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Electrochemical aspects of the aqueous oxidation of copper sulphides Etienne, Arlette 1970-12-31

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ELECTROCHEMICAL ASPECTS OF THE AQUEOUS OXIDATION OF COPPER SULPHIDES BY ARLETTE ETIENNE Ingenieur civil metallurgists (Universite de Liege, M.A.Sc. (Universite de Montreal, 1966) 1965) A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of METALLURGY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA November, 1970 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree tha permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Metallurgy  The University of British Columbia Vancouver 8, Canada Date November 26, 1970 ii ACKNOWLEDGEMENTS The author wishes to express sincere thanks to Dr. E. Peters for his support and criticism during the course of this work. Special thanks are due to Dr. A. Mitchell for providing many part of the experimental equipment. The assistance of the technical staff, during the experimental program, has been greatly appreciated. Financial assistance in the form of a Canada Council Scholarship and a National Research Council Scholarship is gratefully acknowledged 11X ABSTRACT The Cu-S binary system was subjected to electrochemical studies at temperatures below 100°C in acid solution. Three types of electro chemical experiments were conducted: a) Measurements of electromotive force were made on the galvanic cell, Cu I 0.1 M CuSO., 0.1 M H„S0. I Cu S i 4 2 4 ' y across the Cu-S system (y variable). The range of copper activity corresponding to the zone of stability of digenite Cu^ gS) was accurately determined. From these measurements and the existing thermo dynamic data on covellite (CuS), the standard free enthalpy of formation of digenite Cu^ gS) and djurleite (Cu^ 955^) was calculated. b) Copper sulphides were grown on a copper anode from an acidic solution saturated with IL^S at constant current. The thickening: of the copper sulphide film was accounted for by electrolytic transport in the scale. The diffusion coefficient of cuprous ions in low chalco-cite CCu0S) and low digenite (y Cu. „S) was calculated from the slope of the electrode potential versus time relationship. c) Galyanostatic polarization of rotating disk anodes of digenite and covellite was studied at 55°C in 0.1 M CuSO.-0.1 M H„S0. solutions. 4 2 4 The resistances arising during the anodic dissolution of these sulphides were assessed from the dependence of the electrode potential on time and current density. The above polarization experiments were correlated with the electrolysis of copper matte anodes and the leaching experiments in; acidic ferric solutions described in the literature. iv RESUME Cette these constitue une etude du syst&me binaire Cu-S en solution acide, en dessous de 100°C. Trois types d'experiences, utilisant des me"thodes de mesure Electrochimiques, ont e"te" realisees: a) On a mesure" la force electromotrice de la cellule galvanique, Cu I 0.1 M CuSO., 0.1 M H„S0. I Cu S i 4' 2 4 1 y pour des sulfures de cuivre de diverses compositions et determine, avec precision, les valeurs de 1'activity du cuivre qui correspondent aux limites de la zone de stability de la digenite Cu.. QS). Ces mesures 1. o et les donne*es thermodynamiques sur la covelline qui existent dans litterature, ont permis de calculer l'enthalpie libre standard de formation de la digenite (y Cu^ gS) et de la djurieite (Cu^ 955^)• b) On a fabrique" des sulfures de cuivre par oxydation, a courant constant d'une anode de cuivre plongee dans une solution acide sature"e en H^S. Un modele de transport eiectrolytique dans la couche de sulfure a ete propose pour expliquer la croissance du film. La pente du potentiel de 1'electrode en fonction du temps a permis de calculer le coefficient de diffusion des ions cuivreux dans la chalcosine inferieure (Cu0S) et dans la digenite inferieure (y Cu., QS). c) On a etudie la polarisation galvanostatique de disques tournants du digenite et de covelline k 55°C, en solution 0.1 M CuSO^-0.1 M ^SO^. Les variations du potentiel d'electrode en fonction du temps et de la densite de courant ont permis de determiner les resistances associees a la dissolution anodique de ces sulfures. V On a dtabli la correlation entre les experiences prdcddentes, 1'electrolysed'anodes de mattes de cuivre et les experiences de lixiviation en solutions ferriques d£crites par plusieurs auteurs. vi TABLE OF CONTENTS Page ABSTRACT - RESUME iii LIST OF FREQUENTLY USED SYMBOLS xiv CHAPTER I. LITERATURE SURVEY AND INTRODUCTION 1 A. DIRECT LEACHING OF COPPER SULPHIDES ! 1.1 Stoichiometry of the leaching reactions 2 1.2 Two stage leaching of chalcocite and digenite 4 1.3 Kinetics of dissolution of copper sulphides in acidic chlorine solutions 5 1.4 Kinetics of dissolution of copper sulphides in acidic ferric solutions 6 1.5 Kinetics of dissolution of copper sulphides during oxygen pressure leaching 8 B. DIRECT ELECTROREFINING OF COPPER MATTE H 1.6 Laboratory attempts and related industrial practices H C. ELECTROCHEMICAL ASPECTS OF THE AQUEOUS OXIDATION OF COPPER SULPHIDES 15 1.7 Scope of the present work 1CHAPTER 2. THERMODYNAMIC MEASUREMENTS IN THE Cu-S SYSTEM... 19 2.1 Measurement method 12.2 Experimental 22 2.3 Results 3 2.3.1 Electrode potential measurements 23 vii Page 2.3.2 Standard free enthalpy of formation of low digenite -^1 2.3.3 Variation of the standard free enthalpy of - formation of digenite with composition ^2 2.3.4 Standard free enthalpy of formation of , . 14 djurleite 2.4 Discussion CHAPTER 3. AN ELECTROCHEMICAL METHOD OF MEASURING THE COPPER IONIC DIFFUSIVITY IN A COPPER SULPHIDE SCALE ... 39 3.1 Principle of the method 3.2 Theoretical anode model ^ 3.3 Experimental 3.4 Results and discussionCHAPTER 4. ELECTROLYTIC DISSOLUTION OF ROTATING DISKS OF COPPER SULPHIDES 56 A. GENERALITIES ON ELECTRODE KINETICS 54.1 Various types of overvoltage 6 B. THE ROTATING DISK ELECTRODE TECHNIQUE 4.2 Equation of transport at the disk surface 58 4.3 Ohmic drop in solution 61 4.4 Design of practical R.D.E 2 C. POLARIZATION OF ROTATING DISKS OF COPPER SULPHIDES 64 4.5 Experimental 6Preparation of the copper sulphides 70 viii Page 4.6 Polarization of digenite anodes 71 4.6.1 Results 74.6.2 Discussion of the mode of transport of copper ions through the covellite layer 76 a- Solid state diffusion 77 b. Diffusion in the solution filling the pores. 78 4.6.3 Discussion of the potential increase taking place before the transition 81 a- Diffusion overvoltage and potential drop in the pores 81 6. Interface overvoltage 83 4.7 Polarization of covellite anodes 4 4.7.1 Results 8a- Electrode potential measurements 84 b. Electrode reactions 89 c' Microscopic examination of the reacted electrode 92 4.7.2 DISCUSSIONCHAPTER 5. DISCUSSION OF THE MECHANISMS OF DISSOLUTION OF THE COPPER SULPHIDES 98 5.1 Electrolytic dissolution of chalcocite: constant current oxidation 99 5.2 Leaching of covellite with acidic ferric solutions: electrochemical oxidation x^8 5.3 Leaching of chalcocite and digenite with acidic ferric solutions: constant potential oxidation ... x±5 ix Page CHAPTER 6. CONCLUSIONS 122 6.1 Electrochemical parameters of the copper sulphides.. 122 6.2 Application to the electrolysis of copper matte anodes and to the leaching of copper sulphides 125 APPENDIX 1. Use of a galvanic cell to measure the ionic conductivity of a copper sulphide membrane 126 APPENDIX 2. Division of the total overvoltage in its various components 132 APPENDIX 3. Estimation of the potential drop in a diffusion layer of a partially ionized electrolyte 135 APPENDIX 4. Calculation of the diffusion overvoltage at a R.D.E. 137 APPENDIX 5. Integration of Eq. (5.3) 141 APPENDIX 6. The Fe3+/Fe2+ electrode 143 APPENDIX 7. Integration of Eq. C5.13) 147 REFERENCES 149 • X LIST OF FIGURES Figure Page 1 Portion of the phase diagram in the Cu-S system, taken from Roseboom (11) 7 2 Charge-transfer processes between a Cu^S electrode and a CuSO^ electrolyte 21 3 Temperature dependence of the e.m.f. of the cell S.C.E. (25°C)/0.1 M CuS04-0.1 M I^SO^/Cu 24 4 Relaxation curves obtained at 45°C after anodization and cathodization of CuS-Cu, electrodes 26 1 . / OD 5 Relaxation curves obtained at 60°C after anodization and cathodization of CuS-Cu- -,,,-S electrodes 27 1.765 6 Temperature dependence of the e.m.f. of the cell S.C.E. (25°C)/0.1 M CuS04-0.1 M H^SO^CuS-^ ?65S.. 28 7 Temperature dependence of the e.m.f. of the cell S.C.E.(25°C)/0.1 M CuSO.-O.l M H_SO./Cu S-Cu. 0,CS.. 30 4 2 4 y 1.965 8 Variation of standard free enthalpy of formation and chemical potentials across the Cu-S system at 55°C... 38 9 Micrograph of the copper sulphide scale, separated from its copper substratum 40 10 Model of the Cu^S film growing on the Cu anode 46 11 Model of the copper sulphide scale at the stage of Cu, 0S growth 47 JL. o 12 Temperature dependence of the cuprous ion diffusion coefficient in low chalcocite 52 13 Temperature dependence of the cuprous ion diffusion .. coefficient in low digenite 53 xi Figure Page 14 Pattern of streamlines at a R.D.E. (51) 59 15 Design of the rotating disk electrode 65 16 Design of the stainless steel head » 66 17 Electrolytic cell 67 18 Cell arrangement 68 19 Experimental apparatus 69 20 Potential-time function recorded during the polariz-ation of digenite anode (I = 37.7 mA cm ) 73 21 Dependence between the current density and the transition time 75 22 Interface potential of a digenite-covellite electrode versus the logarithm of the current density 85 23 Potential-time function recorded during the polar-ization of a covellite anode (I = 0.75 mA cm ) 37 24 Potential-time function recorded during the polar-ization of a covellite anode (I = 2.26 mA cm ) 88 25 Polarization curve of covellite anodes 90 26 Micrograph of the surface of an oxidized covellite disk ,93 27,28 Micrograph of the cross section of an oxidized covellite disk , 93,94 29,30 Scanning electron micrograph of oxidized covellite .. 94,95 31 Microprobe picture of oxidized covellite: absorbed electrons 96 32 Microprobe picture of oxidized covellite: Cu emissionxii Figure Page 33 Microprobe picture of oxidized covellite: S° emission 96 34 Constant current multiplelayer oxidation model 102 35,36 Depth of penetration of the digenite and covellite interfaces versus time,during the oxidation of chalcocite 106 3+ 37 Current density-potential curves for the Fe (0.1 M)/ Fe2+(10"2 M) electrode and the Fe3+(0.1 M)/Fe2+(10~3 M) electrode HI 38 Electrochemical leaching of covellite in ferric solutions H2 39 Dependence of the leaching rate of covellite on the ferric ion concentration 114 40 Constant potential multiplelayer oxidation model ... 116 41 Design of a galvanic cell to measure the ionic conductivity of a copper sulphide membrane 129 xiii LIST OF TABLES Table Page 1 Copper electrorefining practices 12 2 Thermodynamic data of the copper sulphides below 100°C 37 3 Experimental measurements used in the determination of the cuprous ion diffusion coefficient in low chalcocite 49 4 Experimental measurements used in the determination of the cuprous ion diffusion coefficient in low digenite 50 5 Polarization of digenite anodes 72 6 Polarization of covellite anodes 86 7 Rates of the first leaching stage of digenite and chalcocite at 55°C in acidic ferric solution 120 XIV LIST OF FREQUENTLY USED SYMBOLS a^ = activity of species i 2 -1 -1 B^ = mobility of species i, cm sec J -3 = concentration of species i, mole cm 2 -1 D_j, = diffusivity of species i, cm sec -3 d = specific weight, g cm E = electrode potential, V E = rest potential of an electrode, V o E = E + n = surface potential, V sos r _i F = Faraday constant, 96,484 clb eqgr i = current, A -2 I = total current density, A cm -2 1^ = current density carried by species i, A cm -2 -1 = flux of species i, mole cm sec I = thickness of a sulphide layer, cm M = molecular weight M,, . = M. = Onsager coefficient, cm Xsec x J x ii l ° ' = charge carried by particle i, clb R = gas constant, 8.31439 J "iT'Snole-1 2 S = surface area, cm T = absolute temperature, °K t = time, sec t = reference for time, sec o x = abscissa at time t, cm x = abscissa at time t o o y = number of copper atoms per sulphur atom in compound Cu^S XV 6 = thickness of a diffusion boundary layer, cm AF = free enthalpy change, cal mole ^ AH enthalpy change, cal mole ^ AS = entropy change, e.u. e o = standard electrode potential, V \ = charge-transfer overvoltage, V = diffusion overvoltage, V nc = crystallization overvoltage, V ns = nr + n = surface overvoltage, V \ = ohmic potential drop, V n = total overvoltage, V = chemical potential of species i, J mole •1 V = 2 kinematic viscosity of a liquid, cm sec •1 al partial conductivity due to species i, 9, "*"cm a = -1 -1 total conductivity, Q cm Ui = angular velocity, rad. sec T = transition time, sec -1 1 CHAPTER 1 LITERATURE SURVEY AND INTRODUCTION A. DIRECT LEACHING OF COPPER SULPHIDES Heap leaching of copper sulphide ores has been practised at Rio Tinto in Spain for over 200 years, but the study of the problems related to the direct oxidation of copper sulphides in acidic aqueous solutions has received attention only in the past 20 years. In spite of the interest manifested by several copper companies for such a process, none of the laboratory attempts has, so far, resulted in industrial application. The reported works deal with ground minerals, sintered synthetic disks or cast specimens. Direct leaching is carried out in sulphuric, hydrochloric or perchloric solutions, using ferric ions, oxygen or chlorine as oxidising agent. The experiments cover a range of temperature between 15°C and 200°C. The variety of conditions make the comparison between these experimental results difficult. Only part of the parameters which affect the leaching of sulphides are controlled or determined and the discussion of mechanisms and rate controlling steps is left open to conjecture CD- A review of the literature published on the subject will none the less sum up our knowledge of the copper sulphide behaviour during oxidation in acidic aqueous solutions. 2 1.1. Stoichiometry of the leaching reactions Oxidation of copper sulphides in acidic solutions yields, ultimately, a.combination of elemental sulphur, dissolved copper and sulphate ions. Nevertheless, suphate is the only oxidized form of sulphur to be stable in these conditions, and the reaction 3Cu ++ + 4H„0 + 4S° > 3CuS + HSO ~ + 7H+ is thermodynamically favourable. The standard free enthalpy change is equal to AF° = -19,402 - 51.9 T, (2), which corresponds to an equilibrium 25  -in constant of 3.74 x 10 at 25°C. Thus, a CuS-HSO^ -Cu system is more — | | stable than a S°-HS04 -Cu system, and the elemental sulphur eventually formed during the reaction could subsequently react to form CuS and HSO^ . Loewen (3) observed, however, that elemental sulphur was not oxidized to sulphate in 0.36 M cupric perchlorate-0.25 M perchloric acid solution under 60.3 p.s.i. of oxygen at 125°C, conditions which led to sulphate formation from covellite (CuS). Elemental sulphur, therefore, would not be an intermediate product in the formation of, sulphate, but sulphur and sulphate would be produced simultaneously by oxidation processes which follow at least two different paths. Sullivan (4) established experimentally that the oxidation of cove llite minerals in acidified ferric sulphate solutions at 35°C produces cupric ions in solution and elemental sulphur according to the reaction CuS + 2Fe+++ Cu** + IVe^ + S° (1.1) 3 The molar percentages of copper dissolved and elemental sulphur liberated were nearly the same. The molar ratio of copper to sulphur in the residue after a carbon disulphide wash, which removed elemental sulphur, was approximately 1:1. The quantities of ferrous and cupric salts produced by the oxidation were also in a ratio corresponding to the stoichiometry of reaction (1.1). ; • Thomas and Ingraham (5) leached pure synthetic CuS in acidic ferric sulphate solutions between 25 and 80°C. They found that the ferrous to cupric ion ratio and the cupric ion to elemental sulphur ratio did not exceed 2.1:1 and 1.1:1 respectively. In addition, when leaching tests were carried out in acidic ferric chloride solutions, only 4% of the covellite which had reacted was found to have been converted to sulphate. The foregoing observations confirm that equation (1.1) represents the predominant leaching reaction of covellite in acidic ferric solutions below 100°C. Jackson and Strickland (6) reported that the reaction of oxidation of chalcocite (C^S) and covellite (CuS) by chlorine in acid solution at 50°C produced almost exclusively elemental sulphur. Oxygen pressure leaching of copper sulphides yields elemental sulphur and sulphate in various proportions depending on the experi mental conditions. These reactions are described by the two following equations: CuS + l/202 + 2H Cu 2+ O (1.2) + S CuS + 2 02 Cu' 2+ + SO 2- (1.3) 4 4 Warren (7), leaching purified covellite (CuS) in sulphuric acid between the melting point of sulphur and 180°C, observed that small quantities of sulphur were produced in experiments carried at high acidity (pH = 0.75, p = 100 p.s.i.). 2 Loewen (3) leached chalcocite (C^S) at 125°C with 60.3 p.s.i. of oxygen and determined that the fraction of sulphur oxidized to sulphate varied from 15 to 72% as the acidity of the starting solution was decreased from 4 M to 0.5 M perchloric acid. Dahms, Gerlach and Pawlek (8) changed the concentration of sulphuric acid from 0.204 M to 0.816 M during the leaching of chalcocite under 10 atm. of oxygen at 130°C. The extraction of copper was completed in 2 hours when using 0.204 M sulphuric acid solution. The quantity of copper leached decreased rapidly as the acid content was raised to 0.4 M and remained constant at higher acidity. The quantity of sulphate produced dropped rapidly as the acid concentration was increased to 0.4 M, then it decreased more slowly till it remained unchanged for initial acidities larger than 0.7 M. The sulphur to sulphate molar ratio reached its maximum value of 1:1 for the latter condition. 1.2 Two stage leaching of chalcocite and digenite Experimental evidence indicates that the oxidation of chalcocite (Cu_S) and digenite ( Cu.. 0S) occurs in two stages. Z. 1. o Sullivan (9), Thomas, Ingraham and MacDonald (10) leached chalcocite with dilute ferric solution below 50°C and noticed that the reaction slowed down markedly after 50% of the copper was dissolved. 5 The residue was then identified to be CuS. The first step of the leaching reaction involved copper oxidation according to the equation Cu2S + 2Fe+++ • 2Fe++ + Cu** + CuS (1.4) The second step proceeded with the oxidation of covellite. Leaching chalcocite at 200°C under 60 p.s.i. of oxygen, Warren (7) noticed a pH increase during the first half of the reaction. This increase was the result of the reaction Cu2S + l/202 + 2H+ —»- Cu2+ + CuS + H^O (1.5) The acidity remained constant during the second half of the reaction. Copper extraction-time curves obtained by Dahms et al. (8) during oxygen leaching (p = 10 atm.) of various copper sulphides of composi-2 tion intermediate between Cu2S and Cu^ gS clearly exhibited two distinct steps. The quantity of copper extracted at the end of the first stage depended upon the initial composition of the sulphide and corresponded to its conversion into CuS. Very little sulphate, if any, was produced during that first stage. 1.3 Kinetics of dissolution of copper sulphides in acidic chlorine,  solutions In the leaching experiments conducted by Jackson and Strickland (6) in acidic chlorine solutions, the dissolution rates of copper sulphides were controlled by chlorine diffusion in the solution. 