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Speciation of the sulfuric acid-ferric sulfate-ferrous sulfate-water system and its application to chalcopyrite… Yue, Guikuan 2015

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    Speciation of the Sulfuric Acid-Ferric Sulfate-Ferrous Sulfate-Water System and its Application to Chalcopyrite Leaching Kinetics up to 150 ºC  by Guikuan Yue B. Eng., Henan University, 2005 M. Eng., Institute of Process Engineering, Chinese Academy of Sciences, 2008     A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF  THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES  (Materials Engineering)   THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) March 2015  © Guikuan Yue, 2015 ii  Abstract Hydrometallurgical oxidation methods are increasingly being considered for the extraction of Cu from chalcopyrite. However, the kinetics of cathodic ferric ion reduction are poorly understood. This thesis investigates the kinetics of cathodic ferric ion reduction on chalcopyrite and its influence on the leaching process in acidic iron sulfate solution, with an emphasis first placed on the development of a speciation model for the H2SO4-Fe2(SO4)3-FeSO4-H2O system from 25°C-150°C.  Speciation results show that most Fe(III) is distributed as complexes or precipitates and the free Fe3+ accounts for only a minor percentage (up to 5.2% of total ferric) whereas a large amount of Fe(II) exists in the form of free Fe2+. The Nernst equation was used to study the redox potential of Fe3+/Fe2+ couple. The speciation model explains the change of redox potential with temperature for all nominal Fe3+/Fe2+ ratios. This model was validated by reliable prediction of measured redox potential, comparison of previously published results of ferric solubility, together with an analysis of the calculated pH and ionic strength. A novel expression was also developed to predict the redox potential of the ferric/ferrous couple. It seems that the redox potential can be easily and accurately determined only based on the variables of temperature and nominal Fe3+/Fe2+ ratio.  The calculated free Fe3+ concentration allowed for a detailed investigation of the reduction kinetics of ferric ion on chalcopyrite by cathodic potentiodynamic polarization. The exchange current densities of the Fe3+/Fe2+ couple are on the order of 10-7-10-5 A/cm2 in the range of 25–150°C, substantially less than that on platinum. Calculated rate constants can be well described by the Arrhenius equation. The transfer coefficient increases linearly with temperature (rather than being constant).  iii  The importance of the cathodic ferric ion reduction reaction on the overall leaching process is progressively increased when increasing the nominal Fe3+/Fe2+ ratio and temperature. Leaching is under anodic control when the nominal Fe3+/Fe2+ ratio is around 1:1, whereas at higher nominal Fe3+/Fe2+ ratios and temperatures it is under mixed control. These findings provide the basis for mechanistic analyses and attendant optimization studies of industrial leaching processes of chalcopyrite and other sulfide minerals.                                   iv  Preface Financial support for this work was provided by SNC Lavalin, Glencore, HudBay and the Natural Sciences and Engineering Research Council of Canada (NSERC). The journal papers and conference presentations listed below have been prepared from the research work presented in the dissertation. I am the primary contributor to all of them and was responsible for conducting the research, preparing and analyzing the results, and writing the manuscripts. The contributing co-authors are as follows: Dr. Edouard Asselin (supervisor) extensively helped with all the aspects of the research work; Dr. Liming Zhao is gratefully acknowledged for her help with programming and numerical methods to solve the non-linear equations (Fortran code by Brent’s method), in order to obtain the species distribution of the model results; Dr. Oscar G. Olvera helped measure the redox potentials at 25-90°C, which is used in Chapter 5. Chapters 5 and 6 are based on journal paper “1”. Chapters 7 and 8 are based on journal paper “2”.  Journal Papers 1. Guikuan Yue*, Liming Zhao, Oscar G. Olvera, Edouard Asselin. Speciation of the H2SO4-Fe2(SO4)3-FeSO4-H2O System and Development of an Expression to Predict the Redox Potential of the Fe3+/Fe2+ Couple up to 150°C. Hydrometallurgy, 2014, Volumes 147-148, Pages 196-209.  2. Guikuan Yue*, Edouard Asselin. Kinetics of Ferric Ion Reduction on Chalcopyrite and its Influence on Leaching up to 150°C. Electrochimica Acta, 2014, Volume 146, Pages 307–321.   Conference Presentations with Proceeding  v  1. Guikuan Yue*, Edouard Asselin. Reduction Kinetics of Fe(III) on Chalcopyrite up to 110°C. In M.J. Collins, D. Filippou, J.R. Harlamovs, E. Peek (Eds.), 42nd Annual Hydrometallurgy Meeting, Pressure Hydrometallurgy 2012 (pp. 241-255), September 30-October 3, 2012. Niagara Falls, ON: Canadian Institute of Mining, Metallurgy and Petroleum. (Conference paper & Oral presentation) 2. Guikuan Yue*, Edouard Asselin. Fundamental Reduction Kinetics of Fe(III) on Chalcopyrite Surface. In M. Free, M. Moats, G. Houlachi, E. Asselin, A. Allanore, J. Yurko, & S. Wang (Eds.), TMS (The Minerals, Metals & Materials Society) 2012 Annual Meeting, Electrometallurgy 2012 (pp. 183-198), March 11-15, 2012. Orlando, FL: John Wiley & Sons, Inc. (Conference paper & Oral presentation)  Conference Presentations 1. Guikuan Yue*, Edouard Asselin. Analysis of Chalcopyrite Leaching Behavior by Mixed Potential Theory in Acidic Iron Sulfate Solution from 25°C to 150°C. The 6th International Conference on Hydrometallurgy, Beijing, China, October 16-19, 2014. (Poster presentation) 2. Guikuan Yue*, Edouard Asselin. Speciation of Acidic Iron Sulfate Solutions and its Application to the Study of the Reduction Kinetics of Fe(III) on Chalcopyrite up to 150°C. Hydrometallurgy 2014, Victoria, British Columbia, June 22-25, 2014. (Poster presentation) 3. Guikuan Yue*, Edouard Asselin. Speciation of the H2SO4-Fe2(SO4)3-FeSO4-H2O System and its Application to Chalcopyrite Leaching from 25°C to 150°C. CQU-UBC Research Workshop on Materials Science and Engineering, Chongqing, China, May 13-15, 2014. (Oral presentation)  vi  4. Guikuan Yue*, Edouard Asselin. Fundamental Reduction Kinetics of Fe(III) or O2 on Chalcopyrite Surface. 23rd Canadian Materials Science Conference, Kelowna, British Columbia, June 22-24, 2011. (Oral presentation)                     vii  Table of Contents  Abstract .......................................................................................................................................... ii Preface ........................................................................................................................................... iv Table of Contents ........................................................................................................................ vii List of Tables ................................................................................................................................ xi List of Figures ............................................................................................................................. xiii Acknowledgements .................................................................................................................... xix Dedication ................................................................................................................................... xxi 1 Introduction ........................................................................................................................... 1 1.1 General Information on the Copper Extraction Industry ........................................... 1 1.2 Analysis and Discussion on Hydrometallurgical Treatment of Chalcopyrite in Acidic Iron Sulfate Solution ...................................................................................... 5 1.3 Scope of the Present Study and Thesis Organization .............................................. 14 2 Literature Review ................................................................................................................ 16 2.1 Oxidation of Chalcopyrite and Cathodic Reduction of Chalcopyrite Itself ............. 16 2.1.1 Chemical or Electrochemical Oxidation of Chalcopyrite in Sulfuric Acid ............. 16 2.1.2 Chemical or Electrochemical Reduction of Chalcopyrite Itself in Sulfuric Acid ... 34 2.1.3 Other Oxidation or Reduction Systems/Methods for Chalcopyrite ......................... 36 2.2 Chemical or Electrochemical Reduction of Ferric or Oxygen on Chalcopyrite ...... 37 2.2.1 Reduction of Ferric or Oxygen on Chalcopyrite...................................................... 37 2.2.2 Reduction of Ferric or Oxygen on Other Sulfide Minerals/Passive Electrodes ...... 39 2.3 Rotating Disc Electrode Studies of Chalcopyrite and Other Related Sulfide Minerals under Leaching Conditions ....................................................................... 41 2.4 Electrochemical Impedance Spectroscopy Studies of Chalcopyrite ........................ 43 2.4.1 Sulfuric Acid ............................................................................................................ 43 2.4.2 Alkaline Solution ..................................................................................................... 44 2.4.3 Sulfuric Acid plus Iron Sulfate ................................................................................ 44  viii  2.5 High Temperature Electrochemistry of Chalcopyrite Electrode and Ferric/Oxygen Reduction Reaction .................................................................................................. 45 2.5.1 Sulfuric Acid ............................................................................................................ 45 2.5.2 Reduction of Ferric or Oxygen on Other Electrodes at High Temperatures ........... 47 2.6 Summary .................................................................................................................. 48 3 Objectives ............................................................................................................................. 49 4 Methodology and Experimental Procedure ...................................................................... 51 4.1 Measurement of the Redox Potential of the Quaternary Acidic Iron Sulfate System from 25°C to 150°C ................................................................................................. 51 4.1.1 Electrode Preparation ............................................................................................... 51 4.1.2 Electrolyte Preparation............................................................................................. 52 4.1.3 Electrochemical Measurements at 25°C, 70°C and 90°C ........................................ 53 4.1.4 Electrochemical Measurements at 110°C and 150°C .............................................. 54 4.1.5 Correction of the Measured Potentials to SHE at 25°C ........................................... 58 4.2 Measurement of the Cathodic Potentiodynamic Polarization Curves ..................... 61 4.2.1 Electrode Preparation ............................................................................................... 61 4.2.2 Electrolyte Preparation............................................................................................. 65 4.2.3 Electrochemical Measurements at 25°C, 70°C and 90°C ........................................ 65 4.2.4 Electrochemical Measurements at 110°C and 150°C .............................................. 66 4.2.5 Correction of the Measured Potentials to SHE at 25°C ........................................... 66 4.3 Scanning Electron Microscope Study ...................................................................... 66 4.4 Optical Microscope Study........................................................................................ 69 5 Development of a Thermodynamic Model to Simulate the Speciation of the Quaternary Sulfuric Acid-Ferric Sulfate-Ferrous Sulfate-Water System ..................... 70 5.1 Introduction .............................................................................................................. 70 5.2 Model Development................................................................................................. 71 5.2.1 Activity Coefficient Model-B-dot Equation ............................................................ 71 5.2.2 Collection and Calculation of Thermodynamic Data and Equilibrium Constants .. 73  ix  5.2.3 Calculation of Models in the Solution ..................................................................... 81 5.3 Results and Discussion ............................................................................................ 82 5.3.1 Speciation Results Calculated at 25°C and 70°C ..................................................... 82 5.3.2 Speciation Results Calculated at 90°C and 110°C ................................................... 85 5.3.3 Speciation Results Calculated at 150°C ................................................................... 88 5.3.4 Model Validity-Comparison with Experimental Results and Previous Work ......... 91 5.4 Summary .................................................................................................................. 99 6 Development of an Expression to Predict the Redox Potential of the Fe3+/Fe2+ Couple up to 150°C ......................................................................................................................... 102 6.1 Introduction ............................................................................................................ 102 6.2 Speciation Results and Their Application to the Prediction of the Redox Potentials of the Fe3+/Fe2+ Couple at 25°C-150°C ................................................................. 103 6.2.1 Speciation Results of the Developed Model to Calculate the Redox Potential of the Fe3+/Fe2+ Couple .................................................................................................... 103 6.2.2 Development of an Expression to Predict the Redox Potential of the Fe3+/Fe2+ Couple up to 150°C ................................................................................................ 111 6.3 Applicability of the Developed Expression-Comparison with Experimental Results by Previous Work .................................................................................................. 113 6.4 Summary ................................................................................................................ 118 7 Reduction Kinetics of Ferric Ion on Chalcopyrite from 25°C to 150°C....................... 120 7.1 Introduction ............................................................................................................ 120 7.2 Results and Discussion .......................................................................................... 121 7.2.1 Determination of the Concentrations of Free Ferric and Ferrous Ions in H2SO4-Fe2(SO4)3-FeSO4-H2O System by the Speciation Model between 25°C and 150°C................................................................................................................................ 121 7.2.2 CPC Results at 25°C .............................................................................................. 124 7.2.3 CPC Results at 70°C .............................................................................................. 130 7.2.4 CPC Results at 90°C .............................................................................................. 133 7.2.5 CPC Results at 110°C ............................................................................................ 136 7.2.6 CPC Results at 150°C ............................................................................................ 140  x  7.2.7 Comparison with i0 of the Fe3+/Fe2+ Couple on Other Electrodes and the Application of i0 to Calculate the Rate Constants at 25°C-150°C ......................... 144 7.2.8 Temperature Dependence of Tafel Slopes and Transfer Coefficients for Ferric Ion Reduction ............................................................................................................... 148 7.3 Summary ................................................................................................................ 154 8 Influence of Ferric Ion Reduction Reaction on Chalcopyrite Leaching Behavior from 25°C to 150°C ..................................................................................................................... 157 8.1 Introduction ............................................................................................................ 157 8.2 Results and Discussion .......................................................................................... 158 8.2.1 Calculated EC and Measured EM Potentials ........................................................... 158 8.2.2 Calculation of Reversible Potential of Anodic Oxidation Reactions of Chalcopyrite from 25°C to 150°C ............................................................................................... 159 8.2.3 Analysis of Leaching Process by Mixed Potential Theory .................................... 162 8.3 Summary ................................................................................................................ 170 9 Conclusions, Industrial Applications and Recommendations ....................................... 172 9.1 Conclusions ............................................................................................................ 172 9.2 Industrial Applications ........................................................................................... 176 9.3 Recommendations .................................................................................................. 178 References .................................................................................................................................. 180 Appendices ................................................................................................................................. 200 Appendix A High Temperature Electrochemical Apparatus .................................................. 200 Appendix B Fortran Code by Brent’s Method Employed in the Present Work for the Speciation Study .................................................................................................... 205        xi  List of Tables Table 1-1 Typical industrial leaching processes (including the general operating parameters) for CuFeS2 based on sulfuric acid. ....................................................................................................... 7 Table 2-1 Kinetic data for oxygen reduction on pyrite electrodes [98]. ....................................... 40 Table 4-1 Results of quantitative phase analysis of the chalcopyrite ........................................... 63 Table 4-2 Chemical analysis (ICP-OES, 4 Acid Digestion) and Au analysis (Fire Assay). Results for elements with concentrations lower than 10 ppm are not presented. ...................................... 64 Table 4-3 Components of the prepared chalcopyrite electrode in this study (wt.%). ................... 68 Table 5-1 Thermodynamic data at 25°C and equilibrium (standard formation) constants for the main species in aqueous Fe(II)-Fe(III)-H2SO4 solutions in the range of 25-35°C. The reference state for aqueous species is infinite dilution (Data given are for 25°C, 1 atm and standard state)........................................................................................................................................................ 74 Table 5-2 Calculated equilibrium (standard formation) constants for the main species in aqueous Fe(II)-Fe(III)-H2SO4 solutions in the range of 70-150°C. ............................................................ 79 Table 6-1 Standard electrode potential of Fe3+/Fe2+ couple calculated by the Criss-Cobble method and redox potential of Fe3+/Fe2+ couple predicted by the model in Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18mol/kg with different nominal Fe3+/Fe2+ ratios in the range of 25-150°C. ................................................................................................................ 110 Table 7-1 The calculated concentrations of free Fe3+ and Fe2+ ions in aqueous Fe(II)-Fe(III)-H2SO4 solutions in the range of 25-150°C according to the developed speciation model (Unit: mol/kg). ....................................................................................................................................... 123 Table 7-2 CPC results at 25°C. ................................................................................................... 126 Table 7-3 CPC results at 70°C. ................................................................................................... 132  xii  Table 7-4 CPC results at 90°C. ................................................................................................... 135 Table 7-5 CPC results at 110°C. ................................................................................................. 139 Table 7-6 CPC results at 150°C. ................................................................................................. 143 Table 7-7 Comparison of exchange current densities Fe3+/Fe2+ couple on various electrodes. . 145 Table 8-1 Calculated standard electrode potentials for the possible anodic oxidation reactions of chalcopyrite in aqueous Fe(II)-Fe(III)-H2SO4 solutions in the range of 25-150°C. ................... 160 Table 8-2 Thermodynamic data at 25°C and Kelley equation coefficients of the solids involved in the anodic chalcopyrite oxidation reactions in the range of 25-150°C. .................................. 161 Table B-1 Calculated concentrations of all species in aqueous Fe(II)-Fe(III)-H2SO4 solutions from 25-150°C using the newly developed speciation model with nominal Fe3+/Fe2+ ratio of 10:1 (Unit: mol/kg). In the cell or autoclave, [Fe(III)]total = 0.18 mol/kg and [Fe(II)]total = 0.018 mol/kg, respectively. ................................................................................................................................ 207             xiii  List of Figures Figure 1-1 Main processes for extracting copper from sulfide ores [1]. ........................................ 2 Figure 1-2 Flowsheet for leaching oxide and Cu2S ores. The dissolved Cu is recovered by solvent extraction purification/strengthening and then electrowinning. Leaching accounts for ~20% of primary (from ore) copper production [1]. ..................................................................................... 3 Figure 1-3 Schematic diagram of the relationship indicating the roles of ferric, oxygen and chalcopyrite in the leaching system. ............................................................................................... 8 Figure 1-4 Hypothetical polarization curves for the anodic and cathodic reactions superimposed on one another. .............................................................................................................................. 10 Figure 2-1 Eh-pH diagram of the Cu-Fe-S-H2O system at 25°C: all solutes at 0.1 M activity except Cu2+ = 0.01 M. All reactions are reversible [56]. .............................................................. 18 Figure 2-2 Anodic polarization curves for CuFeS2 from 6 different locations in 1 M H2SO4, 30 mV/min, 25°C [15]. ...................................................................................................................... 24 Figure 2-3 Effect of scanning rate on the anodic polarization curve of Transvaal CuFeS2 in 1 M H2SO4, 25°C [15]. ......................................................................................................................... 25 Figure 2-4 Effect of cupric ion on the anodic polarization curve of Transvaal CuFeS2 in 1 M H2SO4, 40 mV/min, 25 °C. [Fe2+] was held constant at 0.04 g/1 [15]. ......................................... 26 Figure 2-5 Effect of ferrous ion on the anodic polarization curve of Transvaal CuFeS2 ............. 27 Figure 4-1 Schematic diagram of Ag/AgCl external pressure balanced reference electrode with double porous junction. ................................................................................................................. 57 Figure 4-2 Schematic diagram of the apparatus for high temperature high pressure electrochemical tests by using the EPBRE. .................................................................................. 58  xiv  Figure 4-3 SEM-EDX analysis results of the prepared chalcopyrite electrode surface. The magnification is 300X. .................................................................................................................. 67 Figure 4-4 EDX spectra of the prepared chalcopyrite electrode. .................................................. 68 Figure 5-1 Equilibrium (standard formation) constants used in the present study for the main species in aqueous Fe(II)-Fe(III)-H2SO4 solutions in the temperature range of 25-150°C. ......... 80 Figure 5-2 Calculated aqueous speciation diagram of the main ferric and ferrous species in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios at 25°C. Please note that the sum of the percentage values of Fe(II) species (unfilled symbols) is 100%, which is also the case for the Fe(III) species (filled symbols). ....................................................................................................................................... 83 Figure 5-3 Calculated aqueous speciation diagram of the main ferric and ferrous species in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios at 70°C. Please note that the sum of the percentage values of Fe(II) species (unfilled symbols) is 100%, which is also the case for the Fe(III) species (filled symbols). ....................................................................................................................................... 84 Figure 5-4 Calculated aqueous speciation diagram of the main ferric and ferrous species in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios at 90°C. Please note that the sum of the percentage values of Fe(II) species (unfilled symbols) is 100%, which is also the case for the Fe(III) species (filled symbols). ....................................................................................................................................... 86 Figure 5-5 Calculated aqueous speciation diagram of the main ferric and ferrous species in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios at 110°C. Please note that the sum of the percentage values of  xv  Fe(II) species (unfilled symbols) is 100%, which is also the case for the Fe(III) species (filled symbols). ....................................................................................................................................... 87 Figure 5-6 Calculated aqueous speciation diagram of the main ferric and ferrous species in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios at 150°C. Please note that the sum of the percentage values of Fe(II) species (unfilled symbols) is 100%, which is also the case for the Fe(III) species (filled symbols). ....................................................................................................................................... 90 Figure 5-7 Comparison of the potentials predicted by model and measured by experiments in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios in the temperature range of 25°C-150°C. ............................... 92 Figure 5-8 Calculated pH of the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios in the temperature range of 25°C-150°C. ........................................................................................................................................... 96 Figure 5-9  Calculated real ionic strength of the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios in the temperature range of 25°C-150°C. ................................................................................................................... 98 Figure 6-1 Calculated real Fe3+/Fe2+ ratios in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios in the temperature range of 25°C-150°C. ............................................................................................. 105 Figure 6-2 Comparison of the calculated standard electrode potentials of the Fe3+/Fe2+ couple with those in published literature in the temperature range of 25°C-150°C. .............................. 107 Figure 6-3 Comparison of the potentials predicted by the developed expression Eq. (6-9)  in this work and measured by experiments in the Fe(II)-Fe(III)-H2SO4 solutions from Dry and Bryson  xvi  (1988) at various nominal concentrations of H2SO4 and Fe(III)/Fe(II) with different nominal Fe3+/Fe2+ ratios: (a) at 22°C; (b) at 90°C. The unit of the concentrations in the figure is mol/L. Detailed information on the nominal concentrations of Fe3+ and Fe2+ at 90°C can be found in the literature. ..................................................................................................................................... 114 Figure 6-4 Comparison of the potentials predicted by the developed expression Eq. (6-9) in this work and measured by experiments in the Fe(II)-Fe(III)-H2SO4 solutions from Hiroyoshi et al. (2001), Tshilombo (2004) and Nicol and Lázaro (2002) at various nominal concentrations of H2SO4 and Fe(III)/Fe(II) with different nominal Fe3+/Fe2+ ratios at room temperature. ............ 117 Figure 7-1 Cathodic potentiodynamic polarization curves and corresponding OCP in deaerated aqueous Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg on chalcopyrite with different nominal Fe3+/Fe2+ ratios at 25°C. .................................................... 125 Figure 7-2 OM analysis results of the prepared chalcopyrite electrode surface before (a) and after electrochemical test (b) in the electrolyte with nominal Fe3+/Fe2+ ratio of 1000:1 at 25°C. ...... 129 Figure 7-3 Cathodic potentiodynamic polarization curves and corresponding OCP in deaerated aqueous Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg on chalcopyrite with different nominal Fe3+/Fe2+ ratios at 70°C. .................................................... 131 Figure 7-4 Cathodic potentiodynamic polarization curves and corresponding OCP in deaerated aqueous Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg on chalcopyrite with different nominal Fe3+/Fe2+ ratios at 90°C. .................................................... 134 Figure 7-5 Cathodic potentiodynamic polarization curves and corresponding OCP in deaerated aqueous Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg on chalcopyrite with different nominal Fe3+/Fe2+ ratios at 110°C. .................................................. 138  xvii  Figure 7-6 Cathodic potentiodynamic polarization curves and corresponding OCP in deaerated aqueous Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg on chalcopyrite with different nominal Fe3+/Fe2+ ratios at 150°C. .................................................. 141 Figure 7-7 OM analysis results of the prepared chalcopyrite electrode surface after about 1 hour exposure to the electrolyte with nominal Fe3+/Fe2+ ratio of 1:1 at 150°C. .................................. 142 Figure 7-8 (a) Calculated rate constants (kC) of ferric ion reduction on chalcopyrite as a function of temperature in the range of 25-150°C according to Equation 7-2; (b) ln kC versus 1/T, displays the linear Arrhenius behavior...................................................................................................... 147 Figure 7-9 Comparison of the measured Tafel slopes and the calculated conventional theoretical values (based on α=0.5) in deaerated aqueous Fe(II)-Fe(III)-H2SO4 solutions under different nominal Fe3+/Fe2+ ratios in the temperature range of 25°C-150°C. ............................................ 151 Figure 7-10 Comparison of the calculated transfer coefficients based on the measured Tafel slopes in this work and the conventional value (α=0.5) under different nominal Fe3+/Fe2+ ratios in the temperature range of 25°C-150°C. ....................................................................................... 153 Figure 8-1 Schematic diagram of the mixed potential theory for the oxidative dissolution of chalcopyrite by ferric ion. ........................................................................................................... 158 Figure 8-2 Measured mixed potentials and calculated theoretical cathodic and anodic reversible potentials in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg in the temperature range of 25°C-150°C with nominal Fe3+/Fe2+ ratio of 1:1. ............... 164 Figure 8-3 Measured mixed potentials and calculated theoretical cathodic and anodic reversible potentials in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg in the temperature range of 25°C-150°C under higher nominal Fe3+/Fe2+ ratios: (a) 10:1;  xviii  (b) 100:1; (c) 1000:1. The symbols used in these Figures are the same as those shown in Figure 8-2. .............................................................................................................................................. 165 Figure A-1 High temperature high pressure autoclave. .............................................................. 200 Figure A-2 Inside of the glass reactor for high temperature high pressure autoclave. ............... 201 Figure A-3 Disassembled chalcopyrite working electrode used in the autoclave. ..................... 202 Figure A-4 (a) Assembly and (b) disassembly of the Pt-Nb electrode from Cortest Inc. served as counter electrode for high temperature high pressure electrochemical test in the autoclave. .... 203 Figure A-5 High temperature external pressure balanced reference electrode (EPBRE). .......... 204                 xix  Acknowledgements First of all, I would like to express my sincere gratitude to my supervisor, Dr. Edouard Asselin, for his continuous support, kind guidance and encouragement during this project. The numerous critical discussions that he gave almost every day significantly accelerate my research. Without his help this work would not have been possible.   I would also like to thank my thesis committee members, Dr. Xiaotao Bi, Dr. Akram Alfantazi and Dr. Daan Maijer, for their great comments and input about my research. I also wish to express my thanks to Dr. David Dreisinger and Dr. Marek Pawlik for their great advice, suggestions and comments at my Final Oral Defence. I would like to especially thank Dr. Vladimiros Papangelakis for reviewing my thesis and providing valuable feedback. Colleagues such as Dr. Hamidreza Zebardast, Dr. Berend Wassink are also acknowledged for their helpful discussions.   I gratefully acknowledge the financial support of SNC Lavalin, Glencore, HudBay and the Natural Sciences and Engineering Research Council of Canada (NSERC).  I wish to thank the Department of Earth, Ocean and Atmospheric Sciences at the University of British Columbia (EOAS) for providing the mineral samples. I also wish to thank Ms. E. Czech and Dr. Mati Raudsepp from EOAS, for obtaining the XRD data featured in this work.   xx  Special thanks to all colleagues and officemates in the Department of Materials Engineering at the University of British Columbia for providing a friendly environment that was always a pleasure to work in.  Finally, the author would like to thank his wife, Lirun Zhao, and other family members for their exceptional patience, understanding, support and encouragement, which enabled this work to be carried to completion.                  xxi  Dedication       To my beloved family  1  1 Introduction 1.1 General Information on the Copper Extraction Industry Copper is widely used by human beings and is produced all over the world. Due to its high electrical conductivity, thermal conductivity and corrosion resistance (the most exploited properties), in conjunction with its excellent formability and joinability, copper has been employed in diverse applications, either in metallic form or alloys [1]. The present section aims to briefly describe and discuss the principal methods by which it is obtained. There are three major sources of copper: copper-iron-sulfide and copper sulfide minerals (most common), such as chalcopyrite (CuFeS2) and chalcocite (Cu2S); oxidized minerals (carbonates, oxides, hydroxy-silicates, sulfates); copper and copper alloy scrap [1]. Among the minerals, chalcopyrite is the most abundant copper mineral in nature, accounting for about 70% of known copper reserves in the world [2]. Depending on the mineralogy and grade of the deposit, different extraction routes are required to produce copper [1]. About 80% of the world’s copper-from-ore (~18 million tonnes per year) is produced by concentration/smelting/refining of copper-iron-sulfide ores (CuFeS2). The main processes of the flowsheet for extracting copper from this kind of ore are shown in Figure 1-1. The other 20% is hydrometallurgically produced by heap leaching/solvent extraction/electrowinning of mainly copper oxide, and chalcocite ores (Figure 1-2). This technology dominates in Chile. Copper production from recycled used objects is about 10 or 15% of mine production.  2   Figure 1-1 Main processes for extracting copper from sulfide ores [1].  3   Figure 1-2 Flowsheet for leaching oxide and Cu2S ores. The dissolved Cu is recovered by solvent extraction purification/strengthening and then electrowinning. Leaching accounts for ~20% of primary (from ore) copper production [1].   4  The traditional pyrometallurgical flowsheet remains the dominant existing industrial process. The main drawbacks for pyrometallurgical treatment of chalcopyrite include high capital costs associated with smelting, the limited ability of smelters to handle growing concentrations of As and Sb, and emissions of SO2. The hydrometallurgical method to extract copper from minerals, with leach/solvent extraction/electro-winning operations, is only applied to treat oxide or Cu2S ores. Sulfuric acid is almost always used as the leaching lixiviant. Copper production by this method is steadily increasing as more mines begin to leach all or some of their ore and treat lower-grade materials, some of which were previously considered to be waste [1].  Finally, it should be emphasized that according to the data published by Schlesinger et al. [1], due to the small equipment and infrastructure requirements, the total direct plus indirect costs of producing electrowon copper cathodes from oxide and chalcocite ores (including mining) by heap leach/solvent extraction/electrowinning ($1-$2 per kg of copper) are considerably lower than those for producing electrorefined copper from ore by conventional mining/concentration/smelting/refining (in the range of $3-$6 per kg of copper). This is the reason why leaching is being rapidly adopted around the world, especially in Chile. Please note that the cost data were obtained during early 2011 and are expressed in 2011 USA dollars. Unfortunately, as the world’s largest source of copper, chalcopyrite ore cannot yet be economically processed by heap leach/solvent extraction/electrowinning, and it must usually be treated by conventional concentration/smelting/refining, regardless of the cost.   5  1.2 Analysis and Discussion on Hydrometallurgical Treatment of Chalcopyrite in Acidic Iron Sulfate Solution Obviously, the above brief analysis of copper extraction technology strongly supports the concept that it is important to develop a hydrometallurgical process as an alternative to smelting to treat chalcopyrite, the most abundant copper mineral in nature, in view of the commercial and technological importance of this sulfide ore.  