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An investigation of the Cu-Fe-S-H₂O system at 200⁰C Baratin, François 1980

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AN  INVESTIGATION  OF THE  SYSTEM  CU-FE-S-H 0 2  AT 200°C  by  FRANCOIS Ancien  eleve  de l ' E c o l e DEA  Polytechnique,  de M a t h e m a t i q u e s ,  Ingenieur  A THESIS  BARATIN  au C o r p s  Paris,  1971  des Mines,  1973  SUBMITTED I N P A R T I A L FULFILMENT  THE R E Q U I R E M E N T S DOCTOR OF  in  FOR  THE D E G R E E  OF  PHILOSOPHY  the Department of  Metallurgical  We  accept to  THE  this  Engineering  thesis  the required  UNIVERSITY  conforming  standard  OF B R I T I S H C O L U M B I A  October (cY  as  1980  F. B a r a t i n ,  1968-1971  1980  OF  -6  In p r e s e n t i n g t h i s  thesis  an advanced degree at  further  fulfilment  of  the. requirements  the U n i v e r s i t y of B r i t i s h Columbia, I agree  the L i b r a r y s h a l l make it I  in p a r t i a l  freely  available  for  agree t h a t p e r m i s s i o n for e x t e n s i v e copying o f  of  this  representatives. thesis for  It  financial  this  thesis or  i s understood that copying or p u b l i c a t i o n g a i n s h a l l not be allowed without my  written permission.  Depa rtment The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada  Date  that  reference and study.  f o r s c h o l a r l y purposes may be granted by the Head o f my Department by h i s  for  A B S T R A C T  The  goal  Cu-Fe-S-H20  the  collect  system  solid-aqueous  thermodynamic data  study  Two  i n the  to extend  energies  and  and  Pourbaix's  and  work  to  more s p e c i f i c a l l y ,  display  to d i s c u s s these  to  at 200°C,  to  the r e s u l t s  on  o f f o r m a t i o n G°  equilibria  diagrams,  available  was  200°C,  at  the relevant free  compute  a  of this  diagrams  with  rate  literature.  main d i f f i c u l t i e s  had  t o be o v e r c o m e  to achieve  such  study.  1)  Eh-pH d i a g r a m s  available 2)  plotted  computing  A number o f G°  A method  methods  data  was  semi-quantitatively used  for  the  Cu-Fe-S-H20  were d i f f i c u l t  to  were m i s s i n g , and had  developed represent  in hydrometallurgy,  even  t o compute the  system  by  the  interpret. t o be  and p l o t  complex Cj  those  involving  to  Pourbaix's,  generated.  diagrams C -H20 M  which  systems  several metals  and  ligands. The  fundamentals  systems, However  the  are  similar  diagrams  t h e method  and  p r e v i o u s l y p u b l i s h e d may  presented  here  i s  also  for  simple  be d u p l i c a t e d .  well  adapted  to  Ill  multicomponent temperature the or  and  aqueous  solids,  are  chemical  of  potentials  and  corresponding  generated  extremely  different complex  the  flexible  needed  to  • to  solutes Cj's.  each  the  the  region  presence the  independence the  on  into  c o n d i t i o n s on  for generating  diagrams  of  components  solutes in  This  constant  imposed  converted  corresponding to  be  activities  several  f o r the  equations  method  was  implemented  programs p u b l i s h e d  previously  specific  composite  type  along  Pourbaix's  complex  of with  plots  of  aqueous  makes  the  large variety  reliably  generation  Two  of  describe  a  computer  other  authors  diagram  f o r systems  water  Since  the  program  i t  is  c l a s s e s of  by  program. determine  a  containing  one  strictly  described diagrams,  a p p r o p r i a t e ' to  The  applying  in this even  identify  study  for  i t as  very a  new  program.  approaches have  missing  from  First,  an  the  extension of  in  been  followed to , generate  the  data  literature.  been d e v e l o p e d ,  contained  a  and  different  systems,  by  as  ligands  method.  c o m p u t e s and  has  or  at  system.  The  metal  C o n d i t i o n s can  independently.  classes of  calculated  automatically  The  those  are  constant  one  diagram.  phase are method  activity.  i n . t h e form  conditions  the  diagrams  concentrations of  appropriate of  The  water  phase,  constant  These  systems.  which  the  lever-arm  allows  the  t e r n a r y phase diagrams.  method  to  retrieval A  set of  ternary of  systems  information  inequalities  is  iv  thereby  generated, data  providing a  free  energy  are  the  t e r n a r y phase diagram.  consistent with I t has  Kullerud.Cu-Fe-S  phase diagram  this  minerals  way  f o r the  pyrrhotite  and  chalcocite  phases.  Secondly, determine several  the  solid  interpreted basic  in  terms  and  G°'s  f o r the which  lower  extrapolation  methods  They at  from  chalcopyrite  New  (aq)  and  were p r o v i d e d  in  account  the  out  in  data  1  F  data  S  0  have  to with were  were p r o v i d e d  monohydrated E  and  order  in equilibrium  4 ( a q )  predicted  for  monoclinic  digenite  a  experimental  important  elevated  Yund  the  resulting  temperature  diagrams  and  leaching at  the  those  the  and  of  sulfate,  CUSO4  for  low  Data  The  energies.  than  p o i n t out  200°C,  200°C.  missing data  applied to  composition  ion pairs  the  available  were c a r r i e d  basic ferric  thermodynamic  discussed. formation  of  account  substantially  Selected  at  the  boundaries  experiments  assemblages  been  which  cubanite, digenite,  rich  phase  both  200°C.  at  idaite,  iron  aqueous  cupric sulfate,  sulfate, The  for  solubility  range w i t h i n  n  d  for  ferrous FeSC»4  results by  +  .  are  classical  data.  been  presented  effects the  temperature.  main  of  ion  and pair  features  of  V  T A B L E OF  CONTENTS  Abstract Table  ii  of content  v  List  of tables  x  List  of figures  x i i  Acknowledgments  xvii  INTRODUCTION CHAPTER  1 1 : THERMODYNAMICS  AND  HYDROMETALLURGY.  1-1  :  a necessary  1-2  :  p r e d i c t i n g phase  1-3  :  the l i m i t a t i o n s of this  guideline.  PART I  :  Pourbaix  1-5  :  computation  1-6  :  scope  5  approach f o r  purposes.  9  diagrams.  13  o f Eh-pH d i a g r a m s .  of the present  A METHOD FOR D I S P L A Y I N G HYDROMETALLURGICAL  3  equilibria.  hydrometallurgical 1-4  3  study.  THERMODYNAMIC  PURPOSES.  17 22  DATA  FOR 25  vi  CHAPTER 2 :  DETERMINATION OF SOLID-AQUEOUS EQUILIBRIA IN ELECTROCHEMICAL SYSTEMS.  •  THEORETICAL BACKGROUND AND PRACTICAL METHOD.  26  2-1 :  d e f i n i t i o n o f the problem.  26  2-2 :  a r i g o r o u s s o l u t i o n o f the problem.  31  2-2-1  :  i n t e r p r e t a t i o n o f the Nernst equation.  2-2-2 :  2-2-3 2-3 :  :  :  2- 3-2 :  CHAPTER 3 :  to s o l i d - a q u e o u s  system.  36  equilibrium equations.  40  a p r a c t i c a l method. 2-3-1  2- 4 :  application  31  43  l i n e a r i z a t i o n procedure.  43  c a l c u l a t i o n of the e q u i l i b r i a .  48  discussion.  55  COMPUTING DIAGRAMS FOR HYDROMETALLURGICAL PURPOSES.  3- 1 :  p l o t t i n g procedure - a f i r s t approach.  61  3-2 :  r e d u c t i o n of computing  3-3 :  u n c e r t a i n t y a t the boundary o f two  3-4 :  61  time.  64  s o l u t e zones.  69  other types o f diagrams.  71  3- 4-1 :  composite diagrams.  72  3-4-2 :  metastable diagrams.  74  3-4-3 :  diagrams with v a r i o u s co-ordinates.  76  vii  PART  II  CHAPTER  THE C U - F E - S - H 2 O  4 :  SYSTEM  CONSIDERED  AT 2 0 0 ° C .  COMPOUNDS AND  80  A V A I L A B L E FREE  ENERGY D A T A .  81  4-1  :  generalities.  4-2  :  available  4-3  :  :  phase  diagrams.  84  4-2-1  :  t h e Cu-Fe-0  4-2-2  :  t h e Cu-S-0  ternary.  85  4-2-3  :  t h e Fe-S-0  ternary.  87  4-2-4  :  t h e Cu-Fe-S  4-2-5  :  phase  available solid  4-4  81  ternary.  ternary.  diagrams  free  84  89  involving H2O.  energy  data  f o rthe  compounds.  t h e G°'s  99  f o r the aqueous  phase a t  200°C.  103  4-4-1  the  4-4-2  available  4-4-3  Criss for  4-4-4  5 :  considered  ionic  a t 200°C.  103 104  extrapolation  solutes.  107  extrapolation for 110  F R E E ENERGY DATA FROM A  PHASE DIAGRAM.  5-1  theoretical  background.  5-2  application  t o t h e Cu-Fe-S  diagram.  >  pairs.  E S T I M A T I O N OF TERNARY  data  solutes.  and Cobble  Helgeson's ion  CHAPTER  96  115 115 phase 125  vi ii  CHAPTER  6 i  E S T I M A T I O N OF SOLUBILITY  F R E E ENERGY  FROM 147  DATA.  6-1  theoretical  6-2  available  6-3  DATA  148  background.  data  f o r the s o l i d  sulphates.  151  experimental.  156  6-3-1  :  apparatus  and e x p e r i m e n t a l 156  procedure. 6-3-2  160 sulphate  ferrous  6-4-2  the  cupric  sulphate  system,  165  6-4-3  the  ferric  sulphate  system.  167 168  conclusions.  THE DIAGRAMS  OF THE  CU-FE-S-H2O  SYSTEM  200°C.  176  7-1  the  Cu-Fe-S-0  7-2  presentation  7-3  the  7-4  interpretation  (+H2O)  phase  diagram.  of the diagrams.  diagrams.  176 180 185  as  projection  diagrams. ,  188  discussion*  193  208  CONCLUSION.  CHAPTER  system,  160  the  AT  7-5  158  results.  6-4-1  6-5  7 :  experimental  discussion.  6-4  CHAPTER  :  8 :  SUMMARIES  AND  FURTHER  WORK.  209  IX  Notations.  215  References.  218  APPENDICES.  229  Appendix  list  I :  of data  available  i n the  literature. Appendix  final  II :  data  system Appendix  the  I I I:  230 f o r the  Cu-Fe-S-H20  a t 200°C.  computer  III-A  :  presentation.  III-B  :  description  III-C  :  how  III-D  :  listing  program.  237 241 242  of the program.  t o use the program. o f the program.  243 248 252  L I S T OF  Table  (2.01)  Classes  of diagrams  system Table  (4.01)  for solid  Cu-Fe-S-H20  Table  (4.02)  G° data  (5.01)  retrieved  sources.  a t 200°C a s r e t r i e v e d  G° data  sources  for solid  Cu-Fe-S-H20 from  a t 200°C a s  f o r s o l u t e s o f t h e Cu-Fe-S-H20  literature Table  compounds o f t h e  system  literature  system  f o r t h e Cu-Fe-S-H20  (m=3).  G° d a t a  from  TABLES  Yund  from  only. compounds o f t h e  system  a t 200°C,  evaluated  and K u l l e r u d t e r n a r y  in this  study. Table  (6.01)  Values  of a j , "distance of  approach",  f o r several ions of the  Cu-Fe-S-H20 Table  (6.02)  system.  Solution composition Initial  system  versus  : 5 0 0 cm3  50 g F e S 0 4 . 7 H 0 + 0 . 6 2  Table  (6.03)  Equilibrium aqueous (mole/kg at  closest  between  solution.  H2O+  g Fe°.  HFSu, Mag, Solution  s o l ) and G° v a l u e s  two l i m i t i n g  time.  potentials.  and t h e  composition (cal/mole)  xi  (Fe)  (S0 ) 4  Table  (6.04)  = 2.847 1 0 "  t  t  System  = 2.923 10-2 m o l e / s o l after acid  presented  Table  (6.05)  G° v a l u e s  (A2.01)  173  i n the run  (6.02).  Solution  (mole/kg s o l ) and A  f o r FeSC^.H^O  G  values  precipitation.  (cal/mole)  solubility Table  addition  i n table  composition (cal)  mole/kg s o l  2  obtained  from  data.  The s o l i d  175  compounds c o n s i d e r e d  i n the  C u - F e - S - H 0 s y s t e m a t 200°C. 2  Table  (A2.02)  The s o l u t e s  considered  Cu-Fe-S-H 0 system 2  Table  (A2.03)  Four  phase  Cu-Fe-S-0  phase  238  i n the  a t 200°C.  equilibria (+H2O)  174  239  of the d i a g r a m a t 200°C.  240  LIST  Fig.(1.01)  Pourbaix at  Fig.(1.02)  25°C  diagram  the  F i g . (4.02)  i n the  system  literature  o f E-pH  diagrams  of  system.  of the discrepancy a r i s i n g at  boundary  plotted Fig.(4.01)  1963).  1973).  Fe-H20  Example  system  f o r t h e Cu-Fe-S-H20  The t h r e e c l a s s e s the  Fig.(3.01)  f o r t h e Fe-H20  25°C, a v a i l a b l e  (Peters, Fig.(2.01)  FIGURES  (Pourbaix,  Eh-pH d i a g r a m at  OF  o f two s o l u t e  by t h e  diagram  and  1964).  Condensed  Cu-S  as  program.  Cu-Fe-0 phase Kullerud,  zones,  phase  below  diagram  560°C  (Yund  (Potter,  1977) . Fig.(4.03)  S i m p l i f i e d Fe-S phase the  Fig.(4.04)  various pyrrhotite  Cu-Fe-S phase Kullerud,  Fig.(4.05)  diagram  diagram  phases. a t 700°C  (Yund  and  a t 200°C  (Yund  and  1966).  Fe203-S03~H20 phase (Posnjak  showing  1966).  Cu-Fe-S phase Kullerud,  Fig.(4.06)  diagram,  and Merwin,  diagram 1922).  at  200°C  xi ii  Fig.(4.07)  CUO-SO3-H2O  (Posnjak F i g . (5.01)  Fig.(5.02)  binary  composition  Schematic molar  diagram  and T u n e l l ,  Schematic vs.  phase  free  a t 200°C  1929).  molar  free  97 energy  diagram.  representation energy  118 of  ternary  vs. composition  diagram. Fig.(5.03)  Positional and  Fig.(5.04)  Fig.(5.05)  120 relation  between  the corresponding  assemblages  conditions  they  determine  f o r G°(P).  Practical  determination of the condition  for  from  G°(P)  t h e phase  Stoichiometric approximation Cu-Fe-S  123  phase  diagram,  o f t h e Yund  ternary  diagram.  a t 200°C  124  first  and K u l l e r u d (atomic  percent). Fig.(5.06)  Second Yund  128  (finite)  approximation  and K u l l e r u d  200°C  (atomic  Cu-Fe-S  of the  ternary  at  percent).  128  F i g . (5.07)  The  (MPyh) - z o n e .  132  F i g . (5.08)  The  (Cub) - z o n e .  132  Fig.(5.09)  The  (Ida) - zone.  135  F i g . (5.10)  The  (FCct)  135  F i g . (5.11)  The  (Dig) - zone.  137  Fig.(5.12)  The  (FDig)  137  F i g . (5.13)  Graphical  solution  equations  providing  and  - zone.  - zone.  G°(FDig).  of the system G°(FCct),  The two p o i n t  of  G°(Ida) circles  xiv  correspond Fig.(5.14)  equations  providing  G°(MPyh) a n d  G°(Cub).  The p o i n t  circle  the data  Expansion  i n table  Three  phase  CU-S-O-H2O  Fig.(7.03)  F i g . (7.04)  Fig.(7.06)  final  diagram.  t  phase  diagram  a t 200°C.  system  181  o f the Fe-S-^O system t  = 10  -  3  mole/kg  of the Fe-S-H20 t  2  = 0.3  system mole/kg  system  182  2  system  at  H 0.  183  2  of  a t 200°C f o r H2O.  s t a g e o f t h e E-pH d i a g r a m  CU-S-H2O  at  H 0.  C o m p u t e r o u t p u t o f t h e E-pH d i a g r a m  Final  at  = 0.3 m o l e / k g H 2 O .  f o r ( S ) = 1 mole/kg  Cu-S-H 0  179  output.  for (Fe)  E-pH d i a g r a m  t  178  diagram.  E-pH d i a g r a m  (Cu)  the  the  of the Fe-S-H20  for (Fe)  (b)  the  Fig.(7.07)  2  computer  200°C  ternary,  and  projection  (+H 0)  (a)  200°C Fig.(7.05)  the Cu-S-0  from  ternaries of the  E-pH d i a g r a m 200°C  uncertainties  representing,  quaternary,  (+H2O)  Cu-Fe-S-0  143  143  diagrams  t o bottom,  The f o u r  (5.01).  f o r the source data are  into account.  Cu-S-0  of  corresponds  and G ° ( C u b ) , when  taken  top  142  of the solution l o c i f o r  (estimated)  Fig.(7.02)  (5.01).  s o l u t i o n of the system  G°(MPyh)  F i g . (7.01)  i n table  Graphical  to F i g . (5.15)  to the data  a t 200°C f o r  189 of the  (Cu) Fig.(7.08)  E-pH d i a g r a m o f t h e C U - S - H 2 O 200°C  Fig.(7.09)  200°C f o r ( F e ) (S)  = 10  t  -  system  mole/kg H 2 O  3  = 10  t  mole/kg  -  mole/kg  3  ( S ) = 10  -  6  t  mole/kg  H 0 2  H 0. 2  = 10~  t  system  system  mole/kg H 2 O  3  H 0. 2  E-pH d i a g r a m o f t h e Cu-Fe-S-R^O s y s t e m at  200°C f o r ( C u ) = 1 0 ~  2  t  (S)  and  = 0.32  t  10  -  2  mole/kg  mole/kg  200°C f o r ( C u ) = 1 0 ~  2  t  2  2  system  mole/kg H 2 O  ( S ) = 1 mole/kg H 2 O .  and  t  E-pH d i a g r a m o f t h e C u - F e - S - H 2 0 at  H 0  H 0.  E-pH d i a g r a m o f t h e C u - F e - S - H 2 0 at  system  20Q°C f o r ( C u ) = 1 0 " 2 m o l e / k g t  (S)t  and  effect  =1  mole/kg  o f the complex  E vs. -log(S) Cu-Fe-S-H20 (Cu)  F i g . (7.16)  - 4  200°C f o r ( F e )  and  F i g . (7.15)  = 10  t  E-pH d i a g r a m o f t h e C u - F e - S - H 2 0 at  F i g . (7.14)  2  ( S ) t = 1 mole/kg H 2 O .  and  F i g . (7.13)  H 0.  E-pH d i a g r a m o f t h e C u - F e - S - H 2 0 at  Fig.(7.12)  mole/kg  t  200°C f o r ( F e )  and  Fig.(7.11)  for ( S ) =1  system a t  E-pH d i a g r a m o f t h e Cu-Fe-S-H^O at  F i g . (7.10)  mole/kg H 2 O .  =0.3  t  = 10  t  -  2  = 10  H 2 O , showing the solute  Cu(HS) ~. 2  diagram of the  mole/kg  H 2 O a n d pH = 7 . 2 0 .  E-pH d i a g r a m o f t h e  Cu-Fe-S-H20 t  2  s y s t e m a t 200°C f o r  Metastable  (Fe)  t  H 0  s y s t e m a t 200°C f o r -  3  mole/kg  H 0 and 2  xv i  (S)  t  after  = 3 10"  2  mole/kg  increasing  H2O,  computed  G°(Ida) a n d G°(Pyr)  4 kcal/mole. Fig.(A3.01)  Typical program.  print-out  by 207  o f t h e computer 251  xv i i  ACKNOWLEDGMENTS  I end  always  o f  a  wondered  book,  colleagues, Maybe y o u  why a t t h e e n d o f a t h e s i s  the authors  were acknowledging  typist, friends, just  need  to  neighbours  live  the  or  wife,  and even  more  situation  at  the  children, sometimes.  because  now  I  understand.  I this  spent  years  d o c t o r a t e program, and then  take  the  thesis  job I presently  I wrote.  opportunity improve to  two and a h a l f  wanted  to start  indeed,  full  to  think  b u t deep  of  i n a hole people  to their  such  the  interruption over  more  situations,  generally  good  I  wanted  I w a i t e d , t h e more I  was  wonder  "very s p e c i f i c " case.  a  t h e whole matter, t o  known no t h r o u g h s t i l l  to  with the  was  Soon a f t e r w a r d s  The  well  France  I was n o t p l e a s e d  again, the less  circle,  to  P e t e r s on  on.  the holes.  changes.  with Dr.  I h a d t o go back  b i t more  i t a l l over  vicious  apply  a  to f i l l  substantial  Classical  rules  I n my o p i n i o n ,  the text,  make  carry  working  I  progressing. road,  whether  obvious general  C l a s s i c a l drama i s  transposed  for  betrayed  husbands.  The time. ghost it,  thesis  I n Vancouver,  has  t h e ghost  o f t h e house  f o r a long  we c o u l d n o t t a k e m u c h v a c a t i o n b e c a u s e t h e  was t h e r e w a t c h i n g  b u t I d i d spend  been  us.  no f r e e  In France,  time  Without  I d i d n ' t work trying  much  t o g e t back  on into  xvi i i  it.  I t  was  efficient on  really having  i s  on i t " . feel  working  f o r the thesis,  on i t " .  The g h o s t  I have  feel  which  like  to  my w i f e ,  almost  i s s t i l l thank  t o my a d v i s o r  couple  of  of  a large  part  weeks w o r k i n g  am h a p p y  the Paris  and  s u p p o r t e d me  I  I know  he makes a n y judging...I  so  long.  from  which  was  now.  I  years  I  would  and encouragement,  disappearing  for a  o f mine w i t h o u t showing  those  namely  urged  about  my  who s e n t me  Dr.  work the  me  during  complete  the actual Dr.  that  that i s  head  Renon  period  this  situations  where  responsible  f o r , b u t I am v e r y a w a r e  put on him.  head  I wish  r e c e n t coming  and a l s o  fact a  Levy,  i s  useful  Head  of  t o U.B.C.  years.  to  who m a d e my  School o f Mines,  handle  T u r p i n , former  f o r two and a h a l f  particularly possible,  Dr.  School o f Mines  who  trip  working  and r e l a t i v e f o r  Peters  discussions  on an i d e a  t o thank  people  joking  or  children,  o f what  him f o r f r u i t f u l  at  Paris  think  he  any  life.  I  the  "Is  laughing  Dr.  but incredibly  a l l t h e h y d r o m e t a l l u r g y I knew t h r e e  f o r h i s p a t i e n c e when s u d d e n l y  sign  family.  " I don't  was t h e r e ,  t o thank  thankful  learnt  ago,  to  useful  stood a "man-having-a-thesis-on-his-back"  I have  that  t o p u t p r e s s u r e on t h e whole  i t ? " ; "He  progress  and  not  that back  Research  (Vancouver) t o thank a l l thesis, to  and  Vancouver  of research of the  who m o r e o r l e s s of time.  precisely and  even  o f t h e burden  had  I am  used  one  of  required my  four  to the  t o be month  xix  I  am  happy  Department  at  during  year  thank  that also  during  I spent  recent  the  like  jumping  feel  light  me  Of c o u r s e  plane.  this  i s finished  already Only  short  thesis  and  t o Hani to  Mark  and I f e e l  a parachute.  relieved.  After  t h e jump, you  B e f o r e t h e jump, w a i t i n g resistance  three years  at  I t i s  from the  at  your  the whole  door  of  a  the pressure of the social  environment  became t o o  physical  I shall  period  you f e e l  mind,  the strength  heat  of  a  my  fifth  feel  intensively  after  my  PhD t h e s i s  i n the people  that  life  you love,  a snow c o v e r e d m o u n t a i n  you  wife),  remained  high.  fifth i n  jump.  a  very  o f time!  you l i k e ,  competent  resistance  be a b l e t o w r i t e  when  ours),  i n debt  t h r e e s e c o n d s ^but  you see happiness  people  feel  I hesitated  Sometimes when  Vancouver  jump:  little  Surely,  stood  first  i n  I  the text.  on t h e a i r .  I r e m e m b e r my  particularly  autoclave leakages.  I also  checkproved  I never  the metallurgy  a l l facilities  there.  typing  i n  i n my w o r k ,  with  o f the plane, you face p h y s i c a l  body.  (my  me  a plane with  hanging  people  i n fighting  thesis  from  the  helped  staying  who h e l p e d me  Now  door  U.B.C. who  who v e r y k i n d l y  Seebaran  thank  t h o s e who o f f e r e d  my  Henein  to  peak  s u n s h i n e on y o u r Japanese  restaurant,  Lebanon meal "dessert  skin;  the smile  of the  a  more  meal  Point"  and C a r o l y n from  blue  coming  (good  sky;  into  your  simply  the  - Sashimi  " c o q u e l e t aux r a i s i n s "  from John  Maman  reasoning or a t a good  living,  i n  t h e v e r y m o m e n t o f a "new" i d e a of a rigorous  i s worth  from  from  a  Odile  friends  of  Andre-Pierre (another very  XX  good  friend  o f o u r s ) , my  own  " r i z au  lait"  (I  have  to  f i t in  somewhere) or  I to  share  another,  understand your have  a t t h e end  now  that  happiness  "backed  you  thesis!  an acknowledgment  with up"  of a  a l l the people during  the hard  i s an who, days.  opportunity  i n one  way  or  And  so  do  1  I N T R O D U C T I O N  2  PREAMBLE  "The  study  and  equilibria-. task.  is  In  confirm tests  and  cases,  mapping  most  obtained  i n the  industry. i t  to  systems  deals  consisting  hydrometallurgical  from  their  o r e s r e d u c e s t o an described  transformations. thermodynamic  information results  methods  in  i n the  Nevertheless, electrochemical system.  by  However  hydrometallurgists  not  terms  of of  systems  and  free  always  problems  a  few  to  new  should  of  be  thermodynamics solutions,  extracting  is  metals  should of  be  energy  time,  the  available  provide  the  guidelines  Collecting  a  remain  involved,  only  practical  point  science  energy data,  diagrams  are  may  aqueous  a whole,  present  need.  will  In  entropy decrease, which  at the  do  several  minerals As  tedious  (1978)  thermodynamics,  would  form  Rosenqvist  purposes.  and  further."  the a p p l i c a t i o n  of s o l i d  for  entirely  with  phase  in  which  investigated  study  i t  results  however,  T.  long  cases  possibilities  This  a  of  such  thermodynamic  and  displaying  classical  procedure.  u n s o l v e d , when as  the  the  complex  Cu-Fe-S-H20  3  CHAPTER 1  THERMODYNAMICS AND  SECTION  1-1  : a necessary  Chemical solutions  form  scientists. genesis  Their  exploration. solid order  of  goals  o f hydrothermal  environments  guideline. •  reactions a field  i n  between  Corrosion  solid  broad are  mineral  order  HYDROMETALLURGY.  to  interest varied*  provide  engineers  their  Hydrometallurgists  investigate  minerals  i n aqueous  of  components,  their  economic  recovery  desirable outline  take  place  the  aqueous  under the  i n order  t o s e t up  I n each  case  i n practice.  with for  selective  orebody  i n  which in  conditions. leaching  of  reprecipitation  processes  allowing  their  however, one needs which  their  environments,  working  from  and  study the  ways  s o l u t i o n s , , and the s e l e c t i v e  o f t h e range o f c o n d i t i o n s under  reactions  guidelines  o f t h e u s e f u l compounds  quality.  engineers  in relation  analyse  resistance  for  and aqueous  Geologists  deposits  materials deteriorate i n various t o improve  minerals  ores a  an  i nthe reliable  a number o f g i v e n  4  Providing task.  Water  solutions pairs,  such i s  involve  a  a  composition,  and  must  a l l be  from  leaching  natural  despite process  deal  large  of e f f o r t  laborious.  typical.  Numerous  of  have  for  similar  importance  the systems r e s u l t i n g  to take  n o t been  The  case  described this  into  papers from  have  aqueous  solutions are promising.  by  induces  account  fast,  separation,  the  reduction  requires  much  less  classical  low temperature  ever  the  solid  recovery overall  and  explored conditions  Cu-Fe-S-H20  system i s  dealing  High  of  200°C, leads  copper  energy  Cominco  to  most easy  by h y d r o g e n  than  Yet only  conditions.  with  temperature  140°C a n d  precipitation  electrowinning.  Gordon  results,  of these  published  Between  of  However,  systematically  been  r e c e n t l y under these  Sherritt  to the study  solutions.  c h a l c o p y r i t e CuFeS2.  are r e l a t i v e l y  piloted  devoted  the study  of  recovery  by  solution  a v a i l a b l e experimental  copper  developed  and  to  and  aqueous  i n t e r e s t i n g and  remains  has been  leaching  completely  has been  and  number which  potentially  solid/liquid  ion  of p r a c t i c a l  systems,  minerals  conditions  reactions  aqueous  including  behaviors  Also  be  difficult  and  sensitive  into account.  (and g e o l o g i s t s )  between the  Mineral  are often  cannot  a  systems.  great  reactions  solutes  miscellaneous  ores  i s  solvent,  of  very  simple  hydrometallurgists  A  are  peculiarities  component  more c o m p l e x  polarized  clusters.  show  taken  information  variety  and  and  These  remain  highly  processes  systems.  their  relevant  large  complexes  crystallization  a  by  one  This  the  process process,  (Swinkels  and  5  Berezowsky, older  1978;  Sherritt  Kawulka Gordon  sulfuric  acid.  reached  maturity,  efficient guide  i s needed  setting  up  a l .  and  may  1980).  Basic  for classifying  SECTION  : p r e d i c t i n g phase  1-2  phase e q u i l i b r i a  from  of  to  equilibria  are  thermodynamics.  phase  Gj in  j  be  in  has  not  for  yet  s u b s t a n t i a l y more seems  lacking.  retrieving  The  efficient  up  general  and  means  allows  relatively  calculated  data, the  A for  maximum  i n the  formulation,  for predicting  for a  large  quickly.  framework used  of  body Phase  classical  throughout  this  briefly.  by  i t s own  njj's  are  the  i n phase  j .  the  njj's,  and  given  only  on  at  Gibbs  free  energy  /i;'/= l , . . . , N j  constituents  the  and  data,  built  is described  the  leaching  equilibria.  selected  =Gj(njj,P,T)  which  made  an  available experimental  provides  widely  is recalled  be  i t  of  them.  Thermodynamics  information  improvement  chalcopyrite  knowledge  a d d i t i o n a l experiments of  i s an  research,  s t i l l  out  Each  for  extensive  information  study,  1978),  f  process  Despite  (Peters,  et  concentrations  The  numbers  functions  temperature x j j of  the  model  eq.(l.Ol) of  moles  the  Nj  homogeneous  in  Gj  are  and  pressure  species.  of  they  depend  6  Heterogeneous distinct moles  systems  phases.  dividing  rewritten  represented  A phase  Mj i s s t r i c t l y  . i=Nj • •Hi =• Z " i i i=l By  are  a  j i s p r e s e n t when  juxtaposition i t s total  of  number o f  positive  > 0  by  by  Mj  , different  e q . (1.02)  from  zero,  eq.(1.02)  can  be  as  . i=Nj Z i=l in  which  When is  x j j= 1  J  eq.(1.03)  x j j denotes phases  the molar  ratio  of species  are present, the free  t h e sum o f t h e f r e e  energy  i i n phase j .  o f t h e whole  system  e n e r g i e s o f t h e phases j=J  G(ni,...,n ,P,T) N  In the  =  I Gj(nij,P,T) j=l  eq.(1.04), N denotes system.  remaining  the total  I t i s assumed C =  (N - r ) .  components o f t h e system  that Here  eq.(1.04)  number o f s p e c i e s  r species C  i s  i n the sense  present  i n  c a n b e made o u t o f t h e  t h e number o f i n d e p e n d e n t of the Gibbs  phase  rule.  Let i=N I i k i=l c  be  i  B  =  the r independent  stoichiometric of  k=l.,...,r  0  the  considered  chemical reactions,  coefficients  system.  Any  as s e v e r a l  transfer  of  a  expressed  as a  described  i n t h e same  e q . (1.-05) i n which  and t h e B j ' ss t a n d f o r  the c ^ ' sare the  species  present  i n  several  distinct  species  of  the  species chemical  from  one  reaction  framework.  phase such  to as  species  phases i s  system.  another  eq.(1.05)  Any  i s then and  i s  The  r  equations  such  restraints,  and i n c l o s e d  conforming  to these  r  independent  from  any  species  as  eq.(1.05)  systems,  restraints  defined  by  B j , a l l the possible  through  such  any  mass  balance  virtual  transformation  i s characterized  by t h e v a l u e o f  extents of reaction  state  represent  l .  