward reaction on substance L. For product diffusion reaction through internal and external diffusion layer receive respectively:

  j5'  D1'  C1'  C0'  / 1,

j4'  D2' C2'  C1' / 2 ,

(236) (237)

where D2' and D1' – the diffusion coefficients of the soluble reaction product, respectively, in the solid reaction product layer and in the solution. Since the amounts of the reaction product and the consumed reagent are bound by the stoichiometry of the reaction (234), diffusion fluxes j4' and j5' of reaction product L are linearly related to fluxes of reagent В j4 and j5:





(238)





(239)

b ' b  D2' j4  j4  C2'  C1' , l l  2 b ' b  D1' ' j5  j5  C1  C0' . l l  1

If, at some point in time, the streams j1  j5 are not equal to each other, the concentrations C1, C2 change and these changes lead to an equalization of the flows. For example, if j1 > j2, then the reagent will be fed to the liquid-solid interface more quickly than to be removed from it, i.e. the concentration of C1

H y d r o m e t a l l u r g i c a l P r o c e s s e s | 87

will increase. As a result, the flow j1 will decrease, and j2 increase. An increase in the concentration of C1 will end when the flows are leveled. The process mode, in which the flows at each stage are equal to each other, is called steady. If the leaching rate is not too high and the streams are aligned fairly quickly, we can assume that the steady-state condition is met at any time: (240) j1  j2  j3  j4  j5  j . If C0 , C0' , D1, D2 , D1' , D2' , 1, 2 , k , k , nB , nL , b, l are known, then equations (232, 233, 235–237) form a system with five unknowns. Through the transformation of these equations an expression for the flux that contains only known values can be obtained: n

n

L B  '   1 2   l  1 2   j  k C0  j   (241)    k C 0  j  '  '   . D D b D D  1 2       1 2   One can define the flow from this expression by numerical or graphical methods. The most simple analytical solution exists if nB = nL =1. If we divide the left-hand and right-hand side of the k , group the terms containing j, we get:

1   k  l  1 2   k ' (242) j  1  2   '  '    C0  C0 . D D k k  b k D D 1 2  1 2    Flow calculation of leaching is considerably facilitated if a chemical reaction is virtually irreversible, i.e., the rate constant for the reverse reaction is close to zero. In this case, the concentration of dissolved product has no effect on the leaching rate in equation (235) the second member disappears, and the number of equations in the system is reduced to three:

1  C0  C1  , D1  j  2  C1  C2  , D2 j

j  kC2nB . As a result, we obtain the equation for the flow definition: C0 j , 1 2 1   D1 D2 k for solution of which the graphical method is used. 88 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

(243) (244) (245)

(246)

2.2.10. Features of Leaching Involving Gaseous Reagent In the case of gas participation, the leaching process includes the following main steps: 1) gas absorption by the solution (dissolution of the gas); 2) external diffusion of the dissolved gas to the surface of the solid phase; 3) internal diffusion of the gas through the solid layer, if available; 4) chemical reaction to surface of the solid phase, 5) removal of reaction products into the solution volume. If the reaction is irreversible, then the rate of the process determines the first four stages. When the liquid adjacent to the interface of the liquid and gaseous phases is saturated with gas, the amount of gas passing this boundary per unit time can be determined using equation dQgas D1sgas (247)   Сsat  С0  , dt gas where D1 – the gas diffusion coefficient in solution, sgas – the liquid-gas interface, Сsat – the concentration of gas in a saturated solution, С0 – concentration of dissolved gas in solution, gas – thickness of diffusion layer of a solution at liquid-gas interface. According to Henry's law, the concentration of a saturated solution is related to gas pressure ratio (248) P  K H Сн . Therefore dQgas D1sgas  P    С0  . (249)  dt gas  K H  If we include dilution rate of gas to one surface of the solid phase, we get an expression for the specific gas dissolution rate: D1  sgas  P  j1   С (250)  0 , gas  ssol  K H  where j1 – flux of dissolved gas, ssol – solid phase surface area. The diffusion of dissolved gas flows through the layer of solution, adjacent to the solid phase, j2, and through a layer of solid product, j3, defined by expressions, similar to equations (232) and (233): (251) j2  D1(C0  C1) / 1 , (252) j3  D2 (C1  C2 ) / 2 , H y d r o m e t a l l u r g i c a l P r o c e s s e s | 89

where D2 – the diffusion coefficient of dissolved gas in a layer of solid product reactions, C1 – concentration of dissolved gas on the border of the liquid-solid reaction product, C2 – concentration of dissolved gas on the border of the reaction product-leaching substance, 1 – thickness of diffusion layer solution near the boundary of liquid-solid, 2 – the thickness of a layer of solid product. The expression for the flux of an irreversible chemical reaction, the order of which is assumed to be unity, has the form: (253) j4  kC2 , where k – reaction rate constant. Equating j1  j2  j3  j4  j and doing the conversion we get

 gas ssol 1 2 1     . (254)   D s D D k 1 gas 1 2   If the limiting stage is the absorption of gas, then the rate equation is reduced to the form D Р sgas , (255) j 1 gas К H ssol j

P KH

i.e. leaching rate is directly proportional to the surface contact of the solution with gas. In leaching, which takes place with the participation of a gaseous reagent, the gas is usually bubbled through a layer of liquid, with the bubbles being created by special dispersing devices. The rate of leaching, limited by the dissolution of the gas, increases with increasing gas pressure, the rate of its supply, the height of the apparatus (the thickness of the liquid layer), and the reduction in the size of the bubbles (i.e., the degree of dispersion of the gas).

2.2.11. Regularities of External and Internal Diffusion The transfer of particles of a substance dissolved in a liquid to the surface is due to two simultaneous processes: 1) molecular diffusion caused by the presence of a difference (gradient) of concentrations, 2) the transfer of matter with a liquid flow (convection). The totality of both processes is called convective diffusion. If the rate of the process is limited by external diffusion, then its regularities are determined by the expression 90 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

jD

C0 , d

(256)

where d – the effective thickness of the diffusion layer which is the thickness of the solution adjacent to the surface of the layer, upon substitution of which into the molecular diffusion equation j  D(C0  Csur ) / d the flow is obtained equal to the actual value. Analysis of equation (256) allows us to formulate the main features of the process in the external diffusion mode: 1. The rate of the process depends on the velocity of the liquid relative to the surface of the solid particles, since the effective thickness of the diffusion layer is a function of the velocity of the liquid. This sign is the determining factor: the effect of mixing on the rate of leaching is indicative of either the limitations imposed by external diffusion or the transition regime, and the absence of influence-that external diffusion is a faster stage than the others. 2. The process rate is in linear dependence on the reagent concentration (first order in reagent concentration). 3. The rate of the process is relatively independent of temperature, since the diffusion coefficient and the fluid velocity change insignificantly with temperature. 4. At С0 = const the specific rate of the process does not depend on time. When a certain flow rate is reached, the reaction rate no longer depends on the velocity of the fluid, i.e. exogenous diffusion inhibition is practically excluded. The process is limited either by internal diffusion or by chemical interaction. In cases where a solid product is formed during leaching or a substance in fractures or pores of an inert material is exposed to leaching, the diffusion stage may be diffusion through a shell of a solid product or an inert material (internal diffusion). The possibility of leaching in the internal diffusion area is determined, first of all, by the density of the shell: the larger it is, the more difficult diffusion through it and the less is the rate of internal mass transfer. Approximately estimate the density of the shell of the product can be from the ratio of the volumes of the reaction product and the initial material (Pilling-Bedward's criterion): Vprod M prod / d prod KPB  n n , (257) Vreac M reac / d reac where n – the number of moles of solid product formed from 1 mole of reactant, Vprod and Vreac – the molar volumes of product and reactant, Мprod H y d r o m e t a l l u r g i c a l P r o c e s s e s | 91

and Мreac – molar mass of product and reactant, dprod and dreac – density of product and reactant. If the ratio of volumes is greater than one, a dense shell may form. At the same time, if the volume of the product is much larger than the volume of the initial substance, it is possible to peel the hard shell; in this case it will not interfere with diffusion. During the leaching, the thickness of the product layer increases, and the specific leaching rate due to the growth of the diffusion resistance decreases in time:

j  DC0 / prod 1/ t .

(258)

Signs of the process in the internal diffusion area: 1) in accordance with the last equation, as the duration of leaching increases, the specific leaching rate decreases (at constant reagent concentrations and reaction products), 2) the process rate is directly proportional to the concentration of the reagent, 3) the rate of the process is slightly dependent on temperature, the activation energy is 8–20 kJ/mol. The dependence of the rate of leaching on the concentration of the reagent and temperature is the same for the external diffusion and intra-diffusion regions of the process. Therefore, in order to determine which of the diffusion stages is limiting, it should be determined whether the rate depends on the mixing conditions and the duration of the leaching.

2.2.12. The Regularities of the Process in the Kinetic Region Heterogeneous reactions tend to occur after reagent adsorption on the surface of the solid substance. If the reaction involves two types of adsorbed molecules A and B, and the chemical reaction is the limiting step, then at low reagent concentrations in n n the solution, the reaction rate is proportional to the product C AA CBB , i.e. the or-

der of the reaction equals nA + nB. At high concentrations of reagents, the reaction rate practically does not depend on them, i.e. п = 0. If the concentration of 92 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

one of the substances is significantly less than the other, the reaction rate increases with increasing concentration of the first reagent and decreases with increasing concentration of the second. The order of reaction for the reagent present in a large amount becomes negative. This is because the surface of a solid is almost completely filled with one of the substances, and further increase in the concentration of this substance, without increasing the degree of filling it with the surface, reduces the adsorption of another substance and thereby reduces the reaction rate. If the chemical interaction of adsorbed molecules and solid material proceeds at a high rate, then the overall process rate will be limited by the rate of adsorption of the less adsorbed substance. The order of the reaction with respect to the slowly adsorbed substance is one, and according to the rapidly adsorbed substance depends on its concentration in the solution: at a low concentration of this substance, the reaction rate from it practically does not depend, and the order of the reaction with respect to the substance is zero, and the increase in concentration in the region of high concentrations leads to a decrease in the rate of the reaction, in which case the reaction has a negative order for the rapidly adsorbed substance. As the concentration of the slowly adsorbed substance increases, the reaction rate increases only until the surface fraction occupied by the rapidly adsorbed substance decreases to zero. The kinetic regime of the process is characterized, first of all, by the absence of attributes that are mandatory for external and internal diffusion, i.e. the rate of the process does not depend: 1) on its duration at constant surface and concentrations of participants in the reaction and 2) on the mi xing conditions. In addition, as we have already noted, the rate of the reaction proceeding in the kinetic regime, as a rule, depends strongly on the temperature, and the order of the reaction with respect to the dissolved reagent can differ from unity.

2.2.13. Influence of Surface Modification of Solid Phase The decrease in the rate of leaching of the valuable component over time is explained by the formation of films on the surface, the decrease in the conH y d r o m e t a l l u r g i c a l P r o c e s s e s | 93

centration of the reagent, and also by the decrease in the reaction surface due to dissolution of the grains of the leachable mineral. Suppose that a monodisperse mixture of spherical particles is dissolved. 4 3 The surface of one particle is 4r2, volume  r , and change in surface dur3

s V    ing dissolution  s0  V0 

23

. If we take V  V0 (1  ) ,

(259)

where  – fraction of solute, then

s 23  1    . (260) s0 The same exponent will also be when the mixture of particles of a cubic form is dissolved. For particles of different shapes in general form, we can write the equation s   1    , (261) s0 where  – order for the solid. For needle-shaped particles, it is equal to ½, for flat particles (plates) – 0. This equation is valid under conditions if the process is not complicated by the formation of films, all particles of the same size, the reaction is practically irreversible, and the concentration of the solvent reagent is constant. When this process proceeds in the kinetic regime, the rate of leaching can be expressed by the equation

d  kC n s  kC n s0 (1  ) . dt Dividing the variables and integrating this expression, we obtain

1  (1  )1  (1  )  k  C n  s0  t .

(262)

(263)

This equation can be used to graphically determine the kinetic param1 eters. If we plot the dependence 1  (1  )  f (t ) , then the tangent of the slope angle of the resulting straight line will be equal to

(1  )  k  C n  s0  k ' . Having determined the angular coefficients at several temperatures, ln k '  f (1/ T ) one can calculate the apparent activation energy, and after studying how the value changes k' as the concentration chang94 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

es at a constant temperature, one can find the apparent order of the reaction as the slope of the straight line in the coordinates ln k '  f (ln C ) . To calculate the degree of leaching achieved with a known value of the product k  C n  s0  t , it is more convenient to use the transformed equation: 1 (1)

. (264)   1  1  (1  )k  C n  s0  t    Equations (263) and (264) are suitable for describing the kinetics of leaching, occurring in the kinetic or external diffusion region with a large excess of the reagent or adding it as consumed (the integration is carried out under the condition that k and C are independent of time). When describing the kinetics of leaching occurring in the intradiffusion region, it is necessary to take into account the dependence of the rate on the degree of leaching, due to the change in the thickness of the layer of the solid product. In this case, even at constant concentration, cumbersome expressions are obtained, and therefore, approximate equations are often used. For the monodisperse particles of a spherical shape, the equations of Yander and GinstlingBrownstein are used. The Yander equation 2

1  (1  )1 3   kt   is only valid for small degrees of leaching. A more exact Ginstling-Brownstein equation

(265)

1  2 / 3  (1  )2 3  kt

(266) does not take into account the possible difference in the volumes of the reacted material and the solid product formed. Analogous expressions can also be obtained for monodisperse particles of needle and plate form. However, in the formation of a solid product, it is not possible to derive, in the general case, an equation describing the dependence of the degree of leaching of a polydisperse material on time. In addition, quite often the apparent order of hardness varies with the leaching process, and even then, when leaching takes place in the kinetic or external diffusion regions with k and C independent of time, Eqs. (263) and (264) are inapplicable.

H y d r o m e t a l l u r g i c a l P r o c e s s e s | 95

2.3. EXTRACTION AND ION EXCHANGE PROCESSES

2.3.1. Fundamentals of Extraction Processes. General Information Extraction – is the process of distribution of a substance between two immiscible solvents and an appropriate method of separation and separation of substances based on this distribution. In hydrometallurgy, extraction (liquid extraction) is the process of extracting substances, in particular metal compounds, from an aqueous solution into a liquid organic phase that does not mix with water. The extraction method is versatile, since it is applicable to all metals and their different concentrations. The process is technological, easy to automate. The extraction scheme of the metal from the solution is shown in Fig. 26. Initial solution

Extragent

Extraction raffinate

Extract Re-agent

Into wastes or for other valuable components extraction

Re-extraction Re-extract Deposition of metal or a compound thereof

Extragent Regeneration

Fig. 26. Schematic diagram of extraction of metal from solution

As a result of extraction, extract and raffinate – are respectively, the organic and aqueous phases are obtained. To extract the extracted metal from the organic phase into the aqueous solution, a reverse-directed process-back-extraction is used. The aqueous phase obtained after stripping is called a reextract. The organic phase returns to the extraction cycle, which makes it possible to repeatedly use the extractant, an 96 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

organic substance that forms a compound with a recoverable metal that can dissolve in the organic phase. Extractants can be organic acids, alcohols, ethers, ketones, aldehydes, amines, organophosphorus compounds, etc. Requirements for the extractor: It should: – have a good extraction ability and selectivity with respect to the recovered metal; – have a low solubility in water, aqueous solutions of acids and alkalis; – have easy regeneration to return it to the extraction cycle (ie the chemical reaction between the extractant and the components of the aqueous solution must be reversible); – be stable when it is in contact with aqueous solutions (should not be hydrolyzed, oxidized or reconstituted with solution components); – not change its properties when heated or cooled in the operating temperature range, it should not be oxidized by air oxygen; – be non-toxic, have a low vapor pressure and a sufficiently high flash point. To reduce the viscosity of the extractant, to reduce its loss, and also in some cases to achieve a higher degree of extraction and separation of ions, the extractant is dissolved in an organic diluent such as kerosene, xylene, etc. In industrial use, diluents take into account their availability, cost, toxicity , volatility. In the aqueous solution is sometimes added salting out – an inorganic substance (usually an electrolyte), which improves the extraction. The introduction of a salting out agent promotes the formation of lighter extractable undissociated molecules or leads to the formation of extractable complexes. In aqueous solutions, metals are in the form of hydrated ions. Water is a substance with polar molecules (dipoles), and organic compounds, as a rule, are low-polar substances with low dielectric permittivity. The transition of ions from the aqueous phase to the organic phase is energetically unfavorable. To perform the extraction, two conditions must be fulfilled: 1) neutralization of ion charges by transferring them to an uncharged complex or ionic associate with a suitable ion of the opposite charge, 2) completely or partially releasing from the hydrated shell to form a hydrophobic compound. Depending on the fact that the energy of hydration of the ion is compensated for, the extractants are divided into two groups: 1. Neutral extractants are organic substances whose molecules are capable of forming donor-acceptor-type coordination bonds with the extracted ion, stronger than bonds with water molecules (ie, the energy of solvation by the extractant molecules exceeds the energy of hydration). H y d r o m e t a l l u r g i c a l P r o c e s s e s | 97