The challenge for process development of chalcopyrite leaching is to dissolve copper quickly and completely with, preferably, a high yield of elemental sulfur. Although in the past several decades enormous efforts have been continuing to seek a deeper understanding of the kinetics and mechanisms involved in the proposed hydrometallurgical leaching systems, due to various technical obstacles or economic concerns, few have yet been successfully commercialized and can achieve sustained commercial production above a demonstration plant scale.  Indeed, as stated by Schlesinger et al. [1], development of commercially viable technologies for the hydrometallurgical processing of chalcopyrite remains the holy grail of copper metallurgy, in spite of the fact that a lot of progress in technological advances for modern smelters has been made to tackle the problems faced by the conventional pyrometallurgical treatment. Activity in this area has steadily increased recently due to some inherent advantages associated with hydrometallurgical processing, such as the possibility of treating low-grade ores (increasingly more abundant in the case of copper) and easier control of waste, with the attendant benefits to the environment [3]. Unfortunately, chalcopyrite is highly refractory under most hydrometallurgical conditions, owing to the formation of an anodic passivation layer on the chalcopyrite surface that renders the process kinetics very slow. Most of the currently proposed  6  processes are based on sulfuric acid with ferric ions and/or dissolved oxygen as oxidants (the most important hydrometallurgical oxidants) at elevated temperatures. Sulfuric acid is preferred over all other leaching reagents in terms of cost, environmental friendliness, and ease of its regeneration during electro-winning. Additionally, acidic iron sulfate solution can easily be combined with conventional SX-EW methods. Some of these processes have been piloted or demonstrated in attempts to implement these technologies on an industrial scale, such as Activox [4], Nenatech [5], Dynatec [6], AAC/UBC [7], Total Pressure Oxidation [8], CESL [9] and Galvanox [10]. Table 1-1 summarizes the general operating parameters for those processes.                 7  Table 1-1 Typical industrial leaching processes (including the general operating parameters) for CuFeS2 based on sulfuric acid. Process Temperature Pressure Leaching Solution Galvanox 60-80°C Atmospheric conditions, sparging oxygen and/or air H2SO4+Ferric+Ferrous+Pyrite Pure sulphate medium Activox 90-110°C Oxygen partial pressure 700-1000 kPa H2SO4+Fe/Cu/Cl Fine grinding/high oxygen pressure MIM/Highlands Albion (Nenatech) 60-90°C Atmospheric pressure, sparging oxygen or air H2SO4+Ferric+Ferrous+Lignosol Atmospheric ferric leaching AAC/UBC 150°C Oxygen partial pressure 400-750 kPa H2SO4+Ferric/Ferrous/Cuppric+ Quebracho/lignosulfonate/OPD Dynatec 150°C Oxygen partial pressure 400-750 kPa H2SO4+Ferric/Ferrous+Coal Low grade coal used as an additive Total Pressure Oxidation 220°C Oxygen partial pressure 345-2068.5 kPa H2SO4/Water Extreme conditions of T and P CESL 150°C Oxygen partial pressure 345-1735 kPa H2SO4+Cu+Cl(HCl) Chloride catalyzed in the autoclave   The dissolution of semiconducting chalcopyrite in oxidizing acidic iron sulfate solution can be regarded as an electrochemical corrosion process, with cathodic reduction of the soluble oxidant (ferric regenerated by dissolved oxygen) and anodic oxidation of chalcopyrite. Therefore, the application of electrochemical techniques is also ideal to research the mechanism and rate-determining steps of the anodic and cathodic reactions involved in the leaching process.  According to the published literature, there is considerable evidence that, for the oxidation of  8  sulfide minerals such as PbS, ZnS, CuS and Cu2S in acid solutions and possibly for CuFeS2 as well, the dissolved Fe3+/Fe2+ couple plays an important catalytic role in accelerating the leaching rate with oxygen as an oxidant [1,11]. Hence, it is generally believed that oxygen plays a central role in the regeneration of Fe3+, and the Fe(III)/Fe(II) redox couple acts in a catalytic manner in these reactions [1,11]. Figure 1-3 is a schematic diagram of the relationship indicating the roles of ferric, oxygen and chalcopyrite in the leaching system: chalcopyrite is oxidized by Fe3+ to release copper from the minerals into solution as Cu2+; the produced Fe2+ (from either Fe3+ reduction or CuFeS2 dissolution) is re-oxidized by dissolved O2 to generate Fe3+ (as a surrogate oxidant).    Figure 1-3 Schematic diagram of the relationship indicating the roles of ferric, oxygen and chalcopyrite in the leaching system.  In order to promote the development and application of the hydrometallurgical technologies to treat chalcopyrite on a commercial scale, basic studies that elucidate the chemical  9  and electrochemical aspects governing leaching (i.e. establish the rate-determining step for each leaching system) should be taken into account, and remain topics of ongoing research. Most of the chemical or electrochemical research has traditionally focused on the oxidative processes [12-18] or cathode reduction reactions of chalcopyrite itself [19-22]. However, the cathodic reduction of oxidants (ferric ions or dissolved molecular oxygen), as the most important cathodic process in these systems, are also of great significance due to the fact that they can affect the overall leaching rate of the process and the actual reduction behavior of ferric ions is vital to obtain the true leaching rate, as predicted by mixed potential theory [23, 24]. Figure 1-4 presents a conceptual diagram to show the hypothetical polarization curves for the anodic and cathodic reactions superimposed on one another [23]. A sulfide mineral under leaching conditions is presumed to give up electrons to an oxidant, and hence the potential of the mineral is governed by the electrochemical kinetics of both the anodic process (oxidation of the mineral) and the cathodic process (reduction of the oxidant). At the intersection point of the anodic and cathodic curves, the electrochemical leaching rate is determined, along with the mixed potential. The mixed potential cannot be higher than the reversible potential of the oxidant that is actually collecting electrons from the surface, nor can it be lower than the potential below which the mineral is stable thermodynamically. As seen in Figure 1-4, each individual polarization curve (A: anodic; C: cathodic) has three distinct stages: 1, 2, and 3. Stage 1 represents the equilibrium (steady state) region where the particular electrode reaction is mostly reversible and the potential obeys Nernst Equation. The potential in this region should be related to the current in a linear fashion, and hence kinetics should depend on conduction through the electrode and the electrolyte. Stage 2 is known as the Tafel region, where the potential is directly dependent on the logarithm of the current and the process is under activation control. Stage 3 represents the  10  limiting current region where diffusion of the reactant or the product species controls the reaction singly or jointly. Partial and general kinetic expressions for all the nine situations can be derived from the position of the intersection point with respect to the stage of individual half-cell reactions of a leaching process [23, 24].  Taking various possible combinations between A1-A3 and C1-C3, there can be a total of 9 possible situations for the intersection points of the anodic oxidation branch and cathodic reduction branch. Clearly, the overall leaching rate can also be affected by the cathodic reduction reaction. A detailed analysis of the behavior of cathodic ferric ion reduction on chalcopyrite is required in order to better understand the factors affecting the leaching process.  Figure 1-4 Hypothetical polarization curves for the anodic and cathodic reactions superimposed on one another.   11  Nevertheless, the ferric reduction behavior on chalcopyrite has hardly been investigated, and very few data are available about the reduction processes in leaching systems. Some research has shown that the Fe3+/Fe2+ couple (indeed most redox couples) is much less reversible on corroding or polarized chalcopyrite than on pyrite, platinum or freshly polished chalcopyrite [25-27]. The formation of a passive film slows transport of ions from CuFeS2 to the solution, slows electron transfer to oxidants such as Fe3+ and slows the supply of holes to the solid-solution interface. Compared with the I3-/I- and Cu2+/Cu+ redox couples, the rate of electron transfer between the Fe3+/Fe2+ couple and the surface of CuFeS2 is slower [25, 26] and it follows that the slow kinetics for ferric reduction on a polarized CuFeS2 surface is a contributing factor for CuFeS2 passivation [27]. Some investigators have assumed that it is the cathodic half-cell reaction (i.e. ferric reduction) that limits the overall rate of leaching [28]. These limited studies are typically performed at lower temperatures, and it is generally accepted that the reaction rate of the ferric/ferrous couple on chalcopyrite is much slower than that on platinum or pyrite, for example [25, 26]. However, there is a lack of published reports describing just how slow the reduction rate of ferric ions may be (not to mention a comprehensive study and comparison of reduction kinetics at different temperatures), and to what extent the cathodic reaction can influence the overall leaching reaction.  In order to study the reduction behavior of ferric ions and further obtain its influence on the leaching rate, true ferric ion concentration/activity in the leaching solution is required. In addition, despite the fact that ferric ion plays a central role in the oxidation of chalcopyrite, it has been reported that the reversible/redox potential of the Fe3+/Fe2+ couple, determined by the Fe3+/Fe2+ concentration ratio, also has a predominant effect on chalcopyrite leaching and passivation behavior [13, 29-32]. For example, Kametani and Aoki (1985) found that ferric  12  concentration had little effect on the oxidation rate of chalcopyrite and copper extraction was mainly controlled by the redox potential of the solution (a function of the Fe3+/Fe2+ ratio) [29]. It is clear that a more efficient leaching process, therefore, requires an understanding of the factors affecting the true redox potential in leaching solutions. However, due to the fact that ferric and ferrous ions readily form complexes (charged cations and anions, neutral species, as well as precipitates at higher temperatures) in acidic iron sulfate solutions [33-45], and thus limiting the concentration of ferric and ferrous ions, to date it has been difficult to accurately invoke the Nernst equation. This equation requires the concentrations of free ferric and ferrous ions in the acidic iron sulfate solution. Similarly, this information is required to obtain the redox potential of acidic iron sulphate solutions [33, 34, 37], and to apply other basic electrochemical kinetic equations (Butler-Volmer equation and its extensions). Accurate speciation of this system is thus essential to obtain information relevant to the mechanism of industrial leaching processes. For example, the Nernst equation can be used to distinguish which half reaction, cathodic or anodic, may govern the overall reaction rate [23, 24, 46-50], by comparing the relative polarization degrees of the anodic and cathodic reactions using mixed potential theory. Moreover, although it is generally accepted that ferric ion is an effective oxidant for chalcopyrite leaching, and increased FeSO4 concentration substantially decreases the leaching rate (and the mixed potential) [12], Hiroyoshi et al  [51-53] have observed that some chalcopyrite samples were more effectively leached in ferrous sulfate solution than in ferric sulfate solution. This raises some concerns about the role of ferrous during ferric leaching of chalcopyrite. Speciation analysis of the acidic iron sulfate system can help explain this discrepancy. In addition, during the oxidation of chalcopyrite, there are a number of solution species that can interact by forming complexes that may exert influence on the overall process. Dutrizac  13  et al (1969) [54] and Hirato et al (1987) [12] have shown that chalcopyrite’s leaching rate is strongly affected by ferric ion concentration only at concentrations less than 0.01 or 0.1 M; at higher concentrations the effect is negligible. Hirato et al attributed this to the variation of Fe3+ and/or FeHSO42+ concentrations, according to the species distribution analysis for acidic ferric sulfate solution. A similar trend was observed by Crundwell (1987) [55], who found that the dissolution rate of sphalerite in acidic ferric sulfate solutions was proportional to the sum of the concentrations of the Fe3+ and FeHSO42+ species. Although FeSO4+ was the dominant species present under the leaching conditions, it was inactive as an inner-sphere complex. Clearly, the leaching kinetics at higher ferric concentration may be related to the distribution of iron species in solution. Therefore, based on the above analyses, solution speciation is required to better understand and determine the factors affecting industrial leaching processes, so as to establish the optimum conditions and improve the leaching rates for copper recovery. However, although several studies have examined the speciation of the quaternary acidic iron sulfate system as a function of the initial amounts of iron, acidity, and temperature [33-38], to the knowledge of the present author, most of these are limited to lower concentrations and temperatures. There are very few published data pertaining to a systematic study on the speciation of the H2SO4-Fe2(SO4)3-FeSO4-H2O system, especially at higher concentrations and temperatures where most of the chalcopyrite hydrometallurgical processes operate. Moreover, ferric is a very common oxidant for many other metal sulfide leaching systems, thus its distribution in sulfate solutions is also of general importance.  14  1.3 Scope of the Present Study and Thesis Organization This work is first to explore the possibility of establishing aqueous speciation diagrams of the quaternary acidic iron sulfate system under conditions most relevant to the hydrometallurgical industry, thereby obtaining more detailed information about the electrolytes involved. These speciation results can further provide the data that can enable one to systematically investigate the kinetics of the cathodic ferric ion reduction reaction on chalcopyrite in industrially relevant leaching systems at different temperatures from 25°C to 150°C. This kinetics investigation aims to determine the temperature dependence of the fundamental electrochemical kinetic parameters, such as exchange current density, transfer coefficient and rate constant. The obtained information will finally be employed to shed light on the mechanism of industrial chalcopyrite leaching processes, i.e. by using mixed potential theory to obtain detailed information about which of the cathodic or anodic reactions may, in principle, govern the overall reaction rate [23, 24, 46-50]. The present study yields detailed information about the electrochemical processes involved and enables a deeper understanding of the kinetics and mechanisms in industrially significant leaching conditions relevant to such processes as Activox, Nenatech, Dynatec, AAC/UBC, Total Pressure Oxidation, CESL and Galvanox. In the following chapter (Chapter 2) various important topics and results found in the literature, which are highly related to the present project, will be summarized and discussed. Chapter 3 will present the objectives of this study. The methodology involved, including experimental procedures for the electrochemical and analytical methods, will be provided in Chapter 4. Chapter 5 discusses the development of a thermodynamic model to simulate the speciation of the quaternary sulfuric acid-ferric sulfate-ferrous sulfate-water system and so as to quantify the concentrations of the main species included in the solution through a wide range of  15  solution compositions and temperatures (25°C-150°C). Chapter 6 presents how to calculate the redox potential of the Fe3+/Fe2+ couple based on the speciation results obtained previously. It also presents a novel expression to predict the redox potential of the Fe3+/Fe2+ couple in the above-mentioned quaternary acidic iron sulfate electrolyte (which is widely used in the hydrometallurgical industry for the leaching of minerals and mineral concentrates) up to 150°C (Application 1). The kinetics of ferric ion reduction on chalcopyrite (including the temperature dependence of the exchange current density, transfer coefficient and rate constant) and its influence on the overall chalcopyrite leaching reaction will be presented in Chapter 7 (Application 2) and Chapter 8 (Application 3), respectively. Finally, Chapter 9 presents the conclusions, industrial applications and recommendations for future work in this area. The present work contributes to the research on aqueous speciation of acidic iron sulfate solutions, prediction of redox potential of the Fe3+/Fe2+ couple in acidic iron sulfate solutions, the reduction kinetics of the Fe3+/Fe2+ couple in general and in particular on the surface of chalcopyrite, as well as the mechanistic analysis in industrial leaching processes of chalcopyrite and other sulfide minerals. It is believed that these findings can enable better understanding of the critical factors to make the proposed chalcopyrite leaching process an economic proposition, and eventually reach full commercial acceptance.        16  2 Literature Review From the Introduction, it can be seen that very few studies about the reduction kinetics of ferric and oxygen on chalcopyrite have been published. Nevertheless, the following subjects, previously discussed in the literature, will be presented: the oxidation of chalcopyrite and cathodic reduction of chalcopyrite itself, the chemical or electrochemical reduction of ferric or oxygen on chalcopyrite, rotating disc electrode studies of chalcopyrite and other related sulfide minerals, electrochemical impedance spectroscopy studies of chalcopyrite, and, high temperature electrochemistry of both chalcopyrite and ferric/oxygen reduction. 2.1 Oxidation of Chalcopyrite and Cathodic Reduction of Chalcopyrite Itself To date, much effort has been devoted to understanding the kinetics and mechanisms of the oxidation processes or the cathodic reduction reactions of chalcopyrite itself, in order to develop possible hydrometallurgical leaching processes. In this section, a brief introduction on oxidation of chalcopyrite and cathodic reduction of chalcopyrite will be given. 2.1.1 Chemical or Electrochemical Oxidation of Chalcopyrite in Sulfuric Acid Among the several factors determining choice and effectiveness, leaching reagents are usually assessed in terms of dissolution power, price, and environmental friendliness. In the search for suitable and sustainable alternative leaching reagents, attention has been refocused on the use of easily available and cheap reagents like sulfuric acid. Sulfuric acid has been used for a very long time for sulfide ore leaching, and ways of improving its effectiveness have been investigated by various researchers. For the oxidation of chalcopyrite in sulfuric acid, ferric ions and dissolved oxygen are the most often used oxidants. These processes involve the oxidation of chalcopyrite to elemental sulphur, sulphate or other oxysulfur anions, and can be regarded as an  17  electrochemical reaction with the cathodic reduction of the oxidant and the anodic oxidation of chalcopyrite. These studies have shown that the poor leaching kinetics are a result of anodic passivation. 2.1.1.1 Thermodynamics and Stoichiometry of Chalcopyrite Dissolution The thermodynamics of the dissolution process may be discussed on the basis of Eh-pH diagrams [56]. According to the following diagram (Figure 2-1), a pH lower than 4 and an oxidizing redox potential higher than +0.4V is required to dissolve copper from chalcopyrite. These conditions are achieved using oxidizing agents, the most common being ferric ion as a sulphate or chloride. It may be noticed that information on the kinetics and mechanism of the possible reactions is not provided by this kind of diagram. Chalcopyrite dissolves in the presence of ferric ion according to the following reactions [3]: CuFeS2 + 4Fe3+ = Cu2+ + 5Fe2+ + 2So                                                              (2-1) CuFeS2 + 4Fe3+ + 3O2 + 2H2O = Cu2+ + 5Fe2+ + 2H2SO4                               (2-2)    18   Figure 2-1 Eh-pH diagram of the Cu-Fe-S-H2O system at 25°C: all solutes at 0.1 M activity except Cu2+ = 0.01 M. All reactions are reversible [56].   19  2.1.1.2 Chemical Leaching of Chalcopyrite-Roles of Ferric/Ferrous and Redox Potential Ferric ions are very commonly used in the leaching process of chalcopyrite and other metal sulfides, and widely regarded as an oxidant. Thus, ferric distribution in acid iron sulfate solutions is of major importance. However, it has been reported that increasing the concentration of ferric does not consequently result in a corresponding increase in the leaching rate [12]. In addition, during the oxidation of the chalcopyrite, there are a number of solution species that can interact by forming complexes that may exert influence on the overall process. And, it has been suggested by different authors that the leaching rate of chalcopyrite is strongly affected by redox potential of the solution determined by the ferric/ferrous ratio [29], ferrous concentration [51-53], or low ferric ion concentrations [12]. Thus, this raises some concerns about the real role of ferric, ferrous and the ratio of ferric to ferrous during the ferric leaching of chalcopyrite, which can facilitate the study of ferric reduction kinetics.  Here we take some typical results published in previous studies into account to introduce this question in detail in acidic iron sulfate leaching solutions. Suspension potential control The oxidation rate of chalcopyrite is expected to be dependent on the potential difference between the surface of the suspended particles and the solution. However, it is not possible to measure directly or to control the potential difference, which makes it difficult to compare directly leaching reactions and the electrode processes. A way of conducting the experiments with a constant redox potential in the solution to overcome the problem was reported by Kametani and Aoki [29]. This potential is referred to as the suspension potential. Suspension potential (Pt vs SCE, in the presence of Fe3+/Fe2+) in 1 mol/dm3 sulfuric acid solution at 90℃ was maintained constant in the range 0.54 to 0.89 V (vs SHE). The oxidation appeared to be  20  under surface reaction control. Ferric concentration had little effect on the oxidation rate of chalcopyrite and the copper extraction was mainly controlled by the redox potential of the solution, as a function of the ferric/ferrous ratio. Chalcopyrite in the concentrate was oxidized to form elemental sulfur over the entire suspension potential range. Ferrous-promoted leaching It is generally accepted that ferric ions, as an oxidant, are effective for leaching chalcopyrite but that ferrous ions contribute to leaching only in that, after oxidation, they represent a source of ferric ions. However, Hiroyoshi et al [51] found some chalcopyrite samples were more effectively leached in ferrous sulfate solution than in ferric sulfate solution. It was suggested that ferrous ions enhance the following reaction: CuFeS2+O2 + 4H+ = Cu2++ Fe2++ 2S0+ 2H2O                                          (2-3) The amount of extracted copper increased markedly with increasing ferrous sulfate addition and with decreasing pH. When the leach solution was sparged with nitrogen, the amount of copper extracted was negligible even with ferrous sulfate. A reaction model was proposed [52] and the model considers the leaching in two steps: (1) reduction of chalcopyrite to Cu2S by ferrous ions in the presence of cupric ions and (2) oxidation of the Cu2S to cupric ions and elemental sulfur by dissolved oxygen and/or by ferric ions. Further research [53] also obtained similar results and shows that in the presence of high concentrations of cupric ions, the chalcopyrite oxidation was enhanced by high concentrations of ferrous ions and copper extraction was mainly controlled by the concentration ratio of ferrous to ferric ions or the redox potential of the solutions.    21  Leaching in acidic ferric sulfate solution Leaching of chalcopyrite by Hirato et al [12] showed parabolic-like kinetics during the initial stage, and then linear kinetics over the extended period in acidic ferric sulfate. Leaching was chemically controlled, with apparent activation energy in the range of 76.8-87.7 kJ mol-l. The leaching rate increased with an increase in Fe2(SO4)3 concentration up to 0.1 mol dm-3, but a further increase had little effect on the leaching rate. Both the leaching rate and the mixed potential decreased with an increased FeSO4 concentration.  Córdoba et al [13] reported the effect of redox potential (or Fe3+/Fe2+ ratio) on chalcopyrite leaching in a Fe3+/Fe2+ sulphate solution at pH 1.8 at temperatures of 35℃ and 68℃. The redox potential range used was 497-797 mV (vs SHE) and it was found to be a key factor. A high potential at the onset of leaching provoked rapid passivation due to rapid precipitation of ferric ion as jarosite. They hypothesized that although ferric ion is responsible for the oxidation of chalcopyrite, ferrous ion has an important role in that it controls precipitation and nucleation of jarosites, which ultimately cause passivation. Chalcopyrite dissolves through the intermediate formation of covellite, CuS, which is later oxidized by ferric ion to release Cu2+ ions. The elemental sulphur that formed during chalcopyrite leaching was porous and did not form a passivating layer on the chalcopyrite surface. Further research by Córdoba et al [14] showed the the role of pH in the chalcopyrite leaching with ferric sulphate was found to be exclusively related to control of ferric species hydrolysis rather than oxidation of sulphide. The absence of oxygen in the leaching medium remarkably slows down chalcopyrite dissolution. Oxygen plays a key role in the regeneration of ferric ion as the oxidizing agent of the sulphide.  Vilcáez et al [32] reported that the oxidation of ferrous ion by oxygen did not take place in the absence of sulfides such as Cu2S and CuS. Leaching was insensitive to the addition of ferric  22  ion above about 0.01 M because ferrous ion released during the initial leaching stages did not suffice to reduce the initial ORP to values below 450 mV, where chalcopyrite leaching has been proven to be enhanced. If lower amounts of additional ferric ion were employed, the amount of ferrous ion released by ferric ion attack of chalcopyrite sufficed to reduce the initial ORP to values below a critical value (450 mV) such that the leaching of chalcopyrite was enhanced. The possibility of chalcopyrite being directly leached by ferric ion at high ORP values, and indirectly through the formation of intermediates at low ORP values, was supported by this work. Leaching of chalcopyrite ore using sulphuric acid containing oxygen and iron(III) in PVC columns was reported by Antonijević and Bogdanović [57] and it was also shown that iron(III) concentration had no important influence on the copper leaching rate. Summary The above results would suggest that the observed leaching kinetics may be alternatively due to the ferric/ferrous ratio, ferrous concentration, or ferric ion concentration. Hence, it is necessary to study the reason for this discrepancy to clarify this controversial issue, and speciation analysis of the acidic iron sulfate solution can definitely facilitate this research.  2.1.1.3 Electrochemical Oxidation of Chalcopyrite The fundamentals of chalcopyrite leaching have been extensively studied through electrochemical techniques, since it is thought to be essentially an electrochemical mechanism that takes place at the mineral-solution interface. Munoz et al [58] studied acid ferric sulfate leaching of chalcopyrite (1.0M H2SO4, 0.25 M Fe2(SO4)3, 90℃) using mono-sized particles in a well stirred reactor at ambient pressure and dilute solid phase concentration in order to obtain fundamental details of the reaction kinetics. The electrochemical reaction of chalcopyrite conforms to the stoichiometry of Reaction 2-1.  23  The chief function of the acid appears to be to prevent the hydrolysis of ferric. The rate limiting step is found to be the transport of electrons through the elemental sulfur layer. The reaction rate was independent of Fe3+, Fe2+, Cu2+ and H2SO4 concentrations. Experimental activation energy was 20 kcal/mol (83.68 kJ/mol) and is approximately the same as the apparent activation energy for the electron transfer through elemental sulfur, 23 kcal/mol (96.23 kJ/mol), reported in the literature. Potentiodynamic polarization/Linear potential sweeps Most of electrochemical studies have used relatively fast linear potential sweeps. Warren et al [15] studied electrochemical oxidation of CuFeS2 in 1.0 M H2SO4 using massive electrodes (approximately cubic, 1.0 cm on each side) by potentiodynamic polarization. Chalcopyrite samples obtained from six different localities often produced polarization curves that differed slightly from each other, which could be due to a difference in crystal orientation, impurities, changing surface area, etc (Figure 2-2). The overall shape of the polarization curves was generally the same, consisting of: dissolution, passive and transpassive regions. Although none of the samples exhibited the classical behavior of passivating metals, a portion of the anodic polarization curve exists where the current does not increase with increasing potential. This portion will be referred to as the "passive" region.   24   Figure 2-2 Anodic polarization curves for CuFeS2 from 6 different locations in 1 M H2SO4, 30 mV/min, 25°C [15].  Slower scanning rates shifted the curves to lower currents but did not cause the current to decrease drastically as would be expected (Figure 2-3). The presence of this current plateau was attributed to the formation of a thin layer of a defective copper sulfide intermediate as well as sulfur on the surface.  25    Figure 2-3 Effect of scanning rate on the anodic polarization curve of Transvaal CuFeS2 in 1 M H2SO4, 25°C [15].  Additions of cupric ion up to 50 g/L had little or no effect on the polarization curve (Figure 2-4). Ferrous additions, on the other hand, greatly affect the curves (Figure 2-5). The observed increase of the current in the passive region was directly related to the initial Fe2+ concentration. This is attributed to an additional competing oxidation reaction of the ferrous to ferric ion at the CuFeS2 surface. This result confirms the electron conducting character of the surface products.  26    Figure 2-4 Effect of cupric ion on the anodic polarization curve of Transvaal CuFeS2 in 1 M H2SO4, 40 mV/min, 25 °C. [Fe2+] was held constant at 0.04 g/1 [15].   27   Figure 2-5 Effect of ferrous ion on the anodic polarization curve of Transvaal CuFeS2 in 1 M H2SO4, 40 mV/min, 25 °C. [Cu2+] was held constant at 0.90 g/l [15].  Anodic dissolution of n- and p-type chalcopyrite was studied in both acidic sulphate (0.3 mol dm-3 H2SO4) and acidic chloride (0.3 mol dm-3 HCl) media under conditions relevant to chemical leaching, i.e., at temperatures > 70℃ and over the potential region 0.44-0.84 V vs SHE by McMillan et al [26]. Analysis in both systems indicated the formation of a surface layer, a solid electrolyte interphase (SEI), which slowed the rate of electron transfer. The higher Tafel slopes and anomalous Arrhenius behaviour obtained in H2SO4 suggested the surface layer formed in that medium was different from that produced in HCl electrolyte.   28  Tshilombo et al [27] studied the kinetics of the half-reactions involved in the oxidation of CuFeS2 (potential range 0.44-0.84 V vs SHE) by potentiodynamic polarization techniques in sulfuric acid. Anodic characteristics showed that CuFeS2 passivation was more severe in the potential range 0.69-0.89 V (vs SHE) at 25℃. However, there was no evidence of CuFeS2 passivation at higher temperatures (45 and 65℃). Cu was preferentially dissolved from CuFeS2 at lower potentials and high temperatures at a ratio of copper to iron of about 3:2.  Parker et al [59] used gold plating of chalcopyrite surfaces to stimulate surface enhancement of Raman scattering, thereby detecting oxidation products undetectable using normal Raman spectroscopy. In situ spectroscopic investigations during potentiodynamic scanning revealed that the oxidation product was amorphous, ubiquitous over the surface and showed some evidence of the commencement of S-S bonding in the transpassive potential region. The product was not characteristic of polysulfides or polythionates, indicative of an aging metal-deficient remnant sulfide lattice based on low frequency and the broad nature of the νSS bands on the oxidised surfaces.  Ghahremaninezhad et al [16] studied the dissolution of chalcopyrite electrodes in 0.5M sulfuric acid by means of potentiodynamic, EIS and Mott-Schottky techniques. A sequence of chalcopyrite dissolution and surface layer formation was proposed under different potential regions from open circuit potential (around 415 mV vs SHE) to higher positive potentials. EIS studies at open circuit potential proved the existence of a thin surface layer on the electrode. This layer was stable up to 100 mV and was assumed to be Cu1−xFe1−yS2. Increasing the potential through the range of 100-300 mV results in the partial dissolution of previously formed layer and the formation of a second layer (Cu1−x−zS2). Both of the layers showed the characteristics of passive layers at low potentiodynamic scan rate (0.05 mVs−1) while at high scan rates they acted  29  like pseudo-passive layers. However, in the potential range of 300-420 mV, both of these surface layers dissolved and active dissolution of the electrode started. Further increase in potential caused the formation of a CuS layer which hindered the dissolution rate of the electrode. The formation of CuS was concomitant with Fe2(SO4)3 formation and the latter may have acted as a nucleation precursor for jarosite at higher potentials (around 1.4 V vs SHE). Jarosite precipitation on the electrode surface hindered the dissolution of chalcopyrite at higher potentials. Different equivalent electrochemical circuits were modeled and compared to experimental results to support the proposed sequence of chalcopyrite dissolution and surface layer formation. Potentiostatic polarization It is found that potentiodynamic polarization curves with fast linear potential sweeps in acidic ferric/ferrous sulphate media at atmospheric pressure in the vast literature that exists cannot be used to faithfully predict important operational parameters. These parameters include the range of potentials most appropriate to leach the mineral and the potential for the onset of passivation (in order to avoid exceeding it). However, Viramontes-Gamboa et al [60, 61] found that potentiostatic anodic curves display true active-passive behavior with a passivation potential very well defined and close to the one observed in leaching tests. They show that the passive window is much smaller than predicted by potentiodynamic sweeps, such that the transpassive region is easily reached within the working range of the Fe3+/Fe2+ redox couple.  The oxidative leaching rate of chalcopyrite by ferric ions or by dissolved oxygen in sulfuric acid solutions is known to be faster at low redox potentials but slower at potentials above a critical value, due to the passivation of the mineral. However, most conventional electrochemical studies on the anodic dissolution of chalcopyrite in sulfuric acid solutions have disagreed with the results of leaching studies, i.e., they have reported monotonic increases in the  30  steady-state anodic current with potential. A study by Hiroyoshi et al [17] shows that active-passive behavior occurs only when cupric and ferrous ions coexist (conditions of anodic polarization curves in 0.1 kmol m-3 sulfuric acid with stirring at 298 K in a nitrogen-sparged solution). The current in the active region (at potentials lower than about 0.65V vs SHE) was larger than the current observed without cupric and/or ferrous ions, indicating that the coexistence of these ions (0.1 kmol m-3) causes activation rather than passivation. Hiroyoshi et al [31] also investigated the effects of solution composition on the optimum redox potential by potentiostatic curves using a CuFeS2 electrode at 298 K. Anodic-polarization curves of the CuFeS2 electrode showed that there was a current peak on the curves in the presence of Cu2+ and Fe2+, corresponding to the maximum leaching rate. The redox potential of the peak increased markedly with increasing Cu2+ concentration, while it was less dependent on the H2SO4 and Fe2+ concentrations. An empirical equation for the optimum redox potential for CuFeS2 leaching was proposed: Eop=EA=0.691+0.030 log [Cu2+] + 0.013log [Fe2+]                                    (2-4) where Eop is the optimum redox potential for CuFeS2 leaching and EA is the “rest potential of CuFeS2” dipped in the leaching solutions. Galvanostatic polarization Galvanostatic curves (potential vs time) show two regions: a transient state that is related to anodic film formation; and a steady state represented by a leveling off of potential, corresponding to the condition where the corrosion current is equal to the applied current, resulting in a film thickness of constant value. Research by Sequeira and Santos [62] focused on the study of the anodic film formation on chalcopyrite in the transient time-dependent region (generally data between 0.7 and 0.9 V vs SHE) in sulphuric acid at 25℃. Two passivation sub- 31  regions were observed: the first at lower potentials, shows a slope greater than the second, which occurs at higher potentials. Both followed the Sato-Cohen (logarithmic) model for the growth of anodic passive films. Cupric ion concentration up to 10 g/L had little or no effect on the anodic dissolution. Addition of ferrous ion up to 1.0 g/L had no effect, but for higher concentrations, over 5 g/L, galvanostatic curves show a plateau value at approximately 0.7 V vs SHE, due to the preferred oxidation reaction of ferrous ion at the chalcopyrite surface. Carbon paste electrode An interesting aspect of the published electrochemical studies concerning chalcopyrite is an apparent lack of reproducibility. Chalcopyrite electrodes supported on epoxy resin present low reproducibility, low resolution and a tendency to fracture. In addition, the physical properties of these electrodes are very different from the properties of the mineral on which the process of mineral leaching is performed. For this reason it is not possible to conduct systematic electrochemical studies on this kind of electrode. One alternative is the use of electrodes made of fine particles of the mineral mixed with graphite and a conducting/non-conducting binding material. Lázaro et al [63] have shown that a mixture of pulverized chalcopyrite with graphite and a non-conducting binder (silicon oil) permits electrochemical studies to be performed similar to those with massive mineral electrodes. This has the added advantage of an excellent reproducibility, due to the absence of problems, associated with polishing deficiencies, fracture, and a lack of homogeneity, presented by the larger mineral electrodes. It is thus expected that the electrochemical data would more accurately reflect the mechanisms that occur during an industrial leaching process. The carbon paste electrode has been further employed to study the electrochemical oxidation or reduction processes of chalcopyrite to identify the proposed intermediates such as chalcocite, covellite and bornite [19, 64, 65].  