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Electrochemical aspects of the aqueous oxidation of copper sulphides 1970

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ELECTROCHEMICAL ASPECTS OF THE AQUEOUS OXIDATION OF COPPER SULPHIDES BY ARLETTE ETIENNE Ingenieur c i v i l m e t a l l u r g i s t s ( U n i v e r s i t e de L i e g e , M . A . S c . ( U n i v e r s i t e de M o n t r e a l , 1966) 1965) A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of METALLURGY We accept t h i s t h e s i s as conforming to the r e q u i r e d s tandard THE UNIVERSITY OF BRITISH COLUMBIA November, 1970 In present ing th i s thes is in pa r t i a l fu l f i lment o f the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f r ee l y ava i l ab le for reference and study. I fu r ther agree tha permission for extensive copying of th i s thes is for scho la r l y purposes may be granted by the Head of my Department or by his representat ives . It is understood that copying or pub l i ca t ion o f th i s thes is fo r f inanc ia l gain sha l l not be allowed without my wr i t ten permiss ion. Department of M e t a l l u r g y The Univers i ty of B r i t i s h Columbia Vancouver 8, Canada Date N o v e m b e r 26, 1970 i i ACKNOWLEDGEMENTS The author wishes to express s i n c e r e thanks to D r . E . P e t e r s f o r h i s support and c r i t i c i s m d u r i n g the course of t h i s work. S p e c i a l thanks are due to D r . A . M i t c h e l l f o r p r o v i d i n g many p a r t of the e x p e r i m e n t a l equipment. The a s s i s t a n c e of the t e c h n i c a l s t a f f , d u r i n g the e x p e r i m e n t a l program, has been g r e a t l y a p p r e c i a t e d . F i n a n c i a l a s s i s t a n c e i n the form of a Canada C o u n c i l S c h o l a r s h i p and a N a t i o n a l Research C o u n c i l S c h o l a r s h i p i s g r a t e f u l l y acknowledged 1 1 X ABSTRACT The Cu-S binary system was subjected to electrochemical studies at temperatures below 100°C i n acid s o l u t i o n . Three types of e l e c t r o - chemical experiments were conducted: a) Measurements of electromotive force were made on the galvanic c e l l , Cu I 0.1 M CuSO., 0.1 M H„S0. I Cu S i 4 2 4 ' y across the Cu-S system (y v a r i a b l e ) . The range of copper a c t i v i t y corresponding to the zone of s t a b i l i t y of digenite Cu^ gS) was accurately determined. From these measurements and the e x i s t i n g thermo- dynamic data on c o v e l l i t e (CuS), the standard free enthalpy of formation of digenite Cu^ gS) and d j u r l e i t e (Cu^ 955^) w a s calculated. b) Copper sulphides were grown on a copper anode from an a c i d i c s o l u t i o n saturated with IL^S at constant current. The thickening: of the copper sulphide f i l m was accounted for by e l e c t r o l y t i c transport i n the scale. The d i f f u s i o n c o e f f i c i e n t of cuprous ions i n low chalco- c i t e CCu 0S) and low digenite (y Cu. „S) was calculated from the slope of the electrode p o t e n t i a l versus time r e l a t i o n s h i p . c) Galyanostatic p o l a r i z a t i o n of r o t a t i n g disk anodes of digenite and c o v e l l i t e was studied at 55°C i n 0.1 M CuSO.-0.1 M H„S0. solutions. 4 2 4 The resistances a r i s i n g during the anodic d i s s o l u t i o n of these sulphides were assessed from the dependence of the electrode p o t e n t i a l on time and current density. The above p o l a r i z a t i o n experiments were correlated with the e l e c t r o l y s i s of copper matte anodes and the leaching experiments in; a c i d i c f e r r i c solutions described i n the l i t e r a t u r e . i v RESUME Cet te these c o n s t i t u e une etude du syst&me b i n a i r e Cu-S en s o l u t i o n a c i d e , en dessous de 1 0 0 ° C . T r o i s types d ' e x p e r i e n c e s , u t i l i s a n t des me"thodes de mesure E l e c t r o c h i m i q u e s , ont e"te" r e a l i s e e s : a) On a mesure" l a f o r c e e l e c t r o m o t r i c e de l a c e l l u l e g a l v a n i q u e , Cu I 0 . 1 M CuSO., 0 . 1 M H „ S 0 . I Cu S i 4 ' 2 4 1 y pour des sulfures de c u i v r e de d i v e r s e s composi t ions et determine, avec p r e c i s i o n , l e s v a l e u r s de 1 ' a c t i v i t y du c u i v r e q u i correspondent aux l i m i t e s de l a zone de s t a b i l i t y de l a d i g e n i t e Cu.. Q S ) . Ces mesures 1 . o et l e s donne*es thermodynamiques sur l a c o v e l l i n e q u i e x i s t e n t dans l i t t e r a t u r e , ont permis de c a l c u l e r l ' e n t h a l p i e l i b r e s tandard de f o r m a t i o n de l a d i g e n i t e (y Cu^ gS) et de l a d j u r i e i t e (Cu^ 955^)• b) On a fabrique" des s u l f u r e s de c u i v r e par o x y d a t i o n , a courant constant d'une anode de c u i v r e plongee dans une s o l u t i o n ac ide sature"e en H^S. Un modele de t r a n s p o r t e i e c t r o l y t i q u e dans l a couche de s u l f u r e a ete propose pour e x p l i q u e r l a c r o i s s a n c e du f i l m . La pente du p o t e n t i e l de 1 ' e l e c t r o d e en f o n c t i o n du temps a permis de c a l c u l e r l e c o e f f i c i e n t de d i f f u s i o n des ions c u i v r e u x dans l a c h a l c o s i n e i n f e r i e u r e (Cu 0 S) et dans l a d i g e n i t e i n f e r i e u r e (y Cu., Q S ) . c) On a e t u d i e l a p o l a r i s a t i o n g a l v a n o s t a t i q u e de d isques tournants du d i g e n i t e et de c o v e l l i n e k 55°C, en s o l u t i o n 0 . 1 M C u S O ^ - 0 . 1 M ^ S O ^ . Les v a r i a t i o n s du p o t e n t i e l d ' e l e c t r o d e en f o n c t i o n du temps et de l a d e n s i t e de courant ont permis de determiner l e s r e s i s t a n c e s assoc iees a l a d i s s o l u t i o n anodique de ces s u l f u r e s . V On a d t a b l i l a c o r r e l a t i o n e n t r e l e s e x p e r i e n c e s p r d c d d e n t e s , 1 ' e l e c t r o l y s e d ' a n o d e s de m a t t e s de c u i v r e e t l e s e x p e r i e n c e s de l i x i v i a t i o n en s o l u t i o n s f e r r i q u e s d £ c r i t e s p a r p l u s i e u r s a u t e u r s . v i TABLE OF CONTENTS Page ABSTRACT - RESUME i i i LIST OF FREQUENTLY USED SYMBOLS x i v CHAPTER I. LITERATURE SURVEY AND INTRODUCTION 1 A. DIRECT LEACHING OF COPPER SULPHIDES ! 1.1 S t o i c h i o m e t r y of the l e a c h i n g r e a c t i o n s 2 1.2 Two stage l e a c h i n g of c h a l c o c i t e and d i g e n i t e 4 1.3 K i n e t i c s of d i s s o l u t i o n of copper s u l p h i d e s i n a c i d i c c h l o r i n e s o l u t i o n s 5 1.4 K i n e t i c s of d i s s o l u t i o n of copper s u l p h i d e s i n a c i d i c f e r r i c s o l u t i o n s 6 1.5 K i n e t i c s of d i s s o l u t i o n of copper s u l p h i d e s d u r i n g oxygen pressure l e a c h i n g 8 B. DIRECT ELECTROREFINING OF COPPER MATTE H 1.6 Labora tory attempts and r e l a t e d i n d u s t r i a l p r a c t i c e s H C. ELECTROCHEMICAL ASPECTS OF THE AQUEOUS OXIDATION OF COPPER SULPHIDES 1 5 1.7 Scope of the present work 15 CHAPTER 2. THERMODYNAMIC MEASUREMENTS IN THE Cu-S SYSTEM. . . 19 2 .1 Measurement method 19 2.2 E x p e r i m e n t a l 22 2.3 R e s u l t s 23 2 . 3 . 1 E l e c t r o d e p o t e n t i a l measurements 23 v i i Page 2 .3 .2 Standard f r e e e n t h a l p y of f o r m a t i o n of low d i g e n i t e -̂ 1 2 . 3 . 3 V a r i a t i o n of the s tandard f r e e e n t h a l p y of - f o r m a t i o n of d i g e n i t e w i t h compos i t ion ^2 2 .3 .4 Standard f r e e entha lpy of f o r m a t i o n of , . 14 d j u r l e i t e 2.4 D i s c u s s i o n CHAPTER 3 . AN ELECTROCHEMICAL METHOD OF MEASURING THE COPPER IONIC DIFFUSIVITY IN A COPPER SULPHIDE SCALE . . . 3 9 3.1 P r i n c i p l e of the method 3.2 T h e o r e t i c a l anode model ^ 3.3 E x p e r i m e n t a l 3.4 R e s u l t s and d i s c u s s i o n ^ CHAPTER 4. ELECTROLYTIC DISSOLUTION OF ROTATING DISKS OF COPPER SULPHIDES 56 A. GENERALITIES ON ELECTRODE KINETICS 56 4 .1 V a r i o u s types of o v e r v o l t a g e 56 B. THE ROTATING DISK ELECTRODE TECHNIQUE 4 .2 E q u a t i o n of t r a n s p o r t a t the d i s k s u r f a c e 58 4 .3 Ohmic drop i n s o l u t i o n 61 4.4 Des ign of p r a c t i c a l R . D . E 62 C. POLARIZATION OF ROTATING DISKS OF COPPER SULPHIDES 64 4.5 E x p e r i m e n t a l 64 P r e p a r a t i o n of the copper s u l p h i d e s 70 v i i i Page 4.6 P o l a r i z a t i o n of d i g e n i t e anodes 71 4 . 6 . 1 R e s u l t s 71 4 . 6 . 2 D i s c u s s i o n of the mode of t r a n s p o r t of copper i o n s through the c o v e l l i t e l a y e r 76 a- S o l i d s t a t e d i f f u s i o n 77 b . D i f f u s i o n i n the s o l u t i o n f i l l i n g the p o r e s . 78 4 . 6 . 3 D i s c u s s i o n of the p o t e n t i a l i n c r e a s e t a k i n g p l a c e be fore the t r a n s i t i o n 81 a - D i f f u s i o n o v e r v o l t a g e and p o t e n t i a l drop i n the pores 81 6 . I n t e r f a c e o v e r v o l t a g e 83 4 .7 P o l a r i z a t i o n of c o v e l l i t e anodes 84 4 . 7 . 1 R e s u l t s 8 4 a - E l e c t r o d e p o t e n t i a l measurements 84 b . E l e c t r o d e r e a c t i o n s 89 c ' M i c r o s c o p i c examinat ion of the r e a c t e d e l e c t r o d e 92 4 . 7 . 2 DISCUSSION 92 CHAPTER 5. DISCUSSION OF THE MECHANISMS OF DISSOLUTION OF THE COPPER SULPHIDES 9 8 5.1 E l e c t r o l y t i c d i s s o l u t i o n of c h a l c o c i t e : constant c u r r e n t o x i d a t i o n 9 9 5.2 Leaching of c o v e l l i t e w i t h a c i d i c f e r r i c s o l u t i o n s : e l e c t r o c h e m i c a l o x i d a t i o n x ^ 8 5.3 Leaching of c h a l c o c i t e and d i g e n i t e w i t h a c i d i c f e r r i c s o l u t i o n s : constant p o t e n t i a l o x i d a t i o n . . . x ± 5 ix Page CHAPTER 6. CONCLUSIONS 122 6.1 E l e c t r o c h e m i c a l parameters of the copper s u l p h i d e s . . 122 6.2 A p p l i c a t i o n to the e l e c t r o l y s i s of copper matte anodes and to the l e a c h i n g of copper s u l p h i d e s 125 APPENDIX 1. Use of a g a l v a n i c c e l l to measure the i o n i c c o n d u c t i v i t y of a copper s u l p h i d e membrane 126 APPENDIX 2. D i v i s i o n of the t o t a l o v e r v o l t a g e i n i t s v a r i o u s components 132 APPENDIX 3. E s t i m a t i o n of the p o t e n t i a l drop i n a d i f f u s i o n l a y e r of a p a r t i a l l y i o n i z e d e l e c t r o l y t e 135 APPENDIX 4. C a l c u l a t i o n of the d i f f u s i o n o v e r v o l t a g e a t a R . D . E . 137 APPENDIX 5. I n t e g r a t i o n of E q . (5.3) 141 APPENDIX 6. The F e 3 + / F e 2 + e l e c t r o d e 143 APPENDIX 7. I n t e g r a t i o n of E q . C5.13) 147 REFERENCES 149 • X LIST OF FIGURES F i g u r e Page 1 P o r t i o n of the phase diagram i n the Cu-S system, taken from Roseboom (11) 7 2 C h a r g e - t r a n s f e r processes between a Cu^S e l e c t r o d e and a CuSO^ e l e c t r o l y t e 21 3 Temperature dependence of the e . m . f . of the c e l l S . C . E . ( 2 5 ° C ) / 0 . 1 M C u S 0 4 - 0 . 1 M I^SO^/Cu 24 4 R e l a x a t i o n curves o b t a i n e d at 45°C a f t e r a n o d i z a t i o n and c a t h o d i z a t i o n of CuS-Cu, e l e c t r o d e s 26 1 . / OD 5 R e l a x a t i o n curves ob ta ined at 60°C a f t e r a n o d i z a t i o n and c a t h o d i z a t i o n of CuS-Cu- -,,,-S e l e c t r o d e s 27 1.765 6 Temperature dependence of the e . m . f . of the c e l l S . C . E . ( 2 5 ° C ) / 0 . 1 M C u S 0 4 - 0 . 1 M H ^ S O ^ C u S - ^ ? 6 5 S . . 28 7 Temperature dependence of the e . m . f . of the c e l l S . C . E . ( 2 5 ° C ) / 0 . 1 M C u S O . - O . l M H_SO./Cu S-Cu. 0 , C S . . 30 4 2 4 y 1.965 8 V a r i a t i o n of s tandard f r e e entha lpy of f o r m a t i o n and chemica l p o t e n t i a l s across the Cu-S system at 5 5 ° C . . . 38 9 Micrograph of the copper s u l p h i d e s c a l e , separated from i t s copper substratum 40 10 Model of the Cu^S f i l m growing on the Cu anode 46 11 Model of the copper s u l p h i d e s c a l e at the stage of Cu, 0 S growth 47 JL. o 12 Temperature dependence of the cuprous i o n d i f f u s i o n c o e f f i c i e n t i n low c h a l c o c i t e 52 13 Temperature dependence of the cuprous i o n d i f f u s i o n .. c o e f f i c i e n t i n low d i g e n i t e 53 x i F i g u r e Page 14 P a t t e r n of s t r e a m l i n e s at a R . D . E . (51) 59 15 Design of the r o t a t i n g d i s k e l e c t r o d e 65 16 Design of the s t a i n l e s s s t e e l head » 66 17 E l e c t r o l y t i c c e l l 67 18 C e l l arrangement 68 19 Exper imenta l apparatus 69 20 P o t e n t i a l - t i m e f u n c t i o n recorded d u r i n g the p o l a r i z - a t i o n of d i g e n i t e anode ( I = 37.7 mA cm ) 73 21 Dependence between the c u r r e n t d e n s i t y and the t r a n s i t i o n time 75 22 I n t e r f a c e p o t e n t i a l of a d i g e n i t e - c o v e l l i t e e l e c t r o d e versus the l o g a r i t h m of the c u r r e n t d e n s i t y 85 23 P o t e n t i a l - t i m e f u n c t i o n recorded d u r i n g the p o l a r - i z a t i o n of a c o v e l l i t e anode ( I = 0.75 mA cm ) 37 24 P o t e n t i a l - t i m e f u n c t i o n recorded d u r i n g the p o l a r - i z a t i o n of a c o v e l l i t e anode ( I = 2.26 mA cm ) 88 25 P o l a r i z a t i o n curve of c o v e l l i t e anodes 90 26 Micrograph of the s u r f a c e of an o x i d i z e d c o v e l l i t e d i s k ,93 27,28 Micrograph of the cross s e c t i o n of an o x i d i z e d c o v e l l i t e d i s k , 93,94 29,30 Scanning e l e c t r o n micrograph of o x i d i z e d c o v e l l i t e . . 94,95 31 Microprobe p i c t u r e of o x i d i z e d c o v e l l i t e : absorbed e l e c t r o n s 96 32 Microprobe p i c t u r e of o x i d i z e d c o v e l l i t e : Cu e m i s s i o n 96 x i i F i g u r e Page 33 Microprobe p i c t u r e of o x i d i z e d c o v e l l i t e : S° e m i s s i o n 96 34 Constant c u r r e n t m u l t i p l e l a y e r o x i d a t i o n model 102 35,36 Depth of p e n e t r a t i o n of the d i g e n i t e and c o v e l l i t e i n t e r f a c e s versus t i m e , d u r i n g the o x i d a t i o n of c h a l c o c i t e 106 3+ 37 Current d e n s i t y - p o t e n t i a l curves f o r the Fe (0 .1 M)/ F e 2 + ( 1 0 " 2 M) e l e c t r o d e and the F e 3 + ( 0 . 1 M ) / F e 2 + ( 1 0 ~ 3 M) e l e c t r o d e H I 38 E l e c t r o c h e m i c a l l e a c h i n g of c o v e l l i t e i n f e r r i c s o l u t i o n s H 2 39 Dependence of the l e a c h i n g r a t e of c o v e l l i t e on the f e r r i c i o n c o n c e n t r a t i o n 114 40 Constant p o t e n t i a l m u l t i p l e l a y e r o x i d a t i o n model . . . 116 41 Design of a g a l v a n i c c e l l to measure the i o n i c c o n d u c t i v i t y of a copper s u l p h i d e membrane 129 x i i i LIST OF TABLES Table Page 1 Copper e l e c t r o r e f i n i n g p r a c t i c e s 12 2 Thermodynamic data of the copper s u l p h i d e s below 100°C 37 3 E x p e r i m e n t a l measurements used i n the d e t e r m i n a t i o n of the cuprous i o n d i f f u s i o n c o e f f i c i e n t i n low c h a l c o c i t e 49 4 E x p e r i m e n t a l measurements used i n the d e t e r m i n a t i o n of the cuprous i o n d i f f u s i o n c o e f f i c i e n t i n low d i g e n i t e 50 5 P o l a r i z a t i o n of d i g e n i t e anodes 72 6 P o l a r i z a t i o n of c o v e l l i t e anodes 86 7 Rates of the f i r s t l e a c h i n g stage of d i g e n i t e and c h a l c o c i t e at 55°C i n a c i d i c f e r r i c s o l u t i o n 120 XIV LIST OF FREQUENTLY USED SYMBOLS a^ = a c t i v i t y of spec ies i 2 - 1 -1 B^ = m o b i l i t y of spec ies i , cm sec J - 3 = c o n c e n t r a t i o n of spec ies i , mole cm 2 - 1 D_j, = d i f f u s i v i t y of spec ies i , cm sec - 3 d = s p e c i f i c w e i g h t , g cm E = e l e c t r o d e p o t e n t i a l , V E = r e s t p o t e n t i a l of an e l e c t r o d e , V o E = E + n = s u r f a c e p o t e n t i a l , V s o s r _ i F = Faraday c o n s t a n t , 96,484 c l b eqgr i = c u r r e n t , A -2 I = t o t a l c u r r e n t d e n s i t y , A cm -2 1^ = c u r r e n t d e n s i t y c a r r i e d by spec ies i , A cm -2 -1 = f l u x of spec ies i , mole cm sec I = t h i c k n e s s of a s u l p h i d e l a y e r , cm M = m o l e c u l a r weight M,, . = M. = Onsager c o e f f i c i e n t , cm X s e c x J x i i l ° ' = charge c a r r i e d by p a r t i c l e i , c l b R = gas c o n s t a n t , 8.31439 J "iT'Snole - 1 2 S = s u r f a c e a r e a , cm T = abso lu te temperature , °K t = t i m e , sec t = re fe rence f o r t i m e , sec o x = a b s c i s s a at time t , cm x = a b s c i s s a at t ime t o o y = number of copper atoms per s u l p h u r atom i n compound Cu^S XV 6 = t h i c k n e s s of a d i f f u s i o n boundary l a y e r , cm AF = f r e e entha lpy change, c a l mole ^ AH entha lpy change, c a l mole ^ AS = entropy change, e . u . e o = standard e l e c t r o d e p o t e n t i a l , V \ = c h a r g e - t r a n s f e r o v e r v o l t a g e , V = d i f f u s i o n o v e r v o l t a g e , V n c = c r y s t a l l i z a t i o n o v e r v o l t a g e , V n s = n r + n = s u r f a c e o v e r v o l t a g e , V \ = ohmic p o t e n t i a l d r o p , V n = t o t a l o v e r v o l t a g e , V = chemica l p o t e n t i a l of s p e c i e s i , J mole •1 V = 2 k i n e m a t i c v i s c o s i t y of a l i q u i d , cm sec •1 al p a r t i a l c o n d u c t i v i t y due to spec ies i , 9, "*"cm a = - 1 -1 t o t a l c o n d u c t i v i t y , Q cm Ui = angular v e l o c i t y , r a d . sec T = t r a n s i t i o n t i m e , sec -1 1 CHAPTER 1 LITERATURE SURVEY AND INTRODUCTION A . DIRECT LEACHING OF COPPER SULPHIDES Heap l e a c h i n g of copper s u l p h i d e ores has been p r a c t i s e d a t R io T i n t o i n Spain f o r over 200 y e a r s , but the s tudy of the problems r e l a t e d to the d i r e c t o x i d a t i o n of copper s u l p h i d e s i n a c i d i c aqueous s o l u t i o n s has r e c e i v e d a t t e n t i o n o n l y i n the past 20 y e a r s . In s p i t e of the i n t e r e s t mani fes ted by s e v e r a l copper companies f o r such a p r o c e s s , none of the l a b o r a t o r y attempts h a s , so f a r , r e s u l t e d i n i n d u s t r i a l a p p l i c a t i o n . The r e p o r t e d works d e a l w i t h ground m i n e r a l s , s i n t e r e d s y n t h e t i c d i s k s or cast specimens. D i r e c t l e a c h i n g i s c a r r i e d out i n s u l p h u r i c , h y d r o c h l o r i c or p e r c h l o r i c s o l u t i o n s , u s i n g f e r r i c i o n s , oxygen or c h l o r i n e as o x i d i s i n g agent . The experiments cover a range of temperature between 15°C and 200°C. The v a r i e t y of c o n d i t i o n s make the comparison between these e x p e r i m e n t a l r e s u l t s d i f f i c u l t . Only p a r t of the parameters which a f f e c t the l e a c h i n g of s u l p h i d e s are c o n t r o l l e d or determined and the d i s c u s s i o n of mechanisms and r a t e c o n t r o l l i n g steps i s l e f t open to c o n j e c t u r e CD- A rev iew of the l i t e r a t u r e p u b l i s h e d on the s u b j e c t w i l l none the l e s s sum up our knowledge of the copper s u l p h i d e behaviour d u r i n g o x i d a t i o n i n a c i d i c aqueous s o l u t i o n s . 2 1 . 1 . S t o i c h i o m e t r y of the l e a c h i n g r e a c t i o n s O x i d a t i o n of copper s u l p h i d e s i n a c i d i c s o l u t i o n s y i e l d s , u l t i m a t e l y , a . c o m b i n a t i o n of e lementa l s u l p h u r , d i s s o l v e d copper and su lphate i o n s . N e v e r t h e l e s s , suphate i s the o n l y o x i d i z e d form of s u l p h u r to be s t a b l e i n these c o n d i t i o n s , and the r e a c t i o n 3 C u + + + 4H„0 + 4S° > 3CuS + HSO ~ + 7 H + i s thermodynamical ly f a v o u r a b l e . The s tandard f r e e e n t h a l p y change i s equal to AF° = -19,402 - 51.9 T, ( 2 ) , which corresponds to an e q u i l i b r i u m 25 - -in-constant of 3.74 x 10 at 25°C. Thus, a CuS-HSO^ - C u system i s more — | | s t a b l e than a S° -HS0 4 - C u system, and the e lementa l s u l p h u r e v e n t u a l l y formed d u r i n g the r e a c t i o n c o u l d subsequent ly r e a c t to form CuS and HSO^ . Loewen (3) observed, however, tha t e lementa l s u l p h u r was not o x i d i z e d to su lphate i n 0.36 M c u p r i c p e r c h l o r a t e - 0 . 2 5 M p e r c h l o r i c a c i d s o l u t i o n under 60.3 p . s . i . of oxygen at 125°C, c o n d i t i o n s which l e d to su lphate format ion from c o v e l l i t e (CuS) . E l e m e n t a l s u l p h u r , t h e r e f o r e , would not be an i n t e r m e d i a t e product i n the f o r m a t i o n of , s u l p h a t e , but s u l p h u r and s u l p h a t e would be produced s i m u l t a n e o u s l y by o x i d a t i o n processes which f o l l o w at l e a s t two d i f f e r e n t p a t h s . S u l l i v a n (4) e s t a b l i s h e d e x p e r i m e n t a l l y tha t the o x i d a t i o n of cove- l l i t e m i n e r a l s i n a c i d i f i e d f e r r i c su lphate s o l u t i o n s at 35°C produces c u p r i c ions i n s o l u t i o n and e lementa l s u l p h u r a c c o r d i n g to the r e a c t i o n CuS + 2 F e + + + C u * * + IVe^ + S° (1.1) 3 The molar percentages of copper d i s s o l v e d and e lementa l s u l p h u r l i b e r a t e d were n e a r l y the same. The molar r a t i o of copper to s u l p h u r i n the r e s i d u e a f t e r a carbon d i s u l p h i d e wash, which removed e lementa l s u l p h u r , was approx imate ly 1 : 1 . The q u a n t i t i e s of f e r r o u s and c u p r i c s a l t s produced by the o x i d a t i o n were a l s o i n a r a t i o corresponding to the s t o i c h i o m e t r y of r e a c t i o n ( 1 . 1 ) . ; • Thomas and Ingraham (5) leached pure s y n t h e t i c CuS i n a c i d i c f e r r i c su lphate s o l u t i o n s between 25 and 80°C. They found that the f e r r o u s to c u p r i c i o n r a t i o and the c u p r i c i o n to e lementa l s u l p h u r r a t i o d i d not exceed 2 . 1 : 1 and 1 .1 :1 r e s p e c t i v e l y . In a d d i t i o n , when l e a c h i n g t e s t s were c a r r i e d out i n a c i d i c f e r r i c c h l o r i d e s o l u t i o n s , o n l y 4% of the c o v e l l i t e which had r e a c t e d was found to have been converted to s u l p h a t e . The f o r e g o i n g o b s e r v a t i o n s c o n f i r m tha t e q u a t i o n (1.1) represents the predominant l e a c h i n g r e a c t i o n of c o v e l l i t e i n a c i d i c f e r r i c s o l u t i o n s below 100°C. Jackson and S t r i c k l a n d (6) r e p o r t e d that the r e a c t i o n of o x i d a t i o n of c h a l c o c i t e ( C ^ S ) and c o v e l l i t e (CuS) by c h l o r i n e i n a c i d s o l u t i o n at 50°C produced almost e x c l u s i v e l y e lementa l s u l p h u r . Oxygen pressure l e a c h i n g of copper s u l p h i d e s y i e l d s e lementa l s u l p h u r and su lphate i n v a r i o u s p r o p o r t i o n s depending on the e x p e r i - mental c o n d i t i o n s . These r e a c t i o n s are d e s c r i b e d by the two f o l l o w i n g e q u a t i o n s : CuS + l / 2 0 2 + 2H Cu 2+ O (1.2) + S CuS + 2 0 2 Cu' 2+ + SO 2- (1.3) 4 4 Warren ( 7 ) , l e a c h i n g p u r i f i e d c o v e l l i t e (CuS) i n s u l p h u r i c a c i d between the m e l t i n g p o i n t of s u l p h u r and 180°C, observed that s m a l l q u a n t i t i e s of s u l p h u r were produced i n experiments c a r r i e d at h i g h a c i d i t y (pH = 0 . 7 5 , p = 100 p . s . i . ) . 2 Loewen (3) leached c h a l c o c i t e ( C ^ S ) at 125°C w i t h 60.3 p . s . i . of oxygen and determined tha t the f r a c t i o n of s u l p h u r o x i d i z e d to s u l p h a t e v a r i e d from 15 to 72% as the a c i d i t y of the s t a r t i n g s o l u t i o n was decreased from 4 M to 0.5 M p e r c h l o r i c a c i d . Dahms, G e r l a c h and Pawlek (8) changed the c o n c e n t r a t i o n of s u l p h u r i c a c i d from 0.204 M to 0.816 M d u r i n g the l e a c h i n g of c h a l c o c i t e under 10 atm. of oxygen at 130°C. The e x t r a c t i o n of copper was completed i n 2 hours when u s i n g 0.204 M s u l p h u r i c a c i d s o l u t i o n . The q u a n t i t y of copper leached decreased r a p i d l y as the a c i d content was r a i s e d to 0.4 M and remained constant at h i g h e r a c i d i t y . The q u a n t i t y of s u l p h a t e produced dropped r a p i d l y as the a c i d c o n c e n t r a t i o n was i n c r e a s e d to 0.4 M, then i t decreased more s l o w l y t i l l i t remained unchanged f o r i n i t i a l a c i d i t i e s l a r g e r than 0.7 M. The s u l p h u r to su lphate molar r a t i o reached i t s maximum v a l u e of 1:1 f o r the l a t t e r c o n d i t i o n . 1.2 Two stage l e a c h i n g of c h a l c o c i t e and d i g e n i t e E x p e r i m e n t a l evidence i n d i c a t e s tha t the o x i d a t i o n of c h a l c o c i t e (Cu_S) and d i g e n i t e ( Cu.. 0 S ) occurs i n two s t a g e s . Z. 1 . o S u l l i v a n ( 9 ) , Thomas, Ingraham and MacDonald (10) leached c h a l c o c i t e w i t h d i l u t e f e r r i c s o l u t i o n below 50°C and n o t i c e d t h a t the r e a c t i o n slowed down markedly a f t e r 50% of the copper was d i s s o l v e d . 5 The r e s i d u e was then i d e n t i f i e d to be CuS. The f i r s t s tep of the l e a c h i n g r e a c t i o n i n v o l v e d copper o x i d a t i o n a c c o r d i n g to the e q u a t i o n Cu 2 S + 2 F e + + + • 2 F e + + + C u * * + CuS (1.4) The second step proceeded w i t h the o x i d a t i o n of c o v e l l i t e . Leaching c h a l c o c i t e at 200°C under 60 p . s . i . of oxygen, Warren (7) n o t i c e d a pH i n c r e a s e d u r i n g the f i r s t h a l f of the r e a c t i o n . T h i s i n c r e a s e was the r e s u l t of the r e a c t i o n Cu 2 S + l / 2 0 2 + 2 H + — » - C u 2 + + CuS + H^O (1.5) The a c i d i t y remained constant d u r i n g the second h a l f of the r e a c t i o n . Copper e x t r a c t i o n - t i m e curves obta ined by Dahms et a l . (8) d u r i n g oxygen l e a c h i n g (p = 10 atm.) of v a r i o u s copper s u l p h i d e s of composi - 2 t i o n i n t e r m e d i a t e between Cu 2 S and Cu^ gS c l e a r l y e x h i b i t e d two d i s t i n c t s t e p s . The q u a n t i t y of copper e x t r a c t e d at the end of the f i r s t stage depended upon the i n i t i a l c o m p o s i t i o n of the s u l p h i d e and corresponded to i t s c o n v e r s i o n i n t o CuS. Very l i t t l e s u l p h a t e , i f any, was produced d u r i n g tha t f i r s t s t a g e . 