6 1.4 Kinetics of dissolution of copper sulphides in acidic ferric  solutions The copper-sulphur binary phase diagram (Fig. 1) indicates that the oxidation of chalcocite should result in the appearance of new phases following the sequence: djurleite, digenite, covellite and finally sulphur. However, unstable compositions of these phases or metastable phases may be favoured by the oxidation kinetics (12). King (13) and Burkin (14) studied the solid state transformations occurring during the oxidation of synthetic chalcocite by acidic ferric chloride solutions between 40 and 80°C. Optical microscopy, X-ray diffraction and electron microprobing techniques were used to study the solid residues recovered after leaching. The electron micro probe analysis suggested that, as copper was leached from Cu^S, the composition of the resulting solid varied continuously until the molar ratio of copper to sulphur became 1:1; the covellite (CuS) produced by the reaction extended its range of composition up to Cu_ 0S at 40°C. These authors observed also that the -material was U. o porous and cracked, that the sample could not be polished: these features reduce considerably the significance of microprobe readings. Leaching residues of composition intermediate between Ci^S and CuS were analysed chemically and by X-ray diffraction. Residues of; composition Cu^ gS and CuS exhibited X-ray diffraction patterns, in good agreement with those of low temperature digenite and covellite, respectively^ as given in the A.S.T.M. index file. A regular shift of the lines on the X-ray photographs was interpreted as an extension of the composition range of these sulphides: digenite would exist from Figure 1. Portion of the phase diagram of the binary Cu-S system taken from Roseboom (11). 8 Cu 0S to Cu, CS and covellite from Cun CS to CuS or even down to Cu _S. 1. o JL.J l.j (J.o The results of King (13) and Sullivan (9) showed that the oxidation of copper sulphides proceeded with similar rates in hydrochloric and in sulphuric solutions (anionic concentrations <1 M). Changing the acid content of the solution did not affect significantly the oxidation rate. Except in very dilute solutions where the leaching rate was controlled by the diffusion of ferric ions, varying the ferric ion concentration did not appear to alter the first stage of the chalcocite dissolution, but affected the covellite dissolution to some extent (5,9,10,13). The activation energy calculated for the first stage of the chalcocite and digenite leaching varies betwen 0.8 and 5 kcal. mole \' this value being considered indicative of a transport controlled ; reaction (10,13,14). The activation energy calculated for the second stage of the chalcocite leaching (13,14) and for the covellite leaching (5) is between 22 and 25 kcal.mole \ a range usually associated with processes controlled by an interface reaction. Yet Sullivan's experiments showed that the second step of the leaching of chalcocite was 3 to 4 times faster than the leaching of covellite in otherwise identical conditions (4,9). Furthermore, the rate of , ; oxidation of chalcocite was not dependent on the particle size, though that of covellite was directly proportional to the particle surface; 1.5 Kinetics of dissolution of copper sulphides during oxygen pressure  leaching Leaching chalcocite in 1 M perchloric acid at 110°C under 74 p.s.i. 9 of oxygen, Loewen (3) found oxygen consumption rates equivalent to -2-2 6.3 mA cm and 0.8 .mA cm for the first and second step, respectively. Thomas and al. (10) measured copper dissolution rates equivalent to -2 -2 18 mA cm for the first stage of leaching of chalcocite, and 2 mA cm for the leaching of covellite, at 55°C in 0.1 M Fe3+-0.1 M H2S04 solutions. It follows that copper sulphide leaching is much faster with ferric salts than with oxygen, below the melting point of sulphur. As stated earlier, copper sulphide leaching with oxygen takes place by way of at least two distinct parallel mechanisms, leading to sulphur and sulphate formation. This makes the oxidation kinetics all the more difficult to resolve. The following questions remain largely unanswered, although they have been examined experimentally. Does the sulphur result from the direct electrochemical oxidation of the sulphide or from the oxidation of the hydrogen sulphide evolved by the mineral? Is the sulphate formed by way pf an electrochemical or chemical mechanism? What is the influence of the fusion of sulphur (above 119°C) on the oxidation kinetics? What is the relative importance of the various components of the reaction? . Raising the initial acidity of the solution increases the ratio of elemental sulphur to sulphate produced by the reaction. The first stage of the leaching of chalcocite is accompanied by H+ consumption (Eq. 1.5) and there is a minimum initial acidity required to prevent the subsequent precipitation of basic salts. Warren (7) observed that (T = 160°C, p = 40 p.s.i.) the copper dissolution rate increased as 2 the concentration of sulphuric acid was raised from 30 g/1 to 40; g/1. Any further increase of the acidity resulted in a decrease of the : 10 leaching rate. The results obtained by Dahms and al. (8) have already been reported during the discussion of the stoichiometry of the leaching reactions (Section 1.1). The largest leaching rate was obtained for the minimum acidity, 0.204 M H^O^ (T = 130°C, pQ = 10 atm.). Any further increase of the acidity reduced the copper dissolution rate. In all these experiments, the oxidation rates increased with the partial pressure of oxygen. Dahms and al. (8) observed that the rate of the first leaching step became independent of the oxygen partial pressure above 10 atm. and that the rate of the second leaching step varied as the 1/3 power of the oxygen partial pressure. This relation ship was explained by means of oxygen adsorption on the mineral surface. The discrepancies between the above works are revealed in the activation energies calculated from the reaction rates. Warren (7) estimated the activation energies associated with the dissolution rates of copper to be 6.6 and 1.8 kcal.-mole x for the first and second stage of the leaching of chalcocite, respectively (p^ = 40 p.s.i., 30 g/1 H2S04, 100-200°C) and 11.8 kcal.mole"1 for the leaching of covellite (pH = 0.75, p = 100 p.s.i., 120-180°C). Loewen (3) 2 determined from the oxygen consumption rates that the activation , energies were 1.8 and 11.4 kcal.mole 1 for the first and second leaching steps of chalcocite, respectively (1 M HCIO^, 110-140°C). Dahms and al. (8) investigated the second leaching step of chalcocite (0.4 M H^SO^, pQ = 10 atm.) between 40 and 140°C. They found two distinct rate-temperature dependences: below 80°C, the dissolution rate of copper was associated with, an activation energy of 11 1.9 kcal.mole x and above 120°C, with an activation energy of 20.77 kcal.mole x. Similar activation energies were calculated from the rate of sulphate formation. This type of temperature dependence could be related to a reaction which takes place by two distinct parallel paths. As the temperature is increased, the lightly activated mechanism gives way to the highly activated one. B. DIRECT ELECTROREFINING OF COPPER MATTE 1.6 Laboratory attempts and related industrial practices The electrolysis of copper matte anodes was first attempted by Andre in 1877 (15). This trial as well as later attempts were unsuccessful. The development by the International Nickel Co. of Canada of an electrolytic refining process for nickel matte anodes, which went into plant operation at Thompson (Manitoba) in 1961 (16,17), revived the interest for a similar copper matte refining process. At Inco, nickel matte anodes (76.0% Ni, 2.6% Cu, 0.5% Co, 0.5%; Fe, 20.0% S) are electrolysed in a sulphate-chloride solution (composition ++ of the purified electrolyte: Ni =60 g.p.l., NaCl=100 g.p.l., S0^= -2 100 g.p.l., H3B03=20 g.p.l.). The current density is 20.7 mA cm , and the cell voltage, which is about 2.3 V on the first day, gradually rises to about 5 V near the end of the life of a 2 inch thick anode. The porous and granular anode slime is strongly adherent and contains approximately 95% of elemental sulphur. The sulphide anodes corrode at approximately 94% current efficiency. The remaining 6% of the anodic current is consumed by oxygen evolution which results in an increase of the anolyte acidity. No significant 12 oxidation of sulphur can be detected. The difference between the cathodic and anodic current efficiencies leads to a slight depletion of the electrolyte in nickel. Recently, several researchers investigated the feasibility of the copper matte anode electrolysis on laboratory scale (15,18,19,20). Data on the industrial practice of copper electrorefining are ; summed up in Table 1 to allow the comparison between the conditions of the electrolysis of copper and copper matte anodes. Table 1 Copper electrorefining practice (21,22) Electrolyte composition: Cu, 34-52 g.p.l. H2S04, 125-230 g.p.l. Cl, 0.02-0.052 g.p.l. Fe, 0.2-6 g.p.l. Electrolyte-temperature 55-70 °C Power: Max. cathode current density, 16-25 mA cm _2 up to 32 mA cm Current efficiency, 89-98 % Cell voltage, 0.17-0.40 V At 20°C, the electrolysis of copper matte anodes is accompanied by an important increase in the bath voltage which reaches, in some cases, the prohibitive value of 8 V (20) and is characterized by a very low anode yield (15). 13 The electrolysis of Ci^S anodes (CuSO^ = 30 g.p.l., H2S°4 = _2 100 g.p.l., T = 55°C) at a current density of 15 mA cm yields a bath voltage of 0.9 V during the first 14 hours, then a sharp potential increase develops to a maximum of 2.1 V; the bath voltage finally oscillates between 1.5 and 1.8 V (15). The first part of the electrolysis corresponds to CuS formation. During the second part, S° formation, 0^ evolution and eventually S0^ formation supplement the initial reaction (15). The Cu content of the bath remains constant during the first part of the electrolysis, then it decreases linearly; after 5 days, the solution is depleted of 30% of its copper, with a corresponding increase in acidity (15). The slimes, granular and porous, remain adherent on the anode; they are composed of a mixture of CuS and S° (15,18,19,20). Kuxmann and Biallass (15) observed that the copper content of the slime was decreasing from 20% in electrolyte containing 100 g.p.l. of H^SO^ to 14% in electrolyte containing 250 g.p.l. of E^SO^. The increase, in acidity resulted also in a small decrease in the anodic and cathodic current efficiencies. The amount of elemental sulphur oxidized to sulphate varies widely with the experimental conditions and from author to author. Habashi and al. (20) claimed that the elemental sulphur-sulphide balance closed within 3% (Cu = 30 g.p.l., H2S04 = 100 g.p.l., I = 10 mA cm"2, T = 20°C) but Venkatachalam and al. (19) (Cu = 30 g.p.l., H2S04 = -2 150 g.p.l., I = 10 mA cm , T = 33°C) and Loshkarev and al. (18) (Cu = 35 g.p.l., H2S04 = 200 g.p.l., I = 10 mA cm"2, T = 15°C) described measurements indicating that 55% of the sulphur was oxidized to sulphate. Kuxmann and al. (15) determined that the amount of sulphur oxidized to 14 sulphate varied between 4 and 10% (Cu = 30 g.l.p., ^SO^ = 100-250 g.p.l., I = 15 mA cm"2, T = 55°C). These investigations show that the direct electrorefining of copper matte is heavily penalized by the copper loss in the anode slime (2.8% of the anode Cu content in 250 g.p.l. ^SO^ electrolyte (15)), by the impoverishment of the electrolyte in copper and by the acid build up resulting from the relatively low anode efficiency (- 89% (15)). To compensate for these drawbacks, Kuxmann and al. (15) added HNO^ continuously to the electrolyte ( up to 0.1 g. p. Amp.hr.). This reduced the copper loss in the slime to 0.4% of the copper contained in the anode and reduced the variation of the copper and acid content of the electrolyte. The presence of nitric acid effectively reduced the cathode current efficiency from 98 to approximately 92% as a result of the reaction 3Cu + 2N03~ + 8H* > 2N0 + 3Cu2+ + 4^0, and increased slightly the anode current efficiency according to the equation 0-5) 3CuS + 2N03" + 8H+ —* 3Cu2+ + 3S° + 2N0 + 4H20, The presence of nitric acid did not appear to affect markedly the sulphate formation (sulphur oxidized to sulphate remained below 10% in all cases). The addition of nitric acid to the electrolytic bath seems to improye the feasibility of the direct electrorefining of copper 15 mattes but represents the consumption of a reagent at some additional cost. C. ELECTROCHEMICAL ASPECTS OF THE AQUEOUS OXIDATION OF COPPER SULPHIDES 1.7 Scope of the present work In all cases, the oxidation of copper sulphides imposes a series of solid state transformations releasing copper ions in solution and leading to elemental sulphur formation. This basic reaction sequence is sometimes accompanied by sulphate formation. The development of the oxidation reactions results from the driving force imposed on the system, the mobility of the various interfaces, and the rate of transport of copper through the reaction products. The knowledge of the resistances arising from every reaction step should allow the prediction of the overall oxidation rates. Copper sulphides are electronic conductors; chalcocite is a p-type semiconductor, the conductivity of which increases notably with copper -2 -1 -1 deficiency (a - 10 to 50 9, cm at room temperature) (23,24), 4 digenite and covellite are almost metallic in character (a = 2 x 10 -1-1 J2 cm at room temperature) (23,25). Thus, electrode potential measure ments can be used to monitor the solid state transformations resulting from the oxidation. Since electrode potentials are very sensitive to the presence of a second phase and of impurities, the following electrochemical study was performed on pure, synthetic copper sulphides. Prior to any dynamic study, the knowledge of electrode rest potentials is desired. The stability of the electrode-electrolyte system can then be ascertained and the existence of a thermodynamic 16 equilibrium potential considered. This study began with the measure ments of the electromotive force of the cell Cu I 0.1 M CuSO., 0.1 M H„S0. I Cu S, I i 4' 2 4 1 y which has been established to correspond to the equilibrium relationship E = -RT ln a„ (Cu S) Cu y The sulphide composition was selected to produce a two-phase electrode having a fixed copper activity. The existing thermodynamic data on the Cu-S system were relevant only to the two terminal compounds, Cu^S and CuS (2,26). The stability ranges of the various copper sulphides, Cu^S, Cu^ , =Cu^ gS,:CuS, (Fig. 1) were to be determined. Measurements of cell I e.m.f. with a 13 high impedance electrometer (10 Q input resistance) allowed the accurate determination of the copper activity in digenite-covellite and digenite-djurleite mixtures. The standard free enthalpy of formation of digenite and djurleite was calculated from these measurements and the thermodynamic data on CuS, available in the literature (Chapter 2). The contribution of the solid state diffusion to the transport of copper ions through the oxidation products can be assessed from the range of the copper activities corresponding to the zone of stability of the oxidation products and from the diffusion coefficients of copper ions in these solid phases. The following experiment was designed in order to measure the copper ionic diffusivity in copper sulphides. . An 17 ionic current of copper was forced through a copper sulphide membrane and the associated voltage drop determined. In the absence of surface overvoltages and electronic short-circuits, the ionic resistivity is directly measured by the potential difference across the membrane. The method proved to be inapplicable to digenite, and the irreversibility of the reactions at the covellite electrode obscured these measurements (Appendix 1). More valid results were obtained with the following electrochemical experiments which allowed the indirect determination of the desired diffusion coefficients. A copper anode was oxidized in l^S saturated acid solutions, at constant current. The analysis of the electrode potential versus time relationship permitted the calculation of the copper ion diffusivity in low chalcocite and low digenite. The experiment could not, however, be extended until the formation of a. layer of covellite (Chapter 3). , The apparent electrochemical mechanism of some leaching reactions of copper sulphides (27) suggested that anodic polarization studies could provide useful information on the behaviour of these sulphides during oxidation. Galvanostatic polarization studies of rotating disk anodes of digenite and covellite were thus undertaken. The rotating disk electrode technique was adopted because the well defined geometry and hydrodynamic regime of this system permits the calculation of the ohmic voltage drop in solution and of transport rates in the electrode boundary layer. The relation of the electrode potentials versus time and current density allowed the magnitude and effects of the resistances associated with the dissolution reaction to be assessed (Chapter 4);. 18 The behaviour of chalcocite during similar polarization experiments is derived from the above results with the help of theoretical considera tions and correlated with actual experiments done by other researchers. Leaching rates calculated from information obtained in the present work are consistent with experimental rates observed by other investigators using ferric oxidants in similarly designed leaching experiments. The general features of the leaching of copper sulphides in acidic ferric solution can be accounted for by the oxidation mechanisms proposed in the present work (Chapter 5). 19 CHAPTER 2. THERMODYNAMIC MEASUREMENTS IN THE Cu-S SYSTEM 2.1 Measurement method Many investigations of chemical reactions involving copper sulphides have been explained on the basis of the existence of only the two compounds, C^S and CuS. However, the phase diagram of the Cu-S system as published by Roseboom (11) leads to a more accurate interpreta tion of these reactions. Four copper sulphides exist in a stable form at room temperature and have been observed as minerals: chalcocite (Cu2S), djurleite (Cu1 g65S), digenite (^ C^ gS) and covellite (CuS). The only existing thermodynamic data on the Cu-S system are relative to the two terminal compounds. The thermodyanmic properties of the intermediate copper sulphides, which are electronic conductors (23,24, 25), may be investigated by electrode potential measurements. The equilibrium potential of a two-component electrode, such as a copper sulphide, depends on the particular composition of the solid and on the process of charge-transfer between the electrode and the electrolyte; this charge-transfer can take place through the cation, the anion or a redox. couple present in the solution. When two or more different charge-transfer processes occur independently of each other, at the same electrode surface, currents of opposite sign flow across the electrode-electrolyte boundary, resulting in a change of the chemical composition of the system. The rest potential, which is measured in the absence of an external flow of current, is then a -mixed potential. Charge-transfer processes involving both the Cu and the S species could occur at the surface of a Cu S electrode in contact with a CuSO. y 4 20 electrolyte; this would result in a subsequent alteration of the composition of the solid and of the solution (Fig.2). Studies of the rest potentials of electrodes of synthetic and natural, chalcocite and covellite established that the potential of these electrodes varied with the activity of cupric ions in solution, in a way identical to a copper electrode, and that they were not affected by the presence of sulphate (15,28,29,30). The standard potential of a C^S electrode in cupric solution, at 25°C, was derived from these experiments as 486 mV (15), 490 mV (28) and 505 mV (29). The standard potential of a CuS electrode in cupric solution, at 25°C, was calculated to be 597 mV (30) and 567 mV (29). Further evidence that the SP-SO^ couple is inert has been otained by Loewen (3), who verified that elemental sulphur did not oxidize to sulphate in cupric perchlorate solution at 125°C under 60.3 p.s.i. of oxygen. Sullivan (4,9), who studied the oxidation of copper sulphides in acidic ferric solution below 100°C, established that the final products of oxidation were cupric ions and elemental sulphur, though sulphate was the most stable sulphur species in his experimental conditions. Therefore the potential difference between the sulphide electrode and the cupric sulphate electrolyte is determined by the reaction (Cu)Cu s "—* Cu^ + 2e y The electromotive force of the galvanic cell Cu/0.1 M CuSO,, 0.1 M HS0,/Cu S (I) 4 2 4 y 21 Pt or C e CuyS (Cu)-(SH E-,_. —>. CuS04 (aq) 2+ Cu SO 2-Ox. Red. Charge-transfer processes. Figure 2. Charge-transfer processes between a Cu S electrode and a CuSO. electrolyte. ^ 22 is a direct measurement of the copper activity in the sulphide, -2AE F= uCu(CuyS) - u°u = RT ln a Cu Cell I may be considered as a double cell involving the two individual cells and both the Cu and Cu^S potentials are measured separately versus S.C.E. (25°C). 