32  Rotating electrode (RDE and RRDE) Some of the research by electrochemical techniques has been directed at anodic dissolution in a potential region that is now called the anodic ‘‘prewave’’ which represents the initial stages of oxidation of chalcopyrite. Nevertheless, the reactions involved in this potential region and the mechanism of dissolution are still not resolved. The RDE and RRDE technique provide a means of evaluating the possibility of this reaction because its main feature is its ability to detect very low concentrations of soluble species. The versatility of the RRDE technique allows for independent control of potential and current of the ring and disk and this permits the detection on the ring of the soluble species generated during the dissolution of the mineral disk. Biegler and Swift [66] studied the anodic behaviour of chalcopyrite (connected with Beckman rotating assembly) in 1M acids (H2SO4 and HCl) at 25℃. Voltammograms with a fresh surface showed a small prewave (from the rest potential around 0.4 V vs SHE to 0.85 V/0.95 V) attributed to a surface oxidation process, followed by a region of active dissolution characterized by a steeply rising anodic current (potential 1V and above). No intermediate solid products were detectable on the electrode surface. Surface reaction involved the selective dissolution of iron. There was no indication that the semiconducting nature of chalcopyrite determined its anodic behaviour. A further study [18] showed that the small anodic prewave takes place at around 0.52-0.62V vs SHE. The main anodic reaction, with complete dissolution of copper and iron, occurs at more positive potentials. The prewave is not a consequence of atmospheric oxidation during surface preparation and represents a surface oxidation of chalcopyrite to form a thin passivating film. The prewave reaction is identified with the initial phase of the oxidative dissolution of chalcopyrite. These results indicate a prewave reaction with Fe2+ and Cu2+ dissolving at the ratio 4:1 and a solid product of stoichiometry Cu0.7S2:  33  CuFeS2→0.75CuS + 0.25Cu2+ + Fe2+ + 1.25S + 2.5e-                              (2-5) Anodic dissolution of chalcopyrite in acidic solutions has also been studied using cyclic voltammetry with RDE and RRDE at 298 K by Holliday and Richmond [67]. In the studies on chalcopyrite RDEs, an anodic prewave is observed between +0.44 V and +0.64 V (vs SHE) on the first scan of the electrode. The prewave reaction forms a passive surface layer that inhibits further reaction. RRDE studies show that the prewave reaction results in only partial dissolution of chalcopyrite, with iron being more readily leached from the mineral than copper.  Investigation of the products formed during the initial stages of chalcopyrite dissolution using an RRDE by Lazaro and Nicol [68] provided evidence that the mineral undergoes a non-oxidative dissolution process under freely dissolving conditions in dilute sulfuric acid solutions at 60℃ and in the absence of oxidant. This process involves the formation of soluble copper(II) ions and a soluble sulfur species which is presumably H2S. The dissolution of chalcopyrite under oxidative conditions involves the formation of copper(II) and iron(II) ions together with detectable amounts of a soluble sulfur species (Ring–disk data suggested that this species was thiosulfate). Bulk solution potential/Mineral potentials A number of recent publications have focused on the use of redox (or platinum electrode) potentials to monitor the rate of reduction of iron(III) and also as a means of controlling the rate of oxidation of the mineral by controlling the redox potential. It has been tacitly or inadvertently assumed in these studies that the potential (the so-called EH) of an inert electrode such as platinum in the bulk solution is identical to that experienced by the oxidizing mineral surface (mixed potential). However, this is not the case. Measurements of the potentials of pyrite, arsenopyrite and chalcopyrite rotating disk electrodes in acid sulfate solutions containing iron(III)  34  and iron(II) at 25℃ with pH 1.5 demonstrated that the potential measured in the bulk of the solution can only be approximated to that at the surface of the minerals under conditions of relatively high concentrations of iron(II) (5g/L ferric+5g/L ferrous) [69]. The results of the so-called EH-stat experiments, in which the bulk EH is controlled by the electrochemical or chemical oxidation of iron(II), should be used with caution if used to derive mechanistic information. 2.1.2 Chemical or Electrochemical Reduction of Chalcopyrite Itself in Sulfuric Acid The difficult separation of copper and iron atoms in chalcopyrite by conventional hydrometallurgical procedures has encouraged the proposal of alternative processing routes. These processes consist of the reduction of chalcopyrite, in order to extract the iron from its crystal structure, forming alternate copper sulfides, which are more susceptible to oxidative leaching. Thermodynamic data, summarized in the form of Eh-pH diagrams, predict that the reduction products of chalcopyrite in acid solutions could include hydrogen sulphide and ferrous ion together with the solid phases bornite, chalcocite and elemental copper, formed in this order with decreasing potential. The stability boundaries between these phases are all below the reversible hydrogen potential, which means that their actual formation will depend on kinetic factors, in particular the over-potential for hydrogen evolution. Hydrometallurgical treatments with different reducing agents have been shown to produce copper sulfides with low iron content. Actually, one of the greatest challenges is to determine the optimum reducing agent, medium and temperature, which allow the efficient removal of the iron.  Chalcopyrite electrodes were cathodically reduced typically in 2 M H2SO4 at 20℃ by Biegler and Swift [20]. At current densities below 10 mA cm-2 chalcocite was generally formed (in some runs closely related to djurleite, Cu1.97S; calculated standard potential for the reactions forming chalcocite and djurleite from chalcopyrite were -0.138 V and -0.144 V respectively, vs  35  SHE) and at higher currents (larger than 10 mA cm-2) the solid product contained elemental copper (calculated standard potential is -0.269 V). The other reduction products were H2S and Fe2+. The decreased current efficiency, measured in terms of the Fe2+ produced, was attributed to evolution of hydrogen. Further study [21] using cathodic linear sweep cyclic voltammetry (from 0 V to -0.4 V) with a freshly-polished chalcopyrite electrode (connected with Beckman rotating assembly) shows a narrow cathodic peak (prewave, at -0.1 V) preceding the main voltammetric wave for reduction to chalcocite. The possible identity of the product phase is suggested according to a general electrode reaction: CuFeS2 + (4-2z)H+ + (2x+2y-2z)e → CuxFeySz + (1-x)Cu2+ + (1-y)Fe2+ + (2-z)H2S      (2-6) which represents a cathodic process when x + y > z. Possible products which fulfill this condition include the copper-iron sulphides bornite (Cu5FeS4), haycockite (Cu4Fe5S8), mooihoekite (Cu9Fe9S16) and talnakhite (Cu9Fe8S16), and the several copper sulphides known to exist in the composition range Cul.lS to Cu2S. Research by Arce and González [19] in sulfuric acid solutions at 298 K using carbon paste electrodes has shown that the reduction product of chalcopyrite is chalcocite and bornite is not the formed intermediary species. Transient products preceding chalcocite formation during chalcopyrite reduction were also characterized in 1.7 M H2SO4 using carbon paste electrodes [22]. Several potential intervals could be identified: from 0.115≥Ecat≥−0.085 V vs SHE, an intermediate copper sulfide is formed whose composition is between those of chalcopyrite and bornite, such as talnakhite. The reduction of this product occurs slowly, giving bornite at potentials less than −0.085 V. In the applied potential region −0.085≥Ecat>−0.185 V, the bornite gradually decomposes causing the incomplete conversion to chalcocite. In the potential interval  36  −0.185 >Ecat≥−0.285 V, energetic conditions are large enough to allow the immediate decomposition of bornite, forming chalcocite in a more quantitative manner. 2.1.3 Other Oxidation or Reduction Systems/Methods for Chalcopyrite In addition to the above-mentioned systems and methods, over the years a host of other innovative copper hydrometallurgical processes and methods have been proposed to improve the dissolution rate of chalcopyrite at moderate temperature and/or pressure. These processes and methods are silver-catalyzed chalcopyrite leaching [70, 71], nano-sized silica as an additive to modify the mineral surface [72], galvanic interactions with manganese dioxide and other sulfide minerals (FeS2) [28, 73, 74], electro-assisted reduction of chalcopyrite to chalcocite by transient reactive monatomic hydrogen species produced on an aluminum cathode [75], hydrogen peroxide as a stronger oxidant to accelerate the reaction kinetics [76, 77], sodium chloride-sulfate [78-80], pure chloride systems such as ferric chloride or cupric chloride [81-84], ammoniacal solution [85], in-situ generated ferric sulfate solution by a mixture of O2 and SO2 [86], perchloric acid [87], acid sodium nitrate [88], alkaline solution [89-92], NaCl solution under differential stress [93], sulfidation of chalcopyrite by gaseous sulfur at moderate temperatures to transform its mineralogy to various simple sulfides (such as CuS and FeS2) which can be leached more easily than chalcopyrite [94-96].  Details about these proposed ways to treat chalcopyrite and its mechanism to enhance the leaching rate could be found in the cited literature. Any proposal for an economically viable hydrometallurgical process for the treatment of chalcopyrite should take into account basic studies that elucidate the chemical and electrochemical aspects governing leaching.   37  2.2 Chemical or Electrochemical Reduction of Ferric or Oxygen on Chalcopyrite 2.2.1 Reduction of Ferric or Oxygen on Chalcopyrite Chemical or electrochemical studies of chalcopyrite have generally placed emphasis on understanding the mechanisms of the oxidative processes or reduction reactions of chalcopyrite. However, the reduction of ferric ions or dissolved molecular oxygen is the most important cathodic process in these systems. Cathodic reduction of ferric ions or dissolved oxygen on CuFeS2 is of great significance since the true leaching rate can be predicted based on the mixed potential theory, i.e., by combining the cathodic and anodic branches of the half-cell reactions. Their position can affect the overall leaching rate of the process. Its kinetics, as is usual with corrosion systems, can be examined by electrochemical techniques.  Four electrochemical processes, anodic oxidation of chalcopyrite itself (CuFeS2→Cu2+ + Fe2+ + 2S + 4e-), anodic oxidation of iron(II) on the corroding chalcopyrite, cathodic reduction of Fe3+ or oxygen at the corroding chalcopyrite surface and cathodic reduction of chalcopyrite itself due to the presence of a strong reducing agent, can contribute currents during the leaching of chalcopyrite. Thus, it is important to examine the electrochemistry of each of these processes separately, if possible, to obtain the actual reduction behavior of ferric ions or dissolved molecular oxygen. Research by Parker et al [25] showed that oxidative dissolution of chalcopyrite is controlled by the formation of an unstable, metal-deficient polysulfide film, which is a semi-conductor, on the chalcopyrite surface. This film slows transport of ions from CuFeS2 to the solution, slows electron transfer to oxidants such as Fe3+ and slows the supply of holes to the solid-solution interface. The Fe3+/Fe2+ couple, indeed most redox couples, are much less  38  reversible on corroding chalcopyrite than on pyrite. Values of ic and ia on pyrite were always higher than 20 mA/cm2 but on corroding chalcopyrite, values were often well less than 1 mA/cm2. The sulfur film that forms on corroding chalcopyrite does not account for the electrochemical or kinetic aspects of chalcopyrite leaching. Faster oxidation of chalcopyrite can be achieved by addition to the solution of fast electron acceptors (Cu2+, I2, Br2) under conditions such that a high corrosion potential is achieved. Results from McMillan et al [26] also show that the Fe3+/Fe2+ couple is much less reversible on corroding chalcopyrite than the Cu2+/Cu+ and I3-/I- redox couples in general. Cu2+/Cu+ and I-/I3- species can interact with the chalcopyrite reaction surface to allow facile electron transfer to occur. Fe3+/Fe2+ species indeed passivate the surface towards electron transfer.  Tshilombo et al [27] studied the kinetics of the half-reactions involved in the oxidation of CuFeS2 (potential range 0.44-0.84V vs SHE) by potentiodynamic polarization techniques in sulfuric acid. Cathodic characteristics also showed that the passive layers formed at 25℃ and high potentials strongly inhibit ferric reduction on polarized CuFeS2 surfaces. The Tafel slopes for the reduction of ferric ions after polarization of the CuFeS2 surface ranged between 0.15 and 0.22 V/decade. These high values of Tafel slopes clearly indicate that the polysulphide layer inhibits the transport of electrons. It follows that the slow kinetics for the ferric reduction on polarized CuFeS2 surface is a contributing factor for CuFeS2 passivation. Dixon et al have even assumed that it is the cathodic half-cell reaction (i.e. ferric reduction) that limits the overall leaching rate of chalcopyrite in acidic iron sulfate solution [28].  More attention should been paid to these issues in order to obtain detailed information on the characteristics of ferric ion or oxygen reduction on chalcopyrite, such as kinetic and mechanistic data.  39  2.2.2 Reduction of Ferric or Oxygen on Other Sulfide Minerals/Passive Electrodes Although very few studies are available about the cathodic reduction of ferric ions and/or oxygen on chalcopyrite, there are some published reports related to the reduction kinetics of ferric or oxygen on other sulfide minerals or electrodes. 2.2.2.1 Pyrite The dissolution of pyrite is an oxidation-reduction reaction, as the pyrite is oxidized and the Fe3+ ions and/or O2 are reduced on the pyrite surface. Pyrite can be readily dissolved at fairly anodic potentials in sulfuric acid solutions.  The electro-reduction of oxygen was studied at rotating electrodes of pyrite by Biegler [97, 98]. In oxygen-saturated 1 M acid solutions (H2SO4, HCl, HClO4), the Tafel slopes and exchange currents were of the order of 130 mV and 10-11 A cm-2, respectively. The results at low pH indicated that the first electron transfer step to form O2- is rate-determining. At low rotation speeds, linear sweep voltammograms reached a limiting current corresponding to 4-electron reduction of oxygen to water. The dependence of current on rotation speed, potential and surface roughness was analyzed in terms of a mechanism involving kinetic control of peroxide reduction and diffusion control of its escape into the solution bulk. Further study showed that Pyrite specimens from different sources and with different semiconducting properties show some degree of variation in detailed shapes of voltammograms, Tafel slopes and their electrocatalytic activities for oxygen reduction. The kinetic data are shown in Table 2-1. There was no obvious correlation between kinetic parameters for oxygen reduction and the semiconductive nature of the pyrite.    40  Table 2-1 Kinetic data for oxygen reduction on pyrite electrodes [98]. Sample no. Electrical type In 0.1 M HClO4 In 1 M H2SO4 -(∂E/∂ log i)/ mV Current at 0.1 V vs. SCE/μA cm-2 -(∂E/∂ log i)/ mV Current at 0.1 V vs. SCE/μA cm-2 1 n-type semi. 121 50 130 41 2 n-type semi. 148 186 117 338 3 n-type metallic 125 46 128 56 4 n-type metallic 135 46 129 71 5 n-type metallic 141 29 131 35 6 p-type semi. 154 51 123 78 7 p-type semi. 145 40 158 73 8 p-type semi. 159 142 118 123  Holmes and Crundwell [99] studied the kinetics of the reduction half-reaction of pyrite in H2SO4 in the presence of Fe3+ and/or dissolved oxygen. The current density due to oxidation and reduction of dissolved iron at the pyrite surface was described and the measured Tafel slope, given by 2.303RT/(αFe F) was close to 0.12 V/decade, which yields a value of 0.51 for αFe. The current density due to the reduction of oxygen at the pyrite surface was also obtained and the measured Tafel slope was 0.115 V/decade, which gives a value of 0.53 for αO2.  Rimstidt and Vaughan [100] found during the overall oxidation process of pyrite the reaction at the cathodic sites is the rate-determining step for the overall process. The reduction of Fe3+ ions and/or O2 involved in the pyrite dissolution process were investigated by steady-state voltammetry using three pyrite materials in sulfuric acid [101]. Tafel slope and the apparent  41  transfer coefficient for all of the reactions show that the oxidative dissolution of pyrite and the reduction of Fe3+ ions and O2 were governed by charge transfer processes for all the pyrite samples studied. Pyrite oxidation in chloride solutions (0.5 M HCl+4.5 M NaCl) at 25℃ with cyclic voltammetry [102] indicated the reaction is controlled by the diffusion of ferric ions or electrons through the passive film. 2.2.2.2 Kinetics of Ferric/Ferrous Reaction on Passive Electrodes  Overpotential measurements for the Fe3+/Fe2+ couple on passive Ni, Fe, Ti, Fe-Cr alloy and stainless steel were carried out [103-105] and Tafel lines were generally obtained with exchange currents between 10-8 and 10-5 amp/cm2. Compared to the oxide-free electrodes (e.g. Pt), the exchange current is substantially smaller on passive electrodes, and the sum of the apparent anodic and cathodic transfer coefficients is significantly less than unity. The main difference in the kinetics (aside from difference of the exchange current) is in the apparent transfer coefficient for the anodic reaction. The results show that a potential drop exists within the passive film. The potential drop across the film increases linearly with the total applied potential. This dependence leads to an apparent transfer coefficient for the anodic reaction that is substantially less than what is expected for the oxidation of Fe2+. 2.3 Rotating Disc Electrode Studies of Chalcopyrite and Other Related Sulfide Minerals under Leaching Conditions As mentioned in Section 2.1.1.3, RDE and RRDE techniques have been used to study the oxidation of chalcopyrite, especially in a potential region that is now called the anodic ‘‘prewave’’ which represents the initial stages of oxidation of chalcopyrite. Besides the anodic  42  ‘‘prewave’’ studies of chalcopyrite, there are some other interesting RDE reports about the leaching of chalcopyrite or other sulfide minerals under leaching conditions [54, 106,107]. Dutrizac et al [54] also studied the dissolution kinetics of chalcopyrite in acidic ferric sulfate solutions from 50℃ to 94℃. To avoid the complications of impurities and an indefinite surface area, they used synthetic chalcopyrite that was pressed into disks. The leaching rate decreased with time, according to a parabolic rate law. This result was attributed to a thickening film of elemental sulfur on the surface, which retarded the reaction. An activation energy of 17.3 kcal/mol (72.38 kJ/mol) was determined. The reaction was found to be independent of pH, rotation speed and ferric concentration above a very low level (0.01 M) but sharply dependent on ferrous concentration. It followed that the rate-determining step was the diffusion of ferrous ions away from the surface (through the So film in this case). When the ferric concentration was less than 0.01 M, the leaching rate was probably controlled through a mechanism involving the diffusion of ferric sulfate through the sulfur layer.  Sintered disks of synthetic chalcopyrite were also prepared with known amounts of various sulfide impurities to study the effect of the second phase on the rate of chalcopyrite dissolution [106]. The disks were leached in 0.1 M Fe3+-0.1 M H2SO4 solutions at 80℃ and were rotated at 200 rpm. Chalcopyrite-cubanite mixtures behave almost additively; chalcopyrite-bornite mixtures dissolve slightly more rapidly than would be expected from their additive rates. The presence of pyrite, molybdenite or stibnite (which reacts to form pyrite) accelerates the chalcopyrite dissolution rate; the presence of galena retards its dissolution. High-iron sphalerite slightly retards the chalcopyrite dissolution but low-iron sphalerites behave erratically. These results are consistent with a galvanic corrosion mechanism except for the observed effects of molybdenite.   43  Thomas, using rotating sintered disks of synthetic chalcocite, found that the dissolution rate was linearly dependent on ferric up to about 0.1 M (at 95 rpm and 25℃), and then appeared to level off somewhat [107]. A similar dependence of dissolution rate upon rotation speed was found. These findings, together with an activation energy of 5 kcal/mol (20.92 kJ/mol), were taken as an indication of a process controlled by mass transport of reagents across the boundary layer. 2.4 Electrochemical Impedance Spectroscopy Studies of Chalcopyrite The chalcopyrite electrode/electrolyte interface can be studied by EIS, in order to obtain more insight into the leaching process. Very few papers related to the dissolution of chalcopyrite electrodes have been published 2.4.1 Sulfuric Acid Ghahremaninezhad et al [16] explored the dissolution of a massive chalcopyrite electrode in 0.5 M sulfuric acid at 25℃ by means of potentiodynamic, EIS and Mott-Schottky techniques. EIS studies at open circuit potential (around 415 mV vs SHE) proved the existence of a thin surface layer on the electrode. Different equivalent electrochemical circuits were modeled and compared to experimental results to support the proposed sequence of chalcopyrite dissolution and surface layer formation at different potential regions. A study by Hiroyoshi et al [17] shows that active-passive behavior occurs only when cupric and ferrous ions coexist, based on anodic polarization curves in 0.1 kmol m-3 sulfuric acid with stirring at 298 K in nitrogen. The current in the active region (at potentials lower than about 0.65V vs SHE) was larger than the current observed without cupric and/or ferrous ions, indicating that the coexistence of these ions (0.1 kmol m-3) causes activation rather than  44  passivation. AC impedance spectra indicated that a high-resistance passive layer grows on the chalcopyrite surface without cupric and/or ferrous ions, and that coexistence of these ions causes the formation of another product layer and inhibits the passive layer growth in the active region. A reaction model, assuming the formation of intermediate Cu2S in the active region, was suggested to account for the active-passive behavior of chalcopyrite. 2.4.2 Alkaline Solution EIS results in an alkaline solution [90] for different oxidation potentials reveal the oxidation of chalcopyrite produces a modification of the electrode surface: for values lower than 0.64 V vs SHE a Randles equivalent circuit can be used, but the Nyquist plots present a change when the applied potential is higher than 0.64 V vs SHE and a surface layer model must be used. This change gives rise to a modification of the charge transfer resistance and the diffusion coefficient of charge carriers across the interlayer electrode/electrolyte resistance. This behaviour was attributed to the initial formation of a layer of Fe2O3 and an inner layer of CuO and Fe2O3, which conferred an irregular and non-homogeneous surface to the electrode. 2.4.3  Sulfuric Acid plus Iron Sulfate The corrosion rate of chalcopyrite was studied at various temperatures (25℃-65℃) and concentrations of acid in sulfuric acid containing only 5 g/L ferric (no ferrous) using EIS. The corrosion rate increased with temperature and decreased with the acid concentration [60]. EIS has also been used to investigate the influence of the ferric-ferrous couple on a passivated chalcopyrite electrode in sulfuric acid at 25℃ [108]. In the presence of the ferric-ferrous couple, the double-layer resistance, as a characteristic quantity for the charge transfer step of an electrochemical reaction which indicates its inherent speed, shows a large decrease. It was found that ferric reduction on chalcopyrite is faster than the chalcopyrite oxidation reaction  45  itself. This result indicates the electronic conduction of the passive film is relatively high, and the passive dissolution of chalcopyrite is mass transport controlled by the passive film, which is consistent with the above-mentioned studies from McMillan et al [26]. 2.5 High Temperature Electrochemistry of Chalcopyrite Electrode and Ferric/Oxygen Reduction Reaction Many of the proposed leaching processes for chalcopyrite are operated under pressure oxidation conditions, primarily because fast leaching kinetics can be achieved at the elevated temperatures employed in an autoclave. However, although a large number of important studies have been carried out to understand the mechanisms involved and the key parameters that limit the leaching kinetics, and lots of publications have suggested the electrochemical nature of the oxidation leaching process, except for the very few results reported by Jones and Lázaro [46, 109,110], the majority are limited to low temperatures below 90℃.  According to recent reviews about the high temperature and high pressure (HTHP) electrochemical studies [111, 112], although in recent years significant developments have been made, HTHP electrochemistry remains a relatively unexplored field of research and the relative lack of experimental data is ascribed to the various technical obstacles. In the case of mineral electrochemistry, the major drawback seems to be the mineral electrode preparation and reproducibility of results, which are highly dependent on the nature of the mineral. Furthermore, there are only a few reports of mineral electrochemistry at high temperature and pressure [113]. 2.5.1 Sulfuric Acid Anodic oxidation studies by Jones and Peters [109] using potentiostatic polarization in 0.1M HClO4 or H2SO4 solutions at temperatures from 7℃ to 175℃ show that at low  46  temperatures (up to about 85℃) the polarization curves in the two acids are very similar but at higher temperatures the reactivity of chalcopyrite suddenly drops in H2SO4, whereas in HClO4 it continues to increase steadily with temperature. The current obtained at low potentials (up to around 800 mV vs SHE) is time-dependent whereas it is time-independent at the higher potentials. The time dependence of the current in the low current region is indicative of a rate-controlling diffusion process, such as metals out to the surface, and in the high current region where the current is time-independent it is possible that the formation of holes is rate-determining. Jones [46] reported that for chalcopyrite leaching in ferric sulfate solutions from 20℃ to 175℃ an electrochemical mechanism is operative. Mixed potential measurements at 90℃ indicate that the reaction is under mixed control, and that both anodic and cathodic reactions are quite irreversible, according to the relative position of the mixed potential, the Nernst potentials of the anodic and cathodic reactions having been calculated with some simple assumptions. Small additions, up to 0.05 M ferrous in a 0.2 M H2SO4+1 M Fe2(SO4)3 at 90℃ had little effect, but thereafter a substantial drop in mixed potential was observed. The mixed potential of chalcopyrite is responsive to ferric and ferrous concentration in sulfate solutions. Lázaro and Jeffrey reported a study of the pressure acid leaching of chalcopyrite using a chalcopyrite rotating disc electrode at 150℃ in a 0.2 M H2SO4 solution containing ferric or oxygen [110]. All the potentials measured by a platinum electrode were always higher than those obtained using a chalcopyrite electrode under the same conditions. It is interesting to note that either with platinum or chalcopyrite, the potential of an acid solution in the presence of O2 is lower than that of a platinum electrode in a 0.1 M iron(III) solution. Even though there is Fe2+ being produced through reduction of Fe3+ and oxidation of CuFeS2, it is not a high enough  47  concentration to produce a significant change in potential during the measurement time of the experiment. Mixed potential measurements and anodic behavior of chalcopyrite at 150℃ indicate that pressure acid leaching in a solution containing 0.1 M iron(III) will occur quite rapidly. In comparison, when using 120 psi partial pressure of oxygen, the mixed potential is in the so-called “prewave” region, and hence slow leaching would be expected. 2.5.2 Reduction of Ferric or Oxygen on Other Electrodes at High Temperatures Apart from those directly relevant to chalcopyrite, there are other interesting HTHP reports relating to ferric or oxygen reduction. Clouser et al [114] investigated the temperature dependence of Tafel slope and apparent transfer coefficient for oxygen reduction on platinum by RDE in concentrated H3PO4 over a wide range of temperatures (25-250℃). The observed Tafel slopes were essentially independent of temperature over the 25-250℃ range, and were quite different from the values expected from theory. The apparent transfer coefficient for the oxygen reduction has been found to be approximately proportional to temperature rather than independent of temperature. Cathodic reduction of oxygen was also studied on gold [113] in ammonium chloride solutions by RDE over the temperature range of 30-150℃. The rate of oxygen reduction increases with increasing temperature and pressure. Electrochemical studies by Liu and Nicol [115] demonstrated that the effective oxidant for gold pressure leaching using Au-RDE in acidic sulfate solution containing various concentrations of chloride ions is ferric and not dissolved oxygen. The equilibrium solubility of gold increases with increasing temperature, chloride concentration and iron(III)/iron(II) ratio. The role of oxygen was largely confined to that of maintaining a high ratio of Fe(III) to Fe(II).  48  2.6 Summary Obviously, based on this literature review, most of the published papers are about the above-noted oxidation of chalcopyrite and cathodic reduction of chalcopyrite itself. Even within these studies, most are under a single low temperature and in a discrete range of solution concentration, and it is difficult to compare among the studies.  In addition, the cathodic reduction kinetics of ferric and oxygen on chalcopyrite has hardly been studied, and research on RDE, EIS, as well as high temperature electrochemistry of chalcopyrite and ferric/oxygen reduction on minerals is almost non-existent, not to mention a comprehensive study and comparison of reduction kinetics at different temperatures.                49  3 Objectives The overall objective of this investigation is to determine chalcopyrite leaching mechanisms in acidic iron sulfate solutions-by far the most adopted leaching media.  Although various methods and systems have been used to investigate chalcopyrite leaching, most of the published literature has placed emphasis on understanding the mechanisms of the oxidative processes or reduction reactions of chalcopyrite itself at low temperatures, and very few data are available about the reduction processes in leaching systems. However, the cathodic reduction of ferric ions on CuFeS2 is also of great significance because actual reduction behavior of ferric ions is vital to obtain the true leaching rate.  In view of the preceding discussion, the specific objectives of this thesis are set out as follows: (1) Develop a thermodynamic model to simulate the speciation of the quaternary H2SO4-Fe2(SO4)3-FeSO4-H2O solutions in order to quantify the concentrations of the main species (including Fe3+ and Fe2+) in the solution from 25°C to 150°C.  (2) Develop an expression to predict the redox potentials of the Fe3+/Fe2+ couple in the above-noted solutions under different temperatures, via Nernst equation based on the concentrations of free ferric and ferrous ions determined by the speciation results. The results will also indicate how the real Fe3+/Fe2+ ratios will change with temperature.  (3) Investigate the reduction kinetics of ferric ion on chalcopyrite by cathodic potentiodynamic polarization at elevated temperatures relevant to existing industrial processes, in order to determine temperature dependence of kinetics parameters such as exchange current density, transfer coefficient and rate constant. These parameters can be useful quantities for determining the mechanism of an electrochemical reaction. The free ferric ion concentration  50  previously obtained from the speciation results of the thermodynamic model, together with the calculated redox potentials of the Fe3+/Fe2+ couple, will be employed to analyze the electrochemical experimental curves and so as to obtain the kinetic parameters.  (4) Based on the obtained reversible potentials of the Fe3+/Fe2+ couple (calculated from the speciation results) and the measured mixed potentials, as well as the calculated reversible potentials of possible anodic reactions, the mechanism involved in the chalcopyrite leaching system are further analyzed by mixed potential theory to obtain detailed information about which of the cathodic or anodic reactions may, in principle, govern the overall reaction rate [23, 24, 46-50]. The analysis of control scenario for the electrochemical processes involved can also be used to clarify to what extent the cathodic reaction can influence the overall leaching reaction.  For the first time, to the author’s knowledge, a reliable thermodynamic model is developed to simulate the speciation of the quaternary H2SO4–Fe2(SO4)3–FeSO4–H2O system through a wide range of solution compositions and temperatures (25°C-150°C), and is used to propose a novel equation to predict the redox potential of the ferric/ferrous couple; the kinetics of ferric ion reduction on chalcopyrite was quantified and its influence on the leaching was determined over a wide range of temperature. The findings of the present thesis are an original contribution to the current knowledge of chalcopyrite leaching in acidic iron sulfate media.       51  4 Methodology and Experimental Procedure 4.1 Measurement of the Redox Potential of the Quaternary Acidic Iron Sulfate System from 25°C to 150°C Experimental work to measure the redox potential of the quaternary acidic iron sulfate system was carried out at temperatures ranging from 25°C to 150°C.   4.1.1 Electrode Preparation According to several publications on the redox behavior of the ferric-ferrous couple in H2SO4 on Pt [116-118], the kinetic parameters such as exchange current density (about 1.1 A/cm2) and rate constant (10-2-10-3 cm/s), are relatively large at or near room temperature. The reaction can be considered reversible or highly quasi-reversible according to the literature [119]. In addition, one would expect kinetics to increase with temperature thus preserving the reversibility of the reaction. For this reason Pt has been widely employed for the measurement of reversible potentials in the H2SO4-Fe2(SO4)3-FeSO4-H2O system over a wide range of temperatures, such as room temperature [30, 31, 53, 69], 78°C [55], 90°C [33], and 150°C [110]. The platinum wire used in this investigation for the redox potential measurement was purchased from Sigma-Aldrich. The diameter was 0.5 mm and it had a purity of 99.9% (mass percentage). The electrical contact between the Pt electrode and a copper wire lead (enameled copper wire was used for the experiments in the autoclave) was made with silver conductive epoxy (MG Chemicals) for the experiments conducted at or below 90°C and Silvertech PT-1 Silver-filled Epoxy (Materion Corporation) for the experiments performed in the autoclave. The whole assembly was protected from the solution by mounting it in epoxy resins (832HT-375ML from MG Chemicals) along with an appropriate fitting, leaving only one part of the platinum  52  electrode exposed to the solution. Before each test, the Pt working electrode was activated in a 0.1M H2SO4 solution according to a published method [120]. 4.1.2 Electrolyte Preparation In the present study, the overall composition of the solutions was determined based on the operating conditions described for the above-mentioned industrial leaching chalcopyrite processes. The largest ferric concentration was limited to 0.18 mol/kg, because much of the dissolved ferric could precipitate in the quaternary system, especially at higher temperatures. Deionized water, sulfuric acid (H2SO4, 95.0-98.0%, Fisher Scientific Canada), Iron(III) sulfate pentahydrate (Fe2(SO4)3•5H2O, 97%, Acros), Iron (II) sulfate heptahydrate (FeSO4•7H2O, 99+% for analysis ACS, Acros) were used to prepare the desired electrolyte. Prior to each test, fresh solution was prepared, with the concentration of H2SO4 and ferric ion being 0.31 mol/kg and 0.18 mol/kg, respectively. The ferrous ion concentration was set by the various nominal molar ratios of ferric to ferrous (1:1, 10:1, 100:1, 1000:1). The solution was prepared by first dissolving 16.80 mL H2SO4 (transferred by pipette) in deionized water. Then, 45.22g Fe2(SO4)3•5H2O and the corresponding amount of FeSO4•7H2O were balanced and dissolved in the sulfuric acid solution. The choice of the particular sulfuric acid concentration is due to the fact that it is an appropriate concentration for chalcopyrite leaching and is widely used in industrial leaching processes. Please note that typically the initial sulfuric acid concentration employed in the previously mentioned industrial leaching processes is in the range of 5-60 g/L. Depending on the operating temperature and leaching products (elemental sulfur or sulfate), acid can be consumed or produced due to the ferric hydrolysis reaction. Also, at 150°C, a relatively lower acid concentration can facilitate the formation of Fe2O3, which is the preferred iron precipitate.   