1.3 K i n e t i c s of d i s s o l u t i o n of copper s u l p h i d e s i n a c i d i c c h l o r i n e , s o l u t i o n s In the l e a c h i n g experiments conducted by Jackson and S t r i c k l a n d (6) i n a c i d i c c h l o r i n e s o l u t i o n s , the d i s s o l u t i o n r a t e s of copper s u l p h i d e s were c o n t r o l l e d by c h l o r i n e d i f f u s i o n i n the s o l u t i o n . 6 1.4 K i n e t i c s of d i s s o l u t i o n of copper sulphides i n a c i d i c f e r r i c solutions The copper-sulphur binary phase diagram (Fig. 1) indicates that the oxidation of chalcocite should r e s u l t i n the appearance of new phases following the sequence: d j u r l e i t e , digenite, c o v e l l i t e and f i n a l l y sulphur. However, unstable compositions of these phases or metastable phases may be favoured by the oxidation k i n e t i c s (12). King (13) and Burkin (14) studied the s o l i d state transformations occurring during the oxidation of synthetic ch a l c o c i t e by a c i d i c f e r r i c chloride solutions between 40 and 80°C. O p t i c a l microscopy, X-ray d i f f r a c t i o n and electron microprobing techniques were used to study the s o l i d residues recovered a f t e r leaching. The electron micro- probe analysis suggested that, as copper was leached from Cu^S, the composition of the r e s u l t i n g s o l i d varied continuously u n t i l the molar r a t i o of copper to sulphur became 1:1; the c o v e l l i t e (CuS) produced by the reaction extended i t s range of composition up to Cu_ 0S at 40°C. These authors observed also that the -material was U. o porous and cracked, that the sample could not be polished: these features reduce considerably the s i g n i f i c a n c e of microprobe readings. Leaching residues of composition intermediate between Ci^S and CuS were analysed chemically and by X-ray d i f f r a c t i o n . Residues of; composition Cu^ gS and CuS exhibited X-ray d i f f r a c t i o n patterns, i n good agreement with those of low temperature digenite and c o v e l l i t e , respectively^ as given i n the A.S.T.M. index f i l e . A regular s h i f t of the l i n e s on the X-ray photographs was interpreted as an extension of the composition range of these sulphides: digenite would e x i s t from Figure 1 . P o r t i o n of the phase diagram of the b i n a r y Cu-S system taken from Roseboom ( 1 1 ) . 8 Cu 0 S to Cu, C S and c o v e l l i t e from Cu n CS to CuS or even down to Cu _S. 1 . o JL. J l . j (J .o The r e s u l t s of K i n g (13) and S u l l i v a n (9) showed tha t the o x i d a t i o n of copper s u l p h i d e s proceeded w i t h s i m i l a r r a t e s i n h y d r o c h l o r i c and i n s u l p h u r i c s o l u t i o n s ( a n i o n i c c o n c e n t r a t i o n s <1 M ) . Changing the a c i d content of the s o l u t i o n d i d not a f f e c t s i g n i f i c a n t l y the o x i d a t i o n r a t e . Except i n v e r y d i l u t e s o l u t i o n s where the l e a c h i n g r a t e was c o n t r o l l e d by the d i f f u s i o n of f e r r i c i o n s , v a r y i n g the f e r r i c i o n c o n c e n t r a t i o n d i d not appear to a l t e r the f i r s t stage of the c h a l c o c i t e d i s s o l u t i o n , but a f f e c t e d the c o v e l l i t e d i s s o l u t i o n to some extent ( 5 , 9 , 1 0 , 1 3 ) . The a c t i v a t i o n energy c a l c u l a t e d f o r the f i r s t s tage of the c h a l c o c i t e and d i g e n i t e l e a c h i n g v a r i e s betwen 0.8 and 5 k c a l . mole \ ' t h i s v a l u e b e i n g cons idered i n d i c a t i v e of a transport c o n t r o l l e d ; r e a c t i o n (10 ,13 ,14 ) . The a c t i v a t i o n energy c a l c u l a t e d f o r the second stage of the c h a l c o c i t e l e a c h i n g (13,14) and f o r the c o v e l l i t e l e a c h i n g (5) i s between 22 and 25 k c a l . m o l e \ a range u s u a l l y a s s o c i a t e d w i t h processes c o n t r o l l e d by an i n t e r f a c e r e a c t i o n . Yet S u l l i v a n ' s experiments showed tha t the second step of the l e a c h i n g of c h a l c o c i t e was 3 to 4 t imes f a s t e r than the leaching of c o v e l l i t e i n o therwise i d e n t i c a l c o n d i t i o n s ( 4 , 9 ) . Furthermore , the r a t e of , ; o x i d a t i o n of c h a l c o c i t e was not dependent on the p a r t i c l e s i z e , though tha t of c o v e l l i t e was d i r e c t l y p r o p o r t i o n a l to the p a r t i c l e s u r f a c e ; 1.5 K i n e t i c s of d i s s o l u t i o n of copper s u l p h i d e s d u r i n g oxygen p r e s s u r e l e a c h i n g Leaching c h a l c o c i t e i n 1 M p e r c h l o r i c a c i d at 110°C under 74 p . s . i . 9 of oxygen, Loewen (3) found oxygen consumption r a t e s e q u i v a l e n t to - 2 - 2 6.3 mA cm and 0.8 .mA cm f o r the f i r s t and second s t e p , r e s p e c t i v e l y . Thomas and a l . (10) measured copper d i s s o l u t i o n r a t e s e q u i v a l e n t to -2 -2 18 mA cm f o r the f i r s t stage of l e a c h i n g of c h a l c o c i t e , and 2 mA cm f o r the l e a c h i n g of c o v e l l i t e , at 55°C i n 0 .1 M F e 3 + - 0 . 1 M H 2 S 0 4 s o l u t i o n s . I t f o l l o w s tha t copper s u l p h i d e l e a c h i n g i s much f a s t e r w i t h f e r r i c s a l t s than w i t h oxygen, below the m e l t i n g p o i n t of s u l p h u r . As s t a t e d e a r l i e r , copper s u l p h i d e l e a c h i n g w i t h oxygen takes p l a c e by way of at l e a s t two d i s t i n c t p a r a l l e l mechanisms, l e a d i n g to s u l p h u r and su lphate f o r m a t i o n . T h i s makes the o x i d a t i o n k i n e t i c s a l l the more d i f f i c u l t to r e s o l v e . The f o l l o w i n g ques t ions remain l a r g e l y unanswered, a l though they have been examined e x p e r i m e n t a l l y . Does the s u l p h u r r e s u l t from the d i r e c t e l e c t r o c h e m i c a l o x i d a t i o n of the s u l p h i d e or from the o x i d a t i o n of the hydrogen s u l p h i d e evo lved by the m i n e r a l ? Is the su lphate formed by way pf an e l e c t r o c h e m i c a l or chemica l mechanism? What i s the i n f l u e n c e of the f u s i o n of s u l p h u r (above 119°C) on the o x i d a t i o n k i n e t i c s ? What i s the r e l a t i v e importance of the v a r i o u s components of the r e a c t i o n ? . R a i s i n g the i n i t i a l a c i d i t y of the s o l u t i o n i n c r e a s e s the r a t i o of e lementa l s u l p h u r to su lphate produced by the r e a c t i o n . The f i r s t stage of the l e a c h i n g of c h a l c o c i t e i s accompanied by H + consumption (Eq. 1.5) and there i s a minimum i n i t i a l a c i d i t y r e q u i r e d to prevent the subsequent p r e c i p i t a t i o n of b a s i c s a l t s . Warren (7) observed tha t (T = 160°C, p = 40 p . s . i . ) the copper d i s s o l u t i o n r a t e i n c r e a s e d as 2 the c o n c e n t r a t i o n of s u l p h u r i c a c i d was r a i s e d from 30 g/1 to 40; g/1 . Any f u r t h e r i n c r e a s e of the a c i d i t y r e s u l t e d i n a decrease of the : 10 l e a c h i n g r a t e . The r e s u l t s ob ta ined by Dahms and a l . (8) have a l r e a d y been r e p o r t e d d u r i n g the d i s c u s s i o n of the s t o i c h i o m e t r y of the l e a c h i n g r e a c t i o n s ( S e c t i o n 1 . 1 ) . The l a r g e s t l e a c h i n g r a t e was ob ta ined f o r the minimum a c i d i t y , 0.204 M H ^ O ^ (T = 130°C, p Q = 10 a t m . ) . Any f u r t h e r i n c r e a s e of the a c i d i t y reduced the copper d i s s o l u t i o n r a t e . In a l l these exper iments , the o x i d a t i o n r a t e s i n c r e a s e d w i t h the p a r t i a l pressure of oxygen. Dahms and a l . (8) observed that the r a t e of the f i r s t l e a c h i n g step became independent of the oxygen p a r t i a l pressure above 10 atm. and tha t the r a t e of the second l e a c h i n g s tep v a r i e d as the 1/3 power of the oxygen p a r t i a l p r e s s u r e . T h i s r e l a t i o n - s h i p was e x p l a i n e d by means of oxygen a d s o r p t i o n on the m i n e r a l s u r f a c e . The d i s c r e p a n c i e s between the above works are r e v e a l e d i n the a c t i v a t i o n energies c a l c u l a t e d from the r e a c t i o n r a t e s . Warren (7) es t imated the a c t i v a t i o n energ ies a s s o c i a t e d w i t h the d i s s o l u t i o n r a t e s of copper to be 6.6 and 1.8 kcal .-mole x f o r the f i r s t and second stage of the l e a c h i n g of c h a l c o c i t e , r e s p e c t i v e l y (p^ = 40 p . s . i . , 30 g/1 H 2 S 0 4 , 100-200°C) and 11.8 k c a l . m o l e " 1 f o r the l e a c h i n g of c o v e l l i t e (pH = 0 .75 , p = 100 p . s . i . , 1 2 0 - 1 8 0 ° C ) . Loewen (3) 2 determined from the oxygen consumption r a t e s tha t the a c t i v a t i o n , energies were 1.8 and 11.4 k c a l . m o l e 1 f o r the f i r s t and second l e a c h i n g steps of c h a l c o c i t e , r e s p e c t i v e l y (1 M HCIO^, 1 1 0 - 1 4 0 ° C ) . Dahms and a l . (8) i n v e s t i g a t e d the second l e a c h i n g step of c h a l c o c i t e (0.4 M H^SO^, p Q = 10 atm.) between 40 and 140°C. They found two d i s t i n c t r a t e - t e m p e r a t u r e dependences: below 80°C, the d i s s o l u t i o n r a t e of copper was a s s o c i a t e d wi th , an a c t i v a t i o n energy of 11 1.9 k c a l . m o l e x and above 120°C, w i t h an a c t i v a t i o n energy of 20.77 k c a l . m o l e x . S i m i l a r a c t i v a t i o n energ ies were c a l c u l a t e d from the r a t e of su lphate f o r m a t i o n . T h i s type of temperature dependence c o u l d be r e l a t e d to a r e a c t i o n which takes p l a c e by two d i s t i n c t p a r a l l e l p a t h s . As the temperature i s i n c r e a s e d , the l i g h t l y a c t i v a t e d mechanism g i v e s way to the h i g h l y a c t i v a t e d one. B . DIRECT ELECTROREFINING OF COPPER MATTE 1.6 L a b o r a t o r y attempts and r e l a t e d i n d u s t r i a l p r a c t i c e s The e l e c t r o l y s i s of copper matte anodes was f i r s t attempted by Andre i n 1877 (15) . T h i s t r i a l as w e l l as l a t e r attempts were u n s u c c e s s f u l . The development by the I n t e r n a t i o n a l N i c k e l Co. of Canada of an e l e c t r o l y t i c r e f i n i n g process f o r n i c k e l matte anodes, which went i n t o p l a n t o p e r a t i o n at Thompson (Manitoba) i n 1961 (16 ,17 ) , r e v i v e d the i n t e r e s t f o r a s i m i l a r copper matte r e f i n i n g p r o c e s s . At I n c o , n i c k e l matte anodes (76.0% N i , 2.6% C u , 0.5% Co, 0.5%; Fe , 20.0% S) are e l e c t r o l y s e d i n a s u l p h a t e - c h l o r i d e s o l u t i o n (composi t ion ++ of the p u r i f i e d e l e c t r o l y t e : N i =60 g . p . l . , NaCl=100 g . p . l . , S0^= - 2 100 g . p . l . , H 3 B0 3 =20 g . p . l . ) . The c u r r e n t d e n s i t y i s 20.7 mA cm , and the c e l l v o l t a g e , which i s about 2 .3 V on the f i r s t day , g r a d u a l l y r i s e s to about 5 V near the end of the l i f e of a 2 i n c h t h i c k anode. The porous and g r a n u l a r anode s l i m e i s strongly adherent and c o n t a i n s approximate ly 95% of e l ementa l s u l p h u r . The s u l p h i d e anodes corrode at approx imate ly 94% c u r r e n t e f f i c i e n c y . The remaining 6% of the anodic c u r r e n t i s consumed by oxygen e v o l u t i o n which r e s u l t s i n an i n c r e a s e of the a n o l y t e a c i d i t y . No s i g n i f i c a n t 12 o x i d a t i o n of s u l p h u r can be d e t e c t e d . The d i f f e r e n c e between the c a t h o d i c and anodic c u r r e n t e f f i c i e n c i e s l eads to a s l i g h t d e p l e t i o n of the e l e c t r o l y t e i n n i c k e l . R e c e n t l y , s e v e r a l r esearchers i n v e s t i g a t e d the f e a s i b i l i t y of the copper matte anode e l e c t r o l y s i s on l a b o r a t o r y s c a l e (15 ,18 ,19 ,20 ) . Data on the i n d u s t r i a l p r a c t i c e of copper e l e c t r o r e f i n i n g are ; summed up i n Table 1 to a l l o w the comparison between the c o n d i t i o n s of the e l e c t r o l y s i s of copper and copper matte anodes. Table 1 Copper e l e c t r o r e f i n i n g p r a c t i c e (21,22) E l e c t r o l y t e c o m p o s i t i o n : Cu, 34-52 g . p . l . H 2 S 0 4 , 125-230 g . p . l . C l , 0 .02-0 .052 g . p . l . Fe , 0 .2-6 g . p . l . E l e c t r o l y t e - t e m p e r a t u r e 55-70 °C Power: Max. cathode c u r r e n t d e n s i t y , 16-25 mA cm _2 up to 32 mA cm Current e f f i c i e n c y , 89-98 % C e l l v o l t a g e , 0 .17-0 .40 V At 20°C, the e l e c t r o l y s i s of copper matte anodes i s accompanied by an important i n c r e a s e i n the bath v o l t a g e which reaches , i n some cases , the p r o h i b i t i v e v a l u e of 8 V (20) and i s c h a r a c t e r i z e d by a v e r y low anode y i e l d (15) . 13 The e l e c t r o l y s i s of C i^S anodes (CuSO^ = 30 g . p . l . , H 2 S ° 4 = _2 100 g . p . l . , T = 55°C) at a c u r r e n t d e n s i t y of 15 mA cm y i e l d s a ba th v o l t a g e of 0.9 V d u r i n g the f i r s t 14 h o u r s , then a sharp p o t e n t i a l i n c r e a s e develops to a maximum of 2 .1 V; the bath v o l t a g e f i n a l l y o s c i l l a t e s between 1.5 and 1.8 V (15) . The f i r s t p a r t of the e l e c t r o l y s i s corresponds to CuS f o r m a t i o n . Dur ing the second p a r t , S° f o r m a t i o n , 0^ e v o l u t i o n and e v e n t u a l l y S0^ f o r m a t i o n supplement the i n i t i a l r e a c t i o n (15) . The Cu content of the bath remains constant d u r i n g the f i r s t p a r t of the e l e c t r o l y s i s , then i t decreases l i n e a r l y ; a f t e r 5 d a y s , the s o l u t i o n i s dep le ted of 30% of i t s copper , w i t h a corresponding i n c r e a s e i n a c i d i t y (15) . The s l i m e s , g r a n u l a r and p o r o u s , remain adherent on the anode; they are composed of a m i x t u r e of CuS and S° ( 1 5 , 1 8 , 1 9 , 2 0 ) . Kuxmann and B i a l l a s s (15) observed that the copper content of the s l i m e was d e c r e a s i n g from 20% i n e l e c t r o l y t e c o n t a i n i n g 100 g . p . l . of H^SO^ to 14% i n e l e c t r o l y t e c o n t a i n i n g 250 g . p . l . of E^SO^. The increase , i n a c i d i t y r e s u l t e d a l s o i n a s m a l l decrease i n the anodic and c a t h o d i c c u r r e n t e f f i c i e n c i e s . The amount of e lementa l su lphur o x i d i z e d to s u l p h a t e v a r i e s w i d e l y w i t h the e x p e r i m e n t a l c o n d i t i o n s and from author to a u t h o r . Habashi and a l . (20) c la imed that the e lementa l s u l p h u r - s u l p h i d e balance c l o s e d w i t h i n 3% (Cu = 30 g . p . l . , H 2 S 0 4 = 100 g . p . l . , I = 10 mA c m " 2 , T = 20°C) but Venkatachalam and a l . (19) (Cu = 30 g . p . l . , H 2 S 0 4 = -2 150 g . p . l . , I = 10 mA cm , T = 33°C) and Loshkarev and a l . (18) (Cu = 35 g . p . l . , H 2 S 0 4 = 200 g . p . l . , I = 10 mA c m " 2 , T = 15°C) d e s c r i b e d measurements i n d i c a t i n g tha t 55% of the su lphur was o x i d i z e d to s u l p h a t e . Kuxmann and a l . (15) determined tha t the amount of s u l p h u r o x i d i z e d to 14 su lphate v a r i e d between 4 and 10% (Cu = 30 g . l . p . , ^ S O ^ = 100-250 g . p . l . , I = 15 m A c m " 2 , T = 5 5 ° C ) . These i n v e s t i g a t i o n s show tha t the d i r e c t e l e c t r o r e f i n i n g of copper matte i s h e a v i l y p e n a l i z e d by the copper l o s s i n the anode s l i m e (2.8% of the anode Cu content i n 250 g . p . l . ^ S O ^ e l e c t r o l y t e ( 1 5 ) ) , by the impoverishment of the e l e c t r o l y t e i n copper and by the a c i d b u i l d up r e s u l t i n g from the r e l a t i v e l y low anode e f f i c i e n c y (- 89% (15) ) . To compensate f o r these drawbacks, Kuxmann and a l . (15) added HNO^ c o n t i n u o u s l y to the e l e c t r o l y t e ( up to 0 .1 g . p . A m p . h r . ) . T h i s reduced the copper l o s s i n the s l i m e to 0.4% of the copper conta ined i n the anode and reduced the v a r i a t i o n of the copper and a c i d content of the e l e c t r o l y t e . The presence of n i t r i c a c i d e f f e c t i v e l y reduced the cathode c u r r e n t e f f i c i e n c y from 98 to approx imate ly 92% as a r e s u l t of the r e a c t i o n 3Cu + 2N0 3 ~ + 8H* > 2N0 + 3 C u 2 + + 4 ^ 0 , and i n c r e a s e d s l i g h t l y the anode c u r r e n t e f f i c i e n c y a c c o r d i n g to the equat ion 0 - 5 ) 3CuS + 2 N 0 3 " + 8 H + — * 3 C u 2 + + 3S° + 2N0 + 4 H 2 0 , The presence of n i t r i c a c i d d i d not appear to a f f e c t m a r k e d l y the s u l p h a t e f o r m a t i o n (sulphur o x i d i z e d to s u l p h a t e remained below 10% i n a l l c a s e s ) . The a d d i t i o n of n i t r i c a c i d to the e l e c t r o l y t i c b a t h seems to improye the f e a s i b i l i t y of the d i r e c t e l e c t r o r e f i n i n g of copper 15 mattes but r e p r e s e n t s the consumption of a reagent a t some a d d i t i o n a l c o s t . C. ELECTROCHEMICAL ASPECTS OF THE AQUEOUS OXIDATION OF COPPER SULPHIDES 1.7 Scope of the present work In a l l c a s e s , the o x i d a t i o n of copper s u l p h i d e s imposes a s e r i e s of s o l i d s t a t e t r a n s f o r m a t i o n s r e l e a s i n g copper i o n s i n s o l u t i o n and l e a d i n g to e lementa l su lphur f o r m a t i o n . T h i s b a s i c r e a c t i o n sequence i s sometimes accompanied by s u l p h a t e f o r m a t i o n . The development of the o x i d a t i o n r e a c t i o n s r e s u l t s from the d r i v i n g f o r c e imposed on the system, the m o b i l i t y of the v a r i o u s i n t e r f a c e s , and the r a t e of t r a n s p o r t of copper through the r e a c t i o n p r o d u c t s . The knowledge of the r e s i s t a n c e s a r i s i n g from every r e a c t i o n step should a l l o w the p r e d i c t i o n of the o v e r a l l o x i d a t i o n r a t e s . Copper s u l p h i d e s are e l e c t r o n i c c o n d u c t o r s ; c h a l c o c i t e i s a p - t y p e semiconductor , the c o n d u c t i v i t y of which i n c r e a s e s n o t a b l y w i t h copper -2 - 1 -1 d e f i c i e n c y (a - 10 to 50 9, cm at room temperature) (23 ,24 ) , 4 d i g e n i t e and c o v e l l i t e are almost m e t a l l i c i n c h a r a c t e r (a = 2 x 10 - 1 - 1 J2 cm at room temperature) (23 ,25) . Thus, e l e c t r o d e p o t e n t i a l measure- ments can be used to moni tor the s o l i d s t a t e t r a n s f o r m a t i o n s r e s u l t i n g from the o x i d a t i o n . S ince e l e c t r o d e p o t e n t i a l s are v e r y s e n s i t i v e to the presence of a second phase and of i m p u r i t i e s , the f o l l o w i n g e l e c t r o c h e m i c a l s tudy was performed on p u r e , s y n t h e t i c copper s u l p h i d e s . P r i o r to any dynamic s t u d y , the knowledge of e l e c t r o d e r e s t p o t e n t i a l s i s d e s i r e d . The s t a b i l i t y of the e l e c t r o d e - e l e c t r o l y t e system can then be a s c e r t a i n e d and the e x i s t e n c e of a thermodynamic 16 e q u i l i b r i u m p o t e n t i a l c o n s i d e r e d . T h i s s tudy began w i t h the measure- ments of the e l e c t r o m o t i v e f o r c e of the c e l l Cu I 0.1 M CuSO., 0.1 M H„S0. I Cu S, I i 4 ' 2 4 1 y which has been e s t a b l i s h e d to correspond to the e q u i l i b r i u m r e l a t i o n s h i p E = -RT l n a„ (Cu S) Cu y The s u l p h i d e c o m p o s i t i o n was s e l e c t e d to produce a two-phase e l e c t r o d e having a f i x e d copper a c t i v i t y . The e x i s t i n g thermodynamic data on the Cu-S system were r e l e v a n t o n l y to the two t e r m i n a l compounds, Cu^S and CuS (2,26). The s t a b i l i t y ranges of the v a r i o u s copper s u l p h i d e s , Cu^S, Cu^ , =Cu^ g S , : C u S , ( F i g . 1) were to be determined. Measurements of c e l l I e . m . f . w i t h a 13 h i g h impedance e l e c t r o m e t e r (10 Q i n p u t r e s i s t a n c e ) a l l o w e d the accurate d e t e r m i n a t i o n of the copper a c t i v i t y i n d i g e n i t e - c o v e l l i t e and d i g e n i t e - d j u r l e i t e m i x t u r e s . The s tandard f r e e entha lpy of f o r m a t i o n of d i g e n i t e and d j u r l e i t e was c a l c u l a t e d from these measurements and the thermodynamic data on CuS, a v a i l a b l e i n the l i t e r a t u r e (Chapter 2). The c o n t r i b u t i o n of the s o l i d s t a t e d i f f u s i o n to the t r a n s p o r t of copper ions through the o x i d a t i o n products can be assessed from the range of the copper a c t i v i t i e s corresponding to the zone of s t a b i l i t y of the o x i d a t i o n products and from the d i f f u s i o n c o e f f i c i e n t s of copper ions i n these s o l i d phases . The f o l l o w i n g experiment was designed i n order to measure the copper i o n i c d i f f u s i v i t y i n copper s u l p h i d e s . . An 17 i o n i c c u r r e n t of copper was f o r c e d through a copper s u l p h i d e membrane and the a s s o c i a t e d v o l t a g e drop determined. In the absence of s u r f a c e o v e r v o l t a g e s and e l e c t r o n i c s h o r t - c i r c u i t s , the i o n i c r e s i s t i v i t y i s d i r e c t l y measured by the p o t e n t i a l d i f f e r e n c e across the membrane. The method proved to be i n a p p l i c a b l e to d i g e n i t e , and the i r r e v e r s i b i l i t y of the r e a c t i o n s at the c o v e l l i t e e l e c t r o d e obscured these measurements (Appendix 1 ) . More v a l i d r e s u l t s were ob ta ined w i t h the f o l l o w i n g e l e c t r o c h e m i c a l experiments which a l lowed the i n d i r e c t d e t e r m i n a t i o n of the d e s i r e d d i f f u s i o n c o e f f i c i e n t s . A copper anode was o x i d i z e d i n l ^ S s a t u r a t e d a c i d s o l u t i o n s , at constant c u r r e n t . The a n a l y s i s of the e l e c t r o d e p o t e n t i a l versus time r e l a t i o n s h i p p e r m i t t e d the c a l c u l a t i o n of the copper i o n d i f f u s i v i t y i n low c h a l c o c i t e and low d i g e n i t e . The experiment c o u l d n o t , however, be extended u n t i l the f o r m a t i o n of a. l a y e r of c o v e l l i t e (Chapter 3 ) . , The apparent e l e c t r o c h e m i c a l mechanism of some l e a c h i n g r e a c t i o n s of copper s u l p h i d e s (27) suggested tha t anodic p o l a r i z a t i o n s t u d i e s cou ld p r o v i d e u s e f u l i n f o r m a t i o n on the behaviour of these s u l p h i d e s d u r i n g o x i d a t i o n . G a l v a n o s t a t i c p o l a r i z a t i o n s t u d i e s of r o t a t i n g d i s k anodes of d i g e n i t e and c o v e l l i t e were thus under taken . The r o t a t i n g d i s k e l e c t r o d e technique was adopted because the w e l l d e f i n e d geometry and hydrodynamic regime of t h i s system permi ts the c a l c u l a t i o n of the ohmic v o l t a g e drop i n s o l u t i o n and of t r a n s p o r t r a t e s i n the e l e c t r o d e boundary l a y e r . The r e l a t i o n of the e l e c t r o d e p o t e n t i a l s versus t ime and c u r r e n t d e n s i t y a l l o w e d the magnitude and e f f e c t s of the r e s i s t a n c e s a s s o c i a t e d w i t h the d i s s o l u t i o n r e a c t i o n to be assessed (Chapter 4);. 18 The behaviour of c h a l c o c i t e during s i m i l a r p o l a r i z a t i o n experiments i s d erived from the above r e s u l t s w i t h the help of t h e o r e t i c a l c o nsidera- t i o n s and c o r r e l a t e d w i t h a c t u a l experiments done by other researchers. Leaching r a t e s c a l c u l a t e d from i n f o r m a t i o n obtained i n the present work are c o n s i s t e n t w i t h experimental r a t e s observed by other i n v e s t i g a t o r s using f e r r i c oxidants i n s i m i l a r l y designed l e a c h i n g experiments. The general features of the l e a c h i n g of copper sulphides i n a c i d i c f e r r i c s o l u t i o n can be accounted f o r by the o x i d a t i o n mechanisms proposed i n the present work (Chapter 5). 19 CHAPTER 2. THERMODYNAMIC MEASUREMENTS IN THE Cu-S SYSTEM 2.1 Measurement method Many i n v e s t i g a t i o n s of chemica l r e a c t i o n s i n v o l v i n g copper s u l p h i d e s have been e x p l a i n e d on the b a s i s of the e x i s t e n c e of o n l y the two compounds, C ^ S and CuS. However, the phase diagram of the Cu-S system as p u b l i s h e d by Roseboom (11) leads to a more accura te i n t e r p r e t a - t i o n of these r e a c t i o n s . Four copper s u l p h i d e s e x i s t i n a s t a b l e form at room temperature and have been observed as m i n e r a l s : c h a l c o c i t e ( C u 2 S ) , d j u r l e i t e ( C u 1 g 6 5 S ) , d i g e n i t e (^ C ^ g S ) and c o v e l l i t e (CuS). The o n l y e x i s t i n g thermodynamic data on the Cu-S system are r e l a t i v e to the two t e r m i n a l compounds. The thermodyanmic p r o p e r t i e s of the i n t e r m e d i a t e copper s u l p h i d e s , which are e l e c t r o n i c conductors (23 ,24 , 25) , may be i n v e s t i g a t e d by e l e c t r o d e p o t e n t i a l measurements. The e q u i l i b r i u m p o t e n t i a l of a two-component e l e c t r o d e , such as a copper s u l p h i d e , depends on the p a r t i c u l a r c o m p o s i t i o n of the s o l i d and on the process of c h a r g e - t r a n s f e r between the e l e c t r o d e and the e l e c t r o l y t e ; t h i s c h a r g e - t r a n s f e r can take p l a c e through the c a t i o n , the an ion or a redox . couple present i n the s o l u t i o n . When two or more d i f f e r e n t c h a r g e - t r a n s f e r processes occur independent ly of each o t h e r , at the same e l e c t r o d e s u r f a c e , c u r r e n t s of o p p o s i t e s i g n f l o w across the e l e c t r o d e - e l e c t r o l y t e boundary, r e s u l t i n g i n a change of the chemica l compos i t ion of the system. The r e s t p o t e n t i a l , w h i c h i s measured i n the absence of an e x t e r n a l f l o w of c u r r e n t , i s then a -mixed p o t e n t i a l . C h a r g e - t r a n s f e r processes i n v o l v i n g both the Cu and the S spec ies cou ld occur at the s u r f a c e of a Cu S e l e c t r o d e i n contac t w i t h a CuSO. y 4 20 e l e c t r o l y t e ; t h i s would r e s u l t i n a subsequent a l t e r a t i o n of the c o m p o s i t i o n of the s o l i d and of the s o l u t i o n ( F i g . 