2. Liquid ion exchangers are organic acids and their salts or organic bases and their salts capable of contacting an aqueous solution to the exchange of an inorganic cation or an anion that is part of the extractant into the ion of the same name in solution. In this case, the ions passing from the organic phase to the aqueous phase have a higher hydration energy than the ions extracted from the aqueous solution. Depending on the type of exchanged ions, the extractants are divided into cation exchange and anion exchange. Neutral extractants include organic compounds, which contain active atoms with an electron-donating capacity. They can be divided into oxygencontaining (alcohols, ketones, etc.), nitrogen-containing (amines) and sulfurcontaining (organic sulfides). Extracts of purely anion-exchange type, used in hydrometallurgy,  salts of quaternary ammonium bases. Quaternary ammonium bases are derivatives of the ammonium ion, in which four protons are replaced by alkyl radicals. Depending on the mechanism and type of extractants used, the extraction processes are classified as follows: 1. Extraction not accompanied by a change in the chemical form of the extractable substance (simple physical distribution, extraction of covalent molecules whose solubility in an organic solvent is usually an order of magnitude higher than in water), for example, extraction of I2, HgI2, GeCl4, etc. 2. Cation-exchange extraction – extraction of metals in aqueous solutions in the form of cations, organic acids or their salts. The extraction mechanism consists in the exchange of the extracted cation with a proton or another extractant cation: Men   nHR

MeRn  nH 

(267)

(hereinafter, the organic phase is emphasized, R is the organic radical). 3. Anion-exchange extraction – extraction of metals in aqueous solutions in the form of anions, salts of organic bases. The extraction mechanism consists in the exchange of a metal-containing anion with an anion extractant: (268) R4 NCl  Au(CN)2 R4 NAu(CN)2  Cl . 4. Coordination extraction, in which the extracted compound is formed as a result of coordination of the molecule or ion of the extractant directly to the atom of the extracted metal. This process is associated with the exchange of ligands (water, chlorine ions) per molecule or ion extractant. Thus, the metal and the extractant are in one sphere of the extracted complex: ( RO)3 P  O  HFeCl4 ( RO)3 P  O  HFeCl4 . (269)

98 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

2.3.2. Extractional Equilibrium The most widely used as the characteristic of extraction equilibrium is the distribution coefficient D:  Corg  y D (270)   , С x  water eq where y and х – equilibrium concentrations of the extractable element in the organic and aqueous phases, mol / l. If the element is present in various chemical forms with appropriate concentrations, then y and x are the total analytical concentrations:

y  C1org  С2org  ...  С j org   (271)  . x  C1water  С2water  ...  С j water  eq Two important technological characteristics of the process are directly related to the distribution coefficient. The first is extraction at one extraction stage η – the fraction of the extracted element, which has passed into the organic phase, from the total amount in both phases: D



yVorg xVwater  yVorg



D , 1  D

(272)

where  – ratio of volumes of organic and aqueous phases or their volume flows during continuous extraction. Extraction is often expressed as a percentage and denoted by Е. The second characteristic – separation factor β, equal to the ratio of the distribution coefficients is better and worse than the extracted element: D  2 (273) D1 (usually a larger index is best assigned to the extracted element). By the value of β, one can judge the efficiency of extraction for the separation of a given pair of elements. With a single extraction, the degree of enrichment of the organic phase with respect to the equilibrium aqueous phase is better than the extractable element is equal to the separation coefficient: y2 / y1 y2 / x2 D2   . (274) x2 / x1 y1 / x1 D1 In practice, extraction systems are used with β ≥ 1,5  2. In describing the extraction patterns and calculating the extraction, extraction isotherms are used – the dependence of the equilibrium concentration H y d r o m e t a l l u r g i c a l P r o c e s s e s | 99

of the element in the organic phase on the concentration in the aqueous phase under given extraction conditions.

2.3.3. Synergic Effect with the Use of Two Extragents When using a mixture of two extractants, deviations from the additivity of extraction are observed in a number of cases. These deviations may be positive (synergistic effect) and negative (anti-synergistic effect). Synergism is the joint action of two or more substances, enhancing the effect of each of them. It is observed in many extraction systems and is due to chemical interactions in the organic phase. The mixing effect of extractants (SE) is: (275) SE  Dexp / Dcalc , where Dexp and Dcalc  experimentally found and calculated from the additivity assumption distribution coefficients. If SE = 1, effect is absent, at SE > 1 there is a synergistic effect, at SE < 1 – antisynergic. For a system from a mixture of extractants E1 and E2 determination of Dcalc  DE1  E2 can be carried out by the formula: DE1  E2  DE1 (1  х)q1  DE2 x2q2 ,

(276)

where х2 – mole fraction of the second extractant; q1 and q2 – solvate numbers for extractants E1 and E2. Synergetic effect is observed in a number of systems with salt-forming (organic acids, amines) and neutral (ketones) extractants, with two neutral extractants, with a mixture of cation-exchange and anion-exchange extractants, in systems of chelate-neutral extractants.

2.3.4. Kinetics of Extraction Processes The rate of establishment of the equilibrium distribution of matter between the two contacting liquid phases, water and organic, is determined by: 1) the rate of mass transfer of substances within the aqueous and organic phases 100 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

and across the interface, 2) the rate of chemical reactions in each phase or at the interface. The rate of mass transfer in the "physical" distribution of substances depends on the physicochemical properties of the contacting phases, temperature and mixing conditions, in so far as all these factors affect both the magnitude of the interfacial surface and the diffusion resistance values. For liquids that do not contain surfactants, the extraction rate increases with increasing agitation intensity somewhat faster than the interfacial surface increases. For stationary or quasistationary processes, the flux of matter through the interface is related to the difference in concentration by equation (277) j  βmas  Ci  C  . The mass-transfer coefficient β is proportional to the diffusion coefficient D and inversely proportional to the effective thickness of the diffusion layer ( βmas  Ddif / δeff ), which can be considered as the region in which the main part of the phase resistance is concentrated. Value δeff depends not only on the properties of the medium, but also on the properties of the diffusing substance, for example, the diffusion coefficient, and therefore the mass-transfer coefficient is proportional Dndif, where n < 1. The change in the hydrodynamic situation affects the value of β in terms of δeff. It is established that the total resistance to mass transfer (rtot) is the sum of the phase resistances:

rtot  r1  r2

(278)

or 1/ k1  1/ βmas1  D / βmas2 ,

(279) where k1 – total mass transfer coefficient in phase I, D – distribution coefficient. The last two equations reflect the so-called additivity rule. The dependence of the mass transfer coefficients on the physical and chemical properties of the phases and the intensity of their mixing is often expressed in terms of the ratio between the dimensionless Nusselt numbers ( Nu  βmasl / Ddif ), Reynolds ( Re  ul / , where u – characteristic velocity, m/s; l – characteristic lenght, m;  – kinematic viscosity of the medium, m2/s) and Prandtl ( Pr   / Ddif ): (280) Nu  const Re p Pr q . The exponents p and q reflect the parametric sensitivity of the mass transfer coefficients to the change in the mixing intensity and of the properties of the medium and the substance to be extracted, such as the diffusion coeffiH y d r o m e t a l l u r g i c a l P r o c e s s e s | 101

cient and the kinematic viscosity. The coefficient p depends on the type of mass transfer apparatus and system. Its usual value varies between 0,5 and 1,2. The dependence of the mass-transfer coefficients on temperature is due to a change in the viscosity and the coefficients of molecular diffusion. When the transfer of matter between phases is accompanied by a chemical reaction between the diffusing substance and a reagent specially introduced into the recovery phase, the course of the reaction leads to an acceleration of the mass transfer, and, consequently, the kinetics of the component's reextraction. This fact is explained by the following. As long as the reaction rate is very low, the mass transfer process occurs in the same way as in the absence of a reaction. After a certain time after the start of the process, the concentration of the transferred component in the volume of the extracting phase is reached, practically not differing from the equilibrium one. In the future, the rate of extraction will be completely determined by the rate of chemical reaction. Such an extraction regime, characterized by the absence of dependence of the extraction rate on the intensity of mixing and the magnitude of the interfacial surface, is called the kinetic regime with the reaction in the volume. In this case, the reaction proceeds at all points of the volume, including the points inside the diffusion layer, at the same rate. If the rate of chemical interaction increases, the fraction of the substance that has reacted inside the diffusion layer increases, and the fraction of the reactant in the volume decreases. When the reaction is almost completely completed near the interface, it acquires the properties of a heterogeneous, but only in the sense that the process rate is proportional to the magnitude of the interfacial surface. Such a reaction leads to an intensification of mass transfer due to the fact that the effective thickness of the diffusion layer decreases. With a further increase in the rate of the chemical reaction, the thickness of the zone in which it proceeds continues to decrease, and in the limit the reaction terminates at the very interface (for the first-order reaction). This extreme case corresponds to the diffusion regime.

2.3.5. Fundamentals of Ion Exchange Processes. General Information Ion exchange processes are based on the ability of certain substances called ion exchangers, in contact with solutions of electrolytes to absorb ions in exchange for ions of the same sign that are part of the ion exchanger. 102 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

Ionites are solids that, due to the presence of ionic groups in them, are able to exchange ions contained in them, to other ions present in the solution. Their structure is a three-dimensional polymer or crystalline mesh. Ionogenic groups consist of fixed ions fixed to the grid and exchangeable counter ions whose charge is opposite in sign to the charge of fixed ions. A threedimensional grid with fixed ions is called a framework or a matrix and is an ionite consisting of a framework and counterions. By the sign of the charge of exchanging ions, cation exchangers, anion exchangers and ampholytes are distinguished. If we designate a framework with fixed R ions, then the reaction of the cation exchange of hydrogen protons with calcium ions can be expressed by the equation

2RH  Ca 2  R 2Ca  2H ,

(281)

and the anion exchange reaction SO24 and Cl–

2RCl  SO24  R 2SO4  2Cl .

(282) In the technology, mineral ion exchangers-various aluminosilicates-and synthetic inorganic ion exchangers-permutites and silica gels-have found application. The capacity of mineral and synthetic inorganic ion exchangers is relatively small; in addition, they are decomposed by acids and alkalis, which limits their use. In metallurgy, the use of ion exchangers, artificially obtained from organic monomers by polymerization or polycondensation reactions – ionexchange resins has found application. The matrix of such ion exchangers consists of spatially "crosslinked" hydrocarbon chains (matrices) with rigidly fixed active ionogenic groups on them. Ion exchange resins have high capacity, chemical resistance and mechanical strength. One of the main criteria for assessing the suitability of an ion exchanger for a hydrometallurgical operation is its exchange capacity-the number of active groups (mg-eq) per unit of mass or volume of resin. The total exchange capacity (TEC), which characterizes the maximum number of ions that can be absorbed by the resin upon its saturation, can be calculated from the equivalent weight of a unitary polymer unit containing one ionic group. The capacity of the resin when equilibrium is reached under static conditions with a solution of a certain volume and composition is called a static (equilibrium) exchange capacity (SEC). This value is not constant, and its value is less than EC. When determining the exchange capacity under dynamic conditions by constructing an "output curve" that shows the dependence of the concentration H y d r o m e t a l l u r g i c a l P r o c e s s e s | 103

of exchangeable ions in the filtrate on the volume of the missed solution, it is possible to obtain a total dynamic exchange capacity (TDEC) and dynamic exchange capacity (DEC) up to a "breakthrough" the amount of absorbed ion up to the moment of its appearance in the filtrate behind a layer of ion exchanger. The values of TDEC and DEC are expressed in mg-eq per 1 liter and characterize the effectiveness of this ion exchanger during the process of sorption extraction of metal in columns.

2.3.6. Equilibrium of Ion Exchange Ion exchange between the ion exchanger and the electrolyte solution proceeds until equilibrium is reached. The exchange reaction is reversible and proceeds in equivalent proportions, like an ordinary chemical reaction. In general, the exchange reaction of ions A and B is described by equation

zB A  z A B zB A  z A B , (283) where zA and zB – ion charges А and В, the top line is the phase of the ion exchanger. Since there is no data on ion activity coefficients in the resin phase, in practice, instead of the thermodynamic equilibrium constant, an apparent (concentration) equilibrium constant is used as the quantitative characteristic of ion exchange, which is sometimes called the equilibrium coefficient: z

KC 

C AzB C BA z C AB CBz A

.

(284)

To describe the state of equilibrium, in addition to the ion exchange constants, two more quantities are also convenient for practical purposes: the distribution coefficient D and the separation coefficient, or the selectivity coefficient, ТВ/A. The distribution coefficient is equal to the ratio of the concentrations of the exchanged ion in the resin and solution: C A xA , (285) DA   CA xA where хi – mole fraction of the i-th type of ions. The partition coefficient is equal to the ratio of the distribution coefficients of the exchanged ions:

104 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

C B / C A x B / x A C B / CB DB . (286)    C B / C A xB / x A C A / C A D A The separation coefficient is a quantitative characteristic of the ability of an ion exchanger to separate the counterions A and B, i.e. its selectivity. Ionite is selective with respect to the ion in question, if KС > 1. With equal charges of exchanged ions (zA = zB) the apparent equilibrium constant and the separation coefficient are equal to each other. TA/ B 

2.3.7. Kinetics of Ion Exchange In the ion-exchange process, three stages can be distinguished: 1) the diffusion of counterions absorbed by the ion exchanger from the solution to the phase interface: 2) the diffusion of the exchanging ions in the volume of the resin in opposite directions (the absorbed ion from the surface into the volume of the ion exchanger, displaced – from the volume to the surface of the ion exchanger); 3) diffusion of the ion displaced from the resin, from the interface of the phases into the volume of the solution. The rate of ion exchange is determined by the rate of diffusion either in the ionite grain (gel diffusion) or through the liquid film adjacent to the surface (film diffusion). In some cases, both stages can control the process. For the most part in concentrated solutions (more than 0, 1 mol/l), the exchange rate is limited by diffusion in the grain, at low concentrations by external diffusion.

Fig. 27. Kinetic curves for gel and film kinetics in the case of interruption of ion exchange H y d r o m e t a l l u r g i c a l P r o c e s s e s | 105

The simplest and most reliable method for the experimental determination of the limiting stage is the interrupt method. With gel kinetics after the break, the initial exchange rate is higher than before the break, since the concentration in the grain is leveled, and the initial concentration gradient increases. In the case of film kinetics, the absorption curve has no inflection (Fig. 27).

2.3.8. Influence of Various Factors on the Process of Sorption With the increase in the concentration of hydrogen ions in the solution, the extraction of metal ions into the resin decreases. This is observed when all cation-exchange resins are used. Industrial solutions have a complex ionic composition, and the change in acidity may be undesirable due to the possibility of hydrolysis of ions or a significant consumption of reagents for subsequent acidification or neutralization of solutions. In the event that impurity cations absorbed by the resin in the chosen pH range are present in the solution, the resin capacity by the recovered ion is sharply reduced. Therefore, in practice, either the solutions are first purified from harmful impurities, or the process is carried out under conditions where the sorption of impurities is small. In anion-exchange sorption, the effect of the ionic composition is determined by the interaction of metal ions with complexing ions in the solution, which leads to the formation of complex anions absorbed by anion-exchange resins. There are three types of dependence of absorption on the strength of the formed ion. In the event that strong anionic complexes ( AgCl2– , PtCl62 and others) are formed in the solution, with increasing concentration of the complexing ion, the metal distribution coefficient between the resin and the solution 

2

decreases. If medium-strength ions are formed in the solution ( ZnCl3 ,PbCl4 and others), then at first the distribution coefficient increases with increasing concentration of the complexing ion, and then decreases. In the formation of relatively unstable anionic complexes in the solution, the concentration of which constantly increases with the concentration of complexing ions (Cu2+, Fe2+, Co2+ , etc.), the distribution coefficient increases with increasing concentration of the complexing ion. The thermal effect in ion-exchange processes, as a rule, is insignificant, therefore the influence of temperature on establishing equilibrium is also small. 106 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

In practice, the effect of temperature is often manifested in side effects: changes in the swelling of the ion exchanger, the degree of dissociation of the components of the solution, etc. The effect of temperature on the value of the exchange capacity is explained by an increase in the diffusion of ions into the interior of the resin grain with an increase in temperature, and the loosening of the ion exchanger occurs as a result of swelling. The size of the cationite granules exerts a large influence on the sorption rate of ions from the solution. As the radius of the ion exchanger decreases, the total surface of the loaded sorbent increases and, consequently, the availability of ionogenic groups improves. Therefore, when using fine-grain ion exchangers, the rate of the sorption process is much higher. However, when grinding the resin grains, its losses increase sharply.

2.4. FUNDAMENTALS OF METAL OR THEIR COMPOUNDS ALLOCATION FROM WATER SOLUTIONS

2.4.1. Selection of Small-Solved Compounds In hydrometallurgy, the allocation of various classes of poorly soluble compounds is used: 1) hydroxides (for example, aluminum hydroxides, iron, cobalt, etc.) or basic salts; 2) sulfides (CuS, CoS, MoS, etc.); 3) various salts of inorganic acids (AgCl, CaWO4, phosphates, carbonates of a number of metals); 4) salts of organic acids (oxalates, xanthates, etc.).

2.4.2. Factors Affecting Solubility of Salts The solubility of a sparingly soluble salt is influenced by the ionic strength of the solution, the pH of the solution, hydrolysis, and the presence of complexing ligands. H y d r o m e t a l l u r g i c a l P r o c e s s e s | 107

Effect of the ionic strength of the solution. The presence of a neutral salt leads to an increase in the ionic strength of the solution and, consequently, to a change in the activity of the ions. From the equation for the product of solubility it follows that when the activity coefficients of the sparingly soluble salts decrease, the solubility of the latter should increase, and with an increase in the activity coefficient, decrease. Effect of solution pH. The solubility of salts of weak acids usually increases with an increase in the concentration of hydrogen ions in the solution, since the proportion of undissociated acid molecules increases. Let us consider the effect of the pH of the solution on the solubility of the salt of a weak acid, which has the composition MeAn. Then the expression for the solubility product will have the form:

Men  nA ; SP  [Men ][ A ]n .