53  Furthermore, at low temperatures (≤110°C), such a concentration results in an initial pH lower than 2, which prevents iron precipitation from taking place in the systems considered in this work.  According to Dutrizac (1980) [121], there may be small colloidal particles generated (which are associated with the formation of small iron polymers generated by iron hydroxyl complexes). However, in the present studied solutions, the pH is typically lower than 1 for all conditions (as shown in Section 5.3.4.3), which does not facilitate the formation of iron hydroxyl complexes and iron hydroxides. Even if formed, thermodynamically these polymers or colloids should eventually transform to stable precipitates such as FeOOH and Fe2O3. Therefore, we believe that there should be little or no influence exerted by the formation of colloids on the speciation model in the present work. 4.1.3 Electrochemical Measurements at 25°C, 70°C and 90°C Electrochemical experiments were carried out using a standard three-electrode cell with a thermostated water jacket. The counter electrode (CE) was graphite and the prepared Pt electrode served as the working electrode (WE). A saturated Ag/AgCl electrode (saturated with KCl, Accumet* Glass Body, Fisher Scientific) was used as a reference electrode (RE). All potentials have been converted from Ag/AgCl to the standard hydrogen electrode (SHE). All further potentials in this study are quoted with respect to the SHE at 25°C unless otherwise stated. Details of the corrections used for the measured potential are discussed below. The RE was connected to a Luggin capillary to minimize IR drop. The cell solution was slowly heated to the predetermined temperature by the circulating water from a Cole-Parmer Polystat Heated Circulating Bath with Analog Control, and kept at the constant temperature with an accuracy  54  ±1°C. Prior to use, the CE was immersed in ethanol for degreasing, rinsed with deionized water, and finally dried with cool air.  The test solution was deaerated by sparging high-purity N2 prior to- and throughout the electrochemical experiments at a constant flow rate to eliminate the effect of dissolved oxygen. This was done to ensure that no confounding effects from dissolved oxygen existed. The cell off-gas, after passing through an Allihn condenser, was passed through deionized water and finally discharged to a fumehood. The open circuit potentials (OCP) of the samples were recorded to yield a steady-state potential (as the redox potential). Electrochemical measurements were performed using a Potentiostat/Galvanostat VersaSTAT 3F Electrochemical System with an optional frequency response analyzer contained in a single unit, controlled by the VersaStudio electrochemistry software package (Princeton Applied Research). 4.1.4 Electrochemical Measurements at 110°C and 150°C A 5100 low pressure reactor from the Parr Instrument Company, with a 600 mL glass cylinder and 4848 reactor controller, was used for the electrochemical experiments at 110°C and 150°C. A Pt-Nb electrode from Cortest Inc. was used as a CE and the prepared Pt electrode was used as the WE. The Pt-Nb electrode is relatively inert and can be used for high temperature high pressure electrochemistry experiments because Nb oxides are extremely insoluble in most conditions and actually thicken under polarization. This electrode was used for convenience. An external pressure balanced Ag/AgCl RE (EPBRE) with a double-porous junction filled with 0.1 mol/kg KCl (Cortest Inc.) was used and it was maintained at room temperature. All potentials measured against Cortest’s external Ag/AgCl electrode filled with 0.1 mol/kg KCl have been converted to the SHE at 25°C, as shown in the following section. The cooling loops and the  55  magnetic drives were removed from the three port holes in the head of the 5100 Reactor in order to provide the space necessary for the WE, CE and RE, which were installed in the head by Swagelok 316 stainless steel fittings. Prior to use, the CE was immersed in ethanol for degreasing, rinsed with deionized water, and finally dried with cool air. The test solution was deaerated by sparging high-purity N2 prior to the electrochemical experiments at a constant flow rate for 40 min to eliminate the effect of dissolved oxygen. The autoclave was then heated to 110°C or 150°C. The OCP of the samples were recorded until a steady-state potential was achieved. The external RE used is a commercial high temperature high pressure (HTHP) reference electrode. Such electrodes have been widely used for potential measurements in a significant number of HTHP electrochemical experiments [122-124]. Very stable potentials were achieved during the experiments and no drift was found within the experimental duration (typically one experiment lasted about 2 hours). The OCP experiments for redox potential took approximately 15 minutes. In general, the redox potential measurements were very stable and their values varied to within ±3mV. The potential drift resulting from thermal diffusion (the Soret effect) can be neglected for this kind of RE [125]. The double junction design of the EPBRE can effectively prevent the contamination of the internal reference solution. Herein a brief explanation of the RE is provided for clarity. Figure  4-1 shows the schematic diagram of the EPBRE (Also shown in appendix A, Figure A-5). In this design, the Ag/AgCl electrode itself is maintained at ambient temperature and communication with the high temperature zone is made via a non-isothermal electrolyte bridge. So, there is a temperature gradient along the bridge between the Ag/AgCl RE outside the autoclave and the high temperature zone at the operating temperature inside the autoclave. As demonstrated in the cited literature (see in the following section for the potential correction part), the potential drop  56  resulting from such a temperature difference (including the thermo-electrical effects in the metallic components, temperature influence on the electrochemical half-cell potentials, thermal liquid junction potential and the concentrations changes by thermal diffusion of the solute along the temperature gradient), is discussed in detail. Based on some reasonable assumptions, such as neglecting the thermo-electrical effects in the metallic components and the Soret effect, the influence of the temperature gradient on the measured potential is thus included in the term Ecorrection in Eq. (4-1) as shown in the following section.                   57   Figure 4-1 Schematic diagram of Ag/AgCl external pressure balanced reference electrode with double porous junction.   58    Figure 4-2 Schematic diagram of the apparatus for high temperature high pressure electrochemical tests by using the EPBRE.  Figure  4-2 is a detailed schematic diagram of the setup used in this study. All the experiments were carried out in a high temperature high pressure autoclave (Please see appendix A, Figures A-1 to A-5). 4.1.5  Correction of the Measured Potentials to SHE at 25°C In the present study, it is assumed that the SHE potential is a function of temperature and is zero only at 25°C (Traditionally, the SHE potential is 0 at any temperature by definition). All of the potentials reported herein are thus with respect to the SHE at 25°C. We prefer this definition  59  as the SHE is not in fact 0 at elevated temperature (a potential can be measured between a SHE at 25°C and one at 100°C, for example).  At 110°C and 150°C, all electrode potentials have been converted to SHE at a particular temperature according to the following relationship [125-127]: ESHE (T) = Eobs + Ecorrection = Eobs + EAg/AgCl (T) - ΔEth                            (4-1) where ESHE (T) is the potential of a WE in the autoclave versus the SHE at the operating temperature T; Eobs is the observed potential of a WE in the autoclave versus the external Ag/AgCl RE filled with 0.1 mol/kg KCl; Ecorrection is a potential correction value; EAg/AgCl (T) is the isothermal potential of the Ag/AgCl electrode versus the SHE at the operating temperature T; ΔEth is the measured potential difference of the thermal cell between an internal and an external RE connected by a cooled salt bridge. The ESHE (T) was further corrected and referred to the SHE at 25°C by the following equation:  ESHE (25°C) = ESHE (T) + ΔESHE                                                    (4-2) where ESHE (25°C) is the potential with respect to a SHE at 25°C; ΔESHE is the potential difference of the SHE thermal cell at T and 25°C. ΔESHE data were computed by applying the above-mentioned Criss-Cobble method, with the values being 43.9 mV at 110°C and 54.2 mV at 150°C. Details about the conversion of the measured potentials to the two SHE scales can be found in Ref. [125-127]. As an example of the correction for the experiments in the autoclave, when measuring the redox potential of the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with the nominal Fe3+/Fe2+ ratio of 10:1 at 110°C, the Eobs = 515.57 mV and Ecorrection = 209 mV as published in Ref. [125], and hence ESHE (T) = 724.57  60  mV at 110°C according to Eq. (4-1). Then, by using Eq. (4-2), with ΔESHE being 43.9 mV at 110°C, the ESHE (25°C) at 110°C is 768.47 mV with respect to a SHE at 25°C. A similar method was employed to convert the potentials measured using the Ag/AgCl electrode (saturated with KCl) at 70°C and 90°C to the SHE at 25°C. At these two temperatures, the EAg/AgCl (T) was obtained from the literature [128]. Since ΔEth values are highly related to temperature difference and relatively independent of different chloride-containing alkaline and neutral solutions with various concentrations, as reported by Bosch et al (2003) [125], ΔEth was determined by the data published in the literature for 0.1 mol/kg KCl solution, with the values of about 15 mV at 70°C and 20 mV at 90°C, respectively. This assumption is reasonable and it was verified by measuring the potential for an acid iron sulfate solution with the Cortest external Ag/AgCl RE filled with 0.1 mol/kg KCl. ΔESHE was also calculated, with a value of 26.7 mV at 70°C and 36.1 mV at 90°C. It should be noted that the thermodynamic data of H2 used to calculate the ΔESHE were obtained from the literature [129,130].   As an example of correction for the tests at 70°C and 90°C, when measuring the redox potential of the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with the nominal Fe3+/Fe2+ ratio of 100:1 at 70°C, the Eobs = 671.4 mV, EAg/AgCl (T) = 148.8 mV as published in Ref. [128] and ΔEth = 15 mV, and hence ESHE (T) = 805.2 mV at 70°C according to Eq. (4-1). Then, by using Eq. (4-2), with ΔESHE being 26.7 mV at 70°C, the ESHE (25°C) at 70°C is 831.9 mV with respect to a SHE at 25°C.   The diffusion potential between the test solution and the internal KCl solution in the reference electrode (also known as the isothermal liquid junction potential), can be evaluated by Henderson’s equation for dilute solutions [119] or Harper’s method for more concentrated systems [131]. However, insufficient data are available on the properties (transport number or  61  ionic mobility) of dissolved species included in the present model to accurately predict the liquid junction potentials. In addition, calculations for similar systems (KCl solution in contact with sulfate solution) indicate that the isothermal liquid junction potentials at room temperature are very small, typically no more than several mV [132, 133]. Therefore, it is believed that this potential probably plays a minor role and it was ignored in the calculations in the present work. This assumption is approximately correct, because the experimental results in this work were in good agreement with those calculated by the developed thermodynamic model. 4.2 Measurement of the Cathodic Potentiodynamic Polarization Curves Experimental work to study reduction kinetics of ferric on chalcopyrite in the quaternary acidic iron sulfate system was carried out at temperatures ranging from 25 to 150°C.       4.2.1 Electrode Preparation The chalcopyrite used in this investigation was obtained as massive mineral samples from the Creighton Mine (Sudbury, Ontario). The quantitative phase analysis of the chalcopyrite ore was determined using the Rietveld method and X-ray powder diffraction data, and the result is shown in Table 4-1. The material is of high quality, with a purity of 97.5% (mass percentage) and few impurities. To gather this data, the sample was reduced to fine powder to the optimum grain-size range for X-ray analysis (< 10µm) by grinding in ethanol in a vibratory McCrone Micronising Mill for 7 minutes. Step-scan X-ray powder-diffraction data were collected over a range 3-80°2 with CoKa radiation on a Bruker D8 Focus Bragg-Brentano diffractometer equipped with an Fe monochromator foil, 0.6 mm (0.3°) divergence slit, incident- and diffracted-beam Soller slits and a LynxEye detector. The long fine-focus Co X-ray tube was operated at 35 kV and 40 mA, using a take-off angle of 6°.  The X-ray diffractogram was analyzed using the  62  International Centre for Diffraction Database PDF-4 and Search-Match software by Siemens (Bruker). X-ray powder-diffraction data of the sample were refined with Rietveld program Topas 4.2 (Bruker AXS).  Further analysis results of the ore by multi-element ICP (4 acid digestion, 30 package) and Au analysis (fire assay) are shown in Table 4-2. Please note that the ICP analysis’s focus is on the Ag and Au contents, and that the Cu and Fe amount were above the detection limit and therefore unreliable. Massive electrodes were prepared by cutting the bulk chalcopyrite into approximately cubic shaped pieces with an area of 1 cm2 exposed to the solution. The electrical contact between a copper wire (enameled copper wire was used for the experiments in the autoclave) and the sample was made at the back of the sample with silver conductive epoxy (MG Chemicals) for the experiments at or below 90°C and Silvertech PT-1 Silver-filled Epoxy (Materion Corporation) for the experiments performed in the autoclave. The whole assembly was protected from the solution by mounting it in epoxy resins (Cold Cure for 25°C, 832HT-375ML from MG Chemicals for 70-110°C, Duralco 4460 from Cotronics for 150°C) along with an appropriate fitting, leaving only one face of the electrode exposed to the solution. Before each test, working electrodes were mechanically polished with no. 1200 SiC paper (LECO) so as to begin each experiment with a fresh surface. The surface was examined under an Optical Microscope (OM) before each experiment to verify that no inclusion/significant cracks or voids existed.      63    Table 4-1 Results of quantitative phase analysis of the chalcopyrite  used in this study (wt.%). Mineral Ideal Formula Sample “Chalcopyrite” Chalcopyrite CuFeS2 97.5 Pyrrhotite Fe1-xS 1.7 Mackinawite ? Fe9S8 0.8 Total  100.0            64   Table 4-2 Chemical analysis (ICP-OES, 4 Acid Digestion) and Au analysis (Fire Assay). Results for elements with concentrations lower than 10 ppm are not presented. Method  FA ICPM  ICPM  ICPM ICPM  ICPM  ICPM  ICPM ICPM  ICPM ICPM Element  Au  Ag  Cd Co  Cu Fe  Mn Ni  Pb Sb Zn Unit g/mt ppm ppm ppm  %  %  ppm  ppm ppm  ppm ppm Sample 0.88-2.49 77.3-78.3 100.5-106.5 14-40 28-29 22.6-23.36 65-193 16-535 396-442 10-16 2036-2223          65  4.2.2 Electrolyte Preparation The electrolyte used in this section is the same as that of Section 4.1.2. 4.2.3 Electrochemical Measurements at 25°C, 70°C and 90°C Electrochemical experiments were carried out using a standard three-electrode cell with a thermostated water jacket. The counter electrode (CE) was graphite and the prepared chalcopyrite electrode served as the working electrode (WE). A saturated mercury/mercury (I) sulfate electrode (MSE, saturated with potassium sulfate, London Scientifics) was used as a reference electrode (RE) for the tests at 25°C. At 70°C and 90°C, a saturated Ag/AgCl electrode (saturated with KCl, Accumet* Glass Body, Fisher Scientific) was employed as a RE. All potentials have been converted to the standard hydrogen electrode (SHE). All further potentials in this study are quoted with respect to the SHE at 25°C unless otherwise stated. Details of the corrections used for the measured potential have been discussed previously. The RE was connected to a Luggin capillary to minimize IR drop. The cell solution was slowly heated to the predetermined temperature by circulating water from a Cole-Parmer Polystat Heated Circulating Bath with analog control, and kept at the constant temperature with an accuracy ±1°C.  Prior to use, the WE and CE were immersed in ethanol for degreasing, rinsed with deionized water, and finally dried with cool air. The WE was immersed in the solution for around 30 minutes to stabilize the potential before starting the measurements in order to ensure reproducibility. The test solution was deaerated by sparging high-purity N2 prior to- and throughout the electrochemical experiments at a constant flow rate to eliminate the effect of dissolved oxygen. The cell off-gas, after passing through an Allihn condenser, was passed through deionized water and finally discharged to a fumehood. The open circuit potentials (OCP) of the samples were first recorded for 30 min to yield a steady-state potential, and then the  66  cathodic potentiodynamic polarization curves (CPC) were obtained by changing the electrode potential from OCP to -700 mV (versus OCP) at a scanning rate of 0.5 mV/s. The exchange current density, i0, was obtained from the curves using the intersection of the cathodic linear extrapolation and the reversible potential of the ferric/ferrous couple. 4.2.4 Electrochemical Measurements at 110°C and 150°C The experimental setup is similar to that used for the redox potential measurements, as shown in Section4.1.4. The difference is that the prepared chalcopyrite electrode was used as the WE in this section.  Prior to use, the WE and CE were immersed in ethanol for degreasing, rinsed with deionized water, and finally dried with cool air. The test solution was deaerated by sparging high-purity N2 prior to the electrochemical experiments at a constant flow rate for 40 min to eliminate the effect of dissolved oxygen. The autoclave was then heated to 110°C or 150°C. The OCP of the samples were recorded when a steady-state potential was achieved, and then CPC tests were performed in the same way as those at 25-90°C.  4.2.5 Correction of the Measured Potentials to SHE at 25°C The correction method used in this section is the same as that of Section 4.1.5. 4.3 Scanning Electron Microscope Study The surface morphology and elemental composition of the prepared chalcopyrite electrode was examined via a scanning electron microscope (SEM, Hitachi S-2300) coupled with EDX (Silicon Lithium Detector from Advanced Analysis Technologies). As clearly shown in Figure 4-3, the surface distribution of S, Fe and Cu elements are quite uniform for the chalcopyrite electrode prepared in the present study. In Figure 4-4, it is shown  67  that the electrode sample displays a strong peak for sulfur, and relatively weak peaks of iron and copper. Table 4-3 presents the elemental components of the electrode sample clearly (the raw data was from the EDX data as shown in Figure 4-4).  It should be noted that EDX only measures elemental concentrations near the surface of the electrode and therefore does not constitute a true chemical analysis of the mineral.            Figure 4-3 SEM-EDX analysis results of the prepared chalcopyrite electrode surface. The magnification is 300X. Cu-Fe-S  68   Figure 4-4 EDX spectra of the prepared chalcopyrite electrode.  Table 4-3 Components of the prepared chalcopyrite electrode in this study (wt.%). Element Concentration Theoretical Concentration of CuFeS2  Sulfur 28.88 wt% 34.92 wt%  Iron 32.53 wt% 30.52 wt%  Copper 38.59 wt% 34.56 wt%  Totals 100.00% 100.00%     69  4.4 Optical Microscope Study In order to characterize the surface morphology variation of the chalcopyrite electrode before and after electrochemical experiments, a Nikon MA200 microscope coupled with NIS Elements F3.0 Software was used.                70  5 Development of a Thermodynamic Model to Simulate the Speciation of the Quaternary Sulfuric Acid-Ferric Sulfate-Ferrous Sulfate-Water System  5.1 Introduction As discussed in the Introduction, most of the previous speciation studies on the acidic iron sulfate system are limited to lower temperatures and/or dilute solutions. Hence, the work in the present Chapter was initiated to explore the possibility of establishing aqueous speciation diagrams for the quaternary acidic iron sulfate system at higher temperatures and solute concentrations, thereby obtaining more detailed information about the acidic iron sulfate electrolytes involved and further providing the data that can enable one to predict the redox potential of the Fe3+/Fe2+ couple and study the kinetics of the cathodic reduction reactions on chalcopyrite in industrially relevant leaching systems, at different temperatures from 25°C to 150°C. Herein the main species involved (including H+, Fe2+, Fe3+, SO42-, HSO4-, FeHSO4+, FeSO4°, FeHSO42+, Fe(SO4)2-, FeSO4+, Fe2O3 and H2O) were first investigated, and their thermodynamic data are collected and critically reviewed for the calculation of activity coefficients and equilibrium constants involved in the model. The speciation for the quaternary acidic iron sulfate system is investigated as a function of the initial amounts of iron, acidity, nominal Fe3+/Fe2+ ratio and temperature. The model results are finally validated, by comparing with experimental data by the present author and results published by other authors. An analysis of the calculated pH and ionic strength provide additional justification for the model. This information will be used in further investigations of the electrochemical reduction kinetics of the  71  Fe3+/Fe2+ couple on chalcopyrite as well as to shed light on the mechanism of chalcopyrite leaching, as shown in the following Chapters. 5.2 Model Development When iron sulfates are present in sulfuric acid solution they are distributed as soluble species such as simple cations, neutral or charged complexes, as well as precipitates such as Fe2O3, which forms at high temperatures. Because of the lack of thermodynamic data and analytical techniques for in-situ measurement of ions and ionic complexes at high temperature, chemical modeling is a very useful tool to predict and understand the behavior of complex aqueous processing systems, provided that reliable models exist with acceptable predictive power based on the limited available experimental data [134].  However, modeling the speciation in the H2SO4-Fe2(SO4)3-FeSO4-H2O system at the temperature and concentration of interest requires reliable values of the thermodynamic properties for all species existing in the system. These properties include the standard Gibbs free energy of species to calculate the equilibrium constants, and the activity coefficients of species as a function of solution composition and temperature, to describe the non-ideal thermodynamic behavior. 5.2.1 Activity Coefficient Model-B-dot Equation The activity coefficients for ions can be estimated by using different models such as the Debye-Hückel equation and its extensions, the B-dot, Pitzer, electrolyte NRTL, Bromley-Zaemaitis and the mixed solvent electrolyte (MSE) models. These models have been employed in hydrometallurgical applications, and reviewed by several authors [134-136].  In the present work, the B-dot activity coefficient model was applied. This model has been used to evaluate the activity coefficients of dissolved species in similar aqueous sulfuric  72  acid/metal sulfate systems and has given reasonable predictions through a limited range of temperature and solution composition [35, 134]. It was proposed by Helgeson [137, 138], and is valid for aqueous electrolyte solutions with moderate ionic strengths up to I = 1 molal in a range of 0-300°C [139]: 2log1iiiA z I BIB Iå                                                     (5-1) where åi (Å) is the hard-core diameter of species i, zi is the ionic charge of species i, Aγ (kg0.5 mol-0.5) and Bγ (kg0.5 mol-0.5 cm-1) are Debye-Hückel parameters depending only on the dielectric constant, density and temperature, I (mol kg-1) is the effective (or real/true) ionic strength of the solution, and Ḃ (kg mol-1) is the characteristic B-dot parameter whose value depends only on the temperature. Aγ, Bγ, and Ḃ values were selected from the above literature [137, 138].  This equation is a modification of the classic Debye-Hückel model which is valid for electrostatic (long-range) binary interactions between cations and anions. The term “ḂI” represents a correction for short-range interactions between dissolved species-other than electrostatic ones.  The only two species-specific parameters are the zi and hard-core parameter åi. The å values for H+ (9Å), Fe2+ (6Å), Fe3+ (9Å), HSO4- (4.5Å) and SO42- (4Å) were taken from literature [140,141]. For other species that were not included in the literature, estimates were assigned according to a method published in the literature. For example, å was given a value of 4.0 Å for monovalent ions like FeSO4+, Fe(SO4)2- and FeHSO4+, and 4.5 Å for divalent ions like FeHSO42+ [134]. In the case of polar neutral species, the activity coefficients were assigned a value of unity according to the literature [139, 142]. Actually, given that the zi is zero for neutral species, even  73  when calculating the activity coefficients for the neutral species by the B-dot equation (using the corresponding Ḃ and I values in the present studied solutions), the values are almost always unity. In the systems considered in the present work, only concentrations that are similar to those found in hydrometallurgical processing of chalcopyrite were used, and the real ionic strength of the solution was generally lower than 0.85 molal (see the results in Figure 5-9). These considerations justify the use of the B-dot model. The use of the above-mentioned alternative models may have better described the non-ideal behavior of the ionic solutions examined herein, however, these models usually require a large amount of theoretical or experimental data (such as mean activity coefficient, osmotic coefficient and solubility) in order to obtain numerous interaction parameters by regression, which can be further used to calculate the activity coefficients. Such data are usually unavailable, especially at elevated concentrations and temperatures. 5.2.2 Collection and Calculation of Thermodynamic Data and Equilibrium Constants Standard molar Gibbs free energy of the reaction products and reactants are required to obtain the equilibrium constant of a reaction. Thermodynamic data for all of the species that may exist in the specific system were collected and critically assessed to calculate the equilibrium constants at different temperatures.  Table 5-1 and Table 5-2 present the main species and their corresponding thermodynamic data, formation reactions and thermodynamic equilibrium constants at various temperatures. The equilibrium constants for the main species in the range of 25-35°C were taken from the literature [34, 36], while equilibrium constants at 70-150°C were calculated by the Criss-Cobble method. This set of species and data was found to be the best to accurately predict the experimental results. Detailed information will be given in the following discussion.  74  Table 5-1 Thermodynamic data at 25°C and equilibrium (standard formation) constants for the main species in aqueous Fe(II)-Fe(III)-H2SO4 solutions in the range of 25-35°C. The reference state for aqueous species is infinite dilution (Data given are for 25°C, 1 atm and standard state).   Species ΔG° (kJ/mol) S°            (J/mol K) Species and Formation Reactions Log Kf° Log Kf° 25°C 35°C H+ 0.00 0.00    SO42- -744.63 20.10    HSO4- -756.01 131.80 H+ + SO42- ↔ HSO4- 1.98 2.12 Fe2+ -91.20 -107.10    FeHSO4+ -841.99 134.19 Fe2+ + H+ + SO42- ↔ FeHSO4+ 1.08 1.42 FeSO4° -848.67 3.26 Fe2+ + SO42- ↔ FeSO4° 2.25 2.33 Fe3+ -16.70 -280.30    FeHSO42+ -775.48 34.97 Fe3+ + H+ + SO42- ↔ FeHSO42+ 2.48 2.90 FeSO4+ -784.38 -5.93 Fe3+ + SO42- ↔ FeSO4+ 4.04 4.34 Fe(SO4)2- -1524.60 423.16 Fe3+ + 2SO42- ↔ Fe(SO4)2- 5.38 6.33 Fe2O3 -742.20 87.40 2Fe3+ + 3H2O ↔ Fe2O3 + 6H+   H2O -237.178 69.91       a. The thermodynamic data (ΔG° and S°) for H+, Fe2+, Fe3+, SO42-, HSO4-, Fe2O3 and H2O, and the equilibrium constants for HSO4- and the five iron complexes at 25°C and 35°C were taken from the literature [34, 36, 129].  75     b. The ΔG° and S° of the iron complexes were estimated by the present work. See text for details.    c. The heat capacity parameters (Kelley equation coefficients) of Fe2O3 and H2O used to calculate the equilibrium constants of Fe2O3 were taken from HSC 7.1 [143].         Kelley equation: Cp(T) = A + B*10-3*T + C*105*T-2 + D*10-6*T2 (J/mol*K).         For Fe2O3: A=143.566, B=-36.323, C=-31.433, D=71.792.          For H2O: A=186.884, B=-464.247, C=-19.565, D=548.631.  5.2.2.1 Species Involved in This System   It is well-known that iron forms complexes in H2SO4 solutions [33-38]. The important equilibrium reactions in such a system could include: the association of SO42- and H+ to give rise to HSO4-; formation of complexes between iron ions and SO42- or HSO4-; reaction of iron ions with water to form hydroxyl complexes and protons. Here the most important iron species published in previous studies are taken into account to study the speciation and distribution of ferrous and ferric species involved in H2SO4 solutions as a function of temperature, iron and acid concentration, and the nominal Fe3+/Fe2+ ratio.  The pH value of the acidic iron sulfate solution used in chalcopyrite leaching is usually below 2, because higher pH will lead to the formation of iron hydroxyl complexes and even iron precipitates. Speciation calculations indicate that iron hydroxide complexes always play a minor role in these solutions where pH is below 2. As a result, at the high acidities of interest (pH generally less than 2.0), hydroxide (OH-) ions have not been taken into account herein under equilibrium conditions. Consequently, iron hydroxyl complexes were excluded in the present study.  The changes in the activity of water participating in the chemical reactions are negligible compared to its concentration, and were thus also ignored.  76  It has been reported that at low pH the concentration of Fe(SO4)2- was consistently found to be negligible [33, 37]. In addition, a declining trend was found regarding the temperature dependence of Fe(SO4)2- concentration from about 50°C. At around 70°C it is almost non-existent [36]. Furthermore, Dry and Bryson (1988) also reported that the inclusion of Fe(SO4)2- resulted in poor predictions of redox potential [33]. It was also found in this work that poor solution potential prediction resulted from the inclusion of Fe(SO4)2-, especially at temperatures above 70°C. Particularly, from 90°C to 150°C, at lower nominal Fe3+/Fe2+ ratios such as 1:1 and 10:1, the potential difference between the model result with the inclusion of Fe(SO4)2- and that by experiments ranges from 20 mV to even 100 mV. Thus in the present study, Fe(SO4)2- was considered only at 25°C and 70°C, and was not considered at higher temperatures. FeH(SO4)2° was also not considered because the inclusion of this species always gave a poor fit to the measured experimental data. This complex was reported by Casas et al [35] and no other authors have reported evidence of the existence of this species. Hence, it is possible that FeH(SO4)2° is not a stable species under the conditions of temperature and acidity studied in the present acid iron sulfate solutions.  Fe2O3 was included in the model at 150°C according to reports from the literature, which will be discussed in detail in the following sections. From 25°C to 110°C, as discussed later, there were almost no precipitates formed during the experiments under the conditions in the present work, and consequently they were excluded in the model through this temperature range. It should be emphasized that many discrepancies have been reported in the literature among authors regarding which complexes should be included in the speciation model for the H2SO4-FeSO4-Fe2(SO4)3-H2O system to provide the best results, especially at higher temperature and/or concentration. The criterion for selecting or rejecting different species in this model was  77  based on whether the model calculated redox potentials agreed with those measured by experiments (typically the difference between the calculated potentials from the model and measured potentials at lower temperatures was lower than 5-10 mV and at higher temperatures it was lower than about 20 mV). The most important species reported in previous studies for the thermodynamics of this system were considered. 5.2.2.2 Thermodynamic Data and Equilibrium Constants at High Temperature   After the selection of the possible species, the next step was to collect their thermodynamic data and calculate the equilibrium constants at different temperatures. For many aqueous reactions, there is a lack of equilibrium constants for high temperatures. In most cases, even if available, a big variation often exists among different reports. The Criss-Cobble method [144, 145] and the Helgeson-Kirkham-Flowers (HKF) model [146, 147] are two methods commonly used to calculate the standard Gibbs free energies for a single ionic species at elevated temperature based on thermodynamic data available at room temperature. The Criss-Cobble method has been extensively used in calculating temperature-dependent thermodynamic properties for aqueous ions below 200°C since Criss and Cobble proposed an ion entropy correspondence principle in 1964. This method was selected in the present calculation. For solid and liquid species, this can be achieved with knowledge of the standard Gibbs free energy of formation at 298.15 K and the heat capacity. The heat capacity parameters (Kelley equation coefficients) of Fe2O3 and H2O were taken from HSC 7.1 [143], and ΔG° and S° data for Fe2O3 and H2O at higher temperature were calculated by the Kelley equation. The thermodynamic data at 298.15 K (ΔG° and S°) for H+, Fe2+, Fe3+, SO42-, HSO4-, Fe2O3 and H2O, and the equilibrium constants for HSO4- and the five iron complexes at 25°C and 35°C were taken from the literature [34, 36, 129].   78  Thermodynamic data for the five iron complexes have been reported, and were reviewed and summarized by several reports [33, 38, 129, 135] based on the previous studies and thermodynamic databases. There are differences among these studies with respect to the reported values for the thermodynamic properties. In addition, although there are some reported ways to calculate the ΔS° of some species of interest, such as Fe(SO4)2- [148], no reliable reports of the ΔG° and S° of FeHSO42+ and FeHSO4+, as well as S° of Fe(SO4)2- at 298.15 K could be found in the literature. For the sake of maintaining internal consistency, the thermodynamic data of all the species partaking in these ferrous and ferric equilibria are based on the values reported by Stipp (1990) [34] who studied and examined these data. The ΔG° of the five iron complexes were calculated from the equilibrium constants at 25°C: first, the ΔG° of the formation reaction was calculated using the equation ΔG° = -2.303RTLog Kf°; then, the ΔG° of the single iron complex was estimated based on the calculated ΔG° of the formation reaction and the known available ΔG° for the remaining individual species. As to S° for the five iron complexes, first by using the equilibrium constants at 25°C and 35°C [34, 36], the enthalpy change ΔH° of the formation reactions were calculated based on the van’t Hoff equation. Then, the entropy change ΔS° of the formation reactions were calculated according to the equation ΔG° = ΔH° -T ΔS°. Finally, the S° for the single iron complex was estimated based on the calculated entropy change ΔS° of the formation reaction and the known S° for the remaining single species in the formation reaction. It should be noted that the calculated ΔG° and S° values of the iron complexes in the present work are a little different from those published in the above noted sources, however, they are generally in reasonable agreement with each other.   79  Prior to calculating the speciation, to obtain the equilibrium constants for HSO4- and the five iron complexes at 70°C-150°C, models based on the Lewis formulation of the Criss-Cobble correspondence principle [149] were used to predict ΔG° of the main species in the solution at the temperatures of interest. In addition, because there is a lack of thermodynamic data at high temperatures in the literature for neutral species FeSO4°, the average molal ionic heat capacity at high temperatures was estimated by using the average heat capacity constants of simple cations and simple anions. It was found that this method gave very reasonable equilibrium constant estimations (The model-predicted redox potentials agree very well with those measured by experiments). The calculated equilibrium constants at 70°C–150°C are listed in Table 5-2.  Table 5-2 Calculated equilibrium (standard formation) constants for the main species in aqueous Fe(II)-Fe(III)-H2SO4 solutions in the range of 70-150°C. Species and Formation Reactions Log Kf° Log Kf° Log Kf° Log Kf° 70°C 90°C 110°C 150°C H+ + SO42- ↔ HSO4- 2.64 2.96 3.31 4.05 Fe2+ + H+ + SO42- ↔ FeHSO4+ 2.52 3.09 3.62 4.61 Fe2+ + SO42- ↔ FeSO4° 2.63 2.80 2.98 3.35 Fe3+ + 2SO42- ↔ Fe(SO4)2- 7.48 9.07 10.54 13.16 Fe3+ + H+ + SO42- ↔ FeHSO42+ 4.22 4.89 5.50 6.61 Fe3+ + SO42- ↔ FeSO4+ 5.37 5.92 6.46 7.52 2Fe3+ + 3H2O ↔ Fe2O3 + 6H+ 2.54 3.63 4.59 6.21   80  It is clearly seen in Figure 5-1 that the equilibrium constants for HSO4- and the five iron complexes increase with increasing temperature. That is, these complexes become more stable as temperature is increased.  