2.2 Experimental Copper sulphides of appropriate Cu to S ratio were synthesized at 400°C in sealed quartz tubes from 99.999% pure Cu and S purified according to the method of Bacon and Fanelli (31). The product was pressed under vacuum into a disk, 13 mm in diameter by 1 mm thick. The sulphide was cemented to a platinum foil with epoxy resin made conductive by the addition of graphite powder. The specimen was then mounted in acrylic resin (Koldmount) and polished. The electrolyte (0.1 M CuSO^, 0.1 M H^SO^) was kept free from oxygen by continuously bubbling helium, which had been previously saturated with the same solution.: The cell was immersed in an oil thermostat. The cell e.m.f. was measured by a high impedance electrometer . Cu/0.1 M CuS04, 0.1 M H2S04/S.C.E. (25°C), (ID S.C.E. (25°C)/0.1 M CuSO., 0.1 M HoS0./Cu S 4 2 4 y ' (III) 23 (Keithley 630). The reference electrode was a saturated calomel electrode at 25°C: corrections calculated from de Bethune, Licht and Swendeman's data (32) were made to compensate for the temperature fluctuations of the reference electrode. The Pt-Cu lead contacts were at room temperature. The solution was analysed by electrogravimetry for copper after each final measurement. 2.3. Results 2.3.1. Electrode potential measurements The results of the measurements of the Cu electrode potentials are reported in Fig. 3 as a function of temperature. Measurements were made after an anodizing or cathodizing treatment on electrodes of different purity, some being annealed under H^. The experimental values follow a linear relationship in the temperature range, 35-75°C. E = (70.45 ± 0.33) x 10~3 + (0.632 + 0.025) x 10~3 (T - 328) (V) The equation and the errors were calculated by the classical method of the linear regression for a probability of 98%. Electrodes of composition Cu^ ^^S were then studied. An X-ray diffraction pattern confirmed the existence of the two phases, digenite and covellite. Covellite is reported to be stoichiometric, digenite in equilibrium with covellite has the composition Cu^ ^^^S, this composition limit remaining constant up to 200°C (11). A sample synthesized at high temperature should still be in equilibrium after cooling down to room temperature. To appreciate the reversibility of the electrode reaction, the . digenite-covellite mixture was subjected to anodizing and cathodizing 35 45 55 65 75 T(°C) Figure 3. Temperature dependence of the e.m.f. of the cell S.C.E. (25°C) I 0.1 M CuS04-0.1 M H2S04 ] Cu after anodization after cathodization H„ annealed A • A 2 25 current. The amount of current passed through the specimen resulted in a variation of 0.3% of its average Cu content. After switching off, the electrode potential was recorded as a function of time. The stabilized electrode was then subjected to a current of opposite sign and the rest potential recorded. A series of these relaxation curves is shown on Fig. 4. Though the relaxation curves obtained after successive anodization and cathodization on the same sample were not symmetrical, the relaxation curves obtained after anodization and . cathodization of two fresh specimens were symmetrical and more convergent. The gap between any set of two curves decreased with increasing tempera ture, as it appears from the comparison of Fig. 4 and 5. Forcing current in or out of the electrode forces the following reaction to the right or to the left, CuS + 0.765Cu -—y Cu, ,,,-S, -* 1.765 ' unless one of the sulphides takes care of the Cu by composition changes. The whole specimen homogenizes by diffusion. The equilibrium electrode potential was chosen in the middle of the gap between two corresponding relaxation curves. The results are plotted on Fig. 6 as a function of temperature. They are expressed by a linear relationship in the temperature range, 40-70°C, E = (251.50 + 0.35) x 10~3 + CO.765 + 0.035) x 10~3 CT - 328).-(V). The equation and the errors were calculated by the classical method t (hours) ure 4. Relaxation curves obtained at 45°C after anodization or cathodization of CuS-Cu.. electrodes. AO after cathodization ^ 9 after anodization A O treatment on fresh electrode 260 -255 -0 50 100 t(hrs) Figure 5. Relaxation curves of CuS-Cu-^ 765S electrodes, at 60°C. • o after anodization Q • after cathodization O D treatment on fresh electrode 265 255 > J iii 245 235 40 50 60 70 T(°C) Figure 6. Temperature dependence of the e.m.f. of the cell S.C.E. (25°C) I 0.1 M CuSO' -0.1 M HoS0, I CuS-Cu, 4 z 4 1 1.765 • ' no preliminary electrolysis O • different batches of sulphides 29 of the linear regression for a probability of 98%. Sulphides of composition Cu^ g^S and Cu^ ggS were synthesized. . X-ray diffraction provided evidence for the presence of both digenite and djurleite. According to Roseboom CH) the Cu rich limit of digenite varies with temperature, going from Cu^ ^S at room tempera ture to Cu^ g^S at 83°C where digenite inverts its crystal structure. The electrode potential of the digenite-djurleite mixture was ; measured during heating and cooling cycles. A period from 24 to 96 hours was allowed for equilibration at each temperature. The experimental results are reported on Fig. 7 as a function of temperature. The values can be accommodated by a straight line relationship) E = C242.20 ± 0.45) x 10_3 + CO.62 + 0.06) x 10_3 Ct - 343) CV) The equation and the errors were calculated by the classical linear regression for a probability of 98%. It appears that the reaction Cu S + C1.965 - y)Cu • Cu, „,CS* y 3 1.965 takes place quite readily above 70°C but becomes sluggish below 55°C. This is consistent with Roseboom's CH) observation that the djurleite formation is reversible at 93°C. CUyS represents the Cu rich limit of digenite, y is a function of temperature, 1.79 < y < 1.83. 250 h - 240 230 55 65 75 85 T(°C) Figure 7. Temperature dependence of the e.m.f. of the cell S.C.E. (25°C) | 0.1 M CuSO/-0.1 M HoS0/- | Cu^S-Cu 4 " "2"~4 O A different compositions, after heating • • different compositions, after cooling • excluded from the linear regression. 1.965" o 31 Specimens of composition Cu^ ggS produced, in spite of a cooling rate of 10°C per day, a mixture of chalcocite and metastable tetragonal djurleite identified by X-ray diffraction. Tetragonal djurleite is often reported to be present in sulphide of composition intermediate between chalcocite and digenite synthesized at high temperature (11,33). From the reported set of experimental data, the standard free enthalpy of formation of low digenite and djurleite can be calculated. The standard states are pure Cu, pure orthorhombic S and the pure copper sulphide of the stated composition. 2.3.2. Standard free enthalpy of formation of low digenite The activity of copper in a covellite-digenite mixture in equili brium is directly related to the standard free enthalpy of the reaction CuS + 0.765Cu > Cu.. -,,-,-S, 1.765 which depends only on the standard free enthalpy of formation of CuS and Cu1>765S, AF° (Cu, _,_S) = AF° (CuS) + 0.765 RT ln a„ . 1. /DJ L.U Von Wartenberg (34) measured the heat of formation of CuS at 25°C, is AH298°K. ^CuS) = "I-1'610 * 400 cal .mole-1 * .1 cal. = 4.1840 J. 32 and Kubaschewsky and Weibke (35) assessed the experimental error. Anderson (36) calculated the entropy of CuS at 20°C from specific heat measurements. His value has been selected by K.K. Kelley as the most probable (37). AS298°K ^CuS^ = 0,3 " 0,45 ca1, mole"1 OK_1 These are the only data on CuS resulting from direct measurements. Any value obtained by extrapolation from high temperature measurements, supposing the existence of an equilibrium between CuS and C^S are obviously doubtful. However, Kubaschewsky, Evans and Alcock (26) are in favour of a more negative heat of formation for CuS. In the temperature range, 40-70°C, the standard free enthalpy of formation of Cu-poor digenite is then calculated to be AF° (Cu± 765S) = (-18,140 ± 525) - (4.90 + 2.50) (T - 328) cal.mole-1. 2.3.3. Variation of the standard free enthalpy bf formation of  digenite with composition The effect of composition variations on the standard free enthalpy of formation of digenite can be calculated, yCu + S —> Cu S y The free enthalpy of the system can be expressed in terms of the chemical potential of its constituents, 33 AF°(cuyS) = y(yCu - yCu) + Ms - y; The total derivative of the free enthalpy with respect to y is equal to d[AF°(CuyS)] - (uCu -y°u)dy + y dCy^ - ^ + d(yg - y^) (3,1) This expression of Eq (3.1) can be simplified to d[AF°(CuyS)] = (yCu - y°u)dy (3.2) by utilizing the Gibbs-Duhem relationship Integration of Eq. (3.2) between the composition limits of digenite yields the corresponding difference of the standard free enthalpy of formation, y2 AF°(Cu S) - AF°(Cu S) = / (y - v° )dy y2 y± y^ Lu The right hand side of this equation is equal to the area bounded by the integration limits and located below the experimental curve, ]i - = f(y), which has not been determined. As the chemical potential of a component in a stable compound is a continuously increasing function of composition, this area is intermediate between 34 the surfaces of the rectangles (y„-y1)(y - y° ) and &. JL uu uu (y0-yn)(y - y° ) . In the digenite case, these two values differ by £. x uu uu approximately 12% and the variation of the standard free enthalpy of formation can be approximated by UCu(yl)+vCu(y2) AF°(Cu S)-AF°(Cu S)=(y„-yi) tU 1 CU 1 y9 ' y-, w2 'i' 2 y2--yl 2 RT[ln aCu(yi) + In aCu(y2) introducing an error < 6%. This information makes the calculation of the standard free enthalpy of formation of djurleite possible. 2.3.4. Standard free enthalpy of formation of djurleite In a digenite-djurleite mixture in equilibrium, Cu S + (1.965 - y) Cu -> Cu. -,,-S. y J 1.965 • the Cu activity is related to the standard free enthalpy change of the reaction. In this case, the coefficient multiplying the Cu chemical potential is temperature dependent. The standard free enthalpy of formation of djurleite is given by AF'CCUj^ 965S) = AF°(CuyS) + (1.965 - y)RT In aCu, and in the temperature range, 55-80°C, it has been calculated to be 35 AF' (Ci^ 965S) = (-19,700 ± 550) - (5.5 ± 3.1)(T - 343) cal mole 1. 2.4. Discussion At 93°C, djurleite decomposes into digenite (Cu^ g^S) and chalcocite (Cu1<99S) (11,38), 0.166Cu1>840S + 0.833Cu1>990S —* Cu^S. This equilibrium acts as a reference point for correlating the present measurements with the existing data on the system. The standard free enthalpy of formation of djurleite is derived from the measurements performed in this work, AF°„,,0„(Cu1 r,^rS) = 19,830 i 600 cal mole 366 K 1.965 ' The standard free enthalpy of formation of high digenite can be extrapolated from the present measurements, AF°_,-0 (Cu. Q/S) = job K. JL. OH -18,900 ± 600 cal mole"1. Von Wartenberg (34) determined the heat of formation of Cu^S at 298°K, AH°980K(Cu2S) = 18,970 cal mole"1. Kubaschewsky and Weibke (35) in their discussion on the Cu-S data selected this value as the most probable, assessing the experimental error to 500 cal mole \ Cu2S has been studied in detail by Richardson et al. (39) using R2-H_2S equilibrium in the temperature range 800-1000°K, by Brook (40) in the temperature range 500-1000°K and by J.B. Wagner et al. (41) using e.m.f. measurements at 500°K. Its standard free enthalpy of formation seems to be accurately established in that temperature range, but extrapolation of these values to room temperature can only lead to high 36 errors because of the inaccuracy of the specific heat data. For that reason, Von Wartenberg's data seems more applicable than the value proposed by Kubaschewsky, Evans and Alcock (26). Anderson's (36) and Kelley's (37) data on the entropy of Cu^S yield, along with Von Wartenberg's data for AH°, AF° ,0ir(Cu0S) = 20,900 ± 800 cal mole"1. ODD K Z In these conditions the two sets of data converge within 700 cal. mole ^, a gap which sits in the middle of the experimental error of 1400 cal. mole x. The enthalpies, entropies and free enthalpies of the copper , sulphides below 100°C are summarized in table 2. The digenite and djurleite values are based on measurements described in this work, the covellite and chalcocite values are selected on the basis of the best low temperature data shown in the literature. The major component (90%) of the final error on the values calculated from the present measurements originates from the error associated with the existing data on CuS. The variation of Cu and S chemical potentials across the Cu-S system can then be assessed at any temperature ( Fig. 8). However, the value proposed for the djurleite-chalcocite equilibrium is conjectural: it was not measured directly and the accuracy of the existing data did not allow its calculation. The difference in free enthalpy of formation between djurleite and chalcocite is much smaller than the experimental error on any of these values. Though the Cu chemical potential in the djurleite-chalcocite system is known at 93°C from the present measure ments, the uncertainty on the entropy change of the reaction (0.1 ±, 0.3) e.u. does not allow any extrapolation. Table 2 Thermodynamic data of the copper sulphides below 100°C Composition AF0/ . . -1 cal mole AS°/ . cal mole 1 °K 1 Ref. CuS (c). (-11,610 ± 400) - (0.3 ± 0.45)T 0.3 ± 0.45 34,35,36,37 CU1.765S (D.) • (-18,140 ± 520) - (4.9 ± 2.5(T-328) 4.9 ± 2.5 this work Cu S y (D.). (-18,140 ± 520) - (4.9 ± 2.5(T-328) this work + (y - 1. ,765)[(-7,910 ± 40) - (3.2 ± 3.5) (T-328) CU1.965S (Dj.). (-19,700 ± 550) - (5.5 ± 3.1)(T-343) 5.5 ± 3.1 this work Cu2S (Ch.). -(18,970 ± 500) - (5.3 ± 0.8)T 5.3 ± 0.8 34,35,36,37 OJ + 0 O -5-5 •60 -6-5 IC. 1. ~ 0 u -20 50 _i I 55 i 60 65 %Cu u—CuS 1.765 1.805 1.965 Z Figure 8. Variation of standard free enthalpy of formation and of chemical potentials across the Cu-S system at 55°C. oo 39 CHAPTER 3. AN ELECTROCHEMICAL METHOD OF MEASURING THE COPPER IONIC DIFFUSIVITY IN A COPPER SULPHIDE SCALE 3.1. Principle of the method Copper sulphides can be grown on a copper anode from an acidic solution saturated with ^S. If the operation is conducted at constant current, different sulphide layers of decreasing copper activity are grown as the oxidation proceeds. If equilibrium is established, the successive phases should be, according to the phase diagram (11) (Fig. 1): copper, chalcocite, djurleite, digenite, covellite and sulphur. The reaction occurring at the anode is y Cu + H„S —* Cu S + 2H+ + 2e 2 y The electrochemical potential of such an electrode (Stokholm convention) is given by the following relationship, ay a •n RT , Gu Ho S , /-TIN o ~ ~z¥ Vs aCu S aH+ y The copper activity at the solid-liquid interface reflects the conditions imposed upon the system and the transport properties of the scale being grown. The sulphide activity is taken as unity. In defined geometric and stirring conditions, under a constant current, the hydrogen sulphide 40 and hydrogen ion activities are constant in the vicinity of the electrode. In steady-state conditions, the surface overvoltage for a given sulphide is assumed to be a constant. Therefore, the electrode potential varia tion with time follows the evolution of the copper activity according to the relationship (3.2) derived from Eq. (3.1), dE _ _ RT d_ y dt " 2F dt in ECu dE RT d . „ t dt = " ^2F dT aCu 7 = constant ^3-2) If the sulphide scale grows uniformly on the electrode surface, the copper activity at the liquid-solid interface can be directly linked to the transport properties of the sulphide layer. 3.2 Theoretical anode model In the copper sulphides, the sulphur ion-mobility is considered negligible in comparison with the copper ion mobility (42). In the case of high temperature phases (aCX^S, gCu^S) there is experimental evidence (43,44) to support this. It is also reasonable for the low temperature phases in view of the relatively large size and associated immobility of the anion. The copper sulphides are electronic conductors. Chalcocite is a p-type semiconductor, its conductivity increasing notably with copper -2 -1 -1 deficiency (a =10 ->- 50 Q cm at room temperature) (23,24). Digenite 4 -1 -1 and covellite are almost metallic in character (a = 2.10 Q cm at room temperature (23,25). 41 The phenomenological equations for diffusion relate the particle flux to the forces responsible for their motion. If the interaction effects are neglected, unidimensional transport in a two component system in the presence of a low strength electric field can be equated by JCu+ =-MCu+ &"C«+ + W- k*>> C3'3) Je = " Me 4 ^e+W •> (3'4) The electrical potential gradient can be derived from equation (3.4) and substituted in equation (3.3), T qCu+ MCu+ ,d qCu+ d . r_ JCu+ ~ ~q M~ Je = " MCu+Cdx" vCu+ ~ ~ dx" V (3-5) Chemical potentials of ion and electron are not experimentally accessible values but are related through the measurable quantity, u , VCu = yCu+ + ye Equation (3.5) is then simplified to M + A Jn + + -TT- J " ~ M_ + ~ ii_ (3.6) Cu+ M e Cu*: dx Cu As reported earlier, the copper sulphides are electronic conductors, their electronic conductivity being much larger than their ionic 42 conductivity, and equation (3.6) can be reduced to JCu+ = " MCu+ »Cu (3'7) The Onsager coefficient is directly related to the conductivity, CK, mobility, B_^, and diffusivity, D^, of the particle i. "2 M. = a. q. l l I M. = B.C. (3.8) Di M. = C. i RT i Equation (3.7) can be expressed in terms of any of these four parameters T Cu d /_ n, W - - — dx" yCu (3'9) If the sulphide scale grows uniformly and continuously over the whole electrode surface, the sample thickness at any time is proportional to the number of coulombs passed through the electrolytic cell during that time, TCu+ Ct ~ V ,M, .„ 1n, X " *0 = yl Cd} Cu S C3'10) y Combining equations (3.2), (3.9) and (3.10) yields equation (3.11), 2 1 • M. dE ' UN XCu+ 2? (d}Cu S = +°Cu+ d7 y 43 which permits the calculation of the ionic conductivity of the sulphide scale, formed under steady state conditions, from the slope of the recording of the electrode potential as a function of time. 3.3 Experimental The anode was made of copper rod (99.995% purity) 0.905 cm in diameter, mounted in acrylic resin (Koldmount), and polished so that only one plane was in contact with the solution. The solution, 0.2 M in Na„S0. and 0.2 M in H^SO. , was saturated by continuously bubbled 2 4 2 4 H^S. A strong convection pattern was brought about by a magnetic stirrer. The system was held at constant temperature by a regulated water bath. A 21 volt Ni-Cd battery unit provided current to the system through a set of appropriate resistors. The electrode potential was measured versus a saturated calomel electrode by a Keithley 153 voltmeter which fed the signal to a SargentSRG recorder. Series of experiments were carried out at temperatures between 30 and 73°C (below the digenite transition temperature) and under -4 -2 -3 selected current densities between 1.9 10 A cm and 1.55 x 10 . -2 A cm The sulphide layer showed a uniform thickness over the electrode surface (Fig. 9) which ranged from 50 to 380 V- depending on experimental conditions and the period of oxidation. The reaction products were identified by X-ray diffraction on a powder sample. The scale structure and morphology could not be investigated by microscopy, electron diffraction or -microprobing. The three-sulphide assembly was not in equilibrium and in the absence of an electric Figure 9. Micrograph of the copper sulphide scale separated from its Cu substratum. The CU-CU2S interface was on the right side of the specimen. Digenite and djurleite are the only two phases to remain present. The band structure results from differences in the scale morphology emphasized by polishing. 