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

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ELECTROCHEMICAL ASPECTS OF THE AQUEOUS OXIDATION OF COPPER SULPHIDES  BY  ARLETTE ETIENNE I n g e n i e u r 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 , 1965) M . A . S c . ( U n i v e r s i t e de M o n t r e a l , 1966)  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  i n the  Department of  METALLURGY  We a c c e p t t h i s t h e s i s as conforming to the standard  THE UNIVERSITY OF BRITISH COLUMBIA November, 1970  required  In p r e s e n t i n g t h i s  thesis  an advanced degree at the L i b r a r y I  the U n i v e r s i t y  s h a l l make i t  f u r t h e r agree tha  in p a r t i a l  freely  f u l f i l m e n t o f the of B r i t i s h  available  for  requirements f o r  Columbia, I agree  that  reference and study.  p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s  thesis  f o r s c h o l a r l y purposes may be granted by the Head o f my Department o r by h i s of  this  representatives.  It  thesis for financial  i s understood that copying o r p u b l i c a t i o n gain s h a l l  written permission.  Department o f  Metallurgy  The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada  Date  N o v e m b e r 2 6 , 1970  not be allowed without my  ii  ACKNOWLEDGEMENTS The author w i s h e s t o e x p r e s s  s i n c e r e thanks to D r . E . P e t e r s  for  h i s s u p p o r t and c r i t i c i s m d u r i n g the course o f t h i s w o r k . 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 program, has been g r e a t l y  experimental  appreciated.  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  Scholarship  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  11X  ABSTRACT The  Cu-S b i n a r y  system was s u b j e c t e d  temperatures below 100°C i n a c i d s o l u t i o n .  to e l e c t r o c h e m i c a l  studies at  Three types o f e l e c t r o -  c h e m i c a l experiments were conducted: a) Measurements of e l e c t r o m o t i v e  I 0.1 M CuSO., 0.1 M H„S0.  Cu across  f o r c e were made on the g a l v a n i c  i  4  t h e Cu-S system  corresponding  2  (y v a r i a b l e ) .  4  cell,  I Cu S ' y  The range o f copper  t o the zone o f s t a b i l i t y o f d i g e n i t e  activity  Cu^ gS) was  a c c u r a t e l y determined. From these measurements and the e x i s t i n g thermodynamic data on c o v e l l i t e of d i g e n i t e b)  (CuS), the s t a n d a r d  Cu^ gS) and d j u r l e i t e  (Cu^ 9 5 5 ^ )  w  a  s  of  formation  calculated.  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 IL^S a t constant the copper s u l p h i d e i n the s c a l e . cite  f r e e enthalpy  current.  The t h i c k e n i n g : o f  f i l m was accounted f o r by e l e c t r o l y t i c  transport  The d i f f u s i o n c o e f f i c i e n t o f cuprous i o n s i n low c h a l c o -  CCu S) and low d i g e n i t e 0  (y Cu. „S) was c a l c u l a t e d from the s l o p e of  the e l e c t r o d e p o t e n t i a l v e r s u s time r e l a t i o n s h i p . c) G a l y a n o s t a t i c p o l a r i z a t i o n o f 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 was s t u d i e d a t 55°C i n 0.1 M CuSO.-0.1 M H„S0. s o l u t i o n s . 4 2 4  The  resistances a r i s i n g during  were a s s e s s e d and  current The  the anodic d i s s o l u t i o n o f these  sulphides  from the dependence o f the e l e c t r o d e p o t e n t i a l on time  density.  above p o l a r i z a t i o n experiments were c o r r e l a t e d w i t h the  e l e c t r o l y s i s o f copper matte anodes and the l e a c h i n g experiments i n ; acidic ferric  solutions described  i n the l i t e r a t u r e .  iv RESUME C e t t e t h e s e 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 ,  me"thodes de mesure E l e c t r o c h i m i q u e s , ont e"te" 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 Cu  utilisant  des  realisees: de l a c e l l u l e  galvanique,  I 0 . 1 M CuSO., 0 . 1 M H „ S 0 . I Cu S i 4' 2 4 y 1  pour des s u l f u r e s de c u i v r e de d i v e r s e s c o m p o s i t i o n s et d e t e r m i n e , 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 c o r r e s p o n d e n t 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).  aux  Ces mesures  1. o  et l e s donne*es thermodynamiques s u r l a c o v e l l i n e q u i e x i s t e n t litterature,  dans  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 t a n d a r d 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 p a r o x y d a t i o n , a c o u r a n t constant  d'une anode de c u i v r e plongee dans une s o l u t i o n a c i d e sature"e  en H^S.  Un modele de t r a n s p o r t  eiectrolytique  dans l a couche de  s u l f u r e a e t e propose pour e x p l i q u e r l a c r o i s s a n c e du p o t e n t i e l de 1 ' e l e c t r o d e le coefficient inferieure  du f i l m .  en f o n c t i o n du temps a permis de  de d i f f u s i o n des i o n s c u i v r e u x dans l a  (Cu S) 0  e t dans l a d i g e n i t e i n f e r i e u r e  du d i g e n i t e e t de c o v e l l i n e k 55°C,  Q  S).  de d i s q u e s  tournants  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 c o u r a n t ont permis de d e t e r m i n e r l e s r e s i s t a n c e s a l a d i s s o l u t i o n anodique de ces  calculer  chalcosine  (y Cu.,  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  L a pente  sulfures.  associees  V  On a d t a b l i  la  1'electrolysed'anodes  c o r r e l a t i o n entre de m a t t e s  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  les  experiences  de c u i v r e e t  les  par p l u s i e u r s  prdcddentes,  experiences  auteurs.  de  lixiviation  vi TABLE OF CONTENTS Page ABSTRACT - RESUME  i i i  LIST OF FREQUENTLY USED SYMBOLS  xiv  CHAPTER I. A.  LITERATURE SURVEY AND INTRODUCTION  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 s t a g e l e a c h i n g of c h a l c o c 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  and d i g e n i t e  acidic chlorine solutions 1.4  1.5  6  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  C.  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 i n acidic f e r r i c solutions  B.  1  leaching  8  DIRECT ELECTROREFINING OF COPPER MATTE  H  1.6  H  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  ELECTROCHEMICAL ASPECTS OF THE AQUEOUS OXIDATION OF COPPER SULPHIDES  1 5  1.7  15  Scope of the p r e s e n t work  CHAPTER 2.  THERMODYNAMIC MEASUREMENTS IN THE Cu-S S Y S T E M . . .  19  2.1  Measurement method  19  2.2  Experimental  22  2.3  Results  23  2.3.1  E l e c t r o d e p o t e n t i a l measurements  23  vii 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 digenite  2.3.3  -^1  V a r i a t i o n of the s t a n d a r d 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 c o m p o s i t i o n 2.3.4  Standard f r e e e n t h a l p y of f o r m a t i o n  of  d j u r ,l e i.t e 2.4  14  Discussion  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  3.2  Theoretical  3.3  Experimental  3.4  Results  CHAPTER 4.  anode model  and d i s c u s s i o n  B.  C.  3 9  ^  ^  ELECTROLYTIC DISSOLUTION OF ROTATING DISKS OF COPPER SULPHIDES  A.  ^2  56  GENERALITIES ON ELECTRODE KINETICS  56  4.1  56  V a r i o u s types of o v e r v o l t a g e  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  D e s i g n of p r a c t i c a l R . D . E  62  POLARIZATION OF ROTATING DISKS OF COPPER SULPHIDES  64  4.5  Experimental  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  viii 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  Results  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 t h r o u g h the c o v e l l i t e l a y e r  76  a-  Solid state diffusion  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  taking  p l a c e b e f o r e the t r a n s i t i o n a  -  6. 4.7  81  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  Interface overvoltage  83  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  Results  8 4  E l e c t r o d e p o t e n t i a l measurements  84  Electrode reactions  89  a  -  b. c  '  4.7.2  CHAPTER 5 .  M i c r o s c o p i c e x a m i n a t i o n of the  reacted  electrode  92  DISCUSSION  92  DISCUSSION OF THE MECHANISMS OF DISSOLUTION OF THE COPPER SULPHIDES  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 :  9 8  constant  current oxidation 5.2  L e a c h i n g 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 electrochemical  5.3  9 9  solutions:  oxidation  L e a c h i n g of c h a l c o c i t e ferric solutions:  x  ^  8  and d i g e n i t e w i t h a c i d i c  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 . .  6.2  A p p l i c a t i o n t o the e l e c t r o l y s i s of copper m a t t e anodes and t o the l e a c h i n g o f copper s u l p h i d e s  APPENDIX 1.  126  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 APPENDIX 3.  125  Use of a g a l v a n i c c e l l t o measure the i o n i c  c o n d u c t i v i t y o f a copper s u l p h i d e membrane APPENDIX 2.  122  132  E s t i m a t i o n o f 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  143  APPENDIX 7.  I n t e g r a t i o n of E q . C5.13)  REFERENCES  3 +  /Fe  2 +  electrode  147  149  • X  LIST OF FIGURES Figure 1  Page P o r t i o n o f the phase diagram i n the Cu-S s y s t e m , t a k e n from Roseboom (11)  2  7  C h a r g e - t r a n s f e r p r o c e s s e s 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  3  Temperature dependence of the e . m . f . S.C.E.  4  21  ( 2 5 ° C ) / 0 . 1 M CuS0 -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,  1. /  5  o f the c e l l  electrodes  26  OD  R e l a x a t i o n curves o b t a i n e d a t 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 1.765  6  Temperature dependence of the e . m . f . S.C.E.  7  27  of the c e l l  (25°C)/0.1 M CuS0 -0.1 M H ^ S O ^ C u S - ^ 4  Temperature dependence of the e . m . f .  8  4  y  0  , S..  30  C  1.965  V a r i a t i o n of s t a n d a r d f r e e e n t h a l p y of f o r m a t i o n and chemical potentials across  9  2  28  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 - C u . 4  S..  ? 6 5  the Cu-S system a t 5 5 ° C . . .  M i c r o g r a p h of the copper s u l p h i d e s c a l e ,  38  separated  from i t s copper s u b s t r a t u m  40  10  Model o f the Cu^S f i l m growing on the Cu anode  46  11  Model o f the copper s u l p h i d e s c a l e a t the s t a g e 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  13  52  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  xi  Figure  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 .  15  D e s i g n of the r o t a t i n g d i s k e l e c t r o d e  16  D e s i g n of the s t a i n l e s s  17  Electrolytic cell  67  18  C e l l arrangement  68  19  E x p e r i m e n t a 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 r e c o r d e d d u r i n g the p o l a r i z -  (51)  s t e e l head  59 65 »  a t i o n of d i g e n i t e anode ( I = 37.7 mA cm 21  66  )  73  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  22  75  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  electrode  v e r s u s the l o g a r i t h m o f the c u r r e n t d e n s i t y 23  P o t e n t i a l - t i m e f u n c t i o n r e c o r d e d 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  24  85  )  37  P o t e n t i a l - t i m e f u n c t i o n r e c o r d e d 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  M i c r o g r a p h 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  M i c r o g r a p h of the c r o s s 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 disk  29,30 31  ,  93,94  Scanning e l e c t r o n m i c r o g r a p h of o x i d i z e d c o v e l l i t e M i c r o p r o b e 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 :  M i c r o p r o b e 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 : emission  94,95  absorbed  electrons 32  ..  96 Cu 96  xii Figure 33  Page M i c r o p r o b e 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°  emission 34 35,36  96  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  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 v e r s u s t i m e , d u r i n g the o x i d a t i o n of chalcocite  106 3+  37  C u r r e n t d e n s i t y - p o t e n t i a l c u r v e s f o r the Fe Fe  2 +  (10"  2  M) e l e c t r o d e  and the F e  3 +  (0.1 M)/  (0.1 M)/Fe (10~ 2 +  3  M)  electrode  HI  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  H2  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 ion concentration  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  D e s i g n 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  xiii 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 d a t a of the copper s u l p h i d e s below 100°C  3  37  E x p e r i m e n t a l measurements  used i n the  determination  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  chalcocite 4  49  E x p e r i m e n t a l measurements  used i n the  determination  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  digenite  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 s t a g e of d i g e n i t e and chalcocite  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 s p e c i e s  i  2 -1 B^ = m o b i l i t y of s p e c i e s i , cm sec  -1  J  -3 = c o n c e n t r a t i o n of s p e c i e s i , mole cm 2 -1 D_j, = d i f f u s i v i t y of s p e c i e s i , cm sec -3 d = s p e c i f i c w e i g h t , g cm E = electrode p o t e n t i a l , V E E  o s  = 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 = E o  + n s  = surface p o t e n t i a l , V r  _i  F  = Faraday c o n s t a n t ,  96,484 c l b  eqgr  i  = current, A  I  -2 = t o t a l c u r r e n t d e n s i t y , A cm  1^ = c u r r e n t d e n s i t y c a r r i e d by s p e c i e s i , A cm -2 -1 = f l u x of species I  i , mole cm  -2  sec  = t h i c k n e s s o f a s u l p h i d e l a y e r , cm  M = molecular weight M,, . = M . = Onsager c o e f f i c i e n t , cm s e c ii 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 2 X  x  J  x  -1  S  = s u r f a c e a r e a , cm  T  = absolute temperature,  t t  = t i m e , sec = reference for time,  x x y  o o  °K sec  = a b s c i s s a at time t , cm = a b s c i s s a a t time t  o  = number of copper atoms p e r s u l p h u r atom i n compound Cu^S  XV  = thickness  6  of a d i f f u s i o n boundary l a y e r , cm  AF = f r e e e n t h a l p y change, AH  e n t h a l p y change,  AS = e n t r o p y change,  c a l mole ^  c a l mole ^ e.u.  e = standard electrode p o t e n t i a l , V o = charge-transfer overvoltage, V  \  = diffusion overvoltage, n  c  n  s  \  = c r y s t a l l i z a t i o n overvoltage, = n  r  + n  V  = surface overvoltage, V  = ohmic p o t e n t i a l d r o p , V = t o t a l overvoltage,  n  V  V  = c h e m i c a l p o t e n t i a l of s p e c i e s i , J mole •1 =  V  p a r t i a l c o n d u c t i v i t y due to s p e c i e s i ,  l  a  =  a Ui  T  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 ,  2 •1 cm sec  -1 -1 t o t a l c o n d u c t i v i t y , Q cm  = angular v e l o c i t y , = t r a n s i t i o n time,  rad. sec  sec  9,  "*"cm- 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 o r e s has been p r a c t i s e d  at  R i o T i n t o i n S p a i n f o r over 200 y e a r s , b u t the s t u d y 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 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 p a s t 20 y e a r s . of the i n t e r e s t process,  aqueous In  spite  m a n i f e s t e d by s e v e r a l copper companies f o r such a  none of the l a b o r a t o r y attempts h a s ,  so f a r ,  resulted i n  industrial application. 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 d i s k s or c a s t specimens.  synthetic  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 o r 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 o r c h l o r i n e as o x i d i s i n g a g e n t .  The experiments  c o v e r 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 experimental r e s u l t s d i f f i c u l t .  these  O n l y p a r t of the parameters w h i c h  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 o r d e t e r m i n e d 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 s t e p s i s l e f t  open  to c o n j e c t u r e CD-  subject  A r e v i e w of the l i t e r a t u r e p u b l i s h e d on the  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 b e h a v i o u r d u r i n g o x i d a t i o n i n a c i d i c aqueous  solutions.  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  reactions  O x i d a t i o n o f 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 l e m e n t a l s u l p h u r , d i s s o l v e d copper and s u l p h a t e i o n s . Nevertheless,  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 t h e s e c o n d i t i o n s , and the  3Cu  +  + +  4H„0  +  4S°  i s thermodynamically f a v o u r a b l e . e q u a l to AF° = - 1 9 , 4 0 2 - 51.9 constant  of 3.74 x 10  s t a b l e than a S ° - H S 0  4  25  —  T,  at 25°C.  | |  -Cu  reaction  > 3CuS  +  HSO ~  +  7H  +  The s t a n d a r d f r e e e n t h a l p y change (2),  is  w h i c h corresponds to an e q u i l i b r i u m  - -in-  T h u s , a CuS-HSO^ - C u  system i s more  s y s t e m , and the e l e m e n t a 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 s u b s e q u e n t l y r e a c t to form CuS and HSO^ .  Loewen (3)  o b s e r v e d , however, t h a t e l e m e n t a l s u l p h u r was not  o x i d i z e d to s u l p h a t e i n 0.36  M cupric perchlorate-0.25  a c i d s o l u t i o n under 60.3 p . s . i . led  of oxygen at 125°C, c o n d i t i o n s w h i c h  to s u l p h a t e f o r m a t i o n from c o v e l l i t e ( C u S ) .  therefore,  M perchloric  Elemental sulphur,  would n o t be an i n t e r m e d i a t e p r o d u c t 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 p r o c e s s e s w h i c h f o l l o w a t l e a s t two d i f f e r e n t S u l l i v a n (4)  paths.  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 t h a 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 s u l p h a t e s o l u t i o n s at 35°C produces c u p r i c i o n s i n s o l u t i o n and e l e m e n t a l s u l p h u r a c c o r d i n g to the CuS  +  2Fe  + + +  Cu**  +  IVe^  +  S°  reaction (1.1)  3 The m o l a r p e r c e n t a g e s of copper d i s s o l v e d and e l e m e n t a 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, w h i c h removed s u l p h u r , was a p p r o x i m a t e l y 1 : 1 . salts  The q u a n t i t i e s  elemental  of f e r r o u s and c u p r i c  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 c o r r e s p o n d i n g to  the s t o i c h i o m e t r y of r e a c t i o n Thomas and Ingraham (5)  (1.1).  ;  l e a c h e d pure s y n t h e t i c CuS i n a c i d i c  s u l p h a t e s o l u t i o n s between 25 and 80°C.  They found t h a t  the  • ferric  ferrous  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 l e m e n t a 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  respectively.  I n 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 w h i c h had r e a c t e d was found to have been c o n v e r t e d sulphate.  The f o r e g o i n g o b s e r v a t i o n s  confirm that equation  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  to  (1.1)  f e r r i c s o l u t i o n s below 100°C. J a c k s o n and S t r i c k l a n d (6) of c h a l c o c i t e  (C^S)  r e p o r t e d t h a t the r e a c t i o n of o x i d a t i o n  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 l e m e n t a l s u l p h u r . Oxygen p r e s s u r e 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  elemental  s u l p h u r and s u l p h a t e 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  equations:  CuS  +  l/20  CuS  +  2 0  2  2  +  2H  Cu  2+  2+ Cu'  (1.2)  O  +  S  +  SO  4  2-  (1.3)  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 o f s u l p h u r and 180°C, observed t h a t 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 a t h i g h acidity  (pH = 0 . 7 5 , p  = 100 p . s . i . ) . 2  Loewen (3) l e a c h e d c h a l c o c i t e  ( C ^ S ) a t 125°C w i t h 6 0 . 3 p . s . i .  of oxygen and determined t h a t the f r a c t i o n o f 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 t h e 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 t o 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 t h e c o n c e n t r a t i o n o f 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 t h e l e a c h i n g of under 10 atm. of oxygen a t 130°C.  chalcocite  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 l e a c h e d decreased r a p i d l y as t h e a c i d c o n t e n t was r a i s e d t o 0.4 M and remained c o n s t a n t  at higher 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 t h e 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 t o 0.4 M, then i t decreased more s l o w l y t i l l 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.  i t remained  The s u l p h u r to  s u l p h a t e molar r a t i o reached i t s maximum v a l u e of 1:1 f o r the  latter  condition. 1.2  Two s t a g e l e a c h i n g o f 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 e v i d e n c e i n d i c a t e s t h a t the o x i d a t i o n of  (Cu_S) and d i g e n i t e ( Z.  chalcocite  Cu.. S ) o c c u r s i n two s t a g e s . 1. o 0  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  that  the r e a c t i o n slowed down markedly a f t e r 50% o f t h e 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 t e p of  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  Cu S 2  +  2Fe  •  + + +  2Fe  + +  +  Cu**  The second s t e p proceeded w i t h the o x i d a t i o n of Leaching c h a l c o c i t e (7)  +  the equation  CuS  (1.4)  covellite.  at 200°C under 60 p . s . i .  of o x y g e n , Warren  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 .  i n c r e a s e was the r e s u l t of the  Cu S 2  +  l/20  2  +  reaction  2H  —»-  +  Cu  2 +  +  CuS  +  H^O  (1.5)  The a c i d i t y remained c o n s t a n t d u r i n g the second h a l f of the Copper e x t r a c t i o n - t i m e oxygen l e a c h i n g  (p  curves o b t a i n e d by Dahms e t  = 10 atm.)  This  reaction.  al.  (8)  of v a r i o u s copper s u l p h i d e s of  during  composi-  2 t i o n intermediate d i s t i n c t steps.  between Cu S and Cu^ gS c l e a r l y e x h i b i t e d two 2  The q u a n t i t y of copper e x t r a c t e d  a t the end of  the  f i r s t s t a g e 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.  