To b e s p e c i f i c ,  k  the  number  o f moles  compositions of the  t r a n s f o r m a t i o n s c a n be e x p r e s s e d  starting  n j  0  of  closed i n the  each  system following  form  nj In  k=r T c j k=l  = ni° +  eq.(1.06), the l  the  n j ' s remain  At  constant  any v i r t u a l  above,  independent <3G  The such  energy  state i s  of the  whole  by  =0  eq.(1.07)  transformation  eq.(1.07)  starting  restraints. i s  from  this  state  In the "reacting"  equivalent  to  the  and  system  following  r  equations  I k  lP/T,li^l  = - A  k  = 0  k=l,...,r  eq.(1.08)  k  A 's are the chemical a f f i n i t i e s k  that a l l  I  I I d l  such  and p r e s s u r e , an e q u i l i b r i u m  i s then determined  to the various  described  to values  by a minimum v a l u e o f t h e f r e e  N  I  ' s are restricted  T h i s minimum  conforming  eq.(1.06)  k  positive.  <fc ( n i , . . . , n ) for  l  temperature  characterized system.  k  k  of the respective  a s e q . ( 1 . 0 5 ) , and c a n be e x p r e s s e d  as  a  function  reactions of  the  8  chemical  potentials  I dG I  i=N A  = - T  k  p i by u s i n g  i=l  I I  eq.(1.06)  I d n iI I I  x  I d n i |P,T,nj^ni  | <Jl i=N  = -I  Ci .. i = l  Open  systems  closed  are  systems  which  equilibrium. apply  The  in  equilibrium coincide  Therefore,  to the equilibrium  range  of conditions  present  solving  the r equations such  such  can  as eq.(1.03)  degrees given  of  be  o f open  which  a  time  t  states  i s reduced.  exist  system  i s therefore  x j j .  and  the  with  For instance  njO's,  the N equations such  for  unknown M ' s . k  indifferent unique  the  (Heidemann,  N  unknown  J  equations  a system  to  occur. the  the range  the system  of  i s then  completely  possible  defined  by  with  a l l the  as e q . ( 1 . 0 6 ) , t h e r e q u a t i o n s  state In  of  i s closed  as eq.(1.02)  n j ' s , t h e r unknown  equilibrium  states  1978).  state)  when  and t h e J e q u a t i o n s such  The  solution  J  p r o v i d e d by  The maximum number  of such  on t h e s y s t e m ,  (initial  solved  also  rule  a given state  as eq.(1.08)  in  eq.(1.10)  restraints  then  the  are  as eq.(1.08)  reacting  variance, v  when  f  systems.  as eq.(1.08)  phase  at  t  = N - r - J  When m o r e  such  them  in equilibrium  or  by t h e c l a s s i c a l  v  at a given time  f o r t h e N unknowns  freedom,  e q . ( 1 . 09.)  equations such  states  phases  k  Ui  k  with  the  under  11 j ^ l  k  i s totally  such  reaction  a  l  k  can  ' s and t h e J  defined  c a s e , t h e r e may  equilibrium  be  unless be  no  computation  9  It  must  involving state.  be  noted  the  nj's  For  that are  C  independent  sufficient  instance  when  to  the  known  state)  system,  then  the  r equations  such  as  of  a  equations, such  as  closed the  eq.(1.02)  unknown  can  be  a  result,  the  allow  in  determination  to  available  reaction  for  i t  non-ideal large  C  given  equilibrium mj°  the  N  of  state  corresponding  eq.(1.08)  for  the  amounts  a  information  and  unknown  C  (initial  mass  the  the  J  balance  equations  nj's  and  the  J  k  phases c o n s t i t u t e very  make  for  of  M 's.  As  they  solved  define  total  independent components are  pieces  range  SECTION  of  1-3  be  priori  solved.  fact  imply  any A  energy of  problem  number o f  deal and  free pieces  equilibria  to  phases  (George  with  seem  of  information, of  phase  et  a l . ,  since  methods  1976)  to  are  .  including  enough  the  equilibria  computation  systems  flexible  functions  They several  handle  a  problems.  : the  hydrometallurgical  The  powerful  principle  possible mixed  Gibbs  purposes.  that that  persued.  However,  account  when  an  four  approach important  this  purposes.  of  this  approach  for  /  approach  the  using  hydrometallurgical  limitations  has has  limitations no  factors  approach  to  value must  and be  aqueous  does  not  a  should  not  be  taken systems  into for  10  1)  In order  the Gibbs  free  considered the  t o be f u n c t i o n a l , energy  model  i n the systems.  ideal  solution.  expressed  t h e above  formulation requires  (eq.(l.Ol))  of  a l l the  The s i m p l e s t m o d e l  In  this  case,  phases  i s referred  the  functions  to as  Gj  are  as i= = Mj Z i=l  N  Gj(nij,P,T)  j  x j j (G°(i,P,T) + R T l o g X i j ) eq.(1.11)  Each phase  i s then  component, state,  generally  volume).  regarded  solutions models  described  of  solutions proper  pure  dilute them  i n a wide  equilibria,  i s  Reliable  not  available  Several  Semi-empirical  temperature  partial  They  of  suitable  be for  However,  multicomponent  and t e m p e r a t u r e s . and  ideal  several will  cases.  can  for  The  solid-aqueous  can  only  often  sparse  be  time.  data  values  cases  concentrated  approach  i n t h e framework G°  standard  compounds  are  per  c a p a c i t y and  solutions,  them  yet,  thermodynamic  compounds.  solid  for specific  describe  at the present  even  elevated  or  in a  heat  proposed. of  thermodynamic  fragmentary,  temperature.  been  Several  yet  G°(i,P,T)  are limiting  range o f compositions  the  semi-quantitative  2)  6.  most  F o r aqueous  have  solutions  can  model  (partial  which  compositions).  chapter  function  by i t s v a l u e G°(i)  derivatives  phases,  non-ideality  relatively none  as  in  one  At low temperature,  (fixed  of  by  provided  and by i t s p a r t i a l  partial be  described  are  of ideal are  already  relations heat  solutions  are  and  missing  at  available  capacity of ions  and pure low for  ( C r i s s and  11  Cobble, data  1964;  Taylor,  remains  complex  and  at  of  Furthermore, synthetic natural  elevated  them  comparison  information  the  aqueous  1967).  be  Several (Millero,  only.  in  the  their  laboratory  are  compounds a r e  a v a i l a b l e data  most  may  solutes  hydrometallurgists  and  experimental  solutes  (Helgeson,  measured  crystallized,  from  dealing  generally  "true"  G°'s  corresponding  with neither  may to  on  differ  the  same  phases.  thermodynamics  engineers  relative  are  while  these  temperature  These n a t u r a l  well  Classical  room  for  with  i s available for  although  temperature  data  minerals.  synthetic)  while  at  most  substantially  3)  No  solutes,  materials,  nor  (but  but  volumes were determined  1 9 7 7 ) , most  pure  limited.  neutral  predominant partial  1978),  are  mainly  importance  only  provides  equilibrium  interested  in actual  kinetic  factors  of  states,  reactions.  The  depends  upon  circumstances. For  instance,  have  formed  occurring  geologists over  close  effect,  and  valuable  source  these  Conversely, within "slow",  a  thousands  to  of  be  of  data  may  for  have  Even up  The  very  the  slow  having  equilibrium  which  may  reactions  substantial states  conditions  form  under  a  which  occurred.  hours.  Under  and  for  practical  any  assemblages  end  resolving  hydrometallurgists  with  years.  considered.  few  equilibrium,  mineral  e q u i l i b r i u m may  must  reactions  observe  are  these  seeking  to  conditions,  purpose,  substantial driving  they  forces.  complete  reactions  most  reactions  take  place  far  are from  12  Outstanding chemistry 1950),  examples o f of  sulphides  or i n the solid  case o f sulphate  S O 4  in  with  equilibrium  states.  Nearly  metastable  slow  2  either state  Putnis,  must be s t r e s s e d ,  -  sulphide  systems,  states  at  of  low  often  are  i n aqueous  (e.g.  other  a l l  hydrometallurgists  reactions  provided  solutions  the  (Valensi,  1977 and 1 9 7 8 ) .  since species  economic  o f lower  The  ever  valence  importance  of taking  The  i ti s hardly  temperature.  consists  by  exhibit skill  advantage  of  of these  peculiarities. As  a  result,  considered evidence  4)  A  is  that,  too theoretical on a c t u a l  further  M 's  rather  though  states  have  range  parameters  are  convenient the As  long  as  a function  within  the view  critical  diagrams  of  itself by  i s often  experimental  these  a selected  either  dissolved  or  provide,  at a glance,  process  design.  outlined  i t provides  I n many a  these  parameters,  i s stable,  decomposed. the conditions  and t h e  at  two  I t  parameters  would  as  accurate,  the  single would  range  three be  equilibria  of  co-ordinates. they of  diagrams  o f maximum  or then  and t h e r e f o r e  These  1-2  i n a c o n t i n u o u s and  cases,  process.  are reasonably  phase  them  of the solid-aqueous  with  section  Hydrometallurgists  of the solutions  in  in  the n j ' s of a l l species  system.  a display  on d i a g r a m s ,  as these  which  of  of conditions.  t o have  system  to the approach  present,  a partial  much w i d e r  by  and must be s u p p o r t e d  i tprovides  a l l phases  equilibrium  information  reactions.  limitation  even  of  k  thermodynamic  provide, conditions cannot  be  may  also  opportunity  for  13  For  corrosion  engineers,  co-workers  ( P o u r b a i x , 1963)  a  of  number  collecting systems, them  these  in displaying for  i n the  well  It  would  of  be  last of  i n the  point  complex  1-4  of  systems, the  data  solid  h i s co-workers  (Pourbaix,  main  and  purposes.  work  has  Most  been  display  for an  a similar  difficulties  the  that  the  of  complex  summed  work  l i e  for  i n . the  solid-aqueous  systems.  This  appropriate representation one  cannot  types  of  equilibria  publication 1963).  electrode potential  namely  this  undertake  aqueous  and  solutions,  diagrams,  Metal-H20  always  take  diagrams.  after  important  in  in discussing  in  felt  become p o p u l a r  most  consisted  on  Without  has  co-ordinates,  overcome  already available. '  : Pourbaix  Representing  to  his  for  diagrams  i t is  and  room t e m p e r a t u r e  to  The  and  i s important.  advantage of  SECTION  form  Pourbaix  work  engineering  desirable  data,  of  (ibid.).  purposes.  reliable  equilibria  data  This  c o n s i d e r e d , and  known A t l a s  hydrometallurgical lack  these  at  corrosion  Metal-H20 systems were up  data  work  a s u c c e s s f u l attempt  difficulties.  thermodynamic  thoroughly  was  the  Eh  reactions  electronic  and  In  of  the  these  and  pH,  among ionic  on  Eh-pH  work  of  diagrams, account solids  exchange  diagrams Pourbaix the for  and  two two  aqueous  reactions.  14  These  Eh-pH  constant Several  diagrams  (or Pourbaix diagrams)  t e m p e r a t u r e , c o n s t a n t p r e s s u r e and levels  of metal  corresponding  solute  diagram  for  activity Fe-H20  the  are calculated  unit are  water  activity.  displayed.  system  at  The  i s presented in  fig.(1.01).  Several For  rate  instance,  state  under  H2(g)  and  data are  aqueous  low  high  decompose t o 0 2 ( g ) . water  is  still the  stable  under  which  Insofar  as  metals  film,  in relation  text  the be  reader,  and  this  Following made t o a d a p t have  memorized  explains  Pourbaix's  displayed  at to  rate  which  in  for  directly contact  conditions surface.  a  type  given  The data  diagrams  of  which are  provided i n the  further  use  the  the  real  by  the  Atlas.  numerous a t t e m p t s have  to other f i e l d s .  High  on  for  Eh-pH d i a g r a m s  are  account  the behaviour of for  to  the metal  the success of  work,  in  (Eh-pH) w i t h i n  provided.  a , result,  to  metals  of c o n d i t i o n s  As  largely  region  the diagrams  form  a number o f  these diagrams  been  to  with  efficiently  reduce  represent the  related  also  metastable  where H 2 O s h o u l d  the  the  also  be  in a  should  +  in order  for  likely  is  Atlas.  can  are  diagrams.  solid-aqueous equilibria  region,  They  range  passivate  systems  where H  In p r a c t i c e ,  can  the  but  these  remain  conditions  immunity  solutions.  discussed of  of  oxide films  may  this  of water.  passivation  protecting  in  In Pourbaix diagrams,  the c o n d i t i o n s  aqueous  often  potential  i s depicted,  metastability  with  can  conditions  represented outside  provide  data  systems  potential  under  incorporated  been  temperature metallurgical  15  -2  0  2  4  6  8  10  12  14  16  PH Fig.(1.01) Pourbaix diagram f o r the Fe-E^O system at 2 5 ° c  (Pourbaix, 1963).  16  purposes have in  (Robins,  been  order  t o account  and  Valensi  experiments the  on  a  coefficients Robins,  been  Pourbaix  system  Other  NaOH-H20  L i n  Christ,  1965).  All  the  the  and C r a i g ,  systems  diagrams  1978),  CU-L-H2O  recently  systems  are  1972).  corrosion  on  been  activity and various diagrams  Eh-pH20 d i a g r a m s i n  The  1976)  method to  widely  provided  by  also  displayed  data  by  several and  geologists  (Macdonald  1976).  t h e thermodynamic  been  (Garrels  used  where  have  include  engineers  (Peters,  have  p02(g)-pH  considerations  are  Data  the effect of  extended  under  polarization  (Edenborough  (Santarini,  engineering.  i n this  constant  purposes.  1979) and h y d r o m e t a l l u r g i s t s published  assuming  For instance,  been  f o r several  solution  allow  solutions  above  (Pourbaix,  co-ordinates  species,  (sulphite,  from  solutes  also  diagrams  represented  data  predominant  f o r corrosion has  has been  by  needed  oxysulphides  o f t h e aqueous  t o be e m p h a s i z e d .  ligands  been  ideality  U-H2O  (1963)  the  Moreover,  designed for geological  calculated  (Vaugham  of  incorporated  f o r the  concentrated  al.,  been  1969).  parameters have  (1950).  from  Metastable  t h e G°'s o f s e v e r a l  polysulphides)  have  departure  included  1970).  f o rt h e a c t i v a t i o n energy  The m e t a s t a b i l i t y  thiosulphate, by  Manning,  determined by modifying  reactions.  way  1968;  et  An a t l a s h a s of  various  on Eh-pH d i a g r a m s  (Duby,  1977) .  Hydrometallurgists complex  systems  Including  and g e o l o g i s t s several  a r e mainly  metallic  dealing  components.  with The  17  method  presented  by  Garrels  and  Christ  diagrams  for  number o f  components  increases.  possible  reactions  between  eliminating  multicomponent  the  resolving  diagram  1973)  is  represented the  results. use  published  method  At  digital  available  the  systems It  the lines  s u c c e s s i v e l y the  recent  systems,  portions of  (1965)  becomes consists  species which  in  the  f i g . (1.02). and  end  sixties,  the  for plotting  computational  are  methods  when  the  writing system,  "not  the  and  in  relevant"  by  arise.  The  system  (Peters,  However,  C h r i s t leads  for  to  most  complex  questionable  investigators started  these are  tedious  the  Cu-Fe-S-H20  of G a r r e l s  computers  of  c a l c u l a t e Eh-pH  in  discrepancies which  for  of  to  diagrams.  discussed  to  Presently  i n the  following  section.  SECTION  1-5  An has not  extensive  been be  : computation  published  described  of  review  Eh-pH  of  the  recently  thoroughly  diagrams.  various  (Linkson  again,  but  computing  et  techniques  a l . , 1979).  They  several points  are  will worth  emphasizing. 1) All of  the  the  equilibrium techniques  equations.  published  electrochemical equation,  balanced  between  1973).  A Nernst  system  as  a  the  two  equation  f u n c t i o n of  so  f a r are  based  on  allowing a metallic  metal-containing then the  expresses chemical  the  a  single  component  species  (e.g.  potential  potential  of  Eh  type to  be  Duby, of  the  a l l species  18  0  2  4  6  8  10  12  pH Pig.(1.02) Eh-pH diagram f o r the Cu-Fe-S-I^O system a t 25°C, a v a i l a b l e i n the l i t e r a t u r e ( P e t e r s , 1973).  14  19  involved Nernst  i n the  corresponding  equation  is  metal-containing  2) The  difference noted  generated  between  between  solids  equations  metal-containing  species  solutes).  Verink  In  (1967),  3) In  the  This  by  other  and  solutes  i n the  p o s s i b l e p a i r s of .-, 1  authors  make  system.  no  I t must  be  Pourbaix  (1963)  classified  the  according  to  the  nature  the  one  solid  solids,  solids  procedure  play  peculiarity  imposed  input  of  the  data by  of  generally  considered  f o r each  equations between  and  line  solute  be  is also  the  and  of  one  put  solute,  forward  same p a r t  Verink's  and  method  by  are  seems  not  to  be  system  is  an  on  system  set  conditions  to  such  solutes  each  and  species  i t s free  energy  compounds w i t h as  method  the  the  of  diagram.  agree as  since with  too the  constant  i s often  an  UJ. =  lead  in  0.  to  A  a  and  phase  relation hence  to not  conditions  are  rule.  way  Nernst  is  activity  improper  are  fixed  The  procedure  many  its  Solids  data.  system,  This  the G°(i)  UJ  input  classical pH  of  potential  introduced  consistent  imposed  metal-containing  pure  Eh-pH  thermodynamically the  systems.  chemical  in this  p o t e n t i a l Eh of  the  programs,  its to  generated the  the  on  i t s composition,  state,  of  a  solutes.  far  (two  and  conditions  standard  a  the  Such  adopted.  characterized  pi  and  "simplified"  solutes  distinguished. broadly  a l l  so  originally  electrochemical  two  solids  published  that  for  equation.  species.  distinction  programs  electrochemical  of  However, for  a  a l l  expressing  20  a condition  imposing  solution. could not  be  P o s t and correctly  follow  4) The  this  Robins  of  computer. the  plot  In  The  first  Brook's  and the  diagrams  systems  for Metal-H20 of  the  diagram.  specific  Several  The lines  by  the  such  systems.  the  the  point,  each phase  published  by A  for  right  In Duby's  o f an A  stable  by  compute  point.  No  at  this  1972).  on  the  for  all,  (1973)  species  derived can  then  point  (Duby,  actual  denoted  of  1973; by  boundary  the diagram by  is  from  the diagrams  a  are  symbol  point.  F r o n i n g e t a l . (1976)  line  and  at each  regions of  being  to  equation to  simple algorithm  They  various point  and  program  inequality  compound  the  S-H2O,  program once  a  remained  the  metal-containing  1979).  but  stable  defined  to  for instance  programs were p u b l i s h e d  area point  the diagrams.  the  equation.  Brown,  plotted,  program of  and  made b y  was  fed  R o b i n s , 1969 the  the s i g n  to determine  the p l o t t e d  of  f a r do  E as  plotted  used  choice of  respective  considering  was  and  Eh-pH d i a g r a m s ,  the  point  so  to computing  temperature  (Biernat  the diagram  generated  plotted  a program  (1971), the  of  line  at elevated  be  is  "right"  Such  corresponding Nernst  line  limited  t o be  the  scanning  the  stability.  the  stability  Osseo-Assare  of  condition  the programs p u b l i s h e d  programs were  program  by  last  choice of  valid  determined  this  equation  of a pattern  only  how  electrochemical  r e p r e s e n t e d on  basis  showed  f o r each  Fe-S-H20  and  concentration  procedure.  investigators.  the  Fe-H20  pH  metal  (1976)  handled, but  first-generation  to  constant  determination of  function  be  a  corresponds  t o an  determines  the  equilibrium  {P}  21  with  one  degree  equilibria a  {Q}  segment  whenever then degree  of  present,  points. plot  line  such  is  a  has  been  presented  process.  The  successfully  At  the  present  However,  a  can  methods  (1977),  resulting of  one  with  more  the  program  the diagram  of  based  two  is as  very soon  the  does of  not the  method two-phase  efficient as  and  stable  this  on  one  compound  e t a l . (1976)  improvement  can  the  for  first  one  computed. the  set  problem  of  of determining  possible  equilibria  the is  stable solved,  way.  none o f systems  whether  implemented  Such  algorithm  equilibrium  to  diagram  of a l l the segments  by  a l t h o u g h complex  f o r complex wonder  of Froning  Rosof  i n the  An  between  An  efficient  hydrometallurgists, diagrams  line  points  to {P}.  of these e q u i l i b r i a ,  printed.  time,  among i n an  of  t h e end  a l l the lines  been  "stable"  with  stability  the program  has  One  the  segment  and  as  correspond  i s added  g e n e r a t e s , f o r each  checks  plots  points  are s t a b l e .  a l l the e q u i l i b r i a  are computed  sometimes  {Q}  freedom,  line  equilibria  represented  that  the diagram, but  generating  end  more compound  equilibria  Actually,  simplex  one  Its  written  then  eventually  freedom.  i n which  of  two  be  of  systems  become more u s e f u l  these programs.seems such  there  as  i s any  i n the above  the  to  Cu-Fe-S-H20  internal  computer  able  limitation  programs.  for  compute system. i n the  22  SECTION  1-6  : scope  In  this  investigated generated  at  the  of  lines  required  linear  in  the  Nernst  and  stability  section  for  to  simplicity. diagrams diagram rules  in  be  order  yield.  I t must  f i g . (1.01)  seems  Fe°  i t  are present  condition  for  Fe  2 +  the  be  and  is  of  the phase  a gas on  and the  an  Eh-pH  useful  defined.  Any  t o be  a diagram The  aqueous of  phase) Fe  aware i t  such  horizontal  equilibrium  2 +  .  the  grounds  discrepancies  that  A  thermodynamic  in order  the  activity  this  assumptions.  consistent  well  rule.  t o an  be  computing  a l l t h e most  on  in  may  Nevertheless,  discussed  even  It  strict  i s based  outlined  counterpart to  Actually  for instance,  i s imposed  Therefore,  approach  features.  corresponds  (Fe°,  are  for  under  Eh-pH  inequalities  simplifying  computed  must  noted,  linear  above  provides  to v i o l a t e  and  be  for generating  equilibria.  several  approach  limitations be  then  computing  solved  t h e r e i s any  useful.  assumptions  inherent  be  diagrams  for  i n the  phase  metastable  information  the  one  on  be  thermodynamic  simplifying  phases  to  than  presented  based  incorporate  the  between  methods  above  only  whether  d o e s n o t h a v e t o be  classical  of  inquire  must  diagrams  and  calculating  The  will  must  of  determination.  seems much s i m p l e r  relevant  data  equations are  fundamentals 1-2  system  form  presented  diagrams  for  Cu-Fe-S-H20  purposes.  method  the  study.  Thermodynamic  display  the only  the  200°C.  hydrometallurgical  diagrams,  the present  study,  and  In  of  may as line  where  three  and  where  For  a  three  23  component  system,  must have  zero  point.  This  A  an  equilibrium  degrees  of  freedom  problem  number  Cu-Fe-S-H20  of  poorly  value  of  temperature, results  are  allows  a  directly  of  the  extensive  evaluated,  in a  that  body  the  of  experimental  This The  goal  study of  I  i s to  computer programs  program already  a  large  for  generally partial the  be  pH,  gas  can  such  results  of  these  be  and  data,  the  but  they  i n terms of  are  the  data  These  phase  only  must  with  rule  cannot  be  data  a l l  f r e e energy  compatible  or  decomposition  and  f u n c t i o n s are These  determined.  pressure.  phase diagrams,  of  nature  as  partial  the  number  a c c u r a t e l y determined,  link  be  data,  the  whole  parts. problem  Pourbaix-Verinck's  A  systems,  which  two  Pourbaix's  programs,  s e c t i o n 1-2.  f o r complex  missing  data.  computed  diagrams  single  can  equilibria  implemented of  a  present  calculations.  equilibria,  approach  as  phases  is divided into  Part  are  However,  f r e e energy  solid-aqueous as  data  c o n s i s t e n t manner,  computed  temperature  represented  functions  on  treatment  since  constant  Sometimes, o n l y  the  reported  first  be  available,  potential,  allowing  so  are  thermodynamic  often  used  200°C.  composition  redox  and  energy  exploited.  composition  Sometimes, a phase the  at  at  be i n t e r p r e t e d .  free  results  remain  average  will  system  experimental which  such  method and  should  published, at  and  the will  will be  least  more  be  displaying  method  rigorous be  of  widely  thermodynamic  devised  to  generate  implemented efficient  in certain  than  aspects.  as  a the  24  In  Part  I I ,  investigated. and  to apply  selected  and  Cu-Fe-S-H20  The g o a l t h e method  diagrams,  important at  the  which  s y s t e m ... a t .  i s to generate  i n Part  will  discussed.  to hydrometallurgists,  elevated  as  where  aqueous  where p o t e n t i a l i t i e s  exist  f o r new  temperature sulphide  resulting  at which  compounds,  temperature reactions  processing.  data  In  reliable and  the highest  f o r solutes  are fast  at  200°C  may  system  remain  i s  needed obscure  hydrometallurgical i s  data,  a set of  i s s t i l l  200°C  be  copper  the  lowest  a r e a v a i l a b l e f o r a number temperature  at which  be e x t r a p o l a t e d .  and,  t h e r m o d y n a m i c d i a g r a m s may  hydrometallurgists.  set of  This  systems  addition, data  will  I t o compute  information  temperature,  concentrate  a consistent  presented be  200°C  at  this  be more  of  the low  Finally,  most  temperature,  the  directly  useful  to  25  P A R T  A METHOD FOR  I  DISPLAYING  THERMODYNAMIC  DATA  FOR H Y D R O M E T A L L U R G I C A L  The  problem  representation Ci  Cm  several them  - H  2°  of  the  systems.  different  providing  implemented  i s to obtain,  PURPOSES.  in a graphical  solid-aqueous The method  classes  as a computer  kind  program  equilibria  reliable  "for  presented i n chapter 2  of diagrams  a specific  form, a  complex allows  t o be d e t e r m i n e d , e a c h  of information. i n c h a p t e r 3.  This  of  method i s  26  CHAPTER  DETERMINATION IN  OF S O L I D - A Q U E O U S  ELECTROCHEMICAL  T H E O R E T I C A L BACKGROUND AND  In problem  the systems of  in  s e c t i o n 1-2.  based of  solved  on  generating  fundamentals  diagrams  SECTION  : definition  same  approach  unknowns and e q u a t i o n s the  significant  imposed  on t h e  hydrometallurgical  1)  will  as P o u r b a i x ' s ,  generally  depending  be  outlined  be  presented,  with  the purpose  systems  and  are  are  leads  upon  Several  problems  Hydrometallurgists  approach  can  the  such  as  the  of the problem.  parameters system.  with,  equilibria  method  f o r multicomponent  system.  A  are dealing  solid-aqueous  practical  Cu-Fe-S-H20  2-1  P R A C T I C A L METHOD.  by f o l l o w i n g t h e r i g o r o u s  A more  t h e same  EQUILIBRIA  SYSTEMS.  hydrometallurgists  determining  theoretically  2  the  the  to a different considered  nature  points  must  of the be  set of species,  restraints  noted  when  considered.  dealing  with  multicomponent  27  solid-aqueous several  ligands.  phase, a  be  and  concentrations inadequately  of  known.  d i f f e r e n t independent  be  e a s i l y measured,  a  few  solutes,  development  of  pi's  l e a s t of  (or  near  at  individual  The  devices  most  specific  future.  with  xj's will  restraints  be  on  the  hydrometallurgical  are  often  aqueous phase  can  chemical  p o t e n t i a l s uj  of  of  of  which  the  is H . +  With  the  of  the  in  the  determination become  pi's,  in this  systems  solutes  the  an  the  considered  phase,  °f  v a r i a t i o n s ) may and  poor  (Ci)t  electrodes,  (CjJt's  impurities,  aqueous  Cj  the  The are  concentrations  important  ion  their  The  i n which  components  together  the  total  Several  precipitates of  individual  the  aqueous  phases.  or  the  an  and  experimentally.  (presence  in  the  However  solid  concentrates  defined  metals  include  determined  Similarly x$  generally  several  easily  accurately  crystallization).  2)  systems  compounds, e i t h e r o r e s , not  involving several  m  phase  cannot  generally  the  C -H20,  The  gaseous  parameters solid  systems  routine  rather  than  the  study.  depend  on  the  experimental  investigations  are  carried  out. On  the  one  reactors.  hand, most These  parameters  systems  include  components C j , which the  start  On  the  reactors  of  the  other are  significant  autoclaves are  the values  runs hand,  continous parameters  and  i n the closed,  l a b o r a t o r i e s are and  the  total  amounts  can  experimentally  be  remain  constant  of  i n most  hydrometallurgical  and  represented  are  include  the  actual  as  significant  the  during  batch  independent  determined the  open  at  reaction.  processes,  the  systems.  The  properties  of  the  28  phases  present.  