45 current one phase disappeared during the time required for the sample preparation according to the reaction, 0.8CuoS + 0.2Cu, QS Z l.o 3.4 Results and Discussions So far, three suphides have been identified, chalcocite, djurleite, and digenite. No evidence, either direct or indirect, for the appear ance of covellite was obtained in these experiments. The sulphide growth model, analysed earlier in this paper, is valid only in steady-state conditions; that is, when the cationic and total electric currents are constant. These conditions are satisfied when the first sulphide layer (Cu^S) is deposited. The stoichiometry range of low chalcocite is smaller than 0.5% of its copper content (11) and during Cu^S formation, the ionic current virtually equals the total electric current (Fig. 10). When a new sulphide starts to grow on the anode, the copper flux reaching the solid-liquid interface is changed according to the Cu to Cu+ ratio in the new phase. If the digenite composition is approxi mated by Cu, QS, the reaction occurring at the liquid-solid interface l.o at the stage of digenite growth can be represented by Fig. 11, and the correspondingly cationic (1^ +) and electronic (J°) currents are equal to 90 and 10%, respectively, of the total current (I). The boundary between two solid phases is characterized by a thermodynamically fixed value of copper activity or electrochemical potential; therefore, the potential drop in each sulphide layer is a constant. Consequently, Cu 1.96^ 'Figure 10. Model of the Cu^S film growing on the anode. 47 Cu 1.8 CuS S~~—* C"L8S * 2e I " - Icu*+Ie ICu*- .9r ifc - X - .11 .11 > X»o Figure 11. Model of the copper sulphide scale at the stage of Cu, DS growth. JL. o 48 the abrupt change in cuprous current at the onset of growth of a new phase initiates an unsteady state process during which each sulphide layer adjusts its thickness to the new current conditions. The solid state transformations accompanying the phase boundary motion are believed to generate stresses in the specimen, because the scale always breaks away from the copper before CuS growthis apparent. So far, the digenite stoichiometry range has been ignored. The digenite composition is reported (11) to extend from Cu^ yg^S to Cu, 7nS at room temperature. Although the Cu poor limit is not affected by temperature, the Cu rich limit changes to Cu, 00S at 83°C 1. o J where digenite inverts to high digenite. During the digenite layer growth there is a continuous change in the Cu current flowing through the scale, but this variation represents only 1.75% of the total current and is smaller than the experimental accuracy of the method of measurement. From the set of experimental d&ta, the cationic diffusivity of the chalcocite and digenite in the scale was calculated in the range of temperature from 30 to 73°C (Tables 3 and 4). Though djurleite was present in every sample, the ionic conductivity value could not possibly be derived from the experimental curve. This phase probably did not extend over enough atomic layers to allow a steady state to be established. The measured ionic conductivity of digenite was independent of the current density used. In the chalcocite case, however, there was a current density value above which the experimental results became inconsistent. This limiting current density increased sharply with temperature. The dependence of the apparent ionic conductivity on the Table 3 Experimental measurements used in the determination of the cuprous ion diffusion coefficient in low chalcocite S = 0.644 cm T i E range (mV) Correlation dE n (°C) (mA) Cu2S/H2S 0.2 M Na sat.. 0.2 M H„S0.-2 4 -SO./S.C.E.(25°C) 2 4 Coefficient r dt (mV min X) U (fi cm -1) (cm sec ) 30 0.125 490-410 0.9985 0.0410 0.786 x 10 5 2.93 X io"11 40 0.250 520-465 0.9997 0.0818 1.60 X io"5 6.15 X io"11 40 0.250 425-390 0.9977 0.0835 1.57 X io"5 6.03 X io"11 46 0.250 480-425 0.9971 0.0659 1.98 X io"5 7.74 X io"11 48 0.250 510-475 0.9976 0.0712 1.84 X io"5 7.25 X io"11 50 0.234 525-485 0.9977 0.0521 2.95 X io"5 11.70 X io"11 51 0.250 508-450 0.9921 0.0526 2.45 X io"5 9.75 X io"11 55 0.250 480-445 0.9986 0.0357 3.67 X io"5 14.8 X io"11 55 0.250 465-430 0.9966 0.0403 3.25 X io"5 13.1 X io"11 55 0.500 500-456 0.9990 0.140 3.74 X io"5 15.1 X io"11 58 0.750 510-412 0.9997 0.292 3.97 X io"5 16.1 X io"11 62 0.750 525-410 0.9980 0.222 5.22 X IO"5 21.5 X io"11 66 0.750 515-458 0.9993 0.241 4.81 X io"5 20.0 X io"11 70 0.500 500-465 0.9969 0.0738 7.09 X IO"5 29.9 X io"11 70 1.000 505-435 0.9985 0.282 7.43 X IO"5 31.3 X io"11 73 1.000 505-485 0.9989 0.271 7.61 X IO"5 32.3 X io"11 Table 4 Experimental measurements used in the determination of the cuprous ion diffusion coefficient in low digenite S = 0.644 cm' T i E range (mV) Correlation dE D (°C) (mA) '^Cu1 0.2 0S/H0S sat., 0.2 M H„S0.-M-Na2S04/S.C.E.(25°C) Coefficient r dt (mV min 1) o {Q cm , 2 -(cm sec -1) 30 0.125 235-225 0.9987 0.0137 1.76 X io"5 0.683 X io"10 40 0.250 251-240 0.9936 0.0280 3.50 X io"5 1.40 X io'10 40 0.500 235-200 0.9989 0.110 3.56 X io"5 1.42 X io"10 40 0.500 281-255 0.9976 0.123 3.17 X io'5 1.27 X io"10 40 0.500 275-243 0.9990 0.112 3.50 X io"5 1.40 X io'10 40 0.750 250-225 0.9999 0.292 3.09 X io'5 1.23 X io'10 40 0.750 . 240-210 0.9998 0.253 3.48 X io"5 1.39 X io"10 46 0.250 251-225 0.9968 0.0239 4.08 X io"5 1.66 X io'10 48 0.250 270-260 0.9888 0.0221 4.43 X io"5 1.81 X io'10 51 0.250 268-245 0.9964 0.0168 5.74 X io"5 2.38 X io"10 55 0.500 250-225 0.9973 0.0522 7.50 X io"5 3.14 X io"10 55 0.750 251-225 0.9987 0.107 8.24 X io"5 3.45 X io"10 55 0.250 255-240 0.9815 0.0143 6.85 X io"5 2.87 X io"10 58 0.750 262-238 0.9976 0.0967 8.96 X io'5 3.81 X io"10 62 0.750 255-235 1.0000 0.0833 10.6 X io"5 4.53 X io'10 66 0.750 250-225 0.9966 0.0799 10.9 X io"5 4.74 X io"10 70 0.500 245-230 0.9865 0.0264 14.8 X io"5 6.47 X io"10 70 1.000 247-234 0.9965 0.0833 18.8 X io"5 8.22 X io"10 73 1.000 250-230 0.9940 0.0711 21.7 X io"5 9.62 X io"10 51 current density raises the problem of the morphology of the sulphides grown electrolytically. It is usual practice to classify anodic films as continuous or non continuous films. In most of the cases reported in the literature, the distinction between continuous and non continuous films is based on the nature of the resistance of the film to the current flow. It is characteristic of non continuous film to exhibit an approximately constant and low resistance (a few ohms) to the current flow during the growth of the scale (45). The smooth copper anode and the one . plane electrode surface prevented introducing stresses which might have lead to the cracking of the film. There was no solid state transformation when the useful measurements were made, i.e., when steady-state conditions prevailed. The film growth was kinetically controlled by the copper ion diffusion through the solid, which mechanism favoured the formation of a continuous uniform scale. A decrease of the ionic strength of the solution (0.1 Na^SO^, 0.1 I^SO^) did not affect the experimental results. , The measured diffusion coefficient of cuprous ion in low chalcocite was found to be (Fig. 12) D + = 8.1 x 10~3 exp. - 5,870 T 2 -1 cm sec = 1.1 x 10 -10 2 -1 at 50°C. cm sec The measured diffusion coefficient of cuprous ion in low digenite was found to be (Fig. 13) 52 Figure 12. Temperature dependence of the cuprous ion diffusion coefficient in low chalcocite. 53 In D 23.5 I ' 1 ' 1 L_ 2.9 3.0 3.1 3.2 3.3 i ( IO"3oK~') Figure 13. Temperature dependence of the cuprous ion diffusion coefficient in low digenite. 54 o c -,n~2 .6,100 2 -1 D^u+ = 3.6 x 10 exp. J-JT— cm sec D„ + = 2.4 x 10-10 cm2sec-1 at 50°C. In the temperature range studied, cuprous ions diffuse about twice as fast in digenite as in chalcocite. The activation energy for , * -1 , diffusion (AH) is 11.7 Z 1 kcal mole for chalcocite, and 12.1 X * -1 0.8 kcal mole for digenite. If an activation entropy for diffusion is to be calculated, the nature and concentration of diffusing defects must be known. The diffusion in ionic type crystals is often associated with the migration of Schottky or Frenkel type defects. X-ray investigations have suggested that in some ionic type crystals metallic ions were distri buted virtually at random among a large number of nearly equivalent lattice sites (ctAg^S (46), aAgl (47), aCu^S (44)). In the case of low chalcocite and digenite which have relatively ordered copper lattices, an interstitialcy mechanism (the cations being equally mobile) may, account for the cuprous ion diffusion. This is supported by the experimental observation that no significant variation of the diffusion coefficient has been observed with deviation from stoichiometry. Therefore, the equation of zeolitic diffusion should be applicable (48), 2 kT AS AH X h7~ exp' T~ 6Xp' _ RT' ' where \ is the average distance travelled by the diffusing particle in —8 one j ump (Sk - 2 x 10 cm) The. limits of confidence for the calculated activation energies are estimated for a probability of 95%. 55 k is the Boltzmann constant, 1.380 x 10 erg. molecule ^ °K ^ -27 h is the Planck constant, 6.62 x 10 erg. sec. The activation entropy for diffusion (AS) is then 1.9 e.u. for chalcocite and 1.3 e.u. for digenite,respectively. These low values are consistent with a mechanism which introduces little disordering in the lattice. 56 CHAPTER 4. ELECTROLYTIC DISSOLUTION OF ROTATING DISKS OF COPPER SULPHIDES A. GENERALITIES ON ELECTRODE KINETICS 4.1 Various types of overvoltage An electrode reaction rate, according to Faraday's law, is proportional to the current density, I. The dependence of current density upon electrode potential, concentrations of reactants, and other variables such as stirring and temperature, must be established in order to determine the electrode reaction rate - functions, and to explain the sequence of partial reactions constituting the overall electrode reaction, which is observed by means of chemical analysis. The resistive partial reactions govern the type and magnitude of;the overvoltage, n = E - E o where E is the electrode potential when current flows and E is the o potential in the absence of current, i.e., the equilibrium potential if there is only one reaction taking place at the electrode. The following distinction between the various types of overyoltage, which, correspond to the four possible types of rate-control, was* introduced by Bonhoeffer, Gerisher and Vetter (1950) and is developed in Vetter's "Electrochemical Kinetics" C49): - A charge-transfer overvoltage, n , prevails if only the transport 57 of charge carriers across the electrical double layer existing at the phase boundary is hindered. - If a chemical reaction is hindered, the rate constant of which is, by definition, independent of the potential, the current flow produces a reaction overvoltage, nr. - Diffusion overvoltage, nD, is encountered when mass transport by diffusion to and from the electrode surface is rate-determining : during current flow. - Hindrance of the process by which atoms are incorporated into or removed from the crystal lattice leads to crystallization overvoltage, The various overvoltage types have been analysed individually on a theoretical basis so that the current density versus overvoltage relationship has received a general mathematical expression in several cases. If several of the partial reactions have low rates of similar order of magnitude, the corresponding overvoltages are superimposed to Zovm the total overvoltage. Since the various overvoltages are, interrelated, Vetter (49) proposed a definition for the division of the measured overvoltage in its diffusion, reaction, crystallization and charge-transfer components, which is based on the requirement that upon the disappearance of all overvoltage types but one, the residual overvoltage must agree with the definition for the single remaining overvoltage type (Appendix 2). The components of the measured over voltage can, then, be sorted out on the basis of the theoretical relationships obeyed by the various overvoltage types, provided only « 58 one overall electrode reaction occurs. The experimental investigation of electrode kinetics requires a careful design of the experimental conditions in order to eliminate or calculate the ohmic drops and the mass transport limitations. The rotating disk electrode provides a system where these calculations are possible in the steady-state conditions. B. THE ROTATING DISK ELECTRODE TECHNIQUE 4.2 Equation of transport at the disk surface The calculation of the maximum rate at which a substance can be transported towards or from an electrode, J,. , is in general an lim ° intractable problem. Transport may be effected by diffusion, convection and electrical migration. The situation is still more complex if one of the species takes part in a homogeneous reaction since the chemical reaction rate has to be taken into account in the calculation. A rotating disk of infinite diameter, in a non-turbulent, stationary regime, is one of the few systems where the velocity distri bution throughout the body of the viscous fluid can be calculated (51). Figure 14 illustrates the pattern of streamlines at the surface of a rotating disk. Using this model, Levich (51) solved explicitly the steady-state convective diffusion equation, assuming constant physical properties, in some cases: transport of uncharged particles, transport in a binary electrolyte, transport of an ionic species in the presence of an excess of indifferent electrolyte (3 ions). 'As the Schmidt number, 59 Figure 14. Pattern of streamlines at the surface of a rotating disk (51). 60 Sc = jjt approaches °°, Levich's solution takes the form 0.620 D.2/3 v"1/6 u,1/2(C,-C.) J. - ± (4.1) where t is the transport number of species i in a binary electrolyte, t = 0 for uncharged species or for a charged species in the presence of an excess of indifferent electrolyte, v is the kinematic viscosity of the solution, to is the angular velocity of the disk. The diffusion boundary layer is defined as a region of rapidly changing concentration in the immediate vicinity of the electrode surface, the thickness, 6, of which is defined as 1 _ 1/3 1/6 -1/2 6 = "6T620 Di v and appears to be constant over the entire surface of the disk. Thus, from the diffusion point of view, the rotating disk electrode (R.D.E.) offers a uniformly accessible reaction site. The diffusion overvoltage can be calculated with the Nernst equation and Eq. (4.1), if the physical properties of the solution.are known or if the limiting current density has been determined. The sum of experimental studies intended to verify the validity of equation (4.1) leaves no doubt that Levich's theory is correct (52). The correction suggested by Gregory and Riddiford (53) to take into account the finite value of the Schmidt number, Sc = -g-, (100 < Sc. < 5000 in aqueous solutions) is only significant in the cases of very accurate experimental measurements (54) (experimental error = 1%). 61 The assumption of constant transport properties (D,v) restricts the application of equation (4.1) to dilute solutions; Newman and Hsueh developed a numerical solution to compute the limiting current in the case of variable physical properties (54). 4.3 Ohmic drop in solution Newman studied theoretically the effect of the solution resistance to the current flow, below the limiting current density (55). In the absence of electrode overvoltages, the current distribution is completely determined by the ohmic drop in solution. A calculation shows that the primary current density is infinite at the edge of the disk and half of the average value at the center. Newman assessed the degree of non-uniformity of the current distribution, in the case of kinetic control by mass transport in the solution and charge-transfer at the electrode, against the physical and electrochemical parameters of the system. The predicted current distribution was verified experimentally by measuring the variations in the thickness of a copper deposit in 0.1 M CuSO.-0.1 M H.SO. solution A uniform current density can be expected at a R.D.E. if the ohmic drop in solution is small compared with the electrode overvoltage. Newman established, in the case of the primary current distribution, the following formula to calculate the ohmic drop between the electrode and a point situated in the electrode plane, outside the rim (r > rQ), at a distance, r, from the center (57,58). 4 2 4 (56) . r I -lr/r N2 1/2 o tan (4.2) 2a s 62 where a is the conductivity of the bulk solution, 4.4. Design of practical R.D.E. Riddiford, in his review of the rotating disk electrode technique (52), discussed the design of a practical electrode which conforms as closely as possible to the theoretical requirements. A disk of finite radius will meet the liquid flow requirements provided the radius, rQ, is very much greater than the thickness:of the momentum boundary layer, i.e., f^>1/2 =0, r oi o and provided the Reynolds number, Re = r^ —, is less than the critical value for the onset of turbulence. Experimental studies of the critical Re number at a rotating disk indicate that for a practical R.D.E., the Re number should not exceed 2 x: 10~* at the edge of the v disk. On the other hand, the rotational speed of the disk must be • large enough to exclude any significant contribution from natural convection. The shape and dimensions of an electrode of finite span must be carefully designed and checked to introduce no disturbing edge effect. In that respect, the best design is a conical electrode, the base of which is active for 0 < r < rQ, the region rQ to r^ being inactive. Riddiford pointed out that cylindrical electrodes should be avoided, since it was shown experimentally that, in this case, the fluid flow was turbulent even for very small Re numbers. 63 A further requirement is that the disk surface is the only effective bounding surface in the system. The liquid-gas boundary, the walls of the containing vessel, the counter-electrode, the Luggin capillary, etc. should not interfere with the flow pattern brought about by the spinning disk. Gregory and Riddiford (52) , using disks 5.3 cm in diameter, rotating at 146 r.p.m. in beakers of different sizes, checked that this requirement was satisfied when the solution-air interface and the bottom and side walls of the beaker were all more than 0.5 cm away from the disk. In a practical R.D.E., the Luggin capillary may be located in the lower half of the system projecting up close to the center of the disk along the axis r = 0. More often, . it is located in the upper half of the system with the tip reaching the plane of the disk (y = 0). Flows in the upper and lower part do not interact in this system. Finally thediskmust be horizontal, of minimum eccentricity (eccentri city of 0.025 mm is quoted by a number of workers) and smooth to the extent that the surface irregularities are much smaller than the diffusion boundary layer. Experimentally, the R.D.E. system has been mainly used to . determine diffusion coefficients in liquids and to study the kinetics of moderately fast electrode processes. A 64 C. POLARIZATION OF ROTATING DISKS OF COPPER SULPHIDES Polarization of digenite and covellite rotating disk anodes was investigated, at 55°C, in acidified copper sulphate solution (0.1 M CuSO^, 0.1 M ^SO^) by a galvanostatic method. 4.5 Experimental The rotating disk electrode is shown on Figure 15. The hollow shaft was of acetal plastic (0.62 cm in diameter). The specimen was imbedded in an acrylic resin (Koldmount) mount machined in the shape of a cone. The active surface exposed to the solution was 1.3 cm in diameter. Electrical connections were made through mercury contained in the hollow shaft and separated from the specimen by a platinum foil. Mercury reacted readily with copper sulphides and so direct contact should be avoided. Figure 16 describes the mechanical arrangement of the shaft in the stainless steel cell head. Figure 17 and 18 show the arrangement of the cell. A porous porcelain diaphragm separated the anodic compartement, in the center, from the cathodic compartment. A two-compartment cell was, indeed, necessary because cuprous ions in the solution reacted with the copper sulphides and were regenerated by metallic copper immersed in the same solution. As a matter of fact, covellite and digenite were found, at 40°C, to be transformed into chalcocite, in a few days, in cupric sulpha solutions containing metallic copper. The effect was a shortcircuit in the cell, which was equivalent to a slight electronic conductivity in the electrolyte. 