was produced d u r i n g t h a t f i r s t 1.3  Very l i t t l e s u l p h a t e ,  if  any,  stage.  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  chlorine,  solutions I n the l e a c h i n g experiments (6)  i n acidic chlorine solutions,  conducted by J a c k s o n  and S t r i c k l a n d  the d i s s o l u t i o n r a t e s of  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  copper  solution.  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  ferric  solutions The  c o p p e r - s u l p h u r b i n a r y phase diagram  o x i d a t i o n of c h a l c o c i t e s h o u l d r e s u l t f o l l o w i n g the sequence: sulphur.  King  X-ray  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 of these phases or  be favoured by the o x i d a t i o n k i n e t i c s (13) and  occurring during ferric  i n the appearance of new  However, u n s t a b l e compositions  phases may  ( F i g . 1) i n d i c a t e s t h a t the  the o x i d a t i o n of synthetic c h a l c o c i t e by 80°C.  d i f f r a c t i o n and e l e c t r o n m i c r o p r o b i n g  probe a n a l y s i s suggested  Optical  acidic  microscopy,  t e c h n i q u e s were used  molar r a t i o of copper  t h a t , as copper was l e a c h e d from Cu^S,  0  S  to s u l p h u r became 1:1;  by the r e a c t i o n extended  a t 40°C.  to  The e l e c t r o n m i c r o -  composition of the r e s u l t i n g s o l i d v a r i e d c o n t i n u o u s l y u n t i l  U. o  metastable  (12).  study the s o l i d r e s i d u e s r e c o v e r e d a f t e r l e a c h i n g .  Cu_  finally  B u r k i n (14) s t u d i e d 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  c h l o r i d e s o l u t i o n s between 40 and  produced  phases  the c o v e l l i t e  the the  (CuS)  i t s range of composition up to  These authors observed  a l s o t h a t the -material was  porous and c r a c k e d , t h a t the sample c o u l d not be p o l i s h e d :  these  f e a t u r e s reduce  readings.  Leaching  c o n s i d e r a b l y the s i g n i f i c a n c e of microprobe  r e s i d u e s of composition i n t e r m e d i a t e between Ci^S and  were a n a l y s e d c h e m i c a l l y and by X-ray c o m p o s i t i o n Cu^ gS and CuS  diffraction.  e x h i b i t e d X-ray  Residues of;  d i f f r a c t i o n patterns, i n  good agreement w i t h those of low temperature  d i g e n i t e and  r e s p e c t i v e l y ^ as g i v e n i n the A.S.T.M. index f i l e . the l i n e s on the X-ray photographs was  CuS  covellite,  A regular s h i f t  of  i n t e r p r e t e d as an e x t e n s i o n of  the composition range of these s u l p h i d e s :  d i g e n i t e 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, S and c o v e l l i t e from Cu C  1. o  n  C  S to CuS o r even down to Cu  l . j  JL.J  The r e s u l t s of K i n g  (13)  _S. (J.o  and S u l l i v a n (9)  showed t h a 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 sulphuric solutions  (anionic concentrations  Changing the a c i d c o n t e n t the o x i d a t i o n  <1 M ) .  of the s o l u t i o n d i d n o t a f f e c t  significantly  rate.  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  concentration  d i d not appear to a l t e r the f i r s t s t a g e of the c h a l c o c i t e 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 e x t e n t  dissolution,  (5,9,10,13).  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 t a g e of chalcocite  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 c o n s i d e r e d i n d i c a t i v e of a transport reaction  (10,13,14).  leaching  (13,14) and f o r the c o v e l l i t e  i s between 22 and 25 k c a l . m o l e \  p r o c e s s e s c o n t r o l l e d by an i n t e r f a c e experiments  controlled  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  s t a g e of the c h a l c o c i t e (5)  the  second leaching  a range u s u a l l y a s s o c i a t e d reaction.  was 3 to 4 times f a s t e r than the l e a c h i n g  chalcocite  of c o v e l l i t e i n  F u r t h e r m o r e , 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 , t h a 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  1.5  with  Yet S u l l i v a n ' s  showed t h a t the second s t e p of the l e a c h i n g of  otherwise i d e n t i c a l conditions ( 4 , 9 ) .  ;  ;  though  surface;  K i n e t i c s o f 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  leaching 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) 6.3  mA cm  2 and 0.8  Thomas and a l .  (10)  found oxygen consumption r a t e s e q u i v a l e n t 2 .mA cm  f o r the f i r s t and second s t e p ,  to  respectively.  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 18  mA cm  -2 f o r the f i r s t s t a g e of l e a c h i n g of c h a l c o c i t e ,  f o r the l e a c h i n g of c o v e l l i t e , a t 55°C i n 0.1 M F e solutions.  It  3 +  and 2  -0.1 M H S0 2  mA cm  4  f o l l o w s t h a 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  with f e r r i c salts As s t a t e d  than w i t h o x y g e n , below the m e l t i n g p o i n t of s u l p h u r .  earlier,  copper s u l p h i d e l e a c h i n g w i t h oxygen t a k e s p l a c e  by way of a t l e a s t two d i s t i n c t p a r a l l e l mechanisms, s u l p h u r and s u l p h a t e f o r m a t i o n . the more d i f f i c u l t to r e s o l v e .  l e a d i n g to  T h i s makes the o x i d a t i o n k i n e t i c s The f o l l o w i n g q u e s t i o n s  remain l a r g e l y  unanswered, a l t h o u g h they have been examined e x p e r i m e n t a l l y . 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  all  Does  the  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 e v o l v e d by the m i n e r a l ? I s the s u l p h a t e formed by way pf an e l e c t r o c h e m i c a l  or chemical  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 oxidation kinetics?  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 e l e m e n t a l s u l p h u r to s u l p h a t e produced by the r e a c t i o n . s t a g e of the l e a c h i n g of c h a l c o c i t e (Eq. 1.5)  i s accompanied by H  The +  of  first  consumption  and t h e r e 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 p r e v e n t  the subsequent (T = 160°C, p  2  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 t h a t = 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  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 d e c r e a s e of the  :  10  leaching rate.  The r e s u l t s o b t a i n e d 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 reactions  (Section  1.1).  The l a r g e s t  l e a c h i n g r a t e was o b t a i n e d  the minimum a c i d i t y , 0.204 M H ^ O ^ (T = 130°C, p further increase  leaching  = 10 a t m . ) .  Q  for Any  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 .  I n a l l these e x p e r i m e n t s , p a r t i a l p r e s s u r e of oxygen.  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  Dahms and a l .  (8)  the  observed t h a t the  rate  of the f i r s t l e a c h i n g s t e p became independent of the oxygen p a r t i a l p r e s s u r e above 10 atm. and t h a t the r a t e of the second l e a c h i n g s t e p 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 .  This r e l a t i o n -  s h i p was e x p l a i n e d by means o f oxygen a d s o r p t i o n on the m i n e r a l  surface.  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 .  e s t i m a t e d the a c t i v a t i o n e n e r g i e s r a t e s of copper to be 6.6  2  4  and 1.8 kcal.-mole  covellite  (pH = 0 . 7 5 ,  and 11.8  p  (7)  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  stage of the l e a c h i n g of c h a l c o c i t e , 30 g/1 H S 0 , 1 0 0 - 2 0 0 ° C )  Warren  f o r the f i r s t and second  x  respectively  kcal.mole"  = 100 p . s . i . ,  1  (p^  = 40  p.s.i.,  f o r the l e a c h i n g  120-180°C).  Loewen  of  (3)  2 determined from the oxygen consumption r a t e s t h a t the a c t i v a t i o n energies  were 1.8  and 11.4  kcal.mole  l e a c h i n g s t e p s of c h a l c o c i t e , Dahms and a l . chalcocite  (8)  1  ,  f o r the f i r s t and second  respectively  (1 M HCIO^,  110-140°C).  i n v e s t i g a t e d the second l e a c h i n g s t e p of  (0.4 M H^SO^, p  Q  = 10 atm.) between 40 and 140°C.  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,  They 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 w i t h , 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  kcal.mole  S i m i l a r a c t i v a t i o n e n e r g i e s were c a l c u l a t e d from the  x  .  and above 120°C, w i t h an a c t i v a t i o n energy of 20.77  r a t e of s u l p h a t e 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 w h i c h t a k e s p l a c e by two d i s t i n c t p a r a l l e l paths.  As the temperature i s i n c r e a s e d ,  g i v e s way to the h i g h l y a c t i v a t e d  B. 1.6  the l i g h t l y a c t i v a t e d mechanism  one.  DIRECT ELECTROREFINING OF COPPER MATTE  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).  unsuccessful.  T h i s t r i a l as w e l l as l a t e r attempts  were  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 p r o c e s s f o r n i c k e l matte anodes, w h i c h 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 the i n t e r e s t  (16,17), revived  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 ( c o m p o s i t i o n  ++ of the p u r i f i e d e l e c t r o l y t e : 100 g . p . l . ,  H B0 =20 g . p . l . ) . 3  3  Ni  =60 g . p . l . , NaCl=100 g . p . l . ,  The c u r r e n t d e n s i t y i s 20.7  S0^= -2  mA cm  ,  and the c e l l v o l t a g e , w h i c h i s about 2 . 3 V on the f i r s t d a y , 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  a p p r o x i m a t e l y 95% of e l e m e n t a l s u l p h u r . The s u l p h i d e anodes c o r r o d e a t a p p r o x i m a t e l y 94% c u r r e n t  efficiency.  The r e m a i n i n g 6% of the a n o d i c 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 t h e  c a t h o d i c and a n o d i c c u r r e n t e f f i c i e n c i e s the e l e c t r o l y t e Recently,  l e a d s t o a s l i g h t d e p l e t i o n of  i n nickel. s e v e r a l r e s e a r c h e r s i n v e s t i g a t e d the f e a s i b i l i t y o f t h e  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 t h e 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 a r e  ;  summed up i n T a b l e 1 to a l l o w t h e comparison between t h e 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 composition: Cu,  34-52  g.p.l.  H S0 ,  125-230  g.p.l.  Cl,  0.02-0.052  g.p.l.  Fe,  0.2-6  g.p.l.  55-70  °C  16-25  mA cm _2  up to 32  mA cm  Current e f f i c i e n c y ,  89-98  %  Cell voltage,  0.17-0.40  V  2  4  Electrolyte-temperature Power: Max. cathode c u r r e n t d e n s i t y ,  At 20°C, t h e e l e c t r o l y s i s of copper matte anodes i s accompanied by an i m p o r t a n t i n c r e a s e  i n the b a t h v o l t a g e w h i c h r e a c h e s , i n some c a s e s ,  the p r o h i b i t i v e v a l u e o f 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 l o w 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 bath  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 , t h e n a sharp p o t e n t i a l increase  d e v e l o p s to a maximum of 2 . 1 V ; the b a t h v o l t a g e  o s c i l l a t e s between 1.5  and 1.8 V ( 1 5 ) .  corresponds to CuS f o r m a t i o n .  finally  The f i r s t p a r t of the  electrolysis  D u r i n g 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 (15).  reaction  The Cu content of the b a t h remains c o n s t a n t d u r i n g the f i r s t  of the e l e c t r o l y s i s ,  then i t d e c r e a s e s 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 d e p l e t e d of 30% of i t s c o p p e r , w i t h a c o r r e s p o n d i n g in acidity  part  increase  (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 ) . and B i a l l a s s  (15)  Kuxmann  observed t h a t the copper c o n t e n t 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 14% 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 .  c o n t a i n i n g 250 g . p . l .  of E^SO^.  of H^SO^ to  The i n c r e a s e , 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 a n o d i c and c a t h o d i c current  efficiencies.  The amount of e l e m e n t a l 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 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 a u t h o r to a u t h o r . and a l .  (20)  Habashi  c l a i m e d t h a t the e l e m e n t a l s u l p h u r - s u l p h i d e b a l a n c e  c l o s e d w i t h i n 3% (Cu = 30 g . p . l . , H S 0 2  T = 20°C) but Venkatachalam and a l .  4  (19)  = 100 g . p . l . ,  I = 10  (Cu = 30 g . p . l . ,  mA c m " , 2  H S0 2  4  =  -2 150 g . p . l . ,  I = 10  mA cm  (Cu = 35 g . p . l . , H S 0 2  measurements  4  , T = 33°C) and L o s h k a r e v and a l .  = 200 g . p . l . ,  I = 10  (18)  mA c m " , T = 15°C) 2  described  i n d i c a t i n g t h a t 55% of the s u l p h u r was o x i d i z e d to s u l p h a t e .  Kuxmann and a l .  (15)  determined t h a t the amount of s u l p h u r o x i d i z e d to  14 s u l p h a t e 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 cm" , T = 55°C). 2  These i n v e s t i g a t i o n s show t h a t the d i r e c t e l e c t r o r e f i n i n g o f  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 c o n t e n t i n 250 g . p . l . ^ S O ^ e l e c t r o l y t e 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 To compensate  f o r these drawbacks, Kuxmann and a l .  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  (- 89%  (15)  (15)).  added HNO^  ( up to 0.1 g . p . A m p . h r . ) .  reduced the copper l o s s i n the s l i m e to 0.4% of the copper  This contained  i n the anode and reduced the v a r i a t i o n of the copper and a c i d of the e l e c t r o l y t e .  (15)),  The p r e s e n c e of n i t r i c a c i d e f f e c t i v e l y  content reduced  the cathode c u r r e n t e f f i c i e n c y from 98 to a p p r o x i m a t e l y 92% as a r e s u l t of the  reaction  3Cu  +  2N0 ~ 3  +  8H*  > 2N0  +  3Cu  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  equation 0-5)  3CuS  +  2N0 " 3  +  8H  +  —*  3Cu  2 +  +  3S°  +  2N0  +  4H 0, 2  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 ( s u l p h u r 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 b u t 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  cost.  C. 1.7  ELECTROCHEMICAL ASPECTS OF THE AQUEOUS OXIDATION OF COPPER SULPHIDES Scope of the p r e s e n t work I n 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  series  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 l e m e n t a l s u l p h u r 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 . oxidation reactions  results  The development of  the  from the d r i v i n g f o r c e imposed on the  s y s t e m , the m o b i l i t y o f the v a r i o u s i n t e r f a c e s , of copper t h r o u g h the r e a c t i o n p r o d u c t s .  and the r a t e of  The knowledge of the  a r i s i n g from every r e a c t i o n s t e p s h o u l d a l l o w the p r e d i c t i o n of  transport resistances the  overall oxidation rates. 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 s e m i c o n d u c t o r , the c o n d u c t i v i t y of w h i c h i n c r e a s e s -2  i s a p-type  n o t a b l y w i t h copper  -1 -1 to 50 9, cm a t room temperature)  (23,24),  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  d e f i c i e n c y (a - 10  4 10  -1-1 J2 cm  at room temperature)  (23,25).  T h u s , e l e c t r o d e p o t e n t i a l measure-  ments can be used to m o n i t o r 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 . to the presence  S i n c e 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  of a second phase and of i m p u r i t i e s , the  following  e l e c t r o c h e m i c a l s t u d y 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 potentials is desired.  The s t a b i l i t y of the  rest  electrode-electrolyte  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  equilibrium p o t e n t i a l considered. ments of the e l e c t r o m o t i v e  T h i s s t u d y began  f o r c e of the  w i t h the  measure-  cell  Cu I 0.1 M C u S O . , 0.1 M H„S0. I Cu S, i 4' 2 4 y  I  1  w h i c h has been e s t a b l i s h e d  to c o r r e s p o n d t o t h e 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  t o produce a two-phase  electrode  h a v i n g 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 d a t a on the Cu-S system were r e l e v a n t t o the two t e r m i n a l compounds, Cu^S and CuS (2,26). ranges o f the v a r i o u s copper s u l p h i d e s , C u ^ S , Cu^ (Fig.  1) were to be d e t e r m i n e d .  The  only  stability  , =Cu^ g S , : C u S ,  Measurements o f 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  a c c u r a t e 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 d i g e n i t e - d j u r l e i t e mixtures.  The s t a n d a r d f r e e e n t h a l p y of  formation  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 t h e s e measurements the thermodynamic d a t a on CuS, a v a i l a b l e i n the l i t e r a t u r e  and  and  (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 t o the t r a n s p o r t  of  copper i o n s t h r o u g h the o x i d a t i o n p r o d u c t s can be a s s e s s e d from the range of the copper a c t i v i t i e s c o r r e s p o n d i n g to the zone of s t a b i l i t y the o x i d a t i o n p r o d u c t s and from the d i f f u s i o n c o e f f i c i e n t s ions i n these s o l i d phases. o r d e r to measure  of  of  copper  The f o l l o w i n g experiment was d e s i g n e d i n  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 o f copper was f o r c e d t h r o u g h 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 d e t e r m i n e d . I n the absence of overvoltages  surface  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 t h e p o t e n t i a l d i f f e r e n c e a c r o s s the membrane. The method p r o v e d 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 t h e s e  measurements  (Appendix 1 ) . More v a l i d r e s u l t s were o b t a i n e d w i t h the f o l l o w i n g  electrochemical  experiments w h i c h a l l o w e d 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 diffusion coefficients.  A copper anode was o x i d i z e d i n l ^ S  a c i d s o l u t i o n s , at c o n s t a n t  current.  p o t e n t i a l v e r s u s time r e l a t i o n s h i p  The a n a l y s i s of the  saturated  electrode  p e r m i t t e d the c a l c u l a t i o n of  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  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 of copper s u l p h i d e s (27)  reactions  suggested t h a t a n o d i c p o l a r i z a t i o n s t u d i e s c o u l d  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 b e h a v i o u r of t h e s e s u l p h i d e s d u r i n g oxidation.  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 u n d e r t a k e n . electrode  The r o t a t i n g d i s k  t e c h n i q u e 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 p e r m i t s 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 boundary l a y e r .  electrode  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 v e r s u s  time  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 a s s e s s e d (Chapter  4);.  18  The b e h a v i o u r  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 e r i v e d from t h e above r e s u l t s w i t h t h e h e l p o f t h e o r e t i c a l 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 e x p e r i m e n t s done by o t h e r Leaching  considera-  researchers.  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 o b t a i n e d i n the p r e s e n t  work a r e c o n s i s t e n t w i t h e x p e r i m e n t a l  r a t e s observed by o t h e r i n v e s t i g a t o r s  u s i n g f e r r i c o x i d a n t s i n s i m i l a r l y designed  l e a c h i n g experiments.  g e n e r a l f e a t u r e s o f t h e l e a c h i n g o f copper s u l p h i d e s i n a c i d i c  The  ferric  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 p r e s e n t 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 c h e m i c a 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 o f the e x i s t e n c e two compounds, C ^ S and CuS.  However, the phase diagram o f the Cu-S  system as p u b l i s h e d by Roseboom (11) t i o n o f these r e a c t i o n s .  l e a d s t o a more a c c u r a t e  2  1  g 6 5  interpreta-  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  a t room temperature and have been observed as m i n e r a l s : (Cu S), d j u r l e i t e (Cu  of o n l y the  S),  d i g e n i t e (^ C ^  g  S)  chalcocite  and c o v e l l i t e  The o n l y e x i s t i n g thermodynamic d a t a on the Cu-S system a r e to the two t e r m i n a l compounds.  (CuS).  relative  The thermodyanmic p r o p e r t i e s of  i n t e r m e d i a t e copper s u l p h i d e s , w h i c h are e l e c t r o n i c c o n d u c t o r s  the (23,24,  2 5 ) , 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 p r o c e s s 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 this charge-transfer redox.  can take p l a c e t h r o u g h the c a t i o n , the a n i o n o r a  c o u p l e p r e s e n t i n the s o l u t i o n .  charge-transfer  electrolyte;  processes  When two o r more d i f f e r e n t  occur independently  of each o t h e r , at  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 a c r o s s  the  the  e l e c t r o d e - e l e c t r o l y t e b o u n d a r y , r e s u l t i n g i n a change o f the c h e m i c a l c o m p o s i t i o n o f the s y s t e m .  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 . Charge-transfer processes  i n v o l v i n g b o t h the Cu and the S s p e c i e s c o u l d  o c c u r at the s u r f a c e o f a Cu S e l e c t r o d e i n c o n t a c t w i t h a CuSO. y  4  20 electrolyte;  t h i s would r e s u l t i n a subsequent  c o m p o s i t i o n o f the s o l i d and of the s o l u t i o n  alteration  of  the  (Fig.2).  S t u d i e s of the r e s t p o t e n t i a l s o f 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 t h a t 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 o f 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 t o a copper e l e c t r o d e , by the presence o f s u l p h a t e ( 1 5 , 2 8 , 2 9 , 3 0 ) .  