determining  The  restraints  considered i n this  solid-aqueous equilibria  will  refer  to  study f o r this  last  case. Special  mention  mixed  reactor,  with  the  must be g i v e n t o t h e a q u e o u s p h a s e .  the solid  particles  aqueous  solution  same  Hydrometallurgists reactions the  occuring  aqueous  Similarly formed are  are  i n rock  any s p e c i f i c  3)  Pressure  which  fractures  under  of  the  the flow  temperature  are  (Helgeson, 1969),  (Millero,  water 37  energy  relatively  are  substantial.  200°C tends  aqueous phases  the  dissociation  properties  of  are  waters,  which  problem  i s to  from  the  presence  /When  1956),  from  to the total  pressure of the  m o l a l volumes below  of  the  100 c m 3 / m o l e  on  solid-aqueous  temperature  increases, the  7 8 . 5 a t 25°C t o long  range  less  Under  t h e same  and p K , e q u a l w  than  electrostatic  i n the departure of  increases,  in  Solid-aqueous  so that  ( H e l g e s o n , 1969).  of water  parameters  reasons.  temperature  t o become p r e d o m i n a n t  of  The  generally  of  constant drops  (Frank,  of ground  the p a r t i a l  small,  The e f f e c t s  dielectric  at  since  1977).  equilibria  the  assemblages  important  not very sensitive  are  between  solution.  equilibria  solutes  contact  i n the process.  result  but mainly f o r k i n e t i c  system  relations  environment. which  in  well  residence time.  and t h e a c t u a l  hydrometallurgy, are  their  hydrothermal phase  assemblages  aqueous  and  in  remain  c a n be m o n i t o r e d  the  the solid  of  interested  geology,  characteristic  determine  over  i n the reactors,  solution,  in  of a pulp  In a  ideality  conditions, t o 13.993 a t  29  250C, d r o p s hydrated  al.,  at  200°C  compounds  temperatures.  As  while  FeSC^.H^O  1965).  However,  significant In  11.301  solid  elevated 25°C,  to  an  the  on  phase  a  4)  In  and  reactions which  are  divided  electrochemical designed  a)  into  electronic  phases.  In  they  independently at  partially  involve  few  (25°C -  T  as  as  a  their  data  temperatures  over  the  250°C).  involve  several  "electrochemical"  successive  electrochemistry,  the  ionic  framework  of  be  separately  studied  provided  et  display  several  and,  (Bruhn  (or T~l)  In  cells,  at  pyrometallurgy.  steps.  can  at  stable  180°C  in  rather  Most  considered  as  exchange between  reactions  occur  range  the  electrochemical  place  at  most p r o c e s s e s  reduction  involve  solid  take  practical  hydrometallurgy,  oxidation  the  diagrams  at  not  often  would  small  phase  is  Hydrometallurgists  relatively  least  in hydrometallurgy  phase diagrams  1974).  FeSC>4.7H20 i s  stable  temperature  a l . ,  at  example,  co-ordinate. isothermal  et  dehydrate  is  a parameter  pyrometallurgy,  (Sweeton  this  these  reactions solutes  model,  in a chemical  in  and  these  specially  reactor,  they  that  (approximately)  the  same  electrochemical  potential, b)  no  net  yielded  charge by  electrons This  the  created,  oxidation  captured  mechanism  is  is  by  the  which  1972).  hydrometallurgy,  presented  in this  involve  number  of  electrons  same as  the  number  reactions  i s the  reduction  reactions.  experimentally  reactions In  i . e . the  metals the  supported  and  aqueous  oxidation  electrochemical  for  number  solutions  leaching  framework  a  (Majima  has and  of  of  (Pourbaix, long  been  Peters,  30  1966).  Recently,  experimental oxidation  evidence by  02(g)  Bailey  and  of this  mechanism  at  Peters  110°C.  (1976)  i n the  Careful  have case  provided of  experiments  pyrite  using 0  showed  that  the source  water  and  not  02(g) of  02(g)*  and by means °2(g)  potential S°  S04 ~  study,  calculated  in  considered,  and t h u s  along  this  i s taken  the  by  absence  electrochemical  reaction  results  individual  the total and a few  conditions  imposed  significant  solid-aqueous  agree  ions  i n t h e C^  rather  than  •C -H20.  The  ni  concentrations chemical  parameter (Cj)t's  potentials  on t h e system  parameters.  equilibria  Electrochemical  as a s i g n i f i c a n t  components  these  in  the  of the  Both  context.  into account  with  was  products with  the  model.  this  taken  product  between p y r i t e o x i d a t i o n  proportion  (ibid.).  2  In  S0^~  a c o r r e l a t i o n between  and the r e l a t i v e  and  potential  Comparison  i n the  of p o t e n t i o s t a t i c techniques  established  electrochemical  are  o f the oxygen  18  involve  will,  be  reactions neutral  are salts  electrochemical of  the  system,  of the independent  including the constant  pH. values  The of  31  S E C T I O N 2-2  In section  is  species  is  often  use  of  2-2-1-1  of  term  the  problem.  the  problem  approach defined  outlined  in  the  in  previous  the  relate an  at  the  m u s t be  equations.  the  chemical  electrochemical  system and  Nernst  equilibrium.  different  potentials  reaction, The  notions  term  of  and  the  "potential"  arising  from  the  by  its  distinguished.  : definitions.  The gradient  "electrostatic  which  = V  i s the  The  only  a  has  the  is  defined  E  is exclusively potential  physical  potential  conductors  The  electric field  <t  eq. (2.01)  d e f i n i t i o n of  4  potential"  5zC  conditions.  two  of  in  this  ambiguous  this  measure  of  thermodynamic  to  equations  involved  "potential"  V  the  adapted  interpretation  Nernst  This  solution  2-1.  :  E  rigorous  this section,  1-2  section  2-2-1  : a  of  the  "interface  i s not  meaning.  difference same  valid a  In  under  measurable principle,  between  two  steady  state  quantity  since  one  points  can  only  belonging  to  nature.  potential"  Ej  between  two  p h a s e s Mi  and  M  2  32  is  the  points, each  difference  i n s i d e phases M  the electrostatic  and  2  p o t e n t i a l s a t two  r e s p e c t i v e l y , but s t i l l  close to  other.  Ei  =  A^(M!,M )  electrolyte rf(L,M)  =  2  When t h e s y s t e m  A  between  tf(M )  - ^(Mi)  2  consists of  L,  the  a  eq.(2.02)  solid  electrode  M  and  interface potential Ej generally  of  an  refers to  .  A "liquid  junction"  i s  the  liquids,  generally  Interface  p o t e n t i a l s between  interface  separated  potential  between  two  by a membrane o r a d i f f u s i o n phases  of d i f f e r e n t nature  frit.  are  not  measurable q u a n t i t i e s .  The  following  electrochemical circuits a  which  chemical  interfaces current from  cells.  The c e l l s  include  takes  and e v e n t u a l l y positive  the l e f t  to  connected  to  electrode)  of identical  "electrode  C.I.T.C.E. Definitions cell  (left  on  the electrode that  on  refer  are electrical  solutions  two  to  i n which  electrode-aqueous Conventionally,  within  t h e aqueous The  phases,  electrodes  electrode)  and  the  Sr  are (right  conductors.  has  been  defined  Electrochemical  as " t h e r e v e r s i b l e c e l l  and  aqueous  electrode.  SI  here  junctions.  p o t e n t i a l " Eh  Commission  i n which  electrode  considered  i tflows,  right  leads  potential  place,  liquid  when  the  two  of  one o r s e v e r a l  reaction  i s  The  notions  tension  by  the  Nomenclature  and  A  (Sr,Sl).  on t h e r i g h t i s a s t a n d a r d  the  left  i s  the  of  a  hydrogen  electrode  in  33  question" be  (Van R y s s e l b e r g h e  a c t u a l l y measured  et  since  a l . , 1967).  the  two  leads  This  p o t e n t i a l can  are  of  identical  conductors.  2-2-1-2  : relations  between  chemical  and  junctions  are involved  electrochemical  potentials.  When n o l i q u i d electrode of  i s related  the o v e r a l l chemical  A in  p o t e n t i a l Eh  to the free  the  cell,  energy  by t h e c l a s s i c a l  passing  reaction  the  under  often  and n  cell  equation  during  the  number  one f o r m u l a  c a n be d e r i v e d  (or "half  consider.  i s  of  electrons  occurrence  of the  study.  A similar relation electrochemical  G  eq.(2.03)  F i s the Faraday, through  the  change A  G = - n F Eh  which  cell  reaction  in  The  which  cell")  reactions  following  derivation  involves  only  the  hydrometallurgists i s based  on  several  assumptions. Let  a system  conductors, phase  may  mainly  separated be  elctrochemical  Z i In  q  consist  o f two p h a s e s ,  by a narrow  present. reaction  In  takes  transition  the  place,  electronic layer.  transition  written  A  ionic gaseous  layer,  an  as  Bj = 0  eq.(2.04),  or  eq.(2.04)  a l l the  species  of the systems  are  considered,  34  including  the electron.  positive  for  According  to the sign  the  the  coefficient  the  electrode  The  system  and  i s  energy  of of  i s open.  purely  rJG  where  Maxwell  and  in  of the  be a t u n i f o r m  kinetic  hydrostatic,  energy.  G  which  n  o f the system  i s  of G  e  temperature  transformation following  external  i s assumed  f o r the e l e c t r o s t a t i c i s assumed  t o b e t h e sum system, energy  and  of the  t o be e x p r e s s e d a s eq.(2.05)  charged  obtained  for  species  of  instance,  the  when G  e  system.  This  i s equal  to the  energy  qi  eq.(2.06)  t h e crf^'s a r e l i n e a r  a  cell.  The  of the corresponding neutral  accounts  a l l the  = 0.5 T 4i i  As  when  and t h e e l e c t r o m a g n e t i c  expression of the electrostatic  when  cell,  eq.(2.04)  = y {rfj 6qi i  e  i scans  e  energy  The v a r i a t i o n  expression  G  e  f o r the reactants.  electrode  system  are  electrostatic.  energy  a term G  system.  purely  c j  i n an e l e c t r o c h e m i c a l  i s positive  Let this  coefficients  negative  of the current  no m a c r o s c o p i c  the free  the free  and  i n question i s the l e f t  assumed  Moreover,  products,  of the electron  pressure, with  work  The s t o i c h i o m e t r i c  result, of  different  the  such ways.  a  functions  free  of a l l the q j ' s .  energy  system  change  during  c a n be e x p r e s s e d  any  i n t h e two  35  1) T h e v a r i a b l e s  6G = o G =  -  n  S  +  of the system  oG  <(T +  a r e ( P , T , n i ) and  e  V  dp  +  Z  uj  cinj +  i  As  recalled  by Dambrine  be  c o n s i d e r e d i n eq.(2.07) 2) T h e t w o f i r s t  N  C(G  -s  =  <IT  +  Z  J*i  which  Let  (1979), a l l species including  the  and  expressed  positive,  from  charge  yield  > 0  balance  e q . (2.08)  i s t h e non compensated  given  restraints  on  in the  eq.(2.04). system  dqj = Ci  species  F ol  relation,  Zj  denotes  restraints  the  number  of  charges  of  .  t h e t h r e e e q u a t i o n s eq.(2.07)  transformation  at  are then  relations  Bj.  Combining  and  The  = c j d l  the last  Z i  due t o  eq.(2.09)  I  any  heat  and f r o m d i f f u s i o n .  I  In  must  electron.  the chemical reaction  by t h e f o l l o w i n g  I dnj  i of the system  p r i n c i p l e s o f thermodynamics  1 be t h e e x t e n t o f t h e r e a c t i o n  mass  eq.(2.07)  v d p - cfn"  oTT, a l w a y s  irreversibilities  dqi  i  oTT  in  hence  which  conforms  considered i n this  ( c i p i + C i z i 4i  equilibrium  F) dl  t o eq.(2.09)  yields, for  t o t h e mass and c h a r g e  balance  model, < 0  eq.(2.10)  36  I.(°i i  pi +  In eq.(2.11) as  an can  be  with  1.  is  left  The  e  = - I i  Ci  rigorous  an  equation  is  extend  equivalent  of eq.(2.11)  1  of  to as  to  such  reaction  such  ••eg.(1.08)  of  i s the d e r i v a t i v e  reaction  eq.(2.04)  the e l e c t r o c h e m i c a l  as  of  and  f  affinity  G  i t s A  of  e  (pi +  ZJ  F)  approach  eq.(2.12)  outlined  reactions  in  section  provided that  1-2  eq.(1.08)  can be  handle  replaced  by  corresponding eq.(2.11).  2-2-2  : application  For  a  to solid-aqueous  solid-aqueous  reaction  takes place,  specific  form.  (electronic species or  system,  eq.(2.04)  electrochemical the  eq. (2.11) '  f o r every electrochemical  side  referred  reaction  =0  Eq.(2.11)  respect to the  A  F)  defined  The  negative  tfi  z i  electrochemical  eq.(2.04).  chapter  the  CJ  The  rewritten  electron  belong  electrolyte).  aqueous,  eq.(2.11)  conductor), which  the as  solid  The or  system  is  t o an  can  e,  which  systems.  where be  from  aqueous phase species  the gaseous  phase.  electrochemical  rewritten  belongs  separated  neutral  an  may  L  in  a  to a s o l i d the other (ionic  belong  Eq.(2.04)  phase  M  charged  conductor  to either can  more  then  the be  37  Z  c j Bi + n e = 0  ( n > 0)  eq.(2.13)  .i At  equilibrium  potential,  and  transforms  Z  given  eq.(2.03)  for  potentials  of  This  (^(M)  n  F  (Ej - u /F)  balance,  eq.(2.11)  p /F) e  eq.(2.14)  a  complete  the  species  cell.  v  system the equivalent of  I t  involved  relates in  the  the  electrochemical  eq.(2.15) denoted Ec,  i n the corresponding  solid  involves  t o t h e gas phase, phase  (neutral  the  interface  potential  of  the  phase.  i s not modified  i n the corresponding  solid  chemical  to the express ion  E j o f t h e s y s t e m , and t h e c h e m i c a l  species  by t h e p r e s e n c e o f n e u t r a l  eq.(2.13),  whether  t o t h e aqueous phase component such  as  these  species  ( i o npairs) or to  Fe,  stoichiometric  s u c h a s Fe2C>3) .  Let aqueous  - rf(L) -  i s f o r a solid-aqueous  form o f eq.(2.14)  compound  charge  electrostatic  e  electron  the  uniform  e  "potential",  belong  at  ( E i - U /F)  potential  The  are  overall,  F  eq.(2.13)  Ec =  the  n  Eq.(2.14)  reaction  phases  into  p i =-  i  the  Ec°  phase  be are  the value in  their  o f Ec when standard  a l lthe species of the states.  The  following  38  Nernst  n  equation  F  (Ec -  i s obtained  Ec°)  I cj  =  (ui ui°) i c j l o g ( c r ( i ) .Xj)  = R T 7 i' in  which  o* (i)  aqueous Since  i s the  w  . eq.(2.16)  w  activity  coefficient  of  species i  in  the  phase. the  solid  electrode  the  electron  same  chemical  potential  of  similar  type  Nernst  e q u a t i o n can  be  = R T I  Ci  Xi)  of  the  is  in  both  cases,  cancels i n eq.(2.16), written  for  the  and  a  interface  potentials  n  F  (Ei -  Ei°)  log(cr (i) w  eq.(2.17)  i For  an  cell is  electrode potential, m u s t be  the n  taken  into  the  liquid  account,  and  the  of  the  corresponding  whole  equation  following F  (Eh -  Eh°)  = R T 7 i  c  4  l o g ( o r ( i ) •" x j ) + w  - A Since  the  electrolyte  once  and  for a l l ,  for  both  is  even  through  states  a  L and  large  a  the  of  the  r  eq.(2.18)  r  reference electrode that  no  aqueous  liquid  is  defined  junctions  solution.  The  exist problem  the  solutions  vary  as  eg.(2.16)  can  of concentration.  a Nernst  Ec  that  o ( i ) functions  an  a  L°  express the  as  of  r  A V ( L , L )  (rf(L°,L )  i n h y d r o m e t a l l u r g y where  range  result,  L  i t is unlikely  more a c u t e  As  using  junctions  function  w  appropriate  of are  equation the  solute  known.  equation  such  such  concentrations, provided  Ec° as  can  be  computed  eq.(2.14),  by  when a l l  39  species A  are  similar  in their  Nernst  (eq.(2.17)) The  equation  is valid,  electrode  Nernst  standard  but  E j  hydrometallurgists,  Eh  i s considered instead  of  containing  be  can  only  Eh  of  and  and  u  solid  values,  solid-electrolyte  there  is a  except  the e l e c t r o n  the  reaction  left-hand  electrolyte for  Ec.  2 H  The of  +  side  aqueous  approximated are  by  such  extensively  corrosion  used  e n g i n e e r s , but  the  conductor.  in,  eq.(2.13)  to a s i n g l e  of  eq.(2.14)  and  hence  phases,  electron In  such Ec  system  as  might  interface. where  a  is  those  have  several  However,  i f  a l l the species B i ,  electrolyte depends  phase,  only  upon  t h e same c o n c l u s i o n  there i s always  at  then  least  the  is  true  one  such  namely  - H  value of  2  (g) -  Ec  where  properties,  2 e =  i s then  the p a r t i c u l a r  problem  as  belong  in question, In  reaction,  interested  such  be  phases,  are  a t each  determined.  of  e  hydrometallurgists one  potential  Ec.  electronic  several  interface  eq.(2.16)  potential the  the  cannot  geologists  chemical  characteristic  0  Eq.(2.14)  by  The  involving  potential  equations.  states.  0  characteristic  quantity  only  one  the  emphasis Ec,  to handle.  aqueous  electrochemical  of  solid-aqueous interface  the p o t e n t i a l  proper  eq.(2.19)  put  of  on  although not  When t h e s y s t e m  phase,  potential  is  the  of  Ec the  will  be  system,  aqueous phase, the system.  the  aqueous  measurable, under  study  referred and  will  to be  In  not a  solution is  the  contains as  the  simply  40  noted  E.  2-2-3  : equilibrium  In be  electrochemical  taken  into  account  electroneutrality potential the  equations.  of  systems,  provided the  that  parameter,  determining  the  involving the electrochemical  equations  such  section  a  can  the  C\  and  pressure.  The  system  m  species  considered,  is  of  involves  explicitly  involved  Finally  in  Nernst  potential are similar to  rigorous  followed.  approach  The s o l i d - a q u e o u s  are determined the total  at  outlined  in  equilibria  of  constant  temperature  number o f s p e c i e s  (m + 2) i n d e p e n d e n t  present.  components, and i t i s  (m + 2 ) made  assumed  out  the  electrochemical with  (k=l,...r).  single  the  L e t N denote  c a n be  independent  e,k  electrochemical  that  r = N -  A  be  C -H20 system  assumed  the  as eq.(1.08).  result,  1-2  solutes can express  The  equilibrium.  equations  As  ionic  equations  electrolytes.  E i sa significant  equations  individual  that  their  reactions  corresponding  L e t J denote only  remaining  components. such  as eq.(2.13)  electrochemical  t h e number o f p h a s e s  r  can be  affinities present.  one aqueous s o l u t i o n i s p r e s e n t  potential E characterizes  Then  the electrochemical  so t h a t  I t a  properties  the system.  Conditions constant  are  chemical  imposed  on  potentials  the of  system given  i n t h e form solutes,  or  of either constant  41  concentrations considered  of  given  i n section  components  2-1).  Let  (the s i g n i f i c a n t  Nc  be  the  parameters  number  of  these  cond i t i o n s .  The  system  of  equations  to  be  solved  i s  then  the  following. *  r = N &e k  (m + 2 ) e q u a t i o n s  =  k = 1,  0  r  * J equations i= . Z *ij i=l N  For  such  such  as eq.(1.03)  as eq.(2.11) ,r  eq.(2.20)  f o rthe phases  present  j  = 1  t h e gas  involves  j = 1,...,J  phase,  the  pressure  the  gas  equation  partial  eq.(2.21) corresponding  pressures  Pi's  to and  eq.(2.21) the  total  P, a s f o l l o w s  i=Ng Z ~  Pi = P  eq.(2.22)  i=l  * One e q u a t i o n  expressing  the electroneutrality  of  the  aqueous  phase i=N I i=l  w  z  in  i i w  which  x  =  subscript w refers  * Nc e q u a t i o n s The  eq.(2.23)  0  constant  t o t h e aqueous  f o r t h e c o n d i t i o n s imposed  chemical  potential  P w ( i h ) ~ Fw°(ih) - R T L o g K in  which  When  Kh i s a  the  constant,  total  phase. on t h e aqueous  of a solute i  n  c a n be  phase.  written eq.(2.24)  h  constant. c o n c e n t r a t i o n •'•(Cj )t  the corresponding  1  equation  °f  a  i s written  component as  i s  42  Z t i=l In  h  ( i ) x  eq.(2.25),  component C  =  w  the  phases  present,  solved  f o r the N  At  same f o r m  =  (m +  principle  diagrams rigorous  non  2)  the  species,  of  for neutral  therefore,  the  be The  would  ideality  the  chosen  to  of  total  concentrations  the  1)  rule  for  equations  the  unknown  i s then  the  When  available  +  phase  P.  N  (or  phases,  pressure  are  + Nc  the  the a l l  can E  be and  written  in  system  eq.(2.26)  problem  accuracy  source  N  ( o r P i ' s ) and  computed,  contain  the  atoms  involve  respective  (r + J  temperature,  +  number o f  eq.(2.25)  their  ideality  xjj's  - Nc  of  and  above  unknown  the  to  their  1 - J  way.  reliability  eq.(2.20)  in  the  as  could  diagrams  of  from  departure  constant  t ^ ( i ) are  solute i .  p o t e n t i a l E,  models of  In  of  pressures)  proper  v  eq'. ( 2 . 2 5 )  t  coefficients  p o t e n t i a l s of  electrochemical  the  h  equations  partial  P.  (C )  i n a mole  n  The chemical  i  at of  least the  would data  is  solved. point  by  quantitative entirely  depend  , especially that  represent  Non  the  phases.  of  linear  point, data  these  upon the  in a  the  models  43  S E C T I O N 2-3  : a p r a c t i c a l method.  The computing  plotting t i m e s , and  presented  are  felt  that  not  reliable  several  of  justify  of  the  will  These  with  the d i f f e r e n t  aqueous  apparent this  lack  and  to  the  data  of  a  and  t o a new to  are  of  non  reliable  eliminate  eq.(2.25)  lead  E  phases  precision  made, w h i c h  assumptions  respect  when  large  the present time, i t i s the  be  require  the  or  involving system  of  chemical  species.  : l i n e a r i z a t i o n procedure.  Assumption  1 :  solid  phase  a known f r e e  equation equation  such such  l e a s t one  system,  j  as  is stoichiometric  energy as  stoichiometric at  ideality  assumptions  linear  potentials  and  At  In o r d e r to overcome  fractions.  equations,  Each  to  will  worth-while  e q . ( 2 . 2 1 ) , e q , ( 2 . 2 2 ) , eq.(2.23)  mole  2-3-1  be  quantitative.  enough  model,  l i n e a r diagrams  only  t h e models o f non  diagrams.  the  non  might  truly  linear  modify  of  of  solid  ( J - 2)  independent  generated, which  "replace"  eq.(2.21)  i n the  system.  It  be  must  noted  that  i s then  can  phase  equation such  a known c o m p o s i t i o n  f o r m a t i o n G°(j).  eq.(2.21)  eq.(2.13)  with  be  and  as  corresponding  irrelevant.  written, the  The  which  equilibrium  eq.(2.20).  At  involve  as  eq.(2.20)  the corresponding equations  solutions  can  one this  i s expressed  Therefore i n the  equations such  solid  least  be,  whole  are  then  such  at  by  as  least  44  partially, If  taken  needed  into  several  within  a given  These  compounds, than  Assumption  2 :  The  equation  eliminated, already  make  together,  a single  up  partial  with  "average  compound".  corresponding  the  P will  pressure  has  be  the true  to the gas  pressure  can  appropriate  represent  P i s generally  an a d d i t i o n a l  the  eq.(2.22)  range  compounds  diagrams. chosen  G°(j)'s. phase  phase  more  will  be  n o t be d e t e r m i n e d .  As  little  effect  i n  the  equilibria.  practice,  cases,  stoichiometric  may  and t h e t o t a l  mentioned,  In most  solution  eq.(2.22)  solid-aqueous  i n such  "stoichiometric"  solid  accurately  account  inert  balance.  In  corresponding pressure  of  constant  gas  (N2,  such  the inert  A r , He)  a case,  to the gaseous  and/or  known, b u t i n  i s  present  the equation  phase  g a s , and w i l l  then  such  yields  n o t be  to as the  considered  further.  Assumption The  3 :  eq.(2.21)  corresponding  removed,  and  potential  o f H2O  equation  similar  u (H 0) w  This  2  one  phase  i s then  the  a s s u m e d t o be c o n s t a n t  to eq.(2.24)  w  aqueous  c a n be  2  "replaces" i n the system  phase  c a n n o t be d e t e r m i n e d .  - p °(H 0) = R T Log K  equation  aqueous  unknown  to  the of  and  is  The  also  chemical  known.  An  written  w  eq.(2.21) equations.  eq.(2.27)  corresponding  to the  45  Actually,  the  water  concentrations, the  but  i t s order  d i f f e r e n t aqueous  25°C,  the  6 N CaCl2 These  water  or 8 N NaCl solutions  water  for  dilute  activity  There the  a)  in  0.85  Stokes,  1959).  concentrated  strictly  constant  for to  speaking,  value  of  water  each  solute  solute  coefficient  of  a  difficulty,  provided solute  Accordingly,  c o n c e n t r a t i o n s under t h e I t  constant  i s  (Ch)t,  the following  over  into  then  possible,  to  modify  the  statements.  "solute  the others  zones",  explicitly  where involved  eq.(2.25).  zone,  the a c t i v i t y  c o e f f i c i e n t of the  i s constant.  calculations,  corresponding  as  few compounds i n v o l v i n g  solution.  i s divided  predominates such  very  any  average  predominant that  i t  value  solute  of  the  c a n be u s e d  remains  constant  activity  without within  any the  zone.  l e t an  equation  such  as eq.(2.25)  v  in a  difficulty.  that  as  with  field  t h e same e q u a t i o n  the  and  At  Eh-pH d i a g r a m s c o r r e s p o n d  significant  such  eq.(2.25),  single solute  predominant In  have  condition  In  evidence  i n an aqueous  The d i a g r a m  b)  to about  very  any  any  t h e same i n  4 :  corresponding  a  without  component  each  (Robinson  However,  solute  hydrometallurgy.  equal  already  the  remains  o f one and a r e o n l y v a l i d ,  solutions.  same c o n d i t i o n s for  solution  i s experimental same  in  s t i l l  The p u b l i s h e d  c a n be u s e d  Assumption  with  o f magnitude  i s  are  activity  varies  s o l u t i o n s . used  activity  hydrometallurgists. a  activity  express  46  the  constant  solution.  concentration The  of a  predominance  component  C  of a C -solute n  in  n  the  i° c a n b e  aqueous expressed  as t (i<>)  x(i°) » • t  a l li .  Eq.(2.25)  h  for  t (i°) h  Since  x(i°) =  the activity  constant,  h  ( i ) x(i) then  ( C  )  h  reduces to  eq.(2.29)  t  0* (i°) o f i°  coefficient  eq.(2.25)  •• e q . ( 2 . 2 8 |  w  i s further approximated  i s  assumed  to  by an e q u a t i o n  be such  as  u(i°) = u°(i°) + R T L o g ( o ( i ° ) w  This  equation  At and the  (i ), 2  other  i s only  valid  the boundary  solutes  eq.(2.25).  t  / t (i°))  i ] ^and i  2  zone (i°).  solute  zones ( i i )  predominate "together"  involved  eq.(2.25)  eq.(2.30)  h  two a d j a c e n t  explicitly  Accordingly,  h  inside the solute  between  t h e two s o l u t e s  ( C )  in  the  i s replaced  over  corresponding  by t h e f o l l o w i n g  equation  t (i!)-x(ii)  +  h  The  boundary  and  i  2  h  2  of their  th(ii)  This  for  approximated,  h  o (i].) w  2  )=  ( C  h  )  eq.(2.31)  t  i s defined  as the l o c i  the  C -concentration  same  n  where both i j in  the  yields  x ( i i ) = t ( i )  since  x ( i  zones  are responsible  aqueous phase.  Again,  t ( i )  2  x ( i  and  a t a boundary  2  )  eq.(2.32)  o (i ) w  2  are  of the zones,  constant,  eq.(2.25) i s  b y t h e f o l l o w i n g two  47  equations u(ii)  = p°(i!)  + R T Log(a (i!)  ( C  w  h  ) / 2 t  t (ix)) h  e q . ( 2 . 33) u(i )  = u°(i )  2  2  + R T Log(o (i ) w  ( C  2  h  ) / 2 t  t ( i ) ) h  2  eq.(2.34)  Assumption  5 :  No  approximation  similar  expresses  the  has been  electroneutrality  performed of  f o r eq.(2.23)  the system.  which  Eq.(2.23) i s  simply eliminated. In  practice,  present taking then At  an  to  neutralize  part  unreactive,  eq.(2.23) of  and  as  example  a result,  involve,  eq.(2.20),  As  linear  respect  with  electrochemical  This  solution  a  being  equations  whole,  there  to the N  potential  e x p l a i n s why  be  assumption  "inert"  known  to  explicitly  of t h i s  are  solutes.  to  be  very  CIO4 . -  such  as eq.(2.21),  s o l u t e zone,  (eq.(2.27))  "apparent  without  o f such  solutes  assumed  eq.(2.22),  a r e e l i m i n a t e d and t h e r e s u l t i n g  i n each Nc  then  The v a l i d i t y  the equations  and e q . ( 2 . 2 5 )  activity.  one.  several  one more e q u a t i o n  The  t h e aqueous  i s  the p o s s i b l e presence  the best  equations  such  on  temperature,  As  species  to the equilibria.  relies  low  independent  such  ( r + J - 2)  as eq.(2.24)  expressing  equations  or eq.(2.30)  the constant  a r e ( r + J + Nc - 1)  chemical  system  potentials  and  water  equations to  the  E.  variance"  of  the system  i s i n c r e a s e d by  the e l e c t r o c h e m i c a l systems  represented  48  on  linear  follow one  diagrams  t h e Gibbs'  has t o take  which true  2-3-2  2-3-2-1  pA  system  assumptions solute  Gibbs'  "independent and which  formula,  inert"  solute  then  increases the  i n new s y s t e m s  of equations,  by one.  result  zone.  In order to describe  are introduced  them, t h e  first.  e v e r y compound  = -  ( u ( A ) - u°(A)) / R T L o g ( 1 0 )  C -H20 M  species,  The  long  as they i n  convenient  (m + 2 )  easily  are  l e t B]_,...,  thereafter  o t h e r unknowns  eq.(2.35)  B , m  H  +  and  H2O.be  designated  The c h o i c e o f t h e s e independent the  E-pH d i a g r a m s  measured  as  as  i n  the  unknowns  (m +  2)  reference  u n k n o w n s E, p H , pB]_,./.., p B  presenting  when  A, pA i s d e f i n e d  system,  p r i m a r y unknowns.  