2 ) . S t u d i e s of the r e s t p o t e n t i a l s of e l e c t r o d e s of s y n t h e t i c and n a t u r a l , c h a l c o c i t e and c o v e l l i t e e s t a b l i s h e d that the p o t e n t i a l of these e l e c t r o d e s v a r i e d w i t h the a c t i v i t y of c u p r i c i o n s i n s o l u t i o n , i n a way i d e n t i c a l to a copper e l e c t r o d e , and that they were not a f f e c t e d by the presence of su lphate ( 1 5 , 2 8 , 2 9 , 3 0 ) . The s tandard p o t e n t i a l of a C ^ S e l e c t r o d e i n c u p r i c s o l u t i o n , at 25°C, was d e r i v e d from these experiments as 486 mV (15) , 490 mV (28) and 505 mV (29) . The s tandard p o t e n t i a l o f a CuS e l e c t r o d e i n c u p r i c s o l u t i o n , at 25°C, was c a l c u l a t e d to be 597 mV (30) and 567 mV (29) . F u r t h e r evidence tha t the SP-SO^ couple i s i n e r t has been o t a i n e d by Loewen ( 3 ) , who v e r i f i e d tha t e l ementa l s u l p h u r d i d not o x i d i z e to su lphate i n c u p r i c p e r c h l o r a t e s o l u t i o n at 125°C under 60.3 p . s . i . of oxygen. S u l l i v a n ( 4 , 9 ) , who s t u d i e d the o x i d a t i o n of copper s u l p h i d e s i n a c i d i c f e r r i c s o l u t i o n below 100°C, e s t a b l i s h e d tha t the f i n a l products of o x i d a t i o n were c u p r i c i o n s and e lementa l s u l p h u r , though su lphate was the most s t a b l e s u l p h u r spec ies i n h i s exper imenta l c o n d i t i o n s . Therefore the p o t e n t i a l d i f f e r e n c e between the s u l p h i d e e l e c t r o d e and the c u p r i c s u l p h a t e e l e c t r o l y t e i s determined by the r e a c t i o n ( C u ) C u s " — * C u ^ + 2e y The e l e c t r o m o t i v e f o r c e of the g a l v a n i c c e l l C u / 0 . 1 M CuSO,, 0 .1 M H S 0 , / C u S (I) 4 2 4 y 21 Pt or C e CuyS (Cu)- ( S H E-,_. —>. CuS0 4 (aq) 2+ Cu SO 2- Ox. Red. Charge-transfer processes. F i g u r e 2. C h a r g e - t r a n s f e r processes between a Cu S e l e c t r o d e and a CuSO. e l e c t r o l y t e . ^ 22 i s a d i r e c t measurement of the copper a c t i v i t y i n the s u l p h i d e , -2AE F= u C u ( C u y S ) - u ° u = RT l n a Cu C e l l I may be cons idered as a double c e l l i n v o l v i n g the two i n d i v i d u a l c e l l s and both the Cu and Cu^S p o t e n t i a l s are measured s e p a r a t e l y versus S . C . E . ( 2 5 ° C ) . 2.2 E x p e r i m e n t a l Copper s u l p h i d e s of a p p r o p r i a t e Cu to S r a t i o were s y n t h e s i z e d at 400°C i n sea led q u a r t z tubes from 99.999% pure Cu and S p u r i f i e d a c c o r d i n g to the method of Bacon and F a n e l l i (31) . The product was pressed under vacuum i n t o a d i s k , 13 mm i n diameter by 1 mm t h i c k . The s u l p h i d e was cemented to a p l a t i n u m f o i l w i t h epoxy r e s i n made c o n d u c t i v e by the a d d i t i o n of g r a p h i t e powder. The specimen was then mounted i n a c r y l i c r e s i n (Koldmount) and p o l i s h e d . The e l e c t r o l y t e (0 .1 M CuSO^, 0 .1 M H^SO^) was kept f r e e from oxygen by c o n t i n u o u s l y b u b b l i n g h e l i u m , w h i c h had been p r e v i o u s l y s a t u r a t e d w i t h the same s o l u t i o n . : The c e l l was immersed i n an o i l thermosta t . The c e l l e . m . f . was measured by a h i g h impedance e l e c t r o m e t e r . C u / 0 . 1 M C u S 0 4 , 0 .1 M H 2 S 0 4 / S . C . E . ( 2 5 ° C ) , (ID S . C . E . ( 2 5 ° C ) / 0 . 1 M CuSO. , 0 .1 M H o S 0 . / C u S 4 2 4 y ' ( I I I ) 23 ( K e i t h l e y 630) . The r e f e r e n c e e l e c t r o d e was a s a t u r a t e d ca lomel e l e c t r o d e at 25°C: c o r r e c t i o n s c a l c u l a t e d from de Bethune, L i c h t and Swendeman's data (32) were made to compensate f o r the temperature f l u c t u a t i o n s of the r e f e r e n c e e l e c t r o d e . The P t - C u l e a d c o n t a c t s were at room temperature . The s o l u t i o n was analysed by e l e c t r o g r a v i m e t r y f o r copper a f t e r each f i n a l measurement. 2 . 3 . R e s u l t s 2 . 3 . 1 . E l e c t r o d e p o t e n t i a l measurements The r e s u l t s of the measurements of the Cu e l e c t r o d e p o t e n t i a l s are r e p o r t e d i n F i g . 3 as a f u n c t i o n of temperature . Measurements were made a f t e r an a n o d i z i n g or c a t h o d i z i n g treatment on e l e c t r o d e s of d i f f e r e n t p u r i t y , some be ing annealed under H ^ . The e x p e r i m e n t a l v a l u e s f o l l o w a l i n e a r r e l a t i o n s h i p i n the temperature range, 35-75°C. E = (70.45 ± 0.33) x 10~ 3 + (0.632 + 0.025) x 10~ 3 (T - 328) (V) The equat ion and the e r r o r s were c a l c u l a t e d by the c l a s s i c a l method of the l i n e a r r e g r e s s i o n f o r a p r o b a b i l i t y of 98%. E l e c t r o d e s of c o m p o s i t i o n Cu^ ^^S were then s t u d i e d . An X - r a y d i f f r a c t i o n p a t t e r n conf irmed the e x i s t e n c e of the two phases , d i g e n i t e and c o v e l l i t e . C o v e l l i t e i s r e p o r t e d to be s t o i c h i o m e t r i c , d i g e n i t e i n e q u i l i b r i u m w i t h c o v e l l i t e has the compos i t ion Cu^ ^^^S, t h i s c o m p o s i t i o n l i m i t remaining constant up to 200°C (11) . A sample s y n t h e s i z e d at h i g h temperature should s t i l l be i n e q u i l i b r i u m a f t e r c o o l i n g down to room temperature. To a p p r e c i a t e the r e v e r s i b i l i t y of the e l e c t r o d e r e a c t i o n , the . d i g e n i t e - c o v e l l i t e m i x t u r e was sub jec ted to a n o d i z i n g and c a t h o d i z i n g 35 45 55 65 75 T ( ° C ) F i g u r e 3. Temperature dependence of the e . m . f . of the c e l l S . C . E . (25°C) I 0 .1 M C u S 0 4 - 0 . 1 M H 2 S 0 4 ] Cu a f t e r a n o d i z a t i o n a f t e r c a t h o d i z a t i o n H„ annealed A • A 2 25 c u r r e n t . The amount of c u r r e n t passed through the specimen r e s u l t e d i n a v a r i a t i o n of 0.3% of i t s average Cu c o n t e n t . A f t e r s w i t c h i n g o f f , the e l e c t r o d e p o t e n t i a l was recorded as a f u n c t i o n of t i m e . The s t a b i l i z e d e l e c t r o d e was then sub jec ted to a c u r r e n t of o p p o s i t e s i g n and the r e s t p o t e n t i a l r e c o r d e d . A s e r i e s of these r e l a x a t i o n curves i s shown on F i g . 4. Though the r e l a x a t i o n curves o b t a i n e d a f t e r s u c c e s s i v e a n o d i z a t i o n and c a t h o d i z a t i o n on the same sample were not s y m m e t r i c a l , the r e l a x a t i o n curves ob ta ined a f t e r a n o d i z a t i o n and . c a t h o d i z a t i o n of two f r e s h specimens were symmetr i ca l and more convergent . The gap between any set of two curves decreased w i t h i n c r e a s i n g tempera- t u r e , as i t appears from the comparison of F i g . 4 and 5 . F o r c i n g c u r r e n t i n or out of the e l e c t r o d e forces the f o l l o w i n g r e a c t i o n to the r i g h t or to the l e f t , CuS + 0.765Cu - — y Cu, , , , - S , -* 1.765 ' unless one of the s u l p h i d e s takes care of the Cu by c o m p o s i t i o n changes. The whole specimen homogenizes by d i f f u s i o n . The e q u i l i b r i u m e l e c t r o d e p o t e n t i a l was chosen i n the m i d d l e of the gap between two corresponding r e l a x a t i o n c u r v e s . The r e s u l t s are p l o t t e d on F i g . 6 as a f u n c t i o n of temperature . They are expressed by a l i n e a r r e l a t i o n s h i p i n the temperature range , 40 -70°C, E = (251.50 + 0.35) x 10~ 3 + CO.765 + 0.035) x 1 0 ~ 3 CT - 328).-(V). The equat ion and the e r r o r s were c a l c u l a t e d by the c l a s s i c a l method t (hours) ure 4. R e l a x a t i o n curves obta ined at 45°C a f t e r a n o d i z a t i o n or c a t h o d i z a t i o n of CuS-Cu.. e l e c t r o d e s . A O a f t e r c a t h o d i z a t i o n ^ 9 a f t e r a n o d i z a t i o n A O treatment on f r e s h e l e c t r o d e 260 - 255 - 0 50 100 t ( h r s ) F i g u r e 5 . R e l a x a t i o n curves of CuS-Cu-^ 7 6 5 S e l e c t r o d e s , a t 60°C. • o a f t e r a n o d i z a t i o n Q • a f t e r c a t h o d i z a t i o n O D treatment on f r e s h e l e c t r o d e 2 6 5 2 5 5 > J iii 2 4 5 2 3 5 4 0 5 0 6 0 7 0 T ( ° C ) F i g u r e 6. Temperature dependence of the e . m . f . of the c e l l S . C . E . (25°C) I 0.1 M CuSO' - 0 . 1 M H o S 0 , I CuS-Cu, 4 z 4 1 1.765 • ' no p r e l i m i n a r y e l e c t r o l y s i s O • d i f f e r e n t batches of s u l p h i d e s 29 of the l i n e a r r e g r e s s i o n f o r a p r o b a b i l i t y of 9 8 % . S u l p h i d e s of c o m p o s i t i o n Cu^ g^S and Cu^ ggS were s y n t h e s i z e d . . X - r a y d i f f r a c t i o n p r o v i d e d evidence f o r the presence of both d i g e n i t e and d j u r l e i t e . A c c o r d i n g to Roseboom C H ) the Cu r i c h l i m i t of d i g e n i t e v a r i e s w i t h temperature , go ing from Cu^ ^ S a t room tempera- t u r e to Cu^ g^S at 83°C where d i g e n i t e i n v e r t s i t s c r y s t a l s t r u c t u r e . The e l e c t r o d e p o t e n t i a l of the d i g e n i t e - d j u r l e i t e m i x t u r e was ; measured d u r i n g h e a t i n g and c o o l i n g c y c l e s . A p e r i o d from 24 to 96 hours was a l l o w e d f o r e q u i l i b r a t i o n at each temperature . The e x p e r i m e n t a l r e s u l t s are r e p o r t e d on F i g . 7 as a f u n c t i o n of temperature . The v a l u e s can be accommodated by a s t r a i g h t l i n e r e l a t i o n s h i p ) E = C242.20 ± 0 . 4 5 ) x 1 0 _ 3 + CO.62 + 0 . 0 6 ) x 1 0 _ 3 Ct - 343) CV) The equat ion and the e r r o r s were c a l c u l a t e d by the c l a s s i c a l l i n e a r r e g r e s s i o n f o r a p r o b a b i l i t y of 9 8 % . I t appears that the r e a c t i o n Cu S + C1.965 - y)Cu • Cu, „ , C S * y 3 1 .965 takes p l a c e q u i t e r e a d i l y above 70°C but becomes s l u g g i s h below 55 °C . This i s c o n s i s t e n t w i t h Roseboom's C H ) o b s e r v a t i o n that the d j u r l e i t e f o r m a t i o n i s r e v e r s i b l e at 93°C. CUyS represents the Cu r i c h l i m i t of d i g e n i t e , y i s a f u n c t i o n of temperature , 1.79 < y < 1 . 8 3 . 250 h - 240 230 55 65 75 85 T(°C) F i g u r e 7. Temperature dependence of the e . m . f . of the c e l l S . C . E . (25°C) | 0.1 M CuSO / -0 .1 M H o S0 / - | Cu^S-Cu 4 " "2"~4 O A d i f f e r e n t composi t ions , a f t e r h e a t i n g • • d i f f e r e n t composi t ions , a f t e r c o o l i n g • excluded from the l i n e a r r e g r e s s i o n . 1.965" o 31 Specimens of c o m p o s i t i o n Cu^ g g S produced, i n s p i t e of a c o o l i n g r a t e of 10°C per day, a m i x t u r e of c h a l c o c i t e and metas tab le t e t r a g o n a l d j u r l e i t e i d e n t i f i e d by X - r a y d i f f r a c t i o n . T e t r a g o n a l d j u r l e i t e i s o f t e n r e p o r t e d to be present i n s u l p h i d e of compos i t ion i n t e r m e d i a t e between c h a l c o c i t e and d i g e n i t e s y n t h e s i z e d at h i g h temperature (11 ,33 ) . From the r e p o r t e d set of exper imenta l d a t a , the s tandard f r e e entha lpy of f o r m a t i o n of low d i g e n i t e and d j u r l e i t e can be c a l c u l a t e d . The s tandard s t a t e s are pure Cu, pure orthorhombic S and the pure copper s u l p h i d e of the s t a t e d c o m p o s i t i o n . 2 . 3 . 2 . Standard f r e e e n t h a l p y of f o r m a t i o n of low d i g e n i t e The a c t i v i t y of copper i n a c o v e l l i t e - d i g e n i t e m i x t u r e i n e q u i l i - brium i s d i r e c t l y r e l a t e d to the s tandard f r e e entha lpy of the r e a c t i o n CuS + 0.765Cu > Cu.. -,,-,-S, 1.765 which depends o n l y on the s tandard f r e e e n t h a l p y of f o r m a t i o n of CuS and C u 1 > 7 6 5 S , AF° (Cu, _,_S) = AF° (CuS) + 0.765 RT l n a„ . 1 . / D J L.U Von Wartenberg (34) measured the heat of f o r m a t i o n of CuS at 25°C, is A H 298°K. ^ C u S ) = " I - 1 ' 6 1 0 * 4 0 0 c a l . m o l e - 1 * .1 c a l . = 4.1840 J . 32 and Kubaschewsky and Weibke (35) assessed the e x p e r i m e n t a l e r r o r . Anderson (36) c a l c u l a t e d the entropy of CuS at 20°C from s p e c i f i c heat measurements. H i s v a l u e has been s e l e c t e d by K . K . K e l l e y as the most probable (37) . A S 2 9 8 ° K ^ C u S ^ = 0 , 3 " 0 , 4 5 c a 1 , m o l e " 1 O K _ 1 These are the o n l y data on CuS r e s u l t i n g from d i r e c t measurements. Any v a l u e ob ta ined by e x t r a p o l a t i o n from h i g h temperature measurements, supposing the e x i s t e n c e of an e q u i l i b r i u m between CuS and C ^ S are o b v i o u s l y d o u b t f u l . However, Kubaschewsky, Evans and A l c o c k (26) are i n favour of a more n e g a t i v e heat of f o r m a t i o n f o r CuS. I n the temperature range, 4 0 - 7 0 ° C , the s tandard f r e e entha lpy of f o r m a t i o n of Cu-poor d i g e n i t e i s then c a l c u l a t e d to be AF° (Cu± 7 6 5 S ) = (-18,140 ± 525) - (4.90 + 2.50) (T - 328) c a l . m o l e - 1 . 2 . 3 . 3 . V a r i a t i o n of the s tandard f r e e entha lpy bf f o r m a t i o n of d i g e n i t e w i t h c o m p o s i t i o n The e f f e c t of compos i t ion v a r i a t i o n s on the s tandard f r e e entha lpy of f o r m a t i o n of d i g e n i t e can be c a l c u l a t e d , yCu + S —> Cu S y The f r e e entha lpy of the system can be expressed i n terms of the chemical p o t e n t i a l of i t s c o n s t i t u e n t s , 33 A F ° ( c u y S ) = y ( y C u - y C u ) + M s - y ; The t o t a l d e r i v a t i v e of the f r e e entha lpy w i t h r e s p e c t to y i s e q u a l to d[AF°(Cu y S)] - ( u C u - y ° u ) d y + y d C y ^ - ^ + d ( y g - y^ ) (3,1) T h i s e x p r e s s i o n of Eq (3.1) can be s i m p l i f i e d to d[AF°(Cu y S)] = ( y C u - y ° u ) d y (3.2) by u t i l i z i n g the Gibbs-Duhem r e l a t i o n s h i p I n t e g r a t i o n of E q . (3.2) between the compos i t ion l i m i t s of d i g e n i t e y i e l d s the corresponding d i f f e r e n c e of the s tandard f r e e e n t h a l p y of f o r m a t i o n , y 2 AF°(Cu S) - AF°(Cu S) = / (y - v ° )dy y 2 y ± y ^ L u The r i g h t hand s i d e of t h i s e q u a t i o n i s equal to the area bounded by the i n t e g r a t i o n l i m i t s and l o c a t e d below the e x p e r i m e n t a l c u r v e , ]i - = f ( y ) , which has not been determined. As the chemica l p o t e n t i a l of a component i n a s t a b l e compound i s a c o n t i n u o u s l y i n c r e a s i n g f u n c t i o n of c o m p o s i t i o n , t h i s area i s i n t e r m e d i a t e between 34 the s u r f a c e s of the r e c t a n g l e s ( y „ - y 1 ) ( y - y° ) and &. JL uu uu ( y 0 - y n ) ( y - y° ) . In the d i g e n i t e case , these two v a l u e s d i f f e r by £. x uu uu approximate ly 12% and the v a r i a t i o n of the s tandard f r e e e n t h a l p y of f o r m a t i o n can be approximated by U C u ( y l ) + v C u ( y 2 ) AF°(Cu S)-AF°(Cu S ) = ( y „ - y i ) t U 1 C U 1 y 9 ' y-, w 2 ' i ' 2 y 2 - - y l 2 R T [ l n a C u ( y i ) + In a C u ( y 2 ) i n t r o d u c i n g an e r r o r < 6%. T h i s i n f o r m a t i o n makes the c a l c u l a t i o n of the s tandard f r e e entha lpy of f o r m a t i o n of d j u r l e i t e p o s s i b l e . 2 . 3 . 4 . Standard f r e e entha lpy of f o r m a t i o n of d j u r l e i t e In a d i g e n i t e - d j u r l e i t e m i x t u r e i n e q u i l i b r i u m , Cu S + (1.965 - y) Cu -> Cu. - , , -S . y J 1.965 • the Cu a c t i v i t y i s r e l a t e d to the s tandard f r e e entha lpy change of the r e a c t i o n . In t h i s case , the c o e f f i c i e n t m u l t i p l y i n g the Cu chemical p o t e n t i a l i s temperature dependent. The s tandard f r e e entha lpy of f o r m a t i o n of d j u r l e i t e i s g i v e n by AF'CCUj^ 9 6 5 S ) = AF°(Cu yS) + (1.965 - y)RT In a C u , and i n the temperature range, 55 -80°C, i t has been c a l c u l a t e d to be 35 AF' ( C i ^ 9 6 5 S ) = (-19,700 ± 550) - (5 .5 ± 3 .1 ) (T - 343) c a l mole 1 . 2 . 4 . D i s c u s s i o n At 93°C, d j u r l e i t e decomposes i n t o d i g e n i t e (Cu^ g^S) and c h a l c o c i t e ( C u 1 < 9 9 S ) (11 ,38 ) , 0 . 1 6 6 C u 1 > 8 4 0 S + 0 . 8 3 3 C u 1 > 9 9 0 S — * C u ^ S . T h i s e q u i l i b r i u m ac ts as a r e f e r e n c e p o i n t f o r c o r r e l a t i n g the present measurements w i t h the e x i s t i n g data on the system. The s tandard f r e e entha lpy of f o r m a t i o n of d j u r l e i t e i s d e r i v e d from the measurements performed i n t h i s work , A F ° „ , , 0 „ ( C u 1 r , ^ r S) = 19,830 i 600 c a l mole 366 K 1.965 ' The s tandard f r e e entha lpy of f o r m a t i o n of h i g h d i g e n i t e can be e x t r a p o l a t e d from the present measurements, A F ° _ , - 0 (Cu. Q / S ) = j o b K. JL. OH -18,900 ± 600 c a l m o l e " 1 . Von Wartenberg (34) determined the heat of f o r m a t i o n of Cu^S at 298°K, A H ° 9 8 0 K ( C u 2 S ) = 18,970 c a l m o l e " 1 . Kubaschewsky and Weibke (35) i n t h e i r d i s c u s s i o n on the Cu-S data s e l e c t e d t h i s v a l u e as the most p r o b a b l e , a s s e s s i n g the exper imenta l e r r o r to 500 c a l mole \ Cu 2 S has been s t u d i e d i n d e t a i l by Richardson et a l . (39) u s i n g R 2-H_ 2S e q u i l i b r i u m i n the temperature range 800-1000°K, by Brook (40) i n the temperature range 500-1000°K and by J . B . Wagner et a l . (41) u s i n g e . m . f . measurements at 500°K. I t s s tandard f r e e entha lpy of f o r m a t i o n seems to be a c c u r a t e l y e s t a b l i s h e d i n that temperature range, but e x t r a p o l a t i o n of these v a l u e s to room temperature can o n l y l e a d to h i g h 36 e r r o r s because of the i n a c c u r a c y of the s p e c i f i c heat d a t a . For tha t r e a s o n , Von Wartenberg 's data seems more a p p l i c a b l e than the v a l u e proposed by Kubaschewsky, Evans and A l c o c k (26) . Anderson ' s (36) and K e l l e y ' s (37) data on the entropy of Cu^S y i e l d , a long w i t h Von Wartenberg 's data f o r AH°, AF° , 0 i r ( C u 0 S ) = 20,900 ± 800 c a l m o l e " 1 . ODD K Z In these c o n d i t i o n s the two se t s of data converge w i t h i n 700 c a l . mole ^ , a gap which s i t s i n the m i d d l e of the e x p e r i m e n t a l e r r o r of 1400 c a l . mole x . The e n t h a l p i e s , e n t r o p i e s and f r e e e n t h a l p i e s of the copper , s u l p h i d e s below 100°C are summarized i n t a b l e 2. The d i g e n i t e and d j u r l e i t e v a l u e s are based on measurements d e s c r i b e d i n t h i s work , the c o v e l l i t e and c h a l c o c i t e v a l u e s are s e l e c t e d on the b a s i s of the best low temperature data shown i n the l i t e r a t u r e . The major component (90%) of the f i n a l e r r o r on the v a l u e s c a l c u l a t e d from the present measurements o r i g i n a t e s from the e r r o r a s s o c i a t e d w i t h the e x i s t i n g data on CuS. The v a r i a t i o n of Cu and S chemica l p o t e n t i a l s across the Cu-S system can then be assessed at any temperature ( F i g . 8 ) . However, the v a l u e proposed f o r the d j u r l e i t e - c h a l c o c i t e e q u i l i b r i u m i s c o n j e c t u r a l : i t was not measured d i r e c t l y and the accuracy of the e x i s t i n g data d i d not a l l o w i t s c a l c u l a t i o n . The d i f f e r e n c e i n f r e e entha lpy of f o r m a t i o n between d j u r l e i t e and c h a l c o c i t e i s much s m a l l e r than the e x p e r i m e n t a l e r r o r on any of these v a l u e s . Though the Cu chemica l p o t e n t i a l i n the d j u r l e i t e - c h a l c o c i t e system i s known at 93°C from the present measure- ments, the u n c e r t a i n t y on the entropy change of the r e a c t i o n (0 .1 ±, 0.3) e . u . does not a l l o w any e x t r a p o l a t i o n . Table 2 Thermodynamic data of the copper s u l p h i d e s below 100°C Composi t ion A F 0 / . . - 1 c a l mole AS°/ . c a l mole 1 °K 1 Ref . CuS ( c ) . (-11,610 ± 400) - (0 .3 ± 0.45)T 0.3 ± 0.45 34 ,35 ,36 ,37 C U 1 . 7 6 5 S (D.) • (-18,140 ± 520) - (4.9 ± 2.5(T-328) 4 .9 ± 2.5 t h i s work Cu S y ( D . ) . (-18,140 ± 520) - (4.9 ± 2.5(T-328) t h i s work + (y - 1. ,765)[ ( -7 ,910 ± 40) - (3.2 ± 3.5) (T-328) C U 1 . 9 6 5 S ( D j . ) . (-19,700 ± 550) - (5.5 ± 3.1)(T-343) 5.5 ± 3 .1 t h i s work Cu 2 S ( C h . ) . - (18 ,970 ± 500) - (5 .3 ± 0.8)T 5 .3 ± 0.8 34 ,35 ,36 ,37 OJ + 0 O -5-5 •60 -6-5 IC. 1 . ~ 0 u -20 50 _i I 55 i 60 65 %Cu u — C u S 1.765 1.805 1.965 Z Figure 8. V a r i a t i o n of standard f r e e enthalpy of formation and of chemical p o t e n t i a l s across the Cu-S system at 55°C. oo 39 CHAPTER 3. AN ELECTROCHEMICAL METHOD OF MEASURING THE COPPER IONIC DIFFUSIVITY IN A COPPER SULPHIDE SCALE 3 . 1 . P r i n c i p l e of the method Copper s u l p h i d e s can be grown on a copper anode from an a c i d i c s o l u t i o n s a t u r a t e d w i t h ^ S . I f the o p e r a t i o n i s conducted at constant c u r r e n t , d i f f e r e n t s u l p h i d e l a y e r s of d e c r e a s i n g copper a c t i v i t y are grown as the o x i d a t i o n proceeds . I f e q u i l i b r i u m i s e s t a b l i s h e d , the s u c c e s s i v e phases should be , a c c o r d i n g to the phase diagram (11) ( F i g . 1 ) : copper , c h a l c o c i t e , d j u r l e i t e , d i g e n i t e , c o v e l l i t e and s u l p h u r . The r e a c t i o n occurr ing at the anode i s y Cu + H„S — * Cu S + 2 H + + 2e 2 y The e l e c t r o c h e m i c a l p o t e n t i a l of such an e l e c t r o d e (Stokholm convention) i s g i v e n by the f o l l o w i n g r e l a t i o n s h i p , a y a •n RT , Gu Ho S , /-TIN o ~ ~z¥ V s a C u S a H + y The copper a c t i v i t y at the s o l i d - l i q u i d i n t e r f a c e r e f l e c t s the c o n d i t i o n s imposed upon the system and the t r a n s p o r t p r o p e r t i e s of the s c a l e be ing grown. The s u l p h i d e a c t i v i t y i s taken as u n i t y . In d e f i n e d geometr ic and s t i r r i n g c o n d i t i o n s , under a constant c u r r e n t , the hydrogen s u l p h i d e 40 and hydrogen i o n a c t i v i t i e s are constant i n the v i c i n i t y of the e l e c t r o d e . In s t e a d y - s t a t e c o n d i t i o n s , the s u r f a c e o v e r v o l t a g e f o r a g i v e n s u l p h i d e i s assumed to be a c o n s t a n t . T h e r e f o r e , the e l e c t r o d e p o t e n t i a l v a r i a - t i o n w i t h time f o l l o w s the e v o l u t i o n of the copper a c t i v i t y a c c o r d i n g to the r e l a t i o n s h i p (3.2) d e r i v e d from E q . ( 3 . 1 ) , dE _ _ RT d _ y dt " 2F dt i n E C u dE RT d . „ t dt = " ^2F dT a C u 7 = c o n s t a n t ^ 3 - 2 ) I f the s u l p h i d e s c a l e grows u n i f o r m l y on the e l e c t r o d e s u r f a c e , the copper a c t i v i t y at the l i q u i d - s o l i d i n t e r f a c e can be d i r e c t l y l i n k e d to the t r a n s p o r t p r o p e r t i e s of the s u l p h i d e l a y e r . 3.2 T h e o r e t i c a l anode model I n the copper s u l p h i d e s , the su lphur i o n - m o b i l i t y i s cons idered n e g l i g i b l e i n comparison w i t h the copper i o n m o b i l i t y (42) . In the case of h i g h temperature phases (aCX^S, gCu^S) there i s e x p e r i m e n t a l evidence (43,44) to support t h i s . I t i s a l s o reasonable f o r the low temperature phases i n view of the r e l a t i v e l y l a r g e s i z e and a s s o c i a t e d i m m o b i l i t y of the a n i o n . The copper s u l p h i d e s are e l e c t r o n i c c o n d u c t o r s . C h a l c o c i t e i s a p - t y p e semiconductor , i t s c o n d u c t i v i t y i n c r e a s i n g n o t a b l y w i t h copper -2 -1 - 1 d e f i c i e n c y (a = 1 0 ->- 50 Q cm at room temperature) (23 ,24) . D i g e n i t e 4 -1 - 1 and c o v e l l i t e are almost m e t a l l i c i n c h a r a c t e r (a = 2.10 Q cm at room temperature (23 ,25) . 41 The phenomenological equat ions f o r d i f f u s i o n r e l a t e the p a r t i c l e f l u x to the f o r c e s r e s p o n s i b l e f o r t h e i r m o t i o n . I f the i n t e r a c t i o n e f f e c t s are n e g l e c t e d , u n i d i m e n s i o n a l t r a n s p o r t i n a two component system i n the presence of a low s t r e n g t h e l e c t r i c f i e l d can be equated by J Cu+ = - M C u + & " C « + + W- k * > >  C 3 ' 3 ) J e = " M e 4 ̂ e +W •> (3'4) The e l e c t r i c a l p o t e n t i a l g r a d i e n t can be d e r i v e d from equat ion (3.4) and s u b s t i t u t e d i n equat ion ( 3 . 3 ) , T  q C u + M C u + ,d q C u + d . r _ J Cu+ ~ ~ q M ~ J e = " M Cu+Cdx" v Cu+ ~ ~ dx" V ( 3 - 5 ) Chemical p o t e n t i a l s of i o n and e l e c t r o n are not e x p e r i m e n t a l l y a c c e s s i b l e v a l u e s but are r e l a t e d through the measurable q u a n t i t y , u , VCu = yCu+ + y e Equat ion (3.5) i s then s i m p l i f i e d to M + A Jn + + -TT- J " ~ M_ + ~ i i _ (3.6) Cu+ M e Cu*: dx Cu As repor ted e a r l i e r , the copper s u l p h i d e s are e l e c t r o n i c c o n d u c t o r s , t h e i r e l e c t r o n i c c o n d u c t i v i t y be ing much l a r g e r than t h e i r i o n i c 42 c o n d u c t i v i t y , and equat ion (3.6) can be reduced to J Cu+ = " MCu+ »Cu (3'7) The Onsager c o e f f i c i e n t i s d i r e c t l y r e l a t e d to the c o n d u c t i v i t y , CK, m o b i l i t y , B_^, and d i f f u s i v i t y , D ^ , of the p a r t i c l e i . "2 M. = a . q . l l I M. = B . C . (3.8) D i M. = C. i RT i Equat ion (3.7) can be expressed i n terms of any of these f o u r parameters T Cu d /_ n , W - - — dx" y C u ( 3 ' 9 ) I f the s u l p h i d e s c a l e grows u n i f o r m l y and c o n t i n u o u s l y over the whole e l e c t r o d e s u r f a c e , the sample t h i c k n e s s at any time i s p r o p o r t i o n a l to the number of coulombs passed through the e l e c t r o l y t i c c e l l d u r i n g that t i m e , TCu+ C t ~ V , M , .