and t h a t they were not  affected  The s t a n d a r d 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 , a t 25°C, was d e r i v e d from t h e s e experiments as 486 mV ( 1 5 ) ,  490 mV (28)  and 505 mV ( 2 9 ) .  The  s t a n d a r d 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 , a t 25°C, was c a l c u l a t e d to be 597 mV (30)  and 567 mV ( 2 9 ) .  F u r t h e r e v i d e n c e t h a t the SP-SO^  c o u p l e 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 t h a t e l e m e n t a l s u l p h u r d i d  not  o x i d i z e to s u l p h a t e 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 a t 125°C under p.s.i.  of oxygen.  Sullivan  60.3  ( 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 1 0 0 ° C , e s t a b l i s h e d t h a t  the  f i n a l p r o d u c t s o f o x i d a t i o n were c u p r i c i o n s and e l e m e n t a l s u l p h u r , though s u l p h a t e was the most s t a b l e s u l p h u r s p e c i e s i n h i s e x p e r i m e n t a l conditions.  T h e r e f o r e 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 d e t e r m i n e d by the reaction  (Cu)  C u  s  "—*  Cu^  +  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 4 2 4 y  (I)  21  Pt or C  Cu S  CuS0 (aq)  y  4  (Cu)(SH  e  Charge-transfer  F i g u r e 2.  E  -,_.  2+ Cu 2SO  —>.  Ox. Red.  processes.  C h a r g e - t r a n s f e r p r o c e s s e s 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 S ) Cu  y  u  °  u  = RT l n a  Cu  C e l l I may be c o n s i d e r e d 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 cells  Cu/0.1 M C u S 0 , 0.1 M H S 0 / S . C . E . 4  S.C.E.  2  (ID  (25°C),  4  ( 2 5 ° C ) / 0 . 1 M CuSO., 0 . 1 M H S 0 . / C u S 4 2 4 y '  (III)  o  and b o t h 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 S.C.E.  2.2  versus  (25°C).  Experimental 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 s e a l e d 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 ( 3 1 ) .  The p r o d u c t was  p r e s s e d under vacuum i n t o a d i s k , 13 mm i n d i a m e t e r 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 t h e n 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 . c e l l was immersed i n an o i l  :  thermostat.  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  .  The  23 (Keithley 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 c a l o m e l  e l e c t r o d e a t 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 B e t h u n e , L i c h t and  Swendeman's d a t a (32) were made to compensate f o r t h e 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 . at room t e m p e r a t u r e .  were  The s o l u t i o n was a n a l y s e d 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  2.3.  The P t - C u l e a d c o n t a c t s  measurement.  Results  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 t h e measurements of t h e Cu e l e c t r o d e 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 o f t e m p e r a t u r e .  potentials  Measurements  were made a f t e r an a n o d i z i n g o r c a t h o d i z i n g treatment on e l e c t r o d e s d i f f e r e n t p u r i t y , some b e i n g 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 r a n g e , E = (70.45 ± 0.33) x 1 0 ~ + (0.632 + 0.025) x 1 0 ~ 3  of  35-75°C. 3  (T - 328)  (V)  The e q u a t i o n and the e r r o r s were c a l c u l a t e d by t h e c l a s s i c a l method o f 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 o f 98%. E l e c t r o d e s o f c o m p o s i t i o n Cu^ ^^S were then s t u d i e d . d i f f r a c t i o n p a t t e r n c o n f i r m e d the e x i s t e n c e and c o v e l l i t e .  An X - r a y  of the two p h a s e s ,  digenite  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 c o m p o s i t i o n Cu^ ^ ^ ^ S , t h i s c o m p o s i t i o n l i m i t r e m a i n i n g c o n s t a n t up to 200°C ( 1 1 ) .  A sample s y n t h e s i z e d a t h i g h  temperature s h o u l d 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 , t h e . 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 s u b j e c t e d t o 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 - 0 . 1 M H S 0 ] Cu 4  A  after anodization  2  •  4  after cathodization  A  H„ annealed 2  25  current.  The amount o f c u r r e n t passed t h r o u g h t h e specimen r e s u l t e d i n  a v a r i a t i o n o f 0.3% of i t s average Cu c o n t e n t .  After switching o f f ,  the e l e c t r o d e p o t e n t i a l was r e c o r d e d as a f u n c t i o n o f t i m e . s t a b i l i z e d e l e c t r o d e was then s u b j e c t e d and the r e s t p o t e n t i a l r e c o r d e d . i s shown on F i g . 4.  The  to a c u r r e n t o f o p p o s i t e s i g n  A s e r i e s o f these r e l a x a t i o n c u r v e s  Though the r e l a x a t i o n curves o b t a i n e d  after  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 t h e same sample were n o t s y m m e t r i c a l , t h e r e l a x a t i o n curves o b t a i n e d 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 s y m m e t r i c a l and more c o n v e r g e n t . The gap between any s e t o f two c u r v e s d e c r e a s e d w i t h i n c r e a s i n g temperat u r e , as i t appears from t h e comparison of F i g . 4 and 5 . F o r c i n g c u r r e n t i n o r o u t of t h e e l e c t r o d e forces t h e f o l l o w i n g r e a c t i o n to t h e r i g h t o r t o t h e l e f t ,  CuS  +  0.765Cu  -—y -*  Cu, , , , - S , 1.765 '  u n l e s s one of the s u l p h i d e s t a k e s c a r e of t h e 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 t h e m i d d l e o f t h e gap between two c o r r e s p o n d i n g r e l a x a t i o n c u r v e s .  The r e s u l t s  a r e p l o t t e d on F i g . 6 as a f u n c t i o n of t e m p e r a t u r e .  They a r e  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,  E = (251.50 + 0.35) x 1 0 ~  The e q u a t i o n and t h e e r r o r s  3  + CO.765 + 0.035) x 1 0 ~  were  3  40-70°C,  CT - 328).-(V).  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 c u r v e s 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 or c a t h o d i z a t i o n of CuS-Cu.. electrodes. A O  after cathodization  ^  9  after anodization  A  O  treatment  on f r e s h  electrode  260  -  255  -  100  50  0  t(hrs) Figure  5.  R e l a x a t i o n c u r v e s of CuS-Cu-^  765S  e l e c t r o d e s , a t 60°C.  •  o  after anodization  Q  •  after cathodization  O  D  treatment on f r e s h e l e c t r o d e  265  255  >  J  iii 245  235  40  60  50  T(°C) F i g u r e 6.  Temperature dependence o f the e . m . f . of the c e l l S . C . E . (25°C) I 0.1 M CuSO' - 0 . 1 M H S 0 , I CuS-Cu, 4 z 4 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  1  O  •  d i f f e r e n t batches of  sulphides  70  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 o f 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 e v i d e n c e f o r the p r e s e n c e o f b o t h and d j u r l e i t e .  A c c o r d i n g t o Roseboom C H ) the Cu r i c h l i m i t  d i g e n i t e v a r i e s w i t h temperature,  g o i n g from Cu^ ^ S  t u r e t o Cu^ g^S a t 83°C where d i g e n i t e i n v e r t s i t s The e l e c t r o d e  of  a t room tempera-  crystal  structure.  p o t e n t i a l o f 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 ; A p e r i o d from 24 t o 96  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 .  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 a t each t e m p e r a t u r e .  The  e x p e r i m e n t a l r e s u l t s a r e r e p o r t e d on F i g . 7 as a f u n c t i o n o f The v a l u e s can be accommodated by a s t r a i g h t  E =  C242.20 ± 0 . 4 5 ) x 1 0  _  3  line  It  temperature.  relationship)  + CO.62 + 0 . 0 6 ) x 1 0  The e q u a t i o n and the e r r o r s were c a l c u l a t e d by the linear  digenite  _  3  Ct - 3 4 3 ) CV)  classical  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 % . appears  t h a t the  reaction  Cu S + C1.965 - y ) C u y  •  Cu,  „, S* C  1.965  3  t a k e s 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 5 5 ° C . This i s consistent  w i t h Roseboom's  f o r m a t i o n i s r e v e r s i b l e at  C H ) o b s e r v a t i o n t h a t the  djurleite  93°C.  CUyS r e p r e s e n t s 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 o f 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 C u S O - 0 . 1 M H S 0 | Cu^S-Cu 4 " "2"~4 1.965" /  o  /-  O  A  d i f f e r e n t compositions, a f t e r  heating  •  •  d i f f e r e n t compositions, a f t e r  cooling  •  e x c l u d e d from the l i n e a r  regression.  o  31 Specimens of c o m p o s i t i o n Cu^ g S p r o d u c e d , i n s p i t e of a c o o l i n g g  r a t e of 10°C per d a y , a m i x t u r e of c h a l c o c i t e 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 .  and m e t a s t a b l e  tetragonal  Tetragonal d j u r l e i t e i s  r e p o r t e d to be p r e s e n t i n s u l p h i d e of c o m p o s i t i o n i n t e r m e d i a t e chalcocite  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  often  between  (11,33).  From the r e p o r t e d s e t of e x p e r i m e n t a l d a t a , the s t a n d a r d 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 and d j u r l e i t e can be  free  calculated.  The s t a n d a r d s t a t e s are pure C u , pure o r t h o r h o m b i c 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 t a n d a r d f r e e e n t h a l p y of the  CuS  +  0.765Cu  >  reaction  Cu.. -,,-,-S, 1.765  w h i c h depends o n l y on the s t a n d a r d 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) 1.  Von Wartenberg  =  AF° (CuS)  +  0.765 RT l n a„ . L.U  /DJ  (34) measured the heat of f o r m a t i o n of CuS a t is  AH  *  298°K. ^  C u S )  .1 c a l . = 4.1840 J .  =  "I- ' 1  6 1 0  *  4 0 0  cal .mole  - 1  25°C,  32 and Kubaschewsky and Weibke (35) a s s e s s e d the e x p e r i m e n t a l  error.  Anderson (36) c a l c u l a t e d t h e e n t r o p y o f CuS a t 20°C from s p e c i f i c heat measurements. most p r o b a b l e  AS  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 t h e  (37).  298°K  ^  C u S  ^  =  0  ,  3  "  0  ,  4  5  c  a  1  ,  m o l e  "  1  O K _ 1  These a r e the o n l y d a t a on CuS r e s u l t i n g from d i r e c t measurements. v a l u e o b t a i n e d by e x t r a p o l a t i o n from h i g h temperature supposing the existence obviously doubtful.  Any  measurements,  o f an e q u i l i b r i u m between CuS and C ^ S a r e  However, Kubaschewsky, Evans and A l c o c k (26) a r e  i n f a v o u r o f a more n e g a t i v e heat o f f o r m a t i o n f o r CuS. I n the temperature r a n g e , 4 0 - 7 0 ° C ,  the s t a n d a r d f r e e e n t h a l p y o f  f o r m a t i o n o f Cu-poor d i g e n i t e i s then c a l c u l a t e d t o be  AF° (Cu  ±  2.3.3.  7 6 5  S ) = (-18,140 ± 525) - ( 4 . 9 0 + 2.50) (T - 328)  cal.mole . - 1  V a r i a t i o n o f t h e s t a n d a r d f r e e e n t h a l p y bf f o r m a t i o n of digenite w i t h composition  The e f f e c t o f c o m p o s i t i o n v a r i a t i o n s on the s t a n d a r d f r e e e n t h a l p y of f o r m a t i o n o f 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 e n t h a l p y of t h e system can be e x p r e s s e d i n terms o f t h e c h e m i c a l p o t e n t i a l of i t s  constituents,  33  AF°(cu  y S  = y(y  )  C  u  - y  C  u  ) + M  - y;  s  The t o t a l d e r i v a t i v e o f t h e f r e e e n t h a l p y w i t h r e s p e c t t o y i s e q u a l to  d[AF°(Cu S)] y  ( u  C  u  -y° )dy + y d C y ^- ^ u  +  d ( y - y^) g  (3,1) T h i s e x p r e s s i o n o f Eq ( 3 . 1 )  d[AF°(Cu S)] y  = (y  can be s i m p l i f i e d t o  - y° )dy  C u  (3.2)  u  by u t i l i z i n g t h e Gibbs-Duhem  relationship  I n t e g r a t i o n of E q . (3.2) between t h e c o m p o s i t i o n l i m i t s of y i e l d s the corresponding d i f f e r e n c e  digenite  of the s t a n d a r d f r e e e n t h a l p y o f  formation,  AF°(Cu  y  2  S) - AF°(Cu  y  S) = ±  y  / y  2  ^  (y  -  v  ° )dy 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 e q u a l to t h e a r e a 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  ]i  -  = f ( y ) , w h i c h has n o t been d e t e r m i n e d .  curve,  As t h e c h e m i c a 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 a r e a 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 )(y - y° ) £. x uu uu 0  n  (y„-y )(y  - y° ) and uu uu I n the d i g e n i t e c a s e , t h e s e two v a l u e s d i f f e r by 1  &.  .  JL  a p p r o x i m a t e l y 12% and the v a r i a t i o n of the s t a n d a r d 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  AF°(Cu  S)-AF°(Cu S)=(y„- ) y ' y-, 2 ' i ' y i  U  Cu  ( y  t U  1  l  w  9  y  2-- l 2 RT[ln a  ) + v  2  y  C u  Cu  ( y  C U  (  y i  2  )  1  ) + 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 t a n d a r d f r e e e n t h a l p y of f o r m a t i o n of d j u r l e i t e  2.3.4.  possible.  S t a n d a r d f r e e e n t h a l p y of f o r m a t i o n of  djurleite  In a d i g e n i t e - d j u r l e i t e mixture i n e q u i l i b r i u m ,  Cu S + (1.965 - y) Cu -> Cu. - , , - S . y 1.965 • J  the Cu a c t i v i t y i s r e l a t e d to the s t a n d a r d f r e e e n t h a l p y change of reaction.  the  I n t h i s c a s e , 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 c h e m i c a l  p o t e n t i a l i s temperature dependent.  The s t a n d a r d f r e e e n t h a l p y 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 S) + (1.965 - y)RT I n y  a  C u  ,  and i n the temperature r a n g e , 5 5 - 8 0 ° C , i t has been c a l c u l a t e d to be  35  AF' ( C i ^  2.4.  9 6 5  S)  = (-19,700 ± 550)  -  (5.5 ± 3 . 1 ) ( T - 343)  1  .  Discussion 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  c a l mole  1 < 9 9  S)  (Cu^ g^S)  and  chalcocite  (11,38),  0.166Cu  1 > 8 4 0  S + 0.833Cu  1 > 9 9 0  S  —*  C u ^ S .  T h i s e q u i l i b r i u m a c t s 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 measurements w i t h the e x i s t i n g d a t a on the s y s t e m .  The s t a n d a r d f r e e  e n t h a l p y 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 performed i n t h i s w o r k , A F ° „ , , „ ( C u 0  1  present  r , ^ S ) = 19,830 i  measurements 600 c a l mole  r  366 K 1.965 ' The s t a n d a r d f r e e e n t h a l p y of f o r m a t i o n o f 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 p r e s e n t measurements,  AF°_,job  (Cu.  0  JL.  K.  Q/  S)  =  OH  - 1 8 , 9 0 0 ± 600 c a l m o l e " . 1  Von Wartenberg (34) a t 298°K, A H ° (35)  980K  (Cu S) 2  determined the heat of f o r m a t i o n o f Cu^S = 18,970 c a l m o l e " . 1  Kubaschewsky and Weibke  i n t h e i r d i s c u s s i o n on the Cu-S d a t a s e l e c t e d  most p r o b a b l e , a s s e s s i n g  t h i s v a l u e as  the e x p e r i m e n t a l e r r o r to 500 c a l mole  Cu S has been s t u d i e d i n d e t a i l by R i c h a r d s o n e t a l . 2  (39)  e . m . f . measurements  at 500°K.  Its  Wagner et a l .  \  u s i n g R -H_ S 2  e q u i l i b r i u m i n t h e temperature range 8 0 0 - 1 0 0 0 ° K , by Brook (40) temperature range 5 0 0 - 1 0 0 0 ° K and by J . B .  the  (41)  2  i n the  using  s t a n d a r d f r e e e n t h a l p y of f o r m a t i o n  seems t o be a c c u r a t e l y e s t a b l i s h e d i n t h a t temperature r a n g e ,  but  e x t r a p o l a t i o n of t h e s e v a l u e s t o 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 o f the s p e c i f i c h e a t d a t a .  For  that  r e a s o n , Von W a r t e n b e r g ' s d a t a 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 ( 2 6 ) . and K e l l e y ' s (37)  Anderson's  (36)  d a t a on the e n t r o p y of Cu^S y i e l d , a l o n g w i t h Von  W a r t e n b e r g ' s d a t a f o r AH°, AF°  , ODD  0 i r  (Cu S)  K  0  = 20,900 ± 800 c a l m o l e " . 1  Z  I n these c o n d i t i o n s the two s e t s of d a t a converge w i t h i n 700  cal.  mole ^ , a gap w h i c h s i t s i n the m i d d l e o f 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 w o r k , 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 b e s t low temperature d a t a shown i n the l i t e r a t u r e . (90%)  The m a j o r  component  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  measurements  present  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  d a t a on CuS. The v a r i a t i o n of Cu and S c h e m i c a l p o t e n t i a l s a c r o s s the system can then be a s s e s s e d a t any temperature 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  ( F i g . 8).  equilibrium is  Cu-S  However, the conjectural:  i t was not measured d i r e c t l y and the a c c u r a c y of the e x i s t i n g d a t a 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 e n t h a l p y 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 e r r o r on any of these v a l u e s . djurleite-chalcocite  i s much s m a l l e r than the e x p e r i m e n t a l  Though the Cu c h e m i c a l p o t e n t i a l i n the  system i s known a t 93°C from the p r e s e n t  ments, the u n c e r t a i n t y on the e n t r o p y change of the r e a c t i o n 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 .  measure( 0 . 1 ±,  Table 2 Thermodynamic d a t a o f the copper s u l p h i d e s below 100°C AF /  Composition  CuS C U  1.765  S  Cu S y  0  . . -1 c a l mole  AS°/  . c a l mole  1  ( c ) .  (-11,610 ± 400) -  ( 0 . 3 ± 0.45)T  0 . 3 ± 0.45  (D.) •  (-18,140 ± 520) -  (4.9 ± 2 . 5 ( T - 3 2 8 )  4 . 9 ± 2.5  (D.).  (-18,140 ± 520) - ( 4 . 9 ± 2 . 5 ( T - 3 2 8 )  °K  1  Ref.  34,35,36,37 t h i s work t h i s work  + (y - 1., 7 6 5 ) [ ( - 7 , 9 1 0 ± 40) - ( 3 . 2 ± 3.5) (T-328)  C U  1.965  Cu S 2  S  (Dj.).  (-19,700 ± 550) -  (5.5 ± 3.1)(T-343)  5.5 ± 3 . 1  t h i s work  (Ch.).  - ( 1 8 , 9 7 0 ± 500) -  (5.3 ± 0.8)T  5.3 ± 0.8  34,35,36,37  OJ  -5-5 IC.  + •60  1.  0  O  ~  -6-5  0  u  i  -20 50  _i  I  F i g u r e 8.  55  60  65  %Cu u  1.765  —CuS  1.805 1.965 Z  V a r i a t i o n o f s t a n d a r d f r e e e n t h a l p y of f o r m a t i o n and of p o t e n t i a l s a c r o s s the Cu-S system a t 55°C.  chemical 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 saturated with ^ S . current,  different  If  the o p e r a t i o n i s conducted at  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  grown as the o x i d a t i o n p r o c e e d s . s u c c e s s i v e phases s h o u l d b e , (Fig. 1): sulphur.  copper a c t i v i t y  are  If equilibrium i s established,  the  a c c o r d i n g to the phase diagram  copper, c h a l c o c i t e ,  djurleite,  digenite,  The r e a c t i o n o c c u r r i n g a t the anode  y Cu + H„S 2  —*  The e l e c t r o c h e m i c a l convention)  •n  (11)  c o v e l l i t e and  is  Cu S + 2 H + 2e y +  p o t e n t i a l of such an e l e c t r o d e  (Stokholm  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 ,  RT ,  a  y  Gu  a  Ho S  ,  V  o ~ ~z¥ a  Cu S y  a  H  /-TIN  s  +  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  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 grown.  constant  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 .  and s t i r r i n g c o n d i t i o n s , under a c o n s t a n t c u r r e n t ,  conditions  of the s c a l e b e i n g  In defined  geometric  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 c o n s t a n t In s t e a d y - s t a t e  i n the v i c i n i t y of the  electrode.  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 .  Therefore,  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)  dE dt  _ "  _ RT 2F  dE  dt  If  d e r i v e d from E q .  d_ dt  RT d =  i n  E  (3.1),  y Cu  .  " ^2F dT  „ a  Cu  7  =  t  ^ - )  c o n s t a n t  3  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  copper a c t i v i t y a t the l i q u i d - s o l i d i n t e r f a c e  surface,  2  the  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 s u l p h u r i o n - m o b i l i t y i s  considered  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 ( 4 2 ) . case of h i g h temperature phases evidence  (aCX^S, gCu^S) t h e r e i s  (43,44) to support t h i s .  It  I n the  experimental  i s also reasonable  f o r the low  temperature phases i n v i e w o f 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 .  Chalcocite i s a  p - t y p e s e m i c o n d u c t o r , 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 d e f i c i e n c y (a = 1 0  -1 -1 ->- 50 Q cm at room temperature)  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 room temperature  (23,25).  (23,24). Digenite 4 -1 -1  (a = 2.10  Q  cm  at  41 The p h e n o m e n o l o g i c a l e q u a t i o n s 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 t o 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 . e f f e c t s are neglected,  I f the i n t e r a c t i o n  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 t h e presence o f 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+  J  e  =- Cu M  "  =  M  e  &"C«+  +  4^e  +  W-  +  W  k * > >  C  •>  (3  '  3  '  Cu Cu+ ~ ~ q q  T J  +  M  Cu M ~  )  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 e q u a t i o n and s u b s t i t u t e d i n e q u a t i o n  3  (3.4)  (3.3),  +  ,d Cu u+ dx" Cu+ ~ ~ q  J  e  =  "  M  C  C  v  +  d . dx" V  r ( 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 a r e 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 a r e r e l a t e d t h r o u g h t h e measurable q u a n t i t y , u  Cu  V  =  y  Cu+  +  y  e  E q u a t i o n (3.5) i s then s i m p l i f i e d to  M  J  + Cu+  n  +  +  -TT- J M  A  " ~ M_ ~ e Cu*: dx +  (3.6)  ii_  Cu  As r e p o r t e d e a r l i e r , the copper s u l p h i d e s a r e e l e c t r o n i c  conductors,  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 b e i n g 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 e q u a t i o n (3.6)  J  Cu+ = "  M  Cu+  can be reduced t o  »Cu  The Onsager c o e f f i c i e n t  '  (3  7)  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 , C K ,  m o b i l i t y , B_^, and d i f f u s i v i t y , D ^ , o f the p a r t i c l e i .  M. = a . l  q.  l  "2 I  M. = B . C .  (3.8)  i M. = C. i RT i E q u a t i o n (3.7) can be expressed i n terms of any of t h e s e f o u r parameters D  Cu  T  W If  -  -  d dx" C u  /_  y  —  ( 3  n  '  ,  9 )  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  electrode surface,  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  t o the number of coulombs passed t h r o u g h the e l e c t r o l y t i c c e l l d u r i n g that  time,  T X  " *0  Cu+  Combining e q u a t i o n s  X  Cu+  2  ~ V  C t  yl  =  ,M, d Cu S y  C  (3.2),  (3.9)  }  +  C 3  and (3.10) y i e l d s e q u a t i o n  1 • M. dE 2? d C u S = ° C u + d7 y (  .„  }  '  1 n  '  ,  1 0 )  (3.11),  U N  43 w h i c h p e r m i t s the c a l c u l a t i o n o f the i o n i c c o n d u c t i v i t y o f the s u l p h i d e scale,  formed under steady s t a t e c o n d i t i o n s , from the s l o p e of  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  3.3  the  time.  Experimental The anode was made of copper r o d (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 ( K o l d m o u n t ) , and p o l i s h e d so o n l y one p l a n e was i n c o n t a c t w i t h the s o l u t i o n .  that  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  stirrer.  The system was h e l d at c o n s t a n t  water b a t h .  temperature by a r e g u l a t e d  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  system t h r o u g h a s e t 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  was measured v e r s u s a s a t u r a t e d c a l o m e l e l e c t r o d e v o l t m e t e r w h i c h f e d the s i g n a l to a SargentSRG  recorder.  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) c u r r e n t d e n s i t i e s between 1.9  10  -4  potential  by a K e i t h l e y 153  S e r i e s of experiments were c a r r i e d out a t temperatures  selected  the  between  and under  -2 A cm and 1.55  x 10  -3  . -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 surface  electrode  ( F i g . 9) w h i c h ranged from 50 to 380 V- depending on e x p e r i m e n t a 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 p r o d u c t s 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 microscopy, e l e c t r o n d i f f r a c t i o n or -microprobing.  The  three-sulphide  assembly was n o t i n e q u i l i b r i u m and i n the absence of an  electric  F i g u r e 9.  M i c r o g r a p h of the copper s u l p h i d e s c a l e s e p a r a t e d from i t s Cu s u b s t r a t u m . 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 polishing.  45  c u r r e n t one phase d i s a p p e a r e d d u r i n g the time r e q u i r e d f o r the p r e p a r a t i o n a c c o r d i n g to the  0.8Cu S  +  o  Z  3.4  0.2Cu,  sample  reaction,  S l.o  Cu  Q  1.96^  R e s u l t s and D i s c u s s i o n s So f a r ,  t h r e e s u p h i d e s have been i d e n t i f i e d , c h a l c o c 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  djurleite,  d i r e c t o r i n d i r e c t , f o r the  ance of c o v e l l i t e was o b t a i n e d i n t h e s e  appear-  experiments.  The s u l p h i d e growth m o d e l , a n a l y s e d e a r l i e r i n t h i s p a p e r , 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 ; t h a t i s , when the 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 .  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 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 copper content  (11)  v i r t u a l l y equals the t o t a l e l e c t r i c  cationic  These c o n d i t i o n s  are  (Cu^S) i s d e p o s i t e d .  The  i s s m a l l e r than 0.5% of  and d u r i n g Cu^S f o r m a t i o n , the i o n i c current  (Fig.  is  its  current  10).  When a new s u l p h i d e s t a r t s t o 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 to C u r a t i o i n the new phase. +  mated by Cu,  Q  S,  If  i s changed a c c o r d i n g to the Cu the d i g e n i t e c o m p o s i t i o n i s a p p r o x i -  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  interface  l.o at the s t a g e of d i g e n i t e growth can be r e p r e s e n t e d by F i g . 1 1 , and the correspondingly cationic  (1^ +)  to 90 and 10%, r e s p e c t i v e l y ,  (J°)  and e l e c t r o n i c  of the t o t a l c u r r e n t  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  f i x e d v a l u e of copper a c t i v i t y o r e l e c t r o c h e m i c a l  c u r r e n t s are (I).  equal  The boundary  thermodynamically potential;  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 .  therefore,  Consequently,  'Figure  10.  Model of anode.  the  Cu^S f i l m  growing on  the  47  Cu  1.8  CuS  S~~—*  "L8  S  *  2e  - Ic *+Ie  I "  u  ICu*-  Figure 11.  C  .9  ifc - X  r  .11  .11  > X»o  Model of the copper s u l p h i d e s c a l e a t s t a g e of C u , S g r o w t h . D  JL. o  the  48 the a b r u p t change i n cuprous c u r r e n t a t the onset of growth of a new phase i n i t i a t e s an unsteady s t a t e p r o c e s s d u r i n g w h i c h each s u l p h i d e layer adjusts  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 m o t i o n are b e l i e v e d to g e n e r a t e s t r e s s e s i n  the s p e c i m e n , because the s c a l e always breaks  away from the copper b e f o r e CuS g r o w t h i s a p p a r e n t . 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 .  d i g e n i t e c o m p o s i t i o n i s r e p o r t e d (11) Cu,  7 n  S  a t room t e m p e r a t u r e .  a f f e c t e d by t e m p e r a t u r e ,  The  to extend from Cu^ yg^S t o  A l t h o u g h the Cu poor l i m i t i s not  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 t o h i g h d i g e n i t e .  D u r i n g the d i g e n i t e l a y e r  growth t h e r e i s a c o n t i n u o u s change i n the Cu c u r r e n t f l o w i n g t h r o u g h the s c a l e ,  but t h i s v a r i a t i o n r e p r e s e n t s  o n l y 1.75%  of the  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 a c c u r a c y of  total  the  method of measurement. From the s e t of e x p e r i m e n t a 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 chalcocite  the  and d i g e n i t e i n t h e 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  p r e s e n t i n e v e r y sample, the i o n i c c o n d u c t i v i t y v a l u e c o u l d 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 p r o b a b l y  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 established. 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 u s e d .  I n the c h a l c o c i t e  c a s e , however, t h e r e was  a c u r r e n t d e n s i t y v a l u e above w h i c h the e x p e r i m e n t a l r e s u l t s became inconsistent. temperature.  This l i m i t i n g current density increased sharply with 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 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 S = 0.644 cm  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 T (°C)  i (mA)  E range (mV) Cu S/H S s a t . .  0.2 M H „ S 0 . 2 4 0.2 M Na - S O . / S . C . E . ( 2 5 ° C ) 2 4 2  2  Correlation Coefficient r  dE dt  n  U  (mV m i n ) X  (fi  cm - )  (cm sec  1  30  0.125  490-410  0.9985  0.0410  0.786 x 10  2.93  X  40  0.250  520-465  0.9997  0.0818  1.60  X  io"  5  6.15  40  0.250  425-390  0.9977  0.0835  1.57  X  io"  5  46  0.250  480-425  0.9971  0.0659  1.98  X  io" io"  5  48  0.250  510-475  0.9976  0.0712  1.84  X  50  0.234  525-485  0.9977  0.0521  2.95  X  51  0.250  508-450  0.9921  0.0526  2.45  X  55  0.250  480-445  0.9986  0.0357  3.67  X  55  0.250  465-430  0.9966  0.0403  3.25  55  0.500  500-456  0.9990  0.140  58  0.750  510-412  0.9997  62  0.750  525-410  66  0.750  70  ) 1 1  X  io" io"  6.03  X  io"  1 1  7.74  X  1 1  5  7.25  X  io" io"  5  11.70  X  1 1  5  9.75  X  io" io" io"  X  io" io" io" io"  1 1  3.74  X  0.292  3.97  0.9980  0.222  515-458  0.9993  0.500  500-465  70  1.000  73  1.000  5  1 1  1 1  1 1  5  14.8  X  5  13.1  X  io"  5  15.1  X  X  io"  5  16.1  X  io" io" io"  5.22  X  IO"  21.5  X  io"  1 1  0.241  4.81  X  io"  20.0  X  1 1  0.9969  0.0738  7.09  X  IO"  5  29.9  X  io" io"  505-435  0.9985  0.282  7.43  X  IO"  5  31.3  X  505-485  0.9989  0.271  7.61  X  IO"  5  32.3  X  5  5  io" io"  1 1  1 1  1 1  1 1  1 1  1 1  Table 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 o f  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 T  i  (°C)  (mA)  E range (mV) '^Cu  1  0  S / H S s a t . , 0.2 M H „ S 0 . 0  0.2 M - N a S 0 / S . C . E . ( 2 5 ° C ) 2  Correlation Coefficient r  dE dt  D  o  (mV m i n )  {Q cm  1  4  S = 0.644 cm'  , 2 -) (cm sec 1  30  0.125  235-225  0.9987  0.0137  1.76  X  io"  5  40  0.250  251-240  0.9936  0.0280  3.50  X  io"  5  40  0.500  235-200  0.9989  0.110  3.56  X  io"  5  40  0.500  281-255  0.9976  0.123  3.17  X  io'  5  40  0.500  275-243  0.9990  0.112  3.50  X  io"  5  40  0.750  250-225  0.9999  0.292  3.09  X  io'  5  40  0.750  240-210  0.9998  0.253  3.48  X  io"  5  46  0.250  251-225  0.9968  0.0239  4.08  X  io"  5  48  0.250  270-260  0.9888  0.0221  4.43  X  io"  5  51  0.250  268-245  0.9964  0.0168  5.74  X  io"  5  55  0.500  250-225  0.9973  0.0522  7.50  X  io"  5  55  0.750  251-225  0.9987  0.107  8.24  X  io"  5  55  0.250  255-240  0.9815  0.0143  6.85  X  io"  5  58  0.750  262-238  0.9976  0.0967  8.96  X  io'  5  62  0.750  255-235  1.0000  0.0833  10.6  X  io"  5  66  0.750  250-225  0.9966  0.0799  10.9  X  io"  5  70  0.500  245-230  0.9865  0.0264  14.8  X  io"  5  70  1.000  247-234  0.9965  0.0833  18.8  X  io"  5  73  1.000  250-230  0.9940  0.0711  21.7  X  io"  5  .  0.683  X  io"  10  1.40  X  io'  1 0  1.42  X  io"  10  1.27  X  io"  10  1.40  X  io'  1 0  1.23  X  io'  1 0  1.39  X  io"  10  1.66  X  io'  1 0  1.81  X  io'  1 0  2.38  X  io"  10  3.14  X  io"  10  3.45  X  io"  10  2.87  X  io"  10  3.81  X  io"  10  4.53  X  io'  1 0  4.74  X  io"  10  6.47  X  io"  10  8.22  X  io"  10  9.62  X  io"  10  51 current density raises  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 a n o d i c f i l m s as c o n t i n u o u s o r non c o n t i n u o u s f i l m s .  I n most of the cases r e p o r t e d i n the  literature,  the d i s t i n c t i o n between c o n t i n u o u s and non c o n t i n u o u s f i l m s i s  based  on the n a t u r e 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 . is characteristic constant  It  of non c o n t i n u o u s f i l m to e x h i b i t an a p p r o x i m a t e l y  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 ( 4 5 ) . plane electrode  The smooth copper anode and the one .  s u r f a c e p r e v e n t e d i n t r o d u c i n g s t r e s s e s w h i c h might  have l e a d to the c r a c k i n g of the f i l m .  There was no s o l i d  state  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 steady-state conditions prevailed.  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 t h r o u g h the s o l i d ,  which  mechanism f a v o u r e d the f o r m a t i o n of a c o n t i n u o u s u n i f o r m s c a l e .  A  d e c r e a s e 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 e x p e r i m e n t a 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 was found t o be ( F i g .  D  3  exp.  -10 = 1.1 x 10  The measured d i f f u s i o n c o e f f i c i e n t 13)  of cuprous i o n i n low c h a l c o c i t e  12)  + = 8.1 x 1 0 ~  found to be ( F i g .  ,  -  5,870 T  2 -1 cm sec 2 -1 at cm sec  50°C.  of cuprous i o n i n low d i g e n i t e was  52  F i g u r e 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 .  53  In D  23.5 I  ' 2.9  1  3.0  '  1  3.1  3.2  L_  3.3  i ( IO" K~') 3o  Figure 13.  Temperature dependence of the cuprous ion diffusion coefficient in low digenite.  54 D^  u +  o c  =  3.6  x  -,n~2  10  D„ + = 2.4 x 1 0 I n the temperature  .6,100  exp.  J  cm sec  - 1 0  2  -JT—  at  - 1  cm  2  -1  50°C.  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  , * -1 d i f f u s i o n (AH) i s 11.7 Z 1 k c a l mole for chalcocite, * -1 0.8 k c a l mole for If  sec  for  digenite.  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 ,  n a t u r e 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. 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  suggested  that  X-ray i n v e s t i g a t i o n s  chalcocite  The  have  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  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 sites  (ctAg^S ( 4 6 ) ,  the  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 S c h o t t k y o r F r e n k e l type d e f e c t s .  lattice  , X  and 1 2 . 1  aAgl (47),  aCu^S ( 4 4 ) ) .  distri-  equivalent  I n the case of low  and d i g e n i t e w h i c h have r e l a t i v e l y o r d e r e d copper  lattices,  an i n t e r s t i t i a l c y mechanism (the c a t i o n s b e i n g e q u a l l y m o b i l e ) 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 s u p p o r t e d by t h e  e x p e r i m e n t a l o b s e r v a t i o n t h a 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 coefficient Therefore,  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 . the e q u a t i o n of z e o l i t i c d i f f u s i o n s h o u l d be a p p l i c a b l e  2 X  kT h7~  e x p  '  AS  T~  6 X p  '  AH  _  RT'  (48),  '  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 are e s t i m a t e d f o r a p r o b a b i l i t y of 95%.  energies  55 k i s the Boltzmann c o n s t a n t , 1.380  x 10  e r g . m o l e c u l e ^ °K ^  -27 h i s the P l a n c k c o n s t a n t , 6.62 The a c t i v a t i o n e n t r o p y f o r d i f f u s i o n chalcocite  and 1.3  x 10  erg.  sec.  (AS) i s t h e n 1.9  e.u. for digenite,respectively.  e.u.  for  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 w h i c h 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  lattice.  56 CHAPTER 4. ELECTROLYTIC DISSOLUTION OF ROTATING DISKS OF COPPER SULPHIDES  A. 4.1  GENERALITIES ON ELECTRODE KINETICS  V a r i o u s t y p e s of  overvoltage  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  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  o t h e r v a r i a b l e s such as s t i r r i n g and t e m p e r a t u r e , must be i n o r d e r to determine the e l e c t r o d e  current  established  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 , w h i c h i s observed by means of c h e m i c a 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  of;the  overvoltage,  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 l o w s and E p o t e n t i a l i n the absence of c u r r e n t , i . e . , 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  o  is  the  the e q u i l i b r i u m p o t e n t i a l i f  there  electrode.  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 t y p e s of  overyoltage,  which, c o r r e s p o n d 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 B o n h o e f f e 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 charge-transfer  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  transport  57  of charge c a r r i e r s a c r o s s t h e e l e c t r i c a l double l a y e r e x i s t i n g a t the phase boundary i s h i n d e r e d . - 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 o f the p o t e n t i a l , the c u r r e n t f l o w produces a r e a c t i o n o v e r v o l t a g e ,  n . r  - D i f f u s i o n o v e r v o l t a g e , n , i s encountered D  when mass t r a n s p o r t  by d i f f u s i o n t o and from t h e e l e c t r o d e s u r f a c e i s r a t e - d e t e r m i n i n g : during current flow. - Hindrance  of the p r o c e s s by w h i c h atoms a r e i n c o r p o r a t e d i n t o o r  removed from t h e c r y s t a l l a t t i c e l e a d s t o 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 ,  The v a r i o u s o v e r v o l t a g e t y p e s have been a n a l y s e d 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 t h a t t h e c u r r e n t d e n s i t y v e r s u s relationship  has r e c e i v e d a g e n e r a l m a t h e m a t i c a l  overvoltage  expression i n several  cases. I f s e v e r a l o f 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 o r d e r of magnitude, the c o r r e s p o n d i n g o v e r v o l t a g e s a r e superimposed to Zovm the t o t a l o v e r v o l t a g e .  S i n c e the v a r i o u s o v e r v o l t a g e s a r e ,  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 o f 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  c h a r g e - t r a n s f e r components, w h i c h i s based on the requirement upon the d i s a p p e a r a n c e  o f a l l o v e r v o l t a g e t y p e s but one, the  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 o v e r v o l t a g e type (Appendix  2).  The  residual  remaining  components of the measured o v e r -  v o l t a g e can, t h e n , be s o r t e d out on the b a s i s o f the relationships  that  theoretical  obeyed by the v a r i o u s o v e r v o l t a g e t y p e s , p r o v i d e d o n l y  «  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  occurs.  The e x p e r i m e n t a 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 e x p e r i m e n t a l c o n d i t i o n s i n o r d e r to e l i m i n a t e o r 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 t h e s e 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  B. 4.2  conditions.  THE ROTATING DISK ELECTRODE TECHNIQUE  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  surface  The c a l c u l a t i o n of the maximum r a t e a t w h i c h a substance t r a n s p o r t e d towards o r from an e l e c t r o d e ,  J,.  , i s i n g e n e r a l an  lim i n t r a c t a b l e problem.  can be  °  T r a n s p o r t 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 . complex i f one of the s p e c i e s  The s i t u a t i o n i s s t i l l more  t a k e s p a r t i n a homogeneous  reaction  s i n c e the c h e m i c a l r e a c t i o n r a t e has to be t a k e n i n t o account i n the calculation. 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 r e g i m e , i s one of the few systems where the v e l o c i t y  distri-  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 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  (51).  at the s u r f a c e of a  rotating disk. U s i n g t h i s m o d e l , L e v i c h (51)  s o l v e d e x p l i c i t l y the  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 c o n s t a n t i n some c a s e s :  physical properties,  t r a n s p o r t of uncharged p a r t i c l e s ,  binary 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 s p e c i e s  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 ) .  steady-state  transport i n a i n the presence  of  'As the Schmidt number,  59  F i g u r e 14.  P a t t e r n of s t r e a m l i n e s a t the s u r f a c e of a r o t a t i n g d i s k (51).  60  Sc = jj  t  approaches  °°, L e v i c h ' s  0.620 D .  2 / 3  v "  1  /  s o l u t i o n takes  6  u,  1/2  the  form  (C,-C.)  J. - ±  (4.1)  where t i s the t r a n s p o r t number of s p e c i e s i i n a b i n a r y  electrolyte,  t = 0 f o r uncharged s p e c i e s or f o r a charged s p e c i e s i n the p r e s e n c e 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 k i n e m a t i c of the s o l u t i o n , to i s the a n g u l a r The  v e l o c i t y of the d i s k .  d i f f u s i o n boundary l a y e r i s d e f i n e d as a r e g i o n of r a p i d l y  changing c o n c e n t r a t i o n i n the immediate v i c i n i t y of the s u r f a c e , the t h i c k n e s s , 6,  6  and  viscosity  =  of which i s d e f i n e d  1 _ 1/3 "6T620 i  1/6  D  appears to be c o n s t a n t  electrode  as  -1/2  v  over the e n t i r e s u r f a c e of the d i s k .  from the d i f f u s i o n p o i n t of view, the r o t a t i n g d i s k e l e c t r o d e o f f e r s a uniformly The equation  Eq.  can be c a l c u l a t e d w i t h the Nernst  (4.1), i f 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 . a r e  known or i f the l i m i t i n g c u r r e n t d e n s i t y has The  sum  of e q u a t i o n The  of experimental (4.1)  s t u d i e s intended  been determined. to v e r i f y the  l e a v e s no doubt t h a t L e v i c h ' s  c o r r e c t i o n suggested by Gregory and  theory  R i d d i f o r d (53)  validity  i s correct  5000 i n aqueous s o l u t i o n s ) i s o n l y s i g n i f i c a n t i n the cases e x p e r i m e n t a l measurements (54)  (experimental  (52).  to take i n t o  account the f i n i t e v a l u e of the Schmidt number, Sc = -g-, (100  accurate  (R.D.E.)  accessible reaction site.  d i f f u s i o n overvoltage and  Thus,  < Sc. < of v e r y  error =  1%).  61 The assumption of c o n s t a n t  transport properties  a p p l i c a t i o n of e q u a t i o n (4.1)  (D,v) r e s t r i c t s  the  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  4.3  (54).  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  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 I n the absence of e l e c t r o d e o v e r v o l t a g e s ,  resistance  (55).  the c u r r e n t d i s t r i b u t i o n  i s c o m p l e t e l y determined by the ohmic drop i n s o l u t i o n .  A calculation  shows t h a t the p r i m a r y c u r r e n t d e n s i t y i s i n f i n i t e a t the edge of d i s k and h a l f of the average v a l u e a t the  center.  Newman a s s e s s e d the degree o f n o n - u n i f o r m i t y of the distribution,  the  current  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 ,  and e l e c t r o c h e m i c a l parameters of the s y s t e m .  against  the p h y s i c a l  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 C u S O . - 0 . 1 M H.SO. s o l u t i o n 2 4 4 (56) . 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 . 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  i f the ohmic  overvoltage.  Newman e s t a b l i s h e d , i n the case of the p r i m a r y 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 f o r m u l a to c a l c u l a t e the ohmic drop between the  electrode  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 , r  o  2a  from the c e n t e r I  tan  -l  r /  r  N  s  2  (57,58). 1/2  (4.2)  62  where a i s the c o n d u c t i v i t y of the b u l k s o l u t i o n ,  4.4.  Design of p r a c t i c a l R.D.E. R i d d i f o r d , i n h i s review o f the r o t a t i n g d i s k e l e c t r o d e  (52), d i s c u s s e d  the d e s i g n of a p r a c t i c a l e l e c t r o d e which conforms as  c l o s e l y as p o s s i b l e to the t h e o r e t i c a l  requirements.  A d i s k of f i n i t e r a d i u s w i l l meet the l i q u i d f l o w provided  technique  the r a d i u s , r , i s v e r y much g r e a t e r than the Q  requirements thickness:of  the momentum boundary l a y e r , i . e . ,  f ^ > r  o  and p r o v i d e d  1  /  =0,  2  oi  the Reynolds number, Re = r ^  v a l u e f o r the onset  of t u r b u l e n c e .  —,  i s l e s s than the  Experimental  s t u d i e s of  critical  the  c r i t i c a l Re number at a r o t a t i n g d i s k i n d i c a t e t h a t 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 disk.  On  v  the o t h e r hand, the r o t a t i o n a l speed of the d i s k must be •  l a r g e enough to exclude  any  s i g n i f i c a n t c o n t r i b u t i o n from n a t u r a l  convection. The  shape and  c a r e f u l l y designed  dimensions of an e l e c t r o d e of f i n i t e span must and  be  checked to i n t r o d u c e no d i s t u r b i n g edge e f f e c t .  In t h a t r e s p e c t , the b e s t d e s i g n i s a c o n i c a l e l e c t r o d e , the base of which i s a c t i v e f o r 0 < r < r , the r e g i o n r Q  Q  to r ^ b e i n g  inactive.  R i d d i f o r d p o i n t e d out t h a t c y l i n d r i c a l e l e c t r o d e s should be s i n c e i t was was  shown e x p e r i m e n t a l l y  t h a t , i n t h i s case,  t u r b u l e n t even f o r v e r y s m a l l Re  numbers.  avoided,  the f l u i d  flow  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 s y s t e m .  The l i q u i d - g a s b o u n d a r y , 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 , capillary, etc.  the L u g g i n  s h o u l d n o t 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 b e a k e r s of  different  s i z e s , checked t h a t t h i s r e q u i r e m e n t 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 t h a n 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 c e n t e r of the d i s k a l o n g 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 p l a n e of the d i s k (y = 0 ) . not i n t e r a c t  in this  Flows i n the upper and lower p a r t do  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  (eccentri-  c i t y o f 0.025 mm i s quoted by a number of w o r k e r s ) and smooth t o  the  e x t e n t t h a t 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 of m o d e r a t e l y f a s t e l e c t r o d e  A  i n l i q u i d s and t o s t u d y the k i n e t i c s  processes.  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 investigated,  at 55°C, i n a c i d i f i e d copper s u l p h a t e s o l u t i o n ( 0 . 1 M  CuSO^, 0 . 1 M ^ S O ^ )  4.5  by a g a l v a n o s t a t i c  method.  Experimental The r o t a t i n g d i s k e l e c t r o d e  s h a f t was of a c e t a l p l a s t i c  i s shown on F i g u r e 15.  (0.62  cm i n d i a m e t e r ) .  The h o l l o w  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 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  of  cm i n  diameter. E l e c t r i c a l c o n n e c t i o n s were made t h r o u g h mercury c o n t a i n e d i n the h o l l o w s h a f t and s e p a r a t e d  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  contact  s h o u l d 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 s t a i n l e s s  steel  the m e c h a n i c a l arrangement  of the s h a f t  c e l l head.  F i g u r e 17 and 18 show the arrangement p o r c e l a i n diaphragm s e p a r a t e d from the c a t h o d i c compartment.  of the c e l l .  the a n o d i c compartement,  A porous i n the  center,  A two-compartment c e l l was, i n d e e d ,  n e c e s s a r y 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 s u l p h i d e s and were r e g e n e r a t e d solution.  copper  by m e t a l l i c copper immersed i n the same  As a m a t t e r 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 t r a n s f o r m e d i n t o c h a l c o c i t e , 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.  i n a few d a y s , i n c u p r i c s u l p h a  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 , w h i c h 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 i n the  in  electrolyte.  conductivity  65  Plastic  shaft.  Acrylic  cone.  Platinum  Copper  sulphide. 2!l  F i g u r e 15.  foil.  approximately.  D e s i g n of the. r o t a t i n g d i s k  electrode.  I ." I approx. F i g u r e 16.  D e s i g n of the s t a i n l e s s s t e e l head.  67  n F i g u r e 17.  Electrolytic  cell.  approximately.  Figure  18.  Electrolytic cell  arrangement.  69  F i g u r e 19.  Experimental  apparatus.  70 The a r e a of the copper r i n g cathode was 80 t i m e s l a r g e r than t h a t of the a c t i v e s u r f a c e of the anode. The i n s t r u m e n t s a s s o c i a t e d w i t h the p r e s e n t experiment a r e shown on F i g u r e 19.  I n c l u d e d 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 . o f the e l e c t r o d e w i t h i n 1.5% o f the s e t v a l u e , an E l e c t r o s c a n , Beckman Model 30, as a c o n s t a n t c u r r e n t s o u r c e ,  a  K e i t h l e y Model 153 m i c r o v o l t a m m e t e r m e a s u r i n g the c u r r e n t to +2% of scale,  full  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 m e a s u r i n g  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 t o 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 w a t e r b a t h . Experiments were done i n a h e l i u m atmosphere w i t h d e a e r a t e d 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 t o a s a t u r a t e d c a l o m e l e l e c t r o d e a t  25°C.  The a n g u l a r v e l o c i t y of the d i s k was s e t a t 250 r . p . m . y i e l d i n g  at  the edge of the d i s k a Reynolds number of  R  e  = r  2  - = 6.25 x  10  3  v  w h i c h was c h a r a c t e r i s t i c of a l a m i n a r f l o w regime f o r t h a t k i n d o f g e o m e t r i c 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 a t 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 t o the method o f  71  Bacon and F a n e l l i (31), i n the molar r a t i o , 1.78:1. C o v e l l i t e was  synthesized at 450°C i n an evacuated quartz tube  from 0.99999 pure copper i n the presence of an excess of p u r i f i e d sulphur.  A temperature gradient prevailing along the reaction tube  prevented  the sulphur from condensing on the c o v e l l i t e during the  cooling period. The copper sulphides were ground under helium i n an alumina b a l l m i l l and then cold-pressed under vacuum into disks (1.3 cm i n diameter, approximately  2 mm  thick) i n a Perkin Elmer evacuable die.  The digenite  -2 disks, compacted under a pressure of theoretical density.  8100 kg cm  , had 93% of their  The c o v e l l i t e disks, shaped under a pressure of  -2 2700 kg cm  , were sintered i n the presence of sulphur vapour; t h e i r  f i n a l density was  86% of the theoretical value.  The electrodes were l i g h t l y polished.  The t o t a l i n t e r n a l resistance  of each electrode was measured with a Keithley, model 503, and found to be approximately  0.1 n  milliohmeter  for digenite and 0.05  J2. for  c o v e l l i t e electrodes. 4.6 4.6.1  P o l a r i z a t i o n of digenite anodes  ,  Results  ,  Digenite anodes were studied at 55°C by a galvanostatic p o l a r i z a -2 tion method using current densities between 7.5 and 75 mA  cm  .  The  information obtained by t h i s study i s summed up i n Table 5. A t y p i c a l potential-time curve i s shown on Figure 20.  These curves  were characterized by a region i n which the p o t e n t i a l slowly rose as a function of time, ending i n a p o t e n t i a l discontinuity i n a t r a n s i t i o n  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. I . -2 mA cm  E  ( 2 5 ° C ) / 0 . 1 M C u S O . - O . l M H S 0 . <KCu., „S 4 2. 4 l . o o  E. l  ^fi , s o l . mV  o mV  mV  3.77  248  280  21  7.5  236  298  42  11.3  245  355  64  15.1  237  350  85  18.8  245  405  18.8  244  37.7  V e l . mV  -  E  mV  -  s mV  E  T  mV  E -E. T  T  1  sec  mV  259  1.1  255  760  462  124,800  1.5  1.6  288  725  370  39,060  1.5  2.1  261  515  165  10,950  104  2  2.5  296. 5  575  170  8,670  409  106  2  2.5  298. 5  604  195  7,500  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  a r e 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  fi,sol.  rifi  e  ,  i s t h e 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 )  ^  i s t h e ohmic drop i n s i d e t h e e l e c t r o d e  rip i s t h e 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 boundary l a y e r (Appendix 4) S  X  fi;sol.  ft,el.  D  electrode  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 r e c o r d e d d u r i n g the galvanos 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.(25°C) | 0 1 M CuSO.-0.1 M H S0, Cu 4 2 4 1.78' o  74  time T , beyond w h i c h 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 reproducible. The f i r s t p a r t of the c u r v e up to the t r a n s i t i o n time ponded to the o v e r a l l e l e c t r o d e  Cu. , S 1, lo 0  •  CuS  corres-  reaction  +  0.78  Cu "*"  +  4  1.56  e,  (4.3)  w h i c h was found i n a p r e v i o u s s t u d y (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 .  I n 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 e p a r a t e d from the s u r f a c e of a s p e c i m e n .  solid  No v a r i a t i o n of the copper  c o n t e n t of the s o l u t i o n c o u l d be d e t e c t e d a f t e r 35 h o u r s of  electrolysis  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  reaction  consisting  p r o b a b l y of oxygen d i s c h a r g e and s u l p h u r f o r m a t i o n and p o s s i b l y s u l p h a t e formation  (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 b e i n g c o m p l e t e l y t r a n s f o r m e d 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 n o t c a p a b l e of m a i n -  t a i n i n g a constant  rate.  As the r e a c t i o n p r o c e e d e d , the c o v e l l i t e -  digenite interface  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  s h o u l d d i f f u s e through the CuS l a y e r to e n t e r the  electrolyte.  I t was observed e x p e r i m e n t a l l y t h a t 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 time ( F i g u r e 21)  _2 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 ) .  Figure 21.  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 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 5 5 ° C . ( A were e s t i m a t e d from Kuxman's r e s u l t s by the a u t h o r ) .  76  = 2.5  I^T  A^cm^sec  (4.4)  1  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 , provided 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 t h r o u g h the e l e c t r o d e d u r i n g the time c o n s i d e r e d  2  =  (  M  f D  irMf  }  =  1  *  81  x  1 0  4 l T )  ( 4  -  5 )  25.4  where  n no  =  I  s  a c t u a l molar volume of the i n i t i a l  t n e  digenite  phase. G i v e n the I - x dependence,  the d i s s o l u t i o n c o n s t a n t 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  —  The d i s s o l u t i o n c o n s t a n t d e s c r i b e s  4  .  6  the s t e a d y - s t a t e t r a n s p o r t of  i o n s a c r o s s 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 -9 oxidation,  k^ = 2.35 x 10  -1 mole cm  copper  digenite  -1 sec  i n the p r e s e n t e x p e r i m e n t a l  c o n d i t i o n s (T = 5 5 ° C , 0.1 M CuSO^-0.1 M H S 0 2  4.6.2  )  4  solution, d  D  = 0.93  d  fch  )  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 t h r o u g h the covellite  layer  The c o v e l l i t e l a y e r was p o r o u s ; as a m a t t e r of f a c t , the m o l a r 3  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  -1  ^respectively  ( 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 d e v e l o p s 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 t h r o u g h 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 l o n g g r a i n s o r 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  a.  pores.  Solid state d i f f u s i o n I n 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 t h r o u g h CuS  is  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  valid  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 o r cuprous i o n s ) ,  Ay J  Cu  -IT  cu = - c u M  When the t r a n s i t i o n o c c u r s ,  •  '  (4  the d i f f e r e n c e of copper  7)  electrochemical  p o t e n t i a l a c r o s s the CuS l a y e r ( A u ) , w h i c h can be e x p r e s s e d i n terms r  of e l e c t r o d e p o t e n t i a l s l i m i t s o f CuS. the s t a b l e ,  It  (2FAE = - A u ), r  c o r r e s p o n d s to the  stability  can be c a l c u l a t e d from the thermodynamic d a t a on  s t o i c h i o m e t r i c CuS t h a t AE i s e q u a l to a p p r o x i m a t e l y 75 mV  a t 55°C (Chapter 2 ) .  D u r i n g 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 If  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 f o r m e d , the  p o t e n t i a l d i f f e r e n c e measured m i g h t be a v a i l a b l e t o d r i v e the state d i f f u s i o n process.  The Onsager c o e f f i c i e n t ,  5). entire  solid  capable  of  a c c o u n t i n g f o r the e x p e r i m e n t a l r e s u l t s can be c a l c u l a t e d from e q u a t i o n s 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 t a k e s i n t o account the p o r o s i t y of the layer:  initially,  covellite  the d i g e n i t e had 7% of p o r o s i t y , and the  t i o n developed an e x t r a 19.7% of p o r o s i t y .  transforma-  The i o n i c c o n d u c t i v i t y ,  w h i c h i s r e l a t e d t o 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 -4 - 1 -1  are  the d i f f u s i n g - s p e c i e s and 8 x 10 diffusing species.  Q  cm  i f the cuprous i o n s are  T h i s l a t t e r v a l u e i s 23 and 11 times l a r g e r  the  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 t h e s e 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 t h e r e i s no e v i d e n c e f o r t h i s i n CuS, i t appears r e a s o n a b l e  to c o n s i d e r t h a t the s o l i d  state  d i f f u s i o n t h r o u g h c o v e l l i t e i s n o t a b l e to account f o r the o b s e r v e d 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 If  the  pores  the aqueous e l e c t r o l y t e o c c u p i e s 19.7% o r more (owing t o the,  i n i t i a l p o r o s i t y ) of the c r o s s 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 t h a t i n v a d e s the pores as they f o r m .  electrolyte  E v e n t u a l l y , the pores get so deep  t h a t the c o n c e n t r a t i o n g r a d i e n t s n e c e s s a r y  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 l e a d s 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 . t h i s s t a g e , the r e a c t i o n  (4.3)  At  c l o g s 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 .  Part  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 d o u b l e l a y e r and other electrode 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 p r o d u c t 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 , w h i c h 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 . It  s h o u l d f i r s t be n o t e d t h a t the a c c u m u l a t i o n r a t e of copper i n  the p o r e s , A , r e p r e s e n t s f l u x , JS.  A can be approximated by  "  A  where  _  C  face.  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  C u  C  Cu  f S  of •  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  At the -maximum,  = 2.2 M , w h i c h c o r r e s p o n d s to the  inter-  saturation  i n C u S 0 ' 5 H 0 a t 55°C C 6 0 ) , 4  2  - fS i s the a c t u a l c r o s s s e c t i o n of pores fS < 0.2 dx -  1 =  S,  M  Q yg ^ D  J  '  t  *  i e  i n t e r  f  a c e  velocity.  The a c c u m u l a t i o n r a t e of copper i n the pores was c a l c u l a t e d to r e m a i n lower than 1.4% of the t o t a l copper  flux.  Cupric sulphate d i s s o l v e d i n water i s only 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 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 c o n s t a n t was e s t i m a t e d to be 125  C61).  the  stability  On the b a s i s of t h i s v a l u e ,  can be c a l c u l a t e d t h a t a p p r o x i m a t e l y 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 a t ambient t e m p e r a t u r e . v a l u e i s approximate s i n c e a more a c c u r a t e e s t i m a t i o n r e q u i r e s  This the  it  80 appropriate a c t i v i t y coefficients  to be t a k e n i n t o a c c o u n t .  However  i t i s apparent t h a t a r e l a t i v e l y i m p o r t a n t f r a c t i o n o f 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 .  F u r t h e r m o r e , the  diffusivity  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  t e c h n i q u e 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  R.D.E.  account  d i f f u s i o n of b o t h c u p r i c i o n s and n e u t r a l complex. If  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 e q u a t i o n s can be w r i t t e n ( c o n v e c t i o n term i s negligible )  3C,  JL = - D- — 1 1 3x 9C J  2 = -  j J  3  D  2 ^ T 9C  = - n U  3  9  x  -  -  + +  2  f  D  —  D  U  3  RT  C  S  2 C  "t  C4.9)  9x  a l o n g 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 + J„ = —  the f l o w r e q u i r e m e n t s T J  *  =  l  **  - T  "3  dx C o n v e c t i o n 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 % of the t o t a l f l u x J S . -<1  J r e p r e s e n t s the apparent f l o w normal to the g e o m e t r i c e l e c t r o d e area. 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 t h a t o n l y a f r a c t i o n of the c r o s s s e c t i o n , o c c u p i e d 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 c o p p e r .  81 2 and the c h e m i c a l e q u i l i b r i u m statement I t f o l l o w s a f t e r rearrangement of t h e s e D  T  ? = -  ( D  i  +  D  9C  i ^ * r - * > i  = KC . equations 2  9C  jr>  ( 4  I n t e g r a t i o n of E q . (4.10) o v e r the t h i c k n e s s of the c o v e l l i t e  -  1 0 )  layer  yields  2 + D ^ C C j - C ) + 2D . ( C D  I £ = f 2F  [(D  1  x  1  2  2  - C^],  At t h e 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 a c h i e v e d 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 c o n s t a n t f o l l o w s from E q .  2 I T  4.6.3.  =  and i t  (4.5)  est.  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  taking place before  the  transition 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 If  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  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  the  (E - E ^ )  cracks 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 c u r v e (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 t o 187 mV ( I > 15 mA cm~ ) .  The  e x p e r i m e n t a l v a l u e s l i e i n a band between 152 and 239 mV (Table 5) and  82 seem t o be randomly d i s t r i b u t e d w i t h r e s p e c t t o measured t r a n s i t i o n t i m e , around t h e mean v a l u e s s t a t e d by e q u a t i o n  (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 t h e N e r n s t equation  n  D  =  RT 2F  a  Cu  + +  s a t d  '  C u S 0  4 soln.)  - In a  C u + +  ( i n 0 . 1 M CuSO^, 0.1 M H S 0 ) ] . 2  4  The a c t i v i t y of t h e 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 s e t e q u a l t o t h e square r o o t o f t h e a c t i v i t y of t h e 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 l y t e .  The l a t t e r  AF° i s e q u a l to e x p . (- —=r~ ) where RT  AF° i s t h e s t a n d a r d f r e e e n t h a l p y o f s o l u t i o n o f copper s u l p h a t e according to the equation  CuS0 -5H 0(s) 4  • Cu"* " + S 0 ~ ~ 4  2  4  +  5H 0 2  AF° = 1350 + 9 . 3 T ( 2 ) .  However, e x p e r i m e n t a l d a t a on the s a t u r a t e d copper s u l p h a t e are a v a i l a b l e (0.296 < E  q  < 0.317 V a t 25°C)  (32).  The average v a l u e  of 0.306 V i s r e t a i n e d a l o n g w i t h t h e e x p e r i m e n t a l t h e r m a l coefficient  of 0.93 mV ° C  _ 1  C32).  electrode  temperature  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 a t 55°C w i t h r e s p e c t t o t h e s t a n d a r d 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 e s t i m a t e d to amount t o a p p r o x i m a t e l y 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 s h o u l d then be a b l e account f o r the r e m a i n i n g 165 mV. the case of a weak e l e c t r o l y t e ,  to  I t i s shown i n Appendix 3 t h a t ,  in  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 c o n s t a n t 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.  Interface  overvoltage  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 , w h i c h s h o u l d 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 a p p r o x i m a t e l y 2.5 sec)  after  the c u r r e n t i s s w i t c h e d o n , b e f o r e the i n t e r f a c e b e g i n s 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 c o m p o s i t i o n at the s u r f a c e has been  c a l c u l a t e d to r e a c h the v a l u e Cu, -,,,-S i n 1.25 1.765 -2  10  -3  sec a t a c u r r e n t  d e n s i t y of 10 mA cm  .  potentials  o b t a i n e d by e x t r a p o l a t i n g to zero time a  (E^)  are  I n 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  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 c u r v e ( 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 w h i c h can be c a l c u l a t e d w i t h the h e l p 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  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 .  overThe  d i f f u s i o n o v e r v o l t a g e was e s t i m a t e d w i t h the N e r n s t e q u a t i o n and E q . ( 4 . 1 ) , u s i n g the p h y s i c a l parameters measured by Newman e t a l . i n 0 . 1 M CuSO^-0.1 M ^ S O ^ s o l u t i o n ,  (Appendix  4).  (62)  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 n o t impede c o v e l l i t e f o r m a t i o n  84 -2 8.5 mV a t 75 mA cm ; a t l o w e r 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  p o t e n t i a l , E , v e r s u s S . C . E . (25°C) i s p l o t t e d a g a i n s t of the c u r r e n t d e n s i t y on f i g u r e  interface  the l o g a r i t h m  22.  For s m a l l c u r r e n t d e n s i t i e s , t h e e l e c t r o d e  retains a potential  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 a t 55°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 d a t a  i n the higher current d e n s i t y range. presupposes t h a t a c h a r g e - t r a n s f e r  Such a T a f e l r e l a t i o n s h i p  p r o c e s s 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 d a t a does not p e r m i t e x c l u s i o n of a mechanism i n w h i c h 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 p r o c e s s i s d i f f u s i o n l e s s s t r u c t u r a l change o f s u l p h u r a n i o n s from the form of d i g e n i t e to t h a t of c o v e l l i t e  4.7  P o l a r i z a t i o n of c o v e l l i t e  4.7.1. a.  the  lattice  (12).  