system.  the  For  However,  The  account  i n using  : notations.  species.  most  In fact,  do n o t seem t o  of the equilibria.  i n each  "independent"  as  Pourbaix diagrams  t h e aqueous phase  notations  the C i  the  as  rule.  o f t h e whole  above  system  following  In  into  : calculation  The one  phase  neutralizes variance  such  m  are called  i s arbitrary  Ci— C -H20  system.  -  M  m e t h o d , t h e c h o i c e o f E a n d pH i s a r e computed.  properties  o f an aqueous  They a r e  also  the  solution.  a r e t h e pB's f o r a l l t h e o t h e r s p e c i e s  o ft h e  49  2-3-2-2  : the  ma i n  The  main  eq.(2.16),  which  compound to  free  and  the  tool  of  the method  is written  considered  determine  its  tool.  these  energy  of  f o r every  i n the  the  gaseous The  M  are  PH2O  f o r m a t i o n G°(A) of  solid,  equation such  C -H20 system.  equations  coefficients  i s a Nernst  as  and, a  f o r every  function  of  as  and  solute  data  needed  compound  A,  temperature,  equation  i=m A  I  +  c j ( A ) B j + w(A)  +  H 0 2  h(A)  H  +  + n(A)  e =  0  i=l eq.(2.36) This  equation  charge  is similar  balance  to eq.(2.13)  between  A,  the  and  expresses  reference  mass  and  and  the  results  of  species  electron.  When section  n(A)  2-2-2  equation  can  is  can be  different  be  used  written  from  directly  and  zero, the  the  corresponding  Nernst  as  i=m pA  T  +  Ci(A)  pBj  +  h(A)  pH  +  n(A)  X  E =  Q(A)  i=l  e q . ( 2 . 37)  with  X = F / Q(A)  E°  =  (R T n(A)  i s computed  which their  LoglO) F E°  by  corresponds standard  eq.(2.38)  - w(A)  using to  states  pH 0  eq.(2.39)  2  the Nernst eq.(2.36),  equation and  where  such  as  eq.(2.14)  a l l species are  in  50  n(A)  i=m 7 i=l  F E° = G°(A) +  c  i ( A ) G°(Bj) + w(A)  G°(H 0) 2  + h(A) G°(H )  eq.(2.40)  +  The  following  e x p r e s s i o n o f Q(A) i s then  obtained  i=m Q (A) =  (G°(A) +  1 i=l  + h(A) G°(H ) +  when n ( A ) i s e q u a l equation,  2-3-2-3  : t h e system  be  a given  generated  solid Any  or  once  - w(A) pH 0) / 2  and eq.(2.41)  H  i n t h e form  i s  eq.(2.41)  a  purely  are s t i l l  valid.  chemical  t o be s o l v e d .  Cm~ 2° system,  and f o r  (R T L o g l O )  eq.(2.36)  of equations  Ci  a l l be w r i t t e n  2  zero,  but eq.(2.37)  In can  to  C i ( A ) G°(Bi) + w(A) G O ( H 0 )  the equations  similar  a l l for  t o be s o l v e d  to eq.(2.37).  every  considered  They c a n species,  solute.  equilibrium  i s then  determined  by s o l v i n g  equations  of the  form i=m  y i =l  C j ( A ) p B j + h ( A ) pH + n ( A ) X E = Q * ( A ) " eq.(2.42)  which  are  expressing a ) When  derived  the  pA i n t h e d i f f e r e n t A  equilibrium, Q*(A)  from  i s  a  equations  eq.(2.37)  by  cases.  stoichiometric  pA = 0 a n d  = Q(A)  above  solid  compound  present  i n the  then eq.(2.43)  51  b) When A i s a p r e d o m i n a n t given  = Q(A) + L o g ( O ( A )  A  "together" given  i s  one  of  the  a t t h e boundary  2-3-2-4  : the practical  For  by  i t s Nc  condition  such  calculated  within  of  include  a solute  a)  Ns  b)  i s given  solid  i s given  At  from  i)  two a d j a c e n t s o l u t e  z o n e s , pA  o r e q . ( 2 . 3 4 ) , and  t  hence  eq.(2.45)  h  predominant n  zone  ) f  phase,  a solute  species,  one  L e t an e q u i l i b r i u m  ( A ^ , . . . ,A^c) >  as  3  a n <  N  zone i s  for  { P } t o be  denote  s  each  the  The e q u a t i o n s t o be eq.(2.38),  where  present i n {P}, i n which  A  case  solutes  of the  zone,  i n  which  case  by e q . ( 2 . 4 4 ) .  N c  boundary )  between  two  a n d (A]_, . ., A * j ,. . , A  predominate  predominate  predominate  by e q . ( 2 . 4 3 ) ,  the  ( A 2 , . . / A i ,. . , A  which  ) / 2 t (A))  compounds  f o r t h e Nc p r e d o m i n a n t  Q*(A)  solutes  (Nc + Ns) e q u a t i o n s s u c h  stands  the  eq.(2.44)  h  compounds p r e s e n t i n { P } .  respectively for  t  on t h e aqueous  as constant ( C  solid  pA i s  solution.  Nc c o n d i t i o n s  characterized  n  zone,  ) / t (A))  two  ( C  i t s solute  and t h u s  by t h e c o r r e s p o n d i n g eq.(2.33)  w  solved  h  between  Q*(A) = Q ( A ) + L o g ( O ( A )  number  ( C  w  c ) When  Q*(A)  inside  by t h e c o r r e s p o n d i n g eq.(2.30)  Q*(A)  is  solute  "together"  alone  as  N c  adjacent ) , the A  C -solutes, k  as C i - s o l u t e s .  At such  k  solute  's  and a  zones  (k  different  Aj  and A j '  boundary,  the  52  equations  to  be s o l v e d  eq. ( 2 . 4 2 ) , where A a)  f o r t h e Ns  Q*(A)  (Nc + 1 + Ns)  compounds  present  in  {P},  f o r t h e (Nc - 1) p r e d o m i n a n t  solutes  in  which  eq.(2.44),  c)  for  Q*(A)  both  Aj  as  in  which  case  eq.(2.43),  b)  case  equations such  stands  solid  i s g i v e n by  include  i s g i v e n by  and  A ' j ,  in  A  which  (k d i f f e r e n t  k  case  Q*(A)  from i ) ,  i s given  by  eq.(2.45).  The a  set  calculation  of  linear  inversion,  2-3-2-5  and  equations.  present,  The p r o c e d u r e  o f {P}  in a  {P} be a n e q u i l i b r i u m and which  has  z e r o o r one degree  of  a)  {P} h a s no d e g r e e s  o f freedom  * the p o i n t  of  in a solute  A  involves  a matrix  representing  be a s o l i d  zone  are  (Aj,...,A^c)•  a diagram  (Ns + Nc  whether  {P}  are "truly" {P} l i e s  compound  = m + 2).  as a p o i n t i f  n o t p r e s e n t i n {P} a r e " t r u l y " solutes  compounds  freedom.  i s r e p r e s e n t e d on t h e d i a g r a m  the s o l i d s  solving  solid  be c o n s i d e r e d f o r p l o t t i n g  * the predominant  Let  where Ns  i s calculated  cases w i l l  *  to  diagram.  Two  {P}  {P} r e d u c e s  is classical.  : stability  Let  o f an e q u i l i b r i u m  not present;  predominant;  within  the diagram  field.  n o t p r e s e n t i n { P } , and 1 t h e e x t e n t  i t s corresponding eq.(2.36).  A  i s "truly"  not present  under  53  the  equilibrium  starting  from  following  conditions  {P}  then  f  condition  {P}  d l < 0.  i f  for  any  According  transformation  to  eq.(2.10),  the  i s obtained  i=m  T  Ci(A)  pBi +  h(A)  pH  + n(A)  X  E  <  Q*(A)  i=l in (pA  A  e q . ( 2 . 46)  which  Q*(A)  i s g i v e n by  since A  is a solid  compound  = 0).  C -solute  A  n  solute  t (A)  x(A)  hence  an  given  is  n  "truly"  predominant  i f , f o r every other  A  h  and  eq.(2.43)  by  Finally, written  I  <  t (A ) h  h  x(A )  eg.(2.47)  n  equation such  as  eq.(2.46)  holds,  i n which  the diagram  field  can  be  represented  - E  <  by  conditions  as  -  E  <  B  n  B12  eq.(2.48) -  These  pH  to  {P}  Within  < - B  of  i  has a  are  - pH for  {P}  lying  <  B  2 2  within  the diagram  field  are  eq.(2.46).  one  degree  solute  represented points  2  conditions  similar  b)  is  eq.(2.45).  I  I  Q*(A)  as the  the diagram,  zone,  of  freedom the  diagram  a segment o f intersection a boundary  (Ns + N c  line of  of  between  "line the  is  {P}"  solute  =  m +  1).  linear, two with zone  and  {P]  end-points. either  a  or another  is  These border line  of  54  the  diagram  calculated  under  more  equation.  For  any  finite  (one  generated eq.(2.46)  these  presented  method  to  be d e t e r m i n e d ,  the  "<"  {P} i s s t a b l e  then  _ H  one  there  i s a  generated When o n e o f  and  represented  consists of  equations  a  second  as a  segment  i n computing freedom,  such  as  are the data  T h e y c a n be g e n e r a t e d  a set of  m  for  be  for stability.  of the c a l c u l a t i o n s .  c  can  are  a  which  number c a n be  eq.(2.42)  but f o r the e q u a l i t y / i n e q u a l i t y  equations  present  conditions,  Ci  then  of freedom,  which  The e q u a t i o n s  f o r a l l the other  the system  degree  degrees  same  f o r the solids  equilibrium  sign in  "="  zero  i n based.  the beginning  as {P} b u t  points  points.  of these  at  conditions  {P} i s t h e n  method  the  A l l these  and checked  automatically. are  present).  end-points,  two  with  coefficients  present  one  must be s t a b l e .  equilibria  sign  with  i n the diagram,  between  The  The  t h e same  computed  i s stable  line  of  solid  number o f p o s s i b l e  end-point of  almost  equilibrium  automatically, them  more  2°«  and a  For each are  on once  species,  of  solute  sign. the  and f o r a l l  equilibrium {PJ  generated  and t h e p r e d o m i n a n t set  which  and  equations or solid,  with  the  solutes f o r with  the  considered  55  SECTION  2-4  : discussion.  The grounds states these  method  and of  the  present  with  E-pH  under  a given  to  the  2 - Nc)  in  based  which  on  conditions.  (m +  1 - Nc)  regions  solids, case  thermodynamic  represent equilibrium  s e t o f Nc  correspond  (m +  are singular,  to  solids  (m - N c )  unless  the  In a l l in  solids  the systems  number  of  of  solids  decreases accordingly.  is  conditions.  one  are  phase.  a given Nc  The  n u m b e r Nc  components  classical  of  E-pH  diagrams  C -H20 system,  m  m  considered,  concentration  aqueous  class  I n t h e C^  conditions total  to  is  diagrams  the e l e c t r o l y t e ,  points  There  of  resulting  diagrams, the l i n e s  equations  to  above  the system  equilibrium and  the  outlined  of  each  one  of  keeps  .Cj,...,  Nc  kinds  of  constant  the  or C  number o f c l a s s e s o f d i a g r a m s i s equal  set of  different  which  component  per  in  m  corresponding  t o t h e number o f d i f f e r e n t  out o f the above  m  C j ' s , and  the  i s given  "sets" by  the  formula m!  Nc!  (m-Nc)!  Adding  these  class  of  (2  m  +  1)  numbers  diagrams different  sol id-aqueous  The E-pH  f o r a l l Nc  classes  equilibria  which  2 , m  f o r the s o l u t e zones  Fe-H20 s y s t e m  diagrams  yields  of  of  1)  C  m  - H  adding  results,  diagrams  t h e C^  (m =  and  2°  i s depicted  as  one  more  a whole,  representing  in the  system.  by  are schematically p l o t t e d  three  classes of  i n fig.(2.01a)  to  56  f i g . (2.01c). lines  diagram  two s o l i d s  o r {Mag + Hem},  solid.  (constant and  first  represent  { F e ° + Mag} one  The  The s e c o n d  (Fe)t).  The  (m - N c  diagram  lines  with  the  The  third  = 0).  calculated  with  in equilibrium whereas  i n t h e r e g i o n s between  equilibrium  the  corresponds  computed  correspond lines,  diagram of  the  no  with  electrolyte  one  under  phase,  can  this the  only  condition  solid  solids  presents  The  represent  to a single  electrolyte  value  with  N c = 0.  the regions  was  the  to  be  in  condition  solute  zones  ( F e ) tc o n s i d e r e d i n the second  diagram.  The P o u r b a i x d i a g r a m f i g . (1.01) different limit  (Pourbaix, 1963). (Fe)f-  two  have  corresponding  In to  as  representing  the  solutes  are  predominant  active  "active"  of  lower  much  been  concentrations  i n the  a  truncated  provided  10~^ mole/kg  of  larger  no  practical  than about  electroneutralizing  by f o r m i n g s o l i d  salts  the  i n the  has  been  i s composite, by  the  of fact, H2O,  exact  the e l e c t r o l y t e " solutes  three  f o r iron  the  iron  nature of the  interest.  one mole/kg  o r complex  diagram  and  zones  diagram  than  and  diagrams iron  As a m a t t e r  about  in  lower  diagrams.  detectable i s  to  solute  resulting  shown  These  superimposed,  the  information  was  corresponding to  (Nc = 1 ) .  region,  of  The  useful  solutes  species  has  diagram  well.  hardly  concentrations  diagrams  corresponding  former  Nc = 0  classes  concentrations  plotted  one  the  truncated  superimposed  original  Several  system  a n o t h e r one t o h i g h e r i r o n  aqueous phase.  a  been  regions,  concentrations,  latter,  f o r the Fe-H20  For  H2O,  iron  t h e "non  may  become  which  should  Fig.(2.01) t h r e e c l a s s e s o f E-pH diagrams o f t h e Fe-H20 system.  58  be  considered  i n the  system.  (fig.(2.Ola)),  t h e model  well  region  and  this  important in of  a  given  the  Atlas  the  Ci  C -H20, M  system For  listed  number o f  line  i n the  case,  acid  Furthermore  leaching  the  respective  7  All S-H2O  loss  diagrams  thermodynamic  then  of  group  information  the  success  f o r multicomponent  tool  of diagrams with  present  of  In  this  provide systems  to describe  the  components.  classes table,  equilibria  of  the s o l i d  of  diagrams  Ns°  denotes  represented  would  be  of chalcopyrite classes complex  of  systems,  such  the  needed  in  of diagrams  may  aqueous  by  a  these diagrams  i s as  even  corresponding  of  to understand  the  the  t o Nc  33.  useful. do  upon  constant.  presented  at  this  computed  depending  be  system  0  as  remain  will  =  in  diagrams  ( C i ) t which  equally  but  large  greatly vary,  variations  are not  equilibria  brines,  c a s e .of t h e C u - F e - S - H 2 0  diagrams  of  are 9  i n the  system  of  required  the number  there  to  diagram.  values  examples  i n the  the  same  same s e t o f c o n d i t i o n s  Outstanding chapter  of  f o r such  the  without  diagram  experiments  desirable  (2.01).  representation  with  the  in table  solids  t h e number  f i t the  thereby explaining  system,  Cu-Fe-S-Cl-N-H2O  nitric  the  highly  increases  corresponding  consistent  the  the  t h e number  2  the  A  be  Cu-Fe-S-H 0  are  not  omitted  significant  system,  with  drastically  the  which  but  does  of  1963).  would  hydrometallurgists  region  Pourbaix's composite  Metal-H20  It  be  whole  (Pourbaix,  this  generally  can  information.  a single plot  In  in  200°C.  For not  instance,  contain  any  59  line,  since  Similar However group  there  i s only  situations  one s o l i d  may  i t seems d o u b t f u l a l l the  system. available  useful  that  which  becomes c o m p a r a t i v e l y  for  become  more  c a n be d i s p l a y e d very  i n the  small.  whole  multicomponent  a s i n g l e composite  information  When t h e s y s t e m s data  arise  phase  of  systems.  diagram  a given  complex,  system.  the  might  multicomponent fraction  i n a two d i m e n s i o n a l  of plot  60  TABLE'  Classes for  (2.01)  of  t h e Cu-Fe-S-H20 (m =  1  diagrams system,  3)  Nc = 0  1 no  Nc = 1  1  (Fe)t constant  Ns° = 3  Nc = 1  1  (Cu)t constant  ! Ns° = 3  4  I Nc = 1  1  (S)^  1  5.  1. N c = 2  1  ( F e ) t and  Class  1  Class  2  Class  3  1  Class Class  conditions  Ns° = 4  constant (S)  t  constant  Ns° = 3 Ns° = 2  1 i 1  1  i 1  1  i 1  1  i 1  1  Class  6  I Nc = 2  1  ( F e ) ^ and  (Cu)^ constant  Ns° = 2  1 i  Class  7  I Nc = 2  1  (Cu) t a n d  (S)'t  Ns° = 2  1 i  Class  8  I Nc = 3  1 (Fe)t/  ( C u ) t and  Class  9  1 solute  zones  constant (S)t constant  1 I 1  I Ns° = 1 i  r  i i  I  61  ,  ; ..-^.-..„  •  ;.W :  3  COMPUTING, D I A G R A M S .,.,>•., ,  FOR H Y D R O M E T A L L U R G I C A L  A E-pH C^  ,•../.•,;-;•;.•:•.•..' . C H A P T E R  method  has been d e s c r i b e d  diagrams C -H20.  actual  SECTION  as  a  plotting  3-1  be  The g o a l  m  method  to  Several  depends on  When a l l t h e c o n d i t i o n s  involve  of  i s linear.  the diagram  predominant  l e t  solutes  implement  techniques  Nc  the constant  conditions  divided  into  ( A ^ , . . . , A N ) , c  the  the  allow the  times.  nature  of  the  phase.  o f components C j ' s i n i s then  to  approach.  on t h e aqueous  field  system  - first  imposed  diagram  complex  procedure  conditions  concentrations  i s  allows  computing  of a diagram  generally,  any  which  minimal  pattern  More  3  2,  with  The  solutes,  chapter for  chapter  program.  o f diagrams  : plotting  in  calculated  of this  computer  PURPOSES.  involve  the solute  one p e r  chemical  potentials  the  constant  aqueous  phase.  The  zones,  defined  b y Nc  condition.  In  each  62  solute  zone,  the  approximated potentials is per  by of  conditions conditions  solutes  a consistent  diagrams  a r e computed  constant  water  activity  (i.e.  include,  as  minimum,  T,  T,  and  A,  a solid  the  (CjJt's  constant  Aj's.  set of  The  are  chemical  whole  linear  i=m  Z  o f an  • c j ( A ) B i + w(A)  at constant constant  PH2O,  or solute,  the c o e f f i c i e n t s  A +  constant  diagram  diagrams,  one  zone.  The  species  as  involving  the predominant  t h e n a p p r o x i m a t e d by solute  such  temperature T  PH2O).  and  for  energy of  equation  such  + h(A)  H+  input  each  i t s free  H2O  The  and data  considered  f o r m a t i o n G°  at  as  + n(A)  e =  0  i=l eq.(2.36) The  program  then  corresponding  computes  the  coefficients  Q(A)'s  of  the  equations  i=m pA  +  Z  Cj(A)  p B i + h(A)  pH  + n(A)  X  E =  Q(A)  i=l eq.(2.37) For  every solute  zone  Ns  Nc  solid  = m +  compounds  freedom the Let  1 -  may  be  ( A j , . ..,Ajjc)  (S^,...,SN ), s  an  c o m p u t e d , and  must  and  f o r every set of  equilibrium  with  one  be  for  stability  checked  degree  of in  diagram. {P}  matrix present  be  one  i s formed  of  these e q u i l i b r i a .  with  i n { P } , and  Nc  one  + Ns  rows,  f o r each  In order one  to compute  f o r each  predominant  solid  solute  of  {P}, a  compound the  zone.  63  The  rows c o n t a i n t h e  y  c j ( A ) pBj  coefficients  +  h(A)  pH  +  of  n(A)  the  X  corresponding  E =  equations  Q*(A) eq.(2.42)  in  which  Q*(A)  Inverting  is  this- matrix  Actually, diagram line,  given  is  and  to  the be  only  the  leads  above  the  one  *  replacing  by  two  in  which  *  adding  diagram  i s given  between  E and  i s not  eq.(2.44). pH.  required by  computed. a series  a solid  a  when  a  segment  of  The  of  possible  matrices  by  not  present  to a predominant  to Aj  which  and  to  in  {P},  C j - s o l u t e Aj.  another  Cj-solute,  and  one  of  borders  the  with  zero  degrees  Let  {P }  eq.(2.45),  corresponding  to  the  of  field.  each  computed  case,  by  values  primary  of  the  such  i=m T Ci(A) i= l  equilibrium  pBi  a  matrix.  pB (P»),..., 1  in equilibrium. equations  an  inverting  and  of  to  corresponding  equilibrium,  is  or  i s represented  inverting  correspond  row  eq.(2.43)  above by s u c c e s s i v e l y  row  Q*(A)  In is  the  :  by  corresponding  rows w h i c h  a  calculation  m u s t be  derive  a row  relation  end-points  computed  adding  a  {P}  are  *  to  either  computed.  end-points from  by  unknowns Then  as  +  {P'}  pBmfP'), pH(P') under  are  h(A)  n(A)  +  i n the  freedom  1  be  and  E(P')  conditions  i s stable  eq.(2.45)  pH  the  of  such be  where  diagram  i f a  an the {P'} set  satisfied  X  E  <  Q*(A) eq.(2.46)  In  the  above  equation, A  successively stands  for  64  *  every s o l i d  by  case  Q*(A) i s  given  eq.(2.43),  •every the  not present i n {P'}, i n which  solute  (Ci)f's..  explicitly  (eq.(2.25))  involved in  f  i n one o f t h e c o n d i t i o n s  which  case  Q*(A)  i s  on  given  by  eq.(2.44) , *  one o f t h e b o r d e r s o f t h e d i a g r a m  Whenever  an  equilibrium depicted  by  representing  SECTION  3-2  In  equilibrium {P"} must  be s t a b l e  plotting {P } 1  and  a  : reduction  Similarly, Ns  a  For  instance,  sulphur  the  diagram,  line  between  of computing  be c o n s i d e r e d .  in  solute  compounds  must  number  becomes  the  solutes,  o f Nc  given  The  another and  such  {P}  t h e two  h u g e when m  11  In  iron  For a diagram  are  solutes  computing zone,  i s  points  be  checked  this solutes  increases  system system, and  28  computed under  not  known  ( A ] _ , . .. , A N ) , C  on  the a  (Cj)t's diagram.  a l l the  of calculations  Cu-Fe-S-H20 I I .  solutes  i n the conditions  considered  a  solid  in Part  then  time.  predominant  involved  be  within  procedure  investigated 17  must  equilibrium.  crude  in  and a l l t h e assemblages  = m + 1 - Nc  stable  stable,  straight  the  where A j i s e x p l i c i t l y (eq.(2.25)),  i s  {P"K  principle,  beforehand,  {P'J  field.  sets  for  possible  required  by  beyond  two.  200°C  will  at  9 copper solid  such  be  solutes,  compounds  constant  of  will  ( F e ) t and  65  constant zones,  ( S ) t ,t h e program  one f o reach  couples with  of  56 p o s s i b l e {P }  with  1  zero degrees In  equilibria  would  reached.  there  t o prove  the stability  s h o u l d be a p p l i e d  the  above  computing  times  solid  first  way c o n s i s t s  assemblages  eq.(2.46)  which  f o rsuch  As a m a t t e r  m  to  be " u n s t a b l e "  corresponding these  solids  are  inequality  Ns = m + 2 stable, the  and  a phase  Nc = 0 diagram  and  m  Ns = m + 2)  assemblages can  be  corresponding  sets  zone,  always  T.  o f (m + 1  this once  i n  In practice,  a l l the  conditions  assemblages  since  be  computing  of  eq.(2.46)  satisfied  whether  those  phase and  i s  with  ( i nwhich  case  equilibria which the  portion  t h e aqueous  diagram  of  phase.  (Ns = 1  a diagram,  - Nc) compounds c a n be  with  are not  f o r a l l f o r a  When p l o t t i n g  are  the  the  which  i n equilibrium  listed  C -H20 a t temperature m  the  such  eliminating  of  most  compounds c o n s i d e r e d i n t h e  i s determined  C -0-H20 system the solid  By  as  number i s  beforehand  p r e s e n t i n {P} o r n o t p r e s e n t  i s strict).  but  result  diagrams.  of fact,  must  such  of calculations.  i n any s o l u t e  to the solids  are  equilibrium  times,  would  satisfy  corresponding to the solid  C -H20 system.  bound  not  as {P}  and checked f o r  as unstable before t h i s procedure  378  there  o f an  53  i n eliminating  do  and  3 958 416 e q u i l i b r i a  t o be c o m p u t e d  solute  such  {P},  f o reach  a r e ways o f r e d u c i n g t h e number  The  Ci  makes  be r e j e c t e d  S t i l l ,  unreasonable  Ci  order  70 686 e q u i l i b r i a  Moreover,  o f freedom  as { P ' J r eq.(2.46)  such  All  o f freedom.  187 p o s s i b l e  and s u l p h u r s o l u t e s ,  and t h e r e f o r e  end-points, which  stability.  the  couple of iron  solids,  one degree  should consider  to  given  only the  taken  into  66  account. time.  (chapter  378.  There  A  diagram  in  the  the  aqueous  the In A'j  Nc  the pH, of  the  computed  predominant pCi,...,  Ci,...,  solving solutes  c  number  of  diagram  t o be  any  However  The  given there  1  zone  two  instead  plotting.  of  calculations  zones  of a  given  (Al,..,Aj,..,A^Q)  and  of which  , Cjjc are fixed  between  these  equations  in two  involving  equations corresponding  only with  determined. solids  diagram  of  the  t h e Nc  to  equations  line  zones  times. the  a r e computed  A  "stable"  +  and  not  the zones  involving  2 unknowns  is  E,  independent boundary.  beforehand  again  relatively  small  solute  example,  i n t h e 10  ANc  adjacent  present at this  In t h e above  are l i m i t a t i o n s  (and  two  t o t h e Nc  solute  allows  of  1  straight be  only  above +  respect  the  instead  Al,..,Aj,..,  components  the computing  calculations  the  +  of  z o n e s , and  species  resulting  systematically  drastically  of  C^c  c o m p o u n d s w h i c h may  reduces  Nc  m - Nc  the boundary  pCjj .  the s o l i d  solving and  the  the boundary  the predominant  by  solute  the concentrations  by  of  solute  l e t  sets  solute  number  relevant  adjacent  o  90  computing  present.  then  m  the  In p r i n c i p l e ,  compounds  involve  involving  w  solutes,  when  Computing  t  only  i n each  instance,  i s obtained  practice,  C  e  reduces the  the q u a l i t y  the  For  phase.  zones  solid  on  reducing  components  predominant  be  of  b  above,  considered  effect  way  . ,AJJC)  CN +I,...,C ), can  are  determining  ( A l , .. , A * i , .  solute  7)  beforehand.  be  substantially  presented  i s no  second  consists  the  procedure  I n the example  solids of  This  or  the 20  zones  of  a  equilibria solute  zones  187. in  the  diagrams  which  can  be  67  plotted hi,..  by  ,Ai,..,  (Nc +  1)  ANC  a n c  method.  c a n n o t be  occur  when c o m p l e x  When,  ' i involve  A  the  on  t h e s e. e q u a t i o n s d o e s  not  r  E and  pH  only.  solutes  the  such  programs,  as  which  at  predominant  complexed  by  component  involved  When  restrictions system,  on  and  directly.  complex  conditions  t h u s on  the classes  A  c h o i c e must  programs,  which  handle  diagrams,  and  faster  must be  determined  .A  third  improve  way  the  determined. must  of  be.-, c o m p u t e d  end-points  have  potential  stability  programs  above for  been  zones  the  Nc  considered, there  are  one  be  imposed  that  can  computer solutes  f o r which  of  on  be  time  computed consuming  f o r any  complex  the  class  solute  of  zones  by  .which  example, each  the 56  {P}. long  calculations  stability  i s . to  of  {P}  equilibria  such  A  procedure  simplex  before  a l l  the  as  is {P'} may  possible  determined.  i s based  stability  range  solutes,  r e d u c i n g t h e number o f  . u n s t a b l e .{P}  procedure  complex  solute  are  of diagrams  directly  to  which  can  made b e t w e e n  solute  likely  the  in  are  that  is  in  separately.  In the  an  of  be  procedure  eliminate  This  solutes  the  cases, the  compute  handle.directly  conditions.  result  3)  are considered.  +  cannot  not  the  (Nc +  generally  beforehand  a  least  and,,;; t h i s ,  FeSC>4  species  components,  In such  ;  result,  Nc  depend  determined beforehand,  :  predominant  more t h a n  explicitly;  involving  zones  a  *  Solving  relation  As  a  equations  unknowns. a  such  on  the progressive  (denoted here  i f {P} - i s ; s t a b l e ,  reduction  RPS),  down t o an  down empty  to  of a  range  the  real  range  i f {p}  68  is  unstable.  The  first  divides  ^fe^^'V:  .^<r^.  equilibrium  such  as {P'},  may  be  possible."  t o .A j  i s  ;  second  considered,  satisfies RPS'• i s  equilibrium:  three.cases  eq.(2.46)  corresponding  t h e segment  of line  {P} i s u n s t a b l e .  remains  sole  {P + A 3 }  Firstly,  both  i s  to  are  which  three  {P + A }  {P + A i } o r  end-points. relativelycomputing the  This 'early time  diagrams  2  procedure i n  than  the  which  requires  t h e procedure  described  to  following occur.  eq.(2.46)  b y {P + A i } a n d satisfy  the  above  this  T h e new RPS i s  and  {P + A 3 }  e l i m i n a t e s an u n s t a b l e  process  corresponding  step.  one e n d - p o i n t , f o r  eq.(2.46).  o n e a n d h a s {P + A }  {P'}  segment  may  the  2  only  which  eq.(2.46)  the  {P + A }  this  satisfies  bound  2  the  one  cases  »satisfy  2  instance  the previous  i n  t h e second  When  A }  end-points.  only  similar  Thirdly,  than  case  {P +  case,  satisfied,  2  eq-.-(2.46) a n d { P } i s u n s t a b l e .  smaller  satisfy  versa  two f i r s t  a n d {P + A } .  and  neither  2  2  In this  o f t h e RPS a f t e r  considered,  {P + A } ,  {P + A } , i s  one o f t h e above  A 3 , a n d t h e RPS r e m a i n s  Secondly  2  step.  t h e RPS e v e n t u a l l y b e c o m e s a  {P. +, A i }  {P + A i J  corresponding + A }.  point"  i s bound,  two . e n d - p o i n t s  point  {P  end  vice  to A j .  only in  first  { P + A j } may  and  2  eq.(2.46)  Thirdly,  the  :  between.these  i s not satisfied,  diagram  A  one which i s  a s { P ' }, n o t e d First,  to  inequalities  Since-'the  and; another  corresponding  none o f t h e above  as  such  may o c c u r .  t h e eq.(2.46)  Secondly,  with  { P + A ]_•}•,  w h i c h ;v< t h e , '-\ e q . ( 2 . 4 6 )  i n  i s t h e RPS a f t e r  ;  the  (iie.  verified),  f o r b i d d e n . v The f i r s t r e g i o n  case  f o rinstance  :  corresponding  the  noted  -"•/•  t h e . t J I n e f T e p r e s e n t i n g ,{P}0;into two r e g i o n s , one i n w h i c h  stability  When  >y-  A-.,  ...  i-f?.-:.^  ;  four  times  as {P} less  i n s e c t i o n 3-1 f o r example :  i n  the  69  Cu-Fe-S-H20 the  resulting  which  procedure  be a c h i e v e d  SECTION  3-3  In  This  diagrams.  traditional  simplex can  system.  leads  (1977)  diagrams  were  boundaries  for  uncertainties  "linearize"  Minimal  (1963),  o f t h e s o l u t e zones. which  aqueous  solution H2O.  mole/kg the  solute  refers {p}  l e t  For  the lines  This  a  to the "true"  in  chapter  the  plot  between  4 +  )  and  (Fe  2 +  and equal  ).  the  and  3  boundary  approximations  lines  an  t o 10~ :  The d o t t e d  o f { P } , and t h e s o l i d of  where  i s valid.  hematite  the  to  {P}, the  eq. (2.45)  i n f i g . ( 3 . 