30 50 70 90 110 130 15002468101214  Equilibrium Constant for Main Species in SolutionTemperature (°C) Fe2+/HSO4- FeHSO4+ FeSO4 FeHSO42+ Fe(SO4)2- FeSO4+ (HSO4- ■; FeHSO4+ ○; FeSO4° ★; FeHSO42+ ◆; Fe(SO4)2- ▽; FeSO4+ ◇) Figure 5-1 Equilibrium (standard formation) constants used in the present study for the main species in aqueous Fe(II)-Fe(III)-H2SO4 solutions in the temperature range of 25-150°C.    81   5.2.3 Calculation of Models in the Solution Chemical equilibrium equations (7 in total shown in the Table 5-2) based on the above formation reactions (including the equations of activity coefficient and ionic strength), and additional component mass balance equations in terms of Fe2+, Fe3+ and SO42-, as well as the electroneutrality equation (the solution must remain electrically neutral and a charge balance equation must be able to be written), were obtained and these non-linear equations were solved in a Fortran code employing Brent’s method [150]. Molal concentrations were used in order to exclude the density changes with temperature, thus allowing a comparison of solute concentrations at different temperatures. Each set of the equations (with a specific solution composition at any temperature) was solved with high accuracy and excellent convergence was obtained. Basically, the convergence criteria used in the present work is that the error for each of the equations (please note that each equation was transferred in the form of f(x)=0 when solving each set of equations; the error here thus means the difference between the left hand side and the right hand side of each equation) is smaller than 10-8. Using this method, high accuracy and excellent convergence was obtained. The actual error was typically smaller than 10-15 for each equation. A Fortran code sample for the calculation at 150°C, together with the calculated concentrations of all species in aqueous Fe(II)-Fe(III)-H2SO4 solutions in the range of 25-150°C according to the developed speciation model with nominal Fe3+/Fe2+ ratio of 10:1, are shown in Appendix B. Commercial chemical modeling software were not used in this study (such as OLI, EQ3NR, EQ3/6, and WATEQ), as their internal databases are not currently adequate to model this quaternary system (a modification of the species involved under different temperatures is  82  required in order to fit the experimental data). Hence, it was more convenient to do the calculation of the thermodynamic model by the proposed Fortran code. 5.3 Results and Discussion 5.3.1 Speciation Results Calculated at 25°C and 70°C The results of the aqueous speciation calculation (expressed as a percentage of the total ferric or ferrous) for Fe(II)-Fe(III)-H2SO4 solutions with different nominal Fe3+/Fe2+ ratios at 25°C and 70°C are presented in Figure 5-2 and Figure 5-3. Please note that throughout this thesis, nominal Fe3+/Fe2+ ratio means the ratio of total Fe(III) to total Fe(II) added to the electrochemical cell or autoclave. FeSO4+ is the predominant species for Fe(III) (71.9%-76.2% at 25°C and 61.1%-71.5% at 70°C), followed by the Fe(SO4)2- species (22.9%-16.9% at 25°C and 35.8%-23.7% at 70°C). The remaining Fe(III) is distributed as free ferric and FeHSO42+. The percentage of the free ferric is ~3.8%-5.2% at 25°C, and 0.5%-1.0% at 70°C.     83  1 10 100 100001020304050607080Fe2+  Percentage of Fe3+ and Fe2+ Species[Fe3+]/[Fe2+] Ratio (Nominal)FeSO4+ (Fe2+ ▽; FeHSO4+ ○; FeSO4° ◇; Fe3+ ▼; FeHSO42+ ◆; Fe(SO4)2- ■; FeSO4+ ★) Figure 5-2 Calculated aqueous speciation diagram of the main ferric and ferrous species in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios at 25°C. Please note that the sum of the percentage values of Fe(II) species (unfilled symbols) is 100%, which is also the case for the Fe(III) species (filled symbols).                84  1 10 100 100001020304050607080Fe2+ Fe2+ FeHSO4+ FeSO40 Fe3+ FeHSO42+ Fe(SO4)2- FeSO4+  Percentage of Fe3+ and Fe2+ Species[Fe3+]/[Fe2+] Ratio (Nominal)FeSO4+          (Fe2+ ▽; FeHSO4+ ○; FeSO4° ◇; Fe3+ ▼; FeHSO42+ ◆; Fe(SO4)2- ■; FeSO4+ ★) Figure 5-3 Calculated aqueous speciation diagram of the main ferric and ferrous species in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios at 70°C. Please note that the sum of the percentage values of Fe(II) species (unfilled symbols) is 100%, which is also the case for the Fe(III) species (filled symbols).           Free ferrous ions account for the largest percentage of the total ferrous (61.5%-67.0% at 25°C and 66.1%-73.8% at 70°C), followed by FeSO4° (37.7%-32.2% at 25°C and 29.0%-21.1% at 70°C), and FeHSO4+. The speciation results regarding iron (II) in the present work agree very well with those published by Sahoo et al in 2012 [151]. In addition, the fact that free ferrous ions  85  are the most abundant iron (II) species is in agreement with the previously published results at low temperatures from 25°C to 55°C [35, 36], although the solution conditions and species used in these models are a little different. With the exception of FeSO4° and Fe(SO4)2-, the percentages of all other Fe-sulfate complexes increase with an increase in the nominal Fe3+/Fe2+ ratio from 1:1 to 1000:1 at both 25°C and 70°C. At the same time, it was found that the concentration of free ferric (on the order of 10-3 mol kg-1) slightly increases with increasing nominal Fe3+/Fe2+ ratios, whereas the concentration of free ferrous decreases significantly from the order of 10-1 mol kg-1 to the order of 10-4 mol kg-1 (Please note that the concentration of each species can be calculated by using the total amount of Fe(II) or Fe(III) multiplied by the corresponding percentage, and the total amount of Fe(II) decreases when increasing the nominal Fe3+/Fe2+ ratio).  Under the same nominal Fe3+/Fe2+ ratios, increasing the temperature from 25°C to 70°C results in an increase of the amount of FeHSO42+, Fe(SO4)2-, free ferrous and FeHSO4+, but a decrease in the percentage of free ferric, FeSO4+, and FeSO4°. 5.3.2 Speciation Results Calculated at 90°C and 110°C  Figure 5-4 and Figure 5-5 show the calculated results of the aqueous speciation of the ferric and ferrous species for Fe(II)-Fe(III)-H2SO4 solutions with different nominal Fe3+/Fe2+ ratios at 90°C and 110°C, respectively. It is found that FeSO4+ remains the predominant species of Fe(III), with a proportion larger than 90% under all of the conditions (ranging from about 93.0% to 96.2%). Free ferric ion and FeHSO42+ only account for a minor percentage. In fact, free ferric is the least abundant species with values of 0.3%-0.6% at 90°C, and 0.2%-0.4% at 110°C, respectively.    86   1 10 100 10000102030405060708090100Fe2+ Fe2+ FeHSO4+ FeSO40 Fe3+ FeHSO42+ FeSO4+  Percentage of Fe3+ and Fe2+ Species[Fe3+]/[Fe2+] Ratio (Nominal)FeSO4+ (Fe2+ ▽; FeHSO4+ ○; FeSO4° ◇; Fe3+ ▼; FeHSO42+ ◆; FeSO4+ ★) Figure 5-4 Calculated aqueous speciation diagram of the main ferric and ferrous species in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios at 90°C. Please note that the sum of the percentage values of Fe(II) species (unfilled symbols) is 100%, which is also the case for the Fe(III) species (filled symbols).      87  1 10 100 10000102030405060708090100Fe2+ Fe2+ FeHSO4+ FeSO40 Fe3+ FeHSO42+ FeSO4+  Percentage of Fe3+ and Fe2+ Species[Fe3+]/[Fe2+] Ratio (Nominal)FeSO4+ (Fe2+ ▽; FeHSO4+ ○; FeSO4° ◇; Fe3+ ▼; FeHSO42+ ◆; FeSO4+ ★) Figure 5-5 Calculated aqueous speciation diagram of the main ferric and ferrous species in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios at 110°C. Please note that the sum of the percentage values of Fe(II) species (unfilled symbols) is 100%, which is also the case for the Fe(III) species (filled symbols).       88  On the other hand, a considerable proportion of Fe(II) exists as free ferrous in the range of 60.1-73.0%. This trend was similar to that at 25°C and 70°C. Furthermore, at 90°C, the second most abundant Fe(II) species is FeSO4°, ranging from 31.3% to 19.1% with the nominal Fe3+/Fe2+ ratios of 1:1 to 1000:1, respectively. However, at 110°C, FeSO4° accounts for the second largest percentage of Fe(II) (about 25.5%) only when the nominal Fe3+/Fe2+ ratio was 1:1. Under the other three nominal Fe3+/Fe2+ ratios, the percentage of FeHSO4+ is almost equal to that of FeSO4° (actually a little bit larger), with values in the range of 12.9%-14.1%. Moreover, at both 90°C and 110°C, apart from the FeSO4° and FeSO4+, the relative percentages of all other ferric and ferrous species increases with increasing nominal Fe3+/Fe2+ ratios. Meanwhile, it can be determined that the concentration of free ferric (on the order of 10-4 mol kg-1) slightly increases with increasing nominal Fe3+/Fe2+  ratios, while the concentration of free ferrous decreases significantly from the order of 10-1 mol kg-1 to the order of 10-4 mol kg-1. This trend was the same as that observed at 25°C and 70°C. Furthermore, under the same nominal Fe3+/Fe2+ ratios, a temperature increase from 90°C to 110°C leads to an increase of the relative amounts of FeHSO42+, free ferrous and FeHSO4+, and a decrease in the amounts of free ferric, FeSO4+ and FeSO4°. 5.3.3 Speciation Results Calculated at 150°C As reported in the literature [39-45], precipitates will be formed at 150°C in acid iron sulfate solutions due to the hydrolysis of ferric depending on the acidity and the amount of metal sulfate in the system. The formation of hematite (Fe2O3) is favored by lower solution acidity and a relatively large amount of added divalent metal sulfate, which consequently leads to a small amount of dissolved Fe(III). The effect of the metal sulfates on the hydrolysis has been attributed to the formation of bisulfate ions through combination of the sulfate ion with hydrogen ions in  89  solution which will further facilitate the formation of Fe2O3, according to the following two reactions [42-44]:   SO42- + H+ ↔ HSO4-                                                  (5-2) 2Fe3+ + 3H2O ↔ Fe2O3 + 6H+                                          (5-3) A drop in free hydrogen ion concentration in the system studied could reduce the amount of soluble ferric and based on several published results hematite is a likely precipitate in this system. Thus hematite was included in the speciation calculations at 150°C. Figure 5-6 presents the calculated results of the aqueous speciation of the main ferric and ferrous species for the Fe(II)-Fe(III)-H2SO4 solutions with different nominal Fe3+/Fe2+ ratios at 150°C. FeSO4+ remains the predominant species for Fe(III) in the aqueous solution, with its proportion ranging from about 33.7% to 49.2% at different levels of ferrous sulfate addition. As expected, a large amount of Fe(III) precipitated as Fe2O3, with the largest value of 61.7% obtained when the nominal Fe3+/Fe2+ ratio was 1:1. The percentage of formed Fe2O3 is relatively stable under the other three nominal Fe3+/Fe2+ ratios in the range of 44.4%-42.7%. This variation in the amount of hematite as a function of FeSO4 concentrations is similar to that published in the literature with an addition of divalent metal sulfates like ZnSO4 or MgSO4 for a relatively low free sulfuric acid concentration [42, 43]. Free ferric and FeHSO42+ still account for a minor percentage of the total Fe(III), with the free ferric representing the lowest proportion at 0.1%-0.2%.     90  1 10 100 100001020304050607080Fe2+Fe2O3 Fe2+ FeHSO4+ FeSO40 Fe3+ FeHSO42+ Fe2O3 FeSO4+  Percentage of Fe3+ and Fe2+ Species[Fe3+]/[Fe2+] Ratio (Nominal)FeSO4+ (Fe2+ ▽; FeHSO4+ ○; FeSO4° ◇; Fe3+ ▼; FeHSO42+ ◆; Fe2O3 ■; FeSO4+ ★) Figure 5-6 Calculated aqueous speciation diagram of the main ferric and ferrous species in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios at 150°C. Please note that the sum of the percentage values of Fe(II) species (unfilled symbols) is 100%, which is also the case for the Fe(III) species (filled symbols).  A similar trend to that observed from 25°C to 110°C was found at 150°C in that a large amount of Fe(II) existed in the form of free ferrous ion, in the range of 69.3-72.8%. At 150°C the second most common Fe(II) species was FeHSO4+, ranging from 26.4% to 24.2% with the nominal Fe3+/Fe2+ ratios changing from 1:1 to 1000:1. FeSO4° accounted for the smallest  91  percentage of the total Fe(II). This is in contrast to the 25-90°C range where FeSO4° represented the second most abundant Fe(II) species. From 110-150°C the relative amount of FeHSO4+ increased (except for the point with the nominal Fe3+/Fe2+ ratio of 1:1). At 150°C, besides FeSO4°, FeHSO4+ and Fe2O3, the relative percentages of all other ferric and ferrous species increase with an increase of the nominal Fe3+/Fe2+ ratio from 1:1 to 1000:1. It is interesting to note that for the same nominal Fe3+/Fe2+ ratio, with the temperature increasing from 25°C to 150°C, the free ferric concentration declines from the order of 10-3 mol kg-1 to the order of 10-4 mol kg-1, whereas the free ferrous concentration is relatively stable with similar values of the same order of magnitude. Meanwhile, at lower pH (see results in Figure 5-8), free ferric and ferrous ions are more abundant. 5.3.4 Model Validity-Comparison with Experimental Results and Previous Work The model can only be validated in a restricted range of conditions (as shown in Chapter 4) due to the limited availability of experimental data for this system. Nevertheless, experimental results for redox potential and ferric solubility, together with the calculated pH and ionic strength, were used to validate the model predictions presented previously. 5.3.4.1 Comparison of Redox Potential between Speciation Results and Experimental Measurements from 25°C to 150°C   A comparison of the reversible potentials between experimental measurements performed for this work and model prediction was used to validate the thermodynamic speciation model. Please note that a detailed discussion on how to calculate the redox potential via those speciation results will be presented in Chapter 6. Figure 5-7 shows that the reversible potentials measured by experiment and predicted by the model under different nominal Fe3+/Fe2+ ratios are in excellent agreement from 25°C to 150°C. The difference between experimental and calculated  92  values was typically about ±20 mV depending on the solution composition and temperature. The comparison of experimental and calculated results suggested that the model is qualitatively and quantitatively validated. Therefore, a conclusion can be drawn that the predicted species distribution and solution concentrations are accurate for the Fe(II)-Fe(III)-H2SO4 solutions in the temperature and composition ranges studied here.  30 50 70 90 110 130 15060065070075080085090095010001050   Potentials by Model and Experiments vs SHE at 25°C (mV)Temperature (°C) 1:1 Model 1:1 Exp 10:1 Model 10:1 Exp 100:1 Model 100:1 Exp 1000:1 Model 1000:1 Exp Figure 5-7 Comparison of the potentials predicted by model and measured by experiments in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios in the temperature range of 25°C-150°C.   93  Single ion activity coefficients are also part of the speciation model parameters. The ability of the model to predict the experimental data also indicates that the method for estimating activity coefficients of simple ions and complexes is valid in the present study. The B-dot model was found to be surprisingly applicable for accurate prediction of redox potential at temperatures up to 150°C in the quaternary system studied here. As reported by Truesdell and Jones (1974) [140], the use of any model of single-ion activity coefficients based on experimental measurements made on single salt solutions requires the assumption that, at a given temperature, activity coefficients in simple solutions are equal to those in complex solutions of the same ionic strength. This assumption was fully justified by the reasonable prediction of solution redox potential over a wide range of different nominal Fe3+/Fe2+ ratios and temperatures in this work, owing to the fact that relatively lower real ionic strengths were obtained compared to the higher nominal ionic strength (see the following discussion). The following analysis (three parts) also serves as a justification for the developed model in the present work. 5.3.4.2 Comparison of Ferric Solubility between Speciation Results and Previous Work at 150°C   As mentioned previously, in the present acid iron sulfate solutions, the formation of hematite may occur at 150°C. This results in a significant decrease in the initial amount Fe(III). The model developed in this study can predict the amount of Fe2O3 precipitate as well as the amount of Fe(III) species present in the liquid phase (as solubility of Fe(III)). For example, for the nominal Fe3+/Fe2+ ratio of 1000:1, from Figure 5-6, we can predict that the total dissolved amount of Fe(III) is about 0.103 mol/kg (ignoring the changes in water). The concentration of free sulfuric acid (effective/true acidity of the system) under the same conditions is  94  approximately 0.42 mol/kg, which is larger than the nominal amount of sulfuric acid due to the hydrolysis of free ferric. At present, no experimental data are available for ferric solubility (introduced in the form of Fe2(SO4)3 with equilibrium obtained by hydrolysis) in the pure quaternary H2SO4-Fe2(SO4)3-FeSO4-H2O system under the highly acidic conditions employed in chalcopyrite leaching (pH typically lower than 2). Furthermore, most of the published solubility data has focused on the ternary H2SO4-Fe2(SO4)3-H2O system [39-45]. These reports have found that the extent of Fe2O3 precipitation is highly dependent on temperature, as well as the added divalent metal sulfates and their concentrations. For a relatively low free sulfuric acid concentration, with an increasing concentration of divalent metal sulfates (such as ZnSO4, MgSO4), the solubility of Fe(III) decreases and as a result a relatively large amount of hematite will form, due to the decrease in the true acidity [42, 43]. Therefore, in order to compare the model results with published experimental data, it is reasonable to assume that the behavior of the ternary H2SO4-Fe2(SO4)3-H2O system is similar to that of the quaternary H2SO4-Fe2(SO4)3-FeSO4-H2O system when the concentration of ferrous sulfate is low. In the present study, with the nominal Fe3+/Fe2+ ratio of 1000:1, the concentration of FeSO4 was only about 0.18x10-3 mol/kg. As a result, such a solution could be considered to emulate a ternary H2SO4-Fe2(SO4)3-H2O system. According to the results published by Sasaki et al in 1993 [40], who studied the hydrolysis of acidic ferric sulfate solutions of various concentrations in an autoclave at 150°C, the solubility of ferric is 0.113 mol/kg with the concentration of free sulfuric acid of 0.42 mol/kg. Thus it is demonstrated that there is very little difference between the Fe(III) solubility obtained herein at the 1000:1 Fe3+/Fe2+ ratio and the results of Sasaki et al. The small error between the results is likely caused by the addition of a small amount of FeSO4 in the present case.   95  Actually, the empirical equation regressed by Reid and Papangelakis in 2006 [44] (who studied Fe2O3 solubility in sulfuric acid at 150°C) generates the solubility of ferric as being 0.065 mol/kg with the free sulfuric acid concentration of 0.42 mol/kg. It seems that the ferric solubility data by the current work was also on the same order of magnitude as that obtained by measurement of solubility via the Fe2O3 dissolution method. However, it should be noted that Umetsu et al found a solubility of 0.022 mol/kg for the same free acid concentration [41]. 5.3.4.3  Analysis of Calculated pH     The calculated pH for various solution compositions are shown in Figure 5-8. In Figure 5-8, it can be observed that in general the pH of the solutions are lower than 1.1. For any given temperature, the pH first decreases as the nominal Fe3+/Fe2+ ratio increases from 1:1 to 10:1, and it then levels off between 10:1 and 1000:1.   96   Figure 5-8 Calculated pH of the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios in the temperature range of 25°C-150°C.  Under the same nominal Fe3+/Fe2+ ratio the pH increases gradually with temperature up to 110°C and, as expected, a sharp drop occurs at 150°C, with a terminal pH value even lower than that at 25°C. This phenomenon can be explained by the above-mentioned Eq. (5-3):                                    2Fe3+ + 3H2O ↔ Fe2O3 + 6H+ At 150°C, the hydrolysis of ferric sulfate and precipitation of ferric oxide will take place and this can cause an increase in the free H+ concentration in the solution which governs the solubility of Fe(III). 30 50 70 90 110 130 1500.50.60.70.80.91.01.11.2  pH of Solution (Calculated by Model)Temperature (°C) Fe3+/Fe2+ (Nominal) 1:1 Fe3+/Fe2+ (Nominal) 10:1 Fe3+/Fe2+ (Nominal) 100:1 Fe3+/Fe2+ (Nominal) 1000:1 97  The above results justify the exclusion of hydroxide (OH-) ions in the speciation model since their concentration is negligible in these very acidic solutions. Similarly, iron hydroxyl complexes would play a minor role in these solutions. 5.3.4.4 Analysis of Real Ionic Strength   Figure 5-9 shows the calculated real ionic strength in Fe(II)-Fe(III)-H2SO4 solutions, which are lower than 0.85 throughout the studied temperature range. Similar to the pH variation at a given temperature, the real ionic strength decreases first and finally levels off as the nominal Fe3+/Fe2+ ratio approaches 1000:1.       98   Figure 5-9  Calculated real ionic strength of the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios in the temperature range of 25°C-150°C.  Under the same nominal Fe3+/Fe2+ ratio, increasing the temperature from 25°C to 110°C was observed to result in a gradual decrease of the real ionic strength. This result may be due to ion association to form more stable species (from highly charged ions to less charged ion complexes), which will result in a decrease of the concentration of species with higher charge. In addition, despite the fact that the concentrations of ionic Fe(III) species decreases because of the formation of Fe2O3, an increase of ionic strength from 110 to 150°C was observed for all nominal Fe3+/Fe2+ ratios. This result may be attributed to a combination of the following two 30 50 70 90 110 130 1500.40.50.60.70.80.9  Ionic Strength (Real, mol/kg)Temperature (°C) Fe3+/Fe2+ (Nominal) 1:1 Fe3+/Fe2+ (Nominal) 10:1 Fe3+/Fe2+ (Nominal) 100:1 Fe3+/Fe2+ (Nominal) 1000:1 99  factors: (1) the second-most abundant Fe(II) species at this temperature is FeHSO4+ and (2) there is an increase in the free H+ concentration in the solution owing to the hydrolysis of free ferric. As a result, there is an increase in the concentration of charged ion species in the solution at 150°C.  The nominal ionic strengths for the four different nominal Fe3+/Fe2+ ratios are in the range of 2.26-2.98 mol/kg. It is clear that the calculated real ionic strengths predicted by the model using the real concentration of charged species are much lower than those calculated using the nominal species concentrations in all cases. This is due to the fact that the concentrations of the species with higher charges (such as Fe2+, Fe3+ and SO42-) considerably diminishes due to the formation of various complexes with lower charges (such as HSO4-, FeHSO4+ and FeSO4+). Because the effective ionic strengths of the solutions used in this study are low enough, the use of the B-dot equation to calculate the single ion activity coefficients is reasonable.   Validation of the present model could not be extended to a wider range of composition concentrations and temperatures due to the generation of iron precipitates and the presence of additional species. Further work is required in order to expand our understanding of this quaternary system. 5.4 Summary The speciation of the quaternary H2SO4-Fe2(SO4)3-FeSO4-H2O system was studied by thermodynamic modeling under conditions most relevant to the hydrometallurgical industry. The main species involved were first identified, and then the thermodynamic data for all of the species were collected and critically assessed. These data were used to estimate the activity coefficients of species by B-dot equation, and to calculate the equilibrium constants by the Lewis formulation of the Criss-Cobble correspondence principle from 25°C to 150°C.  100  Results from the calculated distribution of the main ferric and ferrous species as a function of temperature, iron and acid concentration, and the nominal Fe3+/Fe2+ ratio reveal that most of the Fe(III) is distributed as complexes or precipitates and the free ferric ion accounts for only a minor percentage, whereas a large amount of Fe(II) exists in the form of free ferrous ion. Moreover, under the same nominal Fe3+/Fe2+ ratio, a temperature increase in the range of 25°C-150°C leads to a decline in the free Fe3+ concentration, whereas the free Fe2+ concentration is relatively stable. At lower pH, free ferric and ferrous ions are more abundant. Under all of the investigated conditions, FeSO4+ is always the predominant species for Fe(III) in the aqueous solution. At 150°C, a large amount of Fe(III) precipitated as Fe2O3, with the largest value of 61.7% obtained when the nominal Fe3+/Fe2+ ratio was 1:1. The percentage of formed Fe2O3 under the other three nominal Fe3+/Fe2+ ratios is relatively stable and lower than that under nominal Fe3+/Fe2+ ratio of 1:1, due to relatively lower amount addition of FeSO4. This variation in the amount of hematite as a function of FeSO4 concentrations is similar to that published in the literature with an addition of divalent metal sulfates like ZnSO4 or MgSO4 for a relatively low free sulfuric acid concentration. The validity of the proposed model was confirmed by reliable prediction of measured redox potential from 25°C to 150°C. At 150°C, the fact that there exists a very good agreement between the ferric solubility calculated by the present model and that measured by previous work, further justifies the validity of the model. Extensive analysis and review of the calculated pH and real ionic strength of the solution provides an additional affirmation of the validity of the present work.  In summary, this work confirms that the model developed in this study is a promising method for the study of the speciation of the quaternary H2SO4-Fe2(SO4)3-FeSO4-H2O system  101  over a wide range of solution composition and temperature. The reliable prediction of redox potential by the speciation model is particularly valuable. Therefore, it can be expected that the findings in the present work will facilitate the research on the kinetics of the Fe3+/Fe2+ couple in general and in particular on the surface of chalcopyrite.                102  6 Development of an Expression to Predict the Redox Potential of the Fe3+/Fe2+ Couple up to 150°C  6.1 Introduction Fe3+ is the most important and industrially relevant surrogate oxidant in many sulfide mineral leaching processes. It is often already present in hydrometallurgical leaching streams, due to the dissolution of minerals such as chalcopyrite, pyrite, and bornite. As clearly presented in the previous discussions, the redox potential of H2SO4-Fe2(SO4)3-FeSO4-H2O solutions is one of the  key operating parameters, which is determined by the activity ratio of free ferric to free ferrous (rather than the nominal concentration ratio) based on the Nernst equation. As a result, the speciation of the system is important in determining the redox potential (to obtain the relative amounts of free ferric and ferrous and the accompanying activity coefficients in the solution). The model developed in Chapter 5 provides a mathematical tool capable of quantifying the concentration of free ions and complexes (and precipitates at higher temperature) as functions of temperature, acidity level, initial total amount of iron, and nominal ferric-to-ferrous ratio. In the subsequent discussion, results of this thermodynamic model will help in the interpretation of the change of redox potential with temperature for all nominal Fe3+/Fe2+ ratios. The present chapter aims to provide new data on the temperature dependence of the real Fe3+/Fe2+ concentration ratio, real ratios of the activity coefficient for free ferric and free ferrous and the standard electrode potential of the Fe3+/Fe2+ couple. These results are then used to analyze the contribution of each part to the overall redox potential of the Fe3+/Fe2+ couple, and subsequently employed to develop a novel expression to accurately predict the redox potential of the H2SO4-Fe2(SO4)3-FeSO4-H2O system. The proposed expression is determined only by the  103  variables of temperature and nominal Fe3+/Fe2+ ratio. Measured redox potentials by the present author and by others in the literature agree very well with those predicted by this expression, independent of the nominal concentrations of Fe3+ and H2SO4. This information will be used in further investigations of the electrochemical reduction kinetics of the Fe3+/Fe2+ couple on chalcopyrite as well as the mechanism of chalcopyrite leaching processes. 6.2 Speciation Results and Their Application to the Prediction of the Redox Potentials of the Fe3+/Fe2+ Couple at 25°C-150°C As mentioned previously, after obtaining the speciation results for the H2SO4-Fe2(SO4)3-FeSO4-H2O system, what particularly interests us is the temperature dependence of the free ferric and ferrous ion concentrations and their real ratios in order to systematically study the reversible potential of the Fe3+/Fe2+ couple. 6.2.1 Speciation Results of the Developed Model to Calculate the Redox Potential of the Fe3+/Fe2+ Couple The temperature dependence of the calculated real Fe3+/Fe2+ ratio in the Fe(II)-Fe(III)-H2SO4 solutions under different nominal Fe3+/Fe2+ ratios is presented in Figure 6-1. At each temperature, the calculated real Fe3+/Fe2+ ratio is much lower than the nominal ratio, and at the same time, it is worth noting that from 25°C to 150°C, under each given nominal Fe3+/Fe2+ ratio, the calculated real ratios of Fe3+/Fe2+ substantially declines with temperature. This implies that the real Fe3+/Fe2+ ratio is markedly dependent upon temperature and the composition of the electrolyte. In fact, a plot of the logarithm of the real Fe3+/Fe2+ ratio as a function of temperature (°C) is linear. Also, surprisingly, the four linear plots obtained under different nominal Fe3+/Fe2+ ratios display almost the same slope but with different intercepts. Particularly, with the nominal  104  Fe3+/Fe2+ ratios of 10:1, 100:1 and 1000:1, the slopes of these three linear plots were identical. Under each nominal ratio, the best fit for the temperature dependence of the real Fe3+/Fe2+ ratio and the corresponding correlation coefficient were obtained and shown as follows: ferric, real 2ferrous, reallog 2.67 1.35 10 (K)C TC    R2 = 0.9607  (1:1)               (6-1)  ferric, real 2ferrous, reallog 3.25 1.17 10 (K)C TC    R2 = 0.9544  (10:1)              (6-2)   ferric, real 2ferrous, reallog 4.23 1.17 10 (K)C TC    R2 = 0.9548  (100:1)            (6-3)    ferric, real 2ferrous, reallog 5.23 1.17 10 (K)C TC    R2 = 0.9547  (1000:1)          (6-4)       105   Figure 6-1 Calculated real Fe3+/Fe2+ ratios in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg with different nominal Fe3+/Fe2+ ratios in the temperature range of 25°C-150°C.  Apart from the real Fe3+/Fe2+ ratios, in order to calculate the redox potential of Fe3+/Fe2+ couple, the standard electrode potential of the Fe3+/Fe2+ couple (770 mV versus SHE at 25°C), as well as the single ion activity coefficients for free Fe3+ and Fe2+ ions, are also required to invoke the Nernst equation: ferric ferricferrous ferrous2.303 2.303log logo CRT RTE E nF nF                       (6-5) 30 50 70 90 110 130 1501E-30.010.1110100  [Fe3+]/[Fe2+] Ratio (Real)Temperature (°C) Fe3+/Fe2+ (Nominal) 1:1 Fe3+/Fe2+ (Nominal) 10:1 Fe3+/Fe2+ (Nominal) 100:1 Fe3+/Fe2+ (Nominal) 1000:1 106  The standard electrode potential of the Fe3+/Fe2+ couple (E°, mV) at high temperatures was calculated based on thermodynamic data (ΔG°) according to the above-mentioned Lewis formulation of the Criss-Cobble correspondence principle. The values are shown in Table 6-1. These calculated standard potentials for the ferric-ferrous couple agree very well with those in published literature [152-154]. It should be noted that the previously published values usually refer to the SHE at the operating temperature T (with definition of SHE as 0 at any temperature). However, in the present work all of the potentials are with respect to the SHE at 25°C (the SHE potential is defined herein as a function of temperature and is 0 only at 25°C). This definition is preferred as the SHE is not in fact 0 at elevated temperature (a potential can be measured between a SHE at 25°C and one at 100°C). Therefore, to compare the values presented herein to some of those presented in the previously published literature, the latter should be converted first according to Eq. (4-2). A comparison of those standard potentials is presented in Figure 6-2 and it is found that all of these data are in good agreement.   107  30 50 70 90 110 130 15075080085090095010001050  E of Fe3+/Fe2+ Couple vs SHE at 25°C (mV)Temperature (°C) Present Work Bratsch, 1989 Tagirov et al., 2000 Yeager and Salkind, 1972 Figure 6-2 Comparison of the calculated standard electrode potentials of the Fe3+/Fe2+ couple with those in published literature in the temperature range of 25°C-150°C.  Mathematical regression shows that the calculated standard electrode potential of the Fe3+/Fe2+ couple varies linearly with temperature. The best fit was provided by the following relationship (E° data are from Table 6-1): (mV) 1.6 (K) 300.2  oE T                             (6-6) The correlation coefficient was 0.9967. As to the single ion activity coefficients for species involved in the present study, they were estimated by the above-noted B-dot equation. A detailed discussion on the applicability of this model will be given later. Calculated results show that the ratios of the activity coefficient  108  for free ferric and free ferrous are typically only affected by temperature, and remain practically constant at each temperature under different nominal Fe3+/Fe2+ ratios. The ratios of the activity coefficient for free ferric and ferrous ranged from 0.35 to 0.27 (each is an average of the values under four different nominal Fe3+/Fe2+ ratios), with the temperature increasing from 25°C to 150°C. This ratio of activity coefficients also varies linearly with temperature. The obtained activity coefficient ratios for free ferric and ferrous were included in the term (2.303RT/nF)×log (γferric/γferrous) where this entire expression is defined here as E1 (mV), and which yields the potential values resulting from the single ion activity coefficients. The variation of E1 with temperature can be estimated with the following regressed expression (The original E1 values calculated from the model results are -27.02 mV at 25°C, -32.47 mV at 70°C, -35.55 mV at 90°C, -38.97 mV at 110°C and  -48.12 mV at 150°C, respectively): 3 21(mV) 0.6 10 [ (K)] 0.3 (K) 57.5      E T T                   (6-7) The corresponding correlation coefficient was 0.9997. All data calculated using the model results for the standard and reversible potentials of the Fe3+/Fe2+ couple at different temperatures are shown in Table 6-1. The standard electrode potential of the Fe3+/Fe2+ couple increased with temperature. Speciation results indicate that for a given temperature the model-calculated potentials increase considerably with the nominal Fe3+/Fe2+ ratios. However, from 25°C to 150°C, the potentials predicted by the model increase gradually only when the nominal Fe3+/Fe2+ ratios are 10:1, 100:1 and 1000:1. Interestingly, the predicted potentials are relatively stable at the nominal Fe3+/Fe2+ ratio of 1:1 and no significant change was observed as the temperature increased. The reason for this unexpected behavior at the Fe3+/Fe2+ ratio of 1:1 lies in the fact that at each temperature, the real Fe3+/Fe2+ ratio in the solution is much lower in such a condition, typically lower than 0.1 and on the order of 10-2 or  109  10-3. Such small values will result in a large negative value for (2.303RT/nF)×log (Cferric/Cferrous) (this whole item is defined as E2, mV), which is the third component of the Nernst equation. This implies that although the E° increases considerably with temperature, and E1 is relatively stable at each temperature, the calculated reversible potential for the Fe3+/Fe2+ couple based on the sum of E°, E1 and E2 remains essentially unchanged at the 1:1 ratio condition.                    110     Table 6-1 Standard electrode potential of Fe3+/Fe2+ couple calculated by the Criss-Cobble method and redox potential of Fe3+/Fe2+ couple predicted by the model in Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18mol/kg with different nominal Fe3+/Fe2+ ratios in the range of 25-150°C. Fe3+/Fe2+  (Nominal) EFerric/Ferrous (25°C) EFerric/Ferrous (70°C) EFerric/Ferrous (90°C) EFerric/Ferrous (110°C) EFerric/Ferrous (150°C) E° Model E° Model E° Model E° Model E° Model 1:1 770.0  670.5  849.5  673.1  881.6  678.9  912.2  677.1  968.8  674.8  10:1 770.0  735.7  849.5  755.3  881.6  765.7  912.2  774.2  968.8  785.5  100:1 770.0  795.6  849.5  824.8  881.6  839.3  912.2  852.3  968.8  871.8  1000:1 770.0  854.8  849.5  893.1  881.6  911.6  912.2  928.5  968.8  956.0       111  In addition, the very low real Fe3+/Fe2+ ratio for the nominal 1:1 condition can be ascribed to the following two facts: (1) under the nominal Fe3+/Fe2+ ratio of 1:1, a relatively large amount of Fe2+ added to the solution causes a drop in the real Fe3+/Fe2+ ratio; (2) at the same time, a large amount of SO42- (included with Fe2+) addition also diminishes the free Fe3+ concentration due to ion association to form more stable Fe(III) species. 6.2.2 Development of an Expression to Predict the Redox Potential of the Fe3+/Fe2+ Couple up to 150°C  At present, to the knowledge of the author there are no theoretical methods available for predicting the redox potential of the H2SO4-Fe2(SO4)3-FeSO4-H2O system through a wide range of temperature and electrolyte composition. Given the variation of E°, E1 and E2 with temperature and nominal Fe3+/Fe2+ ratio, regression of the dependence of the calculated reversible potential of the Fe3+/Fe2+ couple was carried out, and an empirical relationship was developed. First, according to the Equations 6-2, 6-3 and 6-4, with the nominal Fe3+/Fe2+ ratios of 10:1, 100:1 and 1000:1, the slopes of these three linear plots were identical, with the intercept difference of 1 when increasing the nominal Fe3+/Fe2+ ratio. By taking advantage of this fact, when calculating E2, an equation can be obtained for all three nominal Fe3+/Fe2+ ratios: ferric, nominal3 2 32ferrous, nominal2.303(mV) 2.33 10 [ (K)] 0.45 (K) (K) 10 log CRE T T TnF          (6-8) Then, by adding all three items E°, E1 and E2, the following equation was developed by adjusting constants in order to fit all of the data points in this study: ferric, nominal3 2 3ferrous, nominal2.303(mV) 1 10 [ (K)] 0.91 (K) (K) 10 log 492CRE T T TnF             (6-9) The overall error between the calculated values from the model and the predicted values from the equation was minimized by inspection. Please note that all of the potential E(mV)  112  calculated by the above equation are referred to the SHE at 25°C. This equation can be applied to the cases under the given nominal concentrations of H2SO4 (0.31 mol/kg) and Fe3+ (0.18 mol/kg) when the nominal Fe3+/Fe2+ ratios are 10:1, 100:1 and 1000:1 in the temperature range of 25°C-150°C, with a deviation lower than 5 mV. Its slope is the same as that of the Nernst equation. Regression of the data with the nominal Fe3+/Fe2+ ratio of 1:1 is not included in light of the fact that the potentials calculated by the speciation model were relatively stable and independent of temperature in such a case. Nevertheless, the developed expression can still be used to evaluate the redox potential at lower temperature with the nominal Fe3+/Fe2+ ratio of 1:1. Actually, the difference between the potentials predicted by the speciation model (as shown in Table 6-1) and calculated by the proposed expression is only about 4.5 mV at 25°C, and this deviation increases gradually with increasing temperature, with the largest value of 23.9 mV obtained at 150°C. At 150°C, considering the fact that the Fe(III) existing in the form of Fe2O3 as a precipitate has no influence on the redox potentials of the liquid phase, a modification of Eq. (6-9) was made in order to replace the term “Cferric, nominal” (total nominal ferric added to the autoclave) with “Cferric, dissolved” (total ferric existing in the liquid solution after the approach to equilibrium by hydrolysis). First, the author found that there is a linear relationship between “Cferric, nominal/Cferrous, nominal” and “Cferric, dissolved/ Cferrous, nominal”: ferric, nominal ferric, dissolvedferrous, nominal ferrous, nominal1.74 0.32C CC C                                       (6-10) The corresponding correlation coefficient was 1. Then, by adding Eq. (6-10) into Eq. (6-9), a new equation can be obtained: ferric, dissolved3 2 3ferrous, nominal1.742.303(mV) 1 10 [ (K)] 0.91 (K) (K) 10 log 0.32 492CRE T T TnF C                (6-11)  113  Please note that Eq. (6-11) can be used under the conditions in the present study only at 150°C, and the potentials calculated by Eq. (6-11) agree very well those calculated by Eq. (6-9). Obviously, there is some concern regarding the expression Eq. (6-9): whether it can be supported by other experimental evidence, and be used to calculate the redox potentials under different conditions such as nominal concentrations of H2SO4 and Fe3+, nominal Fe3+/Fe2+ ratio and temperature. This will be discussed in the following section. 