„ 1 n , X " * 0 = yl C d } Cu S C 3 ' 1 0 ) y Combining equat ions ( 3 . 2 ) , (3.9) and (3.10) y i e l d s equat ion ( 3 . 1 1 ) , 2 1 • M. dE ' U N XCu+ 2? ( d } C u S = + °Cu+ d7 y 43 which permits the c a l c u l a t i o n of the i o n i c c o n d u c t i v i t y of the s u l p h i d e s c a l e , formed under steady s t a t e c o n d i t i o n s , from the s lope of the r e c o r d i n g of the e l e c t r o d e p o t e n t i a l as a f u n c t i o n of t i m e . 3 .3 E x p e r i m e n t a l The anode was made of copper rod (99.995% p u r i t y ) 0.905 cm i n d i a m e t e r , mounted i n a c r y l i c r e s i n (Koldmount) , and p o l i s h e d so tha t o n l y one plane was i n contact w i t h the s o l u t i o n . The s o l u t i o n , 0.2 M i n Na„S0. and 0.2 M i n H^SO. , was s a t u r a t e d by c o n t i n u o u s l y bubbled 2 4 2 4 H^S. A s t r o n g c o n v e c t i o n p a t t e r n was brought about by a magnetic s t i r r e r . The system was h e l d at constant temperature by a r e g u l a t e d water b a t h . A 21 v o l t N i - C d b a t t e r y u n i t p r o v i d e d c u r r e n t to the system through a set of a p p r o p r i a t e r e s i s t o r s . The e l e c t r o d e p o t e n t i a l was measured versus a s a t u r a t e d ca lomel e l e c t r o d e by a K e i t h l e y 153 v o l t m e t e r which fed the s i g n a l to a SargentSRG r e c o r d e r . S e r i e s of experiments were c a r r i e d out at temperatures between 30 and 73°C (below the d i g e n i t e t r a n s i t i o n temperature) and under -4 -2 - 3 s e l e c t e d c u r r e n t d e n s i t i e s between 1.9 10 A cm and 1.55 x 10 . -2 A cm The s u l p h i d e l a y e r showed a u n i f o r m t h i c k n e s s over the e l e c t r o d e s u r f a c e ( F i g . 9) w h i c h ranged from 50 to 380 V- depending on exper imenta l c o n d i t i o n s and the p e r i o d of o x i d a t i o n . The r e a c t i o n products were i d e n t i f i e d by X - r a y d i f f r a c t i o n on a powder sample. The s c a l e s t r u c t u r e and morphology c o u l d not be i n v e s t i g a t e d by m i c r o s c o p y , e l e c t r o n d i f f r a c t i o n or - m i c r o p r o b i n g . The t h r e e - s u l p h i d e assembly was not i n e q u i l i b r i u m and i n the absence of an e l e c t r i c F i g u r e 9. Micrograph of the copper s u l p h i d e s c a l e separated from i t s Cu substra tum. The CU-CU2S i n t e r f a c e was on the r i g h t s i d e of the specimen. D i g e n i t e and d j u r l e i t e are the o n l y two phases to remain p r e s e n t . The band s t r u c t u r e r e s u l t s from d i f f e r e n c e s i n the s c a l e morphology emphasized by p o l i s h i n g . 45 c u r r e n t one phase disappeared d u r i n g the t ime r e q u i r e d f o r the sample p r e p a r a t i o n a c c o r d i n g to the r e a c t i o n , 0 .8Cu o S + 0 .2Cu, QS Z l . o 3.4 R e s u l t s and D i s c u s s i o n s So f a r , three suphides have been i d e n t i f i e d , c h a l c o c i t e , d j u r l e i t e , and d i g e n i t e . No e v i d e n c e , e i t h e r d i r e c t or i n d i r e c t , f o r the appear- ance of c o v e l l i t e was obta ined i n these exper iments . The s u l p h i d e growth model , analysed e a r l i e r i n t h i s paper , i s v a l i d o n l y i n s t e a d y - s t a t e c o n d i t i o n s ; that i s , when the c a t i o n i c and t o t a l e l e c t r i c c u r r e n t s are c o n s t a n t . These c o n d i t i o n s are s a t i s f i e d when the f i r s t s u l p h i d e l a y e r (Cu^S) i s d e p o s i t e d . The s t o i c h i o m e t r y range of low c h a l c o c i t e i s s m a l l e r than 0.5% of i t s copper content (11) and d u r i n g Cu^S f o r m a t i o n , the i o n i c c u r r e n t v i r t u a l l y equals the t o t a l e l e c t r i c c u r r e n t ( F i g . 10) . When a new s u l p h i d e s t a r t s to grow on the anode, the copper f l u x r e a c h i n g the s o l i d - l i q u i d i n t e r f a c e i s changed a c c o r d i n g to the Cu to C u + r a t i o i n the new phase. I f the d i g e n i t e compos i t ion i s a p p r o x i - mated by Cu, Q S , the r e a c t i o n o c c u r r i n g at the l i q u i d - s o l i d i n t e r f a c e l . o at the stage of d i g e n i t e growth can be represented by F i g . 11 , and the c o r r e s p o n d i n g l y c a t i o n i c (1^ +) and e l e c t r o n i c (J°) c u r r e n t s are equal to 90 and 10%, r e s p e c t i v e l y , of the t o t a l c u r r e n t ( I ) . The boundary between two s o l i d phases i s c h a r a c t e r i z e d by a thermodynamical ly f i x e d v a l u e of copper a c t i v i t y or e l e c t r o c h e m i c a l p o t e n t i a l ; t h e r e f o r e , the p o t e n t i a l drop i n each s u l p h i d e l a y e r i s a c o n s t a n t . Consequent ly , Cu 1.96^ ' F i g u r e 10. M o d e l o f the Cu^S f i l m g r o w i n g on t h e a n o d e . 47 Cu 1.8 CuS S~~—* C "L8 S * 2e I " - Icu*+Ie I C u * - . 9 r ifc - X - .11 .11 > X»o F i g u r e 1 1 . Model of the copper s u l p h i d e s c a l e a t the stage of Cu, DS growth. JL. o 48 the abrupt change i n cuprous c u r r e n t at the onset of growth of a new phase i n i t i a t e s an unsteady s t a t e process d u r i n g which each s u l p h i d e l a y e r a d j u s t s i t s t h i c k n e s s to the new c u r r e n t c o n d i t i o n s . The s o l i d s t a t e t r a n s f o r m a t i o n s accompanying the phase boundary mot ion are b e l i e v e d to generate s t r e s s e s i n the specimen, because the s c a l e always breaks away from the copper be fore CuS growthis apparent . So f a r , the d i g e n i t e s t o i c h i o m e t r y range has been i g n o r e d . The d i g e n i t e compos i t ion i s r e p o r t e d (11) to extend from Cu^ yg^S to Cu, 7 n S at room temperature . A l t h o u g h the Cu poor l i m i t i s not a f f e c t e d by temperature , the Cu r i c h l i m i t changes to Cu, 0 0 S at 83°C 1. o J where d i g e n i t e i n v e r t s to h i g h d i g e n i t e . Dur ing the d i g e n i t e l a y e r growth there i s a cont inuous change i n the Cu c u r r e n t f l o w i n g through the s c a l e , but t h i s v a r i a t i o n represents o n l y 1.75% of the t o t a l c u r r e n t and i s s m a l l e r than the e x p e r i m e n t a l accuracy of the method of measurement. From the se t of exper imenta l d & t a , the c a t i o n i c d i f f u s i v i t y of the c h a l c o c i t e and d i g e n i t e i n the s c a l e was c a l c u l a t e d i n the range of temperature from 30 to 73°C (Tables 3 and 4 ) . Though d j u r l e i t e was present i n every sample, the i o n i c c o n d u c t i v i t y v a l u e could not p o s s i b l y be d e r i v e d from the e x p e r i m e n t a l c u r v e . T h i s phase probably d i d not extend over enough atomic l a y e r s to a l l o w a steady s t a t e to be e s t a b l i s h e d . The measured i o n i c c o n d u c t i v i t y of d i g e n i t e was independent of the c u r r e n t d e n s i t y used . In the c h a l c o c i t e case , however, there was a c u r r e n t d e n s i t y v a l u e above which the e x p e r i m e n t a l r e s u l t s became i n c o n s i s t e n t . T h i s l i m i t i n g c u r r e n t d e n s i t y i n c r e a s e d s h a r p l y w i t h temperature. The dependence of the apparent i o n i c c o n d u c t i v i t y on the Table 3 Exper imenta l measurements used i n the d e t e r m i n a t i o n of the cuprous i o n d i f f u s i o n c o e f f i c i e n t i n low c h a l c o c i t e S = 0.644 cm T i E range (mV) C o r r e l a t i o n dE n (°C) (mA) C u 2 S / H 2 S 0.2 M Na s a t . . 0.2 M H„S0. -2 4 - S O . / S . C . E . ( 2 5 ° C ) 2 4 C o e f f i c i e n t r dt (mV min X ) U (fi cm -1) (cm sec ) 30 0.125 490-410 0.9985 0.0410 0.786 x 10 5 2.93 X i o " 1 1 40 0.250 520-465 0.9997 0.0818 1.60 X io" 5 6.15 X i o " 1 1 40 0.250 425-390 0.9977 0.0835 1.57 X io" 5 6.03 X i o " 1 1 46 0.250 480-425 0.9971 0.0659 1.98 X io" 5 7.74 X i o " 1 1 48 0.250 510-475 0.9976 0.0712 1.84 X io" 5 7.25 X i o " 1 1 50 0.234 525-485 0.9977 0.0521 2.95 X io" 5 11.70 X i o " 1 1 51 0.250 508-450 0.9921 0.0526 2.45 X io" 5 9.75 X i o " 1 1 55 0.250 480-445 0.9986 0.0357 3.67 X io" 5 14.8 X i o " 1 1 55 0.250 465-430 0.9966 0.0403 3.25 X io" 5 13.1 X i o " 1 1 55 0.500 500-456 0.9990 0.140 3.74 X io" 5 15.1 X i o " 1 1 58 0.750 510-412 0.9997 0.292 3.97 X io" 5 16.1 X i o " 1 1 62 0.750 525-410 0.9980 0.222 5.22 X I O " 5 21.5 X i o " 1 1 66 0.750 515-458 0.9993 0.241 4 .81 X io" 5 20.0 X i o " 1 1 70 0.500 500-465 0.9969 0.0738 7.09 X I O " 5 29.9 X i o " 1 1 70 1.000 505-435 0.9985 0.282 7.43 X I O " 5 31.3 X i o " 1 1 73 1.000 505-485 0.9989 0.271 7.61 X I O " 5 32.3 X i o " 1 1 Table 4 Exper imenta l measurements used i n the d e t e r m i n a t i o n of the cuprous i o n d i f f u s i o n c o e f f i c i e n t i n low d i g e n i t e S = 0.644 cm' T i E range (mV) C o r r e l a t i o n dE D (°C) (mA) '^Cu 1 0.2 0 S / H 0 S s a t . , 0.2 M H„S0. - M - N a 2 S 0 4 / S . C . E . ( 2 5 ° C ) C o e f f i c i e n t r dt (mV min 1 ) o {Q cm , 2 - (cm sec - 1) 30 0.125 235-225 0.9987 0.0137 1.76 X io" 5 0.683 X i o " 1 0 40 0.250 251-240 0.9936 0.0280 3.50 X io" 5 1.40 X i o ' 1 0 40 0.500 235-200 0.9989 0.110 3.56 X io" 5 1.42 X i o " 1 0 40 0.500 281-255 0.9976 0.123 3.17 X i o ' 5 1.27 X i o " 1 0 40 0.500 275-243 0.9990 0.112 3.50 X io" 5 1.40 X i o ' 1 0 40 0.750 250-225 0.9999 0.292 3.09 X i o ' 5 1.23 X i o ' 1 0 40 0.750 . 240-210 0.9998 0.253 3.48 X io" 5 1.39 X i o " 1 0 46 0.250 251-225 0.9968 0.0239 4.08 X io" 5 1.66 X i o ' 1 0 48 0.250 270-260 0.9888 0.0221 4 .43 X io" 5 1.81 X i o ' 1 0 51 0.250 268-245 0.9964 0.0168 5.74 X io" 5 2.38 X i o" 1 0 55 0.500 250-225 0.9973 0.0522 7.50 X io" 5 3.14 X i o " 1 0 55 0.750 251-225 0.9987 0.107 8.24 X io" 5 3.45 X i o " 1 0 55 0.250 255-240 0.9815 0.0143 6.85 X io" 5 2.87 X i o" 1 0 58 0.750 262-238 0.9976 0.0967 8.96 X i o ' 5 3.81 X i o " 1 0 62 0.750 255-235 1.0000 0.0833 10.6 X io" 5 4.53 X i o ' 1 0 66 0.750 250-225 0.9966 0.0799 10.9 X io" 5 4.74 X i o " 1 0 70 0.500 245-230 0.9865 0.0264 14.8 X io" 5 6.47 X i o " 1 0 70 1.000 247-234 0.9965 0.0833 18 .8 X io" 5 8.22 X i o" 1 0 73 1.000 250-230 0.9940 0.0711 21.7 X io" 5 9.62 X i o" 1 0 51 c u r r e n t d e n s i t y r a i s e s the problem of the morphology of the s u l p h i d e s grown e l e c t r o l y t i c a l l y . I t i s u s u a l p r a c t i c e to c l a s s i f y anodic f i l m s as cont inuous or non cont inuous f i l m s . I n most of the cases r e p o r t e d i n the l i t e r a t u r e , the d i s t i n c t i o n between cont inuous and non cont inuous f i l m s i s based on the na ture of the r e s i s t a n c e of the f i l m to the c u r r e n t f l o w . I t i s c h a r a c t e r i s t i c of non cont inuous f i l m to e x h i b i t an approx imate ly constant and low r e s i s t a n c e (a few ohms) to the c u r r e n t f l o w d u r i n g the growth of the s c a l e (45) . The smooth copper anode and the one . p lane e l e c t r o d e s u r f a c e prevented i n t r o d u c i n g s t r e s s e s which might have lead to the c r a c k i n g of the f i l m . There was no s o l i d s t a t e t r a n s f o r m a t i o n when the u s e f u l measurements were made, i . e . , when s t e a d y - s t a t e c o n d i t i o n s p r e v a i l e d . The f i l m growth was k i n e t i c a l l y c o n t r o l l e d by the copper i o n d i f f u s i o n through the s o l i d , which mechanism favoured the f o r m a t i o n of a cont inuous u n i f o r m s c a l e . A decrease of the i o n i c s t r e n g t h of the s o l u t i o n (0 .1 Na^SO^, 0 .1 I^SO^) d i d not a f f e c t the exper imenta l r e s u l t s . , The measured d i f f u s i o n c o e f f i c i e n t of cuprous i o n i n low c h a l c o c i t e was found to be ( F i g . 12) D + = 8 .1 x 10~ 3 exp. - 5,870 T 2 - 1 cm sec = 1.1 x 10 -10 2 -1 at 50°C. cm sec The measured d i f f u s i o n c o e f f i c i e n t of cuprous i o n i n low d i g e n i t e was found to be ( F i g . 13) 52 Figure 12. Temperature dependence of the cuprous ion d i f f u s i o n c o e f f i c i e n t i n low chal c o c i t e . 53 In D 23.5 I ' 1 ' 1 L _ 2.9 3.0 3.1 3.2 3.3 i ( IO" 3 oK~') Figure 13. Temperature dependence of the cuprous ion diffusion coefficient in low digenite. 54 o c -,n~2 .6,100 2 - 1 D ^ u + = 3.6 x 10 exp. J - J T— cm sec D„ + = 2.4 x 1 0 - 1 0 c m 2 s e c - 1 a t 50°C. In the temperature range s t u d i e d , cuprous i o n s d i f f u s e about t w i c e as f a s t i n d i g e n i t e as i n c h a l c o c i t e . The a c t i v a t i o n energy f o r , * - 1 , d i f f u s i o n (AH) i s 11.7 Z 1 k c a l mole f o r c h a l c o c i t e , and 12.1 X * - 1 0.8 k c a l mole f o r d i g e n i t e . I f an a c t i v a t i o n entropy f o r d i f f u s i o n i s to be c a l c u l a t e d , the nature and c o n c e n t r a t i o n of d i f f u s i n g d e f e c t s must be known. The d i f f u s i o n i n i o n i c type c r y s t a l s i s o f t e n a s s o c i a t e d w i t h the m i g r a t i o n of Schot tky or F r e n k e l type d e f e c t s . X - ray i n v e s t i g a t i o n s have suggested tha t i n some i o n i c type c r y s t a l s m e t a l l i c i o n s were d i s t r i - buted v i r t u a l l y a t random among a l a r g e number of n e a r l y e q u i v a l e n t l a t t i c e s i t e s (ctAg^S (46) , a A g l (47) , aCu^S (44 ) ) . I n the case of low c h a l c o c i t e and d i g e n i t e which have r e l a t i v e l y ordered copper l a t t i c e s , an i n t e r s t i t i a l c y mechanism (the c a t i o n s be ing e q u a l l y mobi le ) may, account f o r the cuprous i o n d i f f u s i o n . T h i s i s supported by the exper imenta l o b s e r v a t i o n tha t no s i g n i f i c a n t v a r i a t i o n of the d i f f u s i o n c o e f f i c i e n t has been observed w i t h d e v i a t i o n from s t o i c h i o m e t r y . T h e r e f o r e , the equat ion of z e o l i t i c d i f f u s i o n should be a p p l i c a b l e (48) , 2 kT AS AH X h7~ e x p ' T~ 6 X p ' _ RT' ' where \ i s the average d i s t a n c e t r a v e l l e d by the d i f f u s i n g p a r t i c l e i n —8 one j ump (Sk - 2 x 10 cm) The. l i m i t s of c o n f i d e n c e f o r the c a l c u l a t e d a c t i v a t i o n energies are es t imated f o r a p r o b a b i l i t y of 95%. 55 k i s the Boltzmann c o n s t a n t , 1.380 x 10 e r g . molecule ^ °K ^ -27 h i s the P l a n c k c o n s t a n t , 6.62 x 10 e r g . s e c . The a c t i v a t i o n entropy f o r d i f f u s i o n (AS) i s then 1.9 e . u . f o r c h a l c o c i t e and 1.3 e . u . f o r d i g e n i t e , r e s p e c t i v e l y . These low v a l u e s are c o n s i s t e n t w i t h a mechanism which i n t r o d u c e s l i t t l e d i s o r d e r i n g i n the l a t t i c e . 56 CHAPTER 4. ELECTROLYTIC DISSOLUTION OF ROTATING DISKS OF COPPER SULPHIDES A . GENERALITIES ON ELECTRODE KINETICS 4 .1 V a r i o u s types of o v e r v o l t a g e An e l e c t r o d e r e a c t i o n r a t e , a c c o r d i n g to F a r a d a y ' s l a w , i s p r o p o r t i o n a l to the c u r r e n t d e n s i t y , I . The dependence of c u r r e n t d e n s i t y upon e l e c t r o d e p o t e n t i a l , c o n c e n t r a t i o n s of r e a c t a n t s , and other v a r i a b l e s such as s t i r r i n g and temperature , must be e s t a b l i s h e d i n order to determine the e l e c t r o d e r e a c t i o n r a t e - f u n c t i o n s , and to e x p l a i n the sequence of p a r t i a l r e a c t i o n s c o n s t i t u t i n g the o v e r a l l e l e c t r o d e r e a c t i o n , which i s observed by means of chemica l a n a l y s i s . The r e s i s t i v e p a r t i a l r e a c t i o n s govern the type and magnitude o f ; t h e o v e r v o l t a g e , n = E - E o where E i s the e l e c t r o d e p o t e n t i a l when c u r r e n t f lows and E i s the o p o t e n t i a l i n the absence of c u r r e n t , i . e . , the e q u i l i b r i u m p o t e n t i a l i f there i s o n l y one r e a c t i o n t a k i n g p l a c e at the e l e c t r o d e . The f o l l o w i n g d i s t i n c t i o n between the v a r i o u s types of o v e r y o l t a g e , which, correspond to the f o u r p o s s i b l e types of r a t e - c o n t r o l , was* i n t r o d u c e d by Bonhoef fe r , G e r i s h e r and V e t t e r (1950) and i s developed i n V e t t e r ' s " E l e c t r o c h e m i c a l K i n e t i c s " C49): - A c h a r g e - t r a n s f e r o v e r v o l t a g e , n , p r e v a i l s i f o n l y the t r a n s p o r t 57 of charge c a r r i e r s across the e l e c t r i c a l double l a y e r e x i s t i n g at the phase boundary i s hindered. - I f a chemical r e a c t i o n i s hindered, the r a t e constant of which i s , by d e f i n i t i o n , independent of the p o t e n t i a l , the current flow produces a r e a c t i o n overvoltage, n r . - D i f f u s i o n overvoltage, n D , i s encountered when mass tr a n s p o r t by d i f f u s i o n to and from the e l e c t r o d e surface i s rate-determining : during current flow. - Hindrance of the process by which atoms are in c o r p o r a t e d i n t o or removed from the c r y s t a l l a t t i c e leads to c r y s t a l l i z a t i o n o vervoltage, The various overvoltage types have been analysed i n d i v i d u a l l y on a t h e o r e t i c a l b a s i s so that the current d e n s i t y versus overvoltage r e l a t i o n s h i p has received a general mathematical expression i n s e v e r a l cases. I f s e v e r a l of the p a r t i a l r e a c t i o n s have low r a t e s of s i m i l a r order of magnitude, the corresponding overvoltages are superimposed to Zovm the t o t a l overvoltage. Since the v a r i o u s overvoltages are, i n t e r r e l a t e d , V e t t e r (49) proposed a d e f i n i t i o n f o r the d i v i s i o n of the measured overvoltage i n i t s d i f f u s i o n , r e a c t i o n , c r y s t a l l i z a t i o n and charge-transfer components, which i s based on the requirement that upon the disappearance of a l l overvoltage types but one, the r e s i d u a l overvoltage must agree w i t h the d e f i n i t i o n f o r the s i n g l e remaining overvoltage type (Appendix 2). The components of the measured over- voltage can, then, be sorted out on the b a s i s of the t h e o r e t i c a l r e l a t i o n s h i p s obeyed by the v a r i o u s overvoltage types, provided only « 58 one o v e r a l l e l e c t r o d e r e a c t i o n o c c u r s . The exper imenta l i n v e s t i g a t i o n of e l e c t r o d e k i n e t i c s r e q u i r e s a c a r e f u l d e s i g n of the exper imenta l c o n d i t i o n s i n order to e l i m i n a t e or c a l c u l a t e the ohmic drops and the mass t r a n s p o r t l i m i t a t i o n s . The r o t a t i n g d i s k e l e c t r o d e p r o v i d e s a system where these c a l c u l a t i o n s are p o s s i b l e i n the s t e a d y - s t a t e c o n d i t i o n s . B . THE ROTATING DISK ELECTRODE TECHNIQUE 4.2 E q u a t i o n of t r a n s p o r t at the d i s k s u r f a c e The c a l c u l a t i o n of the maximum r a t e at which a substance can be t r a n s p o r t e d towards or from an e l e c t r o d e , J , . , i s i n g e n e r a l an l i m ° i n t r a c t a b l e problem. Transport may be e f f e c t e d by d i f f u s i o n , c o n v e c t i o n and e l e c t r i c a l m i g r a t i o n . The s i t u a t i o n i s s t i l l more complex i f one of the spec ies takes p a r t i n a homogeneous r e a c t i o n s i n c e the chemica l r e a c t i o n r a t e has to be taken i n t o account i n the c a l c u l a t i o n . A r o t a t i n g d i s k of i n f i n i t e d i a m e t e r , i n a n o n - t u r b u l e n t , s t a t i o n a r y regime, i s one of the few systems where the v e l o c i t y d i s t r i - b u t i o n throughout the body of the v i s c o u s f l u i d can be c a l c u l a t e d (51) . F i g u r e 14 i l l u s t r a t e s the p a t t e r n of s t r e a m l i n e s at the s u r f a c e of a r o t a t i n g d i s k . Using t h i s model , L e v i c h (51) s o l v e d e x p l i c i t l y the s t e a d y - s t a t e c o n v e c t i v e d i f f u s i o n e q u a t i o n , assuming constant p h y s i c a l p r o p e r t i e s , i n some cases : t r a n s p o r t of uncharged p a r t i c l e s , t r a n s p o r t i n a b i n a r y e l e c t r o l y t e , t r a n s p o r t of an i o n i c spec ies i n the presence of an excess of i n d i f f e r e n t e l e c t r o l y t e (3 i o n s ) . 'As the Schmidt number, 59 Figure 14. P a t t e r n of streamlines at the surface of a r o t a t i n g d i s k (51). 60 Sc = jjt approaches °°, Levich's s o l u t i o n takes the form 0.620 D. 2 / 3 v " 1 / 6 u, 1 / 2(C,-C.) J. - ± (4.1) where t i s the transport number of species i i n a binary e l e c t r o l y t e , t = 0 for uncharged species or for a charged species i n the presence of an excess of i n d i f f e r e n t e l e c t r o l y t e , v i s the kinematic v i s c o s i t y of the s o l u t i o n , to i s the angular v e l o c i t y of the disk. The d i f f u s i o n boundary layer i s defined as a region of r a p i d l y changing concentration i n the immediate v i c i n i t y of the electrode surface, the thickness, 6, of which i s defined as 1 _ 1/3 1/6 -1/2 6 = "6T620 D i v and appears to be constant over the e n t i r e surface of the disk. Thus, from the d i f f u s i o n point of view, the r o t a t i n g disk electrode (R.D.E.) o f f e r s a uniformly accessible reaction s i t e . The d i f f u s i o n overvoltage can be calculated with the Nernst equation and Eq. (4.1), i f the p h y s i c a l properties of the solution.are known or i f the l i m i t i n g current density has been determined. The sum of experimental studies intended to v e r i f y the v a l i d i t y of equation (4.1) leaves no doubt that Levich's theory i s correct (52). The c o r r e c t i o n suggested by Gregory and Riddiford (53) to take i n t o account the f i n i t e value of the Schmidt number, Sc = -g-, (100 < Sc. < 5000 i n aqueous solutions) i s only s i g n i f i c a n t i n the cases of very accurate experimental measurements (54) (experimental error = 1%). 61 The assumption of constant t r a n s p o r t p r o p e r t i e s (D,v) r e s t r i c t s the a p p l i c a t i o n of equat ion (4.1) to d i l u t e s o l u t i o n s ; Newman and Hsueh developed a n u m e r i c a l s o l u t i o n to compute the l i m i t i n g c u r r e n t i n the case of v a r i a b l e p h y s i c a l p r o p e r t i e s (54) . 4 .3 Ohmic drop i n s o l u t i o n Newman s t u d i e d t h e o r e t i c a l l y the e f f e c t of the s o l u t i o n r e s i s t a n c e to the c u r r e n t f l o w , below the l i m i t i n g c u r r e n t d e n s i t y (55) . In the absence of e l e c t r o d e o v e r v o l t a g e s , the c u r r e n t d i s t r i b u t i o n i s comple te ly determined by the ohmic drop i n s o l u t i o n . A c a l c u l a t i o n shows tha t the pr imary c u r r e n t d e n s i t y i s i n f i n i t e at the edge of the d i s k and h a l f of the average v a l u e a t the c e n t e r . Newman assessed the degree of n o n - u n i f o r m i t y of the c u r r e n t d i s t r i b u t i o n , i n the case of k i n e t i c c o n t r o l by mass t r a n s p o r t i n the s o l u t i o n and c h a r g e - t r a n s f e r a t the e l e c t r o d e , a g a i n s t the p h y s i c a l and e l e c t r o c h e m i c a l parameters of the system. The p r e d i c t e d c u r r e n t d i s t r i b u t i o n was v e r i f i e d e x p e r i m e n t a l l y by measuring the v a r i a t i o n s i n the t h i c k n e s s of a copper d e p o s i t i n 0 .1 M CuSO. -0 .1 M H.SO. s o l u t i o n A u n i f o r m c u r r e n t d e n s i t y can be expected at a R . D . E . i f the ohmic drop i n s o l u t i o n i s s m a l l compared w i t h the e l e c t r o d e o v e r v o l t a g e . Newman e s t a b l i s h e d , i n the case of the pr imary c u r r e n t d i s t r i b u t i o n , the f o l l o w i n g formula to c a l c u l a t e the ohmic drop between the e l e c t r o d e and a p o i n t s i t u a t e d i n the e l e c t r o d e p l a n e , o u t s i d e the r i m (r > r Q ) , at a d i s t a n c e , r , from the center (57 ,58) . 4 2 4 (56) . r I - l r / r N 2 1/2 o tan (4.2) 2a s 62 where a i s the conductivity of the bulk s o l u t i o n , 4.4. Design of p r a c t i c a l R.D.E. Riddiford, i n h i s review of the r o t a t i n g disk electrode technique (52), discussed the design of a p r a c t i c a l electrode which conforms as c l o s e l y as possible to the t h e o r e t i c a l requirements. A disk of f i n i t e radius w i l l meet the l i q u i d flow requirements provided the radius, r Q , i s very much greater than the thickness:of the momentum boundary layer, i . e . , f ^ > 1 / 2 =0, r oi o and provided the Reynolds number, Re = r ^ —, i s l e s s than the c r i t i c a l value f o r the onset of turbulence. Experimental studies of the c r i t i c a l Re number at a r o t a t i n g disk i n d i c a t e that f o r a p r a c t i c a l R.D.E., the Re number should not exceed 2 x: 10~* at the edge of the v disk. On the other hand, the r o t a t i o n a l speed of the disk must be • large enough to exclude any s i g n i f i c a n t contribution from natural convection. The shape and dimensions of an electrode of f i n i t e span must be c a r e f u l l y designed and checked to introduce no disturbing edge e f f e c t . In that respect, the best design i s a c o n i c a l electrode, the base of which i s a c t i v e for 0 < r < r Q , the region r Q to r ^ being i n a c t i v e . Riddiford pointed out that c y l i n d r i c a l electrodes should be avoided, since i t was shown experimentally that, i n t h i s case, the f l u i d flow was turbulent even for very small Re numbers. 