0 1 ) near 2  made  a s o l u t e zone  (Fe)^ i s constant  (Fe2(OH)  framework  of line  represent  considered  in  2.  When e q . ( 2 . 4 5 ) is  zones.  a r e rounded a t  equilibrium  inside  equilibrium  which  {P} i s shown zones  times  w a s made t o c o m p e n s a t e  given  are different  {P} d e n o t e i n  i n  similar  computing  a r e inherent t o the assumptions  eq.(2.25).  example,  by a  o f two s o l u t e  eq-. ( 2 . 4 4 ) ' . h o l d s , a n d a t t h e b o u n d a r y , w h e r e For  program,  way.  diagrams  t o be s o l v e d  a  computed  : u n c e r t a i n t y a t t h e boundary  the  t o no l i m i t a t i o n s i n  presented  two d i m e n s i o n s .  i n this  Pourbaix's  equations  Rosof  E-pH with  procedure  i s used  f o r both  predominant  solutes,  the point A  obtained.  When t h e e n d - p o i n t s computed  by  neighbouring  of the  simply predominant  solid  adding  to  s o l u t e and  lines {P}  representing one  using  equation eg.(2.45),  {P}  are  f o r the the  two  70  {P} : Hem  present (Fe) }  f  = I0"  3  Solute zone boundary calculated iron concentration's Fe and Solute zone boundary Fe^ and Fe2(OH)2 +  +  by assuming equal as FeglOhOg  calculated by assuming equal concentrations  Fig.(3.01) Example o f the d i s c r e p a n c y a r i s i n g a t the boundary o f two zones, as p l o t t e d by the program.  solute -  71  points.  B  and  eq. (2.44)  in  representing ; intersection \  the  Of  C  ,case.  {P}  looks  :  between  be  three  case  must  accurate solute  SECTION  3-4  two  be  a  the  to  lines  does not  (B,C)  represent  since, although  boundaries,  or  using  the  take  be  the a  plot the  place  third  straight  {P},  the  i t would  part. made  types  of  at  the  plot  (D)  can  line  is  "correct"  would  erroneous  be  more  within  the  linear  or  diagrams.  presented, i n the Nearly  a l l of  i n chapter  2 to These  plotted  using  same  by  "metastable"  diagrams,  sometimes The  the or  useful important  literature  them depend linearize  equations.  the  case,  b u t , . when  thermodynamic  of  from  c o n s i s t e n t , .-. a l t h o u g h .  second  program,  avoided,  diagrams  in  problems.  /last  solid  twovend-points  .: o t h e r  assumptions  are  ^his  results  itself.  Most linear  in  n e a r t h e  zone  point D  more-  alternatives,  between  (A)  the  In  The  boundary....  implemented  plotted  obtained.  ; each  s o l u t e zone  the  are  diagrams method.  diagrams with  to  information presented  implicitely  the  initial  can  on  i s to  different  always  a given  system  the of be  diagrams,  co-ordinates solve  control  diagram.  on  therefore  Composite  h y d r o m e t a l l u r g i s t s to  point  are  the  specific nature  72  3-4-1  : composite  diagrams.  Composite truncating  (C;i)  plotted  t /  the c  . . .,  for  ( Nc) t c  *  often  s  of  a  r  Nc  level  This  diagram, second  one.  The  needed, by  plus  diagram solute  solid,  i s then  dashed  Furthermore, considering  diagrams, borders  several  Cj,  diagrams,  diagram  fora l lj different  Each  o f these diagrams  plots  which  same  which diagram  ( f o r instance  i s then  computed as f o rthe  determining (CNc+l)t* over  the  first  o n t h e same p l o t .  diagrams  such  from  one  c a n be  I f  another  truncated  as eq.(2.46), which  and  bound  the  of solute  d i a g r a m s , f o r a C^  (Cj)t  the  component  For instance,  and t o a g i v e n s e t o f  on  to  lines.  boundaries  each  a  according  c a n be d i s t i n g u i s h e d  thermodynamic  composite  has  be a d d e d  and d o t t e d  the  diagram  condition  of the equilibria for  on a  t h e same Nc c o n d i t i o n s  can also  of the diagram.  Pourbaix's of  as  levels  s i m p l y super imposed  more i n e q u a l i t i e s  stability  concentration  Plotting  another  a l l these diagrams  using  the  namely  zones  of  For instance,  A second  and/or  case  another  very useful.  w i t h Nc + 1 c o n d i t i o n s , first  of  superposing  important  conditions  constant.  e  by  An  plotting  E-pH d i a g r a m .  concentration  Nc+l)  diagrams.  consists  thermodynamic  been  are. plotted  thermodynamic  superposition given  diagrams  the direct  restrict  lines  zones  of  the  and f o r t h e  extension  C -H20 system m  one c o r r e s p o n d i n g t o a g i v e n (m - 1) c o n d i t i o n s  by  imposing  of  consists component constant  from i .  i s the superposition  a r e a l l computed  under  t h e same  of (at least) (m - 1 )  three  conditions  73 on  the (Cj)t's;  more c o n d i t i o n consists  o f a l l , one diagram  i s computed  imposing  (Cj)|.._  t o lower  a constant  whiich*-'divide  corresponding  :  a  ( N c = m)  of lines  r e g i o n s , -one other  First  the  to  higher  Cj concentrations  region.  superimposed the  The  t  by  ranges  similarly  considered i n  The- l i n e s  by t a k i n g  every  solute  predominant  ;  lines  of  solute),  ;  into  two  i s superimposed  diagram  of  the  such  in  the  f o r Nc = m - 1 i s being  solute  t h o s e on  zones  as eq.(2.46)  the - system,  Then,  are  f o r every  when  the  stability  corresponding to these  lines  are being  are  truncated  of  into  diagram  solution;  the conditions  an i n e q u a l i t y  of the equilibria  determined.  for  boundary  adding  solid-compound  region^  one  concentrations, the  zones  a truncated  i n the latter  (Cj) 's.  truncated  Finally,  This  field  i n t h e aqueous  truncated-diagram f o r the solute  former  diagram  with  the  third  account the  an i n e q u a l i t y  system  and  not  that  these  diagram  (or  only  at  such  as  least,  those  eq.(2.46) for  involving  every  the  Cj  components. It  must be e m p h a s i z e d  plotted  when  dissolved  distinction  aqueous  composite the  no  solutes  diagrams  are  programs p u b l i s h e d  Therefore, method  instructions program  i s made b e t w e e n system.  useful,  this  are automatically s o l i d phases  Although  i s a severe  the  and  above  limitation  of  so f a r by o t h e r a u t h o r s .  in  diagrams  this  study,  " o f non-thermodynamic  f o r each  diagrams  i n the  composite  presented  last  type of composite  can :  be  but  plotted,  only  when  nature" are included diagrams.  by  the  special in :.; -  the  74  3-4-2  : metastable  Several  pieces  incorporated  into  referred  as  program  to  written  A more  first  compound  situation destroyed its  G°  G°  has  type  increases i s  force  interpreting  from  conditions  up  the  type  present i n  t o an  of  been  on  a  illustrates  a  the value  by  increasing  t h e G°  a compound  infinite  of  than  i t  cannot  system  be  which of  where,  cannot  be  to the value i t s  from  value,  and  a situation  equal  or  zone  system  force,  m  o f one  the  system,  "metastable with  the  is  list  of a l l  equivalent  thereby  the  A  of  a  a  is  conditions  given  diagram  depending  upon  aqueous of  diagram"  different  computed.  a constant concentration activity  this  the  C —H2O  metastable systems, imposed  by  to  eliminating  diagram.  diagrams  t h e y have or  G°  and  illustrates  a minimum d r i v i n g  Another  constant  less  diagram  Removing  plotted  the s t a b i l i t y  C o n v e r s e l y , by  considered i n the Cj  stable  in  without  i t s  i t s G°,  the diagram,  i s not  increased.  be  be  sometimes  m o d i f y i n g t h e G°'s  present  resulting  can  can  equilibria.  compound  compound  which  i t  on  kinetics  diagrams,  diagrams",  decreasing  been decreased.  increasing the  By  on  These  i s o b t a i n e d by  without a driving  been  species  diagrams.  t o compute s t a b l e  a compound, t h e  formed  information  "metastable  where  has  this  of  the  compounds.  this  if  diagrams.  phase.  For  component  species  j  are  obtained from  those f o r  may  represent  the  thermodynamic  instance,  Cj, two  by  or  imposing  imposing  equally  a  valid  75  conditions are  f o ran e q u i l i b r i u m ,  different.  linear  I f j  diagrams  different second  coincide  outside.  d i a g r a m .can  (j)-zone;  i s required,  of  potential  of  thermodynamic  (e.g; NH4  +  of this  respect  to  Rothwell  (1970)  ammonia  i sr e q u i r e d , t h e inside  the  case,-  i n t h e whole  range  the activities  outside  of  t h es o l u t e  the self-consistency  of  zone  such  a  In  account  of  NH4  type  +  a  to  as  of  ammines  a n d NH3 ( q ) .  elevated with  Hoar  and  should  "metastability"  kinetic  be  However, t h e  a  of  information i s  purposes.  o f metastable diagram  the sulfate  NO3",  f o r the high  certain  NH3 ( g ) a n d  t h e CU-NH3-H2O s y s t e m , t h e  temperature, and t h i s  with  up  literature  a r e "metastable"  NO2• a n d  f o rhydrometallurgical  easily  instance,  predominant  diagrams  out.  i nthe  I n these diagrams,  as  of  a r e provided by t h e  described  (Cu)(- d u e t o t h e p r e s e n c e  diagrams  last  often  these  the oxidation  importance  equilibrate  , and a r e  When a c o n s t a n t a c t i v i t y o f  last  presented  pointed  a t moderate  A  j  "stable"  i s"stable"  1977) .  the formation  o f high  traditional  For  Hepel,  However,  by  as  type o f metastable diagram  are generally  bounded  of  (Cj)£  c a n be v e r y l a r g e  Metal-NH3-H20 s y s t e m s  potentials.  of  be i n t e r p r e t e d  zone  t h e two  diagram.  Hepel . and  region  a -constant  does n o t reduce  diagrams  t h e C^-F^O s y s t e m ,  t h es o l u t e  a n d pH. 3 l n - t h i s  j , butthis  several  to  t h e same d i a g r a m  ,• o t h e r s o l u t e s  Examples  inside  the corresponding  and "metastable" outside.  j  several  belongs  When then  but  involves  species  compounds b u t n o t w i t h  and t h e b i s u l f a t e  ions  which  others.  equilibrate  76  readily  with  reduced  easily  sulfate the  (SO4)  system,  involve  (SO4)  depicted  simply only of  by  lower  be  considered  a diagram  and  the by  above the  sulfate  valence as  can  where the  the  data  for specific  non-thermodynamic  plotted  show t h a t  fed  to  problems, nature  the and  such  case,  the  in  sulfates  (S).  for  here  a  be  "component"  systems  stable  computer.  be  cannot  metastable  that  must  In  where  involve  as  but  independent  sulfides  examples  salts, species.  an  be  same p r o g r a m  changing  apply  basic  into  may and  All be  s u l f a t e s and  systems,  These  again  the  thoroughly  and  can  diagrams  information explicitly  defined.  3-4-3  : diagrams with  Since  the  primary  unknown  unknowns  simply  the  pA  of  diagram  can  be  of  electrolyte.  any  species  involves a solute  linear can  plotted with  c l a s s of the For  at  constant  the  and  taken a  as  a  equilibria  changing  as of  a  the  primary  a  result,  unknown, and  versus  not  co-ordinate  a component Cj  Robins  diagram do  primary  As  the  a  co-ordinate.  shows  Kwok a n d  Such  E,  r e l a t e d to  transformation.  a - l o g ( (Cu) t )  potential.  where  as  is linearly  concentration  instance, on  be  diagrams  total  CU-S-H2O s y s t e m  pA  A  pH  m  the  potentials  of  co-ordinates.  pB^,..., pB ,  any  Another logarithm  pA  various  (1973) pH  in  the the  represented  diagram,••'•computed"  is useful  in a  depend  upon  range E,  of and  77  therefore on  the  ;  where  system.  c  E-pH d i a g r a m s  Post,.and R o b i n s  multi-vanadium-atom • ions  the with  electrolyte.  When  relative  respect  to  with  information  the  complex  predominance pH  i i i - ^ s r ^ ^ , y - ' / i :  i sdivided  p r e d o m i n a t e s ^ -oyer diagram.is  into  solute,:  computed  solute  zones  .; t h e , ; o t h e r s , with  and  of the  ( V )  i n the  t  • <•-•....•-  zone  where  one  and i n each  pAj as the  example,, a,-log.( (Cj) t)  In,each of  minimal  -log((C£).t) , , i s , r e q u i r e d ,as . a , c o - o r d i n a t e , t h e f i e l d  diagram  For  only  (19.76.) d e a l i n g  t  V-H2O.system,^emphasized  provide  (Aj), (CjJt  Cj-solute  solute  corresponding  v e r s u s , pH d i a g r a m  zone  Aj  (Aj), a  co-ordinate.  should  i s related to the  ofthe  be p l o t t e d . concentration  A j as follows  (Ci) The  = -ti(Ai)  t  notations  coefficient  -log(Ci)  are  t  ,segments  solute  zone  the  e q . ( 3 . 01) same  o f A j i s constant  i s first the  pAj-pH  (Aj).  Then  a translation  valid.within  the solute  characterized  (Ci)  t  2.  zone,  The  between  diagram  leads  zone  (Aj).  two  solute  b y t h e two f o l l o w i n g  = 'ti(Ai)  x(Ai)  + titA'i)  activity  and thus  eq.(3.02)  i . e . t h e end-points  of  boundary  chapter  i n i t s solute  conputed,  o f a l l end-points  '  i n  w  co-ordinate  The  as  = pAj - log(ti(Ai)/o (Ai))  A pAj-pH diagram the  x(Ai)  are determined given  of  within the  by eq.(3.02) o f t h e  to a -log((Cj) )-pH t  zones  a l l  ( A j ) and  diagram  ( A ' j )i s  equations  x(A'i)  eq. (3. 03)  78  tj(Ai) and  x(Ai) = tjfA'i)  x(A'i)  eq.(3.04)  then ( o (Ai) tiCA'i) ) pAj - p A ' j = - l o g ( ) ( O (A'i) ti(Ai) ) w  eq.(3.05)  w  For  t h e sake  When both  a  constant  provide  with  When  a  a  between  not  taken  solute  zones  As and  into  a result,  arises  the  time  i s  framework  low since  which  programs  lies  such  using  on t h e  solutes i n cannot  be  the  f o rcomplex  c a n be  valid.  computer  (as i n Duby's  program  on t h e  For instance,  The  t o be i n v e r t e d ,  The m a i n  computed  based  different  programs).  need  compute t h e  diagrams.  programs,  by p o i n t  (1979)  as eq. (2.46).  which  of diagrams  Several  point  no m a t r i c e s  i n that  imposed  zones  t o such  are equally  o f t h e p r e s e n t method,  inequalities technique  variety  c h a p t e r 2.  and Brown's  by  A'j  '  explicitly  two s o l u t e  to  compounds p r e s e n t a t t h e boundary a r e  c a n be computed  Osseo-Assare  therefore,  a n d pH.  t h e same c o m p u t e r  c a n be w r i t t e n  diagrams  between  a large  i n  eq.(3.05)  as f o rt h e complex  The c o m p u t e r  by almost  presented  programs  not  beforehand a r e not adapted  plotted  method  account.  i s  system,  corresponding  pH,  -log(Cj)^  potential  the solid  Cj-I^O  and  unknown.  o n t h e s y s t e m , a n d when  eq.(2.37)  between  diagrams: t h e boundary when  single  pAj  t h e same d i f f i c u l t y  determined  i s imposed  equation  a relation  constant  system,  or  the  a relation  eq.(3.02),  l e t A j be t h e p r i m a r y  potential  A j and A ' j belong t o  together  E-pH  of simplicity,  can  (1973)  computing and, i n the  handle  disadvantage of  s y s t e m s , most  diagrams  only this must  79  be  interpreted  are  sometimes  at  each  point  A lines is  is  now  results  o f a number  presented  projection  diagrams,  r e p r e s e n t e d b y a same  program  described  as  in  i n diagrams  has been  point.  written  which  2.  I t  has  to  the  data  decipher.  actually plots  of diagrams. computed  i n c h a p t e r 7 f o r t h e Cu-Fe-S-H20  investigated.  equilibria  Displaying  difficult  of different classes appendix  and s e v e r a l  system  The the  a l lthe program diagrams  a t 200°C  which  80  P A R. T  I I  THE CU-FE-S-H2O S Y S T E M A T  A tool equilibria  has been  between  multicomponent apply  this  in  Chapter  discussed  data  i n part  an aqueous phase  system  tool  thermodynamic  described  to  4, 5 a n d 6. i n Chapter  The s c o p e  m  needed  7.  Cu-Fe-S-H20 t o compute  The r e s u l t i n g  I f o r representing  and t h e s o l i d  C -H20. the  200°C  system  compounds o f a  of Part at  the equilibria diagrams  the  I I i s to  200°C.  The  are provided  are presented  and  81  ' CHAPTER  CONSIDERED  SECTION  4-1  :  The required their  COMPOUNDS AND  free  energies  standard state,  must a l l  compounds,  state  will  o f the pure  aqueous phase,  state  liquid  phases  solutes  the  such  the standard  o f S° u n d e r water,  species  not a l l have  be  consistent  in  t h e same with  the  to plot  standard  the diagrams: state  i s  the  g a s a t 200°C a n d  at  one  solutes  c a n be g i v e n  chosen  approach  so  as Cu°, Bor o r S ° , except f o r  state  that  o n e when  i s the stable  a pressure  these  of  conditions  the standard  200°C a n d a t i t s s a t u r a t e d  generally  the  may  be u s e d  perfect  c o m p o u n d a t 200°C a n d u n d e r  The  to  G ° , which are  pressure.  the condensed  stable  DATA.  states.  gaseous  For at  The s p e c i e s  but the data  noted  correspond  For  For  The  data,  states  atmosphere  pure  input  standard  the  F R E E ENERGY  formation,  following  hypothetical  the  of  states.  same s e t o f s t a n d a r d The  AVAILABLE  generalities.  as computer  standard  4  state  pressure.  several  standard  activity  the ionic  one i s the  states,  liquid. liquid  H2O  which  are  coefficients  strength  of  of the  atmosphere.  i s the pure  vapor  the  state  the  of the solution  82  approaches depend The an  zero.  Therefore,  on t h e u n i t s  one  i n which  corresponding  ideal  solution  the standard  the concentrations  which  dealing with high  independent standard ideal  of  state  concentration  activity  different  may  and  At  equal  a c t i v i t i e s ' , are difference  terms  25°C  ;  and  t o 0.99708  of  energy liquid  cal/mole.  Molality  when  solute: are this  according  e q u a l , and so a r e t h e i r text,  molality.  the  corresponding  Since  and  :  i t s  pressure, 1973);  this  t h e two  corresponding At  state  i n free  200°C,  i s 0.8628  energy  i s then  d e f i n e d a s t h e number between  solution  t o t h e above  an  of the  over  cal/mole.  the ratio  zero,  of  to the density  the  t o -1.74  whole  state  molarity  i s equal  also be.often  are  the ratio  i n i t s standard  strength approaches  expressed  of  difference  since the  o f s o l u t e p e r kg o f  atmosphere  equal,  and t h e mass o f t h e  the ionic  The  ( P e r r y and C h i l t o n ,  water  moles p e r kg o f s o l v e n t .  pure water  one  used  solution  and p r e s s u r e ,  i s equal  may  mole  of molality  ( i b i d . ) - , , and t h e c o r r e s p o n d i n g  of  one  i n terms  .then,; a l m o s t  i n free  density  -139  pressure.  contains  expressed  expressed.in  i s  in  of  liter.of  .often  be d e f i n e d a s t h e h y p o t h e t i c a l  which  pure water.  unit  :  aqueous s o l u t i o n s , solutes  A t , a given . temperature  activity  the  the  of a,species  density  temperature  temperature  solution  solution;  of  of  expressed.  c o n t a i n s one mole o f s o l u t e p e r ;  concentrations  are  to molarity i s the hypothetical state  solution^. ,Molality-"is:ranother when  states of the solutes  t h e mass o f  approaches  one  t h e two a c t i v i t i e s  of a  definitions  corresponding  free  of  molality  energies.  concentrations of the s o l u t e s are expressed .  - -  In in  83  In depends  the on  individual be  Cu-Fe-S-H20 the  value  aqueous  determined  the  aqueous  be  taken  into  set  equal  will  be  to  H  at  consistent with  is  such  as  equal  temperature  -  5 Cu°  +  Cu°  H  +  +  of  +  0.5  main  are  results.  3 +  )  measured value  of  in  Should value are  2 +  data  G°(Fe  For  2 +  ). or  )  This from be  always  other  compound  instance, for as  Cu(0H) ,  the  +  energy  change  a  -  at  eq.(4.02)  standard  states.  collecting the  As  of  after  and  2 +  and  )  and  the  Fe  3 +  hence  accordingly. a careful  available  the  were  value  /Fe2+  either 2 +  the from  electrode.  measurements, Available  literature  of  couple  d e p e n d s on  Fe°/Fe  improved  in  G°(Fe3+)  determined of  lies  the  below,  the  and  is  potential  data  data  discussed  value  modified  documented  elements  arbitrarily  +  solutions,  changed  must  eq.(4.01)  potential  the  of  reactions  in  last  o f G°(Fe3+) m u s t be not  For  free  constant  are  f o r every  instance, G°(Fe  the  of  cannot a l l  for the  f o r a s o l u t e such  between  perchlorate  G°(Fe  solubility  in their  independently. on  G°'s  conventions.  = Cu(0H)  coherence  relies  G°  G°'s  electroneutrality  ion  +  the  = CusFeS4  difficulty  experimental  The  H  function  they  more a r b i t r a r y  respective  02(g)  a  G°(Fe  these  following  4 S°  one  200°C.  the  +  of the  f o r the  d  the  Fe°  determined  n  b o r n i t e or  maintaining  not  because  to  where a l l s p e c i e s  The  a  energy  Moreover,  A c c o r d i n g l y , the  2(g)  zero  free  constants.  hence  account.  Fe°,.S°, 0 2 ( g ) ,  G°  and  the  considered, . although  independently solution,  phase  five  ions are  Cu°,  solid  of  system,  the data  survey  is  84  often are  required  t osort  i ^ - w l  based.•  out  ^  the f * ' ? y -  experimental facts . •• ;v •  - -/WVK7.-: V  SECTION;;4-2i : c a v a i l a b l e . p h a s e - d i a g r a m s  . ~  - I n f  likely ranges to  this  section  t o be s t a b l e and  a n d Subba  phase  diagrams  2°3»  ranges their (1941) Bovin  200°C,  metal  Rao,'  solid  as-well  CU2O  formula.  four  and  This  measurable  rate  therefore  not a  below  known  A Cu-Fe-0 phase and  oxides:  as  their  are  composition  they e x i s t according  stable  into phase  i n the Fe-Cu  Kullerud  They  below (1964) .  recently  reviewed  and  t h e Cu-O  Fe304,  hematite  a l l have v e r y  narrow  compositions correspond t o  CU4O3  compound  diagram  CuO.  was d e s c r i b e d  was r e c e n t l y  190°C  been  magnetite  and t h e i r  T h e compound  (1978).  compounds w h i c h  A t 200°C, t h e Fe-0  tenorite  andi t s s t r u c t u r e  compounds a r e  o x i d e s have  1974).  o f homogeneity,-  f r o m Yund  the  diagrams.  include  cuprite  ^  ternary.  transition  (Rao  F e  phase  : the Cu-Fe-0  The  at  they  a t 200°C.  the stable:assemblages i n which  the published  4-2-1  are l i s t e d  on which  determined  breaks cuprite at  down and  200°C.  by  Frondel  by O'Keeffe and at a  slow b u t  tenorite, No  and  i s  intermetallic  system.  560°C  i s represented i n  Two t e r n a r y  fig.(4.01)  compounds have  been  85  observed: latter  delafossite  forms  spinel  by t o t a l  structure extending  priori.  This  spinel  into  the  hematite}  this  i s  the magnetite  from  stable.  CuFe204.  Cu(II)  solid  cannot h a s been  There  i n the  excluded  studied a  to cupric  t h e assemblage  ferrite  solid  a  recently  one  phase  ferrite  above  {delafossite  A t 500°C, t h e c o m p o s i t i o n r a n g e s  and t h e c u p r i c  The  solution of  be  i s indeed  magnetite  temperature,  by  stable  ternary  1970).  extending  Below  A  o f t h e diagram  and S h i r a i s h i ,  ferrite  of Fe(II)  magnetite.  region  field  1005°C.  replacement  of  magnetite  (Yamaguchi  CuFeC<2, a n d c u p r i c  solutions  +  o f both  are already  narrow.  4-2-2  : t h e Cu-S-0  There A  i sa large  comprehensive  equilibria  below  electrochemical diagram  body  description  of  250°C w a s p u b l i s h e d investigation  four  of  CU2S, c o v e l l i t e a copper  which  the  content which  and t h e r e c e n t l y  phases,  which  (Morimoto  and Koto,  at  sulfur  decompose 1970).  above  a p r e s s u r e o f 65 k b a r s .  At  phase  93°C  are low  and  70°C  1966).  digenite  reaction  %.  temperature respectively synthesized  For instance at  completely into no  phase  chalcocite  65.5 t o 63.8 atomic  (Munson,  200°C,  careful  phases a r e  copper,  The f i f t h  anilite  300°C, a m i x t u r e o f C o v a n d S° r e a c t s  phase  A condensed  A m i n e r a l CuS2 h a s b e e n  pressure  system.  a  A t 200°C, f i v e  from  observed  after  1977).  sulfur.  ranges  Cu-S  copper-sulfur  recently  (Potter,  CuS and l i q u i d  vapor  on t h e  are stoichiometric:  Djurleite  high  of literature  i s represented i n fig.(4.02).  stable,  has  ternary.  CuS2  occurs  above below  Atomic per cent  Fig.(4.01) Cu-Fe-0  phase  diagram below  560°c  (Yund  and K u l l e r u d ,  1964)  250,  200  Cov + Dig  o  o  e  a>  150  v + S  iia  MS  o  2.  °  IOO  I  Anilite +Dig 75t3°C ~"  E <D  50  ls ° Anilite +Cov +  Anilite + Djurleite  Djurleite  Anilite 10  1.7  1.8  Ratio  1.9  t-fLow Cct Low Cct + Cu° Djurleite i low Cct 2.0  Cu/S  F i g . (4.02) Condensed  Cu-S p h a s e  diagram  (Potter,  1977).  87  12  kbars.  Under,  normal  conditions  at  200°C,  s t r u c t u r e , m i n e r a l , i s not, s t a b l e ,and decomposes  readily  ;  and S ° .  ,  :  The  v:  ternary  anhyd,ro,us cuprous not  i:« 2 .  v  ;:  Cu-S-0 phase, d i a g r a m  cupric;.;sulfate.  s u l f a t e , does, e x i s t ,  which  4-2-3  : the  An region  conditions  Fe-S-0  been  s i m p l i f i e d , Fe-S 200°C,  i t  Pyrite  FeS2  (Kullerud  % Fe. .  composition  at  phase  1959).  small first  range: 50  its  composition  pyrrhotite,  which  rich  rich % Fe,  diagram, with  and an  properties  are  at least  under  1972).  iron  phases  is in  as  and  pyrrhotite  Fine,  1976).  a  cubic  range  and  has  structure  S°.  is. a  an  solid . 46.67  extended  equilibrium  with  t h e same c o m p o s i t i o n a s  i s not as  in  At  and  around has  A  structure  pyrrhotite  established  47.8  equilibrium  a  b e s i d e s Fe°  with  boundary,  i s evaluated  appears  (Power  i n the  pyrrhotite  boundary  shows a d i f f e r e n t  pyrrhotite,  A  .stoichiometric.;  system  Monoclinic  hexagonal  atomic  sulfur  phase,  the  ;  unstable,  .composition  i t s iron  The  hexagonal  - - •.  i s represented i n f i g . (4.03).  stoichiometric  troilite. iron  recently  four  A  Cov  more m i n e r a l ,  Habashi,  least  a  contains  and  t h e Fe-S  .diagram  Yoder,  solution . with atomic  undertaken  includes  and  (Vo V a n  r e v i e w on  phase  is ^  seems  into  ternary.  extensive  has  one  .i s  pyrite  >•  i t s thermodynamic  e s t a b l i s h e d , ; y e t a n d ... i t  hydrothermal  Fe°,  but  .•.••-.:•.•,:"!•_  includes  CUSO4,  this  with  than  distinct  composition evaluated  atomic  the phase as  %„.  the first  yet, A  second  monoclinic hexagonal  in this 47.1  but  phase  atomic  %.  88  300  Hex. L.T. P y h (Dopy  262° 250  o  200  I  Tro +  E  ^254*  il  150  CL  /  Hex. L.T. Pyh (I)  jHex. L.I. P v h l ^ U - P y r  MPyh  V  MPyh+Pyr  //Hex. L.T  100  -'Pyh(2)  ~75  Tro + Hex. L.T. Pyh(2)  50  50  49  (Si+ithite + " MPyh 48  47 Fe  Smithite-i-Pyr U-Greigite  46 Atomic  c  42  38  34  %  Fig.(4.03) S i m p l i f i e d Fe-S phase diagram, showing t h e v a r i o u s p y r r h o t i t e phases.  89  The  transition  pyrrhotite  occurs  denotes  the  phase  200°C.  at  Marcassite pyrite.  i s an  monoclinic  at  near  often  1978),  Fe-S-0 phase  stoichiometric.  4-2-4  : t h e Cu-Fe-S  ternary  phase  diagram.  Until  mainly  investigated  of  The  phase  and  Kullerud  well  :  of  a  two  hexagonal  Tro  pyrrhotite  replacement  as  product  for  more s t a b l e  ferrous  sulfate  of  structural to  pyrite  compounds:  FeSC>4, w h i c h  the Cu-Fe-S-0 system  recently,  this  phase  . due and  a t 700°C and  (1966),  are  are  to  a are  (Barton,  1973)  copper,  sulfur  phase and  and  has  been  conditions.  Many  obscured of  by  close  reactions. determined  in  four  pyrite;  by  fig.(4.04)  assemblages  involve  Cu-Fe-S  assemblages,  s t i l l  200°C, as  represented The  system  compounds  to s l u g g i s h at  the  mineral  i n anhydrous  diagram  is  Cu-Fe-S  o b s e r v i n g quenched  respectively.  iron,  study  1973).  and  structures  diagrams  established  phases  by  this  and  this  environments  includes  difficulties,  compositions  hexagonal  t h e same c o m p o s i t i o n  initial  at given temperatures  experimental  fig.(4.05)  the  in  this  with  first  ternary.  last  synthesized  the  i t i s metastable relative  (Rising,  Fe2(S04)3  both  The  but  diagram  sulfate  features  of  p y r r h o t i te i n supergene  (Fleet,  ferric  boundary  o c c u r s as  and  However,  o r t h o r o m b i c phase  a l l temperatures  The  troilite  140°C.  iron-rich  It  reasons  between  a t 700°C  Yund and seem  stoichiometric and  three  solid  90  S (liquid )  Cu°  Fe° Weight  per cent ,  Fig.(4.0 4) Cu-Fe-S phase  diagram  at  700°c  (Yund  and K u l l e r u d ,  1966).  6 0 Weight  Cu-Fe-S phase  diagram  per  cent  S  Fig.(4.05) a t 200°C ( Y u n d  and K u l l e r u d ,  1966).  92  solutions  : pyrrhotite, bornite  field,i\which  ^ds  now  ( I s s ). •  solution"  and an e x t e n s i v e  referred  •  :  phases  appear  Kullerud  on t h e  ;  phase  200°C; h e x a g o n a l  covellite  501°C,= h e x a g o n a l  chalcocite  and  the immiscibility  between  •:•  •; • fields  shrink,  According  to  contains  appears  very  1ittle  bornite  digenite  The a s s e m b l a g e s  and  +  +  t o be s t a b l e  below  475°C, 328°C a n d 228°C  (ibid.).  