MeAn

(287) Since the acid is weak, it is necessary to take into account the constant of its dissociation:

H   A ; Ka  [ H  ][ A ] / [ HA] .

HA

(288)

If СА – total concentration of A in solution, then C A  [ A ]  [ HA] . We denote the fraction A in the free state , then [ A ]  C A and

SP  [Men  ][ A ]n  [Men ]nC An .

(289)

We express  in terms of Ka and the concentration of hydrogen ions:

 





[ A ] [ A ]  [ HA] K a [ HA]

, [ A ]  

K a [ HA]

[ H ] K a [ HA] / [ H ]  [ HA]

[H  ]

,



Ka



Ka  [ H  ]

(290) .

(291)

Then



 CAn .

SP  [Men  ] K a / ( K a  [ H  ])

n

(292)

This equation can be used to calculate the solubility of the salt of a weak monoacid at a given pH. Effect of complex formation on the precipitating ion. If the sparingly soluble salt complex forms an excess of the precipitating anion, then as the concentration of the anion increases, the solubility first decreases (the action of the common ion), and then increases.

108 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

2.4.3. Conditions of Deposition of Hydroxides and Basic Salts The choice of a precipitant in this case, in addition to the costeffectiveness of the reagent, is determined by the following factors: 1) the precipitator should be as selective as possible so that the resulting precipitate is pure, 2) to facilitate filtration and washing, the precipitate formed must be coarse-grained, 3) to achieve complete precipitation, the precipitate formed The precipitate must have low solubility. It is seldom possible to find a precipitator that meets all these requirements, so the resulting precipitate is often a dirty concentrate that must be redissolved and cleaned. For each hydroxide, there is a narrow pH range in which it precipitates from dilute solutions. Using the difference in pH values, it is possible to achieve separation of metals. The relationship between the pH of precipitation of hydroxides and the concentration of metal ions in solution can be obtained by analyzing the equilibrium

Men  nOH

Me(OH)n .

The equilibrium constant of this reaction 1 KC  , n [Me ][OH  ]n whence

 lg[Men  ]  n pH const .

(293) (294)

(295)

Consequently, the dependence  lg[Men ] from рН – a straight line with a slope equal to 1, 2 or 3 for a single-, two-, or trivalent metal, respectively. Hydroxides adsorb ions of alkali metal (introduced during precipitation) and acid (from the salt of which the precipitation was carried out), which are hard to remove when washing the precipitate. If one do not take special measures, the main salts are precipitated: 3CuO·CuSO4·4H2O, 3CuO·CuCl2·4H2O, 3Zn(OH)2·ZnSO4. Copper, nickel and zinc from ammoniac solutions obtained as a result of leaching are precipitated in the form of basic carbonates. If carbonate ions are present in the solution, the precipitation can be carried out by boiling the solution. If there is no carbonate ion, precipitation is carried out by saturating the solution with carbon dioxide under pressure at room temperature: H y d r o m e t a l l u r g i c a l P r o c e s s e s | 109

2[Zn(NH3 )2 ]2  CO2  3H2O  Zn(OH)2  ZnCO3  4NH4 .

(296) Precipitation of the basic salts is favored by an increase in temperature. When considering the process of precipitation of hydroxides, the following circumstances must be taken into account: 1) the precipitate is formed only in a certain pH range; outside this interval, most sediments return to the solution, 2) at high temperatures, most precipitation either has an increased solubility or decomposes, and 3) the presence in the solution of ions forming a complex compound with this metal hinders the precipitation of this metal, 4) in some cases for precipitation requires an oxidizing agent or a reducing agent. The size of the sediment particles and their shape depend on the conditions under which precipitation is carried out. Coarse crystalline precipitates are formed upon precipitation from dilute solutions, since under these conditions the process proceeds slowly and the crystals have sufficient time for growth. Upon contact with the mother liquor, the freshly precipitated precipitate usually undergoes recrystallization. This phenomenon is called senescence aging. The gelatinous precipitate is poorly filtered and washed. For example, freshly precipitated hydroxides of ferric iron and aluminum have an amorphous structure and are difficult to filter. However, when heated, they become crystalline modifications. When precipitation of the parent metal, precipitation or coprecipitation of impurities is always observed to varying degrees. Coprecipitation is the trapping of impurities by precipitate from an unsaturated solution. If the impurity is precipitated from a supersaturated solution, it is a question of co-precipitation of the compounds. Possible variants of coprecipitation: a) co-precipitation without the formation of solid solutions (nonisomorphic co-precipitation); b) coprecipitation due to the formation of solid solutions (isomorphic coprecipitation); this case can occur if two compounds have a similar crystal structure and / or close radii of the cation and anion; c) adsorption precipitation of the impurity; coprecipitation due to adsorption depends on the deposition rate, the size of the crystals, and the presence of foreign ions; d) inclusion of the mother liquor (capture of the impurity with the mother liquor filling the voids inside the crystals, this case is observed mainly during the crystallization of salts. 110 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

2.4.4. Deposition of Metal Sulfides Among the metal sulfides, only the alkali metal sulfides are highly soluble in water, and they hydrolyze in solution. Sulfides of alkaline earth metals are slightly soluble, but also undergo hydrolysis. This also applies to aluminum and chromium sulfides (Al2S3 and Cr2S3). Sulfides Cu, Co, Ni, Fe, Sn, Mo, As, Sb, Hg, Ag, Zn, Cd are slightly soluble, but when evaluating their solubility, it is necessary to take into account the possibility of partial hydrolysis. Hardly soluble metal sulfides, like hydroxides, are released at a certain pH value, which allows selective precipitation. Sulfides of heavy non-ferrous metals precipitate when processing solutions with hydrogen sulfide, elemental sulfur and its compounds with an intermediate valence (–2, +4), sulfides of more electronegative metals, elemental iron and sulfur.

2.5. CEMENTATION

Cementation is the process of displacement of metals from solutions, based on the electrochemical reaction between the cementing metal and the ion of the displaced metal:

z2Me1z1   z1Me02  z2Me10  z1Me2z2  ,

(297)

where z1 and z2 – cations charges. Cementation is used in hydrometallurgy mainly for the following purposes: 1) for cleaning the solution containing the base metal from impurities, for example, zinc electrolyte (zinc sulfate solution) from impurities of copper, cadmium, thallium by carburizing on zinc; 2) to isolate the base metal from the solution, for example, to extract copper by carburizing on iron, gold – by carburizing on zinc, etc.

2.5.1. Thermodynamics of Cementation The cementation of metals from the solution is based on the difference in the electrode potentials of the deposited metal and the metal precipitant. The H y d r o m e t a l l u r g i c a l P r o c e s s e s | 111

displacing metal must have a more negative electrode potential than the displaced metal. The dependence of the electrode potential on the concentration of its ions in the solution is determined by the Nernst equation: RT (298)   0  ln aMe z  . zF Since as the metal is extracted from the solution its concentration changes, and, consequently, the value of the potential, the process will go on until equilibrium is established, when Me1  Me2 , or

0Me1 

RT RT ln a z1  0Me2  ln a z2  . Me1 Me2 z1F z2 F

Whence a1/ z1z1

Me ln 1/ z 1 a 2z2  Me2





F 0Me2  0Me1 RT

.

(299)

(300)

Calculations using the last equation allow us to determine which metals can be separated from solutions by the cementation method. It should be borne in mind that thermodynamic equilibrium is often not achieved due to kinetic difficulties. In addition, the binding of metal ions to strong complexes can have a significant effect.

2.5.2. Mechanism and Kinetics of Cementation Cementation is a process of internal electrolysis under conditions where both cathodic and anodic reactions occur on the same electrode. The atoms of the dissolving metal are ionized and transferred to the solution, and the ions of the metal to be precipitated assimilate the electrons released on the surface of the dissolving metal and are reduced to atoms. After the cathode regions are formed, metal deposition continues predominantly in these regions, as a result of which the anodic and cathodic zones are separated. The deposition of metal on the cathode regions already formed is energetically more advantageous, since it does not require the expenditure of energy for the formation of new phase nuclei. The controlling stage of the process depends on the magnitude and nature of the electrode polarization. The kinetics of the electrode process can be 112 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

judged from the polarization curves expressing the relationship between the electrode potential displacement and the current flowing through the electrode. The rate of carburization and the limiting stages can vary with time due to a decrease in the concentration of the displaced metal in the solution, an increase in the thickness of the deposited metal layer, and changes in the surface of the cathode and anode sites. In general, the dependence of the carburization rate on time characterizes Fig. 28. In the initial period of time, the rate increases, that corresponds to the formation of cathode sections, and then gradually decreases as the concentration of cemented metal and the growth of the sediment layer change. Since carburization can occur in the kinetic, diffusion or intermediate regions, the specific process rate can be described by the general equation C0 j , (301) 1 2 1   D1 D2 k where С0 – ion Ме1 concentration in solution bulk, 1 – effective thickness of the external diffusion layer, 2 – cemented bed thickness, D1 and D2 – the diffusion coefficients in the external diffusion layer and in the sediment layer, respectively, k is the rate constant of the electrochemical reaction. The realized regime is determined by the ratio of the diffusion and electrochemical resistance values. In addition to the j main reactions, in the process of carburization under certain conditions, hydrogen evolution (the discharge of hydrogen ions) and the reduction of dissolved oxygen at the cathode sites are observed. These side processes lead to additional costs of the cementitious metal and to t the reverse dissolution of Fig. 28. The general character of the change the precipitated metal. in the carburization rate versus time

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2.6. DEPOSITION OF METALS AND OXIDES FROM SOLUTIONS BY MEANS OF REDUCTION WITH HYDROGEN AND OTHER GASES The reaction of metal cation reduction by hydrogen z (302) Me z   H 2  Me  z H  2 can occur in the case if the hydrogen potential is less than the electrode potential of the metal: H2  Me . For reaction ½ H2 = H+ + e the potential can be determined from equation RT aH H 2  ln 1/2 (303) F PH 2

or

2,3RT  1  pH  lg PH2  . (304)  F  2  It follows from the last equation that the value of the hydrogen potential can be reduced by increasing the pH or increasing the hydrogen pressure. More effective pH change. Heavy metals (Pb, Sn, Ni, Co, Cd, Fe) can be completely precipitated from solutions in the pH range 4-10. However, this is practically unworkable due to the isolation of metal hydroxides at high pH values. This difficulty is eliminated in the case of metals such as Cu, Ni, Co, Cd, which form strong ammonium complexes, which allows them to be isolated from ammonia solutions. Hydrogen reduction will be possible if the metal potential in the ammonia medium remains more positive than the hydrogen potential. In addition to hydrogen, CO or SO2 gas can be used as the reducing agent. When silver and copper are recovered from sulfuric acid solutions, reduction by carbon monoxide is followed by reactions 2Ag  CO  H2O  2Ag  CO2  2H , (305) H2  

Cu 2  CO  H2O  Cu  CO2  2H .

(306)

The equilibrium and reaction rate depend on the pH of the solution. The rates of reduction of silver and copper by carbon monoxide are lower than hydrogen. To the disadvantages of carbon monoxide, in addition, it should be attributed its toxicity. Copper can be recovered and sour gas. The total reaction –

Cu 2  SO2  2H2O  Cu  HSO4  3H .

(307) Comparison of data on the reduction of copper from solutions with sulfur dioxide, hydrogen and CO shows that hydrogen is the most efficient reducing 114 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

agent, and the sulfur dioxide is intermediate between hydrogen and CO. However, the use of sulfur dioxide for these purposes in industry is unprofitable.

Control Questions and Tasks 1. The solubility of oxygen in water at 273 and 293 K is 0,049 and 0.0312 (cm3 of gas per cm3 of water). Calculate the thermal effect of dissolution and solubility at 283 K (mole of oxygen per dm3 of water). 2. Henry's constant for CO2 in water at 25 °C is equal to 1.25∙106 Torr. Calculate the solubility (in molality units) of CO2 in water at 25 °C, if the partial pressure of CO2 over water is 0,1 atm. 3. Find the heat of dissolution of MgCl2 in water if its heat of formation is –639,5 kJ/mol, and the heat of formation of Mg+2 and Cl– ions is –466,739 and –166–95 kJ/mol. 4. Derive the equation for calculating the minimum specific consumption of the main reagent in leaching. 5. At 400 K, the equilibrium constant (K) of the reaction of hydrargillite dissolution in the alkali medium Al(OH)3(s) + NaOH(dis) = NaAl(OH)4(dis) is 1,2. Find the concentration of NaOH, which provides a solution with NaAl(OH)4 content equal to 2 mol/dm3. 6. Derive the general equation for the leach stream. 7. In studying the kinetics of the heterogeneous reaction, the following data were obtained for the reaction rate constant: Т, K k  105, g/cm2

273 2,5

293 47,4

313 575,8

333 5478,8

Determine the activation energy of this process. 8. What is the minimum experimental data required to calculate the activation energy of the reaction? 9. Derive the equation for the leaching flux in the case of gas participation. 10. Derive the equation for calculating the solubility of the salt of a weak monoacid at a given pH.

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3 ELECTROMETALLURGICAL PROCESSES

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3.1. ELECTROCHEMICAL SYSTEMS AND THEIR BASIC ELEMENTS

Theoretical electrometallurgy is based on concepts and laws of electrochemistry – the section of physical chemistry, in which the laws of mutual transformation of electrical and chemical energy and the physical and chemical properties of ion systems are studied. For better understanding of theoretical electrometallurgy fundamentals of electrochemistry will be presented below. The mutual transformation of the chemical and electrical energy takes place in electrochemical systems. The electrochemical system consists of: – a second kind conductor (electrolyte), having ionic conductivity; – two first kind conductors17 (electrodes) immersed into an electrolyte, – a metallic first kind conductor (external circuit), which connects electrodes and provides charge transfer between them. Electrolytes are substances in which ions are present in appreciable concentration and cause an electric current flow (ionic conductivity). In particular, electrolytes are substances whose molecules dissolve into ions to make a solution (or melt) due to electrolytic dissociation. There are three types of electrolytes: solid ones, solutions and ionic melts. Electrolyte solutions are often also called electrolytes. An electrode is an electron-conducting body that contacts the electrolyte and provides charge exchange with participants of electrochemical reaction, as well as electron transfer to external circuit. There is a charge transfer at electrode-electrolyte interface, i.e. electrochemical reactions occur. It is necessary to differentiate the concept "electrode process" from the "electrochemical reaction". The electrode process includes the whole set of phenomena: electrochemical, chemical, adsorption and diffusion, which occur when an electric current passes through a solution (melt) and through an electrodeelectrolyte interface. The electrochemical reaction determines an actual interaction between units of a reacting substance (ions, atoms and molecules) and electrons. The electrochemical system can be in equilibrium (Fig. 29, a) or non-equilibrium (Fig. 29, b, c) states. The main criterion for the transition of a system from equilibrium to non-equilibrium state is the flow of an electric current. 17

Conductors of the first kind, or electronic conductors, include all metals and their alloys, graphite, coal, and also some solid oxides, carbides and sulphides of metals. 118 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

In accordance to direction of mutual transformation of electrical and chemical energy, two groups of electrochemical systems are distinguished. The electrochemical system in which the electric energy is produced due to the chemical reactions that take place inside is called a chemical power source or a galvanic cell (Fig. 29, b). Here the electrode that gives electrons to the external circuit is called the negative electrode or the negative pole of a cell. An electrode that receives electrons from an external circuit is called a positive electrode or the positive pole of a cell.

Fig. 29. Schematic representation of an electrochemical system: a – equilibrium electrochemical system; b – chemical power source; c – electrolysis cell; 1 – external circuit, 2 – electrodes, 3 – electrolyte, 4 – positive electrode, 5 – negative electrode, 6 – cathode, 7 – catholyte, 8 – anolyte, 9 – anode

An electrochemical system, in which chemical reactions occur due to external electric energy, is called an electrolysis cell or an electrolytic bath (Fig. 29, c). An electrode that receives electrons from reaction participants and transmits them to an external circuit is called an anode; electrode that gives electrons to reaction participants is called a cathode. The part of an electrolyte adjacent to an anode is an anolyte; the one adjacent to a cathode is a catholyte. An oxidation occurs at an anode, reduction occurs at a cathode. Examples of cathodic reactions: Cu2+ + 2e  Cu, (308) – 2H2O + 2e  H2 + 2OH . (309) Examples of anodic reactions: Zn – 2e  Zn2+, (310) 2OH– – 2e  H2O + ½ O2. (311) Electrolysis is a set of electrochemical oxidation-reduction processes that occur when an electric current passes through an electrolyte with electrodes immersed in it. E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 119

3.2. EQUILIBRIUM IN SOLUTIONS OF ELECTROLYTES

3.2.1. Equilibrium of Electrolytic Dissociation

Svante-August Arrhenius Was born on February 19, 1859 in the Swedish town of Uppsala. Although Svante Arrhenius had a physics education, he is famous for his chemical researches; he became one of the founders of a new science – physical chemistry. For development of the theory of electrolytic dissociation Arrhenius was awarded the Nobel Prize in 1903. The theory of Arrhenius was often criticized by scientist of his time. Among the opponents was the great Russian scientist Dmitri Ivanovich Mendeleyev, the creator of the physicochemical theory of solutions. Mendeleev sharply criticized not only the idea of Arrhenius about dissociation, but also a purely «physical» approach to understand the nature of solutions, not taking into account chemical interactions between the dissolved substance and the solvent. The views of Mendeleev and Arrhenius were later combined into the proton theory of acids and alkalis. Arrhenius was widely known not only as a physicochemist, but also as an author of many textbooks, popular science articles and books on geophysics, astronomy, biology and medicine.