63 A f u r t h e r requirement i s t h a t the d i s k s u r f a c e i s the o n l y e f f e c t i v e bounding s u r f a c e i n the system. The l i q u i d - g a s boundary, the w a l l s of the c o n t a i n i n g v e s s e l , the c o u n t e r - e l e c t r o d e , the L u g g i n c a p i l l a r y , e t c . should not i n t e r f e r e w i t h the f l o w p a t t e r n brought about by the s p i n n i n g d i s k . Gregory and R i d d i f o r d (52) , u s i n g d i s k s 5 .3 cm i n d i a m e t e r , r o t a t i n g at 146 r . p . m . i n beakers of d i f f e r e n t s i z e s , checked t h a t t h i s requirement was s a t i s f i e d when the s o l u t i o n - a i r i n t e r f a c e and the bottom and s i d e w a l l s of the beaker were a l l more than 0.5 cm away from the d i s k . In a p r a c t i c a l R . D . E . , the L u g g i n c a p i l l a r y may be l o c a t e d i n the lower h a l f of the system p r o j e c t i n g up c l o s e to the center of the d i s k a long the a x i s r = 0. More o f t e n , . i t i s l o c a t e d i n the upper h a l f of the system w i t h the t i p r e a c h i n g the plane of the d i s k (y = 0 ) . Flows i n the upper and lower p a r t do not i n t e r a c t i n t h i s system. F i n a l l y thediskmust be h o r i z o n t a l , of minimum e c c e n t r i c i t y ( e c c e n t r i - c i t y of 0.025 mm i s quoted by a number of workers) and smooth to the extent that the s u r f a c e i r r e g u l a r i t i e s are much s m a l l e r than the d i f f u s i o n boundary l a y e r . E x p e r i m e n t a l l y , the R . D . E . system has been m a i n l y used to . determine d i f f u s i o n c o e f f i c i e n t s i n l i q u i d s and to study the k i n e t i c s of moderate ly f a s t e l e c t r o d e p r o c e s s e s . A 64 C. POLARIZATION OF ROTATING DISKS OF COPPER SULPHIDES P o l a r i z a t i o n of d i g e n i t e and c o v e l l i t e r o t a t i n g d i s k anodes was i n v e s t i g a t e d , at 55°C, i n a c i d i f i e d copper su lphate s o l u t i o n (0 .1 M CuSO^, 0 .1 M ^ S O ^ ) by a g a l v a n o s t a t i c method. 4 .5 E x p e r i m e n t a l The r o t a t i n g d i s k e l e c t r o d e i s shown on F i g u r e 15. The h o l l o w s h a f t was of a c e t a l p l a s t i c (0.62 cm i n d i a m e t e r ) . The specimen was imbedded i n an a c r y l i c r e s i n (Koldmount) mount machined i n the shape of a cone. The a c t i v e s u r f a c e exposed to the s o l u t i o n was 1.3 cm i n d iameter . E l e c t r i c a l connect ions were made through mercury conta ined i n the h o l l o w s h a f t and separated from the specimen by a p l a t i n u m f o i l . Mercury r e a c t e d r e a d i l y w i t h copper s u l p h i d e s and so d i r e c t contac t should be a v o i d e d . F i g u r e 16 d e s c r i b e s the mechanica l arrangement of the s h a f t i n the s t a i n l e s s s t e e l c e l l head. F i g u r e 17 and 18 show the arrangement of the c e l l . A porous p o r c e l a i n diaphragm separated the anodic compartement, i n the c e n t e r , from the c a t h o d i c compartment. A two-compartment c e l l was, i n d e e d , necessary because cuprous i o n s i n the s o l u t i o n r e a c t e d w i t h the copper s u l p h i d e s and were regenerated by m e t a l l i c copper immersed i n the same s o l u t i o n . As a matter of f a c t , c o v e l l i t e and d i g e n i t e were f o u n d , at 40°C, to be transformed i n t o c h a l c o c i t e , i n a few d a y s , i n c u p r i c su lpha s o l u t i o n s c o n t a i n i n g m e t a l l i c copper . The e f f e c t was a s h o r t c i r c u i t i n the c e l l , which was e q u i v a l e n t to a s l i g h t e l e c t r o n i c c o n d u c t i v i t y i n the e l e c t r o l y t e . 65 Plastic shaft. Acrylic cone. Platinum foil. Copper sulphide. 2!l approximately. F i g u r e 15. Design of the. r o t a t i n g d i s k e l e c t r o d e . I ." I approx. F i g u r e 16. Design of the s t a i n l e s s s t e e l head. 67 n approximately. F i g u r e 17. E l e c t r o l y t i c c e l l . F i g u r e 18 . E l e c t r o l y t i c c e l l a r r a n g e m e n t . 69 F i g u r e 19. Exper imenta l apparatus . 70 The area of the copper r i n g cathode was 80 t imes l a r g e r than that of the a c t i v e s u r f a c e of the anode. The ins t ruments a s s o c i a t e d w i t h the present experiment are shown on F i g u r e 19. Inc luded were a D . C . servomotor ( E . C . Motomatic E 550 MGHD) l i n k e d to a motor speed c o n t r o l u n i t ( E . C . Motomatic E 550) which c o n t r o l l e d the r . p . m . of the e l e c t r o d e w i t h i n 1.5% of the set v a l u e , an E l e c t r o s c a n , Beckman Model 30, as a constant c u r r e n t s o u r c e , a K e i t h l e y Model 153 microvoltammeter measuring the c u r r e n t to +2% of f u l l s c a l e , and a K e i t h l e y Model 630 p o t e n t i o m e t r i c e l e c t r o m e t e r measuring and a m p l i f y i n g the v o l t a g e s i g n a l f e d to a Sargent Model S . R . G . r e c o r d e r . The c e l l was immersed i n a t h e r m o s t a t - r e g u l a t e d water b a t h . Experiments were done i n a h e l i u m atmosphere w i t h deaerated 0.1 M CuSO^- 0.1 M H.SO. s o l u t i o n s . , 2 4 The measuring c i r c u i t was kept ungrounded. A l l p o t e n t i a l measure- ments were made w i t h r e s p e c t to a s a t u r a t e d ca lomel e l e c t r o d e at 25°C. The angular v e l o c i t y of the d i s k was se t at 250 r . p . m . y i e l d i n g a t the edge of the d i s k a Reynolds number of R = r 2 - = 6.25 x 1 0 3 e v w h i c h was c h a r a c t e r i s t i c of a l aminar f l o w regime f o r that k i n d of geometric arrangement (see 4 . 4 ) . P r e p a r a t i o n of the copper s u l p h i d e s D i g e n i t e was s y n t h e s i z e d at 600°C i n an evacuated q u a r t z tube from 0,99999 pure copper and s u l p h u r , p u r i f i e d a c c o r d i n g to the method of 71 Bacon and Fanelli (31), in the molar ratio, 1.78:1. Covellite was synthesized at 450°C in an evacuated quartz tube from 0.99999 pure copper in the presence of an excess of purified sulphur. A temperature gradient prevailing along the reaction tube prevented the sulphur from condensing on the covellite during the cooling period. The copper sulphides were ground under helium in an alumina b a l l m i l l and then cold-pressed under vacuum into disks (1.3 cm in diameter, approximately 2 mm thick) in a Perkin Elmer evacuable die. The digenite -2 disks, compacted under a pressure of 8100 kg cm , had 93% of their theoretical density. The covellite disks, shaped under a pressure of -2 2700 kg cm , were sintered in the presence of sulphur vapour; their f i n a l density was 86% of the theoretical value. The electrodes were lightly polished. The total internal resistance of each electrode was measured with a Keithley, model 503, milliohmeter and found to be approximately 0.1 n for digenite and 0.05 J2. for covellite electrodes. 4.6 Polarization of digenite anodes , 4.6.1 Results , Digenite anodes were studied at 55°C by a galvanostatic polariza- -2 tion method using current densities between 7.5 and 75 mA cm . The information obtained by this study is summed up in Table 5. A typical potential-time curve is shown on Figure 20. These curves were characterized by a region in which the potential slowly rose as a function of time, ending in a potential discontinuity i n a transition 72 Table 5 P o l a r i z a t i o n of d i g e n i t e anodes S . C . E . ( 2 5 ° C ) / 0 . 1 M C u S O . - O . l M H o S 0 . <KCu., „S 4 2. 4 l . o I . -2 mA cm E o mV E . l mV ^fi , s o l . mV V e l . mV mV E s mV E T mV E - E . T 1 mV T sec 3.77 248 280 21 - - 259 7.5 236 298 42 - 1.1 255 760 462 124,800 11.3 245 355 64 1.5 1.6 288 725 370 39,060 15.1 237 350 85 1.5 2.1 261 515 165 10,950 18.8 245 405 104 2 2.5 296. 5 575 170 8,670 18.8 244 409 106 2 2.5 298. 5 604 195 7,500 37.7 241 526 209 4 4 .7 308. 5 678 152 1,950 45.2 243 659 252 5.5 5.2 396 818 159 1,110 56.5 238 768 316.5 6 6.5 439 978 210 720 56.5 244 765 312 6 6.5 438. 5 1004 239 912 75.3 244 914 423 8 8.5 474. 5 1123 209 420 E ,E ,E are the o c u r r e n t , i n i t i a l and t r a n s i t i o n p o t e n t i a l s , r e s p e c t i v e l y as d e f i n e d i n F i g . 20. n , i s the ohmic drop i n s o l u t i o n , c a l c u l a t e d from E q . (4.2) fi,sol. rifi e ^ i s the ohmic drop i n s i d e the e l e c t r o d e rip i s the c o n c e n t r a t i o n o v e r v o l t a g e due to d i f f u s i o n i n the e l e c t r o d e boundary l a y e r (Appendix 4) S X fi;sol. ft,el. D E (mV) 1000 h 500 0 F i g u r e 20 t (mln) P o t e n t i a l - t i m e curve recorded d u r i n g the galvano- s t a t i c o x i d a t i o n of a d i g e n i t e anode at 55°C S . C . E . ( 2 5 ° C ) | 0 1 M CuSO.-0 .1 M H o S 0 , 4 2 4 Cu 1.78' 74 time T , beyond which the p o t e n t i a l was much h i g h e r (> 1.5 V) and p o o r l y r e p r o d u c i b l e . The f i r s t p a r t of the curve up to the t r a n s i t i o n time c o r r e s - ponded to the o v e r a l l e l e c t r o d e r e a c t i o n Cu. , 0 S • CuS + 0.78 Cu4"*" + 1.56 e , (4.3) 1, lo which was found i n a p r e v i o u s s tudy (Chapter 2) to c o n t r o l the r e s t p o t e n t i a l of a d i g e n i t e - c o v e l l i t e e l e c t r o d e . In f a c t , c o v e l l i t e was i d e n t i f i e d by X - r a y d i f f r a c t i o n i n the p o r o u s , l o o s e l y coherent s o l i d separated from the s u r f a c e of a specimen. No v a r i a t i o n of the copper content of the s o l u t i o n cou ld be detec ted a f t e r 35 h o u r s of e l e c t r o l y s i s under a c u r r e n t d e n s i t y of 7.5 mA cm The sharp i n c r e a s e i n p o t e n t i a l a f t e r the t r a n s i t i o n time i n d i c a t e d the appearance of a h i g h l y r e s i s t i v e e l e c t r o d e r e a c t i o n c o n s i s t i n g probably of oxygen d i s c h a r g e and su lphur f o r m a t i o n and p o s s i b l y su lphate f o r m a t i o n (15) . At the t r a n s i t i o n t i m e , the d i g e n i t e was f a r from be ing complete ly transformed i n t o c o v e l l i t e but r e a c t i o n (4.3) was not capable of m a i n - t a i n i n g a constant r a t e . As the r e a c t i o n proceeded, the c o v e l l i t e - d i g e n i t e i n t e r f a c e receded from the o r i g i n a l s u r f a c e , a n d copper i o n s should d i f f u s e through the CuS l a y e r to enter the e l e c t r o l y t e . I t was observed e x p e r i m e n t a l l y that the c u r r e n t d e n s i t y was p r o p o r t i o n a l to the i n v e r s e of the square r o o t of the t r a n s i t i o n t ime _2 (F igure 21) and t h i s l e d to the r e l a t i o n s h i p (I > 7.5 mA cm ) . F i g u r e 21 . R e l a t i o n s h i p between the c u r r e n t density- and the t r a n s i t i o n time obseryed d u r i n g the g a l v a n o s t a t i c o x i d a t i o n of d i g e n i t e anodes a t 55 ° C . ( A were es t imated from Kuxman's r e s u l t s by the a u t h o r ) . 7 6 I ^T = 2.5 A^cm^sec 1 ( 4 . 4 ) The depth of p e n e t r a t i o n of the d i g e n i t e - c o v e l l i t e i n t e r f a c e , £ , p r o v i d e d i t progresses u n i f o r m l y , i s d i r e c t l y p r o p o r t i o n a l to the number of coulombs passed through the e l e c t r o d e d u r i n g the time cons idered 2 = ( f } D irMf = 1*81 x 1 0 4 l T ) ( 4 - 5 ) M 2 5 . 4 where = n no I s t n e a c t u a l molar volume of the i n i t i a l d i g e n i t e phase. Given the I - x dependence, the d i s s o l u t i o n constant r e l e v a n t to the c o v e l l i t e l a y e r , k , can be d e f i n e d by the r e l a t i o n 2F.k I = — C 4 . 6 ) The d i s s o l u t i o n constant d e s c r i b e s the s t e a d y - s t a t e t r a n s p o r t of copper ions across the porous c o v e l l i t e l a y e r r e s u l t i n g from the d i g e n i t e -9 - 1 - 1 o x i d a t i o n , k^ = 2.35 x 10 mole cm sec i n the present e x p e r i m e n t a l c o n d i t i o n s (T = 55°C, 0 .1 M CuSO^-0.1 M H 2 S 0 4 s o l u t i o n , d D = 0.93 d f c h ) 4 . 6 . 2 D i s c u s s i o n of the mode of t r a n s p o r t of copper ions through the c o v e l l i t e l a y e r The c o v e l l i t e l a y e r was p o r o u s ; as a matter of f a c t , the molar 3 - 1 volume of d i g e n i t e and c o v e l l i t e i s 2 5 . 4 and 2 0 . 4 cm mole ^ r e s p e c t i v e l y ( 5 9 ) and the d i g e n i t e - c o v e l l i t e t r a n s f o r m a t i o n develops 1 9 . 7 % of a d d i t i o n a l p o r o s i t y i f the o r i g i n a l s o l i d volume i s r e t a i n e d . The 77 copper i o n t r a n s p o r t may be e f f e c t u a t e d by b u l k d i f f u s i o n through the s o l i d s u l p h i d e , by s u r f a c e d i f f u s i o n a long g r a i n s or by d i f f u s i o n i n the s o l u t i o n f i l l i n g the p o r e s . a . S o l i d s t a t e d i f f u s i o n In the case of s o l i d s t a t e d i f f u s i o n , the copper f l u x through CuS i s g i v e n by the i n t e g r a t e d form of e q u a t i o n ( 3 . 7 ) , w h i c h i s v a l i d r e g a r d l e s s of the a c t u a l s t a t e of the d i f f u s i n g s p e c i e s ( c u p r i c or cuprous i o n s ) , A y C u J c u = - M c u -IT • (4'7) When the t r a n s i t i o n o c c u r s , the d i f f e r e n c e of copper e l e c t r o c h e m i c a l p o t e n t i a l across the CuS l a y e r ( A u r ) , which can be expressed i n terms of e l e c t r o d e p o t e n t i a l s (2FAE = - A u r ) , corresponds to the s t a b i l i t y l i m i t s of CuS. I t can be c a l c u l a t e d from the thermodynamic data on the s t a b l e , s t o i c h i o m e t r i c CuS t h a t AE i s equal to approx imate ly 75 mV at 55°C (Chapter 2 ) . During p o l a r i z a t i o n of a d i g e n i t e anode, an average p o t e n t i a l r i s e (E -E^) of 187 niV was encountered d u r i n g the; q u a s i - l i n e a r p o t e n t i a l i n c r e a s e p r e c e d i n g the t r a n s i t i o n (Table 5 ) . I f some u n s t a b l e , n o n - s t o i c h i o m e t r i c c o v e l l i t e was formed, the e n t i r e p o t e n t i a l d i f f e r e n c e measured might be a v a i l a b l e to d r i v e the s o l i d s t a t e d i f f u s i o n p r o c e s s . The Onsager c o e f f i c i e n t , capable of account ing f o r the exper imenta l r e s u l t s can be c a l c u l a t e d from equat ions C4.7) and ( 4 . 6 ) . 78 1^= 0.745 x 2F M C u AE. (4.8) The f a c t o r 0.745 takes i n t o account the p o r o s i t y of the c o v e l l i t e l a y e r : i n i t i a l l y , the d i g e n i t e had 7% of p o r o s i t y , and the t r a n s f o r m a - t i o n developed an e x t r a 19.7% of p o r o s i t y . The i o n i c c o n d u c t i v i t y , which i s r e l a t e d to the Onsager c o e f f i c i e n t by e q u a t i o n ( 3 . 8 ) , can -3 - 1 - 1 then be c a l c u l a t e d to be 3 .3 x 10 cm i f the c u p r i c i o n s are -4 - 1 -1 the d i f f u s i n g - s p e c i e s and 8 x 10 Q cm i f the cuprous ions are the d i f f u s i n g s p e c i e s . T h i s l a t t e r v a l u e i s 23 and 11 t imes l a r g e r than the cuprous i o n c o n d u c t i v i t y measured i n c h a l c o c i t e and d i g e n i t e , r e s p e c t i v e l y a t 55°C (Chapter 3 ) . As these two s u l p h i d e s seem to d i s p l a y a r e l a t i v e l y h i g h i o n i c c o n d u c t i v i t y , and there i s no evidence f o r t h i s i n CuS, i t appears reasonable to c o n s i d e r tha t the s o l i d s t a t e d i f f u s i o n through c o v e l l i t e i s not a b l e to account f o r the observed r a t e of t r a n s p o r t of copper towards the s o l u t i o n . b . D i f f u s i o n i n the s o l u t i o n f i l l i n g the pores I f the aqueous e l e c t r o l y t e occupies 19.7% or more (owing t o the, i n i t i a l p o r o s i t y ) of the c ross s e c t i o n , the most l i k e l y mechanism f o r the t r a n s p o r t of c u p r i c i o n i s by d i f f u s i o n through the e l e c t r o l y t e tha t invades the pores as they form. E v e n t u a l l y , the pores get so deep that the c o n c e n t r a t i o n g r a d i e n t s necessary to t r a n s p o r t c u p r i c i o n s as f a s t as they are f o r c e d i n t o s o l u t i o n leads to s a t u r a t i o n of the e l e c t r o l y t e by a c u p r i c s a l t a t the d i g e n i t e - c o v e l l i t e i n t e r f a c e . At t h i s s t a g e , the r e a c t i o n (4.3) c logs the pores p r o g r e s s i v e l y , f o r c i n g the p o t e n t i a l to r i s e a b r u p t l y and impeding the c u r r e n t f l o w . P a r t of 79 the c u r r e n t i s , t h e n , used to charge the e l e c t r i c a l double l a y e r and other e l e c t r o d e r e a c t i o n s , i n v o l v i n g decomposition", r a t h e r than f o r m a t i o n of c o v e l l i t e o c c u r . 2 The constancy of the product I T can be demonstrated f o r a b i n a r y CuSO^ e l e c t r o l y t e , which approximates the a c t u a l s o l u t i o n e x i s t i n g i n the p o r e s . I t should f i r s t be noted that the accumula t ion r a t e of copper i n the p o r e s , A , represents a n e g l i g i b l e f r a c t i o n of the t o t a l copper f l u x , JS . A can be approximated by A " C C u f S o f • where _ C C u i s the copper c o n c e n t r a t i o n at the d i g e n i t e - c o v e l l i t e i n t e r - f a c e . At the -maximum, = 2.2 M , w h i c h corresponds to the s a t u r a t i o n i n C u S 0 4 ' 5 H 2 0 at 55°C C 6 0 ) , - fS i s the a c t u a l c ross s e c t i o n of pores fS < 0.2 S, dx 1 M - = Q yg ^ D J ' t * i e i n t e r f a c e v e l o c i t y . The accumulat ion r a t e of copper i n the pores was c a l c u l a t e d to remain lower than 1.4% of the t o t a l copper f l u x . C u p r i c s u l p h a t e d i s s o l v e d i n water i s o n l y p a r t i a l l y i o n i z e d . I n v e s t i g a t i o n of the U . V . s p e c t r a of these s o l u t i o n s r e v e a l e d the e x i s t e n c e of a complex w h i c h was b e l i e v e d to be CuSO^; i t s s t a b i l i t y constant was es t imated to be 125 C61). On the b a s i s of t h i s v a l u e , i t can be c a l c u l a t e d that approx imate ly 73% of the copper i s i n the complex form i n 0.1 M CuSO^ s o l u t i o n at ambient temperature . T h i s v a l u e i s approximate s i n c e a more accurate e s t i m a t i o n r e q u i r e s the 80 a p p r o p r i a t e a c t i v i t y c o e f f i c i e n t s to be taken i n t o account . However i t i s apparent t h a t a r e l a t i v e l y important f r a c t i o n of CuSO^ remains u n d i s s o c i a t e d i n 0 .1 M CuSO^ s o l u t i o n . Furthermore , the d i f f u s i v i t y of the CuSO^ complex w i l l be assumed e q u a l to the d i f f u s i v i t y quoted i n the l i t e r a t u r e f o r the c u p r i c i o n s . In f a c t , the copper i o n d i f f u s i o n c o e f f i c i e n t s measured by Newman and a l . (54,62) w i t h the R . D . E . technique i n CuSO^ s o l u t i o n s are aggregate v a l u e s t a k i n g i n t o account d i f f u s i o n of bo th c u p r i c i o n s and n e u t r a l complex. I f CuSO^, Cu , and SO^ are n o t e d , 1 , 2 , 3, r e s p e c t i v e l y , the u n i d i m e n s i o n a l d i f f u s i o n equat ions can be w r i t t e n ( c o n v e c t i o n term i s n e g l i g i b l e ) 3C, JL = - D- — -1 1 3x 9C 9C J 2 = - D 2 ^ T - D 2 f C 2 " t C4.9) j = - n - + D — C J 3 U 3 9 x + U 3 RT S 9x a long w i t h the e l e c t r o n e u t r a l i t y c o n d i t i o n = C ^ , J * * the f l o w requirements + J „ = — T = - T J l "3 * - dx Convect ion term = C f S — , where C i s the c o n c e n t r a t i o n i n the b u l k s o l u t i o n , and i s l e s s than 7 x 1 0 - < 1 % of the t o t a l f l u x JS . J r epresents the apparent f l o w normal to the geometr ic e l e c t r o d e a r e a . f . (< 0.2) i s a c o r r e c t i o n f a c t o r to take i n t o account that o n l y a f r a c t i o n of the c ross s e c t i o n , occupied by the p o r e s , i s a v a i l a b l e f o r the t r a n s p o r t of copper. 81 2 and the chemica l e q u i l i b r i u m statement = K C 2 . I t f o l l o w s a f t e r rearrangement of these equat ions T D 9C 9C ? = - ( D i + D i ^ * r - * > i j r > ( 4 - 1 0 ) I n t e g r a t i o n of Eq . (4.10) over the t h i c k n e s s of the c o v e l l i t e l a y e r y i e l d s D 2 I £ = f 2F [ (D 1 + D x ^ C C j - C 1 ) + 2D 2 . ( C 2 - C ^ ] , At the t r a n s i t i o n , i . e . , when s a t u r a t i o n i s achieved i n the bottom of the p o r e s , every term on the r i g h t hand s i d e i s a constant and i t f o l l o w s from E q . (4.5) 2 I T = e s t . 4 . 6 . 3 . D i s c u s s i o n of the p o t e n t i a l i n c r e a s e t a k i n g p l a c e be fore the t r a n s i t i o n a . D i f f u s i o n o v e r v o l t a g e and p o t e n t i a l drop i n the pores I f the copper i s t r a n s p o r t e d i n the s o l u t i o n f i l l i n g the c racks and pores of the c o v e l l i t e l a y e r , the p o t e n t i a l r i s e (E -E^) observed d u r i n g the pseudo l i n e a r p o r t i o n of the p o t e n t i a l - t i m e curve (Jig. 20) i s the sum of the d i f f u s i o n o v e r v o l t a g e and r e s i s t a n c e p o l a r i z a t i o n (ohmic drop + l i q u i d j u n c t i o n p o t e n t i a l ) i n the p o r e s . The average, p o t e n t i a l d i f f e r e n c e measured amounts to 187 mV ( I > 15 mA cm~ ) . The exper imenta l v a l u e s l i e i n a band between 152 and 239 mV (Table 5) and 82 seem to be randomly d i s t r i b u t e d w i t h r e s p e c t to measured t r a n s i t i o n t i m e , around the mean va lues s t a t e d by equat ion ( 4 . 4 ) . The d i f f u s i o n o v e r v o l t a g e can be c a l c u l a t e d w i t h the Nernst equat ion RT n D = 2F a C u + + s a t d ' C u S 0 4 s o l n . ) - I n a C u + + ( i n 0.1 M CuSO^, 0 .1 M H 2 S 0 4 ) ] . The a c t i v i t y of the c u p r i c i o n s i n a s a t u r a t e d c u p r i c s u l p h a t e s o l u t i o n may be se t e q u a l to the square r o o t of the a c t i v i t y of the s a t u r a t e d AF° copper su lphate e l e c t r o l y t e . The l a t t e r i s equal to exp. (- —=r~ ) where RT AF° i s the s tandard f r e e entha lpy of s o l u t i o n of copper su lphate a c c o r d i n g to the e q u a t i o n CuS0 4 -5H 2 0(s ) • Cu"*4" + S0 4 ~~ + 5H 2 0 AF° = 1350 + 9 .3 T (2 ) . However, exper imenta l data on the s a t u r a t e d copper s u l p h a t e e l e c t r o d e are a v a i l a b l e (0.296 < E q < 0.317 V at 25°C) (32) . The average v a l u e of 0.306 V i s r e t a i n e d along w i t h the exper imenta l thermal temperature c o e f f i c i e n t of 0.93 mV ° C _ 1 C32). The p o t e n t i a l o f the 0 .1 M c u p r i c s u l p h a t e - s u l p h u r i c a c i d , copper e l e c t r o d e was measured (Chapter 2) to be 0.312 V at 55°C w i t h r e s p e c t to the s tandard hydrogen e l e c t r o d e . The d i f f u s i o n o v e r v o l t a g e i s then es t imated to amount to approx imate ly 22 mV. 83 The r e s i s t a n c e p o l a r i z a t i o n i n the pores should then be a b l e to account f o r the remaining 165 mV. I t i s shown i n Appendix 3 t h a t , i n the case of a weak e l e c t r o l y t e , the p o t e n t i a l drop i n a d i f f u s i o n l a y e r depends on the magnitude of the complex s t a b i l i t y constant and may be much h i g h e r than the d i f f u s i o n o v e r v o l t a g e i n c o n t r a s t w i t h the case of a f u l l y i o n i z e d e l e c t r o l y t e . b . I n t e r f a c e o v e r v o l t a g e The d i g e n i t e - c o v e l l i t e i n t e r f a c e i s a s s o c i a t e d w i t h a dynamic p o t e n t i a l , which should be a t t a i n e d almost i n s t a n t a n e o u s l y (the response time of the measuring c i r c u i t i s approx imate ly 2.5 sec) a f t e r the c u r r e n t i s switched o n , be fore the i n t e r f a c e begins i t s m i g r a t i o n i n t o the specimen. The d i g e n i t e compos i t ion at the s u r f a c e has been - 3 c a l c u l a t e d to reach the v a l u e Cu, -,,,-S i n 1.25 10 sec at a c u r r e n t 1.765 -2 d e n s i t y of 10 mA cm . In f a c t , the most r e p r o d u c i b l e i n i t i a l 1 p o t e n t i a l s (E^) are obta ined by e x t r a p o l a t i n g to zero time a tangent to the q u a s i - s t r a i g h t i n i t i a l p a r t of the p o t e n t i a l - t i m e curve ( F i g . 20) . These measured p o t e n t i a l s c o n t a i n an ohmic component which can be c a l c u l a t e d w i t h the he lp of e q u a t i o n (4.2) and a c o n c e n t r a t i o n o v e r - v o l t a g e due to the d i f f u s i o n i n the e l e c t r o d e boundary l a y e r . The d i f f u s i o n o v e r v o l t a g e was es t imated w i t h the Nernst e q u a t i o n and Eq . ( 4 . 1 ) , u s i n g the p h y s i c a l parameters measured by Newman e t a l . (62) i n 0 .1 M CuSO^-0.1 M ^ S O ^ s o l u t i o n , ( A p p e n d i x 4 ) . I t was found to be * P r o v i d e d n u c l e a t i o n r e s i s t a n c e s do not impede c o v e l l i t e f o r m a t i o n 84 -2 8.5 mV at 75 mA cm ; at lower c u r r e n t d e n s i t i e s i t was p r o p o r t i o n a l l y s m a l l e r and might be e f f e c t i v e l y n e g l e c t e d . The c o r r e c t e d i n t e r f a c e p o t e n t i a l , E , versus S . C . E . (25°C) i s p l o t t e d a g a i n s t the l o g a r i t h m of the c u r r e n t d e n s i t y on f i g u r e 22. For s m a l l c u r r e n t d e n s i t i e s , the e l e c t r o d e r e t a i n s a p o t e n t i a l v e r y c l o s e to the e q u i l i b r i u m v a l u e r e p o r t e d i n Chapter 2 (252 mV at 5 5 ° C ) . A l i n e a r r e l a t i o n s h i p appears to s a t i s f y the e x p e r i m e n t a l data i n the h i g h e r c u r r e n t d e n s i t y range . Such a T a f e l r e l a t i o n s h i p presupposes t h a t a c h a r g e - t r a n s f e r process i s r a t e d e t e r m i n i n g , but the s c a t t e r of the e x p e r i m e n t a l da ta does not permit e x c l u s i o n of a mechanism i n which the i n t e r f a c e o v e r v o l t a g e i s due to r e c r y s t a l l i z a t i o n . The most i r r e v e r s i b l e p a r t of the r e c r y s t a l l i z a t i o n process i s the d i f f u s i o n l e s s s t r u c t u r a l change of s u l p h u r anions from the l a t t i c e form of d i g e n i t e to that of c o v e l l i t e (12) . 4 .7 P o l a r i z a t i o n of c o v e l l i t e anodes 4 . 7 . 