65 Plastic shaft. Acrylic cone. Platinum foil. Copper sulphide. 2!l approximately. Figure 15. Design of the. rotating disk electrode. I ." I approx. Figure 16. Design of the stainless steel head. 67 n approximately. Figure 17. Electrolytic cell. Figure 18. Electrolytic cell arrangement. 69 Figure 19. Experimental apparatus. 70 The area of the copper ring cathode was 80 times larger than that of the active surface of the anode. The instruments associated with the present experiment are shown on Figure 19. Included were a D.C. servomotor (E.C. Motomatic E 550 MGHD) linked to a motor speed control unit (E.C. Motomatic E 550) which controlled the r.p.m. of the electrode within 1.5% of the set value, an Electroscan, Beckman Model 30, as a constant current source, a Keithley Model 153 microvoltammeter measuring the current to +2% of full scale, and a Keithley Model 630 potentiometric electrometer measuring and amplifying the voltage signal fed to a Sargent Model S.R.G. recorder. The cell was immersed in a thermostat-regulated water bath. Experiments were done in a helium atmosphere with deaerated 0.1 M CuSO^-0.1 M H.SO. solutions. , 2 4 The measuring circuit was kept ungrounded. All potential measure ments were made with respect to a saturated calomel electrode at 25°C. The angular velocity of the disk was set at 250 r.p.m. yielding at the edge of the disk a Reynolds number of R = r2 - = 6.25 x 103 e v which was characteristic of a laminar flow regime for that kind of geometric arrangement (see 4.4). Preparation of the copper sulphides Digenite was synthesized at 600°C in an evacuated quartz tube from 0,99999 pure copper and sulphur, purified according to the method of 71 Bacon and Fanelli (31), in the molar ratio, 1.78:1. Covellite was synthesized at 450°C in an evacuated quartz tube from 0.99999 pure copper in the presence of an excess of purified sulphur. A temperature gradient prevailing along the reaction tube prevented the sulphur from condensing on the covellite during the cooling period. The copper sulphides were ground under helium in an alumina ball mill and then cold-pressed under vacuum into disks (1.3 cm in diameter, approximately 2 mm thick) in a Perkin Elmer evacuable die. The digenite -2 disks, compacted under a pressure of 8100 kg cm , had 93% of their theoretical density. The covellite disks, shaped under a pressure of -2 2700 kg cm , were sintered in the presence of sulphur vapour; their final density was 86% of the theoretical value. The electrodes were lightly polished. The total internal resistance of each electrode was measured with a Keithley, model 503, milliohmeter and found to be approximately 0.1 n for digenite and 0.05 J2. for covellite electrodes. 4.6 Polarization of digenite anodes , 4.6.1 Results , Digenite anodes were studied at 55°C by a galvanostatic polariza--2 tion method using current densities between 7.5 and 75 mA cm . The information obtained by this study is summed up in Table 5. A typical potential-time curve is shown on Figure 20. These curves were characterized by a region in which the potential slowly rose as a function of time, ending in a potential discontinuity in a transition 72 Table 5 Polarization of digenite anodes S.C.E. (25°C)/0.1 M CuSO.-O.l M HoS0. <KCu., „S 4 2. 4 l.o I . -2 mA cm E o mV E. l mV ^fi ,sol. mV Vel. mV mV E s mV E T mV E -E. T 1 mV T sec 3.77 248 280 21 - - 259 7.5 236 298 42 - 1.1 255 760 462 124,800 11.3 245 355 64 1.5 1.6 288 725 370 39,060 15.1 237 350 85 1.5 2.1 261 515 165 10,950 18.8 245 405 104 2 2.5 296. 5 575 170 8,670 18.8 244 409 106 2 2.5 298. 5 604 195 7,500 37.7 241 526 209 4 4.7 308. 5 678 152 1,950 45.2 243 659 252 5.5 5.2 396 818 159 1,110 56.5 238 768 316.5 6 6.5 439 978 210 720 56.5 244 765 312 6 6.5 438. 5 1004 239 912 75.3 244 914 423 8 8.5 474. 5 1123 209 420 E ,E ,E are the o current, initial and transition potentials, respectively as defined in Fig. 20. n , is the ohmic drop in solution, calculated from Eq. (4.2) fi,sol. rifi e^ is the ohmic drop inside the electrode rip is the concentration overvoltage due to diffusion in the electrode boundary layer (Appendix 4) S X fi;sol. ft,el. D E (mV) 1000 h 500 0 Figure 20 t (mln) Potential-time curve recorded during the galvano-static oxidation of a digenite anode at 55°C S.C.E.(25°C) | 0 1 M CuSO.-0.1 M HoS0, 4 2 4 Cu 1.78' 74 time T, beyond which the potential was much higher (> 1.5 V) and poorly reproducible. The first part of the curve up to the transition time corres ponded to the overall electrode reaction Cu. ,0S • CuS + 0.78 Cu4"*" + 1.56 e, (4.3) 1, lo which was found in a previous study (Chapter 2) to control the rest potential of a digenite-covellite electrode. In fact, covellite was identified by X-ray diffraction in the porous, loosely coherent solid separated from the surface of a specimen. No variation of the copper content of the solution could be detected after 35 hours of electrolysis under a current density of 7.5 mA cm The sharp increase in potential after the transition time indicated the appearance of a highly resistive electrode reaction consisting probably of oxygen discharge and sulphur formation and possibly sulphate formation (15). At the transition time, the digenite was far from being completely transformed into covellite but reaction (4.3) was not capable of main taining a constant rate. As the reaction proceeded, the covellite-digenite interface receded from the original surface,and copper ions should diffuse through the CuS layer to enter the electrolyte. It was observed experimentally that the current density was proportional to the inverse of the square root of the transition time _2 (Figure 21) and this led to the relationship (I > 7.5 mA cm ). Figure 21. Relationship between the current density- and the transition time obseryed during the galvanostatic oxidation of digenite anodes at 55°C. (A were estimated from Kuxman's results by the author). 76 I^T = 2.5 A^cm^sec 1 (4.4) The depth of penetration of the digenite-covellite interface, £ , provided it progresses uniformly, is directly proportional to the number of coulombs passed through the electrode during the time considered 2 = (f}D irMf = 1*81 x 10 4lT) (4-5) M 25.4 where = n no Is tne actual molar volume of the initial digenite phase. Given the I-x dependence, the dissolution constant relevant to the covellite layer, k , can be defined by the relation 2F.k I = —C4.6) The dissolution constant describes the steady-state transport of copper ions across the porous covellite layer resulting from the digenite -9 -1 -1 oxidation, k^ = 2.35 x 10 mole cm sec in the present experimental conditions (T = 55°C, 0.1 M CuSO^-0.1 M H2S04 solution, dD = 0.93 dfch) 4.6.2 Discussion of the mode of transport of copper ions through the covellite layer The covellite layer was porous; as a matter of fact, the molar 3 -1 volume of digenite and covellite is 25.4 and 20.4 cm mole ^respectively (59) and the digenite-covellite transformation develops 19.7% of additional porosity if the original solid volume is retained. The 77 copper ion transport may be effectuated by bulk diffusion through the solid sulphide, by surface diffusion along grains or by diffusion in the solution filling the pores. a. Solid state diffusion In the case of solid state diffusion, the copper flux through CuS is given by the integrated form of equation (3.7), which is valid regardless of the actual state of the diffusing species (cupric or cuprous ions), AyCu Jcu = -Mcu -IT • (4'7) When the transition occurs, the difference of copper electrochemical potential across the CuS layer (Aur ), which can be expressed in terms of electrode potentials (2FAE = - Aur ), corresponds to the stability limits of CuS. It can be calculated from the thermodynamic data on the stable, stoichiometric CuS that AE is equal to approximately 75 mV at 55°C (Chapter 2). During polarization of a digenite anode, an average potential rise (E -E^) of 187 niV was encountered during the; quasi-linear potential increase preceding the transition (Table 5). If some unstable, non-stoichiometric covellite was formed, the entire potential difference measured might be available to drive the solid state diffusion process. The Onsager coefficient, capable of accounting for the experimental results can be calculated from equations C4.7) and (4.6). 78 1^= 0.745 x 2F MCu AE. (4.8) The factor 0.745 takes into account the porosity of the covellite layer: initially, the digenite had 7% of porosity, and the transforma tion developed an extra 19.7% of porosity. The ionic conductivity, which is related to the Onsager coefficient by equation (3.8), can -3 -1 -1 then be calculated to be 3.3 x 10 cm if the cupric ions are -4 -1 -1 the diffusing-species and 8 x 10 Q cm if the cuprous ions are the diffusing species. This latter value is 23 and 11 times larger than the cuprous ion conductivity measured in chalcocite and digenite, respectively at 55°C (Chapter 3). As these two sulphides seem to display a relatively high ionic conductivity, and there is no evidence for this in CuS, it appears reasonable to consider that the solid state diffusion through covellite is not able to account for the observed rate of transport of copper towards the solution. b. Diffusion in the solution filling the pores If the aqueous electrolyte occupies 19.7% or more (owing to the, initial porosity) of the cross section, the most likely mechanism for the transport of cupric ion is by diffusion through the electrolyte that invades the pores as they form. Eventually, the pores get so deep that the concentration gradients necessary to transport cupric ions as fast as they are forced into solution leads to saturation of the electrolyte by a cupric salt at the digenite-covellite interface. At this stage, the reaction (4.3) clogs the pores progressively, forcing the potential to rise abruptly and impeding the current flow. Part of 79 the current is, then, used to charge the electrical double layer and other electrode reactions, involving decomposition", rather than formation of covellite occur. 2 The constancy of the product I T can be demonstrated for a binary CuSO^ electrolyte, which approximates the actual solution existing in the pores. It should first be noted that the accumulation rate of copper in the pores, A, represents a negligible fraction of the total copper flux, JS. A can be approximated by A " CCuf S of • where _CCu is the copper concentration at the digenite-covellite inter face. At the -maximum, = 2.2 M, which corresponds to the saturation in CuS04'5H20 at 55°C C60), - fS is the actual cross section of pores fS < 0.2 S, dx 1 M - = Q yg ^DJ' t*ie interface velocity. The accumulation rate of copper in the pores was calculated to remain lower than 1.4% of the total copper flux. Cupric sulphate dissolved in water is only partially ionized. Investigation of the U.V. spectra of these solutions revealed the existence of a complex which was believed to be CuSO^; its stability constant was estimated to be 125 C61). On the basis of this value, it can be calculated that approximately 73% of the copper is in the complex form in 0.1 M CuSO^ solution at ambient temperature. This value is approximate since a more accurate estimation requires the 80 appropriate activity coefficients to be taken into account. However it is apparent that a relatively important fraction of CuSO^ remains undissociated in 0.1 M CuSO^ solution. Furthermore, the diffusivity of the CuSO^ complex will be assumed equal to the diffusivity quoted in the literature for the cupric ions. In fact, the copper ion diffusion coefficients measured by Newman and al. (54,62) with the R.D.E. technique in CuSO^ solutions are aggregate values taking into account diffusion of both cupric ions and neutral complex. If CuSO^, Cu , and SO^ are noted, 1, 2, 3, respectively, the unidimensional diffusion equations can be written (convection term is negligible ) 3C, JL = - D- —-1 1 3x 9C 9C J2 = -D2^T - D2 f C2 "t C4.9) j = - n - + D — C J3 U3 9x + U3 RT S 9x along with the electroneutrality condition = C^, J ** the flow requirements + J„ = — T = -T Jl "3 * - dx Convection term = C f S — , where C is the concentration in the bulk solution, and is less than 7 x 10-<1 % of the total flux JS. J represents the apparent flow normal to the geometric electrode area. f. (< 0.2) is a correction factor to take into account that only a fraction of the cross section, occupied by the pores, is available for the transport of copper. 81 2 and the chemical equilibrium statement = KC2 . It follows after rearrangement of these equations T D 9C 9C ? = -(Di + Di ^*r-*>i jr> (4-10) Integration of Eq. (4.10) over the thickness of the covellite layer yields D2 I£ = f 2F [(D1 + Dx ^CCj - C1) + 2D2 . (C2 - C^], At the transition, i.e., when saturation is achieved in the bottom of the pores, every term on the right hand side is a constant and it follows from Eq. (4.5) 2 IT = est. 4.6.3. Discussion of the potential increase taking place before the  transition a. Diffusion overvoltage and potential drop in the pores If the copper is transported in the solution filling the cracks and pores of the covellite layer, the potential rise (E -E^) observed during the pseudo linear portion of the potential-time curve (Jig. 20) is the sum of the diffusion overvoltage and resistance polarization (ohmic drop + liquid junction potential) in the pores. The average, potential difference measured amounts to 187 mV (I > 15 mA cm~ ). The experimental values lie in a band between 152 and 239 mV (Table 5) and 82 seem to be randomly distributed with respect to measured transition time, around the mean values stated by equation (4.4). The diffusion overvoltage can be calculated with the Nernst equation RT nD = 2F aCu++ satd' CuS04 soln.) - In aCu++(in 0.1 M CuSO^, 0.1 M H2S04)]. The activity of the cupric ions in a saturated cupric sulphate solution may be set equal to the square root of the activity of the saturated AF° copper sulphate electrolyte. The latter is equal to exp. (- —=r~ ) where RT AF° is the standard free enthalpy of solution of copper sulphate according to the equation CuS04-5H20(s) • Cu"*4" + S04~~ + 5H20 AF° = 1350 + 9.3 T (2). However, experimental data on the saturated copper sulphate electrode are available (0.296 < Eq < 0.317 V at 25°C) (32). The average value of 0.306 V is retained along with the experimental thermal temperature coefficient of 0.93 mV °C_1 C32). The potential of the 0.1 M cupric sulphate-sulphuric acid, copper electrode was measured (Chapter 2) to be 0.312 V at 55°C with respect to the standard hydrogen electrode. The diffusion overvoltage is then estimated to amount to approximately 22 mV. 83 The resistance polarization in the pores should then be able to account for the remaining 165 mV. It is shown in Appendix 3 that, in the case of a weak electrolyte, the potential drop in a diffusion layer depends on the magnitude of the complex stability constant and may be much higher than the diffusion overvoltage in contrast with the case of a fully ionized electrolyte. b. Interface overvoltage The digenite-covellite interface is associated with a dynamic potential, which should be attained almost instantaneously (the response time of the measuring circuit is approximately 2.5 sec) after the current is switched on, before the interface begins its migration into the specimen. The digenite composition at the surface has been -3 calculated to reach the value Cu, -,,,-S in 1.25 10 sec at a current 1.765 -2 density of 10 mA cm . In fact, the most reproducible initial 1 potentials (E^) are obtained by extrapolating to zero time a tangent to the quasi-straight initial part of the potential-time curve (Fig. 20). These measured potentials contain an ohmic component which can be calculated with the help of equation (4.2) and a concentration over voltage due to the diffusion in the electrode boundary layer. The diffusion overvoltage was estimated with the Nernst equation and Eq. (4.1), using the physical parameters measured by Newman et al. (62) in 0.1 M CuSO^-0.1 M ^SO^ solution, (Appendix 4). It was found to be * Provided nucleation resistances do not impede covellite formation 84 -2 8.5 mV at 75 mA cm ; at lower current densities it was proportionally smaller and might be effectively neglected. The corrected interface potential, E , versus S.C.E. (25°C) is plotted against the logarithm of the current density on figure 22. For small current densities, the electrode retains a potential very close to the equilibrium value reported in Chapter 2 (252 mV at 55°C). A linear relationship appears to satisfy the experimental data in the higher current density range. Such a Tafel relationship presupposes that a charge-transfer process is rate determining, but the scatter of the experimental data does not permit exclusion of a mechanism in which the interface overvoltage is due to recrystallization. The most irreversible part of the recrystallization process is the diffusionless structural change of sulphur anions from the lattice form of digenite to that of covellite (12). 4.7 Polarization of covellite anodes 4.7.1. Results a. Electrode potential measurements Covellite anodes were studied at 55°C by galvanostatic polarization -2 methods with current d ensities between 0.075 and 2.26 mA cm . This was a much lower range than used in the digenite studies and both ohmic drop and concentration overvoltage due to diffusion in the electrode boundary layer were negligible . The results obtained during these experiments are reported in Table 6. The potential-time curves obtained with covellite were of two types, depending on the current densities. Figure 23 shows a curve 85 Figure 22. Relationship between the logarithm of the current density and the surface potential, observed during the galvano-static oxidation of digenite anodes at 55°C. S.C.E. (25°C) I 0.1 M CuSO., 0.1 M H.SO. I Cu, .,-S. 1 4 2 4 1 1.78 86 Table 6 Polarization of covellite anodes S.C.E. (25°C)/0.1 M CuS04-0.1 M H2S04/CuS I E o EN E . mm E s Ef . -2 mA cm mV mV mV mV mV 0.075 323 557 395 395 0.23 337 592 448.4 448.4 0.38 336 587 498 498 0.57 350 603 496 496 0.75 335 779 568 568 341 626 498 498 1.13 343 690 518 518 1.36 338 670 538 615 1.51 302 802 1.532 1.88 338 774 612 1.526 2.26 338 808 654 1.568 EQ = 0 current potential E^ = maximum of potential obtained shortly after the current is switched on. Emin = t*ie mi-nlmum °f potential measured during the experiment (see Fig. 24). EG = steady-state potential. E^ = final value of the potential recorded after 6 days of electrolysis. _2 typical of low current densities (< 1 mA cm ) while Figure 24 shows a _2 curve found for-higher currents (> 2 mA cm ). In both cases, there was a gradual decline in the potential during the first several hours. In the case of the lower current densities, it gradually levelled off at t (hr.) Figure 23. Potential-time curve recorded during the galvanostatic oxidation of a covellite anode at 55°C. S.C.E. (25°C) | 0.1 M CuSO.-O.l M H„SO,I GuS. 4 2 41 l 1 1 1 1 1 1 r 89 a steady value while in the case of the higher current densities, the potential, undergoing a discontinuity rose abruptly to a very high value. In the latter case, the final potential was about half a volt above the resversible oxygen electrode, where most insoluble electrodes discharge oxygen. The apparent current densities are plotted against the covellite electrode potential versus S.C.E. (25°C) on Figure 25. The two curves drawn in solid line represent the steady-state potentials observed during the electrolysis of covellite. The dashed line extending the first curve toward the higher current densities represents the minimum potential measured on the potential-time recording. It appears on that graph _2 that current densities higher than 1.35 mA cm cause a change of the overall reaction leading to very high electrode potential. The dotted line joining the two curves pictures the behaviour of -2 covellite electrode in the intermediate current range (1.35 mA m < I < -2 1.5 mA m ). The potential of such electrodes increased very slowly during prolonged period of time (1 week), eventually leading to the final value reported on the dotted line. b. Electrode reactions To assess the overall electrode reaction corresponding to the two potential regions, chemical analysis was carried out on the reaction products. An experiment conducted for six days in a 0.01 M CuSO,-0.01 M H„S0. 