The first quantitative theory of electrolyte solutions was proposed by Arrhenius in 1883–1887. The main points of the theory are as follows: 1. Molecules of some complex substances in solutions dissociate (break up) into oppositely charged atoms or groups of atoms which are called ions. Decomposition of electrolytes into ions during dissolution is called electrolytic dissociation; hereof the theory of Arrhenius is called the theory of electrolytic dissociation. Dissociation occurs spontaneously, regardless of whether the substance is exposed to electrical current or not. 2. All changes in solutions of electrolytes, associated with dissociation and causing deviations from the laws of ideal solutions, are determined by the degree of dissociation n  , (312) N i.e. the ratio of a number of molecules that have dissociated into ions (n) to a total number of dissolved molecules (N). Depending on a degree of dissociation, electrolytes are conventionally divided into two groups: 1. Strong electrolytes are substances that, even in concentrated solutions, are almost completely dissociated into ions. Usually these are compounds whose crystal lattice is built of ions. The strong electrolytes group

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includes most water-soluble salts of inorganic acids (NaCl, ZnSO4, KNO3, etc.), aqueous solutions of mineral acids (HCl, HNO3, HClO4, etc.) and alkalis (NaOH, KOH). The degree of dissociation of strong electrolytes is close to 1. 2. Weak electrolytes only partially dissociate into ions. This group includes some inorganic acids (H2S, HCN, H2CO3, H3BO3, etc.), aqueous solutions of ammonia, many organic acids (acetic, tartaric, etc.) and some salts (HgCl2, Fe(SCN)3, etc.). For weak electrolytes, 0 < α E. 164 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

A realized power of a current source IU is less than its theoretical maximum power IE; power consumed during electrolysis is IU greater than theoretically necessary IE. Thus, the efficiency at work of electrochemical systems is less than 100 %. The difference between U and E is made up of the ohmic voltage drop inside an electrochemical cell (between a cathode and an anode), Eohm = IRcircuit (Rcircuit is internal resistance of a circuit), polarization of a cathode EC and polarization of an anode EA. Therefore, if a circuit works as an electrolysis cell, then U  E  Eohm  EC  EA and

Efficiency 

E  100 % . E  Eohm  EC  E A

(498)

On the other hand, in the case of a circuit operating as a chemical current source, U  E  Eоhm  EC  EA and

E  Eоhm  EC  E A  100 %. (499) Е Polarization of each electrode is the change in a galvanic potential caused by passage of electric current trough an electrode/solution boundary as compared to its equilibrium value. Electric current, in turn, is related to a course of an electrode process (Faraday current) and to charging of a double layer (charging current). If the properties of a surface layer do not change with time, then current flowing through an electrode is determined only by rate of an electrode process itself and by dimensions of an electrode. Under these conditions, the current density i = I/S (S stands for su rface area of an electrode) serves as a measure of electrochemical reaction rate. Polarization of an electrode is due to the finite rate of an electrochemical process, and therefore it is some function of current density: E  E (i) . The functional dependence of E on i (or i on E) is called the polarization (volt-ampere) characteristic (curve). The task of electrochemical kinetics is to establish general regularities, to which polarization characteristics obey, in order to regulate the electrode processes rate. This problem is extremely important, since a decrease in polarization at a given current density makes it possible to substantially increase efficiency of electrochemical systems use. Unlike usual homogeneous chemical reaction occurring in the volume of a solution between reactants, an electrochemical reaction proceeds at an interface between an electrode and a solution, that is, it is a heterogeneous reaction. Efficiency 

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It follows that any electrode process always has a series of successive stages: first a reacting substance comes to an electrode, then an electrochemical stage itself occurs, connected with transfer of electrons or ions through an interface (charge transfer stage), and finally reaction products formed depart from an electrode surface to make room for a new portion of the reactant. The first and the third stages have the same regularities and are called the stages of mass transfer. The stages of mass transfer and discharge-ionization are present in all electrode processes, without exception. In addition to these stages, other reactions occur during the course of electrode reactions. So, often electrode processes are complicated by chemical reactions in the solution volume or on a surface of an electrode, in which a starting substance or a product of an electrochemical reaction can participate:  ne (500) A  O   R  B. The stage of substance A transformation into substance O is called a previous chemical reaction, and the stage of transformation R into B is a subsequent chemical reaction. Often, electrode processes are complicated by the stage of new phase formation. Thus, during electrodeposition of metals, the stage of crystalline embryos formation is realized, and in the electrochemical evolution of gases, the stage of gas bubbles nucleation is realized. In the course of an electrochemical process, particles can move along a surface of an electrode (the stage of surface diffusion) from centers at which a discharge occurs, to some others, where product of a reaction is energetically most advantageous. If an electrode surface carries a charge that is the same as the charge of a reacting particle, then electric field of a double layer prevents adsorption of this particle, so it is necessary to take into account the stage of reacting particle occurrence in an electric double layer. If rate of one of the stages of a multistage process is much less than the rate of all the other stages, then such a stage is called limiting. This conclusion is also applicable to electrode processes, with total polarization being practically equal to polarization of the limiting stage. To determine the limiting stage, regularities of an electrode process under investigation are compared with regularities characteristic for different stages. A three-electrode electrochemical cell is used to measure polarization (see Fig. 43), which allows one to determine the change in an individual galvanic potential, and rate of an electrode process is measured with devices that fix electric current. After determining the limiting stage, appropriately changing the conditions of an electrode process, one can change its rate in desired direction. This stage is limited only under certain conditions, 166 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

and a change in these conditions (for example, a change in polarization) may lead to a change in the limiting stage. After that, the variation of the parameter, on which rate of an electrode process depended, can cease to have a noticeable effect on it.

Fig. 43. Scheme of a three-electrode electrochemical cell: A – accumulator; A1 and A2 – galvanometers; S – voltage separator; C.E. – counter electrode; W.E. – working electrode; R.E. – reference electrode; E1 – voltage in power circuit; E2 – voltage in measuring circuit

Thus, in order to control the rate of an electrochemical process, it is necessary to determine the limiting stage and to know the regulations to which it obeys. If nature of the limiting stage is known, then the term "electrode overvoltage" is used instead of the term "electrode polarization". Depending on nature of the limiting stage, the following types of overvoltages are distinguished: – diffusion overvoltage (at the limiting stage of mass transfer); – electrochemical overvoltage (at the limiting stage of dischargeionization); – phase overvoltage (at the limiting stage of a construction or destruction of a crystal lattice or a new phase nucleation – gas, liquid or crystalline); – chemical reaction overvoltage (at the slowed-down stage of the chemical reaction). At the slowed-down stage of mass transfer and chemical reaction, concentration at an electrode surface changes. Therefore, polarization caused by the slowing down mass transfer stage and chemical reaction is also called concentration polarization or concentration overvoltage.

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3.5.1. Types of Transfer in Electrochemical Systems Transfer of reacting substances under conditions of an electrochemical reaction can be carried out by three mechanisms. The first (main) mechanism is molecular diffusion, i.e. movement of matter particles under action of a concentration gradient. When electric current passes through a boundary electrode/solution, concentration of reacting substances at a surface decreases and concentration of reaction products increases simultaneously. Concentration gradients arise that lead to diffusion of discharged substance from volume of a solution to an electrode, and reaction products from an electrode surface to solution volume or to volume of the metal phase (for example, during formation of amalgam during discharge of Tl+ ions at a mercury electrode). Since concentration changes near the surface of an electrode always accompany flowing of an electrochemical reaction, molecular diffusion is observed in all electrode processes without exception, while other mechanisms of mass transfer can be superimposed on diffusion process or absent. Therefore, area of electrochemical kinetics, in which the laws of mass transfer stage are considered, is also called diffusion kinetics. The region of a solution adjacent to an electrode, in which solution concentration changes, but electroneutrality condition remains, is called a diffusion layer. This layer must be distinguished from a diffusive layer (a diffuse part of an electric double layer), which is located closer to an electrode and in which total charges of cations and anions differ not only in sign, but in absolute. Usually, thickness of a diffusion layer exceeds a thickness of a diffuse part of an electric double layer by an order of magnitude or more, and therefore, when solving mass transfer problems, it is assumed that, in the first approximation, an origin of a diffusion layer corresponds to the coordinate x = 0 (the x axis is directed along the normal to the electrode surface). This assumption is equivalent to the fact that time of reacting particle passage through an electric double layer can be neglected in comparison with time of its passage through a diffusion layer. The second mechanism of mass transfer – migration – is associated with charged particles movement under action of electric field, which arises in a diffusion layer when electric current passes through it. Formally, one could speak of an ohmic drop of potential in a diffusion layer. However, such an interpretation is generally erroneous. Nevertheless, by creating an excess of extraneous indifferent electrolyte (background), migration can be eliminated. The third mechanism of mass transfer is convection, that is, transport of matter together with the flow of a moving fluid. In natural conditions, convec168 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

tion arises as a result of density gradient of a solution, which in turn is a consequence of concentration changes in a surface layer or heating of a nearelectrode space due to electric current flow. Natural convection can also be caused by release of gaseous products of electrode reactions. Artificial convection is created by stirring an electrolyte or rotating an electrode. Convection cannot eliminate diffusion, since velocity of a fluid relative to electrode surface decreases with increase of distance between the surface and a liquid, and the concentration gradient increases. Therefore, the closer to the surface, the more important role diffusion mechanism plays in mass transfer process. The role of stirring is manifested in the fact that it causes a decrease in diffusion layer thickness and thereby increases concentration gradient of reactants and reaction products at an electrode surface.

3.5.2. Diffusional Overvoltage Appearance of diffusion overvoltage can be traced in the example of cathodic metal deposition reaction: M z   ze  M . Before switching on current, concentration of metal ions over an electrode surface and in volume is the same. When current is turned on, concentration near an electrode begins to decrease. From volume of a solution to a surface of an electrode a diffusion flux appears. The greater difference in concentrations in volume (C0) and near a surface (Cs), the greater diffusion rate is. As a result, diffusion rate will increase until it becomes equal to discharge velocity of metal ions. In these conditions, the process becomes stationary. Since in the case of diffusion overvoltage all other stages proceed much faster, they can be considered reversible. Potential in this case can be calculated from the Nernst equation: In equilibrium: RT (501) Ep  E  ln C0 . zF Under current: RT (502) E E  ln Cs , zF RT Cs   E  Ep  ln , (503) zF C0 where  denotes overvoltage. As Cs  C0 , for a cathodic reaction, overvoltage has a "minus" sign. E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 169

Similarly, it is possible to trace appearance of diffusion overvoltage in anodic ionization (dissolution) of a metal: M  M z   ze. In this case Cs  C0 , that causes a positive sign of overvoltage. If electrochemical process is accompanied by a decrease in concentration of reacting substances at an electrode, then on a polarization curve (Fig. 44, curve 1) appears a section BC, which is characterized by a sharp shift of potential at an almost constant value of current density. Appearance of this section is associated with a decrease in Cs to zero as current density increases. In accordance with equation (503) under these conditions, the electrode potential should tend to "minus infinity". However, an increase in potential is limited by presence in a solution of other particles capable of taking part in a new electrode process at a higher potential corresponding to the point C. This process corresponds to curve 3. The section CD reflects the joint flow of two processes. For example, when copper is electrodeposited from a solution containing 2+ Cu and H+ ions, the ABC section on curve 1 corresponds to copper ion discharge; curve 1 corresponds to hydrogen evolution process, in the CD region both processes occur simultaneously. The current density corresponding to the horizontal section BC of the polarization curve, excess of which is accompanied by appearance of a new electrode reaction, is called limiting current density (jпр).

jlim

jlim

Fig. 44. Polarization curves for the reduction of two cations: 1 – fixed electrolyte; 2 – stirred electrolyte

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Limiting current density is a kinetic parameter of electrochemical reactions accompanied by diffusion overvoltage. It characterizes maximum rate of an electrode process, possible in the conditions given. There are two types of limiting current: 1) limiting diffusion current that arises when transport of reacting substances to or from an electrode occurs only due to diffusion: zFDC d jlim  , (504)  2) total limiting current corresponding to a case when transport of reacting substances is due to diffusion and migration: zFDC jlim  , (505)  1  ti  Where z stands for number of electrons participating in an electrode process,  is diffusion layer thickness, D is diffusion coefficient of substances participating in a reaction, C is concentration of a participants in a reaction, and ti is number of cation transfer. When metal dissolves anodically, in accordance with the above reaction, a sharp increase in potential and appearance of a limiting current due to a change in concentration of Mz+ ions in a diffusion layer does not occur. In the region of high current density, an increase in electrode potential caused by passivation of an anode can be observed. The value of the limiting current density can be used to calculate diffusion overvoltage. The basic kinetic equations connecting current density j and overvoltage in this case have the form: RT  j  c  ln 1  for cathodic process: (506) , zF  jlim  RT  j  a  ln 1  for anodic process: (507) , zF  jlim  where jlim stands for limiting current density corresponding to cathodic direction of an electrode process. The values of limiting current density and diffusion overvoltage depend on concentration of participants in a reaction, temperature with which diffusion coefficient of a substance increases. Mixing of a solution, accelerating delivery of reactants to an electrode, which leads to an increase in limiting current and reducing overvoltage, is of particular importance.

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3.5.3. Electrochemical Overvoltage Electrochemical overvoltage is due to the maximum inhibition in electrochemical reaction stage – addition or release of electrons. The theory of electrochemical overvoltage is based on general positions of chemical kinetics, establishing a connection between reaction rate and activation energy. The latter for electrochemical processes depends on electrode potential (overvoltage). Electrode reactions, as well as chemical reactions, proceed simultaneously both in direct (for example, cathodic) and in reverse (anodic) directions: Ox  ze Red . Total reaction rate is determined by difference between particular values of current densities jc and ja. Under equilibrium conditions, reaction rates in the forward and reverse directions are the same and correspond to exchange current density jo: jк  ja  jo .

(508) Exchange current density characterizes rate of exchange process under equilibrium conditions and depends on nature of an electrochemical reaction, concentration of substances involved and temperature. For cathode process, the relationship between current density and overvoltage is expressed by the Volmer equation: 1  zF   zF    RT j  jc  ja  jo  e  e RT  , (509)     where jc and ja stand for particular values of current density characterizing rates of direct (cathodic) and reverse (anodic) reactions, z is number of electrons participating in electrode reaction,  is transport coefficient that characterizes fraction of electric field energy that promotes acceleration of direct reaction, and also characterizes degree of electrode electric field influence on activation energy of the electrochemical stage and determines symmetry of cathodic and anodic processes. Current density jo and transport coefficient  are kinetic parameters of reactions accompanied by electrochemical overvoltage. The value of  for a number of electrochemical reactions is close to 0,5. In the special case, when system is slightly deviated from the equilibrium state (in region of low cathode overvoltages), Volmer's equation implies: RT j c   . (510) zF jo 172 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

If significant current passes through a system, it deviates substantially from the equilibrium state. In this case, for a cathode process, the Volmer equation takes the form: RT RT c  ln jo  ln jc . (511) zF zF If we denote: 2,3RT lg jo  ac (512) zF 2,3RT   bc , and (513) zF then equation (511) takes the form of the Tafel formula: (514) c  аc  bc lg jc . Constants a and b are called Tafel constant. Dependence of electrochemical overvoltage on current density is usually represented graphically in coordinates   lg j (Fig. 45). At low values of j and , the region AB is observed on polarization curve, which corresponds to mutual influence on rate of direct and reverse reactions (see equation (510)). In the region of significant currents, in accordance with equation (514), there is a rectilinear section BC. By values of Tafel constants, one can calculate kinetic parameters of the electrode reaction, accompanied by an electrochemical overvoltage – jo and . Tafel constants are determined graphically in that overvoltage region where Tafel equation is valid. Knowing angle tangent b, one can calculate the value of , and exchange current can be found from magnitude of overvoltage at current density equal to 1, i.e. for lg j = 0. Then,   a .

Fig. 45. Dependence of electrochemical overvoltage on current density E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 173

jo  10



azF 2,3 RT



a b

 10 . (515) With one and the same deviation of electrode potential from the equilibrium value, reaction rate (resulting current density) will be the greater, the higher exchange current. If exchange current is very large, then there is practically no shift of potential from the equilibrium value. In this case we speak of an unpolarized electrode. Exchange current, in turn, depends on nature of an electrochemical reaction, electrode material and solution composition.

3.5.4. Chemical Reaction Overvoltage This kind of overvoltage is associated with slowing down of a chemical reaction stage, which can enter into a complex multi-stage electrode process. The chemical stage may precede or follow electrochemical. An example of the latter case is cathodic evolution of hydrogen. Here the electrochemical stage is 

a discharge of hydronium ions: H3O  e  Hads  Н2О . The resulting hydrogen atoms enter into a chemical recombination reaction: 2H ads  H 2 . For such processes, dependence of overvoltage on current density is expressed by the equation: RT  j  (516) xp  ln 1   , nzF  jo  where n stands for order of a chemical reaction. If system is significantly deviated from the equilibrium state and j jo , equation (516) after transformations acquires the following form: RT RT xp   ln jo  ln j, (517) nzF nzF i.e. connection between overvoltage and current density, as in electrochemical kinetics, obeys the Tafel dependence: xp  а  b lg j. (518) Kinetic parameters of chemical reaction overvoltage are order of a chemical reaction and exchange current density.