1 . R e s u l t s a . E l e c t r o d e p o t e n t i a l measurements C o v e l l i t e anodes were s t u d i e d at 55°C by g a l v a n o s t a t i c p o l a r i z a t i o n - 2 methods w i t h c u r r e n t d e n s i t i e s between 0.075 and 2.26 mA cm . T h i s was a much lower range than used i n the d i g e n i t e s t u d i e s and b o t h ohmic drop and c o n c e n t r a t i o n o v e r v o l t a g e due to d i f f u s i o n i n the e l e c t r o d e boundary l a y e r were n e g l i g i b l e . The r e s u l t s obta ined d u r i n g these experiments are r e p o r t e d i n Table 6. The p o t e n t i a l - t i m e curves obta ined w i t h c o v e l l i t e were of two t y p e s , depending on the c u r r e n t d e n s i t i e s . F i g u r e 23 shows a curve 85 F i g u r e 22. R e l a t i o n s h i p between the l o g a r i t h m of the c u r r e n t d e n s i t y and the s u r f a c e p o t e n t i a l , observed d u r i n g the g a l v a n o - s t a t i c o x i d a t i o n of d i g e n i t e anodes at 55°C. S . C . E . (25°C) I 0.1 M CuSO., 0.1 M H.SO. I Cu, . , -S . 1 4 2 4 1 1.78 86 Table 6 P o l a r i z a t i o n of c o v e l l i t e anodes S . C . E . ( 2 5 ° C ) / 0 . 1 M C u S 0 4 - 0 . 1 M H 2 S 0 4 / C u S I E o E N E . mm E s E f . -2 mA cm mV mV mV mV mV 0.075 323 557 395 395 0.23 337 592 448.4 448.4 0.38 336 587 498 498 0.57 350 603 496 496 0.75 335 779 568 568 341 626 498 498 1.13 343 690 518 518 1.36 338 670 538 615 1.51 302 802 1.532 1.88 338 774 612 1.526 2.26 338 808 654 1.568 E Q = 0 c u r r e n t p o t e n t i a l E ^ = maximum of p o t e n t i a l ob ta ined s h o r t l y a f t e r the c u r r e n t i s swi tched on . E m i n = t * i e m i - n l m u m ° f p o t e n t i a l measured d u r i n g the experiment (see F i g . 24) . E G = s t e a d y - s t a t e p o t e n t i a l . E^ = f i n a l v a l u e of the p o t e n t i a l recorded a f t e r 6 days of e l e c t r o l y s i s . _2 t y p i c a l of low c u r r e n t d e n s i t i e s (< 1 mA cm ) w h i l e F i g u r e 24 shows a _2 curve found f o r - h i g h e r c u r r e n t s (> 2 mA cm ) . I n both cases , there was a gradua l d e c l i n e i n the p o t e n t i a l d u r i n g the f i r s t s e v e r a l h o u r s . In the case of the lower current d e n s i t i e s , i t g r a d u a l l y l e v e l l e d o f f at t (hr.) F i g u r e 23. P o t e n t i a l - t i m e curve recorded d u r i n g the g a l v a n o s t a t i c o x i d a t i o n of a c o v e l l i t e anode at 55°C. S . C . E . (25°C) | 0 .1 M C u S O . - O . l M H„SO,I GuS. 4 2 4 1 l 1 1 1 1 1 1 r 89 a steady v a l u e w h i l e i n the case of the h i g h e r c u r r e n t d e n s i t i e s , the p o t e n t i a l , undergoing a d i s c o n t i n u i t y rose a b r u p t l y to a very h i g h v a l u e . I n the l a t t e r case , the f i n a l p o t e n t i a l was about h a l f a v o l t above the r e s v e r s i b l e oxygen e l e c t r o d e , where most i n s o l u b l e e l e c t r o d e s d i s c h a r g e oxygen. The apparent c u r r e n t d e n s i t i e s are p l o t t e d a g a i n s t the c o v e l l i t e e l e c t r o d e p o t e n t i a l versus S . C . E . (25°C) on F i g u r e 25. The two curves drawn i n s o l i d l i n e represent the s t e a d y - s t a t e p o t e n t i a l s observed d u r i n g the e l e c t r o l y s i s of c o v e l l i t e . The dashed l i n e extending the f i r s t curve toward the h i g h e r current d e n s i t i e s represents the minimum p o t e n t i a l measured on the p o t e n t i a l - t i m e r e c o r d i n g . I t appears on that graph _2 tha t current d e n s i t i e s h i g h e r than 1.35 mA cm cause a change of the o v e r a l l r e a c t i o n l e a d i n g to v e r y h i g h e l e c t r o d e p o t e n t i a l . The dot ted l i n e j o i n i n g the two curves p i c t u r e s the behaviour of -2 c o v e l l i t e e l e c t r o d e i n the i n t e r m e d i a t e c u r r e n t range (1.35 mA m < I < -2 1.5 mA m ) . The p o t e n t i a l of such e l e c t r o d e s i n c r e a s e d v e r y s l o w l y d u r i n g prolonged p e r i o d of time (1 week) , e v e n t u a l l y l e a d i n g to the f i n a l va lue r e p o r t e d on the dot ted l i n e . b . E l e c t r o d e r e a c t i o n s To assess the o v e r a l l e l e c t r o d e r e a c t i o n corresponding to the two p o t e n t i a l r e g i o n s , chemica l a n a l y s i s was c a r r i e d out on the r e a c t i o n p r o d u c t s . An experiment conducted f o r s i x days i n a 0.01 M CuSO,-0.01 M H„S0. 4 2 4 -2 s o l u t i o n at 0.75 mA cm r e v e a l e d no v a r i a t i o n of the average copper content i n the e l e c t r o l y t e s , i n d i c a t i n g tha t the anode and cathode I (mA.crrf2) 2 - P o l a r i z a t i o n curve obta ined d u r i n g the g a l v a n o s t a t i c o x i d a t i o n of c o v e l l i t e anodes at 55°C. S.C.E. (25°C) | 0.1 M H SO - 0 . 1 M CuSO | CuS. 1 M CuSO-0.01 M H„ 4 o (• corresponds to 0.01 . -SO, s o l u t i o n ) 2 4 91 r e a c t i o n s were of equal c u r r e n t e f f i c i e n c y , approx imate ly 100% . A s i m i l a r experiment performed at 2.26 mA cm deple ted the copper i n the e l e c t r o l y t e s to an extent tha t would i n d i c a t e an average c u r r e n t e f f i c i e n c y of 39% f o r the anodic p r o c e s s . The porous p o r c e l a i n diaphragm appeared to have been exchanging i o n s w i t h the s o l u t i o n and prevented any reasonable d e t e r m i n a t i o n of the H + content of the s o l u t i o n . The q u a n t i t y of S0^ , i f any, put i n t o s o l u t i o n was too s m a l l to be d e t e c t e d . Both c o v e l l i t e and orthorhombic s u l p h u r were i d e n t i f i e d by an X - r a y d i f f r a c t i o n study of s u r f a c e r e s i d u e s . On the b a s i s of these i n v e s t i g a t i o n s , the c o v e l l i t e anodic r e a c t i o n at lower p o t e n t i a l s conforms t o : CuS * Cu" 1 " + S° + 2e C 4 . H ) The copper i s d i s s o l v e d and s u l p h u r i s l e f t behind as an anode s l i m e . When the s u l p h u r s t r u c t u r e forms there i s a 24% shr inkage i n volume 3 (the molar volume of c o v e l l i t e and of s u l p h u r b e i n g 20.4 and 15.5 cm mole " ^ r e s p e c t i v e l y (59 ) ) , thus the e lementa l s u l p h u r i s a s s o c i a t e d w i t h cracks and pores that permit the e l e c t r o l y t e to r e t a i n access to the i n t e r f a c e between c o v e l l i t e and e lementa l s u l p h u r . C u p r i c i o n s are No b u b b l i n g was ever detec ted at the Cu cathode at any of the c u r r e n t d e n s i t i e s u s e d . The l i m i t i n g c u r r e n t d e n s i t y at the Cu cathode i n 0 .1 M CUSO4 i s r e p o r t e d to be about 15 mA c m - 2 a t 25°C i n f r e e con- v e c t i o n c o n d i t i o n s (51) , a v a l u e which was never approached i n these exper iments . A * _2 The t o t a l d i s s o l u t i o n of 1 g CuS specimen, l eads to o n l y 10 mole of su lphur spec ies i n approx imate ly 1 I of s o l u t i o n . 92 t r a n s p o r t e d from t h i s i n t e r f a c e by d i f f u s i o n i n the s o l u t i o n i n v a d i n g the c r a c k s . Thus, as i n the d i g e n i t e case , when the pores get s u f f i c i e n t l y l o n g , d i f f u s i o n of c u p r i c i o n s can no longer support the a p p l i e d c u r r e n t and supplementary e l e c t r o d e r e a c t i o n s i n v o l v i n g much h i g h e r p o t e n t i a l s must support the excess c u r r e n t d e n s i t y . c . M i c r o s c o p i c examinat ion of the r e a c t e d e l e c t r o d e An examinat ion of c o v e l l i t e a f t e r e l e c t r o l y s i s r e v e a l e d tha t even when 40% of the copper was d i s s o l v e d , the d i s k r e t a i n e d i t s shape and c o h e s i o n . The s u r f a c e of the d i s k presented unreac ted p a r t i c l e s of c o v e l l i t e suspended i n su lphur as seen on the micrograph ( F i g . 26 ) . A p e r p e n d i c u l a r s e c t i o n of the d i s k shows s u l p h u r p e n e t r a t i n g deeply i n t o the specimen and i n f a c t going through i t ( F i g . 27 ) . At h i g h e r m a g n i f i c a t i o n , the s u l p h u r m a t r i x shows a f i n e network of l i n e s t h a t may represent shr inkage pores and cracks ( F i g . 28 ) . Micrographs taken w i t h the scanning e l e c t r o n microscope show the h i g h r e l i e f s u r f a c e . ( F i g . 29 and 30) . An examinat ion of the r e a c t e d d i s k w i t h the e l e c t r o n microprobe was v e r y i n c o n c l u s i v e ( F i g . 3 1 , 3 2 , 3 3 ) . Even v e r y l i g h t p o l i s h i n g ; tore s u l p h u r p a r t i c l e s away from the specimen s u r f a c e , l e a v i n g s u l p h u r depress ions and c o v e l l i t e h i l l s ; the microprobe readings r e f l e c t e d the topography of the h i l l y s u r f a c e more than the compos i t ion of the phases . 4 . 7 . 2 D i s c u s s i o n The i n i t i a l rise of the e l e c t r o d e p o t e n t i a l to a maximum d u r i n g the f i r s t 15 m i n u t e s , or s o , of c u r r e n t f l o w (see F i g . 23,24) are most F i g u r e 26. M i c r o g r a p h o f t h e s u r f a c e o f an o x i d i z e d c o v e l l i t e d i s k ( u n r e a c t e d c o v e l l i t e a p p e a r s w h i t e ) . F i g u r e 27. M i c r o g r a p h o f a s e c t i o n o f an o x i d i z e d c o v e l l i t e d i s k , p e r p e n d i c u l a r to the s u r f a c e . F i g u r e 28. O p t i c a l micrograph of an o x i d i z e d c o v e l l i t e d i s k . F i g u r e 29. Scanning e l e c t r o n micrograph of an o x i d i z e d c o v e l l i t e d i s k . g u r e 30. S c a n n i n g e l e c t r o n m i c r o g r a p h o f an o x i d i z e d c o v e l l i t e d i s k . F i g u r e 31. Absorbed e l e c t r o n s . 97 p r o b a b l y due to s u p e r s a t u r a t i o n and f i n a l l y n u c l e a t i o n of orthorhombic s u l p h u r i n the c o v e l l i t e phase. I t may be p o s t u l a t e d tha t the d e c l i n e i n p o t e n t i a l i s due to the r a p i d i n c r e a s e i n the c o v e l l i t e - s u l p h u r i n t e r f a c e a r e a , which decreases the e f f e c t i v e l o c a l c u r r e n t d e n s i t y and the a s s o c i a t e d o v e r v o l t a g e . In a r e a c t e d d i s k , the i n t e r f a c e area between unreacted c o v e l l i t e and the s u l p h u r product i s v e r y l a r g e com- pared w i t h the exposed geometric s u r f a c e area of the specimen as. i t appears on the v a r i o u s micrographs . The s c a t t e r of the e x p e r i m e n t a l p o i n t s on the p o l a r i z a t i o n curve ( F i g . 25) c o u l d , i n f a c t , r e f l e c t the u n c e r t a i n t y on the m i c r o s c o p i c c u r r e n t d e n s i t y . The appearance of a new e l e c t r o d e r e a c t i o n (probably oxygen _2 e v o l u t i o n ) f o r c u r r e n t d e n s i t i e s l a r g e r than 1.35 mA cm cannot be r a t i o n a l i z e d o n l y i n terms of a l i m i t e d d i f f u s i o n r a t e of copper i o n s i n the s o l u t i o n f i l l i n g the pores r e s u l t i n g from the, c r y s t a l l i z a t i o n of s u l p h u r , as was the case i n d i g e n i t e e l e c t r o d e s , because the a c t i v e i n t e r f a c i a l area and i t s v a r i a t i o n w i t h t ime are complete ly unknown. The minimum v a l u e of c u r r e n t d e n s i t y l e a d i n g to changes i n the o r i g i n a l e l e c t r o d e process i s l i k e l y to depend upon a number of p a r a - meters , the p r e p a r a t i o n and h i s t o r y of the c o v e l l i t e be ing probably one of them ( i n i t i a l p o r o s i t y , g r a i n s i z e , . . . ) . The exper imenta l p o l a r i z a - t i o n curve ( F i g . 25) s h o u l d , however, be ab le to d e s c r i b e , to a f i r s t a p p r o x i m a t i o n , the behaviour of c o v e l l i t e d u r i n g c u r r e n t f l o w . 9 8 CHAPTER 5. DISCUSSION OF THE MECHANISMS OF DISSOLUTION OF THE COPPER SULPHIDES The study of the g a l v a n o s t a t i c p o l a r i z a t i o n of r o t a t i n g d i s k anodes of d i g e n i t e and c o v e l l i t e at 55°C (Chapter 4) suggests the f o l l o w i n g models f o r the o x i d a t i o n of these s u l p h i d e s i n a c i d medium: - The r e a c t i o n t a k i n g p l a c e at the d i g e n i t e - c o v e l l i t e i n t e r f a c e seems to present a r e l a t i v e l y s m a l l r e s i s t a n c e . - The d i g e n i t e o x i d a t i o n r a t e appears to be c o n t r o l l e d by the t r a n s - por t of the copper ions r e l e a s e d by the r e a c t i o n (4.3) through the porous c o v e l l i t e l a y e r ; the main t r a n s p o r t component i s l i k e l y d i f f u s i o n i n the s o l u t i o n f i l l i n g the shr inkage pores of the c o v e l l i t e . - A f t e r n u c l e a t i o n of e l ementa l s u l p h u r , the o x i d a t i o n r a t e of c o v e l l i t e might be c o n t r o l l e d s i m u l t a n e o u s l y by the r e a c t i o n (4.11) at the c o v e l l i t e - s u l p h u r i n t e r f a c e and d i f f u s i o n of c u p r i c i o n s i n the, s o l u t i o n f i l l i n g the pores and cracks r e s u l t i n g from the c r y s t a l l i z a - t i o n of the s u l p h u r . The p e c u l i a r way i n which the s u l p h u r grows i n the c o v e l l i t e anode e x c l u d e s , so f a r , any d i s e u s s i o n of the r e l a t i v e i n f l u e n c e of these two r e s i s t a n c e s on the o v e r a l l r e a c t i o n . However, d u r i n g o x i d a t i o n , c o v e l l i t e appears to e x h i b i t a l i m i t i n g c u r r e n t of d i s s o l u t i o n s i m i l a r to d i f f u s i o n c o n t r o l l e d r e a c t i o n s . In the f o l l o w i n g d i s c u s s i o n , a model , w h i c h i s d e r i v e d from the present work and from Kuxmann and a l . ' s e x p e r i m e n t a l o b s e r v a t i o n s (15) , i s proposed to d e s c r i b e the e l e c t r o l y t i c d i s s o l u t i o n of c h a l c o c i t e . These models w i l l then be used to t r y to account f o r the a c t u a l l e a c h i n g behaviour of the copper s u l p h i d e s u s i n g a c i d i c f e r r i c s o l u t i o n s . 99 5.1 E l e c t r o l y t i c d i s s o l u t i o n of c h a l c o c i t e : constant c u r r e n t o x i d a t i o n Kuxmann and B i a l l a s s (15) s t u d i e d the g a l v a n o s t a t i c p o l a r i z a t i o n of c h a l c o c i t e anodes i n c u p r i c su lphate s o l u t i o n s , w i t h c u r r e n t - 2 d e n s i t i e s i n the range between 3 and 22.5 mA cm . The p o t e n t i a l - t i m e curves were c h a r a c t e r i z e d by an abrupt p o t e n t i a l d i s c o n t i n u i t y o c c u r r i n g a f t e r a t r a n s i t i o n t i m e , s i m i l a r to that encountered i n the present study of d i g e n i t e anodes. The copper content of the e l e c t r o l y t e remained unchanged up to the t r a n s i t i o n , then i t decreased l i n e a r l y w i t h t i m e . C o v e l l i t e (and s u l p h u r i n some cases) was c l e a r l y r e c o g n i z a b l e i n the s u r f a c e l a y e r of the e l e c t r o d e . The t r a n s i t i o n t imes observed at 55°C i n tha t work were back- c a l c u l a t e d from the graphs r e p o r t e d i n the paper - c e r t a i n l y , w i t h a s u b s t a n t i a l l o s s of p r e c i s i o n - and compared w i t h the present data i n F i g u r e 21. The t r a n s i t i o n times measured i n both works appear to be 2 s i m i l a r i n v a l u e s and to obey the same type of r e l a t i o n s h i p , i . e . , I T=cst. In c o n t r a s t to the present r e s u l t s , Kuxmann and B i a l l a s s observed t h a t , be fore the t r a n s i t i o n , the anode p o t e n t i a l remained approx imate ly c o n s t a n t . This o b s e r v a t i o n should r u l e out the p o s s i b i l i t y of a s u b s t a n t i a l t r a n s p o r t of copper ions through the s o l i d c o v e l l i t e . On the o ther hand, the p o t e n t i a l drop r e s u l t i n g from the t r a n s p o r t of the c u r r e n t t h r o u g h ' t h e s o l u t i o n f i l l i n g the pores should remain v e r y s m a l l i n t h i s case s i n c e there was an excess of s u l p h u r i c a c i d i n the e l e c t r o l y t e (30 g/1 CuS0 4~250 g/1 R^SO^). The c o n d u c t i v i t y of a 5 N H_2^4 s o l u t i o n i s 0.673 9 ^cm 1 a t 25°C (63) as compared to a c o n d u c t i v i t y of -0.051 n - 1 c m _ 1 f o r 0 .1 M CUSO^-0.1 M H^SO^ s o l u t i o n at the same temperature (64) . The c o n c e n t r a t i o n o v e r v o l t a g e corresponding 100 to the s a t u r a t i o n of the s o l u t i o n w i t h a c u p r i c s a l t i s s m a l l (- 10 mV). 2 The constancy of the product I T can be supported by the same arguments that were proposed f o r the d i g e n i t e case (4.6.2) i . e . , t r a n s i t i o n of the e l e c t r o d e process r e s u l t i n g from the s a t u r a t i o n of the e l e c t r o l y t e w i t h a c u p r i c s a l t at the d i g e n i t e - c o v e l l i t e i n t e r f a c e and r e a c t i o n i n t e r - face moving at a constant r a t e . In the case of an excess of i n d i f f e r e n t e l e c t r o l y t e , the d i f f u s i o n equat ions are c o n s i d e r a b l y s i m p l i f i e d s i n c e the e f f e c t of the e l e c t r i c f i e l d can be n e g l e c t e d , and i n the aggregate , the f l u x of copper can be d e s c r i b e d by 3 C C u J C u = _ D C u f ~3lT where f i s the e f f e c t i v e f r a c t i o n of the c ross s e c t i o n occupied by p o r e s . ( I f the i n i t i a l c h a l c o c i t e i s f u l l y dense, f < 0.255). I t f o l l o w s a f t e r i n t e g r a t i o n between the l i m i t s of the c o v e l l i t e l a y e r that U = 2F D p f (C_ ^ - C„ ) , Cu C u , s a t . Cu where D i s an average d i f f u s i o n c o e f f i c i e n t f o r the range of c o n c e n t r a - 2 t i o n s c o n s i d e r e d . T h i s l a s t r e l a t i o n s h i p i s e q u i v a l e n t to I i n c o n s t a n t p r o v i d e d the c o v e l l i t e l a y e r t h i c k n e s s i n c r e a s e s l i n e a r l y w i t h t i m e . The o x i d a t i o n of c h a l c o c i t e to c o v e l l i t e i m p l i e s the f o r m a t i o n of the i n t e r m e d i a t e d j u r l e i t e and d i g e n i t e phases . Kuxmann's r e s u l t s , a long w i t h the o b s e r v a t i o n s r e p o r t e d i n Chapters 2, 3 and 4 seems to i n d i c a t e that these i n t e r f a c e r e a c t i o n s are r e l a t i v e l y non r e s i s t i v e , and that the o v e r a l l o x i d a t i o n r a t e i s c o n t r o l l e d by the t r a n s p o r t of 101 copper i o n s through the r e a c t i o n p r o d u c t s . The anode morphology r e s u l t i n g from the o x i d a t i o n of c h a l c o c i t e at constant c u r r e n t can be analysed t h e o r e t i c a l l y : the problem c o n s i s t s i n c a l c u l a t i n g the t h i c k n e s s of the v a r i o u s s u l p h i d e l a y e r s w i t h respec t to t i m e , when the o v e r a l l o x i d a t i o n i s c o n t r o l l e d by d i f f u s i o n through the r e a c t i o n p r o d u c t s . T h e o r e t i c a l model : constant c u r r e n t m u l t i p l e l a y e r o x i d a t i o n ( F i g . 34) The d j u r l e i t e w i l l be c o n s i d e r e d u n d i s t i n g u i s h a b l e from the c h a l c o c i t e . T h i s assumption i s based on the f a c t s tha t the compos i t ion and p h y s i c a l p r o p e r t i e s of the two phases are v e r y s i m i l a r . On the other hand, the s tandard e l e c t r o d e p o t e n t i a l s r e p o r t e d f o r cas t o r m i n e r a l c h a l c o c i t e (15,28,29) are v e r y c l o s e to the s tandard p o t e n t i a l of a d j u r l e i t e - d i g e n i t e e l e c t r o d e d e r i v e d from the measurements repor ted i n Chapter 2 (E = 503 mV at 2 5 ° C ) . The d i g e n i t e c o m p o s i t i o n i s averaged to Cu, -,0S w h i l e the secondary e f f e c t s due i t s s t o i c h i o - 1. / o metry range are n e g l e c t e d . I f the o r i g i n of t imes i s taken when the anodic c u r r e n t i s a p p l i e d , a l a y e r of d i g e n i t e s t a r t s to form at t = 0, and i t s t h i c k n e s s i s g i v e n at t i m e , t , by the r e l a t i o n s h i p ,Ms _1 a l M ; C h 0.22 Cu.S -> Cu, -,0S + 0.22Cu"H" + 0.44e z 1. lo which t r a n s l a t e s a s imple m a t e r i a l balance between the f l u x of copper , J , and the amount of c h a l c o c i t e r e a c t e d . x^ = J t 1 0 2 Cu 2S 011.8 S CuS J 2 Solution Jg* J B const. x 2 x l Steady state : Xj - x 2 = constant Constant current multilayer growth model. F i g u r e 34 103 The mechanism of t r a n s p o r t of copper i o n s through the d i g e n i t e l a y e r i s sub jec t to a d i s c u s s i o n s i m i l a r to that conducted i n s e c t i o n (4 .6 .2 ) f o r c o v e l l i t e . The t r a n s f o r m a t i o n of c h a l c o c i t e i n t o d i g e n i t e , w i t h o u t volume change, i n t r o d u c e s 7% of p o r o s i t y i n the d i g e n i t e l a y e r . No data are a v a i l a b l e to assess the e f f e c t of t h i s p o r o s i t y on the t r a n s p o r t p r o p e r t i e s of the d i g e n i t e l a y e r . C o v e l l i t e forms when the e l e c t r o d e p o t e n t i a l at the o u t s i d e s u r f a c e of the d i g e n i t e has reached the e q u i l i b r i u m p o t e n t i a l of a d i g e n i t e - c o v e l l i t e e l e c t r o d e or when s a t u r a t i o n of the s o l u t i o n f i l l i n g the pores w i t h a c u p r i c s a l t i s reached . At the onset of growth of c o v e l l i t e ( t = t ^ ) , the t h i c k n e s s of the d i g e n i t e l a y e r (x^) i s g i v e n , i n a b o t h c a s e s , by (see s e c t i o n 4 .6 .2 ) k D J - — , x D = Ja± t D , (5.1) where k^ i s the constant of d i s s o l u t i o n through d i g e n i t e . The s imultaneous growth of d i g e n i t e and c o v e l l i t e i s governed by the two f i r s t order d i f f e r e n t i a l equat ions which r e l a t e the r a t e of p r o g r e s s i o n of the i n t e r f a c e s to the copper f l u x , Cu. S —> CuS + 0.78Cu -H- + 1.56e 1.78 where x^ i s the t o t a l t h i c k n e s s of the r e a c t i o n p r o d u c t s , x^ i s the t h i c k n e s s of the c o v e l l i t e l a y e r (see F i g . 34 ) . These can be transformed 104 i n the f o l l o w i n g system of e q u a t i o n s , cu dx dx„ ^ d t 1 + IT • - J a 2 ( 5 ' 2 ) d(x - x ) k- . (a.+OLr.) =  1 1 ^ - J c t (5 .3) dt x l " x 2 2 which can be i n t e g r a t e d to g i v e the f o l l o w i n g s o l u t i o n s (Appendix 5 ) , x l x n X2 + = J ( t - t _ ) (5.4) a l a 2 D X r X 2 ~ X D k D ( a l + a 2 ) l n k D ( a l + a 2 ) ~ J a 2 ( x r X 2 } _ t fc } J a 2 J 2 a 2 n " J a 2 x D ' ^ I t appears i n equat ion (5.5) t h a t the l o g a r i t h m becomes i n f i n i t e f o r a^+a2 k D ^ a l + a 2 ^ = J a 2 ^ x l ~ x 2 ^ o r X 1 _ X 2 = — a — X D (5,. 6) When time i n c r e a s e s , the d i s t a n c e between the two i n t e r f a c e s converges , t h e r e f o r e , towards a constant v a l u e (4.545 x ^ ) , and the two phases penetra te the anode at the same constant r a t e dx dx a a dt dt J ctj-hxj VfJh J The set of equat ions (5.4) and (5 .5) was s o l v e d f o r x^ and x 2 t a k i n g a v a l u e of k^ which corresponds to the s o l i d s t a t e d i f f u s i o n of copper ions i n d i g e n i t e . The i n t e g r a t i o n of equat ion (3.9) w i t h respec t to the t h i c k n e s s of the d i g e n i t e l a y e r at the onset of growth of 105 c o v e l l i t e y i e l d s J X D " " ^ ^ C u » ( 5 ' 8 ) F where A y r = -2FAE corresponds to the range of s t a b i l i t y of d i g e n i t e , which was measured to be 20 mV at 55°C (Chapter 2 ) , and or + i s the copper i o n i c c o n d u c t i v i t y of d i g e n i t e , measured to be a p p r o x i m a t e l y 7.5 10 5 ft "̂ crn 1 at 55°C (Chapter 3 ) . I t f o l l o w s from equat ions (5.1) and (5.8) that k = 2 AE = 3 .1 10 1 1 mole cm "'"sec 1 D r The depth of p e n e t r a t i o n of the two i n t e r f a c e s are p l o t t e d as a f u n c t i o n of t ime on f i g u r e s 35 and 36. I t appears from the c a l c u l a t i o n s tha t the i n t e r f a c e s assume t h e i r steady mot ion f o r time l o n g e r than 90 t p and tha t the t h i c k n e s s of the c o v e l l i t e l a y e r i s then adequate ly d e s c r i b e d by X2 = J C f } C h C t " 4 , 5 4 5 t D ) C 5 , 9 ) Since i t was observed that a l a y e r of c o v e l l i t e formed on the c h a l c o c i t e sample sub jec ted to o x i d a t i o n , the observed t r a n s i t i o n c o u l d not r e s u l t from t r a n s p o r t l i m i t a t i o n i n the i n t e r m e d i a t e d i g e n i t e l a y e r . In f a c t , the t h i c k n e s s of the d i g e n i t e l a y e r a d j u s t s i t s e l f to the f l u x of copper ions which d i f f u s e through i t : J when d i g e n i t e o n l y i s formed, and J < J when b o t h d i g e n i t e and c o v e l l i t e are formed. I t Depth of p e n e t r a t i o n of the c h a l c o c i t e - d i g e n i t e i n t e r f a c e (x-^ and the d i g e n i t e - c o v e l l i t e i n t e r f a c e ( x 2 ) , d u r i n g the o x i d a t i o n of c h a l c o c i t e . I = 30 mA c m - 2 I = 7.5 mA c m " 2 107 f o l l o w s from the t h e o r e t i c a l a n a l y s i s t h a t the t h i c k n e s s of the d i g e n i t e l a y e r converges towards a constant (Eq. (5 .6 ) ) and that the depth of p e n e t r a t i o n of the c o v e l l i t e i s l i n e a r and g i v e n by E q . (5.9) f o r t imes l a r g e r than 90 t (Eq. ( 5 . 1 ) ) . 2 S ince the product I T , r e l e v a n t to the c h a l c o c i t e e l e c t r o l y s i s , was observed to be constant i n Kuxmann's exper iments , i t may be proposed that the c o v e l l i t e had reached i t s s teady r a t e of growth (Eq. 5 .9) when the t r a n s i t i o n o c c u r r e d . T h i s would i n d i c a t e tha t the observed t r a n s i t i o n t i m e , T , i s l a r g e r than 90 t^ and t h e r e f o r e tha t the constant of d i s s o l u t i o n through the d i g e n i t e l a y e r , k ^ , i s much s m a l l e r than the constant of d i s s o l u t i o n through the c o v e l l i t e l a y e r , k , k c > 20 k D , as can be c a l c u l a t e d from the equat ions ( 5 . 