6.3 Applicability of the Developed Expression-Comparison with Experimental Results by Previous Work The applicable scope of the developed expression Eq. (6-9) was investigated based on the experimental results in the literature in terms of nominal amounts of Fe3+ and H2SO4, nominal Fe3+/Fe2+ ratio and temperature. Figure 6-3 shows the comparison of the redox potentials in the Fe(II)-Fe(III)-H2SO4 solutions predicted by the developed expression Eq. (6-9)  and measured by experiments from Dry and Bryson (1988) [33] at various nominal concentrations of H2SO4 and Fe(III)/Fe(II) with different nominal Fe3+/Fe2+ ratios at 22°C and 90°C. In Figure 6-3a it is demonstrated that for each nominal Fe3+/Fe2+ ratio, the measured redox potentials are independent of the nominal concentrations of Fe3+ and H2SO4. The measured redox potentials are in good agreement with the results calculated by the expression. It should be noted that wide ranges of nominal Fe3+ concentration (0.01-0.99 mol/L), nominal H2SO4 concentration (0.102-1.021 mol/L) and nominal Fe3+/Fe2+ ratios (from 0.01:1 to 100:1) are employed, and the nominal ionic strength of the studied solutions is in the range of 0.42-14.45 mol/L. This means that at 22°C, the expression is applicable over a wider range of solution composition, and there is almost no effect of nominal concentrations of Fe3+ and H2SO4 on the redox potential.    114    0.01 0.1 1 10 100550600650700750800 Developed Expression in This Work Exp Data from Dry ([Fe3+]=0.01, [H+]=0.204) Exp Data from Dry ([Fe3+]=0.01, [H+]=2.041) Exp Data from Dry ([Fe3+]=0.099, [H+]=0.204) Exp Data from Dry ([Fe3+]=0.099, [H+]=2.041) Exp Data from Dry ([Fe3+]=0.99, [H+]=0.204) Exp Data from Dry ([Fe3+]=0.99, [H+]=2.041) 22oC Empirical Expression 22oC Exp Data from Dry ([Fe3+]=0.01, [H+]=0.204) 22oC Exp Data from Dry ([Fe3+]=0.01, [H+]=2.041) 22oC Exp Data from Dry ([Fe3+]=0.099, [H+]=0.204) 22oC Exp Data from Dry ([Fe3+]=0.099, [H+]=2.041) 22oC Exp Data from Dry ([Fe3+]=0.99, [H+]=0.204) 22oC Exp Data from Dry ([Fe3+]=0.99, [H+]=2.041) 1 Model 0.01/0.204 0.01/2.04 0.099/0.204 0.099/2.04 0.99/0.204 0.99/2.04  Potentials by Expression and Experiments (mV)[Fe3+]/[Fe2+] Ratio (Nominal)(a) Figure 6-3 Comparison of the potentials predicted by the developed expression Eq. (6-9)  in this work and measured by experiments in the Fe(II)-Fe(III)-H2SO4 solutions from Dry and Bryson (1988) at various nominal concentrations of H2SO4 and Fe(III)/Fe(II) with different nominal Fe3+/Fe2+ ratios: (a) at 22°C; (b) at 90°C. The unit of the concentrations in the figure is mol/L. Detailed information on the nominal concentrations of Fe3+ and Fe2+ at 90°C can be found in the literature.   115  1 10 100600650700750800850900(b)   Potentials by Expression and Experiments (mV)[Fe3+]/[Fe2+] Ratio (Nominal) Developed Expression in This Work  Exp Data from Dry at Various Concentrations of H2SO4 and Fe3+/Fe2+ Figure 6-3 Continued.   Furthermore, in Figure 6-3b, at 90°C, it is interesting to observe that when the nominal Fe3+/Fe2+ ratios are around or larger than 10:1 (the values of the two points around 10:1 in Figure 6-3b are 7.2 and 8.6), the measured redox potentials agree very well with that predicted by the expression, unrelated to the nominal concentrations of Fe3+ and H2SO4. As the nominal Fe3+/Fe2+ ratios decrease (for example, around 3.4 and 4.3), an acceptable deviation of the measured redox potentials from that calculated by the expression occurs. However, when the nominal Fe3+/Fe2+ ratio approaches 1:1, a larger deviation was found and this trend is similar to the findings in this work. It should be noted that the nominal concentrations of Fe3+, Fe2+ and H2SO4 used in the work of Dry and Bryson are discrete values at 90°C in the range of 1.223-1.866 mol/L, 0.013- 116  0.951 mol/L and 0.643-0.889 mol/L, respectively, and the nominal ionic strength typically ranged from 15.08 mol/L to 15.94 mol/L.  From the above analysis, it seems that the redox potential depends significantly on the nominal Fe3+/Fe2+ ratio and temperature, but is almost unaffected by the nominal concentration of Fe3+, Fe2+ and H2SO4. The developed expression Eq. (6-9) can even be applied over a wider range of nominal Fe3+/Fe2+ ratio at lower temperature. To confirm this and to obtain more detailed information, the effect of nominal amounts of Fe3+, Fe2+, H2SO4 and the nominal Fe3+/Fe2+ ratio on the redox potential was investigated at room temperature based on measured data published in the literature [53, 69, 155]. In Figure 6-4, it is shown that at each given nominal Fe3+/Fe2+ ratio, there is almost no difference for the redox potentials between the measured results by three different authors and that calculated by the expression Eq. (6-9) presented herein. At the same time, it is worth noting that the measured redox potentials at the 1:1 ratio from three different sources are nearly identical to each other. Also, it should be emphasized that a wider range of nominal Fe3+/Fe2+ ratio (from 0.01:1 to 2000:1) is used and the solution composition was different in the studies used for Figure 6-4.   117  0.01 0.1 1 10 100 1000550600650700750800850900 Empirical Expression in This Work Exp Data from Tshilombo Exp Data from Hiroyoshi Exp Data from Nicol  Potentials by Expression and Experiments (mV)[Fe3+]/[Fe2+] Ratio (Nominal) 1 Model Alain Hiroyoshi Nicol Figure 6-4 Comparison of the potentials predicted by the developed expression Eq. (6-9) in this work and measured by experiments in the Fe(II)-Fe(III)-H2SO4 solutions from Hiroyoshi et al. (2001), Tshilombo (2004) and Nicol and Lázaro (2002) at various nominal concentrations of H2SO4 and Fe(III)/Fe(II) with different nominal Fe3+/Fe2+ ratios at room temperature. (Hiroyoshi: [H2SO4] = 0.1 mol/L and [Fe3+]total = 0.01 mol/L; Tshilombo: [iron]total = 5 g/L and pH = 1.4; Nicol and Lázaro: pH = 1.5, 10 g/L Fe3+ and 5 mg/L Fe2+ at 2000:1 ratio, 5 g/L Fe3+ and 5 g/L Fe2+ at 1:1 ratio)    118  The above analyses of the experimental results from the literature strongly support the proposed expression Eq. (6-9) in this work. It appears that the redox potential could be easily and accurately determined based on the variables of temperature and nominal Fe3+/Fe2+ ratio, and there is almost no change in redox potential caused by the nominal concentrations of H2SO4 and Fe3+. Moreover, the developed expression Eq. (6-9) is probably applicable to more general cases at or around room temperature (or maybe slightly higher temperature), in spite of the fact that a deviation occurs at higher temperatures (for example at 90°C) under lower nominal ratios. These results are particularly valuable and of interest: at any given temperature, the redox potential of quaternary H2SO4-Fe2(SO4)3-FeSO4-H2O system is solely determined by the nominal Fe3+/Fe2+ ratio and a temperature dependence of the same slope as the Nernst equation. This expression avoids the complicated calculations of the standard electrode potential and the activity coefficient.   6.4 Summary Based on the model developed in Chapter 5, the temperature dependence of the real Fe3+/Fe2+ ratios and their activity coefficient ratios were obtained. The calculated real Fe3+/Fe2+ ratio is much lower than the nominal ratio, and from 25°C to 150°C, under each given nominal Fe3+/Fe2+ ratio, the calculated real ratio of Fe3+/Fe2+ substantially declines with temperature. The activity coefficient ratios are typically only affected by temperature, and remain practically constant at each temperature under different nominal Fe3+/Fe2+ ratios. These results, together with the calculated standard electrode potential of the Fe3+/Fe2+ couple, were employed to systematically study the redox potential of the Fe3+/Fe2+ couple. For a given temperature, the model-calculated potentials increase considerably with the nominal Fe3+/Fe2+ ratio. However, from 25°C to 150°C, the potentials predicted by the model increase gradually only when the  119  nominal Fe3+/Fe2+ ratios are 10:1, 100:1 and 1000:1 (with its values in the range of ~736–956 mV), while at the nominal Fe3+/Fe2+ ratio of 1:1 they are relatively stable (typically between ~671 and 679 mV) and no significant change was observed as the temperature increased. The speciation model explains the change of redox potential with temperature for all nominal Fe3+/Fe2+ ratios.  An expression (Eq. 6-9, reproduced below) determined only by the variables of temperature and nominal Fe3+/Fe2+ ratio was developed to predict the redox potential of the Fe3+/Fe2+ couple. Measured redox potentials in the literature agree very well with those predicted by the developed expression, independent of the nominal concentrations of Fe3+ and H2SO4. Moreover, the expression is probably applicable to more general cases at or around room temperature. Future work will be required to determine the broader range of applicability of this equation.  ferric, nominal3 2 3ferrous, nominal2.303(mV) 1 10 [ (K)] 0.91 (K) (K) 10 log 492CRE T T TnF                   120  7 Reduction Kinetics of Ferric Ion on Chalcopyrite from 25°C to 150°C  7.1 Introduction The results obtained in the previous Chapters open the way to investigate the reduction behavior of ferric ion on chalcopyrite, and provide an opportunity for a comprehensive study and comparison of its reduction kinetics at different temperatures relevant to industrial chalcopyrite leaching processes. The objective of this Chapter is to systematically study the kinetics of ferric reduction in the quaternary H2SO4-Fe2(SO4)3-FeSO4-H2O system on chalcopyrite by electrochemical measurements. This investigation aims to obtain the temperature dependence of fundamental electrochemical kinetic parameters, such as exchange current density, transfer coefficient and rate constant. This study yields detailed information about the ferric ion reduction processes involved in industrially significant leaching conditions relevant to the previously mentioned processes at different temperatures from 25 to 150°C. Since in acidic iron sulfate solution, the concentrations of ferric and ferrous ions are limited by the formation of charged cations and anions, as well as neutral species, herein they are first obtained as a function of electrolyte composition and temperature by the developed speciation model (details can be found in Section 7.2.1). This information is then used to apply thermodynamic and chemical kinetic principles, i.e., to invoke the Nernst equation and other basic electrochemical kinetic equations (Butler-Volmer equation and its extensions). Then, the reduction kinetics of ferric on chalcopyrite are investigated by cathodic potentiodynamic polarization at temperatures relevant to existing industrial processes and thus the temperature  121  dependence of the exchange current density, transfer coefficient and rate constant are determined and discussed.  7.2 Results and Discussion 7.2.1 Determination of the Concentrations of Free Ferric and Ferrous Ions in H2SO4-Fe2(SO4)3-FeSO4-H2O System by the Speciation Model between 25°C and 150°C According to the published literature, the iron sulfates present in sulfuric acid solution are distributed as soluble species including simple metal ions, neutral or charged complexes, as well as precipitates such as Fe2O3 formed at high temperatures [33-45]. Therefore, a speciation model is required to quantify the concentrations of the main species involved in acidic iron sulfate solutions. These results can then be employed to study the reduction kinetics of ferric ions on chalcopyrite (the concentration of free ferric ions is required when invoking basic electrochemical kinetic equations). Further, this information can be used to calculate the exchange current density by extrapolating the cathodic linear Tafel line to the reversible potential of the Fe3+/Fe2+ couple (concentrations of free ferric and ferrous ions are required when invoking the Nernst equation).   However, most existing relevant speciation studies of the quaternary acidic iron sulfate system are limited to lower concentrations and/or temperatures [33-38]. As a result, in Chapter 5, a thermodynamic model was developed and shown to reliably simulate the speciation of the quaternary H2SO4-Fe2(SO4)3-FeSO4-H2O system through a wide range of solution compositions and temperatures (25°C-150°C). The main species involved were identified, and the thermodynamic data for all of the species were collected and critically assessed. These data were used to estimate the activity coefficients of species with the B-dot equation [137-139], and to calculate the equilibrium constants by the Lewis formulation of the Criss-Cobble correspondence  122  principle [144, 145, 149] from 25 to 150°C. Results from the calculated distribution of the main ferric and ferrous species in H2SO4 solutions reveal that most of the Fe(III) is distributed as complexes or precipitates and the free Fe3+ accounts for only a minor percentage, whereas a large amount of Fe(II) exists in the form of free Fe2+. Moreover, under the same nominal Fe3+/Fe2+ ratio, a temperature increase in the range of 25-150°C leads to a decline in the free Fe3+ concentration due to the ion association to form more stable species, whereas the free Fe2+ concentration is relatively stable with similar values of the same order of magnitude. The proposed model was validated by the experimental data in the present work and results published by other authors. Detailed information on the speciation model can be found in Chapter 5 and 6. Table 7-1 presents the obtained concentrations of free Fe3+ and Fe2+ in the above-mentioned aqueous Fe(II)-Fe(III)-H2SO4 solutions in the range of 25-150°C according to the developed speciation model. These results will be subsequently used in the following discussion, in order to investigate the electrochemical reduction kinetics of the Fe3+/Fe2+ couple on chalcopyrite as well as mechanistic analysis in industrial chalcopyrite leaching processes.          123   Table 7-1 The calculated concentrations of free Fe3+ and Fe2+ ions in aqueous Fe(II)-Fe(III)-H2SO4 solutions in the range of 25-150°C according to the developed speciation model (Unit: mol/kg). Fe3+/Fe2+ (Nominal)  Free Iron at 25°C  Free Iron at 70°C  Free Iron at 90°C  Free Iron at 110°C  Free Iron at 150°C Cferric Cferrous Cferric Cferrous Cferric Cferrous Cferric Cferrous Cferric Cferrous 1:1 6.75E-03 1.10E-01 9.44E-04 1.18E-01 5.33E-04 1.08E-01 3.01E-04 1.10E-01 1.51E-04 1.24E-01 10:1 8.92E-03 1.19E-02 1.61E-03 1.31E-02 9.62E-04 1.26E-02 6.40E-04 1.29E-02 3.17E-04 1.30E-02 100:1 9.19E-03 1.20E-03 1.70E-03 1.32E-03 1.02E-03 1.28E-03 6.84E-04 1.31E-03 3.36E-04 1.30E-03 1000:1 9.22E-03 1.20E-04 1.71E-03 1.32E-04 1.02E-03 1.28E-04 6.88E-04 1.31E-04 3.39E-04 1.30E-04         124  7.2.2 CPC Results at 25°C Figure 7-1 shows the CPC and corresponding OCP results at 25°C. It can be observed that the OCP values are quite stable under each nominal Fe3+/Fe2+ ratio. OCP slightly shifted towards positive values when increasing the nominal Fe3+/Fe2+ ratio. The shape of the polarization plots for different nominal Fe3+/Fe2+ ratios are similar, indicating identical processes in the systems. All of the plots exhibit reproducible well-defined linear Tafel regions. The reduction reaches a well-defined limiting current density at approximately E = 100 mV versus SHE. Addition of ferrous by varying the nominal Fe3+/Fe2+ ratio from 1000:1 to 1:1 has no apparent effect on the Tafel plots. In addition, it can be found that the polarization curves cross each other (e.g. the curve at 1:1 nominal Fe3+/Fe2+ ratio crosses over the curves at the three other nominal Fe3+/Fe2+ ratios). This is probably caused by the different free iron concentrations and starting OCP values at the early stages of the experiment, as well as the fact that the measured Tafel slopes are essentially unchanged. Specifically, when a chalcopyrite electrode was immerged in the acidic iron sulfate solution, the starting OCP values were different depending on the solution composition (e.g. the OCP value at 1:1 nominal Fe3+/Fe2+ ratio is lower than that at the nominal Fe3+/Fe2+ ratio of 10:1). Meanwhile, the free ferric ion concentrations are similar (see the results in Table 7-1). This means that the ferric ion reduction behavior should also be in a similar range of the E-Log i figure. Finally, the Tafel slopes of those plots are essentially unchanged. A combination of the above three factors resulted in such a cross-over behavior for the polarization plots. This phenomenon appears for all temperatures used in the present study, as shown in the following sections.   125  0 200 400 600 800 100012001400160018000.640.650.660.670.680.690.700.71  OCP vs SHE (V)Time (S) Fe3+/Fe2+=1:1 Fe3+/Fe2+=10:1 Fe3+/Fe2+=100:1 Fe3+/Fe2+=1000:1  -7 -6 -5 -4 -3 -2-0.2-0.10.00.10.20.30.40.50.60.70.8  E vs SHE (V)Log i (A/cm2) Fe3+/Fe2+=1:1 Fe3+/Fe2+=10:1 Fe3+/Fe2+=100:1 Fe3+/Fe2+=1000:1 Figure 7-1 Cathodic potentiodynamic polarization curves and corresponding OCP in deaerated aqueous Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg on chalcopyrite with different nominal Fe3+/Fe2+ ratios at 25°C.  126  According to the results obtained by the above-mentioned speciation model, it is clearly shown in Table 7-2 that the real Fe3+/Fe2+ ratio in the Fe(II)-Fe(III)-H2SO4 solutions under different nominal Fe3+/Fe2+ ratios is much lower than the nominal ratio at 25°C. By further invoking the Nernst equation (the standard electrode potentials for the Fe3+/Fe2+ couple were also calculated by the Lewis formulation of the Criss-Cobble correspondence principle), the reversible potential of the Fe3+/Fe2+ couple (EC) can be calculated and the results are also presented in Table 7-2.  Table 7-2 CPC results at 25°C. Fe3+/Fe2+ (Nominal) Fe3+/Fe2+ (Real) Tafel Slope  (V/decade) Transfer  Coefficient EM EC EM (V) iM (A/cm2) EC (V) i0 (A/cm2) 1:1 6.13E-02 0.154 0.38 0.6457 3.51E-06 0.6705 2.43E-06 10:1 0.75 0.163 0.36 0.6868 1.65E-06 0.7357 8.27E-07 100:1 7.67 0.162 0.37 0.6982 1.37E-06 0.7956 3.41E-07 1000:1 76.9 0.156 0.38 0.6982 1.48E-06 0.8548 1.46E-07   Based on the obtained cathodic linear Tafel line and the reversible potential of the Fe3+/Fe2+ couple, the transfer coefficients and exchange current densities could be calculated at 25°C. As indicated in Table 7-2, no significant change in the cathodic Tafel slopes for the reduction of ferric ions on the CuFeS2 surface was observed and the slopes ranged between 0.154 and 0.163 V/decade. The measured Tafel slopes, according to Eq. (7-1), yield the values for α in the range of 0.36-0.38. The average values of the transfer coefficient calculated from the  127  cathodic Tafel slopes obtained from CPC are lower than 0.5, which is probably related to the semi-conducting behavior of chalcopyrite and/or the passive film that forms thereon.  Usually, the Tafel slope is considered to be proportional to temperature and transfer coefficient according to the following expression: 2.303  = RTb nF                                                    (7-1) where b is the Tafel slope (V/decade), n is the number of electrons transferred in the rate determining step (n may be taken as unity because the rate determining processes mostly involve single charge transfer steps) [24], F is the Faraday constant (C/mol), α is the transfer coefficient, R is the universal gas constant (J/mol•K) and T is the temperature (K). With the increase of nominal Fe3+/Fe2+ ratio from 1:1 to 1000:1, the obtained exchange current densities (i0) declined from 2.43x10-6 A/cm2 to 1.46x10-7 A/cm2. The reason for this behavior may be attributed to a combination of the following two factors: (1) the calculated reversible potentials are higher as the nominal Fe3+/Fe2+ ratio is increased and (2) at the same time the cathodic Tafel plots remain essentially unchanged under different nominal Fe3+/Fe2+ ratios. Actually, i0 is related to the concentration of free Fe2+ in the solution and increases with a higher concentration of Fe2+. This trend, i.e. the effect of increasing Fe2+ concentration, prevails for all temperatures used in the present study, as shown in the following sections. Please note that in the present study, the total amount of Fe(III) is constant, and hence the total amount of Fe(II) decreases when increasing the nominal Fe3+/Fe2+ ratio. The obtained mixed potential (EM, obtained from Figure 7-1) and mixed current density (iM) are also shown and summarized in Table 7-2. Please note that the iM was calculated by extrapolating the cathodic linear Tafel line to the corresponding mixed potential. Typically, the iM values are on the order of 10-6 A/cm2 at 25°C. The EM decreases with an increase of iron(II)  128  concentration. It is interesting to observe that the mixed potential is approximately equal to the cathodic reversible potential only when the nominal Fe3+/Fe2+ ratio approaches 1:1. This trend is similar to that observed by Nicol and Lázaro in 2002, who demonstrated that the potential measured in the bulk of the solution can only be approximated to that at the surface of the minerals under conditions of relatively high concentrations of iron(II) [69]. The development of corrosion pits on the anodic sites of the chalcopyrite electrode surface under oxidizing conditions could be observed. Hence, the surface of a chalcopyrite specimen before and after electrochemical treatment was examined by OM, to see whether corrosion pits were formed or enlarged. It is suggested in Figure 7-2 that, as expected, numerous small pits appeared after finishing the electrochemical experiment. The kinetic and mechanistic analysis of the anodic oxidation processes (including the generated products) is complicated and is beyond the scope of the present study.      129    Figure 7-2 OM analysis results of the prepared chalcopyrite electrode surface before (a) and after electrochemical test (b) in the electrolyte with nominal Fe3+/Fe2+ ratio of 1000:1 at 25°C. (b) Epoxy Area Chalcopyrite Electrode Surface (a)  130  7.2.3 CPC Results at 70°C The results of OCP and CPC measurement in Fe(II)-Fe(III)-H2SO4 solutions with different nominal Fe3+/Fe2+ ratios at 70°C are presented in Figure 7-3. The OCP values are relatively stable and no obvious deviation was found under each nominal Fe3+/Fe2+ ratio. The polarization plots for different nominal Fe3+/Fe2+ ratios almost overlap with each other, and increasing the nominal Fe3+/Fe2+ ratio has little or no effect on the polarization curve. This trend is similar to that at 25°C. The reduction process approaches a limiting current density at approximately E = 180 mV versus SHE.        131  0 200 400 600 800 100012001400160018000.610.620.630.640.650.660.67  OCP vs SHE (V)Time (S) Fe3+/Fe2+=1:1 Fe3+/Fe2+=10:1 Fe3+/Fe2+=100:1 Fe3+/Fe2+=1000:1 -6 -5 -4 -3 -2 -1-0.2-0.10.00.10.20.30.40.50.60. E vs SHE (V)Log i (A/cm2) Fe3+/Fe2+=1:1 Fe3+/Fe2+=10:1 Fe3+/Fe2+=100:1 Fe3+/Fe2+=1000:1 Figure 7-3 Cathodic potentiodynamic polarization curves and corresponding OCP in deaerated aqueous Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg on chalcopyrite with different nominal Fe3+/Fe2+ ratios at 70°C.  132  Table 7-3 lists the nominal and real Fe3+/Fe2+ ratio in aqueous Fe(II)-Fe(III)-H2SO4 solution at 70°C. It can be seen that the real Fe3+/Fe2+ ratio is still much lower than the nominal ratio, and it is worth noting that the real Fe3+/Fe2+ ratio at 70°C is even smaller than that at 25°C.  Table 7-3 CPC results at 70°C. Fe3+/Fe2+ (Nominal) Fe3+/Fe2+ (Real) Tafel Slope  (V/decade) Transfer  Coefficient EM EC EM (V) iM (A/cm2) EC (V) i0 (A/cm2) 1:1 7.98E-03 0.156 0.44 0.6184 3.86E-05 0.6731 1.72E-05 10:1 0.123 0.151 0.45 0.6491 2.46E-05 0.7553 4.88E-06 100:1 1.29 0.165 0.41 0.6666 2.13E-05 0.8248 2.33E-06 1000:1 12.9 0.154 0.44 0.6525 2.62E-05 0.8931 7.13E-07  The transfer coefficients and exchange current densities were also calculated at 70°C. Table 7-3 shows that there is no significant change in the cathodic Tafel slopes for ferric reduction and the slopes varied between 0.151 and 0.165 V/decade. The measured Tafel slopes are similar to those obtained at 25°C, and give the values for α in the range of 0.41-0.45 according to Eq. (7-1). When increasing the nominal Fe3+/Fe2+ ratio from 1:1 to 1000:1, the exchange current densities decreased from 1.72x10-5 A/cm2 to 7.13x10-7 A/cm2. This tendency is the same as that observed at 25°C. At 70°C, there is a decrease in the measured EM in comparison with that at 25°C under the same nominal Fe3+/Fe2+ ratio, and at the same time the Tafel slopes are relatively stable, which subsequently leads to an increased iM. In general, the iM values are on the order of 10-5 A/cm2. In addition, under the same nominal Fe3+/Fe2+ ratio,  133  increasing the temperature from 25°C to 70°C gives rise to an increase of the iM and i0 for the Fe3+/Fe2+ couple on chalcopyrite, by almost one order of magnitude. 7.2.4 CPC Results at 90°C Figure 7-4 presents the CPC and corresponding OCP results at 90°C. It is shown again that the OCP values are quite stable under each nominal Fe3+/Fe2+ ratio, and are larger when increasing the nominal Fe3+/Fe2+ ratio. The polarization plots for different nominal Fe3+/Fe2+ ratios display similar behavior, apart from the fact that there is deviation at the very beginning of scanning due to the different OCP values. A limiting current density is obtained at approximately E = 210 mV versus SHE. The addition of ferrous ion when changing the nominal Fe3+/Fe2+ ratio from 1000:1 to 1:1 has no obvious influence on the Tafel plots.       134  0 200 400 600 800 100012001400160018000.630.640.650.660.670.680.690.700.710.72  OCP vs SHE (V)Time (S) Fe3+/Fe2+=1:1 Fe3+/Fe2+=10:1 Fe3+/Fe2+=100:1 Fe3+/Fe2+=1000:1 -6 -5 -4 -3 -2 -1-0.10.00.10.20.30.40.50.60.7 E vs SHE (V)Log  (A/cm2) Fe3+/Fe2+=1:1 Fe3+/Fe2+=10:1 Fe3+/Fe2+=100:1 Fe3+/Fe2+=1000:1 Figure 7-4 Cathodic potentiodynamic polarization curves and corresponding OCP in deaerated aqueous Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg on chalcopyrite with different nominal Fe3+/Fe2+ ratios at 90°C.  135   All of the CPC results at 90°C are included in Table 7-4. It is seen in Table 7-4 that the calculated real Fe3+/Fe2+ ratios at 90°C are even smaller, compared with those obtained at 25°C and 70°C under the same nominal Fe3+/Fe2+ ratio. A slight decrease in the cathodic Tafel slopes for the reduction of ferric ions on the CuFeS2 surface was observed compared to those obtained at 25°C and 70°C, especially when the nominal Fe3+/Fe2+ ratio is 1:1, 10:1 and 100:1. The slopes ranged between 0.123 and 0.159 V/decade, and were further employed to calculate the transfer coefficients, with values being in the range of 0.45-0.58.  Table 7-4 CPC results at 90°C. Fe3+/Fe2+ (Nominal) Fe3+/Fe2+ (Real) Tafel Slope  (V/decade) Transfer  Coefficient EM EC EM (V) iM (A/cm2) EC (V) i0 (A/cm2) 1:1 4.96E-03 0.123 0.58 0.6448 2.11E-05 0.6789 1.11E-05 10:1 0.08 0.125 0.58 0.6650 1.85E-05 0.7657 2.88E-06 100:1 0.80 0.139 0.52 0.6819 2.66E-05 0.8393 1.96E-06 1000:1 8.01 0.159 0.45 0.6966 2.67E-05 0.9116 1.19E-06   As to the EM and iM, it was found that when increasing the temperature from 70°C to 90°C, there is a slight increase in EM under the same nominal Fe3+/Fe2+ ratio, whereas the iM data are relatively stable with similar values of the same order of magnitude (10-5 A/cm2). As expected, the i0 increases by increasing the concentration of ferrous. Furthermore, although the i0 at 70°C and 90°C are still on the same order, the temperature increase results in a small decline in i0. The  136  reason for this unexpected behavior can be ascribed to the following two facts: (1) the temperature increase causes an increase in the reversible potentials of the Fe3+/Fe2+ couple; (2) the Tafel slopes diminished a little in contrast to those measured at 70°C. 7.2.5 CPC Results at 110°C Currently, most of the proposed leaching processes for chalcopyrite are operated under pressure, primarily because fast leaching kinetics can be achieved at the elevated temperatures employed in an autoclave. However, although in the past several decades a lot of effort has been expended to understand the mechanisms involved in the leaching system and the key parameters that limit the leaching kinetics, except for very few reported results [46, 109, 110], the majority are limited to temperatures below 90°C. According to recent reviews of high temperature and high pressure (HTHP) electrochemical studies [111, 112], although in recent years significant developments have been made, HTHP electrochemistry remains a relatively unexplored field of research and the relative lack of experimental data is ascribed to the various technical obstacles. As to HTHP mineral electrochemistry, very few reports are available [113]. In the following sections, the reduction kinetics of ferric on chalcopyrite will be discussed at 110°C and 150°C. Figure 7-5 presents the CPC and corresponding OCP results at 110°C. It can be observed that the OCP values are relatively stable and no obvious deviation was found under each nominal Fe3+/Fe2+ ratio. A very similar tendency in the polarization plots for different nominal Fe3+/Fe2+ ratios was observed: there is a relatively smaller slope existing in the Tafel region, despite the fact that the OCP values of the 100:1 and 1000:1 nominal Fe3+/Fe2+ ratios are a little larger than those of the 10:1 and 1:1 nominal Fe3+/Fe2+ ratios. As the current increases, the current becomes independent of the applied potential, indicating that the reaction becomes mass transfer  137  controlled. The reduction reaches a limiting current density at approximately E = 230 mV versus SHE.               138  0 100 200 300 400 500 600 700 8000.560.570.580.590.600.610.620.630.640.650.66  OCP vs SHE (V)Time (S) Fe3+/Fe2+=1:1 Fe3+/Fe2+=10:1 Fe3+/Fe2+=100:1 Fe3+/Fe2+=1000:1 -5 -4 -3 -2-0.2-0.10.00.10.20.30.40.50.60.7 E vs SHE (V)Log i (A/cm2) Fe3+/Fe2+=1:1 Fe3+/Fe2+=10:1 Fe3+/Fe2+=100:1 Fe3+/Fe2+=1000:1 Figure 7-5 Cathodic potentiodynamic polarization curves and corresponding OCP in deaerated aqueous Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg on chalcopyrite with different nominal Fe3+/Fe2+ ratios at 110°C.  139   In Table 7-5, it is worth noting that a continuous drop in the calculated real Fe3+/Fe2+ ratio is found at 110°C, compared with that obtained at or below 90°C under the same nominal Fe3+/Fe2+ ratio. In addition, it may be mentioned that the Tafel slopes of the polarization plots under different nominal Fe3+/Fe2+ ratios are very similar and relatively smaller than those obtained at lower temperatures. The cathodic Tafel slopes for ferric reduction varied in the range of 0.117-0.129 V/decade, which can subsequently be used to calculate α with values in the range of 0.59-0.65.  Table 7-5 CPC results at 110°C. Fe3+/Fe2+ (Nominal) Fe3+/Fe2+ (Real) Tafel Slope  (V/decade) Transfer  Coefficient EM EC EM (V) iM (A/cm2) EC (V) i0 (A/cm2) 1:1 2.73E-03 0.120 0.64 0.5786 1.16E-04 0.6771 1.74E-05 10:1 0.05 0.129 0.59 0.5829 1.92E-04 0.7742 6.31E-06 100:1 0.52 0.119 0.64 0.6400 3.56E-05 0.8523 5.91E-07 1000:1 5.26 0.117 0.65 0.6510 1.58E-05 0.9285 6.74E-08   Under the same nominal Fe3+/Fe2+ ratio, the measured EM is lower than that obtained at lower temperatures, while the iM is larger due to the increased kinetics at elevated temperatures. Similarly, with the nominal Fe3+/Fe2+ ratios of 1:1 and 10:1, the i0 at 110°C also begins to increase, in spite of the fact that larger reversible potentials of the Fe3+/Fe2+ couple and smaller Tafel slopes are obtained in contrast to those measured at 70°C. However, at the 100:1 and 1000:1 ratios, a drop in the i0 was found again, which probably results from the relatively higher  140  reversible potentials of the Fe3+/Fe2+ couple under such high temperatures and nominal Fe3+/Fe2+ ratios. 7.2.6 CPC Results at 150°C Figure 7-6 shows the CPC and corresponding OCP measurement results at 150°C. Under each nominal Fe3+/Fe2+ ratio, it appears that there is a very slight variation in the OCP values. Due to the fast kinetics at such a temperature, the time for OCP measurements was shorter compared to that of the previous experiments in order to avoid significant changes on the electrode surface associated with long term exposure to the electrolyte. As shown in Figure 7-7, at 150°C, about 1-hour of immersion of the chalcopyrite electrode in the electrolyte will result in significant corrosion on the surface. The pits are substantially enlarged compared to those formed at 25°C. Hence, for the tests at 150°C, the time for OCP test was shortened to about 7 minutes. The overall shape of the polarization curves is generally the same for different nominal Fe3+/Fe2+ ratios, and these polarization plots exhibit linear Tafel regions. The reduction reaches a limiting current density at approximately E = 250 mV versus SHE.   141  0 100 200 300 400 5000.600.610.620.630.640.650.660.670.680.69  OCP vs SHE (V)Time (S) Fe3+/Fe2+=1:1 Fe3+/Fe2+=10:1 Fe3+/Fe2+=100:1 Fe3+/Fe2+=1000:1 -4 -3 -2 -1-0.2-0.0.00.10.20.30.40.50.60.7 E vs SHE (V)Log i (A/cm2) Fe3+/Fe2+=1:1 Fe3+/Fe2+=10:1 Fe3+/Fe2+=100:1 Fe3+/Fe2+=1000:1 Figure 7-6 Cathodic potentiodynamic polarization curves and corresponding OCP in deaerated aqueous Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg on chalcopyrite with different nominal Fe3+/Fe2+ ratios at 150°C.  142    Figure 7-7 OM analysis results of the prepared chalcopyrite electrode surface after about 1 hour exposure to the electrolyte with nominal Fe3+/Fe2+ ratio of 1:1 at 150°C.  In Table 7-6, it should be noted that a similar trend to that observed from 25 to 110°C was found at 150°C in that the calculated real Fe3+/Fe2+ ratio is much smaller than the nominal Fe3+/Fe2+ ratio. For any given nominal Fe3+/Fe2+ ratio, the smallest value of the calculated real Fe3+/Fe2+ ratio was observed at 150°C, due to ion association. The Tafel slopes under different nominal Fe3+/Fe2+ ratios are in the range of 0.114-0.136 V/decade. The calculated value of α ranged from 0.62 to 0.74.    143   Table 7-6 CPC results at 150°C. Fe3+/Fe2+ (Nominal) Fe3+/Fe2+ (Real) Tafel Slope  (V/decade) Transfer  Coefficient EM EC EM (V) iM (A/cm2) EC (V) i0 (A/cm2) 1:1 1.22E-03 0.114 0.74 0.6226 1.08E-04 0.6748 3.76E-05 10:1 0.02 0.136 0.62 0.6398 1.99E-04 0.7855 1.68E-05 100:1 0.26 0.136 0.62 0.6368 2.23E-04 0.8718 4.14E-06 1000:1 2.60 0.126 0.67 0.6526 1.32E-04 0.9560 5.07E-07   Under all of the nominal Fe3+/Fe2+ ratios, the measured EM is relatively stable. At 150°C, as expected, the highest iM values are obtained and are on the order of 10-4 A/cm2 due to the fast kinetics achieved at this temperature. In addition, it should be emphasized that the largest values of i0 were also observed with the nominal Fe3+/Fe2+ ratios of 1:1 and 100:1, despite the fact that largest reversible potentials of the Fe3+/Fe2+ couple and relatively smaller Tafel slopes are obtained in comparison to lower temperatures. At the 1000:1 ratio, the value of i0 is of the same order of magnitude as that obtained at 25°C, 70°C and 90°C. Given the fact that the reversible potentials at 150°C are so high and that the Tafel slopes are relatively invariant with temperature, the similarity in the values of i0 indicates that the increased kinetics at 150°C play a dominant role in determining i0. Based on the above analyses, it is interesting to note that at each temperature the exchange current densities increase with an increasing amount of ferrous (i.e. when decreasing the nominal Fe3+/Fe2+ ratios). In addition, a substantial increase in iM from the order of 10-6 A/cm2 to the  144  order of 10-4 A/cm2 is found when increasing the temperature from 25 to 150°C, i.e. an increase of approximately two orders of magnitude. 7.2.7 Comparison with i0 of the Fe3+/Fe2+ Couple on Other Electrodes and the Application of i0 to Calculate the Rate Constants at 25°C-150°C As mentioned in the Introduction, after obtaining the reduction kinetics of ferric on chalcopyrite at different temperatures, what particularly interests us is the temperature dependence of the exchange current density, transfer coefficient and rate constant. In this and the following section, this temperature dependence is discussed. 7.2.7.1 Comparison with i0 of the Fe3+/Fe2+ Couple on Other Electrodes   The obtained exchange current densities for the Fe3+/Fe2+ couple on chalcopyrite were compared with those obtained on other electrodes [103-105]. All of the results are presented in Table 7-7. The reaction rate of the Fe3+/Fe2+ couple is quite fast on the surface of oxide free metals such as platinum and was reported to have an exchange current density of 1.5x10-2 A/cm2. A distinct decrease by several orders of magnitude in the exchange current densities of the Fe3+/Fe2+ couple on Ni, Fe, Ti, Fe-Cr alloy and 304 stainless steel (with passive oxide films) was observed and the values are on the order of 10-5-10-8 A/cm2. Such small exchange current densities found for the Fe3+/Fe2+ reaction on passive electrodes are probably a consequence of the semiconductor characteristics of the passive film [103]. In the case of chalcopyrite, the results are consistent with the exchange current densities of the Fe3+/Fe2+ couple on the above-noted passive electrodes. The exchange current densities are substantially less than those on platinum, on the order of 10-7-10-5 A/cm2 in a wide range of 25°C-150°C, almost certainly due to the formation of the passive film. In general, at the same nominal Fe3+/Fe2+ ratio, increasing the  145  temperature from 25 to 150°C was observed to give rise to an increase in i0, especially when a larger amount of free ferrous existed in the solution.  