anodes  Results  Electrode potential  measurements  C o v e l l i t e anodes were s t u d i e d a t 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  .  This  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  electrode  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 o b t a i n e d d u r i n g these  experiments are r e p o r t e d i n T a b l e  6.  The p o t e n t i a l - t i m e c u r v e s o b t a i n e d 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 c u r v e  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 a t 55°C. S . C . E . (25°C) I 0.1 M CuSO., 0.1 M H.SO. I Cu, .,-S. 4 2 4 1.78 1  1  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 S.C.E.  I  anodes  (25°C)/0.1 M CuS0 -0.1 M H S0 /CuS 4  E  2  4  o mV  mV  E . mm 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  1.51  302  802  1.88  338  774  612  1.526  2.26  338  808  654  1.568  E Q = 0 current  potential  . -2 mA cm  E  N  E  E  s mV  f  mV  615 1.532  E ^ = maximum of p o t e n t i a l o b t a i n e d s h o r t l y a f t e r t h e c u r r e n t i s  switched  on. E  min  =  t  *  i e  Fig.  m  i- l n  m u m  ° f p o t e n t i a l measured d u r i n g the experiment  (see  24).  EG  = steady-state potential.  E^  = f i n a l v a l u e of the p o t e n t i a l r e c o r d e d a f t e r 6 days of  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 curve found f o r - h i g h e r c u r r e n t s  electrolysis.  _2 (< 1 mA cm ) w h i l e F i g u r e 24 shows a _2 (> 2 mA cm  ).  I n b o t h c a s e s , t h e r e was  a g r a d u a 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 . the case of the lower c u r r e n t d e n s i t i e s ,  i t gradually levelled off  In at  t F i g u r e 23.  (hr.)  P o t e n t i a l - t i m e curve r e c o r d e d d u r i n g the g a l v a n o s t a t i c 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  o x i d a t i o n of a c o v e l l i t e  l  1  1  1  1  1  1  r  89  a s t e a d y 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 , u n d e r g o i n g a d i s c o n t i n u i t y r o s e a b r u p t l y to a v e r y h i g h value.  I n the l a t t e r  c a s e , 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  electrodes  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 e l e c t r o d e p o t e n t i a l v e r s u s S . C . E . (25°C) on F i g u r e 25. drawn i n s o l i d l i n e r e p r e s e n t  the  covellite  The two c u r v e s  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 e x t e n d i n g the f i r s t toward the h i g h e r c u r r e n t d e n s i t i e s r e p r e s e n t s 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 .  It  curve  the minimum p o t e n t i a l appears on t h a t graph  _2 t h a t c u r r e n t d e n s i t i e s h i g h e r than 1.35 mA cm  cause a change o f  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  potential.  the  The d o t t e d l i n e j o i n i n g the two c u r v e s p i c t u r e s the b e h a v i o u r of -2 c o v e l l i t e electrode  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  increased very slowly  d u r i n g p r o l o n g e d p e r i o d of time (1 w e e k ) , e v e n t u a l l y l e a d i n g to  the  f i n a l v a l u e r e p o r t e d on the d o t t e d l i n e . b.  Electrode  reactions  To a s s e s s 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 c o r r e s p o n d i n g to the two p o t e n t i a l r e g i o n s , c h e m i c a l a n a l y s i s was c a r r i e d out on the  reaction  products. An experiment conducted f o r s i x days i n a 0.01 M C u S O , - 0 . 0 1 M H„S0. 4  -2 s o l u t i o n a t 0.75 mA cm content  r e v e a l e d no v a r i a t i o n of the average  i n the e l e c t r o l y t e s ,  2 copper  i n d i c a t i n g t h a t the anode and cathode  4  I  (mA.crrf ) 2  2 -  P o l a r i z a t i o n curve o b t a i n e d 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. M H„ .-SO, s o l u t i o n ) ( • c o r r e s p o n d s to 0.01 M CuSO-0.01 4 2 4 1  o  91 r e a c t i o n s were of e q u a l c u r r e n t e f f i c i e n c y , a p p r o x i m a t e l y 100% . s i m i l a r experiment performed at 2.26 mA cm the e l e c t r o l y t e s  d e p l e t e d the copper i n  to an e x t e n t t h a t would i n d i c a t e an average  e f f i c i e n c y of 39% f o r the a n o d i c p r o c e s s .  A  current  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 p r e v e n t e d any r e a s o n a b l e q u a n t i t y of S0^  d e t e r m i n a t i o n of the H  +  c o n t e n t of the s o l u t i o n .  The  , 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  detected. B o t h c o v e l l i t e and o r t h o r h o m b i c 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 s t u d y of s u r f a c e  residues.  On the b a s i s of t h e s e i n v e s t i g a t i o n s , the c o v e l l i t e a n o d i c r e a c t i o n at l o w e r p o t e n t i a l s conforms  CuS  *  Cu" " + 1  to:  S°  +  2e  C4.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 b e h i n d 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 t h e r e i s a 24% s h r i n k a g e 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 mole " ^ r e s p e c t i v e l y  ( 5 9 ) ) , thus the e l e m e n t a l s u l p h u r i s  w i t h c r a c k s and pores t h a t p e r m i t the e l e c t r o l y t e  and 15.5 cm associated  to r e t a i n a c c e s s to  the i n t e r f a c e between c o v e l l i t e and e l e m e n t a l s u l p h u r .  Cupric ions  are  No b u b b l i n g was ever d e t e c t e d a t the Cu cathode a t 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 a t 25°C i n f r e e c o n v e c t i o n c o n d i t i o n s ( 5 1 ) , a v a l u e w h i c h was never approached i n these e x p e r i m e n t s . - 2  A*  The t o t a l d i s s o l u t i o n of 1 g CuS specimen, l e a d s to o n l y 10 of s u l p h u r s p e c i e s i n a p p r o x i m a t e l y 1 I of s o l u t i o n .  _2  mole  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 .  T h u s , as i n the d i g e n i t e c a s e , 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 l o n g e r s u p p o r t 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 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  c.  M i c r o s c o p i c e x a m i n a t i o n of the r e a c t e d  the  i n v o l v i n g much  density.  electrode  An e x a m i n a t i o n 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 t h a 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 cohesion.  The s u r f a c e of the d i s k p r e s e n t e d u n r e a c t e d p a r t i c l e s  c o v e l l i t e suspended i n s u l p h u r as seen on the m i c r o g r a p h ( F i g .  of 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 d e e p l y i n t o the specimen and i n f a c t g o i n g t h r o u g h 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 may r e p r e s e n t  s h r i n k a g e pores and c r a c k s  ( F i g . 28).  that  Micrographs taken  w i t h the s c a n n i n g e l e c t r o n m i c r o s c o p e show the h i g h r e l i e f  surface .  ( F i g . 29 and 3 0 ) . An e x a m i n a t i o n 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 m i c r o p r o b e was v e r y i n c o n c l u s i v e  (Fig. 31,32,33).  Even v e r y l i g h t p o l i s h i n g ;  t o r e 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 , d e p r e s s i o n s and c o v e l l i t e h i l l s ;  leaving sulphur  the m i c r o p r o b e r e a d i n g s r e f l e c t e d  topography of the h i l l y s u r f a c e more than the c o m p o s i t i o n of the  4.7.2  the  phases.  Discussion 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 , o r s o , of c u r r e n t f l o w (see F i g . 23,24) are most  Figure  26.  Micrograph of disk  Figure  27.  Micrograph of disk,  the  (unreacted  surface  covellite  a section  perpendicular  to  of the  of  an o x i d i z e d  appears  an o x i d i z e d surface.  covellite  white).  covellite  F i g u r e 28.  F i g u r e 29.  O p t i c a l m i c r o g r a p h of an o x i d i z e d c o v e l l i t e  Scanning e l e c t r o n m i c r o g r a p h of an oxidized covellite disk.  disk.  g u r e 30. Scanning m i c r o g r a p h o f an covellite disk.  electron oxidized  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 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 t h a t the  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 interface  overvoltage.  decline  i n the c o v e l l i t e - s u l p h u r  a r e a , w h i c h d e c r e a s e s the e f f e c t i v e  and the a s s o c i a t e d  orthorhombic  l o c a l current  density  I n a r e a c t e d d i s k , the i n t e r f a c e  area  between u n r e a c t e d c o v e l l i t e and the s u l p h u r p r o d u c t i s v e r y l a r g e compared w i t h the exposed g e o m e t r i c s u r f a c e a r e a of the specimen as. i t appears on the v a r i o u s m i c r o g r a p h s . 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) current  could, in fact, reflect  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  density.  The appearance  of a new e l e c t r o d e  reaction  ( p r o b a b l y oxygen _2  evolution) for current densities  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 o f 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 a r e a and i t s v a r i a t i o n w i t h time are  completely  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 meters,  i s l i k e l y to depend upon a number of p a r a -  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 b e i n g p r o b a b l y 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 , . . . ) . t i o n curve ( F i g . 25)  The e x p e r i m e n t a l p o l a r i z a -  s h o u l d , however, be a b l e 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 b e h a v i o u r 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 .  98  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  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)  disk  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 a t the d i g e n i t e - c o v e l l i t e  interface  seems to p r e s e n t 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 p o r t of the copper i o n s r e l e a s e d porous c o v e l l i t e l a y e r ;  to be c o n t r o l l e d by the  by the r e a c t i o n  the main t r a n s p o r t  (4.3)  trans-  through the  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 s h r i n k a g e pores o f the  covellite.  - A f t e r n u c l e a t i o n of e l e m e n t a 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 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  (4.11)  at  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 c r a c k s 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  peculiar  the c o v e l l i t e anode e x c l u d e s ,  so f a r ,  way i n w h i c h the s u l p h u r grows i n any d i s e u s s i o n of the  relative  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 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  of  reactions.  I n the f o l l o w i n g d i s c u s s i o n , a m o d e l , w h i c h i s d e r i v e d from the p r e s e n t work and from Kuxmann and a l . ' s 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  experimental observations d i s s o l u t i o n of  These models w i l l then be used t o t r y to account  (15),  chalcocite.  f o r the  l e a c h i n g b e h a v i o u r 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  actual solutions.  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 : Kuxmann and B i a l l a s s  of c h a l c o c i t e  (15)  constant  current o x i d a t i o n  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  anodes i n c u p r i c s u l p h a t e s o l u t i o n s , w i t h  current  -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 a b r u p t 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 t h a t encountered i n the study of d i g e n i t e anodes.  The copper c o n t e n t of the  electrolyte  remained unchanged up to the t r a n s i t i o n , then i t decreased with time.  present  linearly  C o v e l l i t e (and s u l p h u r i n some c a s e s ) 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  electrode.  The t r a n s i t i o n times observed a t 55°C i n t h a t work were b a c k c a l c u l a t e d from t h e graphs r e p o r t e d i n the paper  - certainly, with 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 p r e s e n t d a t a i n F i g u r e 21. The t r a n s i t i o n times measured i n b o t h works appear to be 2  T=cst.  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 In contrast that,  to the p r e s e n t  r e s u l t s , Kuxmann and B i a l l a s s  observed  b e f o r e the t r a n s i t i o n , the anode p o t e n t i a l remained a p p r o x i m a t e l y  constant.  T h i s o b s e r v a t i o n s h o u l d 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 i o n s t h r o u g h the s o l i d c o v e l l i t e . the o t h e r h a n d , 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  On 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 s h o u l d remain v e r y s m a l l i n t h i s case s i n c e t h e r e was an excess of s u l p h u r i c a c i d i n the electrolyte  (30 g/1 CuS0 ~250 g/1 R^SO^). 4  5 N H_2^4 s o l u t i o n i s 0.673 9 ^cm c o n d u c t i v i t y of -0.051 n the same temperature  - 1  cm  (64).  _ 1  1  The  a t 25°C (63)  c o n d u c t i v i t y of a as compared to a  f o r 0.1 M CUSO^-0.1 M H^SO^ s o l u t i o n a t  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 c o r r e s p o n d i n g  100  to the s a t u r a t i o n o f 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 p r o d u c t I T can be s u p p o r t e d by the same arguments t h a t were proposed f o r the d i g e n i t e c a s e (4.6.2) i . e . , 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  w i t h 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 f a c e moving at a c o n s t a n t electrolyte,  rate.  the e f f e c t of the e l e c t r i c  electrolyte  and r e a c t i o n  I n the case of an excess of  the d i f f u s i o n e q u a t i o n s  transition  inter-  indifferent  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  f i e l d can be n e g l e c t e d ,  and i n the a g g r e g a t e ,  the f l u x of copper can be d e s c r i b e d by 3 C  J  Cu  =  _ D  Cu  where f i s the e f f e c t i v e pores.  (If  Cu  ~3lT  f  f r a c t i o n of the c r o s s s e c t i o n o c c u p i e d by  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).  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  It layer  that  U  where D  = 2F D f Cu p  (C_ ^ Cu,sat.  C„ ) , Cu  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  concentra-  2 tions considered.  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  inconstant  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 p h a s e s . a l o n g 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 and t h a t  Kuxmann's r e s u l t s ,  reactions  are r e l a t i v e l y non r e s i s t i v e ,  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 t h r o u g h t h e 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 at constant consists  c u r r e n t can be a n a l y s e d t h e o r e t i c a l l y :  chalcocite  t h e problem  i n c a l c u l a t i n g the thickness of the v a r i o u s s u l p h i d e l a y e r s  with respect to time,  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 t h e 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  current 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 t h e chalcocite.  T h i s assumption i s based on t h e f a c t s t h a t t h e c o m p o s i t i o n  and p h y s i c a l p r o p e r t i e s of the two phases a r e v e r y s i m i l a r .  On t h e  o t h e r h a n d , the s t a n d a r d 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 c a s t o r mineral chalcocite  (15,28,29) are very close to the standard 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 t h e measurements r e p o r t e d i n Chapter 2 (E  = 503 mV a t 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, -, S w h i l e t h e secondary e f f e c t s due i t s s t o i c h i o 0  1. / o  metry range a r e n e g l e c t e d . If  the o r i g i n o f times i s taken when t h e a n o d i c c u r r e n t i s  a p p l i e d , a l a y e r o f d i g e n i t e s t a r t s t o form a t t = 0 , and i t s t h i c k n e s s i s g i v e n a t t i m e , t , by t h e r e l a t i o n s h i p x^ = J t  a  Cu.S z  which t r a n s l a t e s  ,Ms _1 M C h 0.22  l  ;  ->  Cu, -, S + 0.22Cu" " + 0.44e 1. lo 0  H  a s i m p l e m a t e r i a l b a l a n c e between t h e f l u x of c o p p e r ,  J , and the amount of c h a l c o c i t e  reacted.  102  Cu S 2  1.8  01  CuS  S  J  Solution  2  Jg* J const. B  x x  Steady  state :  Constant current  l  Xj - x  2  = constant  multilayer  Figure  2  34  growth model.  103  The mechanism of t r a n s p o r t of copper i o n s t h r o u g h the  digenite  l a y e r i s s u b j e c t to a d i s c u s s i o n s i m i l a r to t h a t conducted i n section  (4.6.2) for 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  d i g e n i t e , w i t h o u t volume change, digenite layer.  into  i n t r o d u c e s 7% of p o r o s i t y i n the  No d a t a are a v a i l a b l e to a s s e s s the e f f e c t of  this  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 .  Covellite  forms when the e l e c t r o d e  the  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  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 electrode  o r 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  cupric salt  i s reached.  section  the pores w i t h a  At the onset of growth of c o v e l l i t e  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 by (see  digenite-covellite  (x^)  (t =  t^),  i s given, i n b o t h cases, a  4.6.2) D — , k  J -  x  D  = Ja  t ,  (5.1)  D  ±  where k^ i s the c o n s t a n t of d i s s o l u t i o n t h r o u g h d i g e n i t e . The s i m u l t a n e o u s 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 o r d e r d i f f e r e n t i a l e q u a t i o n s w h i c h 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  flux,  S —> CuS + Cu. 1.78  -H0.78Cu +  where x^ i s the t o t a l t h i c k n e s s o f the r e a c t i o n p r o d u c t s , x^ i s 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  1.56e  the  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  ^  dt  dx„ 1  • -  IT  +  d(x - x )  J a  2  ( 5  1  dt  x  ^  1  l" 2  -  (5.3)  J c t  x  2  w h i c h 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  l  x  n  X  + a  X  l  2 a  r 2~ D Ja X  2 )  k-.(a.+OLr.) =  x  '  X  =  2 k  5),  J(t-t_)  (5.4)  D  D  2  ( a  J  2  l  2 2  + a  a  I t appears i n e q u a t i o n (5.5)  )  k  l n  D  ( a  l  + a  2  ~  )  J a  n  2  r 2 " Ja ( x  X  2  x  }  _  t  D  fc  '  }  ^  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^+a —a— D 2  k  D^ l a  + a  2^  =  When time i n c r e a s e s , therefore,  J a  2^ l~ 2^ x  x  o r  X  1  _ X  2  =  (5,. 6)  X  the d i s t a n c e between the two i n t e r f a c e s  converges,  towards a c o n s t a n t v a l u e (4.545 x ^ ) , and the two phases  p e n e t r a t e the anode at the same c o n s t a n t dx  dx  dt  dt  rate  a a J  ctj-hxj  The set of e q u a t i o n s (5.4)  VfJh  and ( 5 . 5 )  J  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^ w h i c h corresponds to the s o l i d s t a t e d i f f u s i o n of copper i o n s i n d i g e n i t e .  The i n t e g r a t i o n of e q u a t i o n (3.9)  with  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 a t the onset of growth of  respect  105 covellite yields  D  J X  "  "  ^  ^Cu »  ( 5  '  8 )  F where A y  = -2FAE c o r r e s p o n d s t o the range of s t a b i l i t y of  r  which was measured to be 20 mV a t 55°C (Chapter 2 ) ,  and o  r  digenite, + is  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  and (5.8)  at 55°C (Chapter 3 ) .  1  It  f o l l o w s from e q u a t i o n s  that  k  D  = 2  r  AE  = 3.1 10  1 1  mole cm "'"sec  The d e p t h 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 of  (5.1)  time on f i g u r e s 35 and 36.  the i n t e r f a c e s  1  are p l o t t e d as a f u n c t i o n  I t appears from the c a l c u l a t i o n s  that  assume t h e i r s t e a d y m o t i o n f o r time l o n g e r than  90 t p and t h a 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 a d e q u a t e l y d e s c r i b e d by  2  X  =  J C  f Ch }  C t  "  4 , 5 4 5  t  D  )  C 5 , 9 )  S i n c e i t was observed t h a t 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 s u b j e c t e d  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 layer.  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  the f l u x of copper i o n s w h i c h d i f f u s e t h r o u g h i t : i s f o r m e d , and J  digenite itself  to  J when d i g e n i t e o n l y  < 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.  It  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 ) , d u r i n g the o x i d a t i o n o f c h a l c o c i t e . I = 30 mA c m I = 7.5 mA c m " 2  - 2  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 c o n s t a n t  ( E q . ( 5 . 6 ) ) and t h a t  the  depth o f p e n e t r a t i o n o f 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 . f o r times l a r g e r than 90 t  (Eq.  (5.9)  (5.1)).  2 S i n c e the p r o d u c t I T , r e l e v a n t observed t o be c o n s t a n t  t o the c h a l c o c i t e  i n Kuxmann's e x p e r i m e n t s ,  e l e c t r o l y s i s , was  i t may be proposed  that  the c o v e l l i t e had reached i t s s t e a d y r a t e o f growth ( E q . 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 t h a 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  that the  constant  of d i s s o l u t i o n t h r o u g h 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 t h r o u g h t h e 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 e q u a t i o n s I t would be meaningless  (5.9),  (5.1),  (4.6).  t o compare the v a l u e o f the c o n s t a n t  of  d i s s o l u t i o n t h r o u g h 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 p r e s e n t work ( E q . ( 4 . 