9 ) , ( 5 . 1 ) , ( 4 . 6 ) . I t would be meaningless to compare the v a l u e of the constant of d i s s o l u t i o n through the c o v e l l i t e l a y e r c a l c u l a t e d from the present work (Eq. (4 .6) ) w i t h the constant that c o u l d be c a l c u l a t e d from Kuxmann's work, i n t e r p r e t e d by Eq . (5.9) and the data of F i g u r e 2 1 . : - I n a s o l u t i o n c o n t a i n i n g 250 g/1 of I^SO^ and 30 g/1 CuSO^ the m i g r a t i o n c u r r e n t i s l i k e l y to be n e g l i g i b l y s m a l l w h i l e i t i s f a r from be ing so i n a 0 .1 M CuSO^-0.1 M H^SO^ s o l u t i o n . - The c u p r i c s a l t which p r e c i p i t a t e s i n the pores i n the case of the 0 .1 M CuSO^-0.1 M H^SO^ s o l u t i o n may be a b a s i c s u l p h a t e w h i l e i t i s more l i k e l y to be a su lphate m the case of the 30 g/1 CuSO^ - 250 ; g/1 H„S0. s o l u t i o n . 108 - The t h e o r e t i c a l p o r o s i t y of the c o v e l l i t e r e s u l t i n g from the o x i d a t i o n of the c h a l c o c i t e and of the d i g e n i t e i s 25.5% and 19.7% r e s p e c t i v e l y . As the d i s s o l u t i o n constant depends on the e f f e c t i v e f r a c t i o n of the c ross s e c t i o n occupied by the p o r e s , i t must be c o r r e c t e d to take that e f f e c t i n t o account . I f the model proposed f o r the d i s s o l u t i o n of c h a l c o c i t e and d i g e n i t e i s c o r r e c t , i t would be of i n t e r e s t to attempt the d i r e c t e l e c t r o l y s i s of copper matte i n a c h l o r i d e or a mixed c h l o r i d e - s u l p h a t e e l e c t r o l y t e s i n c e the s o l u b i l i t y of c u p r i c c h l o r i d e i n water i s 6.6 M at 55°C (63) w h i l e the s o l u b i l i t y of c u p r i c s u l p h a t e i s 2.2 M at 55°C (60 ,63) . 5.2 Leaching of c o v e l l i t e w i t h a c i d i c f e r r i c s o l u t i o n s : e l e c t r o c h e m i c a l o x i d a t i o n An e l e c t r o c h e m i c a l p r o c e s s , i n v o l v i n g two s imultaneous r e a c t i o n s , has o f t e n been proposed to account f o r the aqueous o x i d a t i o n of s u l p h i d e s ( 1 , 2 7 , 5 , 6 5 ) : the r e d u c t i o n of the o x i d a n t and the o x i d a t i o n of the s u l p h i d e take p l a c e at d i f f e r e n t s i t e s of the m i n e r a l and the e l e c t r o n s are t r a n s f e r r e d through the s u l p h i d e l a t t i c e . The process i s analogous to the c o r r o s i o n of meta ls and the e l e c t r o n i c c o n d u c t i v i t y of many s u l p h i d e s makes t h i s f e a s i b l e . Thomas and Ingraham (5) leached r o t a t i n g d i s k s of c o v e l l i t e i n 3+ 0 .1 M Fe - 0 . 1 M H^SO^ s o l u t i o n s , t h e i r experiments were u s u a l l y cont inued u n t i l 20% of the copper was d i s s o l v e d . Up to t h i s p o i n t , the d i s k s r e t a i n e d t h e i r smooth s u r f a c e s , shape, dimensions and e l e c t r i c a l c o n d u c t i v i t y . The r e a c t e d d i s k s were a m i x t u r e of e l ementa l su lphur and unreacted c o v e l l i t e s i m i l a r to what was observed a f t e r the e l e c t r o l y s i s 109 of c o v e l l i t e anodes ( 4 . 7 . 1 ) ; the c o v e l l i t e p e r s i s t e d on the o u t e r s u r f a c e of the specimen. The morphology of the leached specimens suggested tha t the i n t e r f a c e where the c o v e l l i t e was o x i d i s e d to s u l p h u r was p e n e t r a t i n g the d i s k w h i l e the e l e c t r o n s r e l e a s e d by the o x i d a t i o n r e a c t i o n were t r a v e l l i n g through the p e r s i s t i n g network of c o v e l l i t e p a r t i c l e s towards the specimen s u r f a c e where the f e r r i c i o n s c o u l d be reduced. Dur ing l e a c h i n g , copper s u l p h i d e s should assume mixed e l e c t r o d e p o t e n t i a l s which depend on the nature and magnitude of the e l e c t r o - chemica l r e a c t i o n s t a k i n g p l a c e and which cou ld be d i r e c t l y measured. In the case of an aqueous e l e c t r o c h e m i c a l o x i d a t i o n , the l e a c h i n g r a t e s and the corresponding mixed p o t e n t i a l taken by the s u l p h i d e can be es t imated from the c u r r e n t - v o l t a g e curves o b t a i n e d d u r i n g anodic ; p o l a r i z a t i o n of the s u l p h i d e and c a t h o d i c p o l a r i z a t i o n of the o x i d a n t . T h i s c a l c u l a t i o n has been made i n the case of the l e a c h i n g of a c o v e l l i t e d i s k r o t a t i n g at 500 r . p . m . i n a c i d i c f e r r i c s o l u t i o n s at 55°C; these c o n d i t i o n s correspond to the l e a c h i n g experiments conducted by Thomas and Ingraham (5 ) . The e l e c t r o d e k i n e t i c s of the F e ' ' ' / F e " ^ " c o u p l e , which has been abundantly i n v e s t i g a t e d on p l a t i n u m e l e c t r o d e s , r e s u l t from the i n t e r p l a y of d i f f u s i o n and c h a r g e - t r a n s f e r r e s i s t a n c e s (49) . The c o n t r i b u t i o n of the d i f f u s i o n r e s i s t a n c e can be c a l c u l a t e d i n the case of a r o t a t i n g d i s k e l e c t r o d e . A l l the data w h i c h are necessary f o r the I | [ | | c a l c u l a t i o n of the c u r r e n t d e n s i t y - p o t e n t i a l curves of the Fe /Fe couple have been compiled from the a v a i l a b l e l i t e r a t u r e and are r e p o r t e d i n Appendix 6. The c a t h o d i c curves c a l c u l a t e d i n that f a s h i o n 110 f o r a f e r r i c i o n c o n c e n t r a t i o n of 0 .1 M and f o r a f e r r o u s i o n c o n c e n t r a - - 3 -2 t i o n of 10 and 10 M are p l o t t e d on F i g u r e 37 ( these c o n c e n t r a t i o n v a l u e s have been s e l e c t e d to match Thomas' e x p e r i m e n t a l l e a c h i n g c o n d i t i o n s ) , and can be confronted w i t h the p o l a r i z a t i o n curve of cove- l l i t e anode determined i n the present work ( F i g . 25 ) . The l e a c h i n g r a t e d e r i v e d , a t 55°C, from Thomas' and Ingraham's -2 experiments i s e q u i v a l e n t to a c u r r e n t d e n s i t y of 1.97 mA cm ; the l e a c h i n g r a t e s remained constant a f t e r a t r a n s i e n t p e r i o d of s e v e r a l h o u r s . They s t u d i e d the e f f e c t of the v a r i a t i o n of the f e r r i c i o n c o n c e n t r a t i o n s at 50°C and found tha t the l e a c h i n g r a t e was independent of f e r r i c i o n c o n c e n t r a t i o n f o r c o n c e n t r a t i o n s l a r g e r than 0.1 M. T h i s r e s u l t s from a l i m i t i n g d i s s o l u t i o n r a t e of the c o v e l l i t e and c o u l d correspond to the l i m i t i n g c u r r e n t d e n s i t y observed d u r i n g the e l e c t r o l y s -2 of c o v e l l i t e anodes ( I , . - 1.40 mA cm , see S e c t i o n 4 . 7 . 1 ) , s i n c e l i m ' ' ' I j | | | the p o t e n t i a l exer ted by the Fe /Fe couple i s not s u f f i c i e n t to f o r c e the t r a n s i t i o n to o c c u r . An attempt tha t was made to d e r i v e the v a r i a t i o n of the l e a c h i n g r a t e of c o v e l l i t e at 55°C a g a i n s t the f e r r i c i o n c o n c e n t r a t i o n w i l l be d e s c r i b e d w i t h the e x p e r i m e n t a l p o l a r i z a t i o n curve f o r a c o v e l l i t e -2 anode u s i n g 1 ^ = 2 mA cm and a se t of c a l c u l a t e d c u r r e n t d e n s i t y I | | | | | p o t e n t i a l curves f o r v a r i o u s Fe c o n c e n t r a t i o n s , the r a t i o Fe /Fe be ing assumed constant ( F i g u r e 38 ) , T h i s e s t i m a t i o n leads o n l y to s e m i - q u a n t a t i v e i n f o r m a t i o n s i n c e i t i s d e r i v e d from p o l a r i z a t i o n curves which have not been p r e c i s e l y e s t a b l i s h e d f o r the l e a c h i n g c o n d i t i o n s : - The p o l a r i z a t i o n curve f o r a c o v e l l i t e anode remains somewhat I mA.cm 112 F i g u r e 38. E l e c t r o c h e m i c a l o x i d a t i o n o f CuS by f e r r i c s u l p h a t e s o l u t i o n s R.D.E. s p i n n i n g a t 500 r.p.m., 55°C. F e 3 + ( 0 . 2 5 M) F e 3 + ( 0 . 1 M) ,o) ?+ -3 /Fe (10 M) / F e 2 + ( 1 0 _ 2 M) / F e 2 + ( 1 0 ~ 3 M) / F e 2 + ( 1 0 - 2 M) 3+ -2 F e J (10 Z M) / F e 2 + ( 1 0 _ 4 M) / F e 2 + ( 1 0 _ 3 M) o, . / F e 2 + ( 1 0 _ 5 M) Fe ( I O " 3 M) I / F e 2 + ( 1 Q - 4 M ) ) 113 approximate s i n c e i t depends upon the a c t u a l i n t e r f a c i a l area w h i c h , i n t u r n , i s the r e s u l t o f the morphology of the s u l p h u r growth . - In a d d i t i o n , the p o l a r i z a t i o n of c o v e l l i t e anode was s t u d i e d i n 0 .1 M CuSO^ s o l u t i o n w h i l e Thomas and Ingraham s t a r t t h e i r l e a c h i n g experiment w i t h a s o l u t i o n c o n t a i n i n g no copper . - The c h a r g e - t r a n s f e r parameters of the F e + + + / F e + + couple have been measured at a p l a t i n u m e l e c t r o d e . - The whole apparent s u l p h i d e area i s supposed to be a c t i v e f o r the r e d u c t i o n of f e r r i c i o n s . The l e a c h i n g r a t e s expressed i n c u r r e n t d e n s i t i e s were c a l c u l a t e d from F i g u r e 38 and are r e p o r t e d on F i g u r e 39 i n regard of the e x p e r i m e n t a l l e a c h i n g r a t e s measured by Thomas and Ingraham. Both* c a l c u l a t e d and e x p e r i m e n t a l curves seem to f o l l o w the same type of dependence upon the f e r r i c i o n c o n c e n t r a t i o n . The l e a c h i n g r a t e of c o v e l l i t e i s independent of the f e r r i c i o n c o n c e n t r a t i o n above a c e r t a i n v a l u e , which i s l i k e l y to be temperature dependent, and i s , t h e n , c o n t r o l l e d o n l y by the o x i d a t i o n k i n e t i c s of the s u l p h i d e . In very d i l u t e s o l u t i o n s , the l e a c h i n g r a t e i s determined by the l i m i t e d r a t e of d i f f u s i o n of the f e r r i c i o n s towards the c o v e l l i t e . In the i n t e r m e d i a t e range of c o n c e n t r a t i o n s , the l e a c h i n g r a t e r e s u l t s from b o t h the o x i d a t i o n k i n e t i c s of c o v e l l i t e and the r e d u c t i o n k i n e t i c s of f e r r i c i o n s . I t f o l l o w s from the f o r e g o i n g d i s c u s s i o n t h a t , so f a r , an e l e c t r o - chemica l mechanism appears to be adequate to e x p l a i n the o x i d a t i o n of c o y e l l i t e i n a c i d i c f e r r i c s o l u t i o n . 114 measured at 60° C (5) mA.crrf2 calculated at 55°C log C F e 3 + gure 39. Leaching r a t e of r o t a t i n g c o v e l l i t e d i s k s (500 r . p . m . ) versus f e r r i c i o n c o n c e n t r a t i o n i n s o l u t i o n . 115 5 .3 Leaching of c h a l c o c i t e and d i g e n i t e w i t h a c i d i c f e r r i c s o l u t i o n s : constant p o t e n t i a l o x i d a t i o n The d r i v i n g f o r c e exer ted by a c i d i c f e r r i c s o l u t i o n s i s l a r g e enough to o x i d i s e any copper s u l p h i d e to e lementa l s u l p h u r but the s u l p h u r f o r m a t i o n , which has to overcome a n u c l e a t i o n s t a g e , i s s u f f i c i e n t l y r e s i s - t i v e to occur o n l y to a n e g l i g i b l e extent d u r i n g the c h a l c o c i t e and d i g e n i t e o x i d a t i o n , e i t h e r u n t i l these s u l p h i d e s are comple te ly exhausted (ground m i n e r a l s ) or u n t i l the d i f f u s i o n r e s i s t a n c e of the c o v e l l i t e l a y e r ( s o l i d sample) has markedly slowed down the r e a c t i o n ( 4 . 3 ) . T h i s e x p l a i n s the c h a r a c t e r i s t i c two stage r e a c t i o n g e n e r a l l y observed d u r i n g the l e a c h i n g of c h a l c o c i t e and c o v e l l i t e . In the f o l l o w i n g d i s c u s s i o n , the f i r s t l e a c h i n g stage of d i g e n i t e and c h a l c o c i t e w i l l be t r e a t e d as a r e a c t i o n c o n t r o l l e d by the t r a n s p o r t of copper i o n s across fhe o x i d a t i o n p r o d u c t s , as i t f o l l o w s from the model proposed at the b e g i n n i n g of t h i s c h a p t e r . Except f o r the i n i t i a l p e r i o d , t h i s l e a c h i n g r e a c t i o n can be approximated as an o x i d a t i o n a t constant p o t e n t i a l , the r a t e of w h i c h i s c o n t r o l l e d by d i f f u s i o n through the r e a c t i o n p r o d u c t s . T h e o r e t i c a l l y the problem c o n s i s t s i n c a l c u l a t i n g the t h i c k n e s s of the v a r i o u s s u l p h i d e l a y e r s as a f u n c t i o n of t i m e . At t h i s p o i n t , the analogy between the f i r s t l e a c h i n g stage of c h a l c o c i t e and d i g e n i t e and the o x i d a t i o n of metals i s o b v i o u s . T h e o r e t i c a l model : constant c u r r e n t m u l t i p l e l a y e r o x i d a t i o n ( F i g . 40) The p r e l i m i n a r y assumptions are the same as the ones s t a t e d f o r constant c u r r e n t o x i d a t i o n model . 116 Cu2S Cu | Q S CuS J 2 Solution j . ko kC J 2 ° " x ^ X. Steady state : = constant. x 2 Constant potential multilayer growth model. F i g u r e 40 117 During the oxidation of digenite, the c o v e l l i t e grows according to the parabolic law , 0 1 vl/2 .1/2 x = ( 2 k c > D a ) -t where k i s the constant of d i s s o l u t i o n through the c o v e l l i t e layer M 1 defined by Eq. (4.6) and a = (-j-)D jj-^-g . The copper f l u x crossing the c o v e l l i t e layer i s i n v e r s e l y propor- t i o n a l to i t s thickness k C D k C D V 2 "1/2 J = or J = (-^) t (5.10) x 2a During chalcocite oxidation, the growth of the digenite (subscript 1) and c o v e l l i t e (subscript 2) layers w i l l obey the two following d i f f e r e n t i a l equations which t r a n s l a t e a material balance between the copper fluxes and the i n t e r f a c e motions (Fig. 40), d X l _ V l _ rM. 1 ... dT - K ~ ^ 2 al ~ ^ C h C~22 ( 5 a i ) d X2 ^ kC,Ch°2 V 2 = M dt x 2 X l - x 2 a2 M ;CH 0.78 where k D i s the d i s s o l u t i o n constant through the digenite layer as defined by Eq. (5.1). The d i v i s i o n of equation (5.12) by equation (5.11) y i e l d s d X l  kD °1 *2 " l kD 118 The most general s o l u t i o n of t h i s c l a s s i c a l , f i r s t order homogeneous d i f f e r e n t i a l equation i s (Appendix 7). U l U2 £ = ( x 2 - u ^ ) U2 U l ( x 2 - u z X l ) VU2 , (5.14) where C i s the i n t e g r a t i o n constant^ and u^ and u 2 are the roots of the second degree equation 2 4. ^ n x kC,Ch, kC,Ch. a2 . U + (1 + — j - 5 )u r-* = 0. a l kD kD a l The condition that x^ and x 2 are s t r i c t l y p o s i t i v e f o r t > 0 and zero at t = 0 s i m p l i f i e s equation (5.14) considerably to x 2 = u^x 1 u^ > 0 (5.15) °r a2 k a 2 k 2 k a 1/2 (1 + _£i£h) + [ ( - i ) ( i + ^ C h ) + 4 CiCh a l kD a l kD kD V X2 2 x l The r e l a t i o n s h i p (5.15) has already been proposed by Valensi (66,67) for metal oxidation leading to the formation of several oxide layers and c o n t r o l l e d by d i f f u s i o n through the oxidation product. The i n t e g r a t i o n of equations (5.11) and (5.12) y i e l d s k a 1/2 1/2 X l = ( 2 1 ^ ) t ' ( 5 * 1 6 ) k a 1/2 1/2 X2 = [ 2 C kC,Ch a2 * l l ^ 7 ) j t ' ( 5 ' 1 7 ) u 119 Both phases grow acc or d i ng to a p a r a b o l i c law and the r a t i o between the q u a n t i t y of the two phases remains c o n s t a n t . The f l u x c r o s s i n g the c o v e l l i t e l a y e r i s i n v e r s e l y p r o p o r t i o n a l to i t s t h i c k n e s s and equals . k a - 1 / 2 -1 /2 J = k C , C h [ 2 ( k C , C h a 2 ' - r̂ ->] t (5.18) u 1 j I t f o l l o w s from the c a l c u l a t i o n s o r from the analogy w i t h meta l o x i d a t i o n t h a t the depth of p e n e t r a t i o n of the d i g e n i t e and of the c o v e l l i t e v a r i e s as a p a r a b o l i c f u n c t i o n of t ime (Eq. (5.16) and (5 .17)) and tha t the r a t i o between the depth of p e n e t r a t i o n of the two phases remains constant (Eq. ( 5 . 1 5 ) ) . The r a t e of the f i r s t l e a c h i n g stage of d i g e n i t e and c h a l c o c i t e w i l l be c a l c u l a t e d from equat ion (5.10) and from equat ions (5.18) and (5.15) u s i n g the f o l l o w i n g d i s s o l u t i o n c o n s t a n t s : As i t has a l r e a d y been p o i n t e d out e a r l i e r , the d i s s o l u t i o n c o n s t a n t , k , through the c o v e l l i t e l a y e r depends upon the f r a c t i o n of the c ross s e c t i o n occupied by the pores and i s assumed to be p r o p o r t i o n a l to i t . As the c o v e l l i t e r e s u l t i n g from the o x i d a t i o n of d i g e n i t e and c o v e l l i t e t h e o r e t i c a l l y c o n t a i n s 19.7% and 25.5% of p o r e s , r e s p e c t i v e l y , i t f o l l o w s tha t = ^ k C,Ch 19.7 C , D ' -9 - 1 - 1 where k = 2.35 10 mole cm sec was d e r i v e d from the e x p e r i m e n t a l r e s u l t s r e p o r t e d i n s e c t i o n ( 4 . 6 . 2 ) . The v a l u e of kp r e l e v a n t to the l e a c h i n g of c h a l c o c i t e has a l r e a d y been d i s c u s s e d i n s e c t i o n (5.1) ( t h e o r e t i c a l model ) . In the absence of o ther d a t a , k was c a l c u l a t e d i n 120 the case of s o l i d s t a t e d i f f u s i o n to be 3.1 10 "*"x mole cm x s e c The • M 3 - 1 molar volumes (-j) of c h a l c o c i t e and d i g e n i t e are 27.5 and 25.4 cm mole , r e s p e c t i v e l y (59) . The c a l c u l a t e d r a t e s f o r t imes equal to 1 and 5 h o u r s , as w e l l as the r a t e averaged over t h i s time i n t e r v a l , fc2 JAt = / J d t , (5.19) are r e p o r t e d i n Table 7. Table 7 Rates of the f i r s t l e a c h i n g stage of massive d i g e n i t e and c h a l c o c i t e a t 55°C i n a c i d f e r r i c s o l u t i o n s ( n r ) mA cm c a l c u l a t e d 1 19.3 24.1 5 8.6 10.8 averaged,Eq . (5.19) 11.9 14.9 measured (10) 12.9 18.2 Ch mA cm -2 Thomas and a l . (.10) measured d i s s o l u t i o n r a t e s of r o t a t i n g d i s k s of c h a l c o c i t e and d i g e n i t e d u r i n g the f i r s t s tage of l e a c h i n g i n 0 .1 M 3+ Fe - 0 . 1 M ^ S O ^ s o l u t i o n . T h e i r e x p e r i m e n t a l v a l u e s , w h i c h d i d not depend upon f e r r i c i o n c o n c e n t r a t i o n at 500 r . p . m . , are r e p o r t e d i n Table 7. Though the p l o t of the observed q u a n t i t y of copper d i s s o l v e d 121 a g a i n s t t ime was s l i g h t l y c u r v e d , they c a l c u l a t e d average d i s s o l u t i o n r a t e s f o r the range of 0.5 to 2.5 g of copper d i s s o l v e d , which s h o u l d approximate ly correspond to the s e l e c t e d t ime i n t e r v a l . The agreement between the two se t s of v a l u e s i s s a t i s f a c t o r y g i v e n the assumptions which were i n t r o d u c e d and g i v e n the u n c e r t a i n t y on the measured d i s s o l u t i o n constant (k ) . From the d i v i s i o n of e q u a t i o n (5.10) by e q u a t i o n (5.18) i t f o l l o w s ft that d i g e n i t e should d i s s o l v e a t 80% of the c h a l c o c i t e r a t e i n o t h e r w i s e i d e n t i c a l c o n d i t i o n s . In:Thomas and a l ' s exper iments , the r a t e of d i s s o l u t i o n of d i g e n i t e ranges between 70 and 84% of the r a t e of c h a l c o c i t e . I t can be d e r i v e d from E q . (5.15) t h a t , i n the c o n d i t i o n s s t a t e d f o r these c a l c u l a t i o n s , the c o v e l l i t e represents approximate ly 96% of the o x i d a t i o n p r o d u c t s . There fore i t appears tha t the r a t e of the f i r s t s tage of d i s s o l u t i o n of massive c h a l c o c i t e and d i g e n i t e may be reasonably accounted f o r by a model corresponding to a r a t e c o n t r o l l i n g t r a n s p o r t of copper ions through the o x i d a t i o n p r o d u c t s . The second l e a c h i n g stage of these s u l p h i d e s , which i n v o l v e s the o x i d a t i o n of c o v e l l i t e , should f o l l o w the same mechanism as t h i s l a t t e r . A d i f f e r e n c e r e s i d e s i n the f a c t tha t t h i s p a r t i c u l a r c o v e l l i t e a l r e a d y c o n t a i n s 20 or 25% of p o r o s i t y w h i c h e x p l a i n s the l a r g e r d i s s o l u t i o n r a t e s observed i n t h i s case ( 4 , 9 ) . * T h i s r a t e r a t i o i s a f f e c t e d r e l a t i v e l y l i t t l e by the v a l u e chosen f o r kj). I n f a c t , a v a l u e of 78% i s c a l c u l a t e d to correspond to k^ = 3 l O - - ^ mole cm - l sec - - ' - , the c o v e l l i t e then r e p r e s e n t i n g 74% of the o x i d a t i o n p r o d u c t s . 122 CHAPTER 6. CONCLUSIONS 6.1 E l e c t r o c h e m i c a l parameters of the copper sulphides E l e c t r o c h e m i c a l s t u d i e s performed on copper sulphides provided some fundamental i n f o r m a t i o n on the Cu-S system. 1. E.m.f. measurements were conducted i n the range between 40 and 80°C on the f o l l o w i n g g a l v a n i c c e l l s , S.C.E. (25°C) | 0.1 M CuS0 4, 0.1 M H 2S0 4 | Cu , S.C.E. (25°C) I 0.1 M CuSO., 0.1 M H„S0. I Cu S. i 4 2 4 1 y The copper sulphide composition was s e l e c t e d to produce a two phase e l e c t r o d e having a f i x e d copper a c t i v i t y . The p o t e n t i a l s of the i n v e s t i g a t e d e l e c t r o d e s w i t h respect to S.C.E. (25°C) (Stockholm Convention) were measured to be: E(Cu) = (70.45 ± 0.33) x 1 0 _ 3 + (0.632 ± 0.025) x 1 0 - 3 (T-328) V, E(D.-C.) = (251.50 ± 0.35) x 1 0 - 3 + (0.765 ± 0.035) x 10 - 3(T-328) V, E(D.-Dj.)=(242.20 ± 0.45) x I O - 3 + (0.62 ± 0.060) x 10""3 (T-343) V. The v a r i a t i o n of the chemical p o t e n t i a l of copper and sulphur across the Cu-S system could be assessed from the above measurements and from e x i s t i n g thermodynamic data. Consequently, the standard f r e e enthalpy of formation of d i g e n i t e and d j u r l e i t e were c a l c u l a t e d i n the i n v e s t i g a t e d range of temperature w i t h the noted p r e c i s i o n , as f o l l o w s : 123 AF°(C U ; L ? 6 5 S ) = (-18,140 ± 520) - (4.9 ± 2 .5) (T-328) c a l m o l e " 1 , AF°(C U ; L 9 6 5 S ) = (-19,700 ± 550) - (5.5 ± 3 .1) (T-343) c a l m o l e " 1 . The v a r i a t i o n of the s tandard f r e e entha lpy of f o r m a t i o n of d i g e n i t e , was es t imated as a f u n c t i o n of c o m p o s i t i o n (1.765 < y < 1 . 8 3 ) : AF°(Cu yS) = (-18,140 ± 520) - (4.9 ± 2 .5) (T-328) + (y - 1 .765) [ ( -7 ,910 ± 40) - (3.2 ± 2 .5 ) (T-328) ] c a l mole 1 . The major component (approximate ly 90%) of the f i n a l e r r o r on the above thermodynamic v a l u e s o r i g i n a t e d from the e r r o r on the e x i s t i n g data f o r CuS. 2. Copper s u l p h i d e s were grown on a copper anode from an a c i d i c s o l u t i o n s a t u r a t e d w i t h l ^ S a t constant c u r r e n t . The t h i c k e n i n g of the copper s u l p h i d e f i l m , at low e l e c t r i c f i e l d s t r e n g t h , was accounted f o r by e l e c t r o l y t i c t r a n s p o r t i n the s c a l e and a t h e o r e t i c a l model f o r the s c a l e growth was proposed f o r s t e a d y - s t a t e c o n d i t i o n s . The d i f f u s i o n c o e f f i c i e n t of cuprous i o n s i n c h a l c o c i t e and d i g e n i t e was c a l c u l a t e d i n the temperature range between 30 and 73°C from the s lope of the e l e c t r o d e p o t e n t i a l versus t ime r e l a t i o n s h i p . The d i f f u s i o n c o e f f i c i e n t of cuprous ions i n low c h a l c o c i t e was found to be D C u + = 8.1 x 1 0 " 3 exp (- ' ^ 0 ) and i n low d i g e n i t e D C u + = 3.6 x 10 exp ( —) 2 - 1 cm sec , 2 - 1 cm sec , 124 The phase boundary r e a c t i o n s d i d not appear to be too r e s i s t i v e to i n t e r f e r e w i t h these measurements. 3. P o t e n t i a l - t i m e curves were recorded d u r i n g the g a l v a n o s t a t i c p o l a r i z a t i o n of r o t a t i n g d i s k anodes of d i g e n i t e and c o v e l l i t e i n 0 .1 M CuSO^-0.1 M H 2 S 0 4 s o l u t i o n s at 55°C, and were a n a l y s e d . D i g e n i t e anodes always underwent a p o t e n t i a l d i s c o n t i n u i t y i n a t r a n s i t i o n t i m e , x t such t h a t the r e l a t i o n s h i p between the c u r r e n t d e n s i t y and the t r a n s i t i o n time was T 2 OK . 2 — 4 I T = 2 . 5 A cm s e c . I t was proposed t h a t , at the t r a n s i t i o n , the r a t e of the o v e r a l l I [ e l e c t r o d e r e a c t i o n , Cu, -, 0S -> CuS + 1.56e + 0.78Cu , was l i m i t e d by the t r a n s p o r t of the copper i o n s r e l e a s e d by the o x i d a t i o n r e a c t i o n , though the porous c o v e l l i t e l a y e r ; the main t r a n s p o r t component was l i k e l y d i f f u s i o n i n the s o l u t i o n f i l l i n g the shr inkage pores of the c o v e l l i t e . The d i s s o l u t i o n c o n s t a n t , k , through the c o v e l l i t e l a y e r k C has been d e f i n e d (J = -T— ) and c a l c u l a t e d from the e x p e r i m e n t a l d a t a . The i n t e r f a c e r e a c t i o n seemed to i n t r o d u c e l i t t l e r e s i s t a n c e i n the o v e r a l l o x i d a t i o n p r o c e s s . The anodic r e a c t i o n on c o v e l l i t e , CuS -> Cu + S" + 2e, appeared to be r e l a t i v e l y r e s i s t i v e . Dur ing o x i d a t i o n , c o v e l l i t e e x h i b i t e d a l i m i t i n g c u r r e n t of d i s s o l u t i o n s i m i l a r l y to d i f f u s i o n . c o n t r o l l e d r e a c t i o n s . The apparent c u r r e n t d e n s i t y - p o t e n t i a l curve has been e s t a b l i s h e d f o r the s t e a d y - s t a t e w h i c h o c c u r r e d a f t e r long d i s s o l u t i o n times of c o v e l l i t e . 