As a r e s u l t ,  Yund  and  includes  four  Kullerud's  ternary  chalcopyrite  and cubanite.  composition  corresponds  to  #  and, t o a l e s s e r  some  extend  and hence  It bornite This  has  i sstable  phase  between  been  recently  has a cubic  form  structure  temperature (Kanazawa  • In thelast  decade,  the - o t h e r  phases,  extensively  studied.;:  Among  #  degree,  that  which  occurs  pyrrhotite},  from  diagram  at  bornite, and  i t s  contain  a polymorph o f 170°C a n d 225°C.  i san intermediate  form  are  respectively  chalcocite  determined range  435°C  the "binary"  diagram.  cubic  near  idaite,  theternary  i n t h etemperature  t h eh i g h  tetrahedral  into  idaite at  i s stoichiometric  Cu5 5FeS6 5.'  compounds, d i g e n i t e iron  phase  compounds:  Idaite  and  chalcopyrite}  reported  200°C  Yund  bornite  {copper  and { d i g e n i t e  a n d new  copper a t  a t 507°C, h e x a g o n a l  s e p a r a t e s from  pyrrhotite}  solid  •  solution  'between  200°C a n d 300°C.  {chalcopyrite•"•+•  as t h e"intermediate  diagram.  (1966); - p y r r h o t i t e  solution  to  ;.^«r.a^x;r.  On c o o l i n g 'from 7 0 0 ° C , t h e s o l i d  solid  stage  and t h elow temperature  e t a l . , 1978).  t h e Iss' phase  mainly chalcopyrite Cubanite  and i t s  relation  and cubanite,  i s t h el o w copper  with  have  boundary  been  of  Iss  93  and  i s «a " v e s t i g e "  Natural  cubanite  transforms, centered the  of this i s  between  cubic  •' t h e  structure  high  1973; is  with  Dutrizac,  s t i l l  temperature  form  structure  the  cubic  temperature.  temperature  directly  to  i n  the  results  which  laboratory.  to  of cubanite  1977).  The s t a b l e  face  However,  i n exsolution  leads  and  the  e t a 1 . , 1973).  matrix  1976; P u t n i s ,  which  was  measurements  (Pankratz  transition,  but- an  (MacLean  a  of a  metastable  (Cabri state  reported  only  that,  Iss  determined  et a l . ,  at  200°C  from  on t h e CuFe-S  with  transition"  not  breakdown  a  join,  for  first  order  i n t o p y r i t e and I s s  of chalcopyrite  the stoichiometric  Moreover,  I s s a t any  557°C b y c a l o r i m e t r i c  i s  The c o m p o s i t i o n  (1973).  at least  as  1970)  incongruent  slightly  by Barton  be a s s i m i l a t e d  "tetragonal/cubic  and K i n g ,  e t a l . , 1972).  deviate  cannot  The s o - c a l l e d  chalcopyrite,  with  room  210°C,  o f Iss' (Cabri  chalcopyrite  temperature.  suggest  at  low  questionable.  Conversely,  to  and  at  seems-.irreversible  phase o f c h a l c o p y r i t e assemblage  stable  orthorombic  200°C  -transformation  Cooling  phase,  composition,  Barton's  chalcopyrite  appears  results  as  (1973)  i s i n equilibrium  a b o v e 400°C, and maybe s t i l l  a b o v e 300°C ( b y  extrapolation). T h r e e new m i n e r a l s been  observed  compositions, within  the  initially and  well  Recently,  talnakhite, mooihoekite  (Cabri, very  Iss  close field  considered defined fine  1967; to that at  structures  at  and  haycockite  Hall,  1972).  of chalcopyrite,  600°C  as s t a b l e  particles  Cabri  and  (Cabri,  phases with low  of metal  1973K distinct  temperature  enriched  are  have Their  included  They  were  compositions  (Hall,  chalcopyrite  1975). and more  94  specifically a  m o o i h o e k i t e and  transmission  Putnis, The  electron  1978).  The  temperature  microscope  samples  could  by  that  a l l cases, the  structure  should  structure appear  of  on  the  form  the  cooling  were  not  modulated in  varying  talnakhite  focus of stable  directly  Iss with  transformation  t e m p e r a t u r e , and  on  the  cooling  of  substantially electron fact  by  X  microscope,  and  300°C  by  solutions overcome  the  conditions, method  consists  end  solution, of  the  TTT  of  behavior  curves,  differs of  the  of  recently  in  metastable  phases,  structures  observed  the system  been  The  the  compounds appear  of  region  below  resolution  and  sluggish  will as  the  a  still  be  function  of  ternary.  investigated from  technique  reactions  in  above  aqueous seems  to  anhydrous  300°C. a  temperature  contains  several  vessel.  P4~2m  investigations  in establishing  and  by  This  which  tetragonal  just  a l . , 1975). of  show  down.  the  variety  studies  phases  assemblages  above  vessel,  further  was  metastable  mineral  difficulty at least  pressure  chloride  et  has  beam.  F4~3m  two  temperature  state  electron  temperature  P4~3m  With  Further  system  (Sugaki  that  illustrated  the apparent  precipitating  the high  I43m  composition in this  Cu-Fe-S  temperature  of stable  to assess the s t a b l e  The  hot  to  the  1976;  These  beam.  group  low  assemblages  leading  temperature  a  the  McConnel,  the  but  composition.  ray d i f f r a c t i o n .  needed  The  with  as d i s t i n c t  thereby  Iss phase,  under  under  determined, but  from  space  and  studied  precisely  low  phase, the  (Putnis  heated  be  have been  sulfides  These  a  gradient  concentrated as  sulfides  nutrients dissolve,  along  ammonium near they  the are  95  transported  by  precipitate  as c o e x i s t i n g  electrolyte, four  near  enough  electron This  to  be  microprobe  work  confirms  homogeneity  the  s u l f i d e phases cool  vessel,  as  composition their  was a l s o Barton's  low  as  observed  used  they  with  After  the  three  crystals  or are  an o p t i c a l m i c r o s c o p e  (an  in their investigation).  r e s u l t s about  the  and t h e p r e s e n c e  300°C.  by Yund  conclusions  with  and  i n equilibrium  end o f t h e v e s s e l .  identified  of chalcopyrite  temperature  at  the  across  w e e k s a t 300°C o r a t 350°C, t h e p r e c i p i t a t e d  large  of  convection  I t  small  also  (1966).  are i n disagreement  of  o f t h e I s s phase a t  confirms  and K u l l e r u d  range  with  the idaite  However  previous  some  results  300°C a n d 3 5 0 ° C : Two  pyrrhotite  phase  and  stable  above  The  very  atomic  the  254°C  %)  may  structure  i n  0.2 a t o m i c  % Cu.  Yund  and  precipitate  monoclinic  little  Bornite  phases  phase,  be  contained  sufficient  the ternary.  has a wider Kullerud  (Power  to  (1966),  and  since  Fine,  the  pyrrhotite  field  hexagonal i snot 1976).  p y r r h o t i t e (0.07  stabilize  solution  a  the latter  i n monoclinic  Hexagonal  solid  300°C,  although  i n t h e Fe-S s y s t e m  copper  at  monoclinic  contains  than  i t s Cu/Fe a t o m i c  about  observed ratio  by  reaches  3. 2 a t 3 0 0 ° C . Idaite  develops  equilibrium The  with  assemblage  between  228°C  been o b s e r v e d Sugaki's  large  euhedral  covellite,  {bornite  (Yund  i n hydrothermal  experimental  pyrite,  + pyrite}  a n d 568°C  device  crystals  which  bornite  (Sugaki  or  i s thought  and K u l l e r u d ,  conditions  which  are  in  chalcopyrite. t o be  stable  1966), has  neither  a t 300°C n o r a t 3 5 0 ° C . et  a l . ,  1975)  i s  96  interesting,  but  the  interpreted.  For  instance,  electrolyte  composition  constant i n the course is  reached  features  above  disagreements i t  near  should  the cool  of  the  already  fairly  remains  the  Cu-Fe-S  well  best  be  and  diagram  established,  available  checked  and  Cu-Fe-S  at  the  remains  time,  t h e main  seem t o be  Kullerud  phase  be  equilibrium  200°C  the  to  that  that  At the present  phase  have  end o f t h e v e s s e l  of the experiment,  a t t h e end o f t h e r u n ;  will  diagram  diagram  at  this  diagrams  have  t e m p e r a t u r e . . . . . . .  4-2-5  : phase  In been  (Posnjak  the  and Merwin,  ferric  with  hematite  the  monohydrated  basic  or with  as a s t a b l e difficult  compounds/ measured the  cupric  but  the  by Posnjak  stoichiometric  sulfate  when  1929)  more  i s  compounds:  c a n be i n e q u i l i b r i u m conditions,  and  antlerite  with  tenorite  The u n h y d r a t e d  cupric  of water  composition  o f the above  (1922 and 1929) a r e  compositions.  fig.(4.06),  i n hydrothermal  the a c t i v i t y  compositions  in  CUSO4.H2O,  the  Fe2O3-S03~H2O  Tunell,  three  i n equilibrium  ascertain  et a l .  The  and  include  sulfate.  phase to  (Posnjak  sulfate be  200°C.  FeSO^OH, w h i c h  ferric  may  at  They  cupric  monohydrated  often  system  sulfate  CuSO/j. 2 C u (OH) 2 w h i c h  is  two more p h a s e  1922) i s r e p r e s e n t e d  in fig.(4.07).  the  appears  H2O.  experimentally  CUO-SO3-H2O  represented  the  involving  t h e Cu-Fe-S-H20 s y s t e m ,  determined  system and  diagrams  or  sulfate  i s low. of  with  It  hydrated  three  compounds  very  close  to  97  Hem  j  Fig.(4.07)  i CUO-SO3-H2O phase diagram  a t 200°C  (Posnjak and T u n e l l ,  1929).  98  Under  reducing  observed  in equilibrium  solubility 1965). all  except  Above  about  dehydrate  into  hematite  pH  hydroxide  90°C, f e r r i c  mentioned  of  that  in of  into  turn,  1950).  Biernat  with  water of  Ferrous  a i r  at  150°C  last  low (1972)  to  four  relatively  into  depending  Robins  above  the  observed  1949). of  in  eta l . ,  is  165°C,  and  these  tenorite  dehydrates  Kidd,  and  et a l . ,  Gainsford  presence  a t 200°C u n d e r  as  (SO4)4.6H2O have  are  the  Their as  i n aqueous  a whole  a  result  both of  guildite  been r e c e n t l y  reported  study at  involving  and  et al.,1978).  observed  As  (Bruhn  130°C and  the  neither  sulfates  in Arizona  structures  this  in  is  form  hydrated  low  water  pressures considered here.  reported  They  (e.g.  ( S m i t h and  in  reacts  Therefore,  hydrated  Wan  between  readily  i t  media  sulfate  temperatures,  t o 180°C  which  the s o l u t i o n  compounds a r e s t a b l e  2  rates  (Partington,  magnetite.  CuFe  at elevated  hydroxide i n water  goethite,  oxidizes  temperature  Two  water  in chloride  at detectable  the  vapor  with  ferrous  C u p r i c h y d r o x i d e i s known t o d e h y d r a t e  1975).  upon  the monohydrated  d a t a h a v e b e e n p r o v i d e d up  conditions  to  conditions,  a  mine  soluble  conditions.  and  iron  fire  :  has  been  ransomite  CuFe(SO4) 0H.4H2O,  whose  2  investigated  thermodynamic  easily  copper  (Wood,  properties minerals,  They w i l l  not  1970;  Ch'ng  are not  known.  and be  have not considered  been in  200°C.  therefore,  27  solid  Cu-Fe-S-H20 s y s t e m  thermodynamic  at  d a t a m u s t be  compounds  are  likely  200°C, f o r w h i c h found.  t o be  stable  a consistent  set  99  SECTION  4-3  :  available  free  energy  data  for  the  solid  compounds.  The S°,  H  thermodynamic  (g)  2  Hultgren used  0 (g)  ferric  et  a l . (1973).  for  details  of  (4.01)  should  kept.  m u s t be  The listed of  two  water  value Tunell,  is  the  more  not  at  than  result  of  (Stull  and  f o r the  ferrous  and  points  for  which  1.  The  Given  the  significant in  the  1977).  i n appendix  listed  a  are  tables  200°C.  three  numbers  activity  that  of  with the  H 0  table  figures (4.01)  calculation.  can  be  noted  to  Posnjak's  from  the  acid  with  than  i n the  0.86  observations  unhydrated  availaible stable  dehydrates  is less  2  solutions,  i s s t a b l e i n more d i l u t e  is  G°'s  (1974)  chalcocite for  reported  cupric sulfate  sulfuric  - According ferrite  are  of  a l . (1973)  and  Fe°,  review  Mills  recently (Potter,  resulting no  et  Cu°,  values  (4.01):  consistent  concentrated sulfate  as  and  from King  provided  following  the  1929),  and  from  "JANAF"  oxides  elements  critical  data  the  iron  extended  monohydrated when  from  the  the  for covellite  data,  The  in table the  the  these  considered  from  calculations  lists  of  be  been  the  accuracy  the  except  have  of  Selected  sulfates,  compounds data  taken  sulfides,  anhydrous  accurate  table  iron  1971)  copper  are  2  f o r the  Prophet,  The  and  properties  sulfate  is  while  the  .  presence Such  (Posnjak stable  a and in  monohydrated  solutions.  data  (King  respect  e t a l . , 1 9 7 3 ) , to t e n o r i t e  and  cupric hematite  100  below  about  cupric  425°C.  ferrite  Kullerud,  This result  does  '1964),  not and  i s consistent  exist  i n natural  that  i t  be  (Gainsford  Kullerud  experiment where c u p r i c  at  made a n  300°C f o r 270  "stability" anhydrous  days  must  (4.01)  the  known a t t h e  often  made  of  resulting  However, For from  Tro,  low  to  heat  at  has  25°C ±0.3  points  values Tro The  but  under  Yund  here  and  remained  again,  this  reactions  K  Burgmann from are  in  Gronvold,  good  recently 1969)  are  assumptions  difficult  capacities et  the  in not are  uncertainty  to assess.  (Coughlin,  measured  have  a l . ,1959), 1950).  by  been as  The  solution  measured  well  as  heat  high  content  calorimetry  as  and  K i n g , 1964).  This result  is in  high  temperature  equilibrium  data  extrapolated  to -24.15 k c a l / m o l e  very  accuracy of  have been  heat  (Adami  listed  noted:  et a l 1 9 6 8 ) /which,  then  comparatively  s h o u l d be  recent  -24.0  values  systematic errors  i s therefore  capacities  kcal/mole  The  G°  e x p e r i m e n t , and  (Gronvold  been  the  f o r m i s s i n g d a t a , and  temperature  agreement w i t h  (e.g.  of  figures  350  temperature  good  and  ferrite  sluggish  of  task.  t i m e o f an  to compensate  several  5 K  -23.9  to  accuracy  is a difficult  always  the  (Yund  conditions.  Estimating table  attributed  that  a l . , 1975).  without decomposing,  be  fact  crystallized  hydrothermal-conditions (1964)  the  assemblages  cannot et  with  at  25°C,  yield  (Mills,  1974).  The  data  binary  oxides  is  also  reliable. t h e G°  f o r the  in table remeasured  and  from  four  (4.01). at 300  low K  The  heat  capacities  temperatures  t o 550  K  (Bartel  of  (Westrum and  Mag and  Westrum,  101  1975).  There  reported these  are slight  by  t h e JANAF S e l e c t i o n  differences  capacity  and  present  differences  are  less  (Stull  than  f o r the entropy.  with  respect  to  and P r o p h e t ,  1 cal/mole. K They  the  data  1971), but  for  the  are not significant  heat  i n the  work.  Conversely: The  e n t r o p y o f B o r was e s t i m a t e d .  The  heat  from  53 K  between  to  -40.1  in not  They  into  pyrrhotite  have  solid  sulfur  been  solution  Below  53 K a n d  estimated  (Stull  measured  by  and P r o p h e t ,  for  the  ferric  e s t i m a t e d by c o m p a r i s o n  with  large  of  for  either  Cpy have  not  At high  data  25°C  from  temperatures,  The  assumptions  for this  d e p a r t u r e from  was d e t e r m i n e d  pyrrhotite  "Cpy"  and Wagner,  the  the  ideality  (but  are  of the  only  above  (1964).  copper  these high temperature i s  at  ( e . g . Bog and R o s e n q u i s t , 1959)  and .Barton activity  1974).  of reliable  which  available  which  measured  been  gas and p y r r h o t i t e .  the  ( e . g . Pemsler  synthetic  been  (Mills,  pyrite  temperature  Moreover,  have  content of Pyr scatter  sulfur  with  by Toulmin  The  phase,  have  the lack  with  consistent  they  been  sulfate.  overcome  equilibrium  have  o f manganese s u l f a t e  -42.5 kcal/mole  to  sulfate  8 7 0 K t o 1 0 8 2 K.  of values,  values o f the heat  decomposes  600°C)  and from  capacities  (ibid.).  to  made  of ferrous  those  of ferrous  The  Pyr  with  No h e a t  sulfate those  295^K  t h e two s e t s  comparison 1971).  capacities  Cpy  been measured  has  been  1975), or  the  measurements phase. recently  measured but iron  refer  The h e a t at  high  no  at high data  i s  activities. to  the  Iss  capacities of temperatures  102  (Pankratz has  and  been  King,  treated  incongruent  of  temperature  sulfur  capacities.  As  by  the  -51  kcal/mole  at  result, not  higher  10%  The  As  f o r Cpy.  and  compounds and  pyrrhotite  and  the  digenite,  idaite,  and  hydrated  the  hexagonal  these  I t must  hence  free  to  energy  will  in  high  these  heat  ranges  from  to  selected  by  figures.  table less  however  (4.01) than  that  compounds which  accurate  data  are  cupric  in  1% the  react  thermodynamic  described in  available  which  Tro  for  19  are: monoclinic  ferric  Except  between  generated  as  equilibrium  and  sulfate.  be  on  two  listed  for eight  intermediate  the  kcal/mole  these  noted  an  hydrometallurgists.  phase  c u b a n i t e , the  data  -40  kcal/mole  to those  of  values, provided  Cu-Fe-S-H^O s y s t e m  are missing  ferrous  be  f o r which  hexagonal  pyrrhotite  pyrrhotite,  t h e G°'s  based  t h e G°  between  557°C  instead  using  from  uncertainty  i n the  previous section,  solid  average  at  This.increases  data  v a l u e -45.5  interest  result,  Iss.  (1974),  correspond  of great  a  fair  the  and  o f Cpy  transition  scatter  a c c u r a c i e s of  sluggishly  are not  Pyr  Jones  25°C.  and  order  e x t r a p o l a t e d by  Cpy,  uncertainties  the most  the  the  by  decomposition  temperature  for  consistent  to about  low  is a  the  into  activities  literature  As  data  first  a  noted  et a l . (1973)  up  as  the  King  are  but  decomposition  uncertainty  a  1970),  with  basic  for and  in chapters  i t ,  sulfates  the  second  monoclinic 5 and  6.  103  SECTION  4-4-1:  4-4  The  : t h e G°'s  f o r the  considered  solutes.  The is  very  number large,  identification. the  solutes  elevated  ions  ions  Except be  the  Very  little  S ~  only  1974),  cannot  for a  few  be  which  ignored  in  sulfur  species,  system, where  and  the  (Biernat  complexes  25°C r e l i a b l e p.43)  and  Special  predominate  those  of  to the  ion pairs  not  predominate  at  formation  available at  the  of at  of  the  150°C  present  temperature  and  time.  solutes  will  1969;  Valensi,  established  be  be  low  at  Of  the  in  can  will  the  be  be  numerous  i n the metastable  that low  of  stable system  considered  cuprous-thiosulfite  temperature, but i s lacking  even  (Duby,  at  1977,  discarded.  g i v e n to the complex  FeS04( q) a  diagram.  zone  the  1950).  information  will  solute  "removed"  and  i n c h a p t e r 2,  predominate  predominate been  will  any  any  have  these solutes  and  the  quantities  f o r them,  in  which  which  quantitative  consideration  the p r o p e r t i e s  approximations described  of cuprous-sulfite  have been  their  study.  calculation  Robins,  with  are  the low  sulfates  existence  data  phase  above  only  those  and  no  aqueous  significant  species,  only  to the starts  instance,  become  200°C.  detectable  account  never the  For  in  into  the  at  i s known a b o u t  occur  but  belong  taken  considered in this  solutes  which  difficulty  might  n  Furthermore, with  The  and  which  (Giggenbach, these  of species  temperatures.  radical  aqueous phase  and  CUSO4  temperature,  (aq)• but  solute  These the  FeS04  solutes  drop  of  +  do the  104  dielectric the  electrostatic  high  for  each  from  water  K  free  w  (1974).  a  i s  total  species,  common  especially  of  36  species  energy  of formation of l i q u i d  constant  temperatures  = -11.302  The  K  w  (Sweeton  (Wicks was et  water  were  with  be  i s needed  and B l o c k , 1 9 6 3 ) . recently  data  for  gaseous  H S (g) 2  are  The  remeasured  a l . , 1974).  i s provided, thereby obtaining  At  at  200°C,  G°(OH~).  taken  from  Mills  equilibrium  Henry's  experimental  The  at  a t 200°C i s  e q . ( 4 . 03)  2  (1967)  will  A G ° v a l u e a t 200°C  2 S (g) = H S ( a q )  follows  and  a t 200°C.  t h e U.S.B.M. s e l e c t i o n  Thermodynamic  H  data  dissociation  elevated  charged  raises  them.  The taken  temperature  ions.  f o r t h e aqueous phase.  of  increasing  association  t h e Cu-Fe-S-H20 s y s t e m ,  4-4-2: A v a i l a b l e  log  ion  and t r i v a l e n t  considered  with  i n t e r a c t i o n s between  temperature  divalent  For  constant of water  law  data  at  over  low a large  pressures, range  o b t a i n e d t h e v a l u e l o g K = 1.54  equilibrium  c o n s t a n t s o f aqueous  recently  reviewed  extrapolation  of  data  spectroscopic  measurements  by  provided  Rao  and  by  of temperature,  fitting Helgeson  a t 200°C. hydrogen and  at  leads to pK  Hepler  167°C 2  sulfide  and  = 7.20  H Siaq)  (1977).  2  The  228°C  from  a t 200°C.  There  105  are  very  large  discrepancies  literature  even  on  of neutralization  the heat  dissolution pK  a t room  on t h e  o f KHS ( j c  ranging  temperature.  12.9  measurements,  a  shoulder  concentration  of  high  as  17  was  Giggenbach,  determined  and  Hepler  to  1971). pK  2  pK  2  The  i s  not  Stephens  2  1971;  = 10.8  up  NaOH s o l u t i o n  that  > 1 2 . 5 a t 200°C  2  and  G°(S "") 2  i s  2  Ellis  to  at  at  and a p K  2  in a I N pK  with  appearing  and C o b b l e ' s  considered i n this  critical,  on t h e heat o f  to S ~  measurements pK  measurements  In spectroscopic  band  (Giggenbach,  the  interpreted  25°C.  attributed  derived  first  dissociation  o f H S04  t o 225°C f r o m  accurate heat  capacity  recently  a as  and  (1971) 95°C,  Cp Rao  200°C,  while  up  250°C  to  (Giggenbach,  study, the  value  calculated  by  t o be c o m p l e t e  dissociation  (Lietzke  et al.,  was  of  using  i nthe studied  1961) and t h e  cal/mole f o r the reaction  /  eq.(4.04)  change  up t o 1 0 0 ° C  G ° o f e q . (4.04). a t 9 5 ° C  agreement.  data  G ° a t 200°C w a s 9 7 5 7  2  assumed  s  The s e c o n d  solubility  4  measured  i  2  being considered.  HS0 - = SO4 - + H+  A  was  in  = 12.5.  resulting A  An  at  were  t h e . HS~  using  conclusion  I n t h e pH r a n g e  pH r a n g e up  the  on  measurements  Calorimetric  solutions  by c a l o r i m e t r i c  (1977)  spectroscopic lead  By  given  :  a  13.8  evaluated  1971).  value  2  to  3 N NaOH  values  2  o f H S ( q) and a l s o  in alkali  from  2  pK  forbisulfate  (Readnour  i n both  studies  dissociation  and C o b b l e ,  was  1969).  The  are i n relatively  good  106  The  magnetite  dilute  KOH  solubility and  HCl  has been measured  solutions  pressures  (Sweeton  solubility  data are consistent  solutes  Fe  2 +  equilibrium  ,  and  Fe(OH) ,  {Cpy  the  + Pyr + Bor}  equilibrium  0.25 C u F e S 4 5  given  1970).  The  results  the presence and F e ( 0 H )  2  solutes  The  the  cuprous  of  240  ferrous  and lead  to the  magnetite.  The these  4-3.  solubility  of  solutions  the  very  hydrogen  of four  i n section  explained  of the solutions  ,  in  a t 200°C f r o m  i n NaHS a q u e o u s  authors  o f a complex  3  with  be d e t e r m i n e d  have measured  assemblage  concentrations  the presence  was  can then  (1976)  200°C a n d 350°C.  by  defined  t h e v a l u e o f G°(Mag) g i v e n  and Barnes  copper  well  constants of these four  and from  Crerar  under  with  Fe(0H)  +  G°'s o f t h e s e s o l u t e s data  Baes,  up t o 350PC  between  relatively  (a f e w h u n d r e d s  a n i o n Cu(HS)2~.  the  of  At  high ppm) 200°C  constant of the reaction  +  H  S  ~  +  °«  5  H  2 (g) s  =  °-  2 5  a s l o g K = -2.3 ± 0.7, w h i c h  CuFeS  2  +  yields  Cu(HS) ~ e q . ( 4 . 05) 2  t h e G° v a l u e f o r  Cu(HS) ". 2  For  the other solutes,  and data.  high temperature  t h e G ° ' s a t 200°C m u s t  data  be e x t r a p o l a t e d  are not from  available,  low temperature  107  4-4-3: C r i s s  For two  and Cobble  a reversible  temperatures  J  T  T  2  T2  C ( T ) dT - T p  pressure data  (Millero,  100 c m ^ / m o l e , 200°C  lower  i s widely  the  ignored  of temperature  one  the  reviewed  various  by Duby  For  ionic  partial  40 c a l / m o l e .  up t o 2 0 0 ° C . empirical  solutes,  Criss  data  energy  at  f o r common  volumes  I t must  are  change of  lower between  pressure  be  estimated  t h a t have been  and Cobble's  Gp(Tj,T ).  the  scarce  by  recently  (1977).  T ,  thereafter  such  under  The e f f e c t  methods  and  temperature  i n t h e system  o f C p ( T ) i s g e n e r a l l y n o t known a s a  partial  (1964),  water  among h y d r o m e t a l l u r g i s t s .  e s t i m a t i n g an a v e r a g e  Cobble  molal  pressure of  extremely  a free  for  2  are  of  change  to available  yields  solutes the value  function of  According  than  the  However  volumes  eq.(4.06)  the effect  account 2  which  expression  V ( P ) dP  states,  and T .  1977),  between  dT  _ 1  p  S°(T!) + )  molar  change  by t h e c l a s s i c a l  C (T) T  into  between  energy  2  standard  temperatures.  25°Cand  For  - Ti)  to take  on p a r t i a l  electrolytes  G°'s  2  to t h e chosen  elevated  on  (T  T  solutes.  l  T  must be c o n s i d e r e d vapour  J  2  T-i  According  than  i s given  2  2  J  dG =  heating, the free  and T  -  study,  extrapolation f o r ionic  noted  a suitable that  corresponding  molal 2  standard  the Cp(Ti,T )'s  entropies  2  at  heat  method  are  be  used  c a p a c i t y b e t w e e n T]_  According state  will  to  Criss  c a n be c h o s e n linearly  25°C f o r a l l i o n s  and  a t each  related  to  i n t h e same  108  class.  Four  oxyanions up  to  and acid  473  K are  S°(298).  T  free  C  p  ( T i  #  been  oxyanions) for  the  2  )  (T  -  2  four  change  following  T  a  The  G°  iron S  n  2  for  needed  *  every  data  and S° from  for  values  the  and the  -  Tx  T  from  copper  of  Cp(298,T)  classes  as  a  between  for  function  Tj- a n d T  i s  2  T of  then  Log(T /T^))  2  2  a l . ,  1976) .  The  value  the  Fe  3+  of  hydrolysis E°(Fe  average (1934),  2  25°C  eq.(4.07)  S°(Ti)  are  the  2  are  Selection  for  S°(T!)  and the  taken  except  G°(Fe  (Wagman  except  for  which  of 3 +  3 +  /Fe  F e 2 +  )  a n d Schumb  3  review for  et  the  a l . , 1969)  for  polysulfide  recent  )  at  of  the  studied  couple  +  between  procedures.  G°(Ti)  at  solutes,  recently  / F e  Tx)  G°(T ).  c r i t i c a l  solutes, been  -  2  data  are  the  anions  available  1974);  the  have  (T  i o n , the  N.B.S.  sulfur  (Giggenbach,  value  values  calculating  (n=2,...,5),  -  *  anions,  l  result,  only  (cations,  equation  +  As  proposed  and the  energy  by the  dG =  have  provided  The  approximated  J  classes  Gedansky  cupric  i n 0.1  25°C  is  derived  0.771  0.772  V  V chosen and 0.770  and S h e r r i l l  The v a l u e  of  G°(Fe  3 +  at by  (1970)  from  the  (Arena  corrected  for  i n f i n i t e  d i l u t i o n .  Latimer  (1952)  V found  by Bray  respectively  by  )  then  to  bound  et  of the The  is  and  the  which  potential  (1937) is  for  cations  solutions  solutions,  and e x t r a p o l a t e d =  a l .  hydrolytic  N NaClC>4  i n perchlorate  +  et  an  Hershey  different that  of  109  G°(Fe The  2 +  ).  G°(Fe  )  2 +  obtained  equal  t o -21.89  with  the  al.  at  25°C  kcal/g.ion.  This  value  water.  this  G°  -0.467 V found G°(Fe  (Wagman  2 +  )  et  potential  which  spontaneous  Fe°/Fe  i s  reaction  derived  of  H  misinterpreted  +  a in  agreement  by  Larson  than  et  o f FeS04.7H20 potential  (1958).  However  N.B.S.  figure  o l d measurements  of the  in  the  sealed  o n Fe° m i g h t h a v e  as  good  agreement w i t h t h e  and H u r l e n  from  (1970) i s  standard good  lower  electrodes  2 +  in  of dissolution  a t 20°C b y H o a r  a l . , 1969)  and Baes  forward  to  i s 3.0 k c a l / g . i o n  of  potentials  leads  i s  put  the heat  = - 0.474 V  2 +  value  measuring  This  E°(Fe /Fe°)  figure  -21.8 k c a l / g . i o n  (1968) a f t e r  in  by Sweeton  equilibrium  cells.  The  l e d to high  rest  potentials  at  that  time. In  order  Fe  2 +  Fe  3 +  all  to  adopted /Fe  are s t i l l  and Robins  Cobble  and  missing.  (1963),  (1973).  limitations  were  for  coefficients  a  very  were  with  They  Biernat  o f t h e method  few  the  potential  of  on the  b y 3.0 k c a l / g . f e r r i c i o n .  The d e t a i l s  determined,  t h e thermodynamic data  a t 2 5 ° C , t h e N . B . S . G ° ' s a t 25°C f o r  (1964) must be n o t e d .  Cp(298,T) except  study,  measured  Pourbaix  The  consistent with  s o l u t e s are lowered  data  (1952), Kwok  i n this  couple  2 +  ferric  Several  remain  data  are  taken  and Robins  species.  (1969;  Latimer 1972) and  are reported  i n appendix  put forward  by  I n 1 9 6 4 , when were  from  already extrapolations  up t o  200°C v a l u e s of  and  the coefficients  only available The  Criss  the  of  1.  