6 ) ) w i t h the c o n s t a n t  t h a t c o u l d be c a l c u l a t e d from  Kuxmann's w o r k , i n t e r p r e t e d by E q . ( 5 . 9 ) and the d a t a o f 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 t o 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 b e i n g 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 w h i c h 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 t o be a s u l p h a t e m the case of the 30 g/1 H„S0. s o l u t i o n .  CuSO^ 250 g/1 -  ;  108 - The t h e o r e t i c a l p o r o s i t y o f 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% respectively.  As  the d i s s o l u t i o n c o n s t a n t  depends on the  effective  f r a c t i o n of the c r o s s s e c t i o n o c c u p i e d by the p o r e s , i t must be to t a k e t h a t e f f e c t i n t o If  corrected  account.  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  is correct,  i t would be of i n t e r e s t  to attempt the d i r e c t  electrolysis  of copper matte i n a c h l o r i d e o r a mixed c h l o r i d e - s u l p h a t e  electrolyte  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 w a t e r i s 6.6 M at 55°C 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 a t 55°C  5.2  (63)  (60,63).  L e a c h i n g 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 :  electrochemical  oxidation 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 i m u l t a n e o u s  reactions,  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 sulphides (1,27,5,65): of the s u l p h i d e t a k e electrons  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 p l a c e a t 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  a r e t r a n s f e r r e d t h r o u g h the s u l p h i d e l a t t i c e .  The p r o c e s s  is  analogous to the c o r r o s i o n of m e t a l s 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 Thomas and Ingraham (5)  feasible. l e a c h e d 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 e x p e r i m e n t s were u s u a l l y  c o n t i n u e d u n t i l 20% of the copper was d i s s o l v e d . 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 , conductivity.  Up to t h i s p o i n t ,  shape, dimensions and e l e c t r i c a l  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 e m e n t a l s u l p h u r and  u n r e a c t e d 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  electrolysis  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  s u r f a c e of the specimen.  The morphology of the l e a c h e d  outer  specimens  suggested t h a 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 t o 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 t h r o u g h the p e r s i s t i n g network of  covellite  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. D u r i n g l e a c h i n g , copper s u l p h i d e s s h o u l d assume mixed e l e c t r o d e p o t e n t i a l s w h i c h depend on the n a t u r e and magnitude of the chemical reactions  electro-  t a k i n g p l a c e and w h i c h c o u l d be d i r e c t l y measured.  I n 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 c o r r e s p o n d i n g mixed p o t e n t i a l taken by the s u l p h i d e can be e s t i m a t e d 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 a n o d i c  ;  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 a t 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 a t 55°C;  these  c o n d i t i o n s c o r r e s p o n d 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 , w h i c h has been a b u n d a n t l y 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 , 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 u l t from the  resistances  (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 d a t a w h i c h are n e c e s s a r y f o r I | [  c a l c u l a t i o n of t h e c u r r e n t d e n s i t y - p o t e n t i a l c u r v e s o f the Fe  the | |  /Fe  c o u p l e 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 t h a t  fashion  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 t i o n of 10  -2 and 10  M are p l o t t e d on F i g u r e 37 ( t h e s e  v a l u e s have been s e l e c t e d  concentration  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 c o n f r o n t e d w i t h the p o l a r i z a t i o n c u r v e of l l i t e anode determined i n the p r e s e n t work ( F i g .  cove-  25).  The l e a c h i n g r a t e d e r i v e d , a t 5 5 ° 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 l e a c h i n g r a t e s remained c o n s t a n t hours.  a f t e r a t r a n s i e n t p e r i o d of  ;  the  several  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 o f the f e r r i c i o n  concentrations  a t 50°C and found t h a 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 .  This  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 c o r r e s p o n d 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 lim ' ' ' I j |  the p o t e n t i a l e x e r t e d by the Fe  ||  /Fe  c o u p l e 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 t h a 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 described  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  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  anode u s i n g 1 ^  -2 = 2 mA cm and a s e 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  p o t e n t i a l curves f o r v a r i o u s Fe b e i n g assumed c o n s t a n t  (Figure  I||  concentrations,  the r a t i o Fe  |||  /Fe  38),  T h i s e s t i m a t i o n l e a d s 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 c u r v e s 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 c u r v e f o r a c o v e l l i t e anode remains somewhat  I mA.cm  112  Figure  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 b y f e r r i c solutions R.D.E. s p i n n i n g a t 5 0 0 r.p.m., 55°C. /Fe  Fe  Fe  3 +  3 +  (0.25  (0.1  M) M) ,o)  ?+  /Fe  2 +  /Fe  2 +  /Fe  2 +  (10 (10  -3 _ 2  (10~ (10  3  - 2  M) M)  Fe  M) M)  3+ J  o, Fe  sulphate  /Fe  2 +  (10  _ 4  M)  /Fe  2 +  (10  _ 3  M)  . /Fe ( I O " M) I 2  2 +  (10 -4  -2 (10 M) Z  )  3  / F e  + ( 1 Q  M)  _ 5  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 a r e a 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 g r o w t h . - I n 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  leaching  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 c o p p e r . - The c h a r g e - t r a n s f e r  parameters  of the F e  + + +  /Fe  + +  c o u p l e 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 a r e a i s supposed to be a c t i v e the r e d u c t i o n of f e r r i c  for  ions.  The l e a c h i n g r a t e s e x p r e s s e d  i n current densities  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 r e g a r d of 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.  the  Both*  c a l c u l a t e d and e x p e r i m e n t a l c u r v e s seem to f o l l o w the same type of dependence upon the f e r r i c i o n  concentration.  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 o f 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 , w h i c h i s l i k e l y t o be dependent,  temperature  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 . I n v e r y 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  is  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 . rate results  I n 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  leaching  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  ions.  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 , c h e m i c a l mechanism appears to be adequate 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 .  so f a r , an  electro-  to e x p l a i n the o x i d a t i o n  114  measured at 6 0 ° C (5)  mA.crrf calculated at 5 5 ° C  log C 3 F e  gure  39.  +  L e a c h i n g 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 versus f e r r i c ion concentration i n s o l u t i o n .  r.p.m.)  2  115 5.3  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 w i t h a c i d i c f e r r i c  solutions:  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 e x e r t e d 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 to o x i d i s e any copper s u l p h i d e to e l e m e n t a l  enough  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 , w h i c h 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 t i v e to o c c u r o n l y to a n e g l i g i b l e e x t e n t d u r i n g the c h a l c o c i t e 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 t h e s e s u l p h i d e s are exhausted  (ground m i n e r a l s )  c o v e l l i t e layer (4.3).  and  completely  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  ( s o l i d sample) has markedly slowed down the  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 s t a g e r e a c t i o n  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  resis-  the  reaction generally  and c o v e l l i t e .  I n 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 s t a g e of d i g e n i t e and c h a l c o c i t e transport  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  of copper i o n s a c r o s s fhe o x i d a t i o n p r o d u c t s , as i t  from the model proposed a t the b e g i n n i n g of t h i s  follows  chapter.  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 c o n s t a n t 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 t h r o u g h the r e a c t i o n p r o d u c t s . 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  l a y e r s as a f u n c t i o n of t i m e . first  is  of the v a r i o u s s u l p h i d e  A t t h i s p o i n t , the analogy between  l e a c h i n g s t a g e of c h a l c o c i t e  metals  Theoretically  the  and d i g e n i t e and the o x i d a t i o n of  obvious.  T h e o r e t i c a l model:  constant current 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 .  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 constant current o x i d a t i o n model.  40)  for  116  Cu S 2  CuS  Cu S |Q  J  j .  k  state :  2  C 2°"x^ k  o J  Steady  Solution  X. x  2  = constant.  Constant potential multilayer growth  Figure  40  model.  117  D u r i n g the o x i d a t i o n to the p a r a b o l i c  x  where k  vl/2  01  (2k  i s the  c > D  a)  -t  .1/2  constant o f d i s s o l u t i o n through the M  defined  by Eq.  The  (4.6)  and a =  jj-^-g .  D  the  =  CD  or  covellite  covellite layer i s inversely  x  J  During c h a l c o c i t e o x i d a t i o n , and  (subscript  2)  X  l  dT  2 dt  defined  D  K~^  k  _ M. ^Ch  l  V2 -x X l  "1/2  two  (5.1).  The  = a 2  2  r  ~  M M CH ;  X  l  D  k  °1  *2  (subscript  1)  differential  copper  fluxes  1  "l  k  D  ...  C~22  ( 5 a i )  0.78  d i v i s i o n o f e q u a t i o n (5.12) by  yields  d  (5.10)  following  i s the d i s s o l u t i o n constant through the d i g e n i t e by Eq.  propor-  40),  a  2  t  b a l a n c e between the  2  C,Ch°2 x  V 2  D  the growth of the d i g e n i t e  V l  -  ^  dX  where k  _  C  (-^) 2a  l a y e r s w i l l obey the  the i n t e r f a c e motions ( F i g .  d  k  =  equations which t r a n s l a t e a m a t e r i a l and  layer  thickness k  J  covellite  1  (-j-)  copper f l u x c r o s s i n g  t i o n a l to i t s  c o v e l l i t e grows a c c o r d i n g  law  ,  =  of d i g e n i t e , the  layer  as  equation  (5.11)  118  The most g e n e r a l  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 e q u a t i o n i s (Appendix 7 ) . l  U  £ = (x  - u ^ )  2  U  2  U  l  U  (x -u 2  2  ) V2  ,  U  z X l  where C i s t h e i n t e g r a t i o n constant^ and u^ and u  (5.14)  a r e the r o o t s of the  2  second degree e q u a t i o n  4. ^  2  U  n x C,Ch, (1 + — j )u D k  5  + a  l  k  The c o n d i t i o n t h a t x^ and x at  = u^x  2  °  X  k  a  (5.14) c o n s i d e r a b l y  k  a  a  . = 0.  a  to  (1 + _£i£h) +  l  k  D  (5.15)  a  [(-i) a  2  k  (i+ ^ C h )  l  k  2  D  2  +  k 4  k  CiCh  D  The i n t e g r a t i o n of e q u a t i o n s  k =  ( 2  1 ^  a  1/2  )  2  =  [  2 C k  a  product.  (5.11) and (5.12) y i e l d s  '  t  C,Ch 2 *  (66,67)  1/2  k X  V  of s e v e r a l o x i d e l a y e r s  c o n t r o l l e d by d i f f u s i o n through the o x i d a t i o n  l  1/2  x  f o r m e t a l o x i d a t i o n l e a d i n g t o the f o r m a t i o n  X  a  2  The r e l a t i o n s h i p (5.15) has a l r e a d y been proposed by V a l e n s i  and  zero  u^ > 0  1  2  r  C,Ch. 2 r-* D l  a r e s t r i c t l y p o s i t i v e f o r t > 0 and  2  t = 0 s i m p l i f i e s equation  x  k  a  ll^7 u  ( 5  1/2 ) j  1/2 t  '  *  '  1 6 )  (5 17)  l  119 Both phases grow a c c o r d i n g t o a p a r a b o l i c l a w and the r a t i o between the q u a n t i t y o f t h e two phases remains  constant.  The f l u x c r o s s i n g t h e 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 e q u a l s . k a J  = C,Ch k  [ 2 ( k  C , C h 2 ' - r^->] a  -1/2  -1/2 t  (5.18)  u 1 It  j  f o l l o w s from the c a l c u l a t i o n s o r from t h e analogy w i t h m e t a l  o x i d a t i o n t h a t the depth o f p e n e t r a t i o n of t h e d i g e n i t e and o f 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 o f time ( E q . (5.16) and ( 5 . 1 7 ) ) and t h a t the r a t i o between t h e d e p t h o f p e n e t r a t i o n o f t h e two phases remains c o n s t a n t  (Eq. ( 5 . 1 5 ) ) .  The r a t e of the f i r s t l e a c h i n g s t a g e o f 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 e q u a t i o n ( 5 . 1 0 ) and from e q u a t i o n s (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 : been p o i n t e d out e a r l i e r , t h e d i s s o l u t i o n c o n s t a n t ,  ( 5 . 1 8 ) and  As i t has a l r e a d y k , through the  c o v e l l i t e l a y e r depends upon t h e f r a c t i o n o f t h e c r o s s s e c t i o n o c c u p i e d by t h e pores and i s assumed t o be p r o p o r t i o n a l t o i t .  As t h e c o v e l l i t e  r e s u l t i n g from t h e o x i d a t i o n o f d i g e n i t e and c o v e l l i t e  theoretically  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 t h a t C,Ch  = ^ 19.7  k C,D'  -9 where k  = 2.35 10  -1  -1  m o l e cm sec  results reported i n section  (4.6.2).  was d e r i v e d from t h e e x p e r i m e n t a l The v a l u e o f k p r e l e v a n t t o t h e  l e a c h i n g o f 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 ( t h e o r e t i c a l model).  I n the absence o f o t h e r d a t a , k  (5.1)  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 t o be 3.1 10 "*" mole cm s e c x  M molar volumes (-j) respectively  of c h a l c o c i t e and d i g e n i t e are 27.5  (59).  The •  x  and 25.4  3 - 1 cm mole ,  The c a l c u l a t e d r a t e s f o r times e q u a l 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 ,  fc  JAt =  /  2  Jdt,  (5.19)  are r e p o r t e d i n T a b l e 7.  Table 7 Rates o f the f i r s t l e a c h i n g s t a g e of m a s s i v e d i g e n i t e and c h a l c o c i t e 55°C i n a c i d f e r r i c  solutions  Ch ( )  mA cm  1  19.3  24.1  5  8.6  10.8  11.9  14.9  12.9  18.2  nr  calculated  averaged,Eq. measured (10)  Thomas and a l .  at  (5.19)  mA cm  -2  (.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 t a g e of l e a c h i n g i n 0.1 M 3+ Fe  -0.1 M ^ S O ^ solution.  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 . , a r e r e p o r t e d i n T a b l e 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 against  time was s l i g h t l y c u r v e d , t h e y 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 o f copper d i s s o l v e d , w h i c h s h o u l d  a p p r o x i m a t e l y c o r r e s p o n d to the s e l e c t e d  time i n t e r v a l .  The agreement between the two s e t s of v a l u e s i s s a t i s f a c t o r y  given  the assumptions w h i c h 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 c o n s t a n t  (k  ).  From the d i v i s i o n of e q u a t i o n ( 5 . 1 0 ) by e q u a t i o n ( 5 . 1 8 ) i t  follows  ft t h a t d i g e n i t e s h o u l d d i s s o l v e a t 80% of the c h a l c o c i t 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  experiments,  rate  i n otherwise  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 chalcocite. It  can be d e r i v e d from E q . (5.15) t h a t ,  f o r these c a l c u l a t i o n s ,  i n the c o n d i t i o n s  the c o v e l l i t e r e p r e s e n t s  stated  a p p r o x i m a t e l y 96% of  the o x i d a t i o n p r o d u c t s . Therefore  i t appears t h a t the r a t e of the f i r s t s t a g e 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 r e a s o n a b l y accounted f o r by  a model c o r r e s p o n d i n g 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  t h r o u g h 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 s t a g e of these s u l p h i d e s , w h i c h i n v o l v e s o x i d a t i o n of c o v e l l i t e , s h o u l d f o l l o w the same mechanism as t h i s A difference resides contains  i n the f a c t t h a t t h i s p a r t i c u l a r c o v e l l i t e  the latter.  already  20 o r 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 c o r r e s p o n d to k^ = 3 l O - ^ mole c m l s e c - ' - , 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 products. -  -  -  122 CHAPTER 6. CONCLUSIONS 6.1  E l e c t r o c h e m i c a l parameters o f t h e copper s u l p h i d e s 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 s u l p h i d e s p r o v i d e d  some fundamental i n f o r m a t i o n on t h e Cu-S system. 1.  E.m.f. measurements were conducted i n t h e range between 40 and  80°C on t h e f o l l o w i n g g a l v a n i c  cells,  S.C.E. (25°C) | 0.1 M C u S 0 , 0.1 M H S 0 4  2  | Cu  4  ,  S.C.E. (25°C) I 0.1 M CuSO., 0.1 M H„S0. I Cu S. i 4 2 4 y 1  The copper 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 t o produce a two phase e l e c t r o d e h a v i n g 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 o f t h e  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 r e s p e c t t o S.C.E. (25°C) (Stockholm Convention) were measured t o be:  E(Cu) = (70.45 ± 0.33) x 1 0  _ 3  E(D.-C.) = (251.50 ± 0.35) x 1 0 E(D.-Dj.)=(242.20  + (0.632 ± 0.025) x 1 0 - 3  ± 0.45) x I O  - 3  - 3  (T-328)  V,  + (0.765 ± 0.035) x 1 0 ( T - 3 2 8 )  V,  + (0.62 ± 0.060) x 10"" (T-343)  V.  -3  3  The v a r i a t i o n o f the c h e m i c a l p o t e n t i a l o f copper and s u l p h u r a c r o s s the Cu-S system c o u l d be a s s e s s e d from t h e above measurements and from e x i s t i n g thermodynamic  data.  Consequently, the standard f r e e enthalpy  of f o r m a t i o n o f 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 t h e i n v e s t i g a t e d range o f temperature w i t h t h e n o t e d 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)  cal mole" ,  AF°(C  U;L  9 6 5  S)  = (-19,700 ± 550) -  (5.5 ± 3.1)(T-343)  cal mole" .  1  1  The v a r i a t i o n o f t h e s t a n d a r d 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 , was e s t i m a t e d 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 S) = (-18,140 ± 520) y  (4.9 ± 2 . 5 ) ( T - 3 2 8 )  + (y - 1 . 7 6 5 ) [ ( - 7 , 9 1 0  ± 40) -  (3.2 ± 2.5)(T-328)] c a l mole  The major component  1  ( a p p r o x i m a t e l y 90%) o f t h e f i n a l e r r o r on t h e  above thermodynamic v a l u e s o r i g i n a t e d from t h e e r r o r on the e x i s t i n g d a t a 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  solution saturated with l^S  a  t  constant  copper s u l p h i d e f i l m , a t low e l e c t r i c  current.  The t h i c k e n i n g o f the  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 . coefficient  of cuprous i o n s i n c h a l c o c i t e  The d i f f u s i o n  and d i g e n i t e was c a l c u l a t e d  i n t h e temperature range between 30 and 73°C from t h e s l o p e o f t h e e l e c t r o d e p o t e n t i a l v e r s u s time 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 i o n s 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)  2 -1 cm sec ,  —)  2 -1 cm sec ,  and i n l o w d i g e n i t e D  C u +  = 3.6 x 10  exp (  .  124  The phase boundary r e a c t i o n s i n t e r f e r e w i t h these 3.  d i d not appear to be too r e s i s t i v e  to  measurements.  P o t e n t i a l - t i m e curves were r e c o r d e d d u r i n g the  galvanostatic  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 S 0 2  4  s o l u t i o n s a t 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 time, x  such t h a t the r e l a t i o n s h i p between the  t  current  d e n s i t y and the t r a n s i t i o n time was  T  2  I T  — 4 sec. A . 2cm  = 2 OK .5  I t was proposed t h a t ,  at t h e 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 [ electrode  reaction,  Cu, -, S -> CuS + 1.56e 0  + 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 s h r i n k a g e pores of  the  covellite.  k , t h r o u g h the c o v e l l i t e  layer  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  data.  The d i s s o l u t i o n c o n s t a n t , k  The i n t e r f a c e  C  r e a c t i o n seemed t o 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  process.  The a n o d i c r e a c t i o n on c o v e l l i t e , CuS -> Cu appeared to be r e l a t i v e l y r e s i s t i v e .  +  S"  During o x i d a t i o n ,  +  2e,  covellite  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 . controlled  reactions.  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  established  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 l o n g d i s s o l u t i o n times covellite.  of  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 t o 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 d a t a 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 o b t a i n e d i n the p r e s e n t w o r k , suggests d i s s o l u t i o n of c h a l c o c i t e ,  t h a t the r a t e of;  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 i o n s i n the h i g h e r s u l p h i d e l a y e r . L e a c h i n g 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  e s t i m a t e d from the d a t a e s t a b l i s h e d i n the p r e c e e d i n g p a r t s of  this  work on the b a s i s o f 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 m e t a l c o r r o s i o n .  T h i s model appears adequate  the b e h a v i o u r of c o v e l l i t e i n the presence o x i d a n t , as observed by o t h e r  of an aqueous  to e x p l a i n  ferric  researchers.  