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3.5.5. Phase Overvoltage Phase overvoltage is caused by inhibition of a phase transformations stage occurring during an electrode reaction: formation of gases, solid and liquid metals, oxides, etc. A particular case of phase overvoltage – crystallization overvoltage – corresponds to process of crystallization during electrolytic deposition of metal. With cathodic evolution of metal, as a result of an electrochemical reaction, a primary product, which has not yet been released into a new phase, is being formed, – metal atoms. These atoms are in adsorbed state on a surface of a cathode and are called ad-atoms. Formation of a new phase – electrocrystallization – generally takes place in two stages: appearance of crystalline nuclei (crystallization centers) and their growth. In both stages, ad-atoms are involved. Center of crystallization is the smallest crystal that can exist under given conditions. There are two-dimensional (one atom thick) and three-dimensional (thicker than one atom) nuclei. The first ones are formed predominantly on a substrate that is the same as metal deposited, the second ones are formed on a foreign surface. In general case, both types of nuclei are being simultaneously formed. Crystalline nuclei do not appear on entire surface of a cathode, but only on a limited number of surface centers that have a certain energy reserve. Therefore, ad-atoms must be displaced by surface diffusion from places of their origin to places where nuclei appear or grow. Any of the process stages of metal extraction – formation of a primary product, its surface diffusion, emergence of nuclei and its growth – can be limiting and determine energy expenditure (electrode potential, overvoltage) for process as a whole. Phase overvoltage itself is due to predominant inhibition in the last three stages. Calculations show that formation of crystalline nuclei requires a greater expenditure of energy than for their growth. The magnitude of crystallization overvoltage depends on nature of metal to be deposited, composition of an electrolyte, its temperature, current density and time of metal precipitate formation.

E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 175

3.6. REGULARITIES AND MECHANISM OF SOME ELECTRODE PROCESSES

3.6.1. Electrolytic Evolution of Hydrogen Electrolytic evolution of hydrogen from acidic and alkaline solutions occurs in various ways. Source of hydrogen in acidic solutions is hydronium ions, discharge of which on a cathode leads to formation of hydrogen gas:

2H3O  2e  H2  2H2O.

(519) In alkaline solutions, direct attachment of electrons to water molecules with their subsequent decomposition into hydrogen and hydroxyl ions is expected:

2H2O  2e  H2  2OH .

(520) It is assumed that the reaction (520) can also occur in acidic solutions, but at high current densities. Sometimes in acid media hydrogen is released directly from molecules of acid:

2HA  2e  H2  2A ,

(521) for example, in hydrogen evolution at a mercury cathode from aqueous solutions of carbonic acid. Equations (519), (520), and (521) represent the cumulative expression of cathodic hydrogen evolution under various conditions of electrolysis. This process consists of a series of successive stages and can proceed along different paths depending on specific conditions. The first stage – delivery of particles serving as a resulting cathodic hydrogen source to an electrode surface, proceeds in this case without significant inhibition. The second stage following it corresponds to discharge of hydrogen ions (or water molecules) with adsorbed hydrogen atoms formation:

H3O  e  Hads  Н2О.

(522) Regardless of whether discharge occurs in an acidic or alkaline medium, its immediate product is hydrogen atoms adsorbed by the electrode. For a steady flow of electrolysis, it is necessary to maintain a constant surface concentration of hydrogen atoms, i.e. to ensure their continuous withdrawal from a cathode surface. Hydrogen atoms can be removed in three ways: by catalytic recombination, by electrochemical desorption and by emission.

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With a catalytic mechanism, removal of hydrogen atoms occurs due to their recombination into molecules with simultaneous desorption: (523) 2Hads  H2 , the role of catalyst is performed by electrode metal. In the case of electrochemical desorption, removal of hydrogen atoms from an electrode surface occurs as a result of hydrogen ions (or a water molecule) discharge on already adsorbed atoms according to the equations

H3O  Hads  е  Н2  Н2О.

(524) With emission mechanism, adsorbed hydrogen atoms evaporate from hydrogen surface in form of free atoms (525) Hads  H with their subsequent volumetric recombination into hydrogen molecules. Molecular hydrogen, formed from adsorbed atomic hydrogen, must be removed from an electrode-electrolyte interface into a gas phase. Thus, a process of cathodic hydrogen evolution can be represented by the sheme in Fig. 46.

Fig. 46. Staged cathodic hydrogen evolution process

E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 177

Hydrogen evolution is accompanied by appearance of an overvoltage, depending on nature of an electrode, composition of a solution, and conditions of electrolysis. The relationship between current density and overvoltage is expressed by the Tafel formula (514). The Tafel formula also reflects the effect of electrode material on overvoltage, since constants in this equation are not the same for different metals. For platinum and palladium, the values of a and b are relatively small. At the same time, we can distinguish a group of metals with high overvoltage: cadmium, mercury, lead. For most metals, the coefficient b varies little and averages 0,11–0,12. Known assumptions about the most probable mechanism of hydrogen evolution on various metals can be stated on the basis of general electrochemical kinetics positions applied to a given electrode reaction. Thus, it was suggested that as heat of hydrogen atoms adsorption increases on a cathode metal, delayed discharge probability decreases, and slowed-down recombination probability increases. This is due to different effect of change in heat of hydrogen atoms adsorption on discharge rate and on recombination rate. Activation energy of discharge decreases with increasing heat of adsorption. Energy of activation of recombination process, on the contrary, increases with strengthening of a bond between metal and surface hydrogen atoms, the quantitative characteristic of which is heat of adsorption. At the same time, an increase in heat of adsorption should increase hydrogen atoms surface concentration and, consequently, increase rate of recombination, i.e. lead to the opposite effect. As a result of superimposition of these two opposite effects, rate of recombination may decrease or increase with increasing heat of adsorption, but its accelerating influence should always be less than in the case of a discharge. Although experimental data on heats of hydrogen adsorption are small and contradictory, nevertheless, they make it possible to state that heats of hydrogen adsorption on mercury, zinc and cadmium are much less than on metals of platinum group and iron family. Consequently, mercury, for example, is more favorable for slow discharge, and nickel for slower recombination. These considerations, expressed by L.I. Antropov, led to the conclusion about existence of two extreme groups of metals with different mechanisms of hydrogen overvoltage. The first group includes metals of platinum and iron groups, which have a high adsorption capacity with respect to hydrogen. On these metals, the recombination stage should play a decisive role in cathodic hydrogen evolution kinetics. The second group includes mercury, lead, cadmium and other metals that almost do not adsorb hydrogen. On 178 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

metals of the second group, kinetics of hydrogen evolution is determined by the discharge stage. The magnitude of hydrogen overvoltage on the same metal essentially depends on state of its surface: for identical linear dimensions of an electrodes and the same amperage, overvoltage on a rough surface is lower than on a smooth, polished one. As temperature rises, hydrogen overvoltage drops, temperature coefficient depends on nature of metal and ranges from 1 to 4 mV/K. Due to high mobility of hydronium ions and high concentration of water in a solution, the transport stage hardly affects a value of hydrogen overvoltage. Phase overvoltage in gas formation is usually small. For most metals, the discharge stage is the limiting one, and the theory of hydrogen overvoltage coincides with the theory of electrochemical overvoltage. On metals of the platinum group, the slowest is hydrogen atoms recombination into a molecule. In this case, overvoltage of hydrogen corresponds to overvoltage of a chemical reaction and is described by the equations (516–518).

3.6.2. Electrodeposition of Metals Electrodeposition is metal coating formation on a surface of base material, resulting from electrochemical reduction of metal ions from an electrolyte solution. Appropriate technology is often called electroplating. In addition to producing metal coatings or foils, electrochemical reduction is used to extract metals from their ores (electrometallurgy), to manufacture products with precisely defined shape and dimensions (electroforming). In most cases, metal precipitate is crystalline, which is why the process is called electrocrystallization; this term was introduced in the early XX century by Russian chemist V. Kistyakovski. The process of metal electrocrystallization on a cathode begins with appearance of a bulk crystalline nucleus (center of crystallization) on it. To form such a nucleus, it is necessary to commit work connected with deviation of an electrochemical system from the equilibrium state: K (526) W . 2  Ek  Thus, the condition for appearance of a new phase is displacement of potential from Ep, that is, cathodic polarization (∆Ek). E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 179

A surface of a growing crystal is energetically inhomogeneous, i.e. there are areas on it where completion of a crystal lattice is more difficult or easier. The beginning of new edge growth is accompanied by the highest difficulties. On the contrary, completion of an edge by multiple additions of atoms in the most energetically favorable places occurs with minimal inhibition. The most important physical and mechanical properties of metal coatings (hardness, wear resistance, tension, porosity, brittleness, etc.) are determined by features of their crystal structure. With decrease in crystal size, metal coatings, as a rule, are denser, harder, and more wear-resistant. Therefore, in practice, it is important to obtain compact fine crystalline precipitation. Structure of a precipitate depends on ratio between crystals growth rate and crystallization centers formation rate. The higher formation of crystallization centers rate with respect to crystals growth rate, the more fine precipitate will be. Formation of nuclei requires more energy than growth of existing crystals, so an increase in overvoltage contributes to an increase in crystallization centers formation rate. Thus, the more cathode potential under current is shifted in the negative direction from the equilibrium value, the more fine-grained will be the precipitate. In electrodeposition from solutions of simple salts, the magnitude of polarization and nature of cathodic deposits are determined, first of all, by nature of deposited metal. By the values of exchange current density, and consequently, overvoltage and average grain size, metals can be conditionally divided into three groups. 1. Metals with high exchange current density: Ag, Pb, Sn, Cd; Jo = 10–1 – – 10–3 A/cm2. These metals are released with low overvoltage, not exceeding several millivolts. When precipitating, they produce coarse crystalline precipitates with average grain size of more than 10–2 mm. 2. Cu, Zn, Bi. For these metals, jо = 10–4 – 10–5 A/cm2. Overvoltage is tens of millivolts; average crystal size is 10–2 – 10–3 mm. 3. Fe, Ni, Co – metals with a low value of jo = 10–7– 10–8 A/cm2. When they precipitate, overvoltage reaches hundreds of millivolts; crystal size is less than 10–4 mm. These metals are released in form of compact fine-grained sediments without any additional measures, in contrast to metals of groups 1 and 2, to reduce crystal size of which special techniques aimed at increasing overvoltage are used. Cathodic polarization can be increased, reducing concentration of discharged ions. This can be achieved either by diluting an electrolyte with water or by adding to it alkali or rare earth metal salts having a common anion with the salt of metal to be precipitated (for example, the addition of Na 2SO4 to sul180 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

furic acid nickel electrolyte). The latter method is preferable, because when diluted with water, solution conductivity decreases noticeably. Replacement of simple metal ions by complex ions in an electrolyte leads to significant changes in conditions of its electrodeposition (Fig. 47). This is primarily expressed in displacement of equilibrium electrode potential toward negative values, which depends on stability constant of a complex compound: RT (527) Ek  Еп  ln Ksteady , zF where Ek , En stand for standard metal potentials in solutions of simple and complex salt, Ksteady – for complex stability constant. Shift of equilibrium potential to the negative side when using complex electrolytes is used to suppress contact exchange reaction that occurs if coating metal has more positive potential than base metal. Shift of equilibrium potential to the negative side when using complex electrolytes is used to suppress the contact exchange reaction that occurs if the coating metal has a more positive potential than the base metal. High polarization in metals electrodeposition from solutions of complex salts is due to additional energy requirements necessary to destroy a strong complex compound. The process of metals electrodeposition is very sensitive to presence of surfactants that can be adsorbed on a surface of a cathode. When using surfactants, it is possible to obtain fine crystalline, and sometimes shiny precipitates. A surfactant makes it possible to significantly increase polarization due to inhibition of the electrochemical stage of a cathodic process (Fig. 48).

Fig. 47. Cathode polarization curves for electrodeposition of metal from solutions of simple salt (1) and from a solution of complex (2)

E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 181

Fig. 48. Cathode polarization curves during electrodeposition of metal from solutions that do not contain surfactant additives (1) and with surfactant additive (2)

In accordance with the theory of electrochemical overvoltage, the effect of surfactants is due to their influence on electrical double layer structure and electrode surface blocking. The blocking effect is most manifested at surface filling degree of  = 1. In this case, reaction rate is much lower and remains constant in a wide range of potentials. On a polarization curve, limiting current of nondiffusion character appears. It is connected with difficulty of passing an ion through a continuous film of surfactants. This contributes to formation of a fine crystalline precipitate. Since metal precipitation turns out to be fine-grained with high polarization, in electroplating technology of metals, especially in electroplating, electrolytes based on complex salts, surfactant additives and other conditions that enhance overvoltage and improve the structure of cathode deposits are widely used. The structure of metal coatings depends on electrolysis regime. Increasing current density in most cases enhance formation of more finegrained metal deposits on a cathode. This is explained by increase in number of active, simultaneously growing cathode surface locations. The most noticeable effect of current density is on the precipitate structure in electrolytes with a sharply expressed cathodic polarization. However, it is impossible to increase current density limitlessly. At very high values (close to the limiting diffusion current of ions values), loose sediments form as dendrites (Fig. 49) on edges and other projecting places of a cathode or solid spongy mass over its entire surface. Such sediments consist of separate particles, which are aggregates in crystals that are loosely connected with each other and with a surface to be coated. After discharge from an electrolyte they are easily separated from a sur182 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

face of the cathode, and sometimes (with prolonged build-up) they fall from a cathode to a bottom of a cell during electrolysis.

Fig. 49. Copper dendrites taken from a cathode

Formation of dendrites is explained by predominant growth of crystals at individual cathode sites, due to uneven distribution of current, especially at low cathodic polarization, a current density exceeding the permissible limit for a given electrolyte is established. In most cases, such places are areas of a relief cathode closest to an anode, as well as edges of plates, peaks, etc., near which, due to high discharge rate, ion concentration sharply decreases. Resulting crystals continue to grow along the discharge lines of discharging ions, mainly toward an anode, and sometimes reach an anode surface, causing short circuits. At very high current densities, other complications often arise in a cathodic process: hydrogen evolution and a sharp decrease in current efficiency, formation of hydroxides due to depletion of a solution by hydrogen ions and alkalinization of a medium. Accumulation of hydroxides at a cathode, as indicated above, can lead to contamination of a cathode deposit, which causes its fragility and formation of voids and ulcers in it. Therefore, current density must be chosen in accordance with composition of an electrolyte, mainly with deposited metal salt and hydrogen ions concentrations in solution, with temperature and electrolyte mixing conditions. The greater deposited metal salt concentration, electrolyte temperature and mixing intensity, the higher allowable current density. In some cases, an increase in current density to a certain limit enhances a certain orientation of crystals in a precipitate. Temperature rise with other constant conditions (electrolyte composition and current density), as a rule, reduces cathodic polarization, contributing to formation of more coarse precipitates. In this connection, the permissible current density and, consequently, process rate with increasing temperature can be, respectively, increased. An increase in current density, as was mentioned above, helps to reduce size of crystals in the sediment and compensates the reverse efE l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 183

fect of temperature on the structure. In addition, in almost all electrolytic processes, as temperature of the electrolyte increases, current efficiency increases (with the exception of chromium process), internal stresses in precipitations and their brittleness decrease, and precipitation turns out to be more plastic. Temperature increase in many cases is maintained in order to increase salts solubility, anodic current efficiency (passivation of anodes is being prevented or eliminated), electrical conductivity and reduce the amount of hydrogen introduced into an electrolytic precipitate. In some cases, temperature of an electrolyte also affects orientation of crystals in a precipitate. When temperature is raised above the optimum, a perfection of a texture is reduced. Stirring of an electrolyte is very often used in electrolytic cells in order to maintain a constant concentration of a solution at electrodes and eliminate concentration polarization. Therefore, in cells with a stirred electrolyte, dense, finegrained, smooth precipitates can be produced at higher current densities with an increased current efficiency. The higher assumed current density, the more intense electrolyte mixing should be. When stirring an electrolyte, it is necessary to periodically or continuously filter the solution to clean it from contamination with anodic (and bottom) sludge, otherwise quality of a sediment can deteriorate significantly. Sludge particles, being in a suspended state, fall on a cathode, pollute a precipitate, and cause formation of knobby outgrowths on it. Solutions are being mixed with mechanical mixers, often with compressed air, cleaned from oil and dust in special filters before being supplied to a cell. Mixing with compressed air can be used in acidic copper, nickel, zinc and other cells, whose composition does not change under the influence of oxygen and carbon dioxide contained in air. For this reason, use of compressed air is not suitable for iron electrolytes and cyanide solutions. Recently, much attention was paid to studying the influence of ultrasound on metals electrodeposition cathodic process. Basically, this influence reduces to intensive mixing of an electrolyte near a cathode, which makes it possible to obtain compact precipitates at very high current densities, when hydroxides or sponges are formed by other methods without sti rring or even with stirring of an electrolyte. However, for a very high intensity of ultrasonic field, its action is not confined to just aligning metal ions concentration in a cathode layer. In some cases, under the influence of ultrasound, depending on intensity and frequency of oscillations, conditions of adsorption, passivation, etc. change, which, accordingly, affects the structure of electrolytic precipitation. 184 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

3.6.3. Joint Reduction of Metal and Hydrogen Cations If there are two or more kinds of cations in an electrolyte, then their simultaneous discharge is possible. This phenomenon is of great practical importance. Electrolytic production and refining of metals can be accompanied by a simultaneous reduction of several different cations. With a combined discharge of several kinds of cations, recovery rate of each of them corresponds to certain current density. Total current density jk is equal to the sum of current densities of all the reduction reactions flowing on a cathode: jk   ji i . (528) When for practical purposes it is necessary to reduce only one type of ions, discharge of accompanying ions is a technical hindrance. To reduce them, some electricity is consumed, i.e. part of current flowing in a cell. Simultaneous discharge of cations occurs in the case when cation deposition potentials are close to each other. Quite often the second cation discharged simultaneously with a metal cation is the hydrogen ion. Hydrogen released together with a main metal reduces current efficiency and in some cases worsens appearance and properties of coatings, causing formation of spongy and powdery precipitation, pitting and other defects. If cathode potential is more negative than equilibrium hydrogen potential in a given solution, then both types of ions must inevitably be reduced. This can occur in both cases if equilibrium potential of a metal in a given solution is more negative than equilibrium hydrogen potential and if it is more positive, but a cathode is sufficiently polarized. Principle possibility of joint separation of metal and hydrogen on a cathode and quantitative ratio of these processes are determined by the course of polarization curves of metal and hydrogen, and also by the magnitude of hydrogen overvoltage on evolving metal. Thus, potential for copper extraction from acid electrolytes (for example, sulfates) is much more positive than hydrogen evolution potential, so even with significant acid concentration in an electrolyte within commonly used current densities, copper is released at a cathode with current efficiency close to theoretical one. Completely different picture is observed in electrodeposition of iron subgroup metals (Fe, Ni, Co), which are released on a cathode with large polarizaE l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 185

tion. High acid concentration in the electrolyte in this case leads to sharp decrease in current efficiency and to deterioration in quality of coatings. At the same time, electrolytic reduction of other electronegative metals such as zinc, lead, tin from acid electrolytes can proceed with theoretical or close to theoretical current efficiency because ion discharge of these metals proceeds with insignificant cathodic polarization (especially in absence of surfactants), and hydrogen evolution overvoltage on these metals is quite large. Let us consider the case when equilibrium potential of metal is more negative than equilibrium hydrogen potential (Fig. 50). Hydrogen reduction proceeds with a large overvoltage (flat curve 2), and metal with small one (steep curve 1). Such a relationship occurs, for example, in reduction of zinc from aqueous solutions.