4 2 4 -2 solution at 0.75 mA cm revealed no variation of the average copper content in the electrolytes, indicating that the anode and cathode I (mA.crrf2) 2 -Polarization curve obtained during the galvanostatic oxidation of covellite anodes at 55°C. S.C.E. (25°C) | 0.1 M H SO -0.1 M CuSO | CuS. 1 M CuSO-0.01 M H„ 4 o (• corresponds to 0.01 .-SO, solution) 2 4 91 reactions were of equal current efficiency, approximately 100% . A similar experiment performed at 2.26 mA cm depleted the copper in the electrolytes to an extent that would indicate an average current efficiency of 39% for the anodic process. The porous porcelain diaphragm appeared to have been exchanging ions with the solution and prevented any reasonable determination of the H+ content of the solution. The quantity of S0^ , if any, put into solution was too small to be detected. Both covellite and orthorhombic sulphur were identified by an X-ray diffraction study of surface residues. On the basis of these investigations, the covellite anodic reaction at lower potentials conforms to: CuS * Cu"1" + S° + 2e C4.H) The copper is dissolved and sulphur is left behind as an anode slime. When the sulphur structure forms there is a 24% shrinkage in volume 3 (the molar volume of covellite and of sulphur being 20.4 and 15.5 cm mole "^respectively (59)), thus the elemental sulphur is associated with cracks and pores that permit the electrolyte to retain access to the interface between covellite and elemental sulphur. Cupric ions are No bubbling was ever detected at the Cu cathode at any of the current densities used. The limiting current density at the Cu cathode in 0.1 M CUSO4 is reported to be about 15 mA cm-2 at 25°C in free con vection conditions (51), a value which was never approached in these experiments. A* _2 The total dissolution of 1 g CuS specimen, leads to only 10 mole of sulphur species in approximately 1 I of solution. 92 transported from this interface by diffusion in the solution invading the cracks. Thus, as in the digenite case, when the pores get sufficiently long, diffusion of cupric ions can no longer support the applied current and supplementary electrode reactions involving much higher potentials must support the excess current density. c. Microscopic examination of the reacted electrode An examination of covellite after electrolysis revealed that even when 40% of the copper was dissolved, the disk retained its shape and cohesion. The surface of the disk presented unreacted particles of covellite suspended in sulphur as seen on the micrograph ( Fig. 26). A perpendicular section of the disk shows sulphur penetrating deeply into the specimen and in fact going through it ( Fig. 27). At higher magnification, the sulphur matrix shows a fine network of lines that may represent shrinkage pores and cracks (Fig. 28). Micrographs taken with the scanning electron microscope show the high relief surface . (Fig. 29 and 30). An examination of the reacted disk with the electron microprobe was very inconclusive (Fig. 31,32,33). Even very light polishing ; tore sulphur particles away from the specimen surface, leaving sulphur depressions and covellite hills; the microprobe readings reflected the topography of the hilly surface more than the composition of the phases. 4.7.2 Discussion The initial rise of the electrode potential to a maximum during the first 15 minutes, or so, of current flow (see Fig. 23,24) are most Figure 26. Micrograph of the surface of an oxidized covellite disk (unreacted covellite appears white). Figure 27. Micrograph of a section of an oxidized covellite disk, perpendicular to the surface. Figure 28. Optical micrograph of an oxidized covellite disk. Figure 29. Scanning electron micrograph of an oxidized covellite disk. gure 30. Scanning electron micrograph of an oxidized covellite disk. Figure 31. Absorbed electrons. 97 probably due to supersaturation and finally nucleation of orthorhombic sulphur in the covellite phase. It may be postulated that the decline in potential is due to the rapid increase in the covellite-sulphur interface area, which decreases the effective local current density and the associated overvoltage. In a reacted disk, the interface area between unreacted covellite and the sulphur product is very large com pared with the exposed geometric surface area of the specimen as. it appears on the various micrographs. The scatter of the experimental points on the polarization curve (Fig. 25) could, in fact, reflect the uncertainty on the microscopic current density. The appearance of a new electrode reaction (probably oxygen _2 evolution) for current densities larger than 1.35 mA cm cannot be rationalized only in terms of a limited diffusion rate of copper ions in the solution filling the pores resulting from the, crystallization of sulphur, as was the case in digenite electrodes, because the active interfacial area and its variation with time are completely unknown. The minimum value of current density leading to changes in the original electrode process is likely to depend upon a number of para meters, the preparation and history of the covellite being probably one of them (initial porosity, grain size,...). The experimental polariza tion curve (Fig. 25) should, however, be able to describe, to a first approximation, the behaviour of covellite during current flow. 98 CHAPTER 5. DISCUSSION OF THE MECHANISMS OF DISSOLUTION OF THE COPPER SULPHIDES The study of the galvanostatic polarization of rotating disk anodes of digenite and covellite at 55°C (Chapter 4) suggests the following models for the oxidation of these sulphides in acid medium: - The reaction taking place at the digenite-covellite interface seems to present a relatively small resistance. - The digenite oxidation rate appears to be controlled by the trans port of the copper ions released by the reaction (4.3) through the porous covellite layer; the main transport component is likely diffusion in the solution filling the shrinkage pores of the covellite. - After nucleation of elemental sulphur, the oxidation rate of covellite might be controlled simultaneously by the reaction (4.11) at the covellite-sulphur interface and diffusion of cupric ions in the, solution filling the pores and cracks resulting from the crystalliza tion of the sulphur. The peculiar way in which the sulphur grows in the covellite anode excludes, so far, any diseussion of the relative influence of these two resistances on the overall reaction. However, during oxidation, covellite appears to exhibit a limiting current of dissolution similar to diffusion controlled reactions. In the following discussion, a model, which is derived from the present work and from Kuxmann and al.'s experimental observations (15), is proposed to describe the electrolytic dissolution of chalcocite. These models will then be used to try to account for the actual leaching behaviour of the copper sulphides using acidic ferric solutions. 99 5.1 Electrolytic dissolution of chalcocite: constant current oxidation Kuxmann and Biallass (15) studied the galvanostatic polarization of chalcocite anodes in cupric sulphate solutions, with current -2 densities in the range between 3 and 22.5 mA cm . The potential-time curves were characterized by an abrupt potential discontinuity occurring after a transition time, similar to that encountered in the present study of digenite anodes. The copper content of the electrolyte remained unchanged up to the transition, then it decreased linearly with time. Covellite (and sulphur in some cases) was clearly recognizable in the surface layer of the electrode. The transition times observed at 55°C in that work were back-calculated from the graphs reported in the paper - certainly, with a substantial loss of precision - and compared with the present data in Figure 21. The transition times measured in both works appear to be 2 similar in values and to obey the same type of relationship,i.e., I T=cst. In contrast to the present results, Kuxmann and Biallass observed that, before the transition, the anode potential remained approximately constant. This observation should rule out the possibility of a substantial transport of copper ions through the solid covellite. On the other hand, the potential drop resulting from the transport of the current through'the solution filling the pores should remain very small in this case since there was an excess of sulphuric acid in the electrolyte (30 g/1 CuS04~250 g/1 R^SO^). The conductivity of a 5 N H_2^4 solution is 0.673 9 ^cm 1 at 25°C (63) as compared to a conductivity of -0.051 n-1cm_1 for 0.1 M CUSO^-0.1 M H^SO^ solution at the same temperature (64). The concentration overvoltage corresponding 100 to the saturation of the solution with a cupric salt is small (- 10 mV). 2 The constancy of the product I T can be supported by the same arguments that were proposed for the digenite case (4.6.2) i.e., transition of the electrode process resulting from the saturation of the electrolyte with a cupric salt at the digenite-covellite interface and reaction inter face moving at a constant rate. In the case of an excess of indifferent electrolyte, the diffusion equations are considerably simplified since the effect of the electric field can be neglected, and in the aggregate, the flux of copper can be described by 3CCu JCu = _DCu f ~3lT where f is the effective fraction of the cross section occupied by pores. (If the initial chalcocite is fully dense, f < 0.255). It follows after integration between the limits of the covellite layer that U = 2F Dp f (C_ ^ - C„ ), Cu Cu,sat. Cu where D is an average diffusion coefficient for the range of concentra-2 tions considered. This last relationship is equivalent to I inconstant provided the covellite layer thickness increases linearly with time. The oxidation of chalcocite to covellite implies the formation of the intermediate djurleite and digenite phases. Kuxmann's results, along with the observations reported in Chapters 2, 3 and 4 seems to indicate that these interface reactions are relatively non resistive, and that the overall oxidation rate is controlled by the transport of 101 copper ions through the reaction products. The anode morphology resulting from the oxidation of chalcocite at constant current can be analysed theoretically: the problem consists in calculating the thickness of the various sulphide layers with respect to time, when the overall oxidation is controlled by diffusion through the reaction products. Theoretical model: constant current multiplelayer oxidation (Fig. 34) The djurleite will be considered undistinguishable from the chalcocite. This assumption is based on the facts that the composition and physical properties of the two phases are very similar. On the other hand, the standard electrode potentials reported for cast or mineral chalcocite (15,28,29) are very close to the standard potential of a djurleite-digenite electrode derived from the measurements reported in Chapter 2 (E = 503 mV at 25°C). The digenite composition is averaged to Cu, -,0S while the secondary effects due its stoichio-1. / o metry range are neglected. If the origin of times is taken when the anodic current is applied, a layer of digenite starts to form at t = 0, and its thickness is given at time, t, by the relationship ,Ms _1 al M;Ch 0.22 Cu.S -> Cu, -,0S + 0.22Cu"H" + 0.44e z 1. lo which translates a simple material balance between the flux of copper, J, and the amount of chalcocite reacted. x^ = Jt 102 Cu2S 011.8 S CuS J2 Solution Jg* J B const. x2 xl Steady state : Xj -x2 = constant Constant current multilayer growth model. Figure 34 103 The mechanism of transport of copper ions through the digenite layer is subject to a discussion similar to that conducted in section (4.6.2) for covellite. The transformation of chalcocite into digenite, without volume change, introduces 7% of porosity in the digenite layer. No data are available to assess the effect of this porosity on the transport properties of the digenite layer. Covellite forms when the electrode potential at the outside surface of the digenite has reached the equilibrium potential of a digenite-covellite electrode or when saturation of the solution filling the pores with a cupric salt is reached. At the onset of growth of covellite (t = t^), the thickness of the digenite layer (x^) is given, inaboth cases, by (see section 4.6.2) kD J - — , xD = Ja± tD, (5.1) where k^ is the constant of dissolution through digenite. The simultaneous growth of digenite and covellite is governed by the two first order differential equations which relate the rate of progression of the interfaces to the copper flux, Cu. S —> CuS + 0.78Cu -H- + 1.56e 1.78 where x^ is the total thickness of the reaction products, x^ is the thickness of the covellite layer (see Fig. 34). These can be transformed 104 in the following system of equations, cu dx dx„ ^ dt1 + IT • - Ja2 (5'2) d(x -x ) k-.(a.+OLr.) = 1 1 ^ - Jct (5.3) dt xl"x2 2 which can be integrated to give the following solutions (Appendix 5), xl xn X2 + = J(t-t_) (5.4) al a2 D XrX2~XD kD(al+a2) ln kD(al+a2) ~ Ja2(xrX2} _ t fc } Ja2 J2a 2 n " Ja2xD ' ^ It appears in equation (5.5) that the logarithm becomes infinite for a^+a2 kD^al+a2^ = Ja2^xl~x2^ or X1_X2 = —a— XD (5,. 6) When time increases, the distance between the two interfaces converges, therefore, towards a constant value (4.545 x^), and the two phases penetrate the anode at the same constant rate dx dx a a dt dt J ctj-hxj VfJh J The set of equations (5.4) and (5.5) was solved for x^ and x2 taking a value of k^ which corresponds to the solid state diffusion of copper ions in digenite. The integration of equation (3.9) with respect to the thickness of the digenite layer at the onset of growth of 105 covellite yields JXD " " ^ ^Cu » (5'8) F where Ayr = -2FAE corresponds to the range of stability of digenite, which was measured to be 20 mV at 55°C (Chapter 2), and or + is the copper ionic conductivity of digenite, measured to be approximately 7.5 10 5 ft "^crn 1 at 55°C (Chapter 3). It follows from equations (5.1) and (5.8) that k = 2 AE = 3.1 10 11 mole cm "'"sec 1 D r The depth of penetration of the two interfaces are plotted as a function of time on figures 35 and 36. It appears from the calculations that the interfaces assume their steady motion for time longer than 90 tp and that the thickness of the covellite layer is then adequately described by X2 = JCf}Ch Ct " 4,545 tD) C5,9) Since it was observed that a layer of covellite formed on the chalcocite sample subjected to oxidation, the observed transition could not result from transport limitation in the intermediate digenite layer. In fact, the thickness of the digenite layer adjusts itself to the flux of copper ions which diffuse through it: J when digenite only is formed, and J < J when both digenite and covellite are formed. It Depth of penetration of the chalcocite-digenite interface (x-^ and the digenite-covellite interface (x2), during the oxidation of chalcocite. I = 30 mA cm-2 I = 7.5 mA cm"2 107 follows from the theoretical analysis that the thickness of the digenite layer converges towards a constant (Eq. (5.6)) and that the depth of penetration of the covellite is linear and given by Eq. (5.9) for times larger than 90 t (Eq. (5.1)). 2 Since the product I T, relevant to the chalcocite electrolysis, was observed to be constant in Kuxmann's experiments, it may be proposed that the covellite had reached its steady rate of growth (Eq. 5.9) when the transition occurred. This would indicate that the observed transition time, T, is larger than 90 t^ and therefore that the constant of dissolution through the digenite layer, k^, is much smaller than the constant of dissolution through the covellite layer, k , kc > 20 kD, as can be calculated from the equations (5.9), (5.1), (4.6). It would be meaningless to compare the value of the constant of dissolution through the covellite layer calculated from the present work (Eq. (4.6)) with the constant that could be calculated from Kuxmann's work, interpreted by Eq. (5.9) and the data of Figure 21.: - In a solution containing 250 g/1 of I^SO^ and 30 g/1 CuSO^ the migration current is likely to be negligibly small while it is far from being so in a 0.1 M CuSO^-0.1 M H^SO^ solution. - The cupric salt which precipitates in the pores in the case of the 0.1 M CuSO^-0.1 M H^SO^ solution may be a basic sulphate while it is more likely to be a sulphate m the case of the 30 g/1 CuSO^-250;g/1 H„S0. solution. 108 - The theoretical porosity of the covellite resulting from the oxidation of the chalcocite and of the digenite is 25.5% and 19.7% respectively. As the dissolution constant depends on the effective fraction of the cross section occupied by the pores, it must be corrected to take that effect into account. If the model proposed for the dissolution of chalcocite and digenite is correct, it would be of interest to attempt the direct electrolysis of copper matte in a chloride or a mixed chloride-sulphate electrolyte since the solubility of cupric chloride in water is 6.6 M at 55°C (63) while the solubility of cupric sulphate is 2.2 M at 55°C (60,63). 5.2 Leaching of covellite with acidic ferric solutions: electrochemical  oxidation An electrochemical process, involving two simultaneous reactions, has often been proposed to account for the aqueous oxidation of sulphides (1,27,5,65): the reduction of the oxidant and the oxidation of the sulphide take place at different sites of the mineral and the electrons are transferred through the sulphide lattice. The process is analogous to the corrosion of metals and the electronic conductivity of many sulphides makes this feasible. Thomas and Ingraham (5) leached rotating disks of covellite in 3+ 0.1 M Fe -0.1 M H^SO^ solutions, their experiments were usually continued until 20% of the copper was dissolved. Up to this point, the disks retained their smooth surfaces, shape, dimensions and electrical conductivity. The reacted disks were a mixture of elemental sulphur and unreacted covellite similar to what was observed after the electrolysis 109 of covellite anodes (4.7.1); the covellite persisted on the outer surface of the specimen. The morphology of the leached specimens suggested that the interface where the covellite was oxidised to sulphur was penetrating the disk while the electrons released by the oxidation reaction were travelling through the persisting network of covellite particles towards the specimen surface where the ferric ions could be reduced. During leaching, copper sulphides should assume mixed electrode potentials which depend on the nature and magnitude of the electro chemical reactions taking place and which could be directly measured. In the case of an aqueous electrochemical oxidation, the leaching rates and the corresponding mixed potential taken by the sulphide can be estimated from the current-voltage curves obtained during anodic; polarization of the sulphide and cathodic polarization of the oxidant. This calculation has been made in the case of the leaching of a covellite disk rotating at 500 r.p.m. in acidic ferric solutions at 55°C; these conditions correspond to the leaching experiments conducted by Thomas and Ingraham (5). The electrode kinetics of the Fe'''/Fe"^" couple, which has been abundantly investigated on platinum electrodes, result from the interplay of diffusion and charge-transfer resistances (49). The contribution of the diffusion resistance can be calculated in the case of a rotating disk electrode. All the data which are necessary for the I | [ | | calculation of the current density-potential curves of the Fe /Fe couple have been compiled from the available literature and are reported in Appendix 6. The cathodic curves calculated in that fashion 110 for a ferric ion concentration of 0.1 M and for a ferrous ion concentra--3 -2 tion of 10 and 10 M are plotted on Figure 37 (these concentration values have been selected to match Thomas' experimental leaching conditions), and can be confronted with the polarization curve of cove llite anode determined in the present work (Fig. 25). The leaching rate derived, at 55°C, from Thomas' and Ingraham's -2 experiments is equivalent to a current density of 1.97 mA cm ; the leaching rates remained constant after a transient period of several hours. They studied the effect of the variation of the ferric ion concentrations at 50°C and found that the leaching rate was independent of ferric ion concentration for concentrations larger than 0.1 M. This results from a limiting dissolution rate of the covellite and could correspond to the limiting current density observed during the electrolys -2 of covellite anodes (I,. - 1.40 mA cm , see Section 4.7.1), since lim ' ' ' I j | | | the potential exerted by the Fe /Fe couple is not sufficient to force the transition to occur. An attempt that was made to derive the variation of the leaching rate of covellite at 55°C against the ferric ion concentration will be described with the experimental polarization curve for a covellite -2 anode using 1^ = 2 mA cm and a set of calculated current density I|| ||| potential curves for various Fe concentrations, the ratio Fe /Fe being assumed constant (Figure 38), This estimation leads only to semi-quantative information since it is derived from polarization curves which have not been precisely established for the leaching conditions: - The polarization curve for a covellite anode remains somewhat I mA.cm 112 Figure 38. Electrochemical oxidation of CuS by ferric sulphate solutions R.D.E. spinning at 500 r.p.m., 55°C. Fe3+(0.25 M) Fe3+(0.1 M) ,o) ?