125 6.2 A p p l i c a t i o n to the e l e c t r o l y s i s of matte anodes and to the l e a c h i n g of copper s u l p h i d e s The d i s c u s s i o n of the data e x i s t i n g i n the l i t e r a t u r e on the constant c u r r e n t e l e c t r o l y s i s of c h a l c o c i t e anodes, supplemented by the i n f o r m a t i o n obta ined i n the present work , suggests that the r a t e of; d i s s o l u t i o n of c h a l c o c i t e , as i s the case of d i g e n i t e , i s l i m i t e d by the d i f f u s i o n of copper ions i n the h i g h e r s u l p h i d e l a y e r . Leaching r a t e s of c o v e l l i t e i n a c i d i c f e r r i c s o l u t i o n s are es t imated from the data e s t a b l i s h e d i n the preceeding p a r t s of t h i s work on the b a s i s of an e l e c t r o c h e m i c a l mechanism of o x i d a t i o n , analogous to meta l c o r r o s i o n . T h i s model appears adequate to e x p l a i n the behaviour of c o v e l l i t e i n the presence of an aqueous f e r r i c o x i d a n t , as observed by other r e s e a r c h e r s . The r a t e s of the f i r s t l e a c h i n g step of c h a l c o c i t e and d i g e n i t e by an aqueous o x i d a n t are c a l c u l a t e d on the b a s i s of a constant p o t e n t i a l o x i d a t i o n model , where the r a t e of the process i s c o n t r o l l e d by the t r a n s p o r t of copper ions through the o x i d a t i o n p r o d u c t s . The r e s u l t s of these c a l c u l a t i o n s are found to be i n agreement w i t h the r e l e v a n t exper imenta l data e x i s t i n g i n the l i t e r a t u r e . 126 APPENDIX 1. USE OF A GALVANIC CELL TO MEASURE THE IONIC CONDUCTIVITY OF A COPPER SULPHIDE MEMBRANE a. Measurement method ; The a p p l i c a t i o n of an e l e c t r i c f i e l d to an i n i t i a l l y homogeneous copper sulphide gives r i s e to a c t i v i t y gradients and for larger f i e l d s , when the a c t i v i t y gradients tend to exceed the s t a b i l i t y l i m i t s , to decomposition. The type of current ( i o n i c , e l e c t r o n i c or mixed) depends on the contacts or electrodes. In a c e l l , where the copper sulphide i s inserted between two i o n i c conductors, e.g., the a p p l i c a t i o n of a d.c. p o t e n t i a l forces an i o n i c current through the copper sulphide. However the current i s not e x c l u s i v e l y i o n i c since copper i s i n the cupric form i n s o l u t i o n and may e x i s t i n the cuprous form i n the s o l i d . The f l u x of copper atoms, flowing through; the copper sulphide depends on the t o t a l current flowing through the c e l l . 2F = JCu' C A which i s rel a t e d to the Onsager c o e f f i c i e n t through Eq. (3.7) Cu | CuSO, aq | Cu S | CuSO, aq. | Cu (AI) 3y Cu J Cu = -M Cu C3, 7) 127 I n t e g r a t i o n of E q . (3.7) over the t h i c k n e s s of the s u l p h i d e t a b l e t y i e l d s J C u = 2F ^ _ AE (A1.2) where M i s the average v a l u e of the Onsager c o e f f i c i e n t i n the a c t i v i t y g r a d i e n t , and A u r = -2F AE r e p r e s e n t s the drop of e l e c t r o - chemical p o t e n t i a l across the s u l p h i d e . I t appears from E q . A l . l and A1.2 tha t the average Onsager c o e f f i c - i e n t can be c a l c u l a t e d from the e x p e r i m e n t a l c u r r e n t - p o t e n t i a l r e l a t i o n s . The c o n v e r s i o n of the Onsager c o e f f i c i e n t i n i o n i c c o n d u c t i v i t y or d i f f u s i o n c o e f f i c i e n t (Eq. 3.8) r e q u i r e s the d e t e r m i n a t i o n of the charge of the d i f f u s i n g s p e c i e s . The Onsager c o e f f i c i e n t may depend upon the p o t e n t i a l drop across the s u l p h i d e . S ince the thermodynamic p o t e n t i a l s are not f i x e d at the copper s u l p h i d e - e l e c t r o l y t e i n t e r f a c e , the r e s u l t s may depend on the sample, b . E x p e r i m e n t a l S e v e r a l des igns and c o n s t r u c t i o n s of c e l l were a t tempted: 1. A f i r s t type of c e l l was made of two t e f l o n c y l i n d e r s pressed a g a i n s t a copper s u l p h i d e membrane by a v i s e . The t e f l o n was c reeping under the compression s t r e s s and the c e l l l e a k i n g . 2. A second type of c e l l was made of two pyrex tubes cemented to the copper s u l p h i d e membrane w i t h epoxy r e s i n . The leads of the two copper e l e c t r o d e s were s e a l e d i n the c e l l w i t h epoxy r e s i n and the c e l l was evacuated and s e a l e d a f t e r having been f i l l e d w i h the s o l u t i o n . The manufacture of these c e l l s was extremely d e l i c a t e and the t h i n epoxy j o i n t was not s t a n d i n g the s o l u t i o n d u r i n g more than one or two days . 128 3. A t h i r d type of c e l l , which was made of t e f l o n , i s p i c t u r e d on F i g . 41 . The experiments were performed w i t h t h i s l a s t c e l l , which was open to the atmosphere. The c e l l was f i l l e d w i t h a b o i l e d s o l u t i o n ( 0.5 M CuSO. , 0.5 M H . S O . ) , 4 2 4 deaerated under vacuum and kept under a h e l i u m atmosphere. T h i s t r e a t - ment was in tended to prevent the e v o l u t i o n of b u b b l e s , which were dragging the s o l u t i o n out of the c e l l d u r i n g the course of the exper iments . In s p i t e of t h i s p r e c a u t i o n many experiments were d i s c o n t i n u e d by b u b b l i n g . T h i s gas e v o l u t i o n however c o u l d not be a t t r i b u t e d to an e l e c t r o d e r e a c t i o n . Each h a l f c e l l was d i v i d e d by a f r i t t ed . p o l y e t h y l e n e d i s k i n t o an anodic and c a t h o d i c compartment (see s e c t i o n 4 . 5 ) . The c e l l was enclosed i n a pyrex tube c l o s e d at bo th ends w i t h . m e t a l l i c c o v e r s . The e l e c t r i c a l l eads were cased i n rubber tub ings f i t t e d to one of the c o v e r s . A h e l i u m atmosphere was m a i n t a i n e d i n . t h e tube. The above assembly was immersed i n a t h e r m o s t a t - r e g u l a t e d e t h y l e n e g l y c o l b a t h . i An e lectroscan,Beckman 30, was used as a constant c u r r e n t s o u r c e . The c u r r e n t was measured by a K e i t h l e y , model 153, microvol tammeter . The p o t e n t i a l drop across the two t e r m i n a l copper e l e c t r o d e s was measured w i t h a K e i t h l e y , model 630, e l e c t r o m e t e r . The copper e l e c t r o d e s were made of 0.99999 pure copper p l a t e . The c o v e l l i t e membrane was s y n t h e s i z e d and shaped i n the way d e s c r i b e d i n s e c t i o n 4 . 5 . I!l approximately. k\\\1 Teflon cell. g§§M§§ Copper sulphide. f Copper electrodes. St. steel washers. |g&&#l Teflon membranes. V O F i g u r e 41 . Design of a g a l v a n i c c e l l to measure the i o n i c c o n d u c t i v i t y of a copper s u l p h i d e membrane. 130 c . R e s u l t s and d i s c u s s i o n The c e l l was f i r s t c a l i b r a t e d w i t h a copper membrane. The p o t e n t i a l drop between the two t e r m i n a l copper e l e c t r o d e s of the c e l l Cu | C u S 0 4 , H 2 S 0 4 a q . | Cu | CuSO^, ^ S O ^ aq . | Cu remained s m a l l e r than 1 mV up to c u r r e n t s of 10 uA. Consequent ly , the d i f f e r e n c e of e l e c t r o c h e m i c a l p o t e n t i a l across the s u l p h i d e membrane could be d i r e c t l y measured by the p o t e n t i a l drop o c c u r r i n g i n c e l l A I f o r c u r r e n t s s m a l l e r than 10 uA. The data r e p o r t e d f o r d i g e n i t e i n Chapters 2 and 3 i n d i c a t e that t h i s range of c u r r e n t c o u l d be adequate. At 55°C, the maximum p o t e n t i a l d i f f e r e n c e tha t can be imposed on d i g e n i t e i s 20 mV and i t s cuprous c o n d u c t i v i t y i s 7.5 10 5 "''cm "*". Eq . (A1.2) a l l o w s the c a l c u l a t i o n of the maximum c u r r e n t tha t can be f o r c e d through a d i g e n i t e d i s k , 3 mm t h i c k by 9.55 mm i n d iameter . i _ 4 x 7.5 10 x 2 10 5 „ ,„-2 - 14 uA 0.3 Any c u r r e n t h i g h e r than t h i s v a l u e would cause the e l e c t r o l y s i s of the s u l p h i d e . The maximum p o t e n t i a l d i f f e r e n c e tha t can e x i s t across a c o v e l l i t e membrane i s approx imate ly 75 -uV, but i t s i o n i c c o n d u c t i v i t y may be expected to be s m a l l e r than that of d i g e n i t e . So, i n f i r s t a p p r o x i m a t i o n , the same range of c u r r e n t can be used f o r t h i s experiment . A c e r t a i n q u a n t i t y of coulombs must be passed through the specimen i n order to e s t a b l i s h the copper a c t i v i t y g r a d i e n t necessary to support the s t e a d y - s t a t e f l o w of copper . I f , i n f i r s t a p p r o x i m a t i o n , a 131 l i n e a r c o n c e n t r a t i o n g r a d i e n t i s assumed across the membrane, the time necessary to e s t a b l i s h the s t e a d y - s t a t e i n a d i g e n i t e membrane, i n the above c o n d i t i o n s , can be e s t i m a t e d . The i n i t i a l compos i t ion of d i g e n i t e i s assumed to be Cu ^ Q O S, i t s s t a b i l i t y l i m i t s be ing Cu, Q S JL. / O Z j JL. o SJl d and Cu, - , £ C S at 55°C. A q u a n t i t y bf copper equal to AC„ - r — (TT)„ „ i s 1.765 Cu 2 M Cu S y necessary to shape the c o n c e n t r a t i o n g r a d i e n t across the d i s k , • r _ (1 .8-1 .7825) x 0.72 x 0.3 5 1 2 x 25.4 1 U t - 12 days . 3 By that t i m e , the c e l l , which c o n t a i n s o n l y about 4 cm of s o l u t i o n , w i l l be dryed o f f by e v a p o r a t i o n . S ince c o v e l l i t e i s r e p o r t e d to be s t o i c h i o m e t r i c , the time necessary to e s t a b l i s h the s t e a d y - s t a t e f l o w should be c o n s i d e r a b l y s m a l l e r . Measurements made on c o v e l l i t e membrane, approx imate ly 2 mm t h i c k , at c u r r e n t below 10 uA were not r e p r o d u c i b l e e i t h e r i n time on the same sample, or on d i f f e r e n t samples. The p o t e n t i a l drops measured i n i d e n t i c a l c o n d i t i o n s cou ld be as d i f f e r e n t as 1 to 10. The r e s i d u a l p o r o s i t y of the d i s k c o u l d s h o r t - c i r c u i t the membrane and account f o r the low v a l u e s . The v e r y h i g h p o t e n t i a l drop observed immediate ly a f t e r the s w i t c h i n g of the c u r r e n t , w h i c h was d e c a y i n g , t h e r e a f t e r , seemed to i n d i c a t e tha t s u l p h u r was probably formed a t the anodic s i d e of the c o v e l l i t e . I n f a c t , the s y n t h e t i c c o v e l l i t e i s v e r y c l o s e to s u l p h u r s a t u r a t i o n , and c u r r e n t f l o w should cause the su lphur f o r m a t i o n at the anode d u r i n g the t r a n s i e n t p e r i o d . As the c o v e l l i t e - s u l p h u r e l e c t r o d e appears i r r e v e r s i b l e ( S e c t i o n 4 . 7 ) , the s u l p h u r f o r m a t i o n would remoye a l l s i g n i f i c a n c e to the p o t e n t i a l measurements. 132 APPENDIX 2 . DIVISION OF THE TOTAL OVERVOLTAGE IN THE VARIOUS COMPONENTS The v a r i o u s o v e r v o l t a g e s are c l e a r l y d e f i n e d when there i s o n l y one r a t e - c o n t r o l l i n g step i n the e l e c t r o d e process but the d e f i n i t i o n s are s t i l l c o n t r o v e r s i a l when s e v e r a l r e s i s t a n c e s a r i s e c o n c u r r e n t l y d u r i n g the r e a c t i o n (50) . I f e i t h e r c o n c e n t r a t i o n o v e r v o l t a g e or c r y s t a l l i z a - t i o n o v e r v o l t a g e occurs a l o n e , the e l e c t r o d e p o t e n t i a l d u r i n g c u r r e n t f l o w can be c a l c u l a t e d w i t h the h e l p of the N e r n s t ' s e q u a t i o n f o r e q u i l i b r i u m p o t e n t i a l s , s i n c e the c h a r g e - t r a n s f e r r e a c t i o n i s i n e q u i l i b r i u m . In the mixed c o n t r o l case , t h i s equat ion i s , s t r i c t l y s p e a k i n g , no longer a p p l i c a b l e . K . J . V e t t e r (49) gave a d e f i n i t i o n f o r the d i v i s i o n of the measured o v e r v o l t a g e i n i t s d i f f u s i o n , r e a c t i o n , c r y s t a l l i z a t i o n and charge- t r a n s f e r components, which i s based on the requirement that upon the disappearance of a l l o v e r v o l t a g e types but one, the r e s i d u a l o v e r v o l t a g e must agree w i t h the d e f i n i t i o n f o r the s i n g l e remaining o v e r v o l t a g e t y p e . The d e t e r m i n i n g q u a n t i t y f o r c h a r g e - t r a n s f e r c o n t r o l i s the exchange c u r r e n t d e n s i t y I ; when I q becomes i n f i n i t e l y g r e a t , charge- t r a n s f e r r a t e - c o n t r o l no longer e x i s t s , so tha t f o r I ->•<», n t 0» . The r e a c t i o n o v e r v o l t a g e w i l l v a n i s h i f the d e t e r m i n i n g exchange r e a c t i o n r a t e v Q r ~* °°' a S W l x x t * i e d i f f u s i o n component f o r D °o. The c r y s t a l l i z a t i o n component w i l l d i sappear i f the c r y s t a l l i z a t i o n i s i n f i n i t e l y r a p i d ( V Q ^ » ) . The order i n which these l i m i t s are taken i s important f o r p r e c i s e o v e r v o l t a g e d e f i n i t i o n s . V e t t e r proposed the f o l l o w i n g sequence, 133 V -»- oo o,r D -> 0 0 V oo o,C n - n r + n D + - n c % + \ + nD n c - 0 An An An An = n = n T = n . (A2.1) The charge-transfer component, because i t depends upon the concentrations at the electrode surface, is influenced by the existence of the other overvoltage. Therefore the limit I -v » should be carried out f i r s t . On the basis of this definition, the current-potential relationship (50) for simultaneous occurrence of charge-transfer and concentration overvoltage w i l l be treated. C.z . _ C.z . • • / • ! • • \ -p. , . T f T I / i \ r , i n qzF , i . o,x (,1-q)zF , n 0. I = I [n (—) exp n - II(—) ' exp - - — — — n J C A 2 . 2 ) ° i C. R T i £ R i i C. and C. are the concentrations of species i at the electrode surface i i r and in the bulk of the solution, respectively. I i s the exchange current density, z . and z . the electrochemical reaction orders, J ' o,x r , i ' z the charge transfer valence, and a the charge transfer coefficient. T „/ is r,x azF i . o,i (l-a)zF i °°> nC—) exp - r = - n = TT (—) exp - -— n o i c i C R T C z —z zF , i . r , i o,i exp - - n = TJC—) 134 w i t h z . - z . = v . — (49) 0,1 r , i 1 n where v . i s the s t o i c h i o m e t r i c c o e f f i c i e n t of the r e a c t i o n a n d , n the e l e c t r o d e r e a c t i o n va lence change. RT . , C i , V l 1 T h i s equat ion c o i n c i d e s w i t h the Nernst e q u a t i o n f o r a c o n c e n t r a t i o n c e l l . T h i s i s i n c o n t r a d i c t i o n w i t h the theory of c o n c e n t r a t i o n o v e r v o l t a g e proposed r e c e n t l y by M. Enyo and T. Yokoyama (50) who used e q u a t i o n (A2.2) to demonstrate t h e i r p o i n t , but took the l i m i t s (A2.1) i n the i n v e r t e d sequence. 135 APPENDIX 3. ESTIMATION OF THE POTENTIAL DROP IN A DIFFUSION LAYER OF A PARTIALLY IONIZED ELECTROLYTE The set of equat ions (4.9) d e s c r i b i n g the d i f f u s i o n i n a CuSO^ e l e c t r o l y t e a r e : 3C J l - " D l JT  (A3- 1} J 3 = - D 3 ^  + I D3Sl CA3'3) The s u b s c r i p t s 1 , 2, 3 s tand f o r CuSO^, Cu , SO^ r e s p e c t i v e l y . The e l e c t r o n e u t r a l i t y c o n d i t i o n i s C^ = C^ The f l o w requirement i s = - J ^ 2 The chemica l e q u i l i b r i u m statement i s C^ = K.C^ A d d i t i o n of Eq . (A3.1) and E q . (A3.3) y i e l d s a f t e r rearrangement of the v a r i a b l e s D l 3 C 2 1 9 C ? 9P a* D 3 ax C 9 X RT 3x For steady-state d i f f u s i o n across a boundary l a y e r , of defined t h i c k n e s s , i n t e g r a t i o n of Eq.(A3.4) w i t h respect to the thickness of the l a y e r y i e l d s n r RT 1 — RT 9 A * = F r T K ( c 2 _ c 2 } + IF" L N - ( A 3 , 5 ) 3 136 When the s a t u r a t i o n i n a c u p r i c s a l t i s reached a t the e l e c t r o d e - e l e c t r o l y t e i n t e r f a c e , + = C g , and can be c a l c u l a t e d from K C 2 + C„ - C = 0 . I l s The p o t e n t i a l drop i n the d i f f u s i o n l a y e r i s es t imated from E q . (A3.5) t a k i n g the f o l l o w i n g v a l u e s f o r the p h y s i c a l parameters . - C g = 2.2 mole 1 1 corresponds to the s a t u r a t i o n of the s o l u t i o n w i t h CuS0 4 -5H 2 0 a t 55°C (60 ,63) . - = D 2 t h i s assumption has been proposed i n s e c t i o n (4 .6 .2 ) ++ Since the t r a n s p o r t number of Cu has been measured to be 0.36 i n 0 .1 M CuSO^ at 25°C (75) and should not be temperature dependent, • • Q' i t can be assumed tha t — = _ * _, .• = 0 .485. 0.74 - The complexat ion c o n s t a n t , K , has been es t imated to be 127 at ambient temperature by Nasanen and K l a i l e (61) but the a p p r o p r i a t e v a l u e of t h i s constant i n concentra ted s o l u t i o n s a t 55°C i s not known. In these c o n d i t i o n s , the p o t e n t i a l drop amounts to 76 mV, 185 mV and 249 mV f o r v a l u e s of the complexat ion constant of 10, 100 and 200 r e s p e c t i v e l y . 137 APPENDIX 4. CALCULATION OF THE DIFFUSION OVERVOLTAGE AT A ROTATING DISK ELECTRODE. The c o n c e n t r a t i o n o v e r v o l t a g e a r i s i n g at a R . D . E . from l i m i t e d d i f f u s i o n r a t e across the e l e c t r o d e boundary l a y e r can be c a l c u l a t e d from E q . (4 .1) and the Nernst e q u a t i o n . Hsueh and Newman (58) measured the l i m i t i n g c u r r e n t d e n s i t y f o r the d e p o s i t i o n of copper from a 0.1 M CuSO^ s o l u t i o n as a f u n c t i o n of the angular v e l o c i t y of the r o t a t i n g d i s k e l e c t r o d e . i _2 I = 72 mA cm at 25°C and 250 r . p . m . i Since the t r a n s p o r t number of the c u p r i c i o n s i n a 0 .1 M CuSO^ s o l u t i o n , i s 0.36 (75) , i t i s p o s s i b l e to e x t r a p o l a t e from t h i s measurement, the corresponding l i m i t i n g c u r r e n t d e n s i t y i n the presence of an excess of i n d i f f e r e n t e l e c t r o l y t e . T h i s case i s h y p o t h e t i c a l s i n c e the presence of an excess of i n d i f f e r e n t e l e c t r o l y t e would modify the , p h y s i c a l p r o p e r t i e s of the s o l u t i o n . -2 1^ =. 46 mA cm at 25°C and 250 r . p . m . A 0 .1 M CuSO.-0 ,1 M H„S0. s o l u t i o n i s i n t e r m e d i a t e between these two 4 2 4 cases ; i t s p h y s i c a l p r o p e r t i e s are 'very c l o s e to a 0 .1 M CuSO^ s o l u t i o n C62). The l i m i t i n g d i f f u s i o n c u r r e n t d e n s i t y d e r i v e d from 138 Mara the ' s and Newman's experiments i n a 0 .1 M CuSO^-0.1 M E^SO^ s o l u t i o n i s (56) _2 I = 59 mA cm at 25°C and 250 r . p . m . I t f o l l o w s from Eq . (4.1) that C I — = 1 - •=- I > 0 a t an anode C D I < 0 at a cathode The d i f f u s i o n o v e r v o l t a g e w i l l be c a l c u l a t e d at 55°C i n the case I | of a 0 .1 M CuSO^ s o l u t i o n and i n the h y p o t h e t i c a l case of 0 .1 M Cu i n the presence of an excess of i n d i f f e r e n t e l e c t r o l y t e . S ince the l i m i t i n g c u r r e n t d e n s i t y i s g i v e n by E q . (4.1) I D - 0.62 D 2 / 3 v " 1 / 6 . 1 / 2 2F C i t can be e x t r a p o l a t e d to 55°C, D and v be ing the o n l y temperature dependent parameters . T - D = A — A i s a constant and u i s the v i s c o s i t y of water (76) V 328 y 25 D 55 D 25 298 y 5 5 ^55 d_25 V 55 " V 25 u 2 5 d 5 5 139 The v i s c o s i t y and d e n s i t y of water are t a b u l a t e d i n chemica l handbooks (77) D 5 5 - 1.945 D 2 5 = 0.573 I D (55) = 1.71 I D (25) B i n a r y e l e c t r o l y t e : Excess of i n d i f f e r e n t e l e c t r o l y t e _2 1^ = 123 mA cm -2 79 mA cm -2 I (mA cm ) n D CmV) n D CmV) D D 75.3 1.61 6.7 1.95 9.4 56.5 1.46 5 .3 1.71 7.6 37.7 1.31 3.8 1.48 5.5 18.8 1.15 2.0 1.24 3.0 15 .1 1.13 1.7 1.19 2.5 11.3 1.09 1.2 1.14 1.9 7.5 1.07 1.0 1.09 1.2 The average v a l u e of the d i f f u s i o n o v e r v o l t a g e over the two extreme cases was s e l e c t e d f o r use i n other c a l c u l a t i o n s i n t h i s t h e s i s . Though such a c a l c u l a t i o n i s o n l y an a p p r o x i m a t i o n , the magnitude of the d i f f u s i o n o v e r v o l t a g e remains s m a l l and i s l i k e l y s m a l l e r than the exper imenta l e r r o r on the p o t e n t i a l . A r e s i s t a n c e p o l a r i z a t i o n i s g e n e r a l l y a s s o c i a t e d w i t h a c o n c e n t r a t i o n g r a d i e n t i n s o l u t i o n : t h i s term which i s zero i n the presence of excess of i n d i f f e r e n t e l e c t r o l y t e equals the d i f f u s i o n o v e r v o l t a g e i n a b i n a r y e l e c t r o l y t e . In the present case , however, i t has been shown i n Appendix 3 that t h i s v a l u e , c a l c u l a t e d f o r a d i s s o c i a t e d e l e c t r o l y t e , was not a p p r o p r i a t e . The ohmic drop c a l c u l a t e d w i t h the 140 r e s i s t i v i t y o f t h e b u l k s o l u t i o n i s a l r e a d y t a k e n i n t o a c c o u n t i n t h e t e r m , n ^ . The s m a l l c o n c e n t r a t i o n v a r i a t i o n i n t h e b o u n d a r y l a y e r i s u n l i k e l y t o m o d i f y much o f ' t h e r e s i s t i v i t y o f . t h e s o l u t i o n , and t h e r e m a i n i n g p a r t o f the r e s i s t a n c e p o l a r i z a t i o n i s n e g l e c t e d . 141 APPENDIX 5. INTEGRATION OF EQUATION (5.3) d ( x 1 ~ x 2 ) k D ( a ; L + a 2 ) _ = _ j (5.3) at x l - x 2 L e t us set x i " x 2 = Y k D ( a 1 + a 2 ) = A J a 2 = B Eq . (5.3) can then be w r i t t e n y dy = (A-By) dt which can be d i r e c t l y i n t e g r a t e d 1 j^m ^ = t + c Let us se t A - By = z -B dy = dz I t f o l l o w s o r ~ / — dz = t + C B 2 ~ ( z - A In z) = t + C B 142 R e p l a c i n g z by i t s v a l u e y i e l d s [ A - B ( X ; L - x 2 ) J l n [ A - B ( X l - x 2 ) ] = t + C B B The s o l u t i o n (5.5) can be w r i t t e n , a f t e r t a k i n g i n t o account the i n i t i a l c o n d i t i o n x , - x „ = x_ a t t = t x l ^2 X D k D ( a 1 + a 2 ) k D ( a 1 + a 2 ) - J a 2 ( x 1 ~ x 2 ) l n T 2 2 J a 2 k D ( a l + a 2 } " J a 2 X D = t - t„ 143 APPENDIX 6. THE F e 3 + / F e 2 + ELECTRODE The c u r r e n t d e n s i t y - p o t e n t i a l r e l a t i o n s h i p i s expressed i n the 3+ 2+ case of the Fe /Fe e l e c t r o d e by T h i s equat ion t r a n s l a t e s the e f f e c t of c h a r g e - t r a n s f e r and d i f f u s i o n r e s i s t a n c e s . Parameters of the c h a r g e - t r a n s f e r process (measured a t a p l a t i n u m e l e c t r o d e ) I , the exchange c u r r e n t d e n s i t y was determined to s a t i s f y the r e l a t i o n s h i p I o = k o [ F e 2 + ] exp § E e q > = k ^ F e ^ J exp - ^ E ^ (49,68,69) 3+ 2+ I f the s e l e c t e d r e f e r e n c e i s the s tandard Fe /Fe e l e c t r o d e i t s e l f (E = 0 ) , the e x p r e s s i o n of I i s s i m p l i f i e d to I = k l F e 3 + J a j F e 2 + ] 1 _ a o o The f o l l o w i n g e x p e r i m e n t a l d a t a are a y a i l a b l e : a = 0.58 (68) k (25°C) = 300 mA c m ^ m o l e ' 1 1 (68) o 144 31n I .. r - 2 - = - ^ AH = 7,500 c a l m o l e " (70,71) Parameters of the d i f f u s i o n p r o c e s s : case of a r o t a t i n g d i s k ' e l e c t r o d e ( s e c t i o n 4 . 2 ) . In the presence of an excess of i n d i f f e r e n t e l e c t r o l y t e , the l i m i t i n g d i f f u s i o n c u r r e n t d e n s i t i e s of the f e r r o u s and f e r r i c i o n s towards a R . D . E . are g i v e n by (Eq. 4 .1) T _ n , 9 _ 2/3 - 1 / 6 1/2 . 2+ T _ n n 2/3 -1 /6 1/2 3+, I D 3 = 0.62 D^ v to F IFe ] The d i f f u s i o n c o e f f i c i e n t s of f e r r o u s and f e r r i c i o n s (D2, D^, r e s p e c t i v e l y ) i n s u l p h u r i c s o l u t i o n s have been measured to be D 2C25°C) = 5.4 1 0 - 6 cm 2 sec 1 (72) D 3 (25°C) = 4 . 4 I O - 6 c m 2 s e c - 1 (72) The other parameters were chosen to f i t the c o n d i t i o n s of Thomas' and Ingraham's l e a c h i n g experiments (5)• 2TT x 500 - I — 7 7 : r a d i a n sec 60 The k i n e m a t i c v i s c o s i t y of the s o l u t i o n was approximated by the k i n e m a t i c - v i s c o s i t y of a 0 .1 M I^SO^ s o l u t i o n > 1 145 v(25°C) = 0.99 10 -2 2 -1 cm sec (62) Temperature c o r r e c t i o n s f o r the d i f f u s i o n c o e f f i c i e n t s and k i n e m a t i c v i s c o s i t y were done a c c o r d i n g to the method d e s c r i b e d i n Appendix 4. 3+ 2+ E q u i l i b r i u m p o t e n t i a l o f the Fe /Fe couple 3+ 2+ The s tandard e l e c t r o d e p o t e n t i a l of the Fe /Fe couple i s at 25°C (Stockholm Convention) e (25°C) = 771 mV (2) o or i f the S . C . E . (25°C) i s chosen as r e f e r e n c e e (25°C) = 529.5 mV o 3+ 2+ The e l e c t r o d e p o t e n t i a l of the normal Fe /Fe couple a t 55°C w i t h respect to the S . C . E . (25°C) can then be c a l c u l a t e d w i t h the h e l p of the thermal temperature c o e f f i c i e n t of the e l e c t r o d e , de 1 ( - £ ) = +2.059 mV (°C) (32) t h e [ S . C . E . (25°C)J = 592 mV at 55°C o The a c t u a l e l e c t r o d e p o t e n t i a l s t i l l depends upon the i o n i c s t r e n g t h of the s o l u t i o n (2 ,73,74) and i s approx imate ly 30 mV lower than the t h e o r e t i c a l v a l u e i n s o l u t i o n of i o n i c s t r e n g t h l a r g e r than 0.3 (73) . 146 A c o r r e c t i o n t a k i n g i n t o a c c o u n t t h e d i f f e r e n c e i n a c t i v i t y c o e f f i c i e n t s o f t h e f e r r i c and f e r r o u s i o n s ^ r e s u l t i n g f r o m t h e c o n c e n t r a - t i o n d i f f e r e n c e . w a s n o t made b e c a u s e o f t h e l a c k o f d a t a . 147 APPENDIX 7. INTEGRATION OF EQUATION (5.13) ^ 2 = k G ? G h «2 _-«2 a + \ ^ ( 5 1 3 ) d x l k D a l *2 «1 Q k D ) C } Let us set A = k C , C h ^2 k D a l B = — (1 + ) a l k D ' f i X l = u I t f o l l o w s tha t = u dx^ + x ^ du or dx 2 du = X „ -z + U d x 1 1 dx.^ du = Au 1 - B - u d x 1 " x x I n t e g r a t i o n of the former equat ion y i e l d s x = C exp. / — (A7.1) Au - B - u 148 or a f t e r r e d u c t i o n i n s imple f r a c t i o n s U l U 2 u - u u - u / — - — — du - / £ du (A7.2) u " u l u " u 2 where u ^ and are the r o o t s of the second degree e q u a t i o n u 2 + Bu - A = 0 I t f o l l o w s a f t e r i n t e g r a t i o n of Eq . CA7.2) U l V l n ( u - u ) + — In ( u - u j (A7.3) u 2 _ u i 1 u r u 2 2 and replacement of Eq . (A7.3) i n E q . (A7.1) U l U 2 x = C C u - u 1 ) ( u - u 2 ) X 2 Replacement of u by — y i e l d s x l U l U 2 i , sV ui , , u r u 2 — - ( x 2 - u 1 x 1 ) (x^-u^&j) C 3 ' 1 ^ ) w h i c h i s t h e p r o p o s e d s o l u t i o n , E q . ( 5 . 1 4 ) . 149 REFERENCES 1. J . T . 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