Fig. 50. Polarization curves for the joint reduction of metal and hydrogen: 1 – Me2+ + 2e = Me; 2 – 2H+ + 2e = H2

As long as electrode potential is more positive than Hp , neither hydrogen nor metal can be reduced. If potential assumes a value lying between Hp and Me p , only hydrogen will be reduced; metal cannot be reduced yet. With poten-

tials more negative than Me p , metal and, hydrogen can be reduced. In these conditions expression jk  jMe  jH is valid. 186 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

A polarization curve depicting total current density can be obtained by summarizing the ordinates of curves 1 and 2 (dotted line ). At potential  of an operating cathode, metal will be reduced at rate measured by current density jMe, hydrogen – by jH. The graph allows us to find current efficiency: jMe т  . (529) jMe  jH Since curve 1 goes steeper upward than curve 2, an increase in polarization (shift of potential  to the right) should be accompanied by an increase in current efficiency (Fig. 50). If polarization curves for a solution of this composition are found experimentally, then a diagram similar to that shown in Fig. 50, allows us to determine quantitatively how ratio between jMe and jH will vary as potential changes. Current efficiency depends on concentration (activity) of metal and hydrogen cations. Change in their concentrations changes the values of equilibrium potentials, and, consequently, the position of polarization curves. Reduction of hydrogen ions concentration, i.e. an increase in pH of a solution, shifts Hp toward more negative values (in the diagram, to the right). This leads to an increase in current efficiency of metal. The same effect is exerted by an increase in metal ions concentration. Potential shifts in more positive direction. Participation of hydrogen cations in a cathodic reaction and in transfer of electrical charges leads to change in pH of a cathode layer. If rate of H + cations discharge exceeds rate of their arrival into a cathode layer, then the solution is depleted by H + cations, and its acidity decreases. An increase in pH of a cathode layer of a solution may lead to undesirable results. When pH reaches a value at which metal cations form a poorly soluble hydroxide or basic salt, precipitation will begin. Sediment, mixing with deposited metal, worsens its quality. To complicate change in pH of a cathode layer, substances forming a buffer systems are added to a solution. Addition of weak acids, for example, boric, or ammonium salts, pursues this exact goal. If cations H+ discharge rate is less than rate of their arrival at a cathode layer, solution acidity increases, which may lead to decrease in current efficiency, since concentration of hydrogen ions will increase. All factors contributing to equalization of solution concentration should reduce pH change of a near-cathode layer. For this purpose, stirring a solution and raising temperature are used.

E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 187

3.6.4. Joint Reduction of Multiple Metals When two metals are jointly reduced, the following relations are observed, which basically coincide qualitatively with the ones considered above for reduction of metal and hydrogen. The difference lies in the fact that reduction of two metals leads to formation of an alloy on a cathode surface. Possibility of forming an alloy at a cathode changes potential at which reduction of each metal begins. This potential shifts towards the most positive values. In other words, formation of an alloy facilitates discharge of cations. Possibility of joint electrodeposition of metals with formation of an alloy at a cathode is due to presence of certain thermodynamic and electrochemical conditions. Study of electrochemical processes has been established that simultaneous deposition of two metals on a cathode is possible under the condition that their deposition potentials are equal, i.e.  p1  1   p 2  2 . (530) From this equation it follows that equality of potentials for deposition of two metals can be achieved by varying both the values of equilibrium potentials (φρ) and polarization. The magnitude of equilibrium potential of a given metal depends both n! on activity of discharging ions  aM z   and on activity of metal at an r ! n  r ! electrode (ам), i.e. RT aM x  ln . zF aM Simultaneous solution of Eqs. (530) and (531) gives RT aM1z1  RT aM 2z 2 1  ln  1  2  ln  2 . z1F aM1 z2 F aM 2 p   

(531)

(532)

Thus, for joint discharge of two kinds of ions, certain ratios of ion activities in an electrolyte, activities of metals in an alloy, and overvoltages in the conditions of their joint deposition are necessary. Let us consider ways to change each of these factors. One way to achieve equality of potentials for deposition of metals is to change their ions activity in simple salts solutions. However, in this way only a small shift in potential can be achieved (a tenfold change in activity of monovalent ions at room temperature causes a displacement of equilibrium potential by 188 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

58 mV and divalent by 29 mV). Therefore, it is possible to use this method only if metals are being deposited together with close values of standard potentials, such as Co-Ni, Sn-Pb. A very effective way of changing ions activity can be binding them into complex ions. In this case, both change in ion activity in a solution and change in kinetic conditions of their discharge occur, i.e., equilibrium part of potential and polarization value change. Therefore, by complex formation, it is possible not only to approximate potentials for release of metals, but even to change their mutual position. This method of approaching potentials is used in practice to produce alloys, components of which are metals with significantly different standard potentials, such as Cu-Zn, Cu-Sn, Sn-Ni, Sn-Zn, Zn-Cd, Zn-Ni, Cu-Ni, Ag-Au, Cu-Au, Ag-Pb and others. The simultaneous separation of two metals can also be carried out under limiting current conditions of more positive metal. In this way, alloys of Zn-Cd and Cu-Pb were obtained from solutions of their simple salts. When studying cathode processes of copper-lead alloy deposition, it was found that fraction of current flowing into copper precipitation reaches almost the same limit value in presence of various additives (HNO3, KNO3, NH4Cl) at different values of cathode potential. The joint deposition of lead and copper occurs at potentials close to deposition potential of pure lead, and under limiting current conditions of copper. In this case, proportion of current flowing for copper evolution increases and reaches values much higher than limiting current of copper when it is separated without lead. This increase is explained by increase in solution convection at a cathode with discharge of heavy lead ions on it, as a result of which a flow of copper ions from a solution to a cathode surface increases. In this case, content of copper in sediment for a given concentration of its ions in a solution is determined by conditions of their diffusion to a cathode surface. Thus, composition of sediment under these conditions does not depend on cathode potential and can be regulated by change in current density consumed in deposition of lead. It is generally believed that production of alloys under limiting current conditions of one of the components leads to precipitation of unsatisfactory quality. It was established that quality of precipitation is determined by ratio of alloy components amounts released on a cathode. Dense, fine crystalline precipitates can be obtained only by discharging ions of more electropositive metal into a dense mass of the second. For a copper-lead alloy, satisfactory sediments were obtained at current efficiencies of at least 50 %. E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 189

The second condition for joint deposition of metals, which follows from Eq. (37), is presence of certain proportions of metals activities in an alloy. However, it must be taken into account that formation of an alloy at a cathode can also occur due to interaction between deposited metal and cathode material. In the case of deposition of metal on a liquid cathode, the depolarizing effect of cathode material is manifested continuously as a result of constant surface renewal due to diffusion of an alloy formed deep into a cathode. The magnitude of depolarization in this case, obviously, will be determined by nature of interaction that takes place during formation of an alloy. In practice, alloy formation of released metal with cathode material is realized when alkali metals are deposited on a mercury cathode and during molten salts electrolysis with liquid metal cathodes. In the case of electrodeposition of metal on a solid cathode, depolarizing action of a cathode material disappears as a result of enrichment of a cathode surface by evolving metal. The value of cathode potential in this case takes a low value at the beginning of process and then increases. The third condition is change in overvoltage values in conditions of alloy electrodeposition. State of a cathode surface during electrolysis can cause an increase or decrease in overvoltage. Thus, with joint deposition of molybdenum and nickel, an increase in nickel overvoltage was found due to enrichment of an alloy with molybdenum. Change in overvoltage with temperature can also lead to change in joint metals deposition conditions. If, at low temperatures, presence of high overvoltage in a more negative metal interferes with joint discharge of ions, then with overvoltage decrease and temperature rise, it b ecomes possible to electrodeposit an alloy. If higher voltage is characterizes more electropositive metal, an increase in temperature can lead to a shift in its potential and a violation of co-precipitation process. However, the magnitude of overvoltage will have a significant effect on potentials bias of a small number of metals released with significant overvoltage. For metals characterized by slight overvoltage (as is observed for most metals), it can be expected that under conditions of joint electrodeposition overvoltage will be small. Change in discharge conditions of ions can also be achieved by introducing surfactant into an electrolyte. Such additives in practice of galvanotechnics are used to improve quality of recovered metal. 190 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

In process of metals electrodeposition, ratio between rates of surfactants adsorption and metal release is of considerable importance. Depending on this ratio, there are two possible types of surfactants influence: 1) if rate of surfactant adsorption is less than rate of new metal surface formation, crystal nuclei can appear only on certain non-passivated sections of an electrode. In this case, polarization of an electrode varies depending on change in true current density, and remains unchanged in respect to it; 2) if adsorption rate of a surfactant is sufficiently high, discharge of ions is possible only after penetrating them through an adsorption layer, which requires an activation energy, the magnitude of which is determined both by nature of an ion and by nature of an adsorption layer. In this case, kinetics of the whole process is determined by the stage preceding actual discharge process, which explains appearance of an almost constant limiting current. Precipitation, deposited under these conditions, differs in their uniformity.

3.6.5. Anodic Dissolution of Metals In anodic polarization, non- precious metals are oxidized and, in absence of complexing agents, pass into solution as simple hydrated ions: M  M z   ze. (533) z+ During this process, concentration of M ions begins to increase at an electrode surface; some of these will diffuse into the interior of a solution, and some will be reduced again at an electrode. In steady mode of anodic dissolution of metal in a solution that does not contain molecular oxygen or other depolarizers, density of polarizing current (j) is equal to the difference between rates of the anodic ionization process (ja) and cathodic discharge of metal ions process (jс): (534) j  ja  jc or, according to the theory of slowed discharge,  zFE   zFE  z j  k1 exp  (535)   k2  M  s exp   ,  RT   RT  where  M z   stands for metal ions concentration at an electrode surface, s E – for electrode potential reckoned from reference electrode potential,  and  are transfer coefficients, with α + β = 1, k1 and k2 are rate constants of anode and cathode processes, respectively, at E = 0, i.e. at reference electrode potential. E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 191

Equations (534) and (535) do not take into account possible participation of hydrogen ions and atoms in electrode reactions, which is true, for example, for metals with high hydrogen overvoltage (cadmium, lead, etc.). Depending on relationship between the values (ja) and (jс), two extreme cases are realized during anodic dissolution: Case 1: Dissolution at nonequilibrium metal potential The case under consideration is realized when rate of metal anodic ionization process significantly exceeds rate of metal ions cathodic discharge, i.e. (536) ja  jc ; ja  j. If condition (536) is satisfied, equation (535) can be simplified and goes into  zFE  j  k1 exp  (537) , RT   from which we obtain an expression for potential, which coincides with the Tafel equation E

RT RT ln k1  ln j  a  b lg j. zF zF

(538)

The coefficient b = 2,3RT / βzF in equation (538) at 25 °C, (z = 2,  = 0,5) is equal to 0,059 V. The given value of the constant b is characteristic for metals that dissolve at potentials substantially displaced from equilibrium potential of metal given. In such metals processes of discharge-ionization correspond to large activation energies or, in other words, M/Mz+ systems with small exchange currents. This group of metals includes iron, cobalt, nickel and chromium. Case 2: Dissolution at almost equilibrium metal potential The case under consideration is realized when rates of metal anodic ionization process and the opposite cathodic process far exceed density of polarizing current i, i.e. at practical equality of cathode and anode processes rates: (539) ja  j; ja  jc  jo . In this case, metal ions transition to a solution proceeds under conditions very close to equilibrium. Condition (539) is satisfied in case of small activation energies of metal discharge-ionization processes, i.e. in case of M/Mz+ systems with high exchange currents. This group of metals includes cadmium, lead, and metals amalgams. When condition (539) is satisfied, equation (535) can be written in the form:

 zFE0   zFE0  z k1 exp    k2  M  s exp   , RT RT     192 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

(540)

where E0 is metal electrode equilibrium potential. Solving equation (540) with respect to E0 with the condition α + β = 1, we obtain the well-known expression for metal electrode equilibrium potential: E0  E '

RT ln  M z   , zF

(541)

where E ' stands for so-called formal potential of the system M/Mz+, equal to RT (542) E ' E  ln f M z  , zF Where E0 is standard potential of the system M/Mz+, and f M z  is activity coefficient of Mz+ ions in a solution. With reversible electrochemical stage and slow removal of metal ions into a solution, anodic current density under steady-state conditions is equal to rate of metal ions diffusion into a solution, expressed in electric units, i.e. D  M Z     M z   , , ja  zF (543) s o  where ja stands for anodic current density, z is number of transferred electrons, D is diffusion coefficient of metal ions,  is diffusion layer thickness,  M Z  





s

and  M z   is concentration of metal ions at an electrode surface and in soluo

tion volume, respectively. From the equation (543) we obtain j  M Z     M z    , (544) s o K i.e. metal ions concentration at an electrode surface increases linearly with increasing anodic current. If concentration of metal ions is expressed in mol/l, then constant K in equation (544) will be equal to

D . (545)  Substitution of the expression for metal ions concentration at an electrode surface from equation (544) into equation (541) leads to expression RT  j E0  E ' ln   M z     . (546) 0 zF  K If metal being polarized is in a solution of an indifferent electrolyte that does not contain substantially ions of a metal being studied, then this expression is simplified K  103 zF

E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 193

RT RT (547) ln K  ln j. zF zF Thus, in anodic dissolution of metals in a solution that does not contain metal ions, according to Eq. (547) between E and lnj, a linear relationship with angular coefficient b = RT / zF of 0,029 V at 25 ° C and z = 2 (in difference from electrochemical polarization, considered earlier, when b > 0,029 V) should be observed. If metal ions are present in an initial indifferent electrolyte, whose concentration in solution volume is [Mz+]o, then, according to equation (546), a linear dependence with angular coefficient b = 2,3RT / zF in coordinates E – log ([Mz +] O + j / K) should be observed. Polarization dependencies in dissolution of metals can take many forms. Fig. 51 shows total anodic polarization curve for the case of metal passivation. E0  E '

Fig. 51. Full anodic polarization curve: I – active dissolution; II – transition to a passive state; III – passivity; IV – re-passivation; V – release of oxygen

This dependence initially has an area of increasing current density, characteristic for metal active dissolution. After reaching a certain potential, called critical passivation potential п, there is a sharp decrease in current. This effect is due to formation of protective layers of particular nature on a metal surface. The phenomenon of inhibition of metal dissolution during its anodic polarization is called passivation.