+ -3 /Fe (10 M) /Fe2+(10_2 M) /Fe2+(10~3 M) /Fe2+(10-2 M) 3+ -2 FeJ (10 Z M) /Fe2+(10_4 M) /Fe2+(10_3 M) o, . /Fe2+(10_5 M) Fe (IO"3 M) I /Fe2+(1Q-4 M) ) 113 approximate since it depends upon the actual interfacial area which, in turn, is the result of the morphology of the sulphur growth. - In addition, the polarization of covellite anode was studied in 0.1 M CuSO^ solution while Thomas and Ingraham start their leaching experiment with a solution containing no copper. - The charge-transfer parameters of the Fe+++/Fe++ couple have been measured at a platinum electrode. - The whole apparent sulphide area is supposed to be active for the reduction of ferric ions. The leaching rates expressed in current densities were calculated from Figure 38 and are reported on Figure 39 in regard of the experimental leaching rates measured by Thomas and Ingraham. Both* calculated and experimental curves seem to follow the same type of dependence upon the ferric ion concentration. The leaching rate of covellite is independent of the ferric ion concentration above a certain value, which is likely to be temperature dependent, and is, then, controlled only by the oxidation kinetics of the sulphide. In very dilute solutions, the leaching rate is determined by the limited rate of diffusion of the ferric ions towards the covellite. In the intermediate range of concentrations, the leaching rate results from both the oxidation kinetics of covellite and the reduction kinetics of ferric ions. It follows from the foregoing discussion that, so far, an electro chemical mechanism appears to be adequate to explain the oxidation of coyellite in acidic ferric solution. 114 measured at 60° C (5) mA.crrf2 calculated at 55°C log CFe3+ gure 39. Leaching rate of rotating covellite disks (500 r.p.m.) versus ferric ion concentration in solution. 115 5.3 Leaching of chalcocite and digenite with acidic ferric solutions: constant potential oxidation The driving force exerted by acidic ferric solutions is large enough to oxidise any copper sulphide to elemental sulphur but the sulphur formation, which has to overcome a nucleation stage, is sufficiently resis tive to occur only to a negligible extent during the chalcocite and digenite oxidation, either until these sulphides are completely exhausted (ground minerals) or until the diffusion resistance of the covellite layer (solid sample) has markedly slowed down the reaction (4.3). This explains the characteristic two stage reaction generally observed during the leaching of chalcocite and covellite. In the following discussion, the first leaching stage of digenite and chalcocite will be treated as a reaction controlled by the transport of copper ions across fhe oxidation products, as it follows from the model proposed at the beginning of this chapter. Except for the initial period, this leaching reaction can be approximated as an oxidation at constant potential, the rate of which is controlled by diffusion through the reaction products. Theoretically the problem consists in calculating the thickness of the various sulphide layers as a function of time. At this point, the analogy between the first leaching stage of chalcocite and digenite and the oxidation of metals is obvious. Theoretical model: constant current multiplelayer oxidation (Fig. 40) The preliminary assumptions are the same as the ones stated for constant current oxidation model. 116 Cu2S Cu|QS CuS J2 Solution j . ko kC J2°"x^ X. Steady state : = constant. x2 Constant potential multilayer growth model. Figure 40 117 During the oxidation of digenite, the covellite grows according to the parabolic law ,01 vl/2 .1/2 x = (2kc>Da) -t where k is the constant of dissolution through the covellite layer M 1 defined by Eq. (4.6) and a = (-j-)D jj-^-g . The copper flux crossing the covellite layer is inversely propor tional to its thickness kCD kCDV2 "1/2 J = or J = (-^) t (5.10) x 2a During chalcocite oxidation, the growth of the digenite (subscript 1) and covellite (subscript 2) layers will obey the two following differential equations which translate a material balance between the copper fluxes and the interface motions (Fig. 40), dXl _ Vl _ rM. 1 ... dT - K~^2 al ~ ^Ch C~22 (5ai) dX2 ^ kC,Ch°2 V2 = M dt x2 Xl-x2 a2 M;CH 0.78 where kD is the dissolution constant through the digenite layer as defined by Eq. (5.1). The division of equation (5.12) by equation (5.11) yields dXl kD °1 *2 "l kD 118 The most general solution of this classical, first order homogeneous differential equation is (Appendix 7). Ul U2 £ = (x2 - u^) U2 Ul (x2-uzXl) VU2 , (5.14) where C is the integration constant^ and u^ and u2 are the roots of the second degree equation 2 4. ^ n x kC,Ch, kC,Ch. a2 . U + (1 + —j-5 )u r-* = 0. al kD kD al The condition that x^ and x2 are strictly positive for t > 0 and zero at t = 0 simplifies equation (5.14) considerably to x2 = u^x1 u^ > 0 (5.15) °r a2 k a 2 k 2 k a 1/2 (1 + _£i£h) + [(-i) (i + ^Ch) + 4 CiCh al kD al kD kD V X2 2 xl The relationship (5.15) has already been proposed by Valensi (66,67) for metal oxidation leading to the formation of several oxide layers and controlled by diffusion through the oxidation product. The integration of equations (5.11) and (5.12) yields k a 1/2 1/2 Xl = (2 1^) t ' (5*16) k a 1/2 1/2 X2 = [2CkC,Cha2 * ll^7)j t ' (5'17) u 119 Both phases grow according to a parabolic law and the ratio between the quantity of the two phases remains constant. The flux crossing the covellite layer is inversely proportional to its thickness and equals . k a -1/2 -1/2 J = kC,Ch[2(kC,Cha2' - r^->] t (5.18) u 1 j It follows from the calculations or from the analogy with metal oxidation that the depth of penetration of the digenite and of the covellite varies as a parabolic function of time (Eq. (5.16) and (5.17)) and that the ratio between the depth of penetration of the two phases remains constant (Eq. (5.15)). The rate of the first leaching stage of digenite and chalcocite will be calculated from equation (5.10) and from equations (5.18) and (5.15) using the following dissolution constants: As it has already been pointed out earlier, the dissolution constant, k , through the covellite layer depends upon the fraction of the cross section occupied by the pores and is assumed to be proportional to it. As the covellite resulting from the oxidation of digenite and covellite theoretically contains 19.7% and 25.5% of pores, respectively, it follows that = ^ k C,Ch 19.7 C,D' -9 -1 -1 where k = 2.35 10 mole cm sec was derived from the experimental results reported in section (4.6.2). The value of kp relevant to the leaching of chalcocite has already been discussed in section (5.1) (theoretical model). In the absence of other data, k was calculated in 120 the case of solid state diffusion to be 3.1 10 "*"x mole cm xsec The • M 3-1 molar volumes (-j) of chalcocite and digenite are 27.5 and 25.4 cm mole , respectively (59). The calculated rates for times equal to 1 and 5 hours, as well as the rate averaged over this time interval, fc2 JAt = / Jdt, (5.19) are reported in Table 7. Table 7 Rates of the first leaching stage of massive digenite and chalcocite at 55°C in acid ferric solutions (nr) mA cm calculated 1 19.3 24.1 5 8.6 10.8 averaged,Eq. (5.19) 11.9 14.9 measured (10) 12.9 18.2 Ch mA cm -2 Thomas and al. (.10) measured dissolution rates of rotating disks of chalcocite and digenite during the first stage of leaching in 0.1 M 3+ Fe -0.1 M ^SO^ solution. Their experimental values, which did not depend upon ferric ion concentration at 500 r.p.m., are reported in Table 7. Though the plot of the observed quantity of copper dissolved 121 against time was slightly curved, they calculated average dissolution rates for the range of 0.5 to 2.5 g of copper dissolved, which should approximately correspond to the selected time interval. The agreement between the two sets of values is satisfactory given the assumptions which were introduced and given the uncertainty on the measured dissolution constant (k ). From the division of equation (5.10) by equation (5.18) it follows ft that digenite should dissolve at 80% of the chalcocite rate in otherwise identical conditions. In:Thomas and al's experiments, the rate of dissolution of digenite ranges between 70 and 84% of the rate of chalcocite. It can be derived from Eq. (5.15) that, in the conditions stated for these calculations, the covellite represents approximately 96% of the oxidation products. Therefore it appears that the rate of the first stage of dissolution of massive chalcocite and digenite may be reasonably accounted for by a model corresponding to a rate controlling transport of copper ions through the oxidation products. The second leaching stage of these sulphides, which involves the oxidation of covellite, should follow the same mechanism as this latter. A difference resides in the fact that this particular covellite already contains 20 or 25% of porosity which explains the larger dissolution rates observed in this case (4,9). * This rate ratio is affected relatively little by the value chosen for kj). In fact, a value of 78% is calculated to correspond to k^ = 3 lO--^ mole cm-lsec--'-, the covellite then representing 74% of the oxidation products. 122 CHAPTER 6. CONCLUSIONS 6.1 Electrochemical parameters of the copper sulphides Electrochemical studies performed on copper sulphides provided some fundamental information on the Cu-S system. 1. E.m.f. measurements were conducted in the range between 40 and 80°C on the following galvanic cells, S.C.E. (25°C) | 0.1 M CuS04, 0.1 M H2S04 | Cu , S.C.E. (25°C) I 0.1 M CuSO., 0.1 M H„S0. I Cu S. i 4 2 4 1 y The copper sulphide composition was selected to produce a two phase electrode having a fixed copper activity. The potentials of the investigated electrodes with respect to S.C.E. (25°C) (Stockholm Convention) were measured to be: E(Cu) = (70.45 ± 0.33) x 10_3 + (0.632 ± 0.025) x 10-3 (T-328) V, E(D.-C.) = (251.50 ± 0.35) x 10-3 + (0.765 ± 0.035) x 10-3(T-328) V, E(D.-Dj.)=(242.20 ± 0.45) x IO-3 + (0.62 ± 0.060) x 10""3 (T-343) V. The variation of the chemical potential of copper and sulphur across the Cu-S system could be assessed from the above measurements and from existing thermodynamic data. Consequently, the standard free enthalpy of formation of digenite and djurleite were calculated in the investigated range of temperature with the noted precision, as follows: 123 AF°(CU;L ?65S) = (-18,140 ± 520) - (4.9 ± 2.5)(T-328) cal mole"1, AF°(CU;L 965S) = (-19,700 ± 550) - (5.5 ± 3.1)(T-343) cal mole"1. The variation of the standard free enthalpy of formation of digenite, was estimated as a function of composition (1.765 < y < 1.83): AF°(CuyS) = (-18,140 ± 520) - (4.9 ± 2.5)(T-328) + (y - 1.765)[(-7,910 ± 40) - (3.2 ± 2.5)(T-328)] cal mole 1. The major component (approximately 90%) of the final error on the above thermodynamic values originated from the error on the existing data for CuS. 2. Copper sulphides were grown on a copper anode from an acidic solution saturated with l^S at constant current. The thickening of the copper sulphide film, at low electric field strength, was accounted for by electrolytic transport in the scale and a theoretical model for the scale growth was proposed for steady-state conditions. The diffusion coefficient of cuprous ions in chalcocite and digenite was calculated in the temperature range between 30 and 73°C from the slope of the electrode potential versus time relationship. The diffusion coefficient of cuprous ions in low chalcocite was found to be DCu+ = 8.1 x 10"3 exp (- '^0) and in low digenite DCu+ = 3.6 x 10 exp ( —) 2 -1 cm sec , 2 -1 cm sec , 124 The phase boundary reactions did not appear to be too resistive to interfere with these measurements. 3. Potential-time curves were recorded during the galvanostatic polarization of rotating disk anodes of digenite and covellite in 0.1 M CuSO^-0.1 M H2S04 solutions at 55°C, and were analysed. Digenite anodes always underwent a potential discontinuity in a transition time, x t such that the relationship between the current density and the transition time was T2 OK .2—4 IT =2.5 A cm sec. It was proposed that, at the transition, the rate of the overall I [ electrode reaction, Cu, -,0S -> CuS + 1.56e + 0.78Cu , was limited by the transport of the copper ions released by the oxidation reaction, though the porous covellite layer; the main transport component was likely diffusion in the solution filling the shrinkage pores of the covellite. The dissolution constant, k , through the covellite layer k C has been defined (J = -T— ) and calculated from the experimental data. The interface reaction seemed to introduce little resistance in the overall oxidation process. The anodic reaction on covellite, CuS -> Cu + S" + 2e, appeared to be relatively resistive. During oxidation, covellite exhibited a limiting current of dissolution similarly to diffusion . controlled reactions. The apparent current density-potential curve has been established for the steady-state which occurred after long dissolution times of covellite. 125 6.2 Application to the electrolysis of matte anodes and to the leaching  of copper sulphides The discussion of the data existing in the literature on the constant current electrolysis of chalcocite anodes, supplemented by the information obtained in the present work, suggests that the rate of; dissolution of chalcocite, as is the case of digenite, is limited by the diffusion of copper ions in the higher sulphide layer. Leaching rates of covellite in acidic ferric solutions are estimated from the data established in the preceeding parts of this work on the basis of an electrochemical mechanism of oxidation, analogous to metal corrosion. This model appears adequate to explain the behaviour of covellite in the presence of an aqueous ferric oxidant, as observed by other researchers. The rates of the first leaching step of chalcocite and digenite by an aqueous oxidant are calculated on the basis of a constant potential oxidation model, where the rate of the process is controlled by the transport of copper ions through the oxidation products. The results of these calculations are found to be in agreement with the relevant experimental data existing in the literature. 126 APPENDIX 1. USE OF A GALVANIC CELL TO MEASURE THE IONIC CONDUCTIVITY OF A COPPER SULPHIDE MEMBRANE a. Measurement method ; The application of an electric field to an initially homogeneous copper sulphide gives rise to activity gradients and for larger fields, when the activity gradients tend to exceed the stability limits, to decomposition. The type of current (ionic, electronic or mixed) depends on the contacts or electrodes. In a cell, where the copper sulphide is inserted between two ionic conductors, e.g., the application of a d.c. potential forces an ionic current through the copper sulphide. However the current is not exclusively ionic since copper is in the cupric form in solution and may exist in the cuprous form in the solid. The flux of copper atoms, flowing through; the copper sulphide depends on the total current flowing through the cell. 2F = JCu' CA which is related to the Onsager coefficient through Eq. (3.7) Cu | CuSO, aq | Cu S | CuSO, aq. | Cu (AI) 3y Cu J Cu = -M Cu C3, 7) 127 Integration of Eq. (3.7) over the thickness of the sulphide tablet yields JCu = 2F ^_ AE (A1.2) where M is the average value of the Onsager coefficient in the activity gradient, and Aur = -2F AE represents the drop of electro-chemical potential across the sulphide. It appears from Eq. Al.l and A1.2 that the average Onsager coeffic ient can be calculated from the experimental current-potential relations. The conversion of the Onsager coefficient in ionic conductivity or diffusion coefficient (Eq. 3.8) requires the determination of the charge of the diffusing species. The Onsager coefficient may depend upon the potential drop across the sulphide. Since the thermodynamic potentials are not fixed at the copper sulphide-electrolyte interface, the results may depend on the sample, b. Experimental Several designs and constructions of cell were attempted: 1. A first type of cell was made of two teflon cylinders pressed against a copper sulphide membrane by a vise. The teflon was creeping under the compression stress and the cell leaking. 2. A second type of cell was made of two pyrex tubes cemented to the copper sulphide membrane with epoxy resin. The leads of the two copper electrodes were sealed in the cell with epoxy resin and the cell was evacuated and sealed after having been filled wih the solution. The manufacture of these cells was extremely delicate and the thin epoxy joint was not standing the solution during more than one or two days. 128 3. A third type of cell, which was made of teflon, is pictured on Fig. 41. The experiments were performed with this last cell, which was open to the atmosphere. The cell was filled with a boiled solution ( 0.5 M CuSO., 0.5 M H.SO.), 4 2 4 deaerated under vacuum and kept under a helium atmosphere. This treat ment was intended to prevent the evolution of bubbles, which were dragging the solution out of the cell during the course of the experiments. In spite of this precaution many experiments were discontinued by bubbling. This gas evolution however could not be attributed to an electrode reaction. Each half cell was divided by a fritted. polyethylene disk into an anodic and cathodic compartment (see section 4.5). The cell was enclosed in a pyrex tube closed at both ends with . metallic covers. The electrical leads were cased in rubber tubings fitted to one of the covers. A helium atmosphere was maintained in.the tube. The above assembly was immersed in a thermostat-regulated ethylene glycol bath. i An electroscan,Beckman 30, was used as a constant current source. The current was measured by a Keithley, model 153, microvoltammeter. The potential drop across the two terminal copper electrodes was measured with a Keithley, model 630, electrometer. The copper electrodes were made of 0.99999 pure copper plate. The covellite membrane was synthesized and shaped in the way described in section 4.5. I!l approximately. k\\\1 Teflon cell. g§§M§§ Copper sulphide. f Copper electrodes. St. steel washers. |g&&#l Teflon membranes. VO Figure 41. Design of a galvanic cell to measure the ionic conductivity of a copper sulphide membrane. 