The r a t e s of the f i r s t l e a c h i n g s t e p of c h a l c o c 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  and d i g e n i t e constant  p o t e n t i a l o x i d a t i o n m o d e l , where the r a t e of the p r o c e s s 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 i o n s t h r o u g h the o x i d a t i o n p r o d u c t s . r e s u l t s of t h e s e c a l c u l a t i o n s are found to be i n agreement w i t h r e l e v a n t e x p e r i m e n t a l d a t a e x i s t i n g i n the  literature.  The the  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 o f an e l e c t r i c f i e l d  t o an i n i t i a l l y homogeneous  copper s u l p h i d e g i v e s r i s e t o a c t i v i t y g r a d i e n t s and f o r l a r g e r f i e l d s , when t h e a c t i v i t y g r a d i e n t s tend decomposition.  t o exceed the s t a b i l i t y l i m i t s , t o  The type o f c u r r e n t  ( i o n i c , e l e c t r o n i c o r mixed)  depends on t h e c o n t a c t s o r e l e c t r o d e s . In a c e l l , where the copper s u l p h i d e i s i n s e r t e d between two i o n i c conductors, e.g.,  Cu  | CuSO, aq | Cu S | CuSO, aq. | Cu  (AI)  the a p p l i c a t i o n o f a d.c. p o t e n t i a l f o r c e s an i o n i c c u r r e n t the copper s u l p h i d e .  through  However the c u r r e n t i s not e x c l u s i v e l y i o n i c  s i n c e copper i s i n the c u p r i c 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 o f copper atoms, f l o w i n g through; the copper  sulphide  depends on the t o t a l c u r r e n t f l o w i n g through the c e l l .  2F  =  J  Cu'  C  which i s r e l a t e d to t h e Onsager c o e f f i c i e n t  J  Cu  =  -M  3y Cu Cu  A  through Eq. (3.7)  C3, 7)  127 I n t e g r a t i o n o f E q . (3.7)  over the t h i c k n e s s o f the s u l p h i d e t a b l e t  yields J  where M  C u  =  2F  ^ _  AE  (A1.2)  i s the average v a l u e o f 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 represents  the drop o f  electro-  c h e m i c a l p o t e n t i a l a c r o s s the s u l p h i d e . I t appears from E q . A l . l and A 1 . 2 t h a t the average Onsager  coeffic-  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 o f 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 o r diffusion coefficient  (Eq. 3.8)  charge o f the d i f f u s i n g s p e c i e s .  r e q u i r e s the d e t e r m i n a t i o n o f  the  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 a c r o s s the s u l p h i d e .  S i n c e the thermodynamic  p o t e n t i a l s a r e 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.  Experimental S e v e r a l d e s i g n s and c o n s t r u c t i o n s o f c e l l were a t t e m p t e d :  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 p r e s s e d a g a i n s t a copper s u l p h i d e membrane b y a v i s e .  The t e f l o n was  c r e e p i n g 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 o f c e l l was made of two p y r e x tubes cemented to copper s u l p h i d e membrane w i t h epoxy r e s i n .  the  The l e a d s 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 h a v i n g been f i l l e d w i h the solution.  The manufacture of t h e s e c e l l s was e x t r e m e l y  delicate  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 o r two d a y s .  128 3.  A t h i r d type of c e l l , w h i c h 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  cell,  w h i c h 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  d e a e r a t e d under vacuum and k e p t under a h e l i u m atmosphere.  2 This  4  treat-  ment was i n t e n d e d to p r e v e n t the e v o l u t i o n of b u b b l e s , w h i c h were d r a g g i n g the s o l u t i o n out of the c e l l d u r i n g the c o u r s e of experiments.  the  I n 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  reaction.  Each h a l f c e l l was d i v i d e d by a f r i t t e d . p o l y e t h y l e n e d i s k i n t o an a n o d i c 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 e n c l o s e d i n a p y r e x tube c l o s e d at b o t h ends w i t h . m e t a l l i c covers.  The e l e c t r i c a l l e a d s were cased i n r u b b e r t u b i n g s  f i t t e d t o one of the c o v e r s . tube.  A h e l i u m atmosphere was m a i n t a i n e d i n . t h e  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 i  glycol bath. An e l e c t r o s c a n , B e c k m a n  ethylene  30, was used as a c o n s t a n t c u r r e n t  source.  The c u r r e n t was measured by a K e i t h l e y , model 153, m i c r o v o l t a m m e t e r . The p o t e n t i a l drop a c r o s s 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,  electrometer.  The copper e l e c t r o d e s were made o f 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 section  4.5.  I!l  approximately.  k\\\1  Teflon cell.  g§§M§§  Copper sulphide.  f  Copper electrodes. St. steel  |g&&#l  washers.  Teflon membranes. VO  Figure 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.  drop between the two t e r m i n a l copper e l e c t r o d e s  Cu | C u S 0 , H S 0 4  2  4  aq.  of the  cell  | Cu | CuSO^, ^ S O ^ a q .  | 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. 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  The p o t e n t i a l  Consequently,  the  p o t e n t i a l a c r o s s the s u l p h i d e membrane  c o u l d 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 for currents  s m a l l e r than 10 uA.  The d a t a 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 t h a t t h i s range of c u r r e n t c o u l d be At 55°C, the maximum p o t e n t i a l d i f f e r e n c e  t h a 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 Eq.  (A1.2)  adequate.  10  "''cm "*".  5  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 t h a 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 i a m e t e r .  i  _  4 x 7.5  5 „ ,„-2 10 x 2 10 0.3  - 14 uA  Any c u r r e n t h i g h e r t h a n t h i s v a l u e would cause the e l e c t r o l y s i s sulphide.  The maximum p o t e n t i a l d i f f e r e n c e  t h a t can e x i s t  of  the  across a  c o v e l l i t e membrane i s a p p r o x i m a t e l y 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 t h a t 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 t h r o u g h the  specimen  i n o r d e r t o 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 n e c e s s a r y to s u p p o r t the s t e a d y - s t a t e f l o w of c o p p e r .  If,  i n f i r s t approximation, 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 a c r o s s t h e membrane,  the  time n e c e s s a r y to e s t a b l i s h t h e 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 . d i g e n i t e i s assumed to be Cu  ^  Q O  JL. / O Z j  The i n i t i a l c o m p o s i t i o n o f  S, i t s s t a b i l i t y l i m i t s b e i n g C u , S Q  JL. o  SJl d A q u a n t i t y b f copper e q u a l t o AC„ - r — (TT)„ „ i s Cu 2 M Cu S y n e c e s s a r y t o shape t h e c o n c e n t r a t i o n g r a d i e n t a c r o s s t h e d i s k ,  and C u , - , S a t 55°C. 1.765 £C  • 1  r  _ ( 1 . 8 - 1 . 7 8 2 5 ) x 0.72 x 0 . 3 2 x 25.4  t -  5 1 U  12 d a y s . 3  By t h a t  t i m e , t h e c e l l , w h i c h 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 i n c e c o v e l l i t e i s r e p o r t e d t o be  s t o i c h i o m e t r i c , the time n e c e s s a r y t o e s t a b l i s h t h e s t e a d y - s t a t e f l o w s h o u l d be c o n s i d e r a b l y  smaller.  Measurements made on c o v e l l i t e membrane, a p p r o x i m a t e l y 2 mm t h i c k , at c u r r e n t below 10 uA were n o t 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, o r 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 c o u l d be as d i f f e r e n t as 1 t o 1 0 .  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 i m m e d i a t e l y a f t e r  the s w i t c h i n g o f 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 t h a t s u l p h u r was p r o b a b l y formed a t t h e a n o d i c s i d e of the covellite.  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 s h o u l d cause t h e s u l p h u r f o r m a t i o n a t the anode d u r i n g t h e t r a n s i e n t  period.  electrode  ( 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  appears i r r e v e r s i b l e  As t h e c o v e l l i t e - s u l p h u r  would remoye a l l s i g n i f i c a n c e to t h e 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 t h e r e i s o n l y one r a t e - c o n t r o l l i n g s t e p i n the e l e c t r o d e p r o c e s s b u t 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 the r e a c t i o n  (50).  arise concurrently during  I f e i t h e r c o n c e n t r a t i o n overvoltage 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 o c c u r s 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  current  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 equilibrium potentials, equilibrium.  In  s i n c e the c h a r g e - t r a n s f e r  reaction i s i n  the mixed c o n t r o l c a s e , t h i s e q u a t i o n i s , s t r i c t l y  s p e a k i n g , no l o n g e r a p p l i c a b l e . K.J.  Vetter  (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 c h a r g e transfer  components, w h i c h i s based on the r e q u i r e m e n t t h a t upon the  d i s a p p e a r a n c e of a l l o v e r v o l t a g e types but o n e , 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 r e m a i n i n g o v e r v o l t a g 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 exchange c u r r e n t d e n s i t y I ; when I  q  control is  the  becomes i n f i n i t e l y g r e a t ,  t r a n s f e r r a t e - c o n t r o l no l o n g e r e x i s t s ,  so t h a t  for I  ->•<», n  charget  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 rate  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  type.  0» . reaction  °o. The  c r y s t a l l i z a t i o n component w i l l d i s a p p e a r 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 rapid ( V is the  Q  ^  »).  The o r d e r i n w h i c h t h e s e l i m i t s are  important f o r p r e c i s e overvoltage d e f i n i t i o n s . following  sequence,  taken  V e t t e r proposed  133  n-n V  -»-  +  r  n +-n D  An  c  oo  An =  n  An =  n  An =  n.  o,r D  ->  00  V  oo  o,C %  \  +  n  +  n  D  0  -  c  (A2.1)  T  The charge-transfer component, because i t depends upon the concentrations at the electrode surface, i s influenced by the existence of the other overvoltage.  Therefore the l i m i t I  -v »  should be carried out  first.  On the basis of this d e f i n i t i o n , the current-potential r e l a t i o n s h i p (50) for simultaneous occurrence of charge-transfer and  concentration  overvoltage w i l l be treated.  , .  I = I T  C.z (—)  .  / i \r,i  [n  fTI  ° i  n  C. i  exp  qzF R T  _  C.z . o,x II(—) '  , i.  n -  i£  exp  • • / • ! • • \ -p. (,1-q)zF - -———  n  J  ,  .  CA2.2)  n  0  R  i  C. and C. are the concentrations of species i at the electrode surface i i r  and i n the bulk of the solution, respectively.  I  i s the exchange  current density, z . and z . the electrochemical reaction orders, ' o,x r,i ' J  z the charge transfer valence, and a the charge transfer c o e f f i c i e n t .  T i  o  °°>  „/ is r,x nC—) i  azF exp - r = - n =  c  exp  zF  - - n  =  i  C z —z , i . r , i o,i  TJC—)  TT  i . o,i  (—) C  exp -  (l-a)zF -— R T  n  134 with z  . - z  0,1  . = v. — r,i 1 n  (49)  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 electrode r e a c t i o n valence  RT  .  of the r e a c t i o n a n d , n the  change.  , i, l C  V  1 T h i s e q u a t i o n c o i n c i d e s w i t h the N e r n s t 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  cell.  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 t h e o r y 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 s e t of e q u a t i o n s electrolyte  (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^  are: 3C  J  J  l - " l JT  -  (A3 1}  D  3 = -  3 ^  D  +  I 3Sl  '  D  CA3  The s u b s c r i p t s 1 , 2, 3 s t a n d f o r CuSO^, Cu  , SO^  3)  respectively.  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 c h e m i c a 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 E q . (A3.1) and E q . (A3.3) y i e l d s a f t e r rearrangement  of  the  variables D  l  D  3 C  2  1 C  ax  3  ?  9 C  9  a*  9P RT  X  3x  For s t e a d y - s t a t e d i f f u s i o n a c r o s s a boundary l a y e r , o f d e f i n e d 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 r e s p e c t t o t h e t h i c k n e s s o f t h e l a y e r  RT A  *  =  F  n  1  rT  3  — K  ( c  2  _  c  2  }  r  RT +  IF"  L  N  -  yields  9 (  A  3  ,  5  )  136  When t h e 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 t h e e l e c t r o d e electrolyte interface, K C  + C„ - C  2  I  l  +  = C g , and  can be c a l c u l a t e d from  =0.  s  The p o t e n t i a l drop i n t h e d i f f u s i o n l a y e r i s e s t i m a t e d 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 p a r a m e t e r s . - C = 2.2 mole 1 w i t h C u S 0 - 5 H 0 a t 55°C 4  -  (60,63).  2  = D  2  c o r r e s p o n d s t o t h e s a t u r a t i o n of the s o l u t i o n  1  g  t h i s a s s u m p t i o n has been proposed i n s e c t i o n  (4.6.2)  ++ S i n c e the t r a n s p o r t number o f Cu  has been measured to be 0.36  i n 0 . 1 M CuSO^ at 25°C (75) and s h o u l d n o t be temperature •  i t can be assumed t h a t —  •  =  dependent,  Q'  _ * _, .• = 0 . 4 8 5 . 0.74  - The c o m p l e x a t i o n c o n s t a n t , K , has been e s t i m a t e d t o be 127 a t ambient temperature by Nasanen and K l a i l e (61) but t h e a p p r o p r i a t e value of t h i s constant  i n c o n c e n t r a t e d s o l u t i o n s a t 55°C i s n o t known.  In t h e s e c o n d i t i o n s , the p o t e n t i a l drop amounts t o 76 mV, 185 mV and 249 mV f o r v a l u e s of the c o m p l e x a t i o n c o n s t a n t of 1 0 , 100 and 200 respectively.  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 a t 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 a c r o s s the e l e c t r o d e boundary l a y e r can be from E q . (4.1)  calculated  and the N e r n s t 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  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 i  a n g u l a r 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 72 mA cm  at 25°C and 250  the  r.p.m. i  S i n c e 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 , is  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  c o r r e s p o n d i n g 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 e x c e s s 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 m o d i f y 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 .  1^  =.  -2 46 mA cm  at 25°C and 250  r.p.m.  A 0 . 1 M C u S O . - 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 t h e s e two 4 2 4 cases; i t s p h y s i c a l s o l u t i o n C62).  p r o p e r t i e s are 'very c l o s e to a 0 . 1 M CuSO^  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 M a r a t h e ' 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 is  (56)  I  It  _2 59 mA cm  =  at 25°C and 250  f o l l o w s from E q . (4.1) C — C  =  that  I •=D  1 -  r.p.m.  I > 0 a t an anode 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 a t 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 i n c e 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 . I  D  -  0.62 D  2 / 3  v"  1 / 6  .  1 / 2  (4.1)  2F C  i t can be e x t r a p o l a t e d to 55°C, D and v b e i n g the o n l y temperature dependent  parameters. T = A—  - D  A i s a c o n s t a n t and u i s the v i s c o s i t y o f w a t e r  V D  55  V  55 "  D  25  V  328 298  ^55 25 u 2 5  25 y y  5 5  _25 d d  5 5  (76)  139 The v i s c o s i t y and d e n s i t y of w a t e r a r e t a b u l a t e d i n c h e m i c a l handbooks  D  5 5  - 1.945  I (55) D  =  D  = 0.573  2 5  1.71  I (25) D  Binary e l e c t r o l y t e :  1^ = 123 mA cm I  -2 (mA cm ) 75.3 56.5 37.7 18.8 15.1 11.3 7.5  (77)  n  _2  Excess of i n d i f f e r e n t electrolyte -2 79 mA cm  CmV)  D  n  D  D  1.61 1.46 1.31 1.15 1.13 1.09 1.07  6.7 5.3 3.8 2.0 1.7 1.2 1.0  9.4 7.6 5.5 3.0 2.5 1.9 1.2  1.95 1.71 1.48 1.24 1.19 1.14 1.09  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 extreme cases was s e l e c t e d  CmV)  D  two  f o r use i n o t h e r c a l c u l a t i o n s i n t h i s  thesis.  Though s u c h 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 e x p e r i m e n t a l e r r o r on the p o t e n t i a l . A resistance p o l a r i z a t i o n i s generally associated with a concentration gradient i n s o l u t i o n :  t h i s term w h i c h i s z e r o 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 e q u a l s the d i f f u s i o n o v e r v o l t a g e i n a binary electrolyte.  I n the p r e s e n t c a s e , however, i t has been shown i n  Appendix 3 t h a t 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 was not a p p r o p r i a t e .  The  electrolyte,  ohmic drop c a l c u l a t e d w i t h the  140 resistivity term, is  n^.  the  bulk  solution is  The s m a l l c o n c e n t r a t i o n  unlikely  remaining  of  to  part  m o d i f y much o f ' t h e of  the  resistance  already  taken  variation resistivity  into  i n the of. the  polarization is  account  boundary  in layer  solution,  neglected.  the  and  the  141 APPENDIX 5. INTEGRATION OF EQUATION (5.3) d(x ~x ) 1  k (  2  D  _  x  +a ) 2  _ j  at L e t us s e t  a;L  = x  i" 2 x  =  l  - x  2  Y  k (a +a ) = A D  Ja Eq.  1  2  = B  2  (5.3) can then be w r i t t e n  y dy = (A-By) dt w h i c h can be d i r e c t l y  j^m  1  L e t us s e t  integrated  ^ = t c +  A - By = z - B dy = dz  It  follows  ~ B  /  —  dz  =  t + C  ( z - A I n z)  =  t + C  2  or  ~ B  (5.3)  142 R e p l a c i n g z by i t s v a l u e  [A-B(  X ; L  yields  l n [A-B( -x )] = t + C  -x )J 2  X l  B The s o l u t i o n initial  ( 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 t h e  condition  x  2  B  l ^2 D X  x , - x „ = x_  k (a +a ) D  1  JT a 2  at t = t  2  2  2  k (a +a ) D  ln  1  k  D  ( a  2  l  + a  2  }  Ja (x ~x ) 2  "  J a  1  2  X  2  D  =  t - t„  143  APPENDIX 6. THE F e  3 +  /Fe  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 e x p r e s s e d i n the 3+ case of the Fe  2+ /Fe  e l e c t r o d e by  T h i s e q u a t i o n 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 resistances. Parameters o f the c h a r g e - t r a n s f e r p r o c e s s  (measured  a t  a  platinum  electrode) I , the exchange c u r r e n t d e n s i t y was determined t o s a t i s f y the relationship  I  o  = k [Fe o  2 +  ] exp §  E  e q >  = k^Fe^J  exp - ^  3+ I f the s e l e c t e d r e f e r e n c e i s the s t a n d a r d Fe (E  = 0), I  o  the e x p r e s s i o n of I  = k lFe o  3 +  J  a  jFe  2 +  ]  is simplified  /Fe to  1 _ a  (68)  k (25°C) = 300 o  mA c m ^ m o l e '  1  1  (49,68,69)  2+  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 a r e a y a i l a b l e :  a = 0.58  E ^  (68)  electrode  itself  144  31n I - r  =  2  -  ^  AH = 7,500 c a l m o l e "  Parameters of the d i f f u s i o n p r o c e s s : electrode  (section  ..  (70,71)  case of a r o t a t i n g d i s k '  4.2).  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 ,  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 . a r e g i v e n by ( E q .  _  T  I T  n  3  9  _ = 0.62 n  D  ,  4.1)  _ 2/3  -1/6  1/2  .  2+  2/3 D^  -1/6 v  1/2 to  F IFe  3+, ]  n  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 t o be  D C25°C) = 5.4 1 0 2  D (25°C) = 4 . 4 3  IO  - 6  - 6  cm sec 2  cm sec 2  (72)  1  (72)  - 1  The o t h e r 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  2TT x 500 —77: 60  (5)•  r a d i a n sec  -I  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 b y the k i n e m a t i c - v i s c o s i t y o f a 0 . 1 M I^SO^  s  ol  u t  i  o n  >  1  145 v(25°C)  = 0.99 10  Temperature c o r r e c t i o n s  2 -1 cm sec  -2  (62)  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. E q u i l i b r i u m p o t e n t i a l o f t h e Fe The s t a n d a r d e l e c t r o d e  3+  /Fe  2+  couple 3+  p o t e n t i a l of t h e Fe  2+  /Fe  couple i s at  25°C (Stockholm Convention) e  o  (25°C) = 771 mV  o r i f the S . C . E .  e  o  (2)  (25°C) i s chosen as r e f e r e n c e  (25°C) = 529.5 mV  3+ The e l e c t r o d e  p o t e n t i a l o f t h e n o r m a l Fe  r e s p e c t to t h e S . C . E .  (25°C)  the t h e r m a l temperature de (-£)  e  o  th  coefficient  (25°C)J  The a c t u a l e l e c t r o d e  /Fe  c o u p l e a t 55°C w i t h  can then be c a l c u l a t e d w i t h the h e l p o f  = +2.059 mV (°C)  [S.C.E.  2+  of t h e e l e c t r o d e , 1  (32)  = 592 mV a t 55°C  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 , 7 3 , 7 4 )  and i s a p p r o x i m a t e l y 30 mV l o w e r  t h a n t h e 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 0.3  (73).  than  146  A correction coefficients tion  of  taking  the  difference.was  into  ferric  account  the  and f e r r o u s  n o t made b e c a u s e  of  difference  in  ions^ r e s u l t i n g the  lack  of  activity  from the  data.  concentra-  147 APPENDIX 7. INTEGRATION OF EQUATION ( 5 . 1 3 )  ^2 d  L e t us  k  =  G G h «2  l  x  _-«2  ?  D  k  a  l  *2  «1  a  Q  +  \  ^ k  D  (  )  C  5  1  3  )  }  set A  k  =  C,Ch k  B  =  ^2  D  — l  a  l  (1 +  )  a  'fi X  D  = u  l  It follows  k  that = u dx^ + x ^ du  or dx dx  du dx  2 1  =  = 1  "  du dx.^ -z  X „1  Au  +  U  - B - u x  1  x  I n t e g r a t i o n of the former e q u a t i o n y i e l d s  x = C exp.  /  Au  — - B - u  (A7.1)  148 or a f t e r r e d u c t i o n i n s i m p l e f r a c t i o n s l  U  U  u-u / —-—— " l u  where u ^ and  u  du  2  u - u  - /  u  " 2  (A7.2)  u  a r e t h e r o o t s o f t h e second degree e q u a t i o n  + Bu - A = 0  2  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 E q .  U  u  du  £  u  CA7.2)  V  l  2 i  ln  _ u  (u-u )  +  1  u  r—2  I n ( u2 - u j  u  (A7.3)  and replacement o f E q . (A7.3) i n E q . (A7.1) U  x =  l  U  CCu-u )  2  (u-u )  1  2  2 Replacement o f u by — l X  yields  x  U  i  — -  which i s  , (x  l  sV i u  2  -u x ) 1  the proposed  1  U  , , (x^-u^&j)  solution,  Eq.  u  2  r 2 u  (5.14).  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