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Dissolution of passive metal is characterized by a relatively low rate in a wide range of potentials. The next rise in current with more positive potentials is usually associated with the initiation of another electrode reaction. Such a reaction can be transition of metal into a solution to form ions of another valence or water molecules oxidation to oxygen (or, in general case, solvent molecules oxidation). Renewal of growth is called metal re-passivation. An ability to pass into a passive state is most clearly expressed in transition metals, which is undoubtedly associated with their specific chemical and adsorption properties. For all these metals, dependence of dissolution rate on potential is the same. Only the values of critical parameters are changed: critical passivation potential and corresponding critical dissolution rate, dissolution rate in a passive state, and transition into re-passivation region potential. At even higher potential, the process of hydroxide ions oxidation and oxygen release becomes possible: 4OH  2H2O  O2  4e . This corresponds to the region fg. In the active dissolution region, metal atom escape from a crystal lattice, as in its precipitation, must be accompanied by certain difficulties leading to a phase overvoltage associated with destruction of a crystal lattice. The fracture of this overvoltage in total overvoltage is almost always small. The main kinetic regularities of anodic dissolution are determined by slow ionization stage. The process metal dissolution at high current densities is complicated by diffusion difficulties, while cation concentration at an electrode surface increases. Sometimes this increase is so high that it can exceed solubility product of the salt, which then hits an electrode surface, forming a non-conductive film, and process rate decreases. This phenomenon is called salt passivation of an electrode. At a significant fracture of concentration polarization in dissolution kinetics equation, appropriate corrections must be made for change in cation concentration at an electrode surface. When metal dissolves in solutions of electrolytes that do not contain metal cations, an overvoltage associated with slowness of cation diffusion stage following an ionization reaction can be observed. It follows from the principle of micro-reversibility of an electrode process that near equilibrium potential both in cathodic and anodic processes, one and the same stage should be slowed. Therefore, if slowed stage in a multistage process is transfer of one of the electrons in a cathodic process, then this same stage limits the reaction rate durE l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 195

ing an anodic process as well. Consequently, the Tafel sections of polarization curves must intersect at equilibrium potential. This restriction is removed at a certain distance from equilibrium potential. Rate and mechanism of metal anodic dissolution strongly depend on solution composition. Anionic composition and pH of a solution play an important role in reactions kinetics. The effect of anions on anodic dissolution mechanism can be basically reduced to two factors: a change in structure of a double layer upon their adsorption and formation of complexes both in bulk solution and on an electrode surface. Ions of halides exert a particularly strong influence on ionization rate of metals such as Fe, Ni, Co, Mn, Zn, Cd, Bi, In and Ta. An increase in concentration of an anion above the critical one leads to a sharp increase in rate of an anode process. Anions take a direct part in an electrode reaction or in chemical stages preceding it. During dissolution of many metals, especially iron subgroup ones, solution acidity plays a decisive role. This is due to the fact that hydroxocomplexes of metals participate in an electrode reaction. Rate of metal anodic dissolution depends on nature and concentration of surfactants present in an electrolyte. Mechanism of their action is similar to that considered in the case of electrodeposition of metals.

3.7. MOLTEN SALTS ELECTROCHEMISTRY

Electrolysis of molten salts is widely used to produce light, refractory, rare metals, alloys, fluorine, and chlorine, and for metals refining. In production of metals and non-metals that cannot be evolved from aqueous solutions (alkali and alkaline earth metals, beryllium, magnesium, boron, aluminum, lanthanides, silicon, titanium, zirconium, hafnium, vanadium, niobium, tantalum, tellurium, molybdenum, tungsten), molten salts electrolysis is the main method. Importance of molten salts electrolysis for production and refining of heavy fusible metals such as indium, tin, lead, antimony, bismuth, etc. is increasing. The use of molten salts electrolysis is very promising for production of alloys and compounds, as well as for application of galvanic coatings and metal surface treatment. 196 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

Electrolysis of molten salts has several advantages over aqueous solutions electrolysis: – high intensity of process, which can 25–100 times exceed aqueous solutions electrolysis intensity; – ability to work in a wide range of temperatures and electrolyte concentrations; – significant reduction in water consumption. At the same time, high-temperature electrochemical processes for metal production are associated with a significant specific energy consumption, increased capital and operating costs for environmental protection, especially in molten fluorides and chlorides electrolysis.

3.7.1. General Characteristics of Molten Salts Individual molten salts. For large number of individual molten salts, information on the structure obtained by direct structural studies (X-ray diffraction, neutron diffraction, spectroscopic methods) is available to date. From the results of structural studies it follows that forces of attraction between ions of opposite signs and repulsive force between particles of the same charge sign are very large. Therefore, the closest neighbors of a cation should be anions and vice versa. Another important conclusion that follows directly from the results of structural studies is that cation-anion distance decreases upon melting. Mixtures of molten salts. Depending on number of components and ion charge, the following groups of salt mixtures can be distinguished: 1) Binary systems with symmetric charge and common ion: systems where all ions have the same charge (NaCl-KCl, NaBr-NaCl); 2) Binary systems with an asymmetric charge and a common ion (MgCl2-MgSO4; Na2SO4-MgSO4); 3) Mutual systems in which two salts that do not have a common ion form a melt with four ions (triple mutual systems): systems where ion charge is symmetric (KCl-NaBr); A system in which ion charge is asymmetric (NaCl-AlBr3); 4) Triple systems formed from three salts with a common anion (LiClNaCl-KC1, KC1-NaCl-MgCl2), or with a common cation (LiBr-LiCl-LiF); 5) More complex systems. These include mutual systems that form a melt with a number of ions of more than four, as well as four-component systems with a common anion or cation. E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 197

In addition to structural and spectroscopic studies, information on physicochemical and thermodynamic properties of molten salt mixtures, such as molar volume, viscosity, enthalpy of mixing, and electrical conductivity are important for the ion melt study. Molar volume. Molar volume of individual salts. Molar volume of individual salts depends on number of ions in a molecule, their size and type of bond. An increase in covalent bond fraction leads to decrease in density and, correspondingly, increase in molar volume. Salts that have an ionic structure usually have higher density and smaller molar volume than salts with a molecular crystal lattice. Transition from LiCl with a predominantly ionic bond to BeCl2 is accompanied by an increase in molar volume of more than 24 cm3, which cannot be explained only by appearance of the second chlorine ion. Large molar volume has such molecular compounds as BCl 3, AlCl3, GaCl3. In the series of alkali metal chlorides, molar volume naturally increases with increasing radius of an alkali metal ion. Difference in molar volumes between potassium and calcium chlorides, rubidium and strontium, cesium and barium is small. Presence of the second chlorine ion is compensated by increase in coulomb interaction of a doubly charged ion. Molar volume of binary mixtures. A change in molar volume (VM) during formation of binary mixtures is of great interest. For ideal systems, molar volume is additive property if composition of a system is expressed in molar fractions: VM(ind). = X1V1 ° + x2V2 °, ΔVM = 0, where V1 °, V2 ° are molar volumes of pure components. In the general case, during formation of molten salt solutions, expansion, contraction, and subordination to the additivity rule are observed. In some cases positive-negative deviations from ideal behavior are noted. Analysis of experimental data shows that for salt systems, diagrams whose states are eutectic type or are characterized by formation of a continuous series of solid solutions, isotherms of molar volumes are close to additive straight lines. In the case when congruentlymelting compounds are formed in a system, significant deviations from ideal behavior are observed (both positive and negative). An example of solutions with a significant negative deviation of molar volume is a NaF-AlF3 system. Near the composition corresponding to a Na 3AlF6 compound, a minimum molar volume (maximum density) is observed. In systems PbCl 2-KC1, CdCl2-KC1, ZnCl2-KC1, BaCl2-KC1, CaCl2-KC1 and others, in which unstable compounds are formed, positive deviations of volume from additive values are noted. For vast majority of binary salt systems with a strong interaction between components, volume change is positive. This fact essentially 198 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

distinguishes salt systems from metallic ones, in which formation of intermetallic compounds, as a rule, is accompanied by compression. Viscosity and fluidity of molten salts. Viscosity is one of the most important technological characteristics of electrolyte, it must be known for evaluation of mass and heat transfer in reactors and cells. Viscosity of molten salts varies over a wide range; it increases by several orders of magnitude upon transition from alkali halides to silicate melts. Viscosity of alkali metals molten halides and their mixtures is close to viscosity of water and aqueous solutions. Features of vapor state of salt systems. Thermodynamic properties of steam in equilibrium with salt phase are characterized by number of features. An elementary particle of saturated vapor is a molecule. At equilibrium, transition of salt from liquid to the vapor state and vice versa is accompanied by a rearrangement of its structure: ions or ion complexes (liquid phase) give molecular forms (pairs). The reverse phenomenon is observed in transition from the vapor state to the liquid state. Such restructuring is associated with significant energy changes. The boiling point and enthalpy of evaporation for typical molten salts are large. A change in entropy remains constant. For many salts, the vapor state is the only state in which an elementary structural unit is a molecule. For molten salts, association in a vapor phase is very intrinsic. The most typical type of association is dimerization. Trimers and more complex molecular forms are characteristic mainly for molecules containing light cations (lithium) or anions (fluorine). In series of one group halides, association decreases upon transition to an element of a higher period. In two- and multicomponent systems, in addition to molecular forms characteristic of pure components, one should expect formation of complex molecules: LiNaF2 in the LiF-NaF system, NaAlCl4 in the NaClAlCl3 system. Along with molecular forms, there are a number of ions in saturated vapor over molten electrolytes: simple (A+, X–), complex (A2X+ AX2–) and heavy (A3X2+, A2X3–) ions. The predominant are complex ions.

3.7.2. Electrochemical Thermodynamics of Molten Salt Systems Classification of electrochemical circuits Electrochemical circuits with molten salts can be divided into two main groups – chemical and concentration ones. In the first case, a current-forming process is associated with interaction of pure components and formation of a E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 199

corresponding salt, in the second it is due to concentrations difference of a corresponding component in half-elements of a circuit. Chemical circuits with individual molten salts. The simplest chemical circuit is a circuit with one salt as an electrolyte (a formation circuit) in which electrodes are placed: metal and gaseous, which is carbon, saturated with gas and washed with gas bubbles. For example: (548) Pb PbCl2 Cl2 , C . On electrodes, reactions occur Pb  Pb2  2e,

(549)

Cl2  2e  2Cl . (550) A total current-forming process in a circuit is a salt formation reaction: (551) Pb + Cl2 = PbCl2 , which proceeds reversibly if external resistance has an infinitely large value. In this case a system is in equilibrium, and EMF has a maximum value. Thermodynamic characteristics of reactions based on an EMF measurement and its temperature coefficient are determined using the usual ordinary (418), (419). For compounds existing at a given temperature in the liquid state, the melt saturated with this compound state is taken as a standard state. Thus, a standard state is chosen for oxides solutions in molten salts, for example, alumina in cryolite. Chemical circuit with molten salt mixtures. Typical examples of such circuits are as follows:

Pb PbCl2 , LiCl Cl2 , C;

Ag AgI, KI I2 , C.

(552)

As in the previous case, a current-forming process is MXz (PbCl2, AgI, etc.) salt formation reaction from pure metals and halogen, but this one flows in a mixture. If MXz is considered as the component 1, and an alkali halide is the component 2, then for equilibrium conditions we can write: (553) G1   zFE ,

S1  zF

E , T

(554)

E . (555) T The values G1, S1, H1 characterize one mole of compound MXz formation in a mixture of composition given. Let us consider the following scheme: H1   zFE  zFT

200 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

Thermodynamic characteristics of process I are calculated from measured EMF of a circuit with a molten salt mixture ( G1, S1, H1 ). Process II corresponds to standard values for this compound formation  G1 , S1 , H1  ,

obtained from EMF measurements of a circuit with an individual electrolyte. Process III reduces to transfer of a mole of matter from a pure state to a melt of a given composition. Thermodynamic characteristics of this process are par-





tial molar values for component 1 G1 ,  S 1 ,  H 1 , which can be calculated using the combination of equilibria and the Nernst equation for EMF: G1  G1  G1   zF  E  E   RT ln a1;  dE dE   S 1  S1  S1  zF   ; dT dT  

(556) (557)

 dE  dE (558)  H 1  G1  T  S 1  zF  T  E T  E ; dT dT   zF (559) ln a1   E  E , RT where a1 stands for activity of component 1 in a salt mixture. Concentration circuits. In circuits composed of salt solutions with different salt concentrations in semi-elements, for example, in ()

Ag AgNO3 ,(NaNO3 ) AgNO3 ,(NaNO3 ) Ag

( )

,

(560) a1 a2 when isothermicity condition for the entire circuit is fulfilled, potential di fference between electrodes or EMF of a circuit is due to different activity of potential-determining ions or a salt of potential-determining ions in halfcells. In this case it is Ag + or AgNO3. If a1  a2 , then, according to the Nernst equation, potential of the left electrode is more positive than the right one. E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 201

Neglecting diffusion potential at a boundary of melts, EMF of such a circuit can be expressed by the equation RT a1 E ln  0. (561) zF a2 When electrodes are shorted to an external resistance in a circuit, current from the left electrode to the right one will flow through an external circuit. At the same time, silver is oxidized on the right electrode and passes into solution, as a result of which, activity of silver nitrate in the right semi-element increases. On the left electrode, silver is being recovered, as a result of which activity of AgNO3 in the left half-cell decreases. Thus, current-forming process is transition of AgNO3 from a solution with a higher concentration into a solution with a lower concentration. Current will flow, decreasing from the maximum value to zero, until AgNO3 activity in both half-cells, and, consequently, electrodes potentials become equal, and EMF becomes zero.

3.7.3. Reference Electrodes and Rows of Potentials Basic requirements for reference electrodes. A choice and construction of reference electrodes for molten salts is associated with certain difficulties. Basic requirements for a reference electrode are as follows: stability and reproducibility of its potential, ease of manufacture, reliability in operation. High temperatures and aggressive melts do not always fulfill these requirements. Electrochemistry of ionic melts, unlike electrochemistry of aqueous solutions, does not have universal reference electrodes. Number of reference electrodes proposed for studying molten salts is large. A choice of this or that electrode is carried out taking into account specific conditions of an experiment. A reference electrode with surrounding electrolyte is usually encapsulated, i.e. immersed in a test medium in a separate vessel. Electrical contact is carried out by means of porous diaphragms or solid electrolytes with cationic or anionic conductivity. Chlorine reference electrode. When measuring electrode potentials in chloride melts, a chlorine reference electrode can be used. This electrode is reversible with respect to an anion, potential-determining equilibrium: С12 + 2е ↔ 2С1-. In cases where an electrolyte of a chlorine electrode is cationically different from melt in which metal is to be found, it is necessary to separate electrolytes with porous diaphragms. A resulting potential jump (diffu202 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

sion potential), as a rule, is small and lies in a range from 10–4 to 10–3 V. If the value of EMF is measured to within 10-3 V accuracy, diffusion potentials can be ignored. A chlorine reference electrode is a narrow quartz tube with a hole in a bottom that is covered by a porous asbestos diaphragm. Chlorine is fed through a dense carbon tube with a tip of spectrally pure graphite immersed in a molten chloride electrolyte. Graphite is a more porous material than coal. This provides better chlorine adsorption and potential stability. At the same time, tubes are easier to manufacture from coal, which has greater mechanical strength. The eutectic mixture LiCl-KCl (Tm = 634 K) or the equimolar mixture KC1-NaCl (Tm = 933 K) is most often used as an electrolyte in chloride electrodes. In molten salts electrochemistry, it is conventionally accepted for all chloride melts at any temperatures to regard activity of chlorine anions equal to 1. The main disadvantage of a chlorine electrode is necessity to have or continuously obtain gaseous chlorine. It is easier to work with different metal reference electrodes. Lead reference electrode. One of the simplest in a constructive way is a lead reference electrode. Lead refers to number of low-melting metals (Tm = 600 K), has a fairly low vapor pressure. As an electrolyte, pure PbCl2 (Tm = 772 K) can be used. However, solutions of PbCl2 in alkali metal chlorides (mixtures of LiCl-KC1, KCI-NaCl) are more often used. Solubility of lead in molten PbCl2 is relatively small; at 873 K it equals 0,020 mol. % and at 973 K – 0,052 mol. %. An addition of alkali metal chlorides to PbCl2 leads to a decrease in solubility of lead. A solvent in a reference electrode should be the same as in the system under study. An electrode is reversible with respect to a cation, potential-determining equilibrium is as follows: Pb ↔ Pb2+ + 2e. A lead reference electrode is used in a study of chloride melts; electrode potential is much more negative than potential of a chlorine electrode. Reference electrodes for fluoride melts. Due to high aggressiveness of molten fluorides, it is difficult to select a sufficiently stable structural material for a reference electrode. Recently, boron nitride in a compact state in the form of finished products and in the form of compacted compositions has been used for this purpose. A reference electrode for fluoride melts consists of nickel wire, a cylinder of boron nitride, an inner cylinder of pyrolytic boron nitride, an electrolyte from an eutectic mixture of NaF-NiF2, and a plug from a mixture of boron nitride and sodium fluoride (20 wt.% of NaF). A correct choice of a reference electrode, stability and reproducibility of its potential are extremely important for thermodynamic and kinetic studies of processes on liquid and solid electrodes in molten electrolytes. E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 203

Rows of metal potentials in molten salts. For aqueous solutions, an electrochemical row is based on the values of standard electrode potentials. In ionic melts electrochemistry, everything is much more complicated. For individual substances (halides, oxides), rows of potentials can be compiled from the values of standard EMF, which are either directly measured or calculated on the basis of thermodynamic data. In practice, more often than not individual molten salts are used, but their mixtures (solutions of salts in various solvents). Typical solvents: LiCl-KC1, KC1-NaCl, KC1-NaCl-MgCl2. Nature of a salt phase, its cationic and anionic composition, have a great influence on metal equilibrium potentials. For example, EMF measurements of circuits with metal and chloride electrodes showed that activity coefficients of potential-determining cations decrease as a radius of alkali metal ions in a row of their molten chlorides from LiCl to CsCl decreases, and equilibrium potentials of corresponding metals become more electronegative at the same temperatures and concentrations. A similar phenomenon is observed in bromide and iodide melts. Each solvent requires its own row of potentials. For molten salts it is intrinsic that for a large number of compounds there is neither experimental nor calculated data on the value of standard EMF. Practically only relatively dilute solutions of such compounds in various solvents can be studied. Chloride melts are used for production, refining, separation of metals such as titanium, zirconium, hafnium, thorium and beryllium. Melted chlorides of these metals of ordinary oxidation degrees are highly volatile, so they often work with dilute solutions in alkali or alkaline earth metal chlorides released at a cathode at more electronegative potentials. In real systems, the area of such dilutions can be identified, when Henry's law is fulfilled, and activity coefficient of a dissolved component remains constant. This area is determined by individual features of a system, nature of an interaction between components and depends on accuracy of determining activity coefficient. The lower accuracy of activity coefficient determination, the wider composition range where Henry's law is observed. In connection with peculiarities of molten salt electrochemical behavior, it is necessary to introduce the concept of conditional standard potential (φ*). The value of φ* can be considered as a standard electrode potential of a metal with respect to its ions in a given salt medium. If φ is a quantity that does not depend on solvent salt and characterizes only nature of dissolved salt, then φ* depends on nature of a solvent and takes into account an interaction of dissolved salt with medium. The values of φ° and φ* become identical only if dissolved salt forms an ideal solution with a solvent. 204 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