130 c. Results and discussion The cell was first calibrated with a copper membrane. The potential drop between the two terminal copper electrodes of the cell Cu | CuS04, H2S04 aq. | Cu | CuSO^, ^SO^ aq. | Cu remained smaller than 1 mV up to currents of 10 uA. Consequently, the difference of electrochemical potential across the sulphide membrane could be directly measured by the potential drop occurring in cell AI for currents smaller than 10 uA. The data reported for digenite in Chapters 2 and 3 indicate that this range of current could be adequate. At 55°C, the maximum potential difference that can be imposed on digenite is 20 mV and its cuprous conductivity is 7.5 10 5 "''cm "*". Eq. (A1.2) allows the calculation of the maximum current that can be forced through a digenite disk, 3 mm thick by 9.55 mm in diameter. i _ 4 x 7.5 10 x 2 10 5 „ ,„-2 - 14 uA 0.3 Any current higher than this value would cause the electrolysis of the sulphide. The maximum potential difference that can exist across a covellite membrane is approximately 75 -uV, but its ionic conductivity may be expected to be smaller than that of digenite. So, in first approximation, the same range of current can be used for this experiment. A certain quantity of coulombs must be passed through the specimen in order to establish the copper activity gradient necessary to support the steady-state flow of copper. If, in first approximation, a 131 linear concentration gradient is assumed across the membrane, the time necessary to establish the steady-state in a digenite membrane, in the above conditions, can be estimated. The initial composition of digenite is assumed to be Cu ^QO S, its stability limits being Cu, QS JL. / OZj JL. o SJl d and Cu, -,£CS at 55°C. A quantity bf copper equal to AC„ -r— (TT)„ „ is 1.765 Cu 2 M Cu S y necessary to shape the concentration gradient across the disk, • r _ (1.8-1.7825) x 0.72 x 0.3 5 1 2 x 25.4 1U t - 12 days. 3 By that time, the cell, which contains only about 4 cm of solution, will be dryed off by evaporation. Since covellite is reported to be stoichiometric, the time necessary to establish the steady-state flow should be considerably smaller. Measurements made on covellite membrane, approximately 2 mm thick, at current below 10 uA were not reproducible either in time on the same sample, or on different samples. The potential drops measured in identical conditions could be as different as 1 to 10. The residual porosity of the disk could short-circuit the membrane and account for the low values. The very high potential drop observed immediately after the switching of the current, which was decaying, thereafter, seemed to indicate that sulphur was probably formed at the anodic side of the covellite. In fact, the synthetic covellite is very close to sulphur saturation, and current flow should cause the sulphur formation at the anode during the transient period. As the covellite-sulphur electrode appears irreversible (Section 4.7), the sulphur formation would remoye all significance to the potential measurements. 132 APPENDIX 2. DIVISION OF THE TOTAL OVERVOLTAGE IN THE VARIOUS COMPONENTS The various overvoltages are clearly defined when there is only one rate-controlling step in the electrode process but the definitions are still controversial when several resistances arise concurrently during the reaction (50). If either concentration overvoltage or crystalliza tion overvoltage occurs alone, the electrode potential during current flow can be calculated with the help of the Nernst's equation for equilibrium potentials, since the charge-transfer reaction is in equilibrium. In the mixed control case, this equation is, strictly speaking, no longer applicable. K.J. Vetter (49) gave a definition for the division of the measured overvoltage in its diffusion, reaction, crystallization and charge-transfer components, which is based on the requirement that upon the disappearance of all overvoltage types but one, the residual overvoltage must agree with the definition for the single remaining overvoltage type. The determining quantity for charge-transfer control is the exchange current density I ; when Iq becomes infinitely great, charge-transfer rate-control no longer exists, so that for I ->•<», nt 0» . The reaction overvoltage will vanish if the determining exchange reaction rate vQ r ~* °°' aS Wlxx t*ie diffusion component for D °o. The crystallization component will disappear if the crystallization is infinitely rapid (VQ ^ »). The order in which these limits are taken is important for precise overvoltage definitions. Vetter proposed the following sequence, 133 V -»- oo o,r D -> 00 V oo o,C n-nr + nD+-nc % + \ + nD nc - 0 An An An An = n = nT = n. (A2.1) The charge-transfer component, because it depends upon the concentrations at the electrode surface, is influenced by the existence of the other overvoltage. Therefore the limit I -v » should be carried out first. On the basis of this definition, the current-potential relationship (50) for simultaneous occurrence of charge-transfer and concentration overvoltage will be treated. C.z . _ C.z . ••/•!•• \ -p. , . T fTI / i\ r,i n qzF , i. o,x (,1-q)zF , n 0. I = I [n (—) exp n - II(—) ' exp - -——— n J CA2.2) ° i C. RT i£ R i i C. and C. are the concentrations of species i at the electrode surface i i r and in the bulk of the solution, respectively. I is the exchange current density, z . and z . the electrochemical reaction orders, J ' o,x r,i ' z the charge transfer valence, and a the charge transfer coefficient. T „/ is r,x azF i. o,i (l-a)zF i °°> nC—) exp -r=- n = TT (—) exp - -— n o i c  C RT C z —z zF , i. r,i o,i exp - -n = TJC—) 134 with z . - z . = v. — (49) 0,1 r,i 1 n where v. is the stoichiometric coefficient of the reaction and, n the electrode reaction valence change. RT . ,Ci,Vl 1 This equation coincides with the Nernst equation for a concentration cell. This is in contradiction with the theory of concentration overvoltage proposed recently by M. Enyo and T. Yokoyama (50) who used equation (A2.2) to demonstrate their point, but took the limits (A2.1) in the inverted sequence. 135 APPENDIX 3. ESTIMATION OF THE POTENTIAL DROP IN A DIFFUSION LAYER OF A PARTIALLY IONIZED ELECTROLYTE The set of equations (4.9) describing the diffusion in a CuSO^ electrolyte are: 3C Jl - "Dl JT  (A3- 1} J3 = -D3^ + ID3Sl CA3'3) The subscripts 1, 2, 3 stand for CuSO^, Cu , SO^ respectively. The electroneutrality condition is C^ = C^ The flow requirement is = -J^ 2 The chemical equilibrium statement is C^ = K.C^ Addition of Eq. (A3.1) and Eq. (A3.3) yields after rearrangement of the variables Dl 3C2 1 9C? 9P a* D3 ax C 9X RT 3x For steady-state diffusion across a boundary layer, of defined thickness, integration of Eq.(A3.4) with respect to the thickness of the layer yields n r RT 1 — RT 9 A* = F rT K (c2 _ c2} + IF" LN - (A3,5) 3 136 When the saturation in a cupric salt is reached at the electrode-electrolyte interface, + = Cg, and can be calculated from K C 2 + C„ - C =0. I l s The potential drop in the diffusion layer is estimated from Eq. (A3.5) taking the following values for the physical parameters. - Cg = 2.2 mole 1 1 corresponds to the saturation of the solution with CuS04-5H20 at 55°C (60,63). - = D2 this assumption has been proposed in section (4.6.2) ++ Since the transport number of Cu has been measured to be 0.36 in 0.1 M CuSO^ at 25°C (75) and should not be temperature dependent, •• Q' it can be assumed that — = _ * _, .• = 0.485. 0.74 - The complexation constant, K, has been estimated to be 127 at ambient temperature by Nasanen and Klaile (61) but the appropriate value of this constant in concentrated solutions at 55°C is not known. In these conditions, the potential drop amounts to 76 mV, 185 mV and 249 mV for values of the complexation constant of 10, 100 and 200 respectively. 137 APPENDIX 4. CALCULATION OF THE DIFFUSION OVERVOLTAGE AT A ROTATING DISK ELECTRODE. The concentration overvoltage arising at a R.D.E. from limited diffusion rate across the electrode boundary layer can be calculated from Eq. (4.1) and the Nernst equation. Hsueh and Newman (58) measured the limiting current density for the deposition of copper from a 0.1 M CuSO^ solution as a function of the angular velocity of the rotating disk electrode. i _2 I = 72 mA cm at 25°C and 250 r.p.m. i Since the transport number of the cupric ions in a 0.1 M CuSO^ solution, is 0.36 (75), it is possible to extrapolate from this measurement, the corresponding limiting current density in the presence of an excess of indifferent electrolyte. This case is hypothetical since the presence of an excess of indifferent electrolyte would modify the , physical properties of the solution. -2 1^ =. 46 mA cm at 25°C and 250 r.p.m. A 0.1 M CuSO.-0,1 M H„S0. solution is intermediate between these two 4 2 4 cases; its physical properties are 'very close to a 0.1 M CuSO^ solution C62). The limiting diffusion current density derived from 138 Marathe's and Newman's experiments in a 0.1 M CuSO^-0.1 M E^SO^ solution is (56) _2 I = 59 mA cm at 25°C and 250 r.p.m. It follows from Eq. (4.1) that C I — = 1 - •=- I > 0 at an anode C D I < 0 at a cathode The diffusion overvoltage will be calculated at 55°C in the case I | of a 0.1 M CuSO^ solution and in the hypothetical case of 0.1 M Cu in the presence of an excess of indifferent electrolyte. Since the limiting current density is given by Eq. (4.1) ID - 0.62 D2/3 v"1/6 .1/2 2F C it can be extrapolated to 55°C, D and v being the only temperature dependent parameters. T -D = A — A is a constant and u is the viscosity of water (76) V 328 y25 D55 D25 298 y55 ^55 d_25 V55 " V25 u25 d55 139 The viscosity and density of water are tabulated in chemical handbooks (77) D55 - 1.945 D25 = 0.573 ID(55) = 1.71 ID(25) Binary electrolyte: Excess of indifferent electrolyte _2 1^ = 123 mA cm -2 79 mA cm -2 I (mA cm ) nD CmV) nD CmV) D D 75.3 1.61 6.7 1.95 9.4 56.5 1.46 5.3 1.71 7.6 37.7 1.31 3.8 1.48 5.5 18.8 1.15 2.0 1.24 3.0 15.1 1.13 1.7 1.19 2.5 11.3 1.09 1.2 1.14 1.9 7.5 1.07 1.0 1.09 1.2 The average value of the diffusion overvoltage over the two extreme cases was selected for use in other calculations in this thesis. Though such a calculation is only an approximation, the magnitude of the diffusion overvoltage remains small and is likely smaller than the experimental error on the potential. A resistance polarization is generally associated with a concentration gradient in solution: this term which is zero in the presence of excess of indifferent electrolyte equals the diffusion overvoltage in a binary electrolyte. In the present case, however, it has been shown in Appendix 3 that this value, calculated for a dissociated electrolyte, was not appropriate. The ohmic drop calculated with the 140 resistivity of the bulk solution is already taken into account in the term, n^. The small concentration variation in the boundary layer is unlikely to modify much of'the resistivity of. the solution, and the remaining part of the resistance polarization is neglected. 141 APPENDIX 5. INTEGRATION OF EQUATION (5.3) d(x1~x2) kD(a;L+a2) _ = _ j (5.3) at xl-x2 Let us set xi"x2 = Y kD(a1+a2) = A Ja2 = B Eq. (5.3) can then be written y dy = (A-By) dt which can be directly integrated 1 j^m ^ = t + c Let us set A - By = z -B dy = dz It follows or ~ / — dz = t + C B2 ~ (z-A In z) = t + C B 142 Replacing z by its value yields [A-B(X;L-x2)J ln [A-B(Xl-x2)] = t + C B B The solution (5.5) can be written, after taking into account the initial condition x,-x„ = x_ at t = t xl ^2 XD kD(a1+a2) kD(a1+a2) - Ja2(x1~x2) ln T2 2 J a2 kD(al+a2} " Ja2 XD = t - t„ 143 APPENDIX 6. THE Fe3+/Fe2+ ELECTRODE The current density-potential relationship is expressed in the 3+ 2+ case of the Fe /Fe electrode by This equation translates the effect of charge-transfer and diffusion resistances. Parameters of the charge-transfer process (measured at a platinum electrode) I , the exchange current density was determined to satisfy the relationship Io = ko[Fe2+] exp § Eeq> = k^Fe^J exp - ^ E^ (49,68,69) 3+ 2+ If the selected reference is the standard Fe /Fe electrode itself (E = 0), the expression of I is simplified to I = k lFe3+Ja jFe2+]1_a o o The following experimental data are ayailable: a = 0.58 (68) k (25°C) = 300 mA cm^mole'1 1 (68) o 144 31n I .. r-2- = - ^ AH = 7,500 cal mole" (70,71) Parameters of the diffusion process: case of a rotating disk ' electrode (section 4.2). In the presence of an excess of indifferent electrolyte, the limiting diffusion current densities of the ferrous and ferric ions towards a R.D.E. are given by (Eq. 4.1) T _ n ,9 _ 2/3 -1/6 1/2 . 2+ T _ n n 2/3 -1/6 1/2 3+, ID 3 = 0.62 D^ v to F IFe ] The diffusion coefficients of ferrous and ferric ions (D2, D^, respectively) in sulphuric solutions have been measured to be D2C25°C) = 5.4 10-6 cm2sec 1 (72) D3(25°C) =4.4 IO-6 cm2sec-1 (72) The other parameters were chosen to fit the conditions of Thomas' and Ingraham's leaching experiments (5)• 2TT x 500 -I —77: radian sec 60 The kinematic viscosity of the solution was approximated by the kinematic -viscosity of a 0.1 M I^SO^ solution> 1 145 v(25°C) = 0.99 10 -2 2 -1 cm sec (62) Temperature corrections for the diffusion coefficients and kinematic viscosity were done according to the method described in Appendix 4. 3+ 2+ Equilibrium potential of the Fe /Fe couple 3+ 2+ The standard electrode potential of the Fe /Fe couple is at 25°C (Stockholm Convention) e (25°C) = 771 mV (2) o or if the S.C.E. (25°C) is chosen as reference e (25°C) = 529.5 mV o 3+ 2+ The electrode potential of the normal Fe /Fe couple at 55°C with respect to the S.C.E. (25°C) can then be calculated with the help of the thermal temperature coefficient of the electrode , de 1 (-£) = +2.059 mV (°C) (32) th e [S.C.E. (25°C)J = 592 mV at 55°C o The actual electrode potential still depends upon the ionic strength of the solution (2,73,74) and is approximately 30 mV lower than the theoretical value in solution of ionic strength larger than 0.3 (73). 146 A correction taking into account the difference in activity coefficients of the ferric and ferrous ions^ resulting from the concentra tion difference.was not made because of the lack of data. 147 APPENDIX 7. INTEGRATION OF EQUATION (5.13) ^2 = kG?Gh «2 _-«2 a+\^ (513) dxl kDal *2 «1 Q kD ) C } Let us set A = kC,Ch ^2 kD al B = — (1 + )  al kD 'fi Xl = u It follows that = u dx^ + x^ du or dx 2 du = X„ -z + U dx1 1 dx.^ du = Au 1 - B - u dx1 " xx Integration of the former equation yields x = C exp. / — (A7.1) Au - B - u 148 or after reduction in simple fractions Ul U2 u-u u-u / —-—— du - / £ du (A7.2) u"ul u"u2 where u^ and are the roots of the second degree equation u2 + Bu - A = 0 It follows after integration of Eq. CA7.2) Ul V ln (u-u ) + — In (u-uj (A7.3) u2_ui 1 uru2 2 and replacement of Eq. (A7.3) in Eq. (A7.1) Ul U2 x = CCu-u1) (u-u2) X2 Replacement of u by — yields xl Ul U2 i , sVui , ,uru2 — - (x2-u1x1) (x^-u^&j) C3'1^) which is the proposed solution, Eq. (5.14). 149 REFERENCES 1. J.T. Woodcock, Proceedings the Aus. I.M.M. 198, 47 (1961), 2. W.M. Latimer, The oxidation states of the elements and their potential in aqueous solutions, Prentice-Hall, Inc., N.Y. (1952), 3. F. Loewen, M.A.Sc. thesis, University of British Columbia (1967), 4. J. Sullivan, U.S. Bur. Mines Tech. Paper 487 (1930). 5. G. Thomas, T.R. Ingraham, Canadian Met. Quarterly, 6, 153 (1967), 6. K.J. Jackson, J.D.H. Strickland, Trans. Met. Soc. A.I.M.E. 212, 373 (1958). 7. I.H. Warren, Aust. J. Appl. Sci., 9, 36 (1956). 8. J. Dahms, J. Gerlach, F. Pawlek, Erzmetall 20, 203 (1967). 9. J. Sullivan, U.S. Bur. Mines Tech. Paper 473 (1930). 10. G. Thomas, T.R. Ingraham, R.J.C. MacDonald, Can. Met. Quarterly, 6, 281 (1967). 11. E. Roseboom Jr., Econ. Geol. 61(4), 641 (1966). 12. P. Cavalloti, G. Salvago, Electrochim. Metal. IV(3), 181 (1969). 13. J.A. King, Ph.D. thesis, University of London (1966). 14. A.R. Burkin, Min. Sci. Engng. 1, 4 (1969). 15. U. Kuxmann, H. Biallass, Erzmetall 22, 53 (1969). 16. L.S. Renzoni, R.C. McQuire, W.V. Barker, J. of Metals 10, 414 (1958). 17. Symposium on the Thompson operation, The Canadian Mining and Metallurgical Bulletin 57, 1181 (1964). 18. A.G. Losharev, A.F. Vozinov, J. of applied Chemistry U.S.S.R. 26, 49 0-953). 150 19. S. Venkatachalam, R. Mallikarjunan, Inst. Min. Met. Trans, section C 77, C45 (1968). 20. F. Habashi, N. Torres-Acuna, Trans. Met. Soc. A.I.M.E. 242, 780 (1968). 21. J.H. Schloen, S.S. Forbes, Industry report on modern tank house practices, Extractive metallurgy of copper, nickel and cobalt, edited by P. Queneau, Interscience Publishers (1961). 22. E. Frenay, L'elaboration des m£taux non ferreux a partir de leurs minerals, University de Li&ge (1961). 23. L. Eisenmann, Ann. Phys. 10, 129 (1952). 24. E. Hihara, J. Phys. Soc. Japan 6, 422 (1951). 25. T. Kamigaishi, J. Sci. Hiroshima Univ. A16, 325 (1952). 26. 0. Kubaschewsky, E. Evans, C. Alcock, Metallurgical thermochemistry, Pergamon Press (1967). 27. H. Majima, E. Peters, Proceedings of the 8th International Mineral Processing Congress, Leningrad, Vol. 2, p. 6, June 1969. 28. M.J. Fraser, M.A.Sc. thesis, University of British Columbia (1965). 29. M. Sato, Economic Geology, 55, 1202 (1960). 30. P. Ruetschi, R.F. Amlie, J. of the Electrochemical Society, 112, 665 (1965). 31. R. Bacon, R. Fanelli, Ind. and Eng. Chemistry 34, 1043 (1942). 32. A. de Bethune, T. Licht, N. Swendeman, J. Electrochem. Soc. 106, a 616 (1959). 33. S. Djurle, Acta Chem. Scand. 12, 1415 (1958). 34. H. von Wartenberg, Z. physikal. Chem. 67, 446 (1909). 35. F. Weibke, 0. Kubaschewsky, Therchemie der Legierungen, Springer-Verlag, (1943). 151 36. CT. Anderson, J. Am. Chem. Soc. 54, 107 (1932). 37. K.K. Kelley, U.S. Bur. Mines Bulletin 584 (I960); U.S. Bur. Mines bulletin 592 (1961). 38. A. Dumon, A. Casalot, E. Poquet, S. Gromb, C.R. Acad. Sc. (Paris) serie B, 269 (17), 835 (1969). 39. F. Richardson, J; Antill, Trans. Faraday Soc. 51, 22 (1955). 40. A. Brooks, J. Am. Chem. Soc. 74, 2464 (1953). 41. J.B. Wagner, C. Wagner, J. Electrochem. Soc. 104, 509 (1957). 42. W. Jost, Diffusion in solids, liquids, gases, Academic Press, Inc., N.Y. (1960). 43. J. Mikulski, S. Mrowec, I. Stronski, T. Werber, Z. phys. Chem. (Frankfurt) N.F. 22, 20 (1959). 44. V. Wehefritz, Z. phys. Chem. (Frankfurt) N.F. 26, 359 (1960). 45. D.A. Vermilyea, Anodic films, Advances in Electrochemistry and Electrochemical Engineering, P. Delahay and CW. Tobias editors, Interscience Publishers, N.Y. (1963). 46. C. Wagner, J. Chem. Phys. 21, 1819 (1953). 47. F.A. Kroger, The Chemistry of imperfect crystals, North Holland Publishing Co. (1964). 48. D.M. Barrer, Trans Faraday Soc. 37, 590 (1941); Trans Faraday Soc. 38, 78 (1942). 49. K.J. Vetter, Electrochemical Kinetics, Theoretical and experimental aspects, Academic Press, N.Y. (1967). 50. M. Enyo, T. Yokoyama, Electrochimica Acta 15, 183 (1970). 51. V. Levich, Physicochemical hydrodynamics, Prentice Hall, Englewood Cliffs, New Jersey (1962). 152 52. A.C. Riddiford, The rotating disk system, Advances in electro chemistry and electrochemical engineering (Vol 4), Delahay and Tobias editors, Interscience Publishers, N.Y. (1963). 53. D.P. Gregory, A.C. Riddiford, J. Chem. Soc. 3756 (1956). 54. J. Newman, L. Hsueh, Electrochimica Acta 12, 417 (1967). 55. J. Newman, J. Electrochem. Soc. 113, 1235 (1966). 56. V. Marathe, J. Newman, J. Electrochem. Soc. 116, 1704 (1969). 57. J. Newman, J. Electrochem. Soc. 113, 501 (1966). 58. L. Hsueh, J. Newman, Electrochimica Acta 12, 429 (1967). 59. A.S.T.M. X-ray diffraction data file. 60. A. Seidell, Solubilities of inorganic and metal organic compounds, Van Nostrand Co. (1940). 61. R. Nasanen, B. Klaile, Suomen Kemistilehti B27, 50 (1954). 62. J.R. Selman, L. Hsueh, J. Newman, Physical properties of CuSO^-H^SO^ solutions, Inorganic Materials Research Division Annual Report 1966, p. 49 (U.C.R.L.-17330, March 1967). 63. Chemical Engineer's Handbook, J.H. Perry editor, McGraw-Hill Book Co. 1950, 64. H.K. Richardson, F.D. Taylor, Trans, of the Am. Electrochem.. Soc. 20, 179 (1911). 65. E. Peters, H. Majima, Annual meeting of the A.I.M.E., New York February 25-29, 1968. 66. G. Valensi, MStaux et Corrosion 12 (145), 145 (1937). 67. G. Valensi, Metaux et Corrosion 12 0-46), 195 (1937). 68. H. Gerisher, Z. Elektrochem. 54, 366 (1950). 69. J.V. Petrocelli, A.A. Paolucci, J. Electrochem. Soc. 98, 291 (1950) 153 70. E. Lewartowicz, J. Chim. Phys. 49, 564 (1952). 71. E. Lewartowicz, J. Chim. Phys. 49, 573 (1952). 72. A.M. Baticle, F. Perdu, P. Vennerau, CR. 264, C12 (1967). 73. W.C. Schumb, M.S. Sherill, S.B. Sweetser, J. Amer. Chem. Soc. 59, 2360 (1937). 74. W.C Bray, A.V. Hershey, J. Am. Chem. Soc. 56, 1889 (1934). 75. J.J. Fritz, CR. Fuget, J. Phys. Chem. 62, 303 (1958). 76. R.C Reid, T.K. Sherwood, The properties of gases and liquids, McGraw Hill Book Co. (1958). 77. Handbook of Chemistry and Physics, R.C. Weast editor, The Chemical Rubber Co. (1968). 

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