Table 7-7 Comparison of exchange current densities Fe3+/Fe2+ couple on various electrodes. Electrode Solution Ferric Ferrous Temperature i0 (A/cm2) Pt H2SO4 0.05M 0.05M 25℃ 1.5x10-2 Fe H2SO4+Na2SO4 0.30M 0.03M 40℃ 1x10-5 Ni H2SO4+MgSO4 0.05M 0.05M 30℃ 7.5x10-5 Ti H2SO4+ MgSO4 0.05M 0.05M 20℃ 2.6x10-7 Fe-Cr Alloy H2SO4+ MgSO4 0.05M 0.05M 30℃ 1x10-6 304 Stainless Steel Ferric-ferrous Sulfate 0.356M 2.52x10-3M 25℃ 4.5x10-8 Chalcopyrite H2SO4 0.179M 1.79x10-4-0.179M 25℃ 1.46x10-7-2.43x10-6 Chalcopyrite H2SO4 0.179M 1.79x10-4-0.179M 70℃ 7.13x10-7-1.72x10-5 Chalcopyrite H2SO4 0.179M 1.79x10-4-0.179M 90℃ 1.19x10-6-1.11x10-5 Chalcopyrite H2SO4 0.179M 1.79x10-4-0.179M 110℃ 6.74x10-8-1.74x10-5 Chalcopyrite H2SO4 0.179M 1.79x10-4-0.179M 150℃ 5.07x10-7-3.76x10-5  7.2.7.2 Calculation of Rate Constants Based on the obtained exchange current densities, the rate constant for ferric reduction, kc, was calculated with the following equation [24]:    C0 C C Ferricexp( )nFEi z Fk C RT                                         (7-2)  146  where i0 is the exchange current density (A/cm2), ZC is the number of electrons involved in the cathodic reaction, F is Faraday constant (C/mol), kc is the rate constant of ferric reduction (cm/s), CFerric is the bulk concentration of ferric ion in the solution (mol/L), α is the transfer coefficient, n is the number of electrons transferred in the rate determining step for the cathodic reaction, EC is the reversible potential of the Fe3+/Fe2+ couple, R is the universal gas constant (J/mol•K) and T is the temperature (K). The bulk concentrations of free Fe3+ in aqueous Fe(II)-Fe(III)-H2SO4 solutions in the range of 25-150°C are shown in Table 7-1 and used to calculate the rate constant in the present study. Please note that for the dilute aqueous solutions used in the present study, the C (molarity mol/L) can be approximately calculated by using the m (molality mol/kg) multiplied by the corresponding solution density. Because of the unavailability of the data on the density of the solutions in this work over such a large range of temperatures, and considering the fact that the water density does not vary significantly under the temperatures of interest (the solution density should be a little higher than that of pure water), for the sake of simplicity and maintaining internal consistency the author assumed a solution density of unity in the following calculations. All of the calculated rate constants by the above equation from the previous kinetic data are demonstrated in Figure 7-8a. Each point represents an average of the values under four different Fe3+/Fe2+ ratios. According to Eq. (7-2), the calculated average rate constants are 0.049 cm/s at 25°C, and 2.80 cm/s at 70°C for nominal Fe3+/Fe2+ ratios ranging from 1:1 to 1000:1, as shown in Figure 7-8a. A further increase in temperature leads to larger rate constants, with the largest value (almost 900 cm/s) obtained at 150°C. It is evident that the kinetics of the ferric reduction reaction on chalcopyrite increase as the temperature is enhanced.   147  30 50 70 90 110 130 1500.11101001000   1Calculated Rate Constants (Kc, cm/s)Temperature (°C)(a) 2. 2.5 2.7 2.9 3.1 3.3 3.5-4-202468(b)   Real RegressLn (Kc)1000/T(K) Figure 7-8 (a) Calculated rate constants (kC) of ferric ion reduction on chalcopyrite as a function of temperature in the range of 25-150°C according to Equation 7-2; (b) ln kC versus 1/T, displays the linear Arrhenius behavior.  148   To further understand the temperature-dependent behavior of the rate constants, the natural logarithm of kc as a function of the inverse of absolute temperature (1/T), ln kc versus 1/T, as seen in Figure 7-8b, was plotted on the basis of the Arrhenius equation [119]: CaERTk Ae                                                                         (7-3) In Eq. (7-3), kc is the rate constant of ferric reduction (cm/s), A is a frequency factor, Ea is the activation energy, R is the gas constant and T is the absolute temperature. If the rate constant follows the Arrhenius behavior given by Eq. (7-3), the plot of ln kc versus 1/T should be linear. Results in Figure 7-8b indicate that the temperature-dependent behavior of the rate constant is consistent with Arrhenius behavior. The best fit was provided by the following relationship: C1ln 10245 31.349(K)k T                                                               (7-4) The correlation coefficient was 0.9887. The fit to the Arrhenius equation gives values for the parameters A and Ea. The activation energy for the ferric reduction reaction was calculated to be 85 ± 1 kJ mol−1 in the temperature range of 25-150°C. The magnitude of this activation energy indicates that the ferric reduction reaction on chalcopyrite in the region of potentials in which chalcopyrite dissolves is under activation control (kinetic control). This is in agreement with the findings previously indicated by the measured cathodic polarization plots. 7.2.8 Temperature Dependence of Tafel Slopes and Transfer Coefficients for Ferric Ion Reduction As indicated in Tables 7-2 to 7-6, it seems that the Tafel slope b is essentially independent of temperature over the range of 25 to 150°C, and consequently the transfer coefficient  149  calculated with Eq. (7-1) increases with temperature rather than being constant. In this section, a more detailed analysis of the effect of temperature on the Tafel slope and transfer coefficient in the Fe(II)-Fe(III)-H2SO4 solutions under different nominal Fe3+/Fe2+ ratios will be discussed and presented. All of the obtained results are presented in Figure 7-9 and Figure 7-10. 7.2.8.1 Variation of Tafel Slopes with Temperature Traditionally, in Eq. (7-1), the transfer coefficient α, is a function of the symmetry factor β and the stoichiometric number ν. For a simple one-electron one-step reaction, α = β. In the classical treatment of electrode kinetics the symmetry factor β (or α for more complex multiple-step reactions) is considered to be independent of both temperature and potential. Therefore, for a given rate-determining step, the Tafel slope is expected to be directly proportional to temperature. However, according to experimental studies in various systems, the temperature dependence of the Tafel slopes can deviate from the direct proportionality of the classical Eq. (7-1) if α is a constant, and hence a temperature-dependent symmetry factor has been suggested. The systems that deviate from the constant α were reviewed by Conway [156], and a detailed analysis related to this subject is found in the published report of Bockris and Gochev [157]. The most widely studied systems are the hydrogen evolution reaction [158, 159] and the oxygen evolution and reduction reaction [114, 160]. Conway suggested that a linear relation exists between the Tafel slope and temperature rather than a direct proportionality [158]. He developed the following empirical formula:   = RTb CF                                                       (7-5) where b is the Tafel slope (V/decade), F is the Faraday constant (C/mol), β is the symmetry factor, C is a constant, R is the universal gas constant (J/mol•K) and T is the temperature (K).  150  An alternative relation between the Tafel slope and symmetry factor was also suggested as follows:   = RTb 'F         = RT' RT FC                                             (7-6) where β′, an apparent symmetry factor, should be temperature-dependent.    In limiting cases, b is almost independent of T, and therefore β should be linearly temperature dependent (β = γT + δ). For such cases, the following form was proposed:   = ( )RTb T F                                              (7-7) where γ and δ are constants.  The measured Tafel slopes observed as a function of temperature in the Fe(II)-Fe(III)-H2SO4 solutions under different nominal Fe3+/Fe2+ ratios is given in Figure 7-9. The dashed line in this figure corresponds to the conventionally expected b-T dependence, i.e., if the apparent transfer coefficient, α, was independent of temperature and equal to 0.5. Although the conditions for the experiments vary widely, it seems that the measured Tafel slopes are relatively independent of temperature and solution composition, and remain within the range of 0.114-0.165 V/decade. From 90 to 150°C the Tafel slopes are in general a little lower than those observed at 25°C and 70°C. This phenomenon of lower Tafel slopes at higher temperature requires further study for clarification, but is probably the result of simultaneous changes in the fundamental nature on the surface of CuFeS2 and in the symmetry of the potential energy barrier for the rate-determining step at elevated temperatures. Please note that all of the Tafel plots were linear over at least one order of magnitude of current density.  151  30 50 70 90 110 130 1500.080.100.120.140.160.180.200.220.24 Measured Tafel Slopes with Fe3+/Fe2+ (Nominal) 1:1 Measured Tafel Slopes with Fe3+/Fe2+ (Nominal) 10:1 Measured Tafel Slopes with Fe3+/Fe2+ (Nominal) 100:1 Measured Tafel Slopes with Fe3+/Fe2+ (Nominal) 1000:1 Calculated Conventional Tafel Solpes (Based on  = 0.5)  Measured and Calculated Tafel Slopes (V/decade)Temperature (°C) Figure 7-9 Comparison of the measured Tafel slopes and the calculated conventional theoretical values (based on α=0.5) in deaerated aqueous Fe(II)-Fe(III)-H2SO4 solutions under different nominal Fe3+/Fe2+ ratios in the temperature range of 25°C-150°C.  In fact, based on the conventional theoretical α value of 0.5, according to Eq. (7-1), it should be expected that the calculated Tafel slopes increase linearly with temperature. However, as clearly demonstrated in Figure 7-9, the difference between the measured Tafel slope and that predicted from Eq. (7-1) is not small, and thus this rule does not apply to the results in the present study. A detailed study is required to explain this phenomenon, but this is probably caused by the result of changes in the fundamental nature of the surface of CuFeS2 and/or in the symmetry of the potential energy barrier for the rate-determining step at different temperatures.   152  Therefore, from the above analysis, it is obvious that contrary to the view commonly held, the Tafel slopes do not follow the conventional temperature dependence. 7.2.8.2 Variation of Transfer Coefficients with Temperature The apparent transfer coefficients in the present work were calculated from the measured Tafel slopes by Eq. (7-1). A comparison of transfer coefficients between the values calculated in this work and the conventional assumption (α=0.5) in the temperature range of 25°C-150°C is plotted in Figure 7-10. Please recall that in the present study α does not have a single value, and the conventional assumption of α=0.5 is only employed for comparison with the values obtained in this work. At each temperature, the obtained transfer coefficient is an average of the values under four different nominal Fe3+/Fe2+ ratios. It can be clearly observed that from 25 to 150°C, the transfer coefficient increases with temperature rather than being independent of temperature. Given the variation of α with temperature, regression was carried out and an expression was developed as follows: 0.0025 (K) 0.3941T                                                    (7-8) The corresponding correlation coefficient was 0.923. The obtained value of the temperature coefficient of α (∂α/∂T=2.5x10-3 K-1) is in reasonable agreement with that (approximately 1.5x10-3 K-1) needed to account for a b that is independent of temperature [157].   153  30 50 70 90 110 130 1500.20.30.40.50.60.70.80.91.0  Calculated and Conventional Transfer CoefficientsTemperature (°C) Calculated  from the Measured Tafel Slopes Regressed Plot of the Calculated  versus Temperature Conventional  = 0.5 Figure 7-10 Comparison of the calculated transfer coefficients based on the measured Tafel slopes in this work and the conventional value (α=0.5) under different nominal Fe3+/Fe2+ ratios in the temperature range of 25°C-150°C.  From the above equation, it seems that over the temperature range investigated, the transfer coefficient for ferric reduction on chalcopyrite increases linearly with the absolute temperature rather than being a constant. A larger value of α can result in a lower free energy of activation. This result is consistent with the previous conclusion that faster kinetics for ferric reduction on chalcopyrite could be achieved at elevated temperatures, as mentioned in Section 7.2.7.2. The above-noted unexpected temperature independence for the Tafel slope, as well as the anomalous temperature-dependent transfer coefficient, are not unique to the ferric reduction  154  reaction on chalcopyrite and have been observed previously in other systems [114, 158-162]. These studies were carried out over a wide range of temperatures. For example, Clouser et al [114] investigated the temperature dependence of the Tafel slope and apparent transfer coefficient for oxygen reduction on platinum in H3PO4. The observed Tafel slopes were essentially independent of temperature over the 25-250°C range, and were quite different from the values expected from theory. The apparent transfer coefficient for oxygen reduction has been found to be approximately proportional to temperature rather than independent of temperature. A similar anomalous temperature dependence of Tafel slopes and transfer coefficients was also observed for oxygen evolution and reduction on a Pt electrode in dilute aqueous H2SO4 and HClO4 solutions in the temperature range of 20-325°C [160].  Various possible factors which may give rise to such behavior and phenomena have been proposed and discussed, including potential dependent adsorption of solution phase species, restructuring of the solution in the compact layer, proton and electron tunneling, a shift in rate-determining step, changes in the symmetry of the potential energy barrier, penetration of the electric field into the electrode phase, insufficient correction for ohmic losses, and impurity effects [114, 157, 158]. Further measurements over a wide range of conditions will be required to confirm the temperature dependency of α and to further study the reason for these observations. 7.3 Summary The kinetics of ferric reduction on chalcopyrite were systematically investigated by electrochemical measurements in aqueous H2SO4-Fe2(SO4)3-FeSO4-H2O solution from 25 to 150°C. Since ferric and ferrous ions readily complex in acidic iron sulfate solution to form cations and anions, as well as neutral species, the concentrations of free ferric and ferrous ions were first obtained as a function of electrolyte composition and temperature by a speciation  155  model developed previously. This information was then employed to analyze the obtained experimental data, by invoking the Nernst equation and other basic electrochemical kinetic equations in order to investigate the electrochemical reduction kinetics of the Fe3+/Fe2+ couple on chalcopyrite as well as mechanistic analysis in industrial chalcopyrite leaching processes.  With potentiodynamic polarization, the temperature dependence of the exchange current density, transfer coefficient and rate constant were determined and discussed. Results reveal that, from 25 to 150°C, all of the polarization plots exhibit reproducible well-defined linear Tafel regions. The exchange current densities of the Fe3+/Fe2+ couple obtained by extrapolating the cathodic linear Tafel line to the reversible potential are on the order of 10-7-10-5 A/cm2 in the range of 25-150°C, substantially less than that on platinum due to the formation of a passive film. In general, at the same nominal Fe3+/Fe2+ ratio, increasing the temperature from 25 to 150°C was observed to give rise to an increase in i0, especially when a larger amount of free ferrous existed in the solution. In addition, at each temperature, i0 increases by increasing the concentration of ferrous in the solution.  Based on the obtained exchange current densities, the rate constant for ferric reduction was calculated, and its values increase with temperature from 0.049 cm/s at 25°C to almost 900 cm/s at 150°C. Further analysis indicates that the rate constant follows Arrhenius behavior and the activation energy for the ferric ion reduction reaction was calculated to be 85 ± 1 kJ mol−1 in the temperature range of 25-150°C. The temperature increase from 25 to 150°C also caused a substantial increase in iM, from the order of 10-6 A/cm2 at 25°C to the order of 10-4 A/cm2 at 150°C. Analysis of the measured Tafel slopes as a function of temperature in the Fe(II)-Fe(III)-H2SO4 solutions under different nominal Fe3+/Fe2+ ratios indicates that the Tafel slopes are  156  essentially independent of temperature and the solution composition over the range of 25 to 150°C, and remain within the range of 0.114-0.165 V/decade. Consequently, the apparent transfer coefficients calculated from the measured Tafel slopes, increase linearly with respect to temperature rather than being a constant from 25 to 150°C. The obtained value of the temperature coefficient of α (2.5x10-3 K-1) is in reasonable agreement with that (in the region of 1.5x10-3 K-1) needed to account for a b independent of temperature. The unexpected temperature independence for the Tafel slope, as well as the anomalous temperature-dependent transfer coefficient, are not unique to the ferric reduction reaction on chalcopyrite, and have been observed previously in various systems.             157  8 Influence of Ferric Ion Reduction Reaction on Chalcopyrite Leaching Behavior from 25°C to 150°C  8.1 Introduction The mixed potential theory involved two half-cell reactions provides a unique advantage of having a greater insight into the mechanism of the dissolution process. In the present Chapter, based on the previously obtained reversible potentials of the Fe3+/Fe2+ couple and the mixed potentials measured under oxidizing conditions, as well as the calculated reversible potentials of possible anodic reactions, the mechanism involved in the chalcopyrite leaching system will be analyzed by mixed potential theory, to obtain detailed information about the electrochemical reactions involved, and hence determine to what extent the cathodic ferric ion reduction reaction can affect the overall leaching process.  The concept of mixed potential (EM) has been widely used to explain the kinetics observed in hydrometallurgical processes [23, 24, 46-50, 163]. Only the mixed potential measured on a mineral surface is representative of the dissolution process. The difference between the mixed potential and the relevant reversible potential, the over-potential (ηC and ηA), represents the driving force for each half-reaction. In the present study, OCP is a mixed potential between the reversible potential of the cathodic reduction of ferric (EC) and the reversible potential of the anodic oxidation of chalcopyrite (EA). A comparison of the calculated reversible potentials and measured mixed potentials was used to analyze the control scenario. The mixed potential of a chalcopyrite electrode in a leaching environment may be used as an indicator of the control mechanism of the leaching reaction. Figure 8-1 is a schematic diagram of the mixed potential theory for the oxidative dissolution of chalcopyrite by ferric ion. The present section aims at a  158  more detailed analysis of the observed trend of the involved potentials versus temperature in the leaching process.   Figure 8-1 Schematic diagram of the mixed potential theory for the oxidative dissolution of chalcopyrite by ferric ion.  8.2 Results and Discussion 8.2.1 Calculated EC and Measured EM Potentials The calculated EC and measured EM potentials in the Fe(II)-Fe(III)-H2SO4 solutions under different nominal Fe3+/Fe2+ ratios in the temperature range of 25–150°C are given in Tables 7-2  159  to 7-6. In order to employ mixed potential theory, however, the reversible potential of the anodic oxidation reaction for chalcopyrite (EA) is also required and this will be calculated and provided as follows.  8.2.2 Calculation of Reversible Potential of Anodic Oxidation Reactions of Chalcopyrite from 25°C to 150°C   In the past decades, although great international efforts have been devoted to understanding the mechanisms of chalcopyrite leaching, no unanimous theory is available to account for its slow kinetics in most leaching environments. Nevertheless, there is consensus that the formation of a passivating layer on the chalcopyrite surface slows the dissolution kinetics. These studies, and the proposed possible anodic oxidation reactions, were summarized and reviewed by several authors [155, 164-166].  Relying on the limited availability of the relevant thermodynamic data for the products generated by the anodic oxidation reaction, herein five typically cited and possible anodic oxidation reactions for chalcopyrite have been considered and their reversible potentials were calculated. Table 8-1 lists the selected possible anodic oxidation reactions for chalcopyrite in aqueous Fe(II)-Fe(III)-H2SO4 solutions [18, 54, 165]. Please note that, for the oxidation of chalcopyrite in acidic iron sulfate solution, Reaction 1 and Reaction 2 are the well-accepted forms, and it is frequently assumed that Reaction 1 is the predominant one. To calculate the reversible potential for these anodic oxidation reactions (EA), the standard electrode potentials of the anodic oxidation reaction of chalcopyrite (EA°), as well as the single ion activity for ionic species, were first obtained. When calculating EA°, the standard Gibbs free energies of ionic species at high temperatures were estimated by the above-mentioned Lewis formulation of the Criss-Cobble  160  correspondence principle based on thermodynamic data available at room temperature. For solid and liquid species, this can be achieved with knowledge of the standard Gibbs free energy of formation at 298.15 K and the heat capacity. The heat capacity parameters (Kelley equation coefficients) of those species were taken from HSC 7.1 [143], and ΔG° at higher temperature were calculated by the Kelley equation. The thermodynamic data at 298.15 K (ΔG° and S°) were taken from the literature [129, 166]. All of the thermodynamic data used in the calculation are shown in Table 8-2, and data of H+, SO42-, Fe2+ and H2O were already shown in Chapter 5.  Table 8-1 Calculated standard electrode potentials for the possible anodic oxidation reactions of chalcopyrite in aqueous Fe(II)-Fe(III)-H2SO4 solutions in the range of 25-150°C. Anodic Oxidation Reactions of Chalcopyrite EA° (V) 25°C 70°C 90°C 110°C 150°C CuFeS2 → Cu2+ + Fe2+ + 2S0 + 4e                   (1) 0.439 0.467 0.476 0.484 0.489 CuFeS2 + 8H2O → Cu2+ + Fe2+ + 16H+ + 2SO42- + 16e  (2) 0.374 0.397 0.405 0.413 0.425 CuFeS2 → CuS + Fe2+ + S0 + 2e                    (3) 0.263 0.290 0.299 0.307 0.313 CuFeS2 → 0.75CuS + 0.25Cu2+ + Fe2+ + 1.25S0 + 2.5e  (4) 0.333 0.361 0.370 0.378 0.383 CuFeS2 → 0.5Cu2S + Fe2+ + 1.5S0 + 2e              (5) 0.311 0.337 0.345 0.352 0.352      161  Table 8-2 Thermodynamic data at 25°C and Kelley equation coefficients of the solids involved in the anodic chalcopyrite oxidation reactions in the range of 25-150°C. Species ΔG° (kJ/mol) S°            (J/mol K) Cp (J/mol K) A B C D Cu2+ 65.7 -97.2     S (100-368.3 K) 0.00 31.8 7.835 79.793 -0.207 -97.893 S (368.3-388.36 K)   968.639 -3355.340 -223.772 3368.169 S (388.36-428.15 K)   -8691.858 28083.985 2467.293 -25321.119 CuFeS2 (298.15-830 K) -195.1 124.9 86.985 53.555 -5.607 0 CuS (298.15-1000 K) -53.2 66.96 43.671 20.136 -2.102 -0.005 Cu2S (298.15-376.00 K) -87.6 118.8 53.438 76.459 -0.117 2.456 Cu2S (376.00-717.00 K)   112.140 -30.973 -0.046 0.147       a. The heat capacity parameters (Kelley equation coefficients) of S, CuFeS2, CuS and Cu2S used to           calculate the equilibrium constants were taken from HSC 7.1 .       b. Kelley equation: Cp(T) = A + B*10-3*T + C*105*T-2 + D*10-6*T2 (J/mol*K).  All of the calculated EA° of the five reactions at different temperatures are shown in Table 8-1. EA° of the five reactions increases with temperature. Interestingly, the calculated EA° for Reaction 1 (100% S0 formation) is larger than that of Reaction 2 (100% SO42- formation), and hence Reaction 2 is thermodynamically more favorable. As to the single ion activities for Fe2+, H+ and SO42- involved in the present study, they were obtained by the above-mentioned speciation model under different conditions. When  162  involving the activity of Cu2+, a value of aCu2+ = 10-5 was assumed. This value is reasonable because at the very beginning of leaching (on the scale of the measurement time used herein), the activity of Cu2+ produced by the oxidation of CuFeS2 should be very small. aCu2+ = 10-3 was also used to compare the calculated reversible potentials. Cu2+ is not included in Reaction 3 and Reaction 5, so their potentials are not affected by the change of Cu2+ activity. For Reaction 1, changing the Cu2+ activity from 10-5 to 10-3 results in an increase of the calculated reversible potential of no more than 45 mV (typically within the range of 30-40mV); for Reaction 2 and Reaction 4, such an increase only leads to an increase in the calculated potentials of no more than 17 mV. Actually, even increasing the Cu2+ activity from 10-3 to 1, the reversible potentials for Reaction 1 (smaller than 60 mV), Reaction 2 and Reaction 4 (smaller than 25 mV) under all of the solution conditions in the present study did not increase to any appreciable extent. Therefore, it appears that the Cu2+ activity does not exert an important influence on EA, and the above assumption employed to estimate the reversible potentials of anodic oxidation reactions is acceptable and applicable.  By using the above methods, EA of the five possible anodic oxidation reactions of chalcopyrite were calculated. A detailed discussion on the obtained results will be given in the following section. 8.2.3 Analysis of Leaching Process by Mixed Potential Theory Figure 8-2 and Figure 8-3 present all of the measured mixed potentials and calculated theoretical cathodic and anodic reversible potentials in the Fe(II)-Fe(III)-H2SO4 solutions for the present study over the temperature range of 25°C-150°C under different nominal Fe3+/Fe2+ ratios. It is observed that the measured mixed potentials lie between the cathodic and anodic reversible potentials. As shown previously, even though there is Fe2+ being produced by the reduction of  163  Fe3+ and oxidation of CuFeS2, the concentration change is not high enough to exert a significant influence on the mixed potential during the measurement time of the experiment. Typically, it is important to observe that all of the measured mixed potentials are generally within the range of 0.64±0.06 V under all of the conditions employed in the present study. At each temperature, in general, there is an obvious drop in the measured EM when a large amount of ferrous exists in the electrolyte, which agrees with the previous finding at 90°C reported by Jones [46].         164  30 50 70 90 110 130 1500.20.30.40.50.60.7  Mixed and Reversible Potentials (V)Temperature (°C) Ec Em R1-0.001 R1-0.00001 R3 R5 R2-0.001 R2-0.00001 R4-0.001 R4-0.00001(1:1)  Figure 8-2 Measured mixed potentials and calculated theoretical cathodic and anodic reversible potentials in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg in the temperature range of 25°C-150°C with nominal Fe3+/Fe2+ ratio of 1:1. (cathodic reversible potential EC ■; mixed potential EM ▼; reversible potential of anodic reaction 1 assuming aCu2+ = 10-3 ▲; reversible potential of anodic reaction 1 assuming aCu2+ = 10-5 △; reversible potential of anodic reaction 3 ◆; reversible potential of anodic reaction 5 ◄; reversible potential of anodic reaction 2 assuming aCu2+ = 10-3 ●; reversible potential of anodic reaction 2 assuming aCu2+ = 10-5 ○; reversible potential of anodic reaction 4 assuming aCu2+ = 10-3 ★; reversible potential of anodic reaction 4 assuming aCu2+ = 10-5 ☆.)   165  30 50 70 90 110 130 1500.10.20.30.40.50.60.70.80.9(a 10:1)  Mixed and Reversible Potentials (V)Temperature (°C) Ec Em R1-0.001 R1-0.00001 R3 R5 R2-0.001 R2-0.00001 R4-0.001 R4-0.00001 Figure 8-3 Measured mixed potentials and calculated theoretical cathodic and anodic reversible potentials in the Fe(II)-Fe(III)-H2SO4 solutions at [H2SO4] = 0.31 mol/kg and [Fe3+]total = 0.18 mol/kg in the temperature range of 25°C-150°C under higher nominal Fe3+/Fe2+ ratios: (a) 10:1; (b) 100:1; (c) 1000:1. The symbols used in these Figures are the same as those shown in Figure 8-2.   166  30 50 70 90 110 130 1500.10.20.30.40.50.60.70.80.91.0(b 100:1)  Mixed and Reversible Potentials (V)Temperature (°C) Ec Em R1-0.001 R1-0.00001 R3 R5 R2-0.001 R2-0.00001 R4-0.001 R4-0.00001  00.10.20.30.40.60.70.80.91.01(c 10 : )  Mixed and Reversible Potentials (V)   - . - .   - . - . - . - . Figure 8-3 Continued.  167   As discussed previously, the reaction rate of the Fe3+/Fe2+ couple is quite fast on the surface of platinum, and the reaction can be considered reversible or highly quasi-reversible. However, the measured EM of chalcopyrite indicates that, in acidic iron sulfate solutions, the Fe3+/Fe2+ couple is much less reversible on the chalcopyrite surface, especially at higher nominal Fe3+/Fe2+ ratio and temperature (in such a case the cathodic over-potential ηC is so large that the back reaction involving Fe2+ is negligible). As to the anodic dissolution reaction of chalcopyrite, the measured EM during ferric sulfate leaching is typically 200-300 mV (or even lager) higher than those calculated EA, and therefore there appears to be a significant degree of anodic polarization. These results are also in agreement with those published by Jones [46], who calculated the Nernst potentials of the anodic and cathodic reactions with some simple assumptions (for example without considering ferrous or ferric complexes in sulfate solutions) and examined the leaching of chalcopyrite in ferric sulfate solution by mixed potential theory at 90°C.  It should be noted that in the region of the mixed potential (at mixed potential the rate of the oxidation reaction is balanced by that of the reduction reaction), the rates of the reverse processes can be ignored. As reported by Nicol [163], this is generally valid for the oxidation of minerals which tend to be highly irreversible systems, but is not always valid for the oxidant (as with iron (III) in his paper). This concept is fully justified by the above analysis of the chalcopyrite leaching in acidic iron sulfate solution. In the present study, EM is approximately equal to EC only when the nominal Fe3+/Fe2+ ratio is 1:1 (the solution contains appreciable amounts of ferrous) and the temperature is low (25°C). This means that, at the mixed potential, the contribution of the anodic current due to the oxidation of chalcopyrite is small, compared to  168  that of the oxidation of ferrous. The mixed potential in such a case is therefore determined by the characteristics of the Fe3+/Fe2+ couple, and not by the anodic characteristics of chalcopyrite (so-called Type III situation from Nicol’s paper). However, when further increasing the nominal Fe3+/Fe2+ ratio and temperature, the contribution of the partial anodic current from the oxidation of ferrous is almost negligible and hence the EM is much lower than EC. Thus, in such a case, only the anodic characteristics of chalcopyrite and the cathodic characteristics of Fe3+ are significant in the region of the mixed potential (so-called Type I situation from Nicol’s paper). It should be mentioned that in Nicol’s paper, an intermediate situation (labeled Type II) is the one for which all of the three half-reactions must be taken into account. From the above results, it appears that under the investigated conditions, Type I leaching plays a more common role in the oxidation of chalcopyrite by acidic iron sulfate solution, while Type III leaching applies only at low temperature with low nominal Fe3+/Fe2+ ratios. In fact, Type I leaching was also observed for chalcopyrite in sulfate solution with oxygen as the oxidant by Yu et al. [167], and in chloride solution with ferric as the oxidant by Majima et al [168], as reported in Nicol’s paper. Type I leaching for sphalerite dissolution in acidic iron sulfate electrolyte at 78°C was also reported by Crundwell [55]. A detailed discussion on the Type I and Type III leaching model (along with schematic diagram) can be found in the literature [163, 165]. Comparison of EM and EC over a wide range of temperature in Figure 8-2 and Figure 8-3 indicates that the mixed potential (a kinetic quantity) is always different from the cathodic reversible potential (a thermodynamic quantity). It is also noteworthy that no significant increase in EM on chalcopyrite was achieved, even at very high nominal Fe3+/Fe2+ ratios and temperatures where the Nernst equation would predict a substantial increase in EC. This raises some concerns about the use of higher concentrations of iron (III) and higher nominal Fe3+/Fe2+ ratios in the  169  industrial hydrometallurgical leaching processes. Actually, it has been reported that chalcopyrite’s leaching rate is strongly affected by ferric ion concentration only at concentrations less than 0.01 or 0.1 M, and at higher concentrations the effect is negligible [12, 54]. Given the importance of the ferric concentration and the nominal Fe3+/Fe2+ ratio in commercial leaching processes, additional investigation would be required to determine the optimum parameters. An electrochemical reaction may be said to be under anodic, cathodic or mixed control, depending on the relative polarization degrees of the anodic and cathodic reactions. It can be clearly seen in Figure 8-2 that ηC is always smaller than ηA, no matter which of the possible anodic oxidation reactions is chosen and no matter the conditions used in the present work. Hence, with the nominal Fe3+/Fe2+ ratio being 1:1, the degree of cathodic polarization is quite small and the leaching reaction could be said to be under anodic control, because the anodic reaction is highly polarized. However, as indicated in Figure 8-3a, Figure 8-3b and Figure 8-3c, when further increasing the nominal Fe3+/Fe2+ ratio and temperature, the effect of the cathodic ferric reduction reaction on the overall leaching process is progressively enhanced, even at lower temperatures. For the 1000:1 nominal Fe3+/Fe2+ ratio, at 110°C and 150°C, ηC is almost equal to ηA when employing Reaction 1 or Reaction 2, which means that the leaching of chalcopyrite in ferric sulfate solution is under mixed control, both by the ferric reduction reaction and the anodic chalcopyrite oxidation reaction. In such a case, both anodic and cathodic reactions are quite irreversible, according to the relative position of the mixed potential and the calculated Nernst potentials of the anodic and cathodic reactions. Thus, based on the above analysis, a conclusion can be drawn that the control scenario is influenced by both the solution composition and temperature for chalcopyrite oxidation in acidic iron sulfate leaching solution, and the importance of the cathodic Fe3+/Fe2+ processes to determine the leaching kinetics in the coupled  170  system is progressively enhanced when increasing the nominal Fe3+/Fe2+ ratio and temperature (not just by the anodic oxidation reaction). In addition, from Figure 8-2 and Figure 8-3, it can be seen that the ferric reduction reaction at potentials near the mixed potential is always in the kinetic-controlled region for the Fe3+/Fe2+ couple. This result is in agreement with the previous finding that a relatively large activation energy was obtained for the ferric reduction reaction, as mentioned in Section 7.2.7.2. As mentioned previously, compared with Reaction 1, Reaction 2 is thermodynamically more favorable, due to the relatively smaller EA. In addition, in Figure 8-2 and Figure 8-3, it is interesting to note that the EA of Reaction 1 approaches that of Reaction 2 under higher nominal Fe3+/Fe2+ ratios and elevated temperatures. This implies that in such a case, Reaction 1 becomes progressively more favorable (Please note that because of its the relatively smaller EA Reaction 2 is still thermodynamically more favorable). In this section, although the present study provided some useful conclusions of the mechanism in chalcopyrite leaching systems, it should be emphasized that some of these conclusions depend on the accuracy of the selection of the anodic reactions and the corresponding EA calculation. Detailed research on the anodic reactions would be required in order to substantiate these results and expand our understanding of this leaching system.  8.3 Summary In this Chapter, a comparison between the calculated reversible potentials of the cathodic and possible anodic reactions and measured mixed potentials was used to analyze the control scenario.  Typically, the measured mixed potentials lie between the cathodic and anodic reversible potentials and are within the range of 0.64±0.06 V under all of the conditions employed in the  171  present study. At each temperature, in general, there is an obvious drop in the measured EM when a large amount of ferrous exists in the electrolyte. The measured EM indicates that, in acidic iron sulfate solutions, the Fe3+/Fe2+ couple is much less reversible on the chalcopyrite surface, especially at higher nominal Fe3+/Fe2+ ratio and temperature. In the region of the mixed potential, Type I leaching prevails in the oxidation of chalcopyrite by acidic iron sulfate solution, while Type III leaching applies only at low temperature with lower nominal Fe3+/Fe2+ ratios.  Analysis by mixed potential theory indicates that in the acidic iron sulfate leaching system the control scenario highly depends on both the solution composition and temperature, and the effect of cathodic ferric reduction reaction on the overall leaching process is progressively enhanced when increasing the nominal Fe3+/Fe2+ ratio and temperature. The leaching reaction is under anodic control when the nominal Fe3+/Fe2+ ratio is around 1:1, whereas at higher nominal Fe3+/Fe2+ ratio and temperature the reaction is under mixed control, both by the ferric reduction reaction and the anodic oxidation reaction. In such a case, both anodic and cathodic reactions are quite irreversible.           172  9 Conclusions, Industrial Applications and Recommendations A thermodynamic model has been developed and shown to reliably simulate the speciation of the quaternary H2SO4-Fe2(SO4)3-FeSO4-H2O system under conditions most relevant to the hydrometallurgical industry. The model results are further employed to predict the redox potential of the Fe3+/Fe2+ couple in acidic iron sulfate solutions, investigate the reduction kinetics of the Fe3+/Fe2+ couple on the surface of chalcopyrite, and carry out a mechanistic analysis relevant to industrial leaching processes for chalcopyrite. 9.1 Conclusions  Results from the calculated distribution of the main ferric and ferrous species as a function of temperature, iron and acid concentration, and the nominal Fe3+/Fe2+ ratio reveal that most of the Fe(III) is distributed as complexes or precipitates and the free ferric ion accounts for only a minor percentage, whereas a large amount of Fe(II) exists in the form of free ferrous ion. Moreover, under the same nominal Fe3+/Fe2+ ratio, a temperature increase within the range of 25°C-150°C leads to a decline in the free Fe3+ concentration, whereas the free Fe2+ concentration is relatively stable. Under all of the investigated conditions, FeSO4+ is always the predominant species for Fe(III) in the aqueous solution. At 150°C, a large amount of Fe(III) precipitated as Fe2O3, with the largest value of 61.7% obtained when the nominal Fe3+/Fe2+ ratio was 1:1. The percentage of formed Fe2O3 under higher nominal Fe3+/Fe2+ ratios is relatively stable and lower than that under nominal Fe3+/Fe2+ ratio of 1:1, due to relatively lower amount addition of FeSO4. The validity of the proposed model was confirmed by reliable prediction of measured redox potential from 25°C to 150°C, and of ferric solubility at  173  150°C. Extensive analysis and review of the calculated pH and real ionic strength of the solution provides an additional affirmation of the validity of the present work.   