Table Electrochemical rows of metals in molten salts Solvent

Temperature, K

Individual fluorides 1273 NaF-KF Individual chlorides LiCl-KCl

1073 723

NaCl-KCl NaCl-KCl-SrCl2 NaCl-KCl-MgCl2

973

723

Individual bromides NaBr-Kbr Individual iodides NaI

973

Electrochemical rows Ba, Sr, Ca, Na, K, Mg, Li, Al, Mn, Cr, Co, Ni, Fe, Cu, Ag Na, Mg, Li, Al, Mn, Zn, Cd, Ce, Pb, Co, Ni, Bi Ba, Sr, K, Li, Na, Ca, La, Mg, Th, Be, Mn, Al, Tl, Zn, Cd, Pb, Sn, Ni, Co, Hg, Bi, Sb Li, La, Mg, Th, Hf, Mn, U, Zr, Al, Be, Ta, Ti, Zn, Tl, W, Cd, Mo, V, Ga, In, Co, Ni, Ag, Sb, Bi, Hg, Cu, Pd, Pt Mg, Th, U, Mn, Hf, Al, Zr, Ti, Zn, Tl, Cr, Fe, Pb, Sn, Co, Cu, Ni, Ag, Pb, Pt, Au Na, Be, Mg, Al, Tl, Zn, Cd, Pb, Sn, Cu, Co, Ni, Ag, Hg, Bi Na, Be, Al, Mn, Zn, Cd, Fe, Pb, Cr, Sn, Co, Ni, Ag, Cu, Pd, Pt, Au Ba, K, Sr, Li, Na, Ca, Mg, Mn, Fe, Al, Zn, Cd, Pb, Sn, Ag, Cu, Co, Hg, Bi, Sb Na, Ca, Mg, Be, Tl, Zn, Al, Cd, Pb, Co, Sn, Ag, Cu, Ni, Hg, Hg, Bi Na, Mg, Mn, Tl, Zn, Cd, Al, Ag, Sn, Pb, Cu, Bi, Hg, Co, Sb Na, Mg, Tl, Be, Zn, Cd, Al, Ag, Sn, Cu, Pb, Co, Ni, Hg, Bi, Sb

The practical use of this concept is beyond doubt. By the values of conventional standard potentials, it is easy to calculate ion discharge potentials in a region of dilute solutions. The rows of metal potentials, compiled using conditional standard potentials for various salt media, are the only rows of potentials for molten salts that have real practical significance. The values of conventional standard electrode potentials for a number of metals in a molten eutectic LiClKC1 mixture can only be determined experimentally, from EMF measurements of corresponding circuits. A comparison of the values φ° and φ* allows one to obtain information on limiting activity coefficient of dissolved salt. On the basis of information on values φ°, rows of potentials in individual molten salts are constructed, and with help of values φ* – in various solvents (Table). Each subsequent metal in the row has a more positive potential value.

E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 205

3.7.4. Kinetics of Electrode Processes in Molten Salts Features of electrochemical kinetics in molten salts. For kinetics of electrode processes in ionic melts, a number of features are inherent: – high speed of all electrode reaction stages, due to the fact that processes usually occur at temperatures of 500–1500 K; – high values of exchange current for discharge-ionization reactions involving metal ions and, as a result, a very small amount of electrochemical overvoltage, especially for processes on liquid electrodes; – various depolarization processes, typical for electrode reactions in ionic melts; – the phenomenon of metal dissolution in a salt phase or appearance of ions with different degrees of oxidation; – a specific phenomenon, called the anode effect, often accompanying the electrolysis of ionic melts with release of gaseous substances on the anode, – high chemical activity of molten salts, which complicates selection of structural materials and can lead to side reactions that significantly affect kinetics of the main process. At present, it is customary to distinguish between the following types of electrode polarization (overvoltage): activation polarization (transition overvoltage) associated with difficulties in transferring a charge carrier through a double layer from one phase to another; concentration polarization (diffusion overvoltage), caused by difficulties in substance delivery an electrode surface or removal of reaction products; phase polarization (crystallization overvoltage), associated with difficulties in electrocrystallization of metals; ohmic polarization (ohmic overvoltage), caused by resistance of an electrolyte and formation of oxide and other films with low conductivity on electrodes. Sometimes polarization is also recognized, due to occurrence of any chemical reactions, rate constants of which do not depend on electrode potential (reaction overvoltage). Total polarization observed experimentally consists of individual components, each of which can have a greater or lesser value. Activation polarization. This kind of polarization in ionic melts is observed when electrolysis is accompanied by formation of gaseous products. In all other cases, activation polarization is very small; electrodes behave almost like reversible systems that obey the laws of equilibrium thermodynamics.

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Concentration polarization. For deposition of metals on cathodes, concentration polarization is very typical, caused by a limited rate of reactant delivery to an electrode surface. A mathematical description of this type of overvoltage is based on the idea of diffusion layer presence at an electrode surface. Matter transfer within this fixed layer can be carried out only by diffusion. Concentration polarization is also observed during anodic dissolution of metals. Content of dissolved metal ions in a diffusion layer near an anode will be higher than in volume of an electrolyte. Phase polarization. Process of metal continuous layer formation on a substrate during electrolysis includes stages of crystal nucleation, growth before merging into a continuous layer, and growth of a crystal collective in a continuous layer. At high temperatures, metal deposition on a substrate is usually complicated by alloying. In order for a substrate to be indifferent, it must be covered with an oxide film or made of metal, diffusion coefficient of deposited metal in which is very small. In this case, it is possible to observe experimentally the value of phase polarization, which should be defined as polarization (overvoltage) necessary for new phase formation on a foreign cathode. Numerically, value Ф is equal to difference in equilibrium potentials of macrocrystals and crystal critical nucleus. Depolarization. Appearance of a new path of electrode process, which ensures a reaction proceeds at a higher rate, can reduce electrode potential, which may even be less than reversible potential. This decrease in electrode potential and process that determines it are called depolarization. Depolarization in alloy formation. The phenomenon of depolarization accompanies processes of alloy formation on liquid and solid electrodes. If deposited metal forms an alloy with cathode metal, a shift in deposition potential toward more positive values is observed. Ion discharge and alloy formation represent a single electrochemical act, for example: Na+ + Pb + e  (Na-Pb) (alloy). Depolarization value depends on activity of released metal, i.e. it is determined by thermodynamic properties of an alloy. A depolarizer of an anodic process, as a rule, is a metal dissolved in an electrolyte and interacting with anodic products. Dissolution of metals in molten salts. When obtaining a number of metals (aluminum, magnesium, lithium, sodium, calcium), the question of metal solubility metals in a salt phase is of great importance and is directly related to kinetic characteristics of processes and electrolysis efficiency. An ability of metals to dissolve in an electrolyte is one of the main reasons for reduction in current efficiency and deterioration of electrolysis perfo rE l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 207

mance. Solubility of metals in molten salts depends on nature of metal and salt, composition of metal and salt phases, and temperature. Large mutual solubility is observed in systems formed by sodium, potassium, rubidium, cesium with their molten halides. Because of large differences in nature of the systems formed by molten salts and metals, there is no single point of view on nature of metal solutions in their molten salts. The most common approach considers a solution of metals in molten salts as ion-electron fluids. The following main types of interaction between components in metalsalt systems can be distinguished: dissolution of metals with their subsequent ionization; dissolution of metals to form dimeric or more complex ions; dissolution of metals with ions of lower valence formation. Only some systems can be assigned to a particular type with sufficient certainty. The other metal-salt systems occupy an intermediate position. Anode effect. In molten salts electrolysis on a gas-evolving electrode, under certain conditions, a disturbance of electrode process normal mode can occur, consisting in a sudden and sharp increase in resistance at an anodeelectrolyte interface. The resulting gas film breaks an electrical contact. Passage of an electric current becomes possible only as a result of short-term ruptures of the film or its electric breakdown. All this is accompanied by a sudden increase in voltage and a drop in current. Temperature of an electrode and adjacent layers of an electrolyte increases. This phenomenon was called an anode effect and is intrinsic of all halide melts, as well as cryolite-alumina and other molten electrolytes. An anode effect is also observed in aqueous solutions of electrolytes during evolution of gaseous products. The most important electrochemical characteristics of an anode effect are critical current density and anode potential at which the effect occurs. Despite the large number of studies devoted to an anode effect, its nature and the causes of its origin have not been fully elucidated. The hypothesis of surface compounds formation during electrolysis, for example, (CF)n, which insulate a surface of an electrode and determine its non-wetting, cannot be extended to all cases of an anode effect. One of the reasons for an anode effect is hydrodynamic instability of a nearelectrode gas-liquid layer, which leads to a transition from bubble to film mode gas evolution. Current efficiency of molten salts electrolysis. In molten salts electrolysis, current efficiency is determined mainly by amount of metal loss from a cathode surface. The process of metal loss consists of stages as follows: – dissolution of metal in an electrolyte; – transfer of dissolution products through a cathode diffusion layer; 208 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

– transfer of dissolution products through an electrolyte to an oxidation zone; – oxidation of dissolved metal by anodic gases, by air oxygen, or electrochemically on an anode surface. Each of these stages depends on many factors: solubility of metal in molten electrolyte, kinetics of metal dissolution and its oxidation, solubility and kinetics of gas dissolution in electrolyte, physicochemical properties of electrolyte and electrolyte velocity in a cell. These factors, in turn, depend on temperature, current density, cell design. Another reason for the reduction in current efficiency is joint discharge of several types of ions. In a deposition of alkali, alkaline earth and light metals from molten salts, cations of these metals co-exist with cations of electropositive elements, for example, iron, copper, zinc, hydrogen, etc. A discharge of these cations is inevitable; therefore it is necessary to avoid electrolytic cations entering electrolyte or to provide a cleaning of electrolyte from them. A joint discharge can occur with metal cations more electronegative than cations of metal being deposited, for example, potassium, sodium, calcium, barium, etc. They are introduced into electrolyte in the form of salts and provide necessary physicochemical properties of the electrolyte. A joint discharge occurs when cathode potential reaches a discharge value of these more electronegative cations. This is possible if there is a concentration polarization caused by depletion of electrolyte by ions of base metal. Alloy formation at a cathode shifts potential of the impurity metal to more positive side, and then a joint discharge also becomes possible. A decrease in current efficiency during molten salt electrolysis can also be associated with mechanical losses of metal, with leakage of current through side walls, with cathode and anode shorts, with presence of electronic conductivity of electrolyte, with chemical losses caused by metal oxidation with oxygen and air moisture or other oxidants. Current efficiency depends on many factors: temperature, current density, interelectrode distance, cell design, and electrolyte composition. An increase in temperature, as a rule, leads to a decrease in current efficiency, since with increasing temperature solubility of metal in electrolyte increases, a diffusion processes are accelerated, convective currents become stronger, oxidation rates of dissolved metal increase. An excessive decrease in temperature of electrolyte is also not permissible, since it leads to an increase in viscosity of electrolyte, to mechanical losses of metal and, ultimately, to a reduction in current efficiency. E l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 209

To reduce the melting point of electrolyte, it is advisable to add salt additives (usually chlorides and fluorides of alkaline and alkaline earth metals) having more negative cations than metal deposited. For example, in aluminum production to cryolite-alumina melt, calcium and magnesium fluorides can be added. The value of additives is not only in reducing the melting point of electrolyte, but also in changing other physical and chemical properties. So, additives reduce solubility of metal in electrolyte, which increases current efficiency. An increase in current density leads to an increase in current efficiency to a certain limit, which depends on circulation rate of electrolyte, which is mainly related to an amount of anode gases evolved. Too high current density increases a voltage drop in an electrolyte layer and increases power consumption. In addition, with an increase in cathodic current density, anodic current density also increases, which leads to appearance of an anode effect. If current density is too high, side processes may occur, for example, evolution of impurities along base metal at a cathode. An increase in interelectrode distance affects current efficiency similarly to an increase in current density, i.e. current efficiency increases to a certain limit. This dependence is explained by the fact that as distance between electrodes is increased, transfer of dissolved metal from a cathode to an anode by diffusion and convection is hampered by elongation of the path for metal movement. At the same time, concentration gradient of dissolved metal and electrolyte circulation velocity decrease with a large volume of melt driven by the same number of anode gases. As a result, an absolute loss of metal decreases and current efficiency increases. With an increase in interelectrode distance, cost of electricity increases and electrolyte can be overheated, which adversely affects current efficiency.

Control Questions and Tasks 1. The dissociation constant of the weak base is 1,5 ∙ 10–5. The pH of this solution at 298 K is 9,86. Determine the degree of dissociation of the electrolyte. 2. The dissociation constant of a weak monovalent acid is 1,5 ∙ 10–5. At what pH of the solution will the degree of dissociation be 1,5 %? 210 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y

3. Determine the equilibrium constant and E for the reaction 2Au + 4CN– + 0,5O2(aq) + H2O = 2Au(CN)2– + 2OH–, using the following data: 1) Au – e + 2CN- = Au(CN)2–;  = 0,543 V, 2) H2O + 0,5O2 + 2e = 2OH–; G2  77,5 kJ , 3) 0,5O2(aq) = 0,5O2(gas);

G3  8,25 kJ .

4. Determine, what reaction is more probable: 2Au + 4CN– + 0,5O2(aq) + H2O = 2Au(CN)2– + 2OH– or Au2S + 4CN– = 2Au(CN)2– + S2–. Use the results of the previous task and the following data: 1) Au – e + 2CN– = Au(CN)2–;  = 0,543 V, 2) 2Au + S2– – 2e = Au2S, G2  82,4 kJ . 5. Calculate the concentration (g/dm3) of silver carbonate in an aqueous solution if the equilibrium constant of the reaction Ag2CO3 = 2Ag+ + CO32– at 298 K is K = 7,8∙10–12. 6. What processes will take place on the cathode and the anode of the element, the scheme of which is given below, and what is its EMF equal to at 298 K? Al | Al(NO3)3 || AgNO3 | Ag 0,01 M 0,005 M 7. The solubility product of AgCl at 298 K is 10–10. Calculate EMF of the galvanic cell: Cl–|AgCl(s)|Ag and the change in Gibbs energy upon formation of AgCl. 8. How long does one need to pass a current of 1,5 A through a 0,1 N solution of CuSO4 to completely extract the metal from the 300 ml solution? The current efficiency is assumed equal to 90 %. 9. Calculate the decomposition voltage of Al2O3 for aluminium reduction 3 cell with inert anode if for the reaction 2Al  O2  Al2O3 2 G1220 K  1 243 kJ/mole . What will be the energy efficiency if the current efE l e c t r o m e t a l l u r g i c a l P r o c e s s e s | 211

ficiency is η = 95%, and the voltage in the cell is 4.5 V? What will these characteristics be for a cell with a carbon anode (G f ,1 220K(CO)  223 kJ/mole , G f ,1220K (CO2 )  395 kJ/mole) ?

10. During the electrolysis of a copper sulphate solution during 5 hours, 10 g of copper and 1 dm3 of hydrogen (298 K and 98 658 Pa) were extracted at the cathode. Determine the amperage and current efficiency of copper.

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CONCLUSION

The development of the metallurgical processes theory at the present stage is characterized by a detailed study of the complex (especially heterogeneous) processes characteristics, the expansion of the scope of physical and chemical methods and concepts application. In recent years, the possibilities of instrumental methods for studying the reactions taking place in metallurgical systems have incomparably increased, which is not least due to the use of computer technology for obtaining and processing experimental data. Understanding the thermodynamics and kinetics of pyro-, hydro- and electrometallurgical processes plays a decisive role in solving the main task of modern physical chemistry in the field of metallurgy – the development of technologies for obtaining metals and their compounds with the maximum yield at minimum costs. Scientific research in this field is the basis for improving metallurgical production and allows us to find the optimal conditions for the complex extraction of metals necessary for the existence and progress of civilization. Knowledge of the laws that determine the course of physicochemical processes allows not only to predict their result, but also to control them, directing the system to a specified goal. An example is the production of dispersed metals and new alloys with predetermined properties. This task is very complicated, and the empirical search for a solution proves to be associated with a huge expenditure of resources and efforts. The successes achieved on this path convince that it can be solved only at the expense of understanding the mechanism of physicochemical processes and knowledge of the "compositionstructure-property" relationships.

C o n c l u s i o n | 213

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Учебное издание

Белоусова Наталья Викторовна Ясинский Андрей Станиславович

ТЕОРИЯ МЕТАЛЛУРГИЧЕСКИХ ПРОЦЕССОВ THEORY OF NON-FERROUS EXTRACTIVE METALLURGY Учебное пособие Корректура и копьютерная верстка А.А. Быковой

Подписано в печать 25.01.2019. Печать плоская. Формат 60×84/16 Бумага офсетная. Усл. печ. л. 12,6. Тираж 100 экз. Заказ № 6005 Библиотечно-издательский комплекс Сибирского федерального университета 660041, Красноярск, пр. Свободный, 82а Тел. (391) 206-26-67; http://bik.sfu-kras.ru e-mail: [email protected] 216 | T h e o r y o f N o n - F e r r o u s E x t r a c t i v e M e t a l l u r g y