Based on the model results, the temperature dependence of the real Fe3+/Fe2+ ratios and their activity coefficient ratios were obtained. The calculated real Fe3+/Fe2+ ratio is much lower than the nominal ratio, and from 25°C to 150°C, under each given nominal Fe3+/Fe2+ ratio, the calculated real ratio of Fe3+/Fe2+ substantially declines with temperature. The activity coefficient ratios are typically only affected by temperature, and remain practically constant at each temperature under different nominal Fe3+/Fe2+ ratios. These results, together with the calculated standard electrode potential of the Fe3+/Fe2+ couple, were employed to systematically study the redox potential of the Fe3+/Fe2+ couple. Results indicate that for a given temperature the model-calculated potentials increase considerably with the nominal Fe3+/Fe2+ ratio. However, from 25°C to 150°C, the potentials predicted by the model increase gradually only when the nominal Fe3+/Fe2+ ratios are 10:1, 100:1 and 1000:1 (with its values in the range of ~736–956 mV), while at the nominal Fe3+/Fe2+ ratio of 1:1 they are relatively stable (typically between ~671 and 679 mV) and no significant change was observed as the temperature increased. The speciation model explains the change of redox potential with temperature for all nominal Fe3+/Fe2+ ratios.   An expression Eq. (6-9) determined only by the variables of temperature and nominal Fe3+/Fe2+ ratio was developed to predict the redox potential of the Fe3+/Fe2+ couple. Measured redox potentials in the literature agree very well with those predicted by the developed expression, independent of the nominal concentrations of Fe3+ and H2SO4.  174  Moreover, the expression is probably applicable to more general cases at or around room temperature.   By using cathodic potentiodynamic polarization, the temperature dependence of the exchange current density, transfer coefficient and rate constant were determined and discussed. Results reveal that, from 25 to 150°C, all of the polarization plots exhibit reproducible well-defined linear Tafel regions. The exchange current densities of the Fe3+/Fe2+ couple obtained by extrapolating the cathodic linear Tafel line to the reversible potential are on the order of 10-7-10-5 A/cm2 in the range of 25-150°C, substantially less than that on platinum due to the formation of a passive film. In general, at the same nominal Fe3+/Fe2+ ratio, increasing the temperature from 25 to 150°C was observed to give rise to an increase in i0, especially when a larger amount of free ferrous existed in the solution. Based on the obtained exchange current densities, the rate constant for ferric reduction was calculated, and its values increase with temperature from 0.049 cm/s at 25°C to almost 900 cm/s at 150°C. Further analysis indicates that the rate constant follows Arrhenius behavior and the activation energy for the ferric ion reduction reaction was calculated to be 85 ± 1 kJ mol−1 in the temperature range of 25-150°C. The temperature increase from 25 to 150°C also caused a substantial increase in iM, from the order of 10-6 A/cm2 at 25°C to the order of 10-4 A/cm2 at 150°C.  Analysis of the measured Tafel slopes as a function of temperature in the Fe(II)-Fe(III)-H2SO4 solutions under different nominal Fe3+/Fe2+ ratios indicates that the Tafel slopes are essentially independent of temperature and the solution composition over the range of 25 to 150°C, and remain within the range of 0.114-0.165 V/decade. Consequently, the apparent transfer coefficients calculated from the measured Tafel slopes, increase linearly  175  with respect to temperature rather than being a constant from 25 to 150°C. The obtained value of the temperature coefficient of α (2.5x10-3 K-1) is in reasonable agreement with that (in the region of 1.5x10-3 K-1) needed to account for a b independent of temperature.   Typically, the measured mixed potentials lie between the cathodic and anodic reversible potentials and are within the range of 0.64±0.06 V under all of the conditions employed in the present study. At each temperature, in general, there is an obvious drop in the measured EM when a large amount of ferrous exists in the electrolyte. The measured EM indicates that, in acidic iron sulfate solutions, the Fe3+/Fe2+ couple is much less reversible on the chalcopyrite surface, especially at higher nominal Fe3+/Fe2+ ratio and temperature. In the region of the mixed potential, Type I leaching prevails in the oxidation of chalcopyrite by acidic iron sulfate solution, while Type III leaching applies only at low temperature with lower nominal Fe3+/Fe2+ ratios.   Analysis by mixed potential theory indicates that in the acidic iron sulfate leaching system the control scenario highly depends on both the solution composition and temperature, and the effect of cathodic ferric reduction reaction on the overall leaching process is progressively enhanced when increasing the nominal Fe3+/Fe2+ ratio and temperature. The leaching reaction is under anodic control when the nominal Fe3+/Fe2+ ratio is around 1:1, whereas at higher nominal Fe3+/Fe2+ ratio and temperature the reaction is under mixed control, both by the ferric reduction reaction and the anodic oxidation reaction. In such a case, both anodic and cathodic reactions are quite irreversible.  176  9.2 Industrial Applications  At 150°C, a relatively large amount of Fe(III) precipitated as Fe2O3 when the nominal Fe3+/Fe2+ ratio was 1:1 as compared to the amount precipitated at higher nominal Fe3+/Fe2+ ratios. This is due to the larger amount of FeSO4 present at the 1:1 condition. Hence, under industrial conditions, such as those processes operated at 150°C (Dynatec, AAC/UBC and CESL), it would be advantageous to maintain larger concentrations of FeSO4 in order to promote Fe2O3 precipitation. There is also supporting evidence (not yet published) from co-workers in the Asselin group that larger amounts of ferrous ion promote the precipitation of hematite and reduce super-saturation. This has important implications for iron control in such processes.    According to the equation developed in this work (Eq. 6-9, reproduced below), the redox potential of the quaternary H2SO4-Fe2(SO4)3-FeSO4-H2O system is solely determined by the variables of the nominal Fe3+/Fe2+ ratio and temperature. This implies that whenever two of these variables are known, the third can be calculated. For example, if the redox potential is measured at a given temperature, the nominal Fe3+/Fe2+ ratio can then be calculated. By further measuring the total iron in the solution, the nominal Fe(II) and Fe(III) amounts can be obtained. Hence, this equation is quite useful for understanding and studying leach chemistry. Moreover, the expression is probably applicable to more general cases at lower temperatures. This is of particular interest in the industrial processes operated at lower temperatures, such as Nenatech, Galvanox, and heap leaching of copper sulfides. Even if oxygen is included in the system, the kinetics of reduction of oxygen are sufficiently slow (as well documented in many literature studies) and ferric  177  reduction is always dominant. Hence the measured redox potential is dominated by the Fe3+/Fe2+ couple. ferric, nominal3 2 3ferrous, nominal2.303(mV) 1 10 [ (K)] 0.91 (K) (K) 10 log 492CRE T T TnF           Very importantly, this expression also avoids the complicated calculations of the standard electrode potential and the activity coefficient.    The present study reveals that in the acidic iron sulfate leaching system the leaching reaction is under anodic control when the nominal Fe3+/Fe2+ ratio is around 1:1. At higher nominal Fe3+/Fe2+ ratios and temperatures the reaction is under mixed control, both by the ferric reduction reaction and the anodic oxidation reaction. In addition, published results of the previously mentioned industrial processes show that the nominal Fe3+/Fe2+ ratios in the leaching solution are typically lower than 7:1 at the initial stages. This implies that the leaching reaction is under anodic control for those processes. Admittedly, during a long term leaching reaction, the nominal Fe3+/Fe2+ ratio in the leaching solution changes. Moreover, it has also been reported that lower nominal Fe3+/Fe2+ ratios (with a corresponding lower redox potential) can enhance the leaching rate, as discussed in Section 2.1.1.2. As a result, the operating parameters, such as nominal Fe3+ concentration, nominal Fe3+/Fe2+ ratio, and oxygen supply could be optimized. Hence, when designing or improving such industrial leaching processes, more attention should be paid to the control mechanism so as to increase the leaching rate according to these theoretical aspects. For example, for chalcopyrite heap leaching, by measuring the iron concentration and obtaining the nominal Fe3+/Fe2+ ratios in the leaching solution, the control mechanism can be known according to the kinetic findings in this work. As an example, under lower nominal Fe3+/Fe2+ ratios, the leaching reaction is usually under anodic  178  control and the only way to increase the leaching rate is to increase the kinetics of the anodic reaction. Thus under these conditions increases in Fe3+ concentration, nominal Fe3+/Fe2+ ratio will not substantially change the leaching rate. 9.3 Recommendations This work forms a baseline to improve the understanding on the chalcopyrite leaching mechanisms in acidic iron sulfate solutions. The following investigations are recommended in order to enable a deeper understanding of the leaching system:  The developed model was validated in a restricted range of conditions (conditions by the author and by others shown in the present study) due to the limited availability of experimental data. When extending to a wider range of solution composition and temperature, due to the generation of iron precipitates and the presence of additional species, further work will be required to expand our understanding of the quaternary system. The influence of other ions such as Cu2+, Cl- on the speciation results and the calculation of redox potential also require further detailed study.  According to the developed expression, Eq. (6-9), at any given temperature, the redox potential of the quaternary H2SO4-Fe2(SO4)3-FeSO4-H2O system is solely determined by the nominal Fe3+/Fe2+ ratio. This result is particularly valuable and of interest: it is highly useful for understanding leach chemistry and calculating nominal Fe3+/Fe2+ ratio based on measured redox potential. Future work should be done to determine the range of applicability of this equation.   Long-term behavior of the leaching process is also important as it may be different from its short-term electrochemical response. Therefore, long term open circuit potential tests, together with polarization resistance and electrochemical impedance spectroscopy tests  179  (these two techniques were selected because they do not polarize the sample significantly from the open circuit potential; therefore, it would be reasonable to assume these tests would not affect the overall trend of the long term open circuit potential test) at specific intervals can be applied to provide data on the evolution of the chalcopyrite/solution interface in acidic iron sulfate leaching system, and hence to learn the influence of the Fe3+/Fe2+ couple on the long-term electrochemical behavior of the leaching process at different temperatures.  Results over a wide range of temperature indicate that no significant increase in the mixed potential on chalcopyrite was achieved, even at very high nominal Fe3+/Fe2+ ratios and temperatures where the Nernst equation would predict a substantial increase in theoretical cathodic reversible potential. 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Canadian Metallurgical Quarterly, 1985, 24(4), 283-291.                     200  Appendices Appendix A High Temperature Electrochemical Apparatus   Figure A-1 High temperature high pressure autoclave.  201      Figure A-2 Inside of the glass reactor for high temperature high pressure autoclave.  202   Figure A-3 Disassembled chalcopyrite working electrode used in the autoclave.  203    Figure A-4 (a) Assembly and (b) disassembly of the Pt-Nb electrode from Cortest Inc. served as counter electrode for high temperature high pressure electrochemical test in the autoclave.     a Counter Electrode Assembly b Counter Electrode Disassembly  204       Figure A-5 High temperature external pressure balanced reference electrode (EPBRE).   205   Appendix B Fortran Code by Brent’s Method Employed in the Present Work for the Speciation Study As an example, the code shown in the following pages were used to carry out the speciation study at 150°C, which is the most complicated one as we need to first make a judgement whether the precipitate (Fe2O3) is formed or not. As discussed previously in Chapter 5, the species involved in the model vary depending on temperature. Hence, for the calculation at lower temperatures the code needs to be adjusted accordingly. For example, at 90°C and 110°C, the part for judging the precipitate formation should be removed; at 25°C and 70°C, information on Fe(SO4)2- should be added to the code. The calculated concentrations of all species in aqueous Fe(II)-Fe(III)-H2SO4 solutions in the range of 25-150°C according to the developed speciation model with nominal Fe3+/Fe2+ ratio of 10:1 was also shown in Table B-1 as an example. The equations involved in the code are shown as follows: (1) The 7 chemical equilibrium equations according to the reactions shown in Table 5-2. For any equilibrium reaction at a given temperature:  iT iK a                                                          (B-1)  i i ia c                                                             (B-2) 2112ni ijI z c                                                       (B-3) Where KT represents the equilibrium constant of the formation reactions shown in Table 5-2, ai is the activity of the species i, ʋi is the stoichiometric coefficient of the species i (positive for products and negative for reactants) in the formation reactions, γi is the activity coefficient of the  206  species i calculated by the B-dot equation, ci is the molal concentration of the species i, j is the number of ionic species involved in the model, I (mol kg-1) is the effective (or real/true) ionic strength of the solution and zi is the ionic charge of species i. (2) The component mass balance equations in terms of Fe2+, Fe3+ and SO42- (three in total):   2+ + o4 4total Fe FeHSO FeSOFe(II) c c c                                                                          (B-4)   3+ 2+ - + 2 34 4 2 4 Fe Ototal Fe FeHSO Fe(SO ) FeSOFe(III) 2c c c c c                                        (B-5) 2 + o 2+ - +4 4 4 4 4 4 2 424 SO HSO FeHSO FeSO FeHSO Fe(SO ) FeSOtotalSO 2c c c c c c c                 (B-6) (3) The electroneutrality equation: 2 2+ + 3+ 2+ - +4 4 4 4 4 2 4H SO HSO Fe FeHSO Fe FeHSO Fe(SO ) FeSO2 2 3 2 0c c c c c c c c c                  (B-7)        207  Table B-1 Calculated concentrations of all species in aqueous Fe(II)-Fe(III)-H2SO4 solutions from 25-150°C using the newly developed speciation model with nominal Fe3+/Fe2+ ratio of 10:1 (Unit: mol/kg). In the cell or autoclave, [Fe(III)]total = 0.18 mol/kg and [Fe(II)]total = 0.018 mol/kg, respectively. Species  at 25°C  at 70°C  at 90°C  at 110°C  at 150°C γi ci γi ci γi ci γi ci γi ci H+ 0.8347 0.2812 0.8339 0.2539 0.8277 0.2025 0.8197 0.1946 0.7882 0.3452 SO42- 0.1842 0.0573 0.1799 0.0152 0.1690 0.0110 0.1572 0.0055 0.1166 0.0009 HSO4- 0.7218 0.3277 0.7216 0.3505 0.7125 0.3981 0.7014 0.4035 0.6553 0.4875 Fe2+ 0.2631 0.0119 0.2557 0.0131 0.2434 0.0126 0.2297 0.0129 0.1836 0.0130 FeHSO4+ 0.7031 0.0001 0.7032 0.0009 0.6937 0.0017 0.6822 0.0025 0.6337 0.0044 FeSO4° 1.0000 0.0059 1.0000 0.0039 1.0000 0.0036 1.0000 0.0025 1.0000 0.0006 Fe3+ 0.0924 0.0089 0.0859 0.0016 0.0787 0.0010 0.0711 0.0006 0.0494 0.0003 FeHSO42+ 0.2045 0.0030 0.1993 0.0067 0.1880 0.0097 0.1757 0.0113 0.1333 0.0136 Fe(SO4)2- 0.7031 0.0313 0.7032 0.0445 - - - - - - FeSO4+ 0.7031 0.1357 0.7032 0.1262 0.6937 0.1683 0.6822 0.1670 0.6337 0.0855 Fe2O3  -  -  -  - -  -  -  -  - 0.0397 [Fe(II)]total by Model - 0.018 - 0.018 - 0.018 - 0.018 - 0.018 [Fe(III)]total by Model - 0.18 - 0.18 - 0.18 - 0.18 - 0.18   208   C     **********                                                                                                       C      THIS PROGRAM SOLVES the NONLINEAR         C     EQUATIONS                                                         C                                                                         C     **********                                                               INTEGER I,INT,INFO,LWA,N,NFCALL,NFEV,NWRITE,kk                              DOUBLE PRECISION FNORM1,FNORM2,H,TEMP,TOL                               DOUBLE PRECISION X(10),FVEC(10),WA(130),gam(9),qi                                  DOUBLE PRECISION DFLOAT,x7,x11                                                  EXTERNAL BVP                                                             COMMON /REFNUM/ NFCALL   open(2,file='a150-1-1.dat',status='unknown',form='formatted')                                              C                                                                        C     LOGICAL OUTPUT UNIT IS ASSUMED TO BE NUMBER 6.                                                                                           00000230       DATA NWRITE /6/                                                    C                                                                        c      DFLOAT(INT) = INT                                                        LWA = 200                                                                TOL = 1.D-30       N = 8 C C     STARTING VALUES. C       H = 1.D0/DFLOAT(N+1)       DO 10 I = 1, N  X(I) = 0.1 c         TEMP = DFLOAT(I)*H c         X(I) = TEMP*(TEMP - 1.D0)     10    CONTINUE C C     INITIAL MAX-NORM OF THE RESIDUALS. C       CALL BVP(N,X,FVEC,110)  FNORM1 = 0.D0       DO 20 I = 1, N c         CALL BVP(N,X,FVEC,I)          FNORM1 = DMAX1(FNORM1,DABS(FVEC(I)))    20    CONTINUE C       NFCALL = 0       CALL BRENT1(BVP,N,X,FVEC,TOL,INFO,WA,LWA)       NFEV = NFCALL/N C C     FINAL MAX-NORM OF THE RESIDUALS.  209  C       FNORM2 = 0.D0  CALL BVP(N,X,FVEC,1)       DO 30 I = 1, N c         CALL BVP(N,X,FVEC,I)          FNORM2 = DMAX1(FNORM2,DABS(FVEC(I)))    30    CONTINUE C       WRITE (NWRITE,1000) N,FNORM1,FNORM2,NFEV,INFO,(X(I),I=1,N)   kk=150  if(kk.eq.130)then  x7=x(1)**3/(10**2.72)  end if   qi=0.765 c      qi=0.5*(x(1)+4*x(2)+x(3)+4*x(4)+x(5)+9*x7+4*x(7)+x(8))  qi=dsqrt(qi)   if(kk.eq.150)then  gam(1)=-0.6855*qi/(1.+9.*0.3525*qi)+0.0470  gam(2)=-4.*0.6855*qi/(1.+4.*0.3525*qi)+0.0470  gam(3)=-1.*0.6855*qi/(1.+4.5*0.3525*qi)+0.0470  gam(4)=-4.*0.6855*qi/(1.+6.*0.3525*qi)+0.0470       gam(5)=-1.*0.6855*qi/(1.+4.*0.3525*qi)+0.0470  gam(6)=0  gam(7)=-9.*0.6855*qi/(1.+9.*0.3525*qi)+0.0470  gam(8)=-4.*0.6855*qi/(1.+4.5*0.3525*qi)+0.0470  gam(9)=-1.*0.6855*qi/(1.+4.*0.3525*qi)+0.0470  end if   if(kk.eq.150)then  x7=(10**gam(1))**3*x(1)**3/(10**3.11)/10**gam(7)  end if    x11=(0.179-x7-x(7)-x(8))*0.5     c write(*,*)x7,(0.179-x7-x(7)-x(8))*0.5 c write(*,*)x(1)-2.*x(2)-x(3)+2.*x(4)+x(5)+3.*x7+2.*x(7)+x(8)  WRITE (2,1000) N,FNORM1,FNORM2,NFEV,INFO,(X(I),I=1,N) c do i=1,6         write(2,*)'c(1)=', x(1)  write(2,*)'c(2)=', x(2)  write(2,*)'c(3)=', x(3)  write(2,*)'c(4)=', x(4)  write(2,*)'c(5)=', x(5)  write(2,*)'c(6)=', x(6)  210   write(2,*)'c(7)=', x7  write(2,*)'c(8)=', x(7)  write(2,*)'c(10)=', x(8)  write(2,*)'c(11)=', x11   write(2,*)'gam(1)=', gam(1)  write(2,*)'gam(2)=', gam(2)  write(2,*)'gam(3)=', gam(3)  write(2,*)'gam(4)=', gam(4)  write(2,*)'gam(5)=', gam(5)  write(2,*)'gam(6)=', gam(6)  write(2,*)'gam(7)=', gam(7)  write(2,*)'gam(8)=', gam(8)  write(2,*)'gam(10)=', gam(9)       a1=dlog10(x(3))-dlog10(x(1))-dlog10(x(2))-4.05+      *gam(3)-gam(1)-gam(2)       a2=dlog10(x(5))-dlog10(x(4))-dlog10(x(1))-dlog10(x(2))-4.61+      *gam(5)-gam(4)-gam(1)-gam(2)       a3=dlog10(x(6))-dlog10(x(4))-dlog10(x(2))-3.35+      *gam(6)-gam(4)-gam(2)       a4=dlog10(x(7))-dlog10(x7)-dlog10(x(1))-dlog10(x(2))-6.61+      *gam(8)-gam(7)-gam(1)-gam(2)       a5=dlog10(x(8))-dlog10(x(2))-dlog10(x7)-7.52+      *gam(9)-gam(2)-gam(7)  a6=x(1)-2.*x(2)-x(3)+2.*x(4)+x(5)+3.*x7+2.*x(7)+x(8) c      fvec(6)=x(1)+x(3)+x(5)+x(8)-0.612       a7=x(4)+x(5)+x(6)-0.179 c fvec(8)=dlog10(x(1))-dlog10(x7)-2.72 c      fvec(8)=x(7)+x(9)+x(8)-0.179       a8=x(2)+x(3)+x(6)+x(5)+x(8)+x(7)-0.7535   qi=0.5*(x(1)+4*x(2)+x(3)+4*x(4)+x(5)+9*x7+4*x(7)+x(8))  qi=dsqrt(qi)   write(*,*)a1,a2,a3,a4,a5,a6,a7,a8,qi**2   write(2,*)'I', qi**2        STOP  1000 FORMAT (5X,10H DIMENSION,I5,5X //      1        5X,34H INITIAL MAX-NORM OF THE RESIDUALS,D15.7 //      2        5X,34H FINAL MAX-NORM OF THE RESIDUALS  ,D15.7 //      3        5X,33H NUMBER OF FUNCTION EVALUATIONS  ,I10 //      4        5X,15H EXIT PARAMETER ,18X,I10 //      5        5X,27H FINAL APPROXIMATE SOLUTION  // (5X,5D15.7)) C  211  C     LAST CARD OF SAMPLE PROGRAM. C       END       SUBROUTINE BVP(N,X,FVEC,IFLAG)                                          INTEGER N,IFLAG,jj,kk       DOUBLE PRECISION X(N),FVEC(N) C     ********** C C     SUBROUTINE BVP DEFINES THE BOUNDARY VALUE PROBLEM. C C     **********       INTEGER INT,NFCALL       DOUBLE PRECISION H,TEMP,TEMP1,TEMP2,gam(9),qi       DOUBLE PRECISION DFLOAT,x7       COMMON /REFNUM/ NFCALL   do jj=1,n  if(x(jj).lt.1.e-7)then  x(jj)=1.e-6  end if  end do           kk=150 c write(*,*)10**2.72              qi=0.765  qi=dsqrt(qi)  gam(1)=-0.6855*qi/(1.+9.*0.3525*qi)+0.0470  gam(2)=-4.*0.6855*qi/(1.+4.*0.3525*qi)+0.0470  gam(3)=-1.*0.6855*qi/(1.+4.5*0.3525*qi)+0.0470  gam(4)=-4.*0.6855*qi/(1.+6.*0.3525*qi)+0.0470       gam(5)=-1.*0.6855*qi/(1.+4.*0.3525*qi)+0.0470  gam(6)=0  gam(7)=-9.*0.6855*qi/(1.+9.*0.3525*qi)+0.0470  gam(8)=-4.*0.6855*qi/(1.+4.5*0.3525*qi)+0.0470  gam(9)=-1.*0.6855*qi/(1.+4.*0.3525*qi)+0.0470 c if(kk.eq.150)then  x7=(10**gam(1))**3*x(1)**3/(10**3.11)/10**gam(7) c end if  c      qi=0.5*(x(1)+4*x(2)+x(3)+4*x(4)+x(5)+9*x7+4*x(7)+x(8)) c qi=dsqrt(qi)           if(kk.eq.150)then     212    fvec(1)=dlog10(x(3))-dlog10(x(1))-dlog10(x(2))-4.05+      *gam(3)-gam(1)-gam(2)       fvec(2)=dlog10(x(5))-dlog10(x(4))-dlog10(x(1))-dlog10(x(2))-4.61+      *gam(5)-gam(4)-gam(1)-gam(2)       fvec(3)=dlog10(x(6))-dlog10(x(4))-dlog10(x(2))-3.35+      *gam(6)-gam(4)-gam(2)       fvec(4)=dlog10(x(7))-dlog10(x7)-dlog10(x(1))-dlog10(x(2))-6.61+      *gam(8)-gam(7)-gam(1)-gam(2)       fvec(5)=dlog10(x(8))-dlog10(x(2))-dlog10(x7)-7.52+      *gam(9)-gam(2)-gam(7)  fvec(6)=x(1)-2.*x(2)-x(3)+2.*x(4)+x(5)+3.*x7+2.*x(7)+x(8) c      fvec(6)=x(1)+x(3)+x(5)+x(8)-0.612       fvec(7)=x(4)+x(5)+x(6)-0.179 c fvec(8)=dlog10(x(1))-dlog10(x7)-2.72 c      fvec(8)=x(7)+x(9)+x(8)-0.179       fvec(8)=x(2)+x(3)+x(6)+x(5)+x(8)+x(7)-0.7535       end if           RETURN C C     LAST CARD OF SUBROUTINE BVP. C       END       SUBROUTINE BRENT1(FCN,N,X,FVEC,TOL,INFO,WA,LWA)                         INTEGER N,INFO,LWA       DOUBLE PRECISION TOL       DOUBLE PRECISION X(N),FVEC(N),WA(LWA)       EXTERNAL FCN C     ********** C C     SUBROUTINE BRENT1 C C     THE PURPOSE OF THIS SUBROUTINE IS TO FIND A ZERO OF C     A SYSTEM OF N NONLINEAR EQUATIONS IN N VARIABLES BY A C     METHOD DUE TO R. BRENT. THIS IS DONE BY USING THE C     MORE GENERAL NONLINEAR EQUATION SOLVER BRENTM. C C     THE SUBROUTINE STATEMENT IS C C       SUBROUTINE BRENT1(FCN,N,X,FVEC,TOL,INFO,WA,LWA) C C     WHERE C C       FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH C         CALCULATES COMPONENTS OF THE FUNCTION. FCN SHOULD BE C         DECLARED IN AN EXTERNAL STATEMENT IN THE USER CALLING  213  C         PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. C C         SUBROUTINE FCN(N,X,FVEC,IFLAG) C         INTEGER N,IFLAG C         DOUBLE PRECISION X(N),FVEC(N) C         ---------- C         CALCULATE THE IFLAG-TH COMPONENT OF THE FUNCTION C         AND RETURN THIS VALUE IN FVEC(IFLAG). C         ---------- C         RETURN C         END C C         THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS C         THE USER WANTS TO TERMINATE EXECUTION OF BRENT1. C         IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. C C       N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER C         OF EQUATIONS AND VARIABLES. C C       X IS AN ARRAY OF LENGTH N. ON INPUT IT MUST CONTAIN C         AN INITIAL ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X C         CONTAINS THE FINAL ESTIMATE OF THE SOLUTION VECTOR. C C       FVEC IS AN ARRAY OF LENGTH N. ON OUTPUT IT CONTAINS C         THE FINAL RESIDUALS. C C       TOL IS A NONNEGATIVE INPUT VARIABLE. THE ALGORITHM CONVERGES C         IF EITHER ALL THE RESIDUALS ARE AT MOST TOL IN MAGNITUDE, C         OR IF THE ALGORITHM ESTIMATES THAT THE RELATIVE ERROR C         BETWEEN X AND THE SOLUTION IS AT MOST TOL. C C       INFO IS AN INTEGER OUTPUT VARIABLE SET AS FOLLOWS. IF C         THE USER HAS TERMINATED EXECUTION, INFO WILL BE SET TO C         THE (NEGATIVE) VALUE OF IFLAG. SEE DESCRIPTION OF FCN. C         OTHERWISE C C         INFO = 0   IMPROPER INPUT PARAMETERS. C C         INFO = 1   ALL RESIDUALS ARE AT MOST TOL IN MAGNITUDE. C C         INFO = 2   ALGORITHM ESTIMATES THAT THE RELATIVE ERROR C                    BETWEEN X AND THE SOLUTION IS AT MOST TOL. C C         INFO = 3   CONDITIONS FOR INFO = 1 AND INFO = 2 BOTH HOLD. C C         INFO = 4   NUMBER OF FUNCTION EVALUATIONS HAS REACHED OR C                    EXCEEDED 50*(N+3). C C         INFO = 5   APPROXIMATE JACOBIAN MATRIX IS SINGULAR. C  214  C         INFO = 6   ITERATION IS NOT MAKING GOOD PROGRESS. C C         INFO = 7   ITERATION IS DIVERGING. C C         INFO = 8   ITERATION IS CONVERGING, BUT TOL IS TOO C                    SMALL, OR THE CONVERGENCE IS VERY SLOW C                    DUE TO A JACOBIAN SINGULAR NEAR THE OUTPUT C                    X OR DUE TO BADLY SCALED VARIABLES. C C       WA IS A WORK ARRAY OF LENGTH LWA. C C       LWA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN C         N*(N+3). C C     SUBPROGRAMS REQUIRED C C       USER-SUPPLIED ...... FCN, BRENTM C C       FORTRAN-SUPPLIED ... DLOG C C     **********       INTEGER I,IVAR,MAXFEV,MOPT,NFEV       DOUBLE PRECISION EMAX,FTOL,TEMP,XTOL,ZERO       DOUBLE PRECISION DFLOAT       DATA ZERO /0.D0/       DFLOAT(IVAR) = IVAR       INFO = 0 C C     CHECK THE INPUT PARAMETERS FOR ERRORS. C       IF (N .LE. 0 .OR. TOL .LT. ZERO .OR. LWA .LT. N*(N+3)) GO TO 30 C C     DETERMINE AN OPTIMAL VALUE FOR MOPT. C       EMAX = ZERO       DO 10 I = 1, N          TEMP = DLOG(DFLOAT(I+1))/DFLOAT(N+2*I+1)          IF (TEMP .LT. EMAX) GO TO 20          MOPT = I          EMAX = TEMP    10    CONTINUE    20 CONTINUE C C     CALL BRENTM. C       MAXFEV = 50*(N + 3)       FTOL = TOL       XTOL = TOL       CALL BRENTM(FCN,N,X,FVEC,FTOL,XTOL,MAXFEV,MOPT,      1           INFO,NFEV,WA(3*N+1),N,WA(1),WA(N+1),WA(2*N+1))  215     30 CONTINUE       RETURN C C     LAST CARD OF SUBROUTINE BRENT1. C       END       SUBROUTINE BRENTM(FCN,N,X,FVEC,FTOL,XTOL,MAXFEV,MOPT,                  1                  INFO,NFEV,Q,LDQ,SIGMA,WA1,WA2)       INTEGER N,MAXFEV,MOPT,INFO,NFEV,LDQ       DOUBLE PRECISION FTOL,XTOL       DOUBLE PRECISION X(N),FVEC(N),Q(LDQ,N),SIGMA(N),WA1(N),WA2(N) C     ********** C C     SUBROUTINE BRENTM C C     THE PURPOSE OF THIS SUBROUTINE IS TO FIND A ZERO TO C     A SYSTEM OF N NONLINEAR EQUATIONS IN N VARIABLES BY A C     METHOD DUE TO R. BRENT. C C     THE SUBROUTINE STATEMENT IS C C       SUBROUTINE BRENTM(FCN,N,X,FVEC,FTOL,XTOL,MAXFEV,MOPT, C                         INFO,NFEV,Q,LDQ,SIGMA,WA1,WA2) C C     WHERE C C       FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH C         CALCULATES COMPONENTS OF THE FUNCTION. FCN SHOULD BE C         DECLARED IN AN EXTERNAL STATEMENT IN THE USER CALLING C         PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. C C         SUBROUTINE FCN(N,X,FVEC,IFLAG) C         INTEGER N,IFLAG C         DOUBLE PRECISION X(N),FVEC(N) C         ---------- C         CALCULATE THE IFLAG-TH COMPONENT OF THE FUNCTION C         AND RETURN THIS VALUE IN FVEC(IFLAG). C         ---------- C         RETURN C         END C C         THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS C         THE USER WANTS TO TERMINATE EXECUTION OF BRENTM. C         IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. C C       N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF C         EQUATIONS AND VARIABLES. C C       X IS AN ARRAY OF LENGTH N. ON INPUT IT MUST CONTAIN C         AN ESTIMATE TO THE SOLUTION OF THE SYSTEM OF EQUATIONS.  216  C         ON OUTPUT X CONTAINS THE FINAL ESTIMATE TO THE SOLUTION C         OF THE SYSTEM OF EQUATIONS. C C       FVEC IS AN ARRAY OF LENGTH N. ON OUTPUT IT CONTAINS C         THE FINAL RESIDUALS. C C       FTOL IS A NONNEGATIVE INPUT VARIABLE. CONVERGENCE C         OCCURS IF ALL RESIDUALS ARE AT MOST FTOL IN MAGNITUDE. C C       XTOL IS A NONNEGATIVE INPUT VARIABLE. CONVERGENCE C         OCCURS IF THE RELATIVE ERROR BETWEEN TWO SUCCESSIVE C         ITERATES IS AT MOST XTOL. C C       MAXFEV IS A POSITIVE INTEGER INPUT VARIABLE. TERMINATION C         OCCURS IF THE NUMBER OF FUNCTION EVALUATIONS IS AT C         LEAST MAXFEV BY THE END OF AN ITERATION. IN BRENTM, C         A FUNCTION EVALUATION CORRESPONDS TO N CALLS TO FCN. C C       MOPT IS A POSITIVE INTEGER INPUT VARIABLE. MOPT SPECIFIES C         THE NUMBER OF TIMES THAT THE APPROXIMATE JACOBIAN IS C         USED DURING EACH ITERATION WHICH EMPLOYS ITERATIVE C         REFINEMENT. IF MOPT IS 1, NO ITERATIVE REFINEMENT WILL C         BE DONE. MAXIMUM EFFICIENCY IS USUALLY OBTAINED IF C         MOPT MAXIMIZES LOG(K+1)/(N+2*K+1) FOR K = 1,...,N. C C       INFO IS AN INTEGER OUTPUT VARIABLE SET AS FOLLOWS. IF C         THE USER HAS TERMINATED EXECUTION, INFO WILL BE SET TO C         THE (NEGATIVE) VALUE OF IFLAG. SEE DESCRIPTION OF FCN. C         OTHERWISE C C         INFO = 0   IMPROPER INPUT PARAMETERS. C C         INFO = 1   ALL RESIDUALS ARE AT MOST FTOL IN MAGNITUDE. C C         INFO = 2   RELATIVE ERROR BETWEEN TWO SUCCESSIVE ITERATES C                    IS AT MOST XTOL. C C         INFO = 3   CONDITIONS FOR INFO = 1 AND INFO = 2 BOTH HOLD. C C         INFO = 4   NUMBER OF FUNCTION EVALUATIONS HAS REACHED OR C                    EXCEEDED MAXFEV. C C         INFO = 5   APPROXIMATE JACOBIAN MATRIX IS SINGULAR. C C         INFO = 6   ITERATION IS NOT MAKING GOOD PROGRESS. C C         INFO = 7   ITERATION IS DIVERGING. C C         INFO = 8   ITERATION IS CONVERGING, BUT XTOL IS TOO C                    SMALL, OR THE CONVERGENCE IS VERY SLOW  217  C                    DUE TO A JACOBIAN SINGULAR NEAR THE OUTPUT C                    X OR DUE TO BADLY SCALED VARIABLES. C C       NFEV IS AN INTEGER OUTPUT VARIABLE SET TO THE NUMBER OF C         FUNCTION EVALUATIONS USED IN PRODUCING X. IN BRENTM, C         A FUNCTION EVALUATION CORRESPONDS TO N CALLS TO FCN. C C       Q IS AN N BY N ARRAY. IF JAC DENOTES THE APPROXIMATE C         JACOBIAN, THEN ON OUTPUT Q IS (A MULTIPLE OF) AN C         ORTHOGONAL MATRIX SUCH THAT JAC*Q IS A LOWER TRIANGULAR C         MATRIX. ONLY THE DIAGONAL ELEMENTS OF JAC*Q NEED C         TO BE STORED, AND THESE CAN BE FOUND IN SIGMA. C C       LDQ IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N C         WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY Q. C C       SIGMA IS A LINEAR ARRAY OF LENGTH N. ON OUTPUT SIGMA C         CONTAINS THE DIAGONAL ELEMENTS OF THE MATRIX JAC*Q. C         SEE DESCRIPTION OF Q. C C       WA1 AND WA2 ARE LINEAR WORK ARRAYS OF LENGTH N. C C     SUBPROGRAMS REQUIRED C C       USER-SUPPLIED ...... FCN C C       FORTRAN-SUPPLIED ... DABS,DMAX1,DSQRT,DSIGN C C     **********       INTEGER I,IFLAG,J,K,M,NFCALL,NIER6,NIER7,NIER8,NSING       LOGICAL CONV       DOUBLE PRECISION DELTA,DIFIT,DIFIT1,EPS,EPSMCH,ETA,FKY,FKZ,      1       FNORM,FNORM1,H,P05,SCALE,SKNORM,TEMP,XNORM,ZERO       DATA ZERO,P05,SCALE /0.D0,5.D-2,1.D1/ C C     WARNING. C C     THIS IS AN IBM CODE. TO RUN THIS CODE ON OTHER MACHINES IT C     IS NECESSARY TO CHANGE THE VALUE OF THE MACHINE PRECISION C     EPSMCH. THE MACHINE PRECISION IS THE SMALLEST FLOATING C     POINT NUMBER EPSMCH SUCH THAT C C           1 + EPSMCH .GT. 1 C C     IN WORKING PRECISION. IF IN DOUBT ABOUT THE VALUE OF C     EPSMCH, THEN THE FOLLOWING PROGRAM SEGMENT DETERMINES C     EPSMCH ON MOST MACHINES. C C     EPSMCH = 0.5D0 C   1 CONTINUE  218  C     IF (1.D0+EPSMCH .EQ. 1.D0) GO TO 2 C     EPSMCH = 0.5D0*EPSMCH C     GO TO 1 C   2 CONTINUE C     EPSMCH = 2.D0*EPSMCH C C     THE IBM DOUBLE PRECISION EPSMCH. C       EPSMCH = 16.D0**(-13) C       INFO = 0       IFLAG = 0       NFEV = 0       NFCALL = 0 C C     CHECK THE INPUT PARAMETERS FOR ERRORS. C       IF (N .LE. 0 .OR. FTOL .LT. ZERO .OR. XTOL .LT. ZERO .OR.      1    MAXFEV .LE. 0 .OR. MOPT .LE. 0 .OR. LDQ .LT. N) GO TO 220 C C     INITIALIZE SOME OF THE VARIABLES. C       NIER6 = -1       NIER7 = -1       NIER8 = 0       FNORM = ZERO       DIFIT = ZERO       XNORM = ZERO       DO 10 I = 1, N          XNORM = DMAX1(XNORM,DABS(X(I)))    10    CONTINUE       EPS = DSQRT(EPSMCH)       DELTA = SCALE*XNORM       IF (XNORM .EQ. ZERO) DELTA = SCALE C C     ENTER THE PRINCIPAL ITERATION. C    20 CONTINUE C C     TO PRINT THE ITERATES, PLACE WRITE STATEMENTS C     FOR THE VECTOR X HERE. C       NSING = N       FNORM1 = FNORM       DIFIT1 = DIFIT       FNORM = ZERO C C     COMPUTE THE STEP H FOR THE DIVIDED DIFFERENCE WHICH C     APPROXIMATES THE K-TH ROW OF THE JACOBIAN MATRIX. C  219        H = EPS*XNORM       IF (H .EQ. ZERO) H = EPS       DO 40 J = 1, N          DO 30 I = 1, N             Q(I,J) = ZERO    30       CONTINUE          Q(J,J) = H          WA1(J) = X(J)    40    CONTINUE C C     ENTER A SUBITERATION. C       DO 150 K = 1, N          IFLAG = K          CALL FCN(N,WA1,FVEC,IFLAG)          FKY = FVEC(K)          NFCALL = NFCALL + 1          NFEV = NFCALL/N          IF (IFLAG .LT. 0) GO TO 230          FNORM = DMAX1(FNORM,DABS(FKY)) C C        COMPUTE THE K-TH ROW OF THE JACOBIAN MATRIX. C          DO 60 J = K, N             DO 50 I = 1, N                WA2(I) = WA1(I) + Q(I,J)    50          CONTINUE             CALL FCN(N,WA2,FVEC,IFLAG)             FKZ = FVEC(K)             NFCALL = NFCALL + 1             NFEV = NFCALL/N             IF (IFLAG .LT. 0) GO TO 230             SIGMA(J) = FKZ - FKY    60       CONTINUE          FVEC(K) = FKY C C        COMPUTE THE HOUSEHOLDER TRANSFORMATION TO REDUCE THE K-TH ROW C        OF THE JACOBIAN MATRIX TO A MULTIPLE OF THE K-TH UNIT VECTOR. C          ETA = ZERO          DO 70 I = K, N             ETA = DMAX1(ETA,DABS(SIGMA(I)))    70       CONTINUE          IF (ETA .EQ. ZERO) GO TO 150          NSING = NSING - 1          SKNORM = ZERO          DO 80 I = K, N             SIGMA(I) = SIGMA(I)/ETA             SKNORM = SKNORM + SIGMA(I)**2    80       CONTINUE  220           SKNORM = DSQRT(SKNORM)          IF (SIGMA(K) .LT. ZERO) SKNORM = -SKNORM          SIGMA(K) = SIGMA(K) + SKNORM C C        APPLY THE TRANSFORMATION AND COMPUTE THE MATRIX Q. C          DO 90 I = 1, N             WA2(I) = ZERO    90       CONTINUE          DO 110 J = K, N             TEMP = SIGMA(J)             DO 100 I = 1, N                WA2(I) = WA2(I) + TEMP*Q(I,J)   100          CONTINUE   110       CONTINUE          DO 130 J = K, N             TEMP = SIGMA(J)/(SKNORM*SIGMA(K))             DO 120 I = 1, N                Q(I,J) = Q(I,J) - TEMP*WA2(I)   120          CONTINUE   130       CONTINUE C C        COMPUTE THE SUBITERATE. C          SIGMA(K) = SKNORM*ETA          TEMP = FKY/SIGMA(K)          IF (H*DABS(TEMP) .GT. DELTA) TEMP = DSIGN(DELTA/H,TEMP)          DO 140 I = 1, N             WA1(I) = WA1(I) + TEMP*Q(I,K)   140       CONTINUE   150    CONTINUE C C     COMPUTE THE NORMS OF THE ITERATE AND CORRECTION VECTOR. C       XNORM = ZERO       DIFIT = ZERO       DO 160 I = 1, N          XNORM = DMAX1(XNORM,DABS(WA1(I)))          DIFIT = DMAX1(DIFIT,DABS(X(I)-WA1(I)))          X(I) = WA1(I)   160    CONTINUE C C     UPDATE THE BOUND ON THE CORRECTION VECTOR. C       DELTA = DMAX1(DELTA,SCALE*XNORM) C C     DETERMINE THE PROGRESS OF THE ITERATION. C       CONV = (FNORM .LT. FNORM1 .AND. DIFIT .LT. DIFIT1 .AND.      1        NSING .EQ. 0)  221        NIER6 = NIER6 + 1       NIER7 = NIER7 + 1       NIER8 = NIER8 + 1       IF (CONV) NIER6 = 0       IF (FNORM .LT. FNORM1 .OR. DIFIT .LT. DIFIT1) NIER7 = 0       IF (DIFIT .GT. EPS*XNORM) NIER8 = 0 C C     TESTS FOR CONVERGENCE. C       IF (FNORM .LE. FTOL) INFO = 1       IF (DIFIT .LE. XTOL*XNORM .AND. CONV) INFO = 2       IF (FNORM .LE. FTOL .AND. INFO .EQ. 2) INFO = 3       IF (INFO .NE. 0) GO TO 230 C C     TESTS FOR TERMINATION. C       IF (NFEV .GE. MAXFEV) INFO = 4       IF (NSING .EQ. N) INFO = 5       IF (NIER6 .EQ. 5) INFO = 6       IF (NIER7 .EQ. 3) INFO = 7       IF (NIER8 .EQ. 4) INFO = 8       IF (INFO .NE. 0) GO TO 230 C C     ITERATIVE REFINEMENT IS USED IF THE ITERATION IS CONVERGING. C       IF (.NOT. CONV .OR. DIFIT .GT. P05*XNORM .OR. MOPT .EQ. 1)      1    GO TO 220 C C     START ITERATIVE REFINEMENT. C       DO 210 M = 2, MOPT          FNORM1 = FNORM          FNORM = ZERO          DO 190 K = 1, N             IFLAG = K             CALL FCN(N,WA1,FVEC,IFLAG)             FKY = FVEC(K)             NFCALL = NFCALL + 1             NFEV = NFCALL/N             IF (IFLAG .LT. 0) GO TO 230             FNORM = DMAX1(FNORM,DABS(FKY)) C C           ITERATIVE REFINEMENT IS TERMINATED IF IT DOES NOT C           GIVE A REDUCTION OF THE RESIDUALS. C             IF (FNORM .LT. FNORM1) GO TO 170             FNORM = FNORM1             GO TO 220   170       CONTINUE             TEMP = FKY/SIGMA(K)  222              DO 180 I = 1, N                WA1(I) = WA1(I) + TEMP*Q(I,K)   180          CONTINUE   190       CONTINUE C C        COMPUTE THE NORMS OF THE ITERATE AND CORRECTION VECTOR. C          XNORM = ZERO          DIFIT = ZERO          DO 200 I = 1, N             XNORM = DMAX1(XNORM,DABS(WA1(I)))             DIFIT = DMAX1(DIFIT,DABS(X(I)-WA1(I)))             X(I) = WA1(I)   200       CONTINUE C C        STOPPING CRITERIA FOR ITERATIVE REFINEMENT. C          IF (FNORM .LE. FTOL) INFO = 1          IF (DIFIT .LE. XTOL*XNORM) INFO = 2          IF (FNORM .LE. FTOL .AND. INFO .EQ. 2) INFO = 3          IF (NFEV .GE. MAXFEV .AND. INFO .EQ. 0) INFO = 4          IF (INFO .NE. 0) GO TO 230   210    CONTINUE   220 CONTINUE C C     END OF THE ITERATIVE REFINEMENT. C       GO TO 20 C C     TERMINATION, EITHER NORMAL OR USER IMPOSED. C   230 CONTINUE       IF (IFLAG .LT. 0) INFO = IFLAG       RETURN C C     LAST CARD OF SUBROUTINE BRENTM. C       END   

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