of  150°C these  corresponding  110  lower  temperature  above  Furthermore  100°C f o r t w o o x y a n i o n s  oxyanion cations No  values.  (HSO4 ) o n l y . -  such  and SO4 )  and f o r one a c i d  No d a t a w e r e  available  f o r hydrolytic  2 -  and f o r complex  +  on  measured  (Re04~  as Cu(0H) ,  improvements  d a t a had been  cations  such  as FeS04 .  t h e c o e f f i c i e n t v a l u e s have been  +  published  s i nee t h e n . Sweeton the  and Baes  ferrous  solutes  Cobble's  method  appendix  1),  between Fe  2 +  ,  to  this  method  i s  for the  by  more  than  8  i s very poor.  and Cobble's  method  aqueous  solutions  recently  adapted  a computer  4-4-4:  ion to  i n a form  Helgeson's  association  (Taylor,  which  (1967)  by  acid  be needed  to test  the  However,  this  i o n belonging  to the  1978) and h a s been  c a n be e a s i l y i m p l e m e n t e d  into  f o ri o np a i r s .  the free  energy  a s t h e sum o f t w o t e r m s ,  and  cation  hydrometallurgists  Scheuerman,  expresses  reaction  change  1978).  extrapolation  electrostatic  respectively.  and  (see  f o r the  solutes.  w i d e l y used  i n 1964 f o r e v e r y  (Barner  program  Helgeson  i ss t i l l  on  f o r the hydrolytic  c o e f f i c i e n t s and even  extrapolation  published  energy  More d a t a would  P r i n c i p l e f o r t h e complex  t h e form  result  "simple"  kcal/g.ion  Correspondence  in  As a  f o r the free  b y 84 c a l / g . i o n  HFeC>2~, w h i c h Criss  on these d a t a .  accounts  data  200°C, a n d C r i s s and  v e r y g o o d , b y 472 c a l / g . i o n  +  improve  thermodynamic  25°C u p t o b e y o n d  c a n be t e s t e d  FeOH , b u t  oxyanion  provide reliable  from  25°C a n d 2 0 0 ° C which  cation  (1970)  non  electrostatic  change o f an corresponding contributions  Ill  The  effect  results  of  from  assuming the  temperature the  that A  on  change of G (T)  the  electrostatic  A  G (T) e  the d i e l e c t r i c constant of water.  is a linear  e  term  function  d i e l e c t r i c constant, Helgeson  of  the  (1967) d e r i v e s  By  reciprocal the  of  following  expression  e  in  e  2  which c =  The  exp(b  + of  a  including  two  or  the  one  such  A  a case,  A  Cp  -  2  w =  the  S°  (1967),  and  A  G°(T ) = A  H°  can  H°(Ti) - A  2  measured A  H°  both G°'s  and  a  are  at  25°C  positive,  CUSO4  by  provided at  of both  1 +  a c  therefore  ion pairs  Therefore,  a G°  at  +  v/w}  non  a  T ) 2  eq.(4.08)  v =  electrostatic  which  i s a power  219,  term  is  series  in  T  parameters.  for determining of  this  t h e non  -  (1 -  et a l . (1969). ionic  eq.(4.09)  term.  be  valid  temperature.  In  as  exp(exp(b  thermodynamic  zero  may  - T j / v ) ) v/w}  2  parameters,  electrostatic  at low  rewritten  c + T  these  approximation  positive  (aq) >  25°C a n d  exp(exp(b  v.  S ° ( T x ) {Ti  Izatt  (1 -  - T\/v))  the  are be  -  b = -12.741,  variation  eq.(4.08)  FeSC>4 ( q )  c + T  function  / n  -  For  1  on  enough d a t a  to Helgeson  both  {Tx  e  three adjustable  ignore  According when  A  absence of  can  and  temperature  by  S (T )  0.01875,  a T^)  described  In  1  a =  effect  A  =AH (T ) -  A G ( T )  a  T ) 2  eq.(4.09)  data The  +  have  value A  strength.  been S°  They  and are  a l l o w s an  estimate of  the  i s known o r  estimated  for  200°C.  value  at  200°C  112  every in  aqueous s p e c i e s  table  G°  the  the next  retrieved  G°*s,  (4.01)  determining complex  study.  They a r e  compounds  data. and  In  .  Any  this  i n table  the missing  s o l u t e FeSC>4  reconsidered  different data  retrieval  types  listed  i n view  +  study,  (4.02) w i l l  f r e e energy  and  the  leads  those  of s o l u b i l i t y  of  both  data  the missing  to  relations  as a f u n c t i o n o f  data  be u s e d  data.  of information  to obtain  and t h e unknown G°*s a r e p r o v i d e d  available  table  two c h a p t e r s ,  i n terms o f f r e e energy  f o r the solid  among  in this  (4.02).  In are  considered  presented  in  as b a s i c data f o r  However ion  provided  t h e G° o f t h e  pairs  will  i n chapter  be 6.  TABLE  G° of as  data  (4.01)  for solid  t h e Cu-Fe-S-H20  retrieved  Symbols  |  from  compounds  system  literature  Formulas  I  at  200°C  sources.  I  G°  I  cal/mole  Cup  I  CU2O  I  32  165  Ten  I  CuO  1 - 2 6  732  Cct  I  Cu S  I  21  440  Cov  I  CuS  1 - 1 2  797  Mag  I  Fe304  I  -  228  914  Hem  I  Fe203  I  -  166  387  Tro  I  FeS  I  ; - 24  108  Pyr  I  FeS  I  — 36  193  Cpy  I  CuFeS  I  - 45  321  Bnt  I  Cu FeS  I  - 95  137  C2Su  I  CUSO4  F2Su  I  FeS04  F3Su  I  Fe (S0 )  C2Fe  I  ClFe HCSu  2  2  2  5  4  ()  -  -  I  -  142  206  I  -  182  459  I  -  495  412  CuFe 04  I  -  191  561  I  CuFeQ  I  -  102  574  I  C U S O 4 . H 2 O  1 - 1 9 4  850  C  2  ( c  4  ) 3  2  2  114  TABLE  G° of as  the  for  Cu-Fe-S~H 0 from  l i t e r a t u r e  G°  I  solutes system  2  retrieved  Formulas  data  (4.02)  at  200°C  sources  Formulas  I  F e  S  |  2+  Cu  1  -  9  395  1  -  6  061  1  9  526  S 2"  1  29  069  |  S 2"  1  26  386  601  I  S 2"  1  24  183  119  239  |  S 2-  1  26  344  94  636  I  HSO4-  1  161  603  129  255  |  S 0  1 - 1 5 1  846  -  59  264  1  HSO3-  1  113  102  -  93  98 3  I  S0 2"  1  91  256  .1-27  536.  1  H S  1  796  1  S  C u S 0  21  111  j  H  2S(g)  36  587  1  H  2S(aq)  50  190  I  8  528  |  -  23  119  -  50  +  Cu  2  (OH)  Cu  3  (OH)4  Cu(OH)  2  +  2  +  2  C u ( O H )  -  _  3  4  2  -  _  Fe(OH)+  I  Fe(OH)2 Fe(OH) "  1  Fe3+  1  3  -  Fe(0H) +  1  -  49  209  I  Fe(OH)  1  -  93  523  1  1  -  95  784  I  I  -  87  441  2  2  Fe (OH) 2  Fe04 ~ 2  +  2  2  +  cal/mole  813  I  -  CuOH+  G°  165  663  2" 2  1  15 -  H 0  1 1  cal/mole  Cu2+  only.  FeS04  +  HS" 2  3  4  5  4  2  -  3  -  -  -  "  1  -  108  401  2 -  1  -  101  436  )  1  -  143  359  FeS0 (aq)  1  -  179  964  -  646  2  2  0  0 3  3  4  (  a  q  4  Cu(HS) ~ 2  1 1 •'•  2  115  CHAPTER  ESTIMATION  OF  5  FREE  ENERGY  DATA  FROM A T E R N A R Y P H A S E D I A G R A M .  An will  now  extention be  of  the  described,  which  compounds o f a t e r n a r y when This  the  G°'s  method  5-1  The function energy  1949),  versus  and  (Hillert,  then  be  applied  diagram  at  200°C.  : theoretical  and  diagram  other  method  extensively  phase  is  derives best  their 1975).  use  to  to  ternary  systems  t h e unknown G°*s o f to  be  compounds  reliably  estimated  already  available.  are  Yund  several  and  Kullerud  (1966)  background.  from  the properties  diagrams* for  this  by  has  section,  of  the  free  considering  These  binary  i n metallurgy In  method  illustrated  composition described  arm  allows  the  will  Cu-Fe-S phase  SECTION  of  lever  diagrams  systems been they  energy  molar  free  have  been  (e.g. Guggenheim, recently  are denoted  reviewed as  (g-x)  116 diagrams. similar A  Their  to  phase  those  of  at  constant  one  more  a  the  represents  the  the  X-Y-Z and  as  free  a  phases  function A  energy  G(x,y,z),  systems  stable  pressure.  molar  function  molar  of  the  stable  and  fractions  diagram  and  free  quite  mole  (g-x)  g,  are  includes  represents  energy  of  the  the  stable  (x,y,z).  The  properties  of  y,  z  are  and  state  ternary  systems.  ternary  for  for  binary  temperature  axis  of  system  for  diagram  assemblages  graph  properties  of  g  a  mixture  system  of  a,  respectively, following  these  diagrams  derive  a l l extensive is  b,  the c  yields  a  of of  minimum  three  system  that  free  stable x  that the  P^,  defined  z  stable  energy.  systems  x,  The P , 2  by  P3 the  equations  b  +  c).x  =  a.xi  +  b.x  2  +  C.X3  (a +  b  +  c).y  =  a.yi  +  b.y  2  +  CY3  ( a + b + c ) . z = a . z i + b . z b  +  c).g  =  2  + c . Z 3  a.G(Xi,yi,zx)  underscripts  1,  2  eq.(5.01)  v  eq.(5.02)  +  and  3  eq.(5.03)  b.G(x ,y ,z ) 2  + where  facts  ( # V1 r<3)  Q123  (a +  (a +  the  q u a n t i t i e s , and  one  moles  from  2  2  c.G(x ,y ,Z3) 3  refer  eq.(5.04)  3  to  P^,  P  and  2  P3  respectively. Such  a mixture  system by  the  is  may  characterized  following  (a +  b  react.  +  The by  resulting  eq.(5.01),  stable  state  eq.(5.02),  of  eq.(5.03)  the and  inequality  c).G(x,y,z)  <> a.G  (xj , y i , zi) + +  b.G  (x ,y ,z )  c.G(X3,y ,Z3) 3  2  2  2  eq.(5.05)  117  A strict the  inequality  assemblage  set  i n eq.(5.05)  {Pi  + P  + P3K  2  o f a, b, c a l l p o s i t i v e ,  graph  of  entirely  G(x,y,z) "above"  assemblage system  expresses Since  {P^ + P  which  i n t h e (g-x) diagram  + P3}  2  instability  eq.(5.05)  the region  any o f i t s tangent  the  holds  i s  i s convex  planes.  As  i s s t a b l e i f and o n l y  (x,y,z,g), stable or not stable,  of  f o r any  "above"  the  and then  lies  a  result,  an  i f , f o r any  the following  real  inequality  holds  (a + b + c ) . G ( x , y , z )  1 a.G ( X ] _ , y ] _ , z i )  which  a,  eq.(5.03). the  same  six  method  systems.  Qj  k  denote  phases. phases  2  by  eq.(5.06)  solving  coefficients  may  eq.(5.01) t o  o r may  not  have  Qkm  represent  limits  provide  which  i s  considered It  can  {j  + k},  this  presents  chapter  a binary  The G° o f phase  system  a s P.  low l i m i t s  with  which  i s classical for  (g-x) diagram  P  i s  with  unknown;  i s a mixture  The e n e r g y  o f G°(P).  an i n t e r v a l  consistent  in  the  are available.  the unstable  the possible value  Qij/  these  presented  t h e same c o m p o s i t i o n  for  calculated  Fig.(5.01)  stoichiometric  Let  are  2  sign.  G°'s o f t h e o t h e r  of  c  I n eq.(5.06)  The binary  b,  2  c.G ( X 3 , y 3 , Z 3 )  +  in  + b.G ( x , y , z )  for  of Q j  Similarly f o rG°(P). the  the  i s a high  the energies The most  possible  stability  k  o f j and k  of  Qhir  restrictive  values of  limit  of  G°(P)  a l l the phases  i n the diagram.  also  be  namely  checked  that  the  { i + j } a n d { k + m},  neighbour provide  assemblages together  of  t h e most  118  U,y,  z)  Fig.(5.01) Schematic binary molar free energy vs. composition diagram.  119  restrictive  low  {h +  be  i} can  P,  results  diagram P i ,  P  such  {Pi  + P2  can  be  the  is  Q123  region  g(P) in  removing  the  the  limit  as  of  of  is valid  from  for  as the  the s t a b i l i t y  c and  g =  free  G°(P)  the  On  of  P2  to Since  convex, { P i + P2  +  P3}  the +  P3}  and  the  is  not  Writing presence  of  of  known  formation  diagram, l e t the involve  assemblages  which  do  t h e non of  P  not  G°(P).  assemblages  appear belong  stability yields  per assemblage,  values  of  assemblages  d i a g r a m , new  the l a t t e r  phase  the phase  the stable  < g(Qi23)  possible  2  g(Qi23)*  energy  the assemblages  in  g(Qi 3),  eq.(5.01)  is  P,  assemblage  (as i n f i g . ( 5 . 0 2 ) ) ,  the  the  system,  denoted  stoichiometric  where  phases  a  the  A  P.  unchanged.  assemblages such  by  equations  i f {Pi +  evaluated.  the region P  represents  G(x,y,z)  P  diagrams. stable  holds i f the assemblage  which  (P)-zone remain  inequality  writing  graph  (P)-zone, while  former  higher  be  four  2  a, b,  stable  for  must  P.  to  a  with  of Qi 3/  unknowns  presence  (x,y,z)  denote  the  such  t h e same c o m p o s i t i o n as  energy  of the presence of  (P)-zone  within  has  four  the  be  to ternary  Q123  the  < g(Qi23)  P  = g(P)  By  extended  free  solving  2  the  because  composition  assemblages  i n the plane defined  > g(Qi 3)  g(P)  Let  G°(P)  by  "above"  stable  other  point  molar  f o r the four  inequality  be  The  lies  The  calculated  stable  can  P3.  + P3}.  inequality  the  i n most c a s e s , w h i c h  that  eg.(5.04)  that  i s presented in fig.(5.02) and  2  hypothetical and  and  ignored.  These (g-x)  limit  and  of one  thus a  Similarly,  i n the  presence  120  Schematic  Fig.(5.02) representation of ternary molar vs. composition diagram.  free  energy  121  of  P  yields  assemblage,  on  inequality  and  thus  a  such  lower  as  limit  G°(P)  > g(Qi23)  f o r the p o s s i b l e  per  values  of  G°(P).  By which  would  Moreover, "stable" of  starting  by on  them  formation  be  stable  removing  P,  the diagram  one  of  on  restrictive  the  by  phases the r i s k  always  y e t , or that  because  of  the  o f P may  - unstable  phases  is  - may  the  range  method,  low values  of  that  free  several  energies  the  which  of  resulting may  possible  should  as  difficulties.  ignored,  conditions  known.  appear  remains  their  Within  assemblages n o t be  experimental  (P)-zone provide  this  diagram,  not  be  values  of  t h e n be  chosen  diagram,  several  practice.  must  assemblages  be  lead  emphasized  t o more  priori.  Two  determine  a consistent  convexity  of  be  i s ,  stable.  assemblages  *  restrictive  conditions  "above" the  less  instance,  the  number  f o r G°(P). G(x,y,z)  of phase  P  restrictive outside  t h e most  let  (A')  a  o f checks needed  to  Both derive (g-x)  assemblage  the  (P)-zone,  (A ') 1  low  limit  three be  from  the  diagram. which  a  than those which  restrictive  and  than  provides  to t r y every combination of  Furthermore,  others  i n the  ( P ) - z o n e , any  i n the absence  provide  i s useless  i n a phase  interval  region  a priori,  For  that,  reduce  or outside  stable  which  results  the  * Within  it  phase  the absence  new  these  enough.  provided  It  not  in  and  are uncertain  assemblages  in  a stable  are not discovered  Whenever  G°(P)  with  the  would  condition would  be  stable  f o r G°(P)  and  phases. two  assemblages,  122  presented and  i n fig.(5.03),  P both  (A'').  lie  the  systems which  always the that  holds.  by  (A  1  (A') and  l e t Q' a n d as P and  (A'') r e s p e c t i v e l y .  Q*'  which Under  yields  the  G°(P3).  instance  a,  P^,  the  latter  (A ) nor ( A 1  result  P  b,  required Such  1 1  can  ) belong  low l i m i t  i s very  (P)-zone,  be  than  omitted.  to the  (P)-zone,  and c a n be  useful  (1967)  to eq.(5.03)  by  ignored  when c o m p l e x  phase  balancing  chemical to the  reaction, phase  inequality  used  are often solved f o r a  Writing the free  calculations  25°C b y i n t e r p r e t i n g o n G°(Cpy)  c  a n d P3.  2  according  Young  a Cu-Fe-S  energy  and s e t t i n g  diagram  involving  have  chemical  as  change A  G  i t positive fig.(5.04)  G ° ( P ) , G°(P]_), G ° ( P 2 )  a l r e a d y been phase  in  equation  performed.  diagram  For  determined  at  mineral  assemblages  i n nature  forproviding  and G°(Bor).  The method  presented  here  when s y s t e m a t i c a l l y conditions  and  the  more r e s t r i c t i v e  1  eq.(5.01)  the corresponding negative  ),  (A ) i s then  restrictive  This  practice,  P,  by  to  as t h e t e r n a r y Cu-Fe-S a r e worked o u t .  coefficients  between  1 1  the less  such  (A'') b e l o n g  1  neither  any r i s k .  In  data  (A*) and  ( A ) and  provided  i f  provides  diagrams  and  diagram,  (A' )  eq.(5.07)  I f both  provided  without  for  between  t h e same c o m p o s i t i o n  d e f i n e d by  limit  Conversely,  the  have  (g-x)  diagram,  < g(Q")  high  (A')  on t h e phase  conditions, the inequality  g(Q')  or  corresponding  i n the planes  these  that,  l i e o n t h e same s i d e o f t h e b o u n d a r y  In  represent  such  followed, allows  t o be w r i t t e n  down  a l l  the  most  however,  restrictive  f o r t h e unknown G°'s, and hence  a  123  Phase  the  diagram  (x,y,z)  .'• / F i g . ( 5 . 0 3 ) P o s i t i o n a l r e l a t i o n between a s s e m b l a g e s and c o r r e s p o n d i n g c o n d i t i o n s t h e y d e t e r m i n e f o r G°(p)  \  p+ap, = | 8 P + / P 2  3  (AG)  Case I: A G < 0  Case 2 = AG > 0  G°(P) > j 3 G ° ( P ) + / G ° ( P ) - a G°(P!) 2  Practical  3  G (P)<,SG (P )+7G (P ) - aG°(P,) o  Fig.(5.04) determination o f thecondition from t h e phase diagram.  o  o  2  3  f o r G°(p)  125  full  retrieval  of  the  information  contained  i n the  ternary  phase  diagrams. The  molar  free  energy-composition  representation in  of  f i g . (5.02).  instance  are  proofs.  which  often  G  the  which  the  than  these  method, but  provide  i s equal  several  involve  easier  Therefore,  presenting  above A  Furthermore,  those  Gfx,y,z)  the  diagrams  to  the  of  geometrical  (g(P)-g(Qi23))  geometrical  convexity  proofs,  the  region  corresponding  diagrams  offer definite  they  not  are  a  for above  analytical advantages  explicitely  used  in  in  the  data  are  Cub  and  outlined  in  calculations.  SECTION  5-2  : a p p l i c a t i o n to  Of available, two  each  eight  solid  compounds  five  belong  to  Cu-Fe-S  in  5-1  diagram  the  i s now  at  is  the  phase  for  to  Yund  200°C f o r e s t i m a t i n g interval  consistent  of  with  the  G°  possible the  stable  Dig,  The  and  diagram.  which  system:  pyrrhotite region.  applied  c o m p o u n d , an  which  Cu-Fe-S  the  phases  section  the  no Ida,  method  Kullerud of G°  these values  (1966)  phase  compounds. m u s t be  assemblages  of  For  found,  the  phase  diagram.  The  approximations  solutions  to  diagram  represented  tempting  as  to  be  made  explicitely  start  with  in  i n Chapter  taken  do  not  into account,  fig.(4.05)  a phase  2  m u s t be  diagram  where  allow  and  the  simplified. the  phases  solid Cu-Fe-S It  is  are a l l  126  stoichiometric.  Such  a  stoichiometric  fig.(5.05). Cov, Ida  phase  I t includes  Pyr, Dig Cui.8 f S  Cus^sFeSg.s,  and  i s  12 c o m p o u n d s , n a m e l y c  P y CuFeS2  a  single  of Tro F e i o o '  properties  diagram  S  a  *  s  #  Yund  in  Cu°, Fe°, S°, C c t ,  Bor Cu5FeS4,  f  pyrrhotite n  represented  Cub CuFe2S3,  phase  with  and K u l l e r u d ' s  the  diagram i n  fig,(4.05). Two d i s c r e p a n c i e s and  f o r G°(Dig) The  Pyr-Cub  first  arise  when c o n s i s t e n t  intervals  for  are sought.  discrepancy results  t i e line  i n such  + Cpy} i n t h e p r e s e n c e CuFe2S3 = C u F e S  a diagram.  the striking  The s t a b i l i t y  absence  s  +  0  F  e  #  the instability  of a  of {Pyr+ Tro  o f Cub i s w r i t t e n  + Fei 00  2  from  S  2  G°(Cub) > G°(Cpy) + G°(Tro) and  G°(Cub)  eq.(5.08)  o f {Cpy + B o r + T r o } i n t h e p r e s e n c e  o f Cub  yields CuFe2S3 = CuFeS2 + F e ; u o O  s  +  0  C  u  5  F  e  S  4  G°(Cub) < G°(Cpy) + G°(Tro) The  two i n e q u a l i t i e s  eq.(5.08)  eq.(5.09) and eq.(5.09)  are  obviously  not  compatible. When  G°(Dig)  conditions  need  discrepancy.  i s  n o t be t a k e n The s t a b i l i t y  + S°} i n t h e p r e s e n c e C u  1.8  s  =  G°(Dig) and  being  C  u  2  s  +  0  determined, into  account  the to  most reach  restrictive a  second  o f { C c t + B o r + Cu°} a n d { C o v + P y r  of Dig are written  C u 5 F e S 4 - 0.2 C u °  > G°(Cct)  eq.(5.10)  127  Cu  1 < 8  S  = 1.8 C u S - 0.8  G ° ( D i g ) > 1.8  S° + 0  FeS  2  G°(Cov) eq.(5.11)  The  instability  leads C u  o f {Bor + Cpy + P y r }  in  the  presence  of  Dig  to the relation 1.8  =0.5  s  G°(Dig)  C u 5 F e S 4 + 0.2  FeS  2  - 0.7  CuFeS  < 0.5 G ° ( B o r ) + 0.2 G ° ( P y r ) - 0.7  2  G°(Cpy) eq.(5.12)  Numerically,  these  equations  yield  G°(Dig)  > -21 440 c a l / m o l e  eq.(5.10B)  G°(Dig)  > -23 035 c a l / m o l e  eq.(5.11B)  G°(Dig)  < -23 082 c a l / m o l e  eq.(5.12B)  These c o n d i t i o n s  This  are not compatible.  last  discrepancy  «could  G ° ( C p y ) b y 2.4 k c a l / m o l e .  Given  table  procedure  (4.01),  alternative required assumed from  such approach  G°  crude  The  alternative  hexagonal  stoichiometric (Power MPyh.  and F i n e , Tro  i s  the  could  taken. data  be  When  listed  by of  that  increasing G°(Cpy)  in  justified.  An  calculating  the  i n table  and t h e above d i s c r e p a n c i e s  (4.01) a r e  as  resulting  h a d b e e n made t o d e t e r m i n e  the  ternary. .  phase diagram  pyrrhotite Tro,  solved  the uncertainty  be  assumptions  above s t o i c h i o m e t r i c  An  will  intervals,  t o be c o r r e c t  the  a  be  but  the  i s  s t i l l  into  i n fig.(5.06).  described  m o n o c l i n i c phase  1 9 7 6 ) i s now t a k e n i n equilibrium  i s presented  account  stable and  by  the  a t 200°C is  noted  w i t h Fe°, Cu°, Bor o r Cub, w h i l e  128  7 0 otomic per cent  S°  Fe°  Cu°  F i g . (5.05) S t o i c h i o m e t r i c phase diagram, f i r s t approximation o f the Y u n d a n d K u l l e r u d C u - F e - S t e r n a r y a t 200°C ( a t o m i c p e r c e n t ) .  7 0 atomic per cent  Cu°  Second  S°  Fe°  Fig.(5.06) ( f i n i t e ) a p p r o x i m a t i o n o f t h e Yund and K u l l e r u d C u - F e - S t e r n a r y a t 200°C ( a t o m i c p e r c e n t ) .  129  MPyh  is in  equilibrium  with  Cub,  Sugaki's  results  (Sugaki  pyrrhotite  in equilibrium with  Cpy  et  or  a l . ,  the  Pyr  according  1975).  The  monoclinic  to  hexagonal  phase  is  s t i l l  igno red. According  to  considered  as  the  Bor  Two the  recent  results  stoichiometric.  already An  m e n t i o n e d , Cpy  average  compound  is  s t i l l  represents  phase.  compounds formula  describe  Cu^s^  *  rich  s p e c i e s , noted  Pyr,  Cpy,  Bor  Similarly,  two  binary  and  Cct,  d i g e n i t e phase:  equilibrium with  n  iron  or  the  the  FDig,  in  either  i t s iron  i n the  describe  rich  the  binary Dig  Cct  equilibrium  c h a l c o c i t e phase  compounds  the  or  Cov,  with  with  and  Cov,  an Ida,  ternary.  c h a l c o c i t e phase:  boundary  in  the  ternary  the  noted  FCct. The.  formula  Fe-S  diagram  already The  of  in fig.  takes  very  digenite  phase  field  200°C l i e s  the  % Fe,  The  rich  formula  of  It into  and  the  the  to  the  copper  at  300°C  straight  line  as  noted  solve  the  discrepancy of  fact  a high  Dig to  to  the  that  both  above  between {Bor  F e  m  +  the Cpy  et  rich Bor,  phase  a l . , 1975).  in  single  boundary with  formula  the  about  Cui 58  F e  #  iron,  at  0.I • s  and  the  0.04 • s  FCct  second  and  Pyr}  FDig  m u s t be  discrepancy.  stability +  this  temperature  Its iron  from  Cuj 92  that  (Sugaki  c h a l c o c i t e i s low  be  instability  Cu5FeS4.  corresponds  i s taken  should  with  " v e s t i g e " of  of  is consistent with  and  beyond  boundary  FCct  account  FDig,  is a  which  which  s  little  extending on  i s Feg.875 ,  (4.03),  phase  4 weight iron  MPyh  of  {Cov  cannot  + be  taken  Without Pyr  +  S°}  removed.  130  Without  FCct,  presence  o f FDig,  C u  1.58  the  0.1  F e  G°(FDig)  s  instability  which °«  =  of  {Bor  +  Cpy + P y r } i n t h e  i s written C u 5 F e S 4 + 0.12 F e S 2 - 0.42 C u F e S  4  2  < 0.4 G ° ( B o r ) + 0 . 1 2 G ° ( P y r ) - 0 . 4 2 G ° ( C p y ) eq.(5.13)  and  yields  G°(FDig)  stability C u  o f { C o v + P y r + S°}  1.58  0.1  F e  G°(FDig) which  compatible  C u  s  =  C  to  with  0.1  F e  S  i s compatible  1  F  e  S  2  -  °«  7 8  s  s  which  eq.(5.14)  of  {Cct +  I t i s still  Bor  +  Cu }  yields  i s written  =0.6 Cu S 2  Modifying  + 0.1 C u 5 F e S 4 - 0 . 1 2 C u °  the  G° v a l u e s  composition  i t does n o t change  might  be  and K u l l e r u d ' s  justified  diagram  in  t h e above s i t u a t i o n .  ( 4 . 0 1 ) a r e t o be k e p t ,  FCct  When  must be  taken  account.  As value  o f t h e FDig  i n table  eg.(5.15)'  cal/mole.  t o t h e u n c e r t a i n t y o f Yund  region,but  into  > -22 378  the choice  according this  G°(FDig)  not  i n the  0  G ° ( F D i g ) > 0.6 G ° ( C c t ) + 0.1 G ° ( B o r ) and  the  °  > -23 839 c a l / m o l e .  the stability  with  written  °-  +  G°(FDig)  of FDig,  1.58  u  cal/mole,  > 1.58 G ° ( C o v ) + 0.1 G ° ( P y r )  leads  presence  < -23 363  a result,  i s  needed:  inequalities independent. required  there  I d a , Cub,  which For  define instance,  to determine  inequalities  must  are.now  then  s i x compounds  MPyh,  the  f o rwhich  D i g , FDig  s i x required  and FCct. G°'s  a condition involving  G°(Ida), and v i c e be w r i t t e n  versa.  and s o l v e d  as a  a  The  are  G° The not  G°(FDig) i s system  whole.  of  131  In  order  "zones" using  to  generate  o f t h e s i x compounds  most  f o r those  are determined  assemblages  conditions  within  most c a s e s ,  the exact  the  unknowns the  species  and  outside  configuration  a  inequalities  but to write  must be n o t e d  represent "in  two  that  diagram compounds  f o r which  However,  whether  FCct-Dig have  {Cub  the last  In  purpose  restrictive  such  speaking.  such  of  i s  a  they can  possible  t i eline  Dig  to FCct-Dig,  and  and t h u s  cannot  of  written  problem: but the  FDig be  simplified  are i n fact  FDig-Cct  i s an a r t i f i c i a l  number  conditions.  as  be  cases,  generating  However, i n the  fig.(5.06),  absence  of the other  different  o f t h e same p h a s e  according  of  distinct formally.  or a t i e line the  figures  corresponding  MPyh. i s represented  two a s s e m b l a g e s + Cpy  the  In  are ignored.  (MPhy)-zone  MPyh,  by  case  The  compounds  equilibrium  there  plotted  inequalities  The  an  ( c f .f i g . (5.10))  been  ***The  in  the  restrictive  i s n o t t o g e t t h e minimum  two  strictly  represented  down.  a l l t h e most  boundaries  equilibrium"  to  by are  compound.  in  beforehand.  corresponding  are a l l written  equations,  t o t h e most  o f t h e zone  and  equations  t h e zone o f each  be d e t e r m i n e d  inequalities  of  the  i n q u e s t i o n depends on t h e v a l u e s  and cannot  system  lead  i n e q u a l i t i e s , the  successively,  section,  which  configurations  It  restrictive  the results of the previous  written  of  the  + Pyr}.  would  The more  assemblage  in fig.(5.07).  become  stable:  restrictive  In the absence o f  { T r o + P y r + Cub}  condition  i s  and  provided  132  Pyr  The  The  ( M P y h ) -. z o n e .  (Cub)  -  zone.  133  8 Fe .875  s  =  CuFe. S  6  0  2  8 G°(MPyh) The  one  of  yields  i s given  s  =  16 G ° ( M P y h )  The  assemblages  a number  w h i c h do n o t b e l o n g t o t h e  of conditions.  C u F e 2 S 3 + 5 Fei.00  5  - G°(Bor)  i s represented  o f C u b may  Bor-MPyh  t i e line.  condition  i s given  eq.(5.17).  i n fig.(5.08).  lead In  t o t h e Cpy-Tro the latter  I n t h e f o r m e r c a s e , t h e two a s s e m b l a g e s  same  inequality CuFe2S3 = CuFeS2 + F e i . 0 0  s  CuFe S3 = CuFeS2 + Fe;uoO  s  + 0  restrictive  +  0  to  {Cpy + B o r +  and b o t h l e a d  F  e  S  to  the  2  < G°(Cpy) + G°(Tro)  eq.(5.18)  the (Cub)-zone:  the assemblages  provide  to . the  Cu5FeS4  2  G°(Cub)  or  by { B o r + MPyh + T r o } and i t i s e q u i v a l e n t  and {MPyh + T r o + C p y } become s t a b l e  Outside  t i el i n e  c a s e , t h e most  Tro}  an  eq.(5.17)  the (Cub)-zone:  absence  {FDig  restrictive  c a s e o f Cub.  Within  of  The most  ~ CusFeS4  s  > 5 G°(Cub) + 5 G°(Tro)  (Cub)-zone  the  the  eq.(5.16)  by { B o r + Cub + T r o }  16 F e n . 8 7 5  ***The  CuFeS2  < 6 G°(Cub) + G°(Pyr) - 6 G°(Cpy)  stability  (MPyh)-zone  + FeS2 - 6  3  t h e most  w h i c h do n o t b e l o n g t o t h e ( C u b ) - z o n e ,  restrictive  conditions:  {Cpy  + B o r + C p y } a n d {Cu° + B o r + T r o } .  inequality s i m i l a r to eq.(5.16).  following  .+  Pyr  The f i r s t  The l a s t  two  +  three MPyh},  one y i e l d s  lead  to  the  equations  3 CuFe2S3 = Cu5FeS4 + 5 F e i . o o S ~ 3 G°(Cub)  > G°(Bor) + 5 G°(Tro)  2  C  u  ° eq.(5.19)  134  and 6 CuFe2S3  = 17 C u F e S 4  6 G°(Cub)  > 1 7 G ° ( B o r ) - 50 G ° ( F D i g )  5  + 0 CuFeS  2  -'50  Cu  1  #  5  8  Fe .iS 0  eq.(5.20)  ***The c a s e o f I d a : The  (Ida)-zone  Within {Cov  the  i s represented  fig.(5.09).  (Ida)-zone:  + Pyr + FDig} 78 C u . F e S 6 . 5 5  in  5  yields = 2 7 1 C u S + 1 0 0 C u i . s s F e n . . ].S +' 68  78 G ° ( I d a ) < 2 7 1 G ° ( C o v ) + 1 0 0 G ° ( F D i g ) + 68  FeS  2  G°(Pyr) eq.(5.21)  Outside  the  (Ida)-zone:  {S° + C o v + P y r } y i e l d s Cu .5FeS6.5 5  G°(Ida) {FDig  = 5.5 C u S + F e S  2  - S°  > 5.5 G ° ( C o v ) + G ° ( P y r )  eq.(5.22)  + Cpy + P y r } y i e l d s  80 C u 5 , 5 F e S 6 . 5 80 G ° ( I d a )  = 450 C u i . s s F e n . i S  +306  FeS  2  - 271 C u F e S  2  > 450 G°(FDig) + 306 G°(Pyr) - 271 G°(Cpy) eq.(5.23)  {Cov + D i g + F D i g } Cu  5 # 5  FeS  G°(Ida)  6 #  5  yields  = 5 C u S + 10 C u x . 5 s F e 0 . i S  - 8.5  > 5 G ° ( C o v ) + 10 G ° ( F D i g ) - 8.5  Cu  1 # 8  S  G°(Dig) eq.(5.24)  135  Cu° ' The  Fig.(5.10) (FCct) - zone.  136  ***The c a s e o f The  FCct.  (FCct)-zone  Within  the  {Dig  +  in  fig.(5.10).  (FCct)-zone:  Cct  meaningful  c a n be s e e n  +  FDig}  condition  i s  ignored;  i s provided  a less  restrictive  by {Bor +  Cct  +  b u t more  FDig}  which  yields 3  C u  l.92  F e  0.04  3 G°(FCct)  ~ «12 Cu S  s  + 0.22 C u 5 F e S 4 -  3  2  Cu1.5sFeo.1S  < 3 . 1 2 G ° ( C c t ) + 0.22 G ° ( B o r ) -  G°(FDig) eq.(5.25)  {FDig  + B o r + Cu°}  yields  10 C u i . 9 2 F e Q . 0 4 10 G ° ( F C c t ) Outside {Bor  {Cov  the  s  =  1  C u  1.58  F e  0.1  s  ~ C U 5 F e S 4 + 2.08  < 14 G ° ( F D i g ) - G ° ( B o r )  Cu°  eq.(5.26)  (FCct)-zone:  + T r o + Cu°} *  yields  100  Cui.92Fe .04  100  G°(FCct)  =  s  0  i # 9 2  Fe .04  2  C u 5 F e S 4 - 28 F e i  <  0  0  s  +  3  2  C  u  °  eq.(5.27)  yields s  0  10 G ° ( F C c t )  3  > 3 2 G ° ( B o r ) - 28 G ° ( T r o )  + D i g + FDig} 10 C u  4  = 4 Cui.  5  8  Fe  0  >  1  S + 8.6 C u  1 < 8  > 4 G ° ( F D i g ) + 8.6 G ° ( D i g ) - 2.6  S  - 2.6  CuS  G°(Cov) eq.(5.28)  ***The c a s e o f D i g . The. ( D i g ) - z o n e Within {Cct is  the  C u  1.8  s  G°(Dig)  in  fig.(5.11).  (Dig)-zone:  + FDig  provided  i s represented  + FCct}  i s i g n o r e d , and a more m e a n i n g f u l  by {Cov + C c t + FDig} =0.8  Cu S 2  +0.2  which  condition  yields  CuS + 0 C u 1 . 5 s F e o . l S  < 0.8 G ° ( C c t ) + 0.2 G ° ( C o v )  eq.(5.29)  137  138  {Cov  + FDig  Outside  + FCct}  the  leads  + I d a + FDig}  leads  {Cct  + Cu° + F C c t }  yields  1.8  =  C  G°(Dig) {FDig  u  2  ~ °*  s  + Bor + FCct}  ***The c a s e  {Bor  C  °  u  to a condition  +  0  1.92  C u  F e  similar  0.04  to  of  eq.(5.24).  s  eq.(5.30)  yields 5 8  Fe .iS  + 0 Cui.92  0  F e  0.04  - 0.1  s  > G ° ( F D i g ) - 0.1 G ° ( B o r )  Cu FeS 5  4  eq.(5.31)  FDig.  (FDig)-zone the  2  = Cui.  0.6 G ° ( D i g )  Within  eq.(5.28).  > G°(Cct)  0.6 C u i . s S  The  similar to  (Dig)-zone:  {Cov  C u  to a condition  i s represented  i n f i g . (5.12).  (FDig)-zone:  + Cpy + P y r } y i e l d s 20  Cui 58Feo.iS  20  G°(FDig)  #  = 8 C u s F e S 4 + 2.4  F e S 2 - 8.4  < 8 G ° ( B o r ) + 2.4 G ° ( P y r )  - 8.4  CuFeS2 G°(Cpy) eq.(5.32)  {Dig Bor  +  FCct  + FCct}  + C c t } i s i g n o r e d , and t h e l e s s  and {Cov + D i g + FCct}  eq.(5.31) and eq.(5.28)  lead  respectively.  + Cpy + P y r } and {Cov + I d a + D i g } l e a d as  eq.(5.23)  Outside {Cov to  the  and e q . ( 5 . 2 4 ) .  restrictive  to conditions  {Dig +  similar to  The two a s s e m b l a g e s { I d a to the  same  conditions  ,  (FDig)-zone:  + Ida + Pyr}, conditions  {Cu° + F C c t  similar  to  + B o r } a n d { B o r + C p y + Cub}  eq.(5.21),  eq.(5.26)  lead  and  eq.(5.20)  be  written,  respectively.  Therefore  as a whole,  17  inequalities  can  139  which  should  G°'s.  By  using  inequalities in  define  lead  consistent intervals  the  data  listed  to the following  in  f o r the s i x required table  numerical  (4.01),  equations  16  < 6 G°(Cub) + 235 733  e q . ( 5 . 16B)  G ° ( M p y h ) > 5 G ° ( C u b ) - 25 4 0 3  e q . ( 5 . 17B)  G°(Cub)  < - 69  429  e q . ( 5 . 18B)  G°(Cub)  > - 71  892  e q . ( 5 . 19B)  3 G°(Cub) > -  > - 106  G°(Ida) 0.8  e q . ( 5 . 20B)  25 G°(FDig) - 808 664  . e q . ( 5 . 21B)  G ° ( I d a ) < G ° ( F D i g ) - 59 2 9 1  0.78  e q . ( 5 . 22B)  576  G ° ( I d a ) > 4.5 G ° ( F D i g ) + 1 2  e q . ( 5 . 23B)  069  e q . ( 5 . 24B)  > 10 G ° ( F D i g ) - 8.5 G ° ( D i g ) - 63 98 5  G°(Ida)  e q . ( 5 . 25B)  3 G ° ( F C c t ) < - G ° ( F D i g ) - 87 8 2 3 G°(FCct)  < 1 .4 G ° ( F D i g ) + 9 5 1 4  G°(FCct)  > - 23  10  e q . ( 5 . 27B)  694  G ° ( F C c t ) > 4 G ° ( F D i g ) + 8.6 G ° ( D i g )  - 33  2 7 2 e q . ( 5 . 28B)  < - 19  711  e q . ( 5 . 29B)  G°(Dig)  > - 21  440  e q . ( 5 . 30B)  G°(Dig) > G°(FDig) + 9514  e q . ( 5 . 31B)  G°(FDig) this  system  * Eq.(5.20B): condition  e q . ( 5 . 27)  e q . ( 5 . 32B)  < -• 23 3 6 3  interdependent,  of  inequalities,  but the system the lower provided  c a n be  the  unknowns  area l l  simplified.  G°(FDig), t h e  by eq.(5.20B).  more  restrictive  Combining  > 0.3 G ° ( B o r ) - 0.2 G ° ( T r o )  numerically  i s  e q . ( 5 . 2 6 ) and  yields  G° ( F D i g ) or  ' e q . ( 5 . 26B)  G°(Dig)  0.6  the  expressed  cal/mole: 8 G°(MPyh)  In  these  eq.(5.33)  140  G°(FDig) The  > - 23 7 1 9 . 5  eq.(5:33B)  minimum v a l u e o f G°(FDig)  value  g i v e n by eq.(5.33B).  yields can  ignored,  eq.(5.16B) G°(MPyh)  to  than o r  Replacing this  t h e same i n e q u a l i t y be  i s greater  value  as eq.(5.19B).  thereby  eq.(5.19B)  separating as  an  equal into  to  the  eq.(5.20B)  T h e r e f o r e , eq.(5.20B) the  four  independent  inequalities  system  defining  and G°(Cub).  * Eq.(5.3lB):  i n eq.(5.31B),  value  g i v e n by eq.(5.30B)  less  restrictive  than  yields  replacing G°(FDig)  eq.(5.32B).  G°(Dig)  by a minimum  < - 22 3 7 8 ,  Eq.(5.3lB)  which  i s  then  be  can  removed. * Eq.(5.28B): by  maximum  i n eq.(5.28B),  v a l u e s p r o v i d e d by eq.(5.32B)  G°(FCct)  > - 29 624 w h i c h  and  eq.(5.28B)  thus  * Eq.(5.24B): value by  i s less  c a n be  i n eq.(5.24B),  restrictive  yields  than  G°(Dig)  i s  G°(FDig)  and  G°(Dig)  and eq.(5.29B)  restrictive  yields  than  eq.(5.27B),  G°(Dig)  by a minimum  eliminated.  g i v e n by e q . ( 5 . 3 0 B ) ,  eq.(5.32B)  and  replacing  replacing  and G°(FDig)  G°(Ida)  > - 1 1 5 375,  eq.(5.22B). defined  b y a maximum  Eq.(5.24B)  independently  value given  which  i s  can t h e n be  less  removed,  by  eq.(5.29B)  and  the  most  restrictive  G°(Ida)  > - 116 331  eq. (5.30B) . *  eq.(5.23B):  minimum v a l u e which  i s  eliminated. G°(FDig)  by  using  provided  redundant G°(Ida)  by  i n view  solution  eq';(5.23B)  of  i s  of eq.(5.22B).  and G°(FCct)  by t h e s i x r e m a i n i n g  The  eq.(5.32B),  are defined  Eq.(5.23B) as a  i s then  function  of  inequalities.  the system  i s presented graphically i n  141  f i g . (5.13) and f i g . ( 5 . 1 4 ) . the  The i n t e r v a l s  s i x c o m p o u n d s a t 200°C a r e t h e n - 21 4 40 < G O ( D i g )  < - 19 711  eq.(5.34)  - 23 720 < G°(FDig)  < - 23 363  eq.(5.35)  < - 105 967  eq.(5.36)  < - 23 1 9 4  eq.(5.37)  - 70 981 < G°(Cub)  < - 69 4 2 9  eq.(5.38)  - 23 7 6 9 < G ° ( M P y h )  < - 22 6 0 5  eq.(5.39)  -  106 576 < G°(Ida) - 23 694  Except the  size  will  <G°(FCct)  f o r G°(Dig), t h e c h o i c e of  f i g . (5.14).  some  other  In t a b l e  be u s e d  thermodynamic  intervals  (5.01)  i n chapter  o f anyone  diagram calculated  experimental  Cu-Fe-S phase  (1966).  The  the  true  assuming and  intervals  to actual figures  t o f i g . ( 5 . 1 3 ) and are  listed  that  t h e E-pH d i a g r a m s .  with  these  data,  In any  the  phase  the i n f o r m a t i o n conveyed by t h e  i s g e n e r a l , a n d c a n be  are  error  0.5% on G°(Tro)  relatively  i n table  uncertainties of the s i x an  reduces  b y Yund  and  applied  to  diagram.  above  correspond  G°'s  d i a g r a m a t 200°C p r o v i d e d  The method  t e r n a r y phase  according  7 t o compute  are consistent with  Kullerud  o f these  t h e s i x G° v a l u e s  assemblages  any  of possible values f o r  above  o f 2% o n G ° ( B o r ) leads  (4.01),  small,  and do n o t  G°*s.  and G°(Pyr),  to the following  but  For  they  reflect  instance,  5% o n G° ( C p y )  relations  8 GO(MPyh) < 6 G°(Cub) + 235 733 +  (< 14 3 2 0 )  eq.(5.16Tj  16 G O ( M p y h )  «  eq.(5.17T)  > 5 G°(Cub) - 25 403 -  G°(Cub)  < - 69 4 2 9 + '•'(< 2 3 8 7 )  G°(Cub)  > - 71 892 -  These  e r r o r s would  «  2505)  e q . ( 5 . 18T )  835)  increase drastically  eq.(5.19T) the  field  of  possible  6°(FDig) 4  -23 3 0 0  N23fe00  [^23+700  234900  •23100  -23300  -23500 G°(FCct)  -106600  •106400  -106200  106000  -105800  G (Ida) 0  Fig.(5.13) s o l u t i o n o f the system o f equations p r o v i d i n g G ° ( F C c t ) , G°(Ida) a n d G ° ( F D i g ) . two p o i n t c i r c l e s c o r r e s p o n d t o t h e d a t a i n t a b l e (5.01).  Graphical The  - 23700  G°(Cub)  G° (Cub)  67000  68000  69000  -70000  -71000  -72000  -73000 -25000 -24000  -23000  G°(MPyh)  -22000  -25000  -24000  -23000  -22000  G° (MPyh)  Fig.(5.14) G r a p h i c a l s o l u t i o n o f the system o f e q u a t i o n s p r o v i d i n g G°(MPyh) and G ° ( C u b ) . The p o i n t c i r c l e c o r r e s p o n d s to t h e d a t a i n t a b l e (5.01). Fig.(5.15) E x p a n s i o n o f the s o l u t i o n l o c i f o r G°(MPyh) and G ° ( C u b ) , when u n c e r t a i n t i e s (estimated) f o r the source d a t a a r e taken i n t o account.  144  values  f o r G°(MPyh)  those  which  when  the  have  are less data  smaller  example,  and G°(Cub). restrictive  i n table  errors,  the  However than  m u s t now b e t a k e n  stability  o f MPyh  eq.(5.16)  (4.01) a r e e x a c t  lead  to the following  - 0 . 1 2 5 Fe<> - 0 C u °  G°(MPyh)  > G°(Tro)  > -24 108 -  = 3 Fej.oO  F e  0.875  s  In  this  s  «  Tro}  of  in  the  121)  eg.(5.40)  (< 3 6 2 )  eg.(5.41)  Cu°  > -72 324 -  0.75 F e i . o O  =  G°(MPyh)  ~ Fe° +  s  GO(Cub) > 3 G°(Tro)  account.  may  inequalities  = Fe^ooS  CuFe2S3  eq.(5.32)  but which  o f {Cub + P y r +  F e . 875S 0  to  figures,  into  conditions,  o f {Cu° + Fe° + T r o } i n t h e p r e s e n c e  MPyh a n d C u b , a n d t h e i n s t a b i l i t y presence  the other  + 0.125 FeS2  + 0  < 0.75 G°(Tro) + 0.125 G°(Pyr)  CuFe S3 2  < -22 605 +  «181)  eq.(5.42) The  resulting  fig.(5.15) -72  intervals  and c o r r e s p o n d  686 < G°(Cub)  -24 2 2 9 < G ° ( M P y h ) When a b s o l u t e Using high which  the  Yund been  method  accuracy  presented  ascertain  two  in  eq.(5.39B) these  i n this  of the results.  that  ploted  < -22 424  chapter  experimental  more  does  i s to phase  are  relevant.  not guarantee  provide  G°  data  diagrams.  t h a t were m i s s i n g  by r e t r i e v i n g  consistency with  intervals  The g o a l  and K u l l e r u d Cu-Fe-S phase shown  then  eq.(5.38B)  are sought,  provided  are  to  o f t h e G° v a l u e s  been  confidence  < -67 042  are consistent with  Out have  values  of  i n chapter  4,  four  the information contained  diagram.  compounds  the available  Furthermore must data.  be  i t has  considered The  in  to  remaining  145  missing in  the  data next  will  be  chapter.  estimated  from  solubility  data  as  presented  TABLE  G° data of evaluated  from  Symbols  (5.01)  f o rs o l i d  compounds  the Cu-Fe-S-H 0 system 2  Yund and K u l l e r u d  I  a t 200°C,  ternary  Formulas  I  i n this stu  I  G°  I  cal/mole  I  - 21 1 0 0  Dig  I  Cu  Mpyh  !  Feo.875S  I  - 23 100  FDig  I  Cui.ssFeo.iS  I  - 23 450  FCct  I  Cu1.92Feo.04S  I  - 23 5 0 0  Ida  I  Cus.sFeSg.s  I  - 106 350  Cub  I  CuFe2S3  I  - 69 7 0 0  1 > 8  S  147  CHAPTER  6  E S T I M A T I O N OF F R E E E N E R G Y D A T A  Solid-liquid G°'s and the  FROM S O L U B I L I T Y  DATA.  equilibria  now b e u s e d  of the hydrated CUSO4.2Cu(OH)2 complex  FeS04( q). a  available experiments  The i n  compounds FeS04.H20  (Ant),  solute  and t o improve  FeS04  +  solubility  the  will  (HFSu),  FeS040H  the available  and on t h e i o n p a i r s data  literature,  described  to estimate  thereafter.  or  to  be  treated  generated  the  (BFSu)  data  on  CUSO4( q)  and  a  are  through  either several  148  SECTION  6-1  : theoretical  Stable 200°C, and  equilibria  and i n v o l v e  aqueous  solutions  closed.  The  components  are given.  are  must  solids  From a thermodynamic  solutes  background.  be  f o rwhich  which  of The  t h e G°*s must  obtained  at  be e s t i m a t e d ,  c a n be m o d e l e d .  point of view,  numbers  experimentally  t h e systems  moles  mj°  activity  of  under  their  potentials  are  independent  coefficients  known, and t h e i r c h e m i c a l  study  aj  of  the  are expressed  as pi  = G°(i) + R T L o g ( a i  Xi)  eq.(6.01)  When t h e G ° ' s o f t h e N q c o n s i d e r e d s o l u t e s  are  a  well  as t h e n a t u r e , c o m p o s i t i o n  present, When  the equilibrium  more  independent  more  unknowns  x^'s  a r e measured  then  one o r more  This G°'s  aqueous  i s totally  as  compounds  determined.  are obtained during the experiments,  a f t e r sampling  For instance, the  when  solution  at  one o r more temperature,  unknown G°(i)'s c a n be c o m p u t e d .  procedure  quickly  phase  may  in  However (or  wide c o m p o s i t i o n and study  and G ° o f t h e Ns s o l i d  c a n be d e t e r m i n e d .  temperature.  model  data  of sulphate salts since  relatively  under  state  a l l known,  are  very  these  aqueous  the excess else  useful  solid  f o rd e t e r m i n i n g t h e  compounds  solutions, free  mainly  energy  equilibrate at elevated  function  of  the set of Oi's) i s not available  temperature  too  of non-ideality  be  range.  When  concentrated, the lack  may l e a d  to  large  the  the ina  solutions  o f an a p p r o p r i a t e  uncertainties  i n the  149  required  G°  values.  Excess calculated  in  Accordingly, charged  this  without be  an  the  ions)  i s  widely  "primitive  represented  moving  More s p e c i f i c a l l y ,  treatments  of this  model  solutions,  in  a  model".  as a s e t o f  continuum  the d i e l e c t r i c  lead  to systems  and excess  b y means o f M o n t e - C a r l o  These c a l c u l a t i o n s  practical  of  are  of  constant  i s t h a t o f t h e pure s o l v e n t .  analytical  1970).  electrolytes  solution  (hydrated  solvent.  calculated  of  framework  aqueous  continuum  Involved  energies  the  spheres  unperturbed of  free  are  free  energies  methods  (Card  too  complex  s t i l l  of  equations must  then  and V a l l e a u , to  be  of  use t o e n g i n e e r s .  A classical  treatment  of this  model y i e l d e d  t h e Debye and  Huckel  equation  l o g O i (T, I) = -  It  accounts  dilute the  solution,  the  literature  (Barner  In eq.(6.02),  A(T)  up  l 0 -  5  | | | •  «  I i s the true  size  i s a temperature of  The v a l u e s to  and Scheuerman,  hydrated  e q . (6. 02)  f o r c e s among ionic  and B ( T ) a r e two p a r a m e t e r s  of the  approach").  2  distance electrostatic  o n l y , and a j f T )  characteristic closest  A(T) Z i  | I 1 + a i ( T ) B ( T ) I°«5  f o r long  solutions.  temperature  I  strength of  depending  dependent ion i  upon  parameter  ("distance  of  o f A, B, a n d a j a r e a v a i l a b l e i n  200°C a n d f o r a n u m b e r o f i o n i c 1978).  ions i n  solutes  150  Eq.(6.02) is  only  represents  valid  for  very  increasing  ionic  increases  again  investigations of  empirical  Kusik  and  at  of  been  for  a  been  devoted or  an  eq.(6.02)  by  a  coefficients. represented  at  20%  series  in and  of  liquid  the  c o e f f i c i e n t s are  for not  a  small  been  Helgeson  of  interaction  periodic  Pitzer's  tested  on  (1969)  applies  by  means  empirical  into  a  single  account the  up  to  activity  t h i s model  H2SO4, a n d  the  100°C  has  to  be  simple  complex an  of  logaj  at  is  not  not  which  involves  yet  can  about  steel  is  also  coefficients.  (Schenk  widely  and  used  systems extended  and used  by  Pitzer's in  Debye  properly 5.  The  reliably  However, for  a l l  Frohberg,  c o e f f i c i e n t s are  ions,  be  of  available  extends  interaction  forces  readily  table  interaction  number o f  and  Numerous  involving  systems  ideality  this  Conversely,  off  with  represent  which  ionic  t h i s method  take  including  to  means  allows  On  eq.(6.02)  However,  ternary  by  which  25°C).  zero.  electrolytes  up  the  to  relations  XJ.XJ  described  of  but  levels  beyond  expression  from  elements  at  eq.(6.02)  error.  departure  case,  I,  temperatures. an  25°C  0.001  engineers  more  mixed  forward  Binary  versus  improving  of  two  electrolytes  put  to  provide  These  above b o i l i n g  (1973)  <  logoj  extensions.  and  within  (I  even  extension T,  of  generally  and  number o f  several  tested  Pitzer  to  temperature.  concentrations  valid  up  constant  of  logaj  (1975)  on  decrease  dilute solutions  variations  coefficients all  have  based  parameter  initial  strength  Meissner  relations  effect  the  in the  1965),  metallurgists. only model  available has  s t i l l  hydrometallurgy. and  Huckel  equation  in  151  which  a term  +B(T).I  eq.(6.02).  Such  temperature  range,  concentrations  which  increasingly of  NaCl,  the dielectric  Very  the  reliably  and  are  Helgeson  valid  in  multicomponent  of  to  added  an e q u a t i o n  predominantly  According  i s  electrolytes other  compared  constant  of  side  ions  to  of  a large  consisting present  that  of  (1969) , t h e Debye and H u c k e l  as temperature  i n  NaCl.  equation i s  increases because  of the  drop  water.  information  i s  available  for  solutions  o f t h e Cu-Fe-S-H20 system  at  elevated  temperature's.  In  following  solution  the  computed  little  hand  represents,, over  of  low  right  at  B = 0.36  10  According  200°C  + 1 0  m  to  _ 1  ,  may  avoided  f o r I > 1.  SECTION  6-2  In use and  their  by and  be  the  using the  Helgeson's  calculations  Free  sections,  data  energy  are only  study  t h e N.B.S. d a t a  A = 0.82,  i n table  the  are  (6.01).  corresponding  I < 0.1 a t 2 0 0 ° C , a n d m u s t  f o r the s o l i d  o f t h e Cu-S-H^O  with  listed  (1969),  for  : available  data  values  statement  valid  compositions  eq.(6.02)  aj  aqueous  available  system,  forantlerite  sulphates.  for antlerite.  Kwok  a t 25°C  and (Wagman  Robins  (1973)  e t a l . , 1969)  estimate S°(298) = 52 c a l / m o l e .  K  C (298,473) p  be  =67  cal/mole.  K  152  which  yields  The  G°(Ant) = - 304 k c a l / m o l e  Kennecott  antlerite  Copper  on  industrial  thermochemical  data  at  given  -  200°C  i s  306.0 k c a l / m o l e  The  source  not  documented.  No G ° d a t a  by In  the  figure  for either  of Ant  CUSO4.2Cu(OH)2  G°(Ant)  a  i n chapter  Handbook o f G°(Ant)  corresponds  chosen  i n this  investigation  to  study.  which  i s  FeSC"4.H20 o r F e S C ^ O H .  The i n f o r m a t i o n t h e y  presented  produces  1978) where  are available  experimentally determined  presence  states  i s an i n t e r n a l  ( f i g . (4 . 0 7 ) ) , t h e i n s t a b i l i t y the  published  as - 312.3 k c a l / m o l e , which  phase diagrams  sulphates.  has  actually  (Barner and Scheuerman,  are available  t h e method  scale  which  with the standard  of this  Several three  Corporation  a t 200°C.  which  contain  involve  c a n be  these  retrieved  5. C U S O 4 - H 2 S O 4 - H 2 O  o f the assemblage  phase  diagram  {HCSu + Ten}  in  yields =  CUSO4.H2O  < G°(HCSu)  +  2  CuO  + H2O  RTLoga(H2O)  + 2 G°(Ten) + G ° ( H 0 ) + 2  eq.(6.03) In  the  Fe203-H2S04~H20  instability  phase  o f { F 3 S u + Hem}  6 FeS040H  = 2 Fe (S04) 2  6 G°(BFSu)  diagram  i n the presence 3  = 2 G°(F3Su)  + Fe 03 2  + 3  + G°(Hem)  (fig.(4.06)), o f BFSu  the  yields  H 0 2  + 3 G°(H 0) +  3RTLoga(H 0)  2  2  e q . ( 6 . 04 ) No  phase  published. ferrous  diagrams Bruhn  involving et  s u l p h a t e above  a l .  FeS04.H20 (1965)  120°C u p t o  at  studied 180°C,  200°C the  and  have  been  solubility  determined  of the  153  presence 180°C.  of  the  If  instability  the  monohydrated monohydrate  o f the anhydrous  FeSO/j.H^O - F e S 0 4 ( ) +  In  the  a(H20)  < G°(F2Su)  three refers  unstable  as  this limits  i n the  can value  and  eq.(6.05),  presence  hardly  be  of  the  determined  i s most p r o b a b l y  lower  f o r t h e t h r e e G°'s u n d e r  than  study.  o n e o b t a i n s a t 200°C  G°(Ant)  < - 298 504 c a l / m o l e  eq.(6.03B)  G°(BFSu)  < - 217 960 c a l / m o l e  eq.(6.04B)  G°(HFSu)  < - 232 649 c a l / m o l e  eq.(6.05B)  The  above phase diagrams  limits the  the  eq.(6.05)  eq.(6.04)  o f water  which  However,  up t o  200°C,  2  eq.(6.03),  to the a c t i v i t y  provides high  Numerically,  at  c a n be e x p r e s s e d  2  assemblage,  which  salt  stable  + G°(H 0) + RTLoga(H 0)  equations  experimentally. one,  remains  i n water  H2O  c  G°(HFSu)  ferrous sulphate  c a n be w r i t t e n .  literature  solid  Posnjak aqueous  Both  figures  are consistent with  Solubility three  are not very  data  at  200°C  i n f o r m a t i v e , a n d no  for  G°(Ant)  lower  available  i n  eq.(6.03B).  have  been  provided  f o r these  sulphates.  and  Merwin  phase  in  (1922)  measured  equilibrium  with  the  composition  of  the  FeS0 OH and h e m a t i t e , and 4  provide Fe2C>3 : 0 . 6 3 % This It  solution must  be  corresponds  SO3  : 5.58%  i s already fairly noted  however  t o t h e most  : 93. 7 9 %  2  concentrated  that this  dilute  H 0  in  sulfuric  solid-aqueous  solution  i n  (weight  %)  acid.  equilibrium  equilibrium  with  154  FeS040H.  Moreover,  provide  a  ideality  legitimate for  such  t e r m s o f G°(BFSu)  Posnjak  and  aqueous and  t h e model  approximation  a solution.  i n e q . ( 6 . 0 2 ) may  of  These  the  s t i l l  departure  data  will  the  composition  from  be r e t r i e v e d i n  i n s e c t i o n 6-4.  Tunell  phase  expressed  (1929)  measured  i n equilibrium with  and  C U S O 4 . H 2 O  of  the  CUSO4.2Cu(OH)2/  provide CuO  which  t  (S04)  t  = 3.763 m o l e / k g  H 0  = 4.017 m o l e / k g  H 0  solution  G°(CUSO4( q)) a  information a(H 0) 2  listed  : 61.71%  (weight  %)  2  can  i n table  =  hand,  (4.02).  by  using  The two above  the  pieces  of  cal/mole  confirms  questionable  Kwok  and Robins*  low.  i n such  { A n t + Ten} w o u l d  eq.(6.02)  i s certainly  would  then  be  Bruhn  et  lead  valid.  figure  The v a l i d i t y  a concentrated  t h e e q u i l i b r i u m between  assemblage  sulphate  computed  0.098  seems u n r e a l i s t i c a l l y  definitely  be  lead to  a calculation  a(H20)  other  2  2  composition  G°(Ant) = -303 730 Such  H 0  yields  (Cu)  The  S O 3 : 19.83%  : 18.46%  solution. phase  value  On t h e and  solution  A more a c c u r a t e  but  o f eq.(6.02) i s  t h e aqueous  to a dilute  (1973),  the  f o r which o f G°(Ant)  obtained.  a l . (1965)  provided  i n water as f o l l o w s  solubility  data  for  ferrous  155  |T  OC  I  I  I  I 1 1 1 140  I  I  g FeS0 /kg  This  2  uncertainties FeS0 /kg  The  documented,  at  on  decreases.  170°C  a  The  linear  Extrapolating  this H2O.  with  t h e G°(FeS0 ( q)) 4  The a  equal  t o e i t h e r 0.2  ranges  from that  of  to  rather  FeS0  4  large around  be i n e r r o r . i s  the  not  well  s o l u t i o n was  to negligible errors  when  between  composition (4.02)  H2O.  150°C  of  yields  a  value  a  ( ) a t 200°C.  of  computed  solubility  cal/mole.  It  4 kcal/mole,  the s o l u b i l i t y that  solubility.  c a n be for  and  T h e r e s u l t i n g G°(HFSu)  almost  consistent c  also  1965)  t o - 233 893  I t m u s t be n o t e d  than  but  stabilize  the logarithm  determining  are  |  Solid  i n table  uncertainty,  hence  7  quenching.  200°C  such  and  200°C  observed  cal/mole  a t 200°C.  at  |  b u t b e c o m e s d i s t u r b i n g when t h e  - 237 804  sulphate  4  lead  4  by e x p e r i m e n t a l l y  FeS0 .H20  may  or 6g FeS0 /kg  an  a l . ,  I  6  may  after  solution  resolved  eq.(6.05B)  et  or  listed  I  J  180°C m i g h t  trend  trend  FeS0 /kg  20  known • w h e t h e r  decrease  0.2g  felt  not  a r e measured,  solubility  4  (Bruhn  quenching  solubilities  i s  i s  at  temperature,  redissolution large  i t  I  solubility  value  procedure  and  65  extrapolated  The  The  I I  I  I I  be  remain.  experimental  filtered  may  H2O.  4  I 111  I  solubility  I I I 160 I 170 I 180 I I I I I  150  I I  I 203  H 0  4  I  6g  I  | 120  both with  of  figures the  could  was be  ferrous satisfy  stability of  156  Therefore, solubility  of  presence  {Ant  in  the  F e S 0 4 . H 0 and  6-3  +  Ten}  at  200°C.  and  These data  experimental  experiments  out  p r e s s u r e PARR a u t o c l a v e made o f mechanically  by  an  by  a chromel-alumel  2°C  a  model  by  Instrument) . autoclave temperature after  An  the  composition i n will  be  the  generated  the  system  before  the  r u n , and  added  to  the  solute  f o r m a t i o n by  by  initial any  at  and  cylinder  20  200°C  min.  to  on  of  several  remaining  in  temperature  is  held  within  (Yellow  Springs  supporting  run  (ten minutes  order  oxygen.  100°C.  from  starts  the room (t=0)  more) .  oxygen  purges  h e a t i n g near  system  is  increase  The  litre  solution  is  sulphate s o l u b i l i t y ,  means  once  The  temperature  than  The  controller  heated  solution  ferrous  titanium.  thermocouple,  electrically  stabilization  i n a s t a n d a r d one  impeller.  thermistemp  t o 200°C i n l e s s  complete  the  71  allows the  measuring  from  on  procedure.  were c a r r i e d  measured  For  the s o l u t i o n  required  : experimental.  The  stirred  are  section.  : apparatus  high  on  2  following  SECTION  6-3-1  of  more e x p e r i m e n t a l d a t a  with  i s removed H  2  (g) , o n c e  Iron  t o p r e v e n t any  Fe°  is  ferric  157  Solutions another of  c a n be added autoclave.  several  runs  redissolution  to the system For instance,  so  that  rather  than  of the solution  The  device  filters any  the solution  solid  along  the tubing  60°C  so  study  are less  that  that  no s o l i d  are  taken,  containing  All  copper  mole/kg  every for  i s  after  autoclave,  on q u e n c h i n g .  a t 200°C t h a n  flushing  on  occurs  A  steel  A water  which  preventing system  sample  below  the  lower  out.  cooling  compounds  under  temperatures  i n the tubing.  valves  sample  frit  thereby  The s o l i d at  solid  c a n be t a k e n  stainless  of  i n the course  reached  outside the autoclave cools  soluble  and  tubing,  reagent  grade  so  A l l samples into  bottles  a f e w g r a m s o f 1:1 H C l .  water.  are prepared The  weighed  The  present.  t h e two r e s p e c t i v e  since  However  are  mole/kg  H2O  t h e y have n o t been  the solutions  and  and a n a l y s e d f o r  results  The c o n c e n t r a t i o n i n  f o r a l l samples  element  are  chemicals  absorption spectrophotometer,  gravimetry.  solution.  from  samples  by atomic  by  determined  a  the  reprecipitation  or iron  sulphate  i s added  a t temperature  no e v a p o r a t i o n o c c u r s .  the solutions  distilled  inside  b y means  precipitation.  includes  redissolution  water  equilibrium  representative sampling  at temperature  and  for  given  i n  cannot  be  assayed f o r  are dilute  c o n c e n t r a t i o n v a l u e s t o be v e r y  enough  close.  158  6-3-2  : experimental  When of  a  the  solution  final  results.  initial  system  containing  solution  10~  composition  consists  mole of  2  obtained  of  lOg  CuO  s u l f u r i c acid  after  4h30  at  and per  0.6  dm  3  dm ,  the  is  the  only  CuO  3  200°C  following (Cu) ( S 0  The  =  t  )  4  T  drop  3.03  10  - 4  mole/kg  sol  =5.50  10  - 4  mole/kg  sol  of  sulphate  the  dissolves,  but  also  This  was  determined  solid  after  a  run  where  autoclave  at  Under  the  above  since  the  copper  is  already  assumed When t h e rate  0.8  dm  of  per  dm , 3  6.76  10~  4.78  10  a  solution  conditions,  the  at  30  final are  solution the  system  sol  - 4  mole/kg  sol  A  t y p i c a l run i s presented  at at  was  removed  min  (3.30  10~  figure.  from  is  the  after  - 4  4h30  sol)  can  and  be  6h30.  in sulfuric acid,  of  lOg  mole  and  is  s t i l l  the  lower.  CuO  of  concentration min  fast  mole/kg  4  substantially  10  is  Equilibrium  obtained  12.5  t=30  For  added  to  sulfuric  acid  equal  to  amounts  to  t=lh30.  carried in  X-ray d i f f r a c t i o n  precipitation  consists  containing copper  mole/kg  precipitates.  the  i s more d i l u t e  crystallization initial  by  not  quenching.  solution  4  FeS04.H20  whole  that  compound  CUSO4.2Cu(0H)2  same r e s u l t s  when t h e  3  to  shows  sulphate  concentration  the  solid  instance  as  the  starting  starting  of  solid  200°C b e f o r e  close  since  a  concentration  out  table  to  determine  (6.02).  The  the  iron  solubility  of  concentration  159  decreases obtained since  of  the run  a f t e r 16h.  No  Bruhn  et  al.'s  solubility  H2O  drop  a l . (1965)  above  after  the  acid,  samples  +  2  H  a +  increases  =  F e ^ the  t=6h?0  that  obtained  in  was  performed  assumed to  the  on  180°C.  level  off observed  a on  the  basis  The  iron  corresponds  temperatures  is  to  of  the  by  Bruhn  170°C.  run  presented  in table  (6.02)  10  H2SO4 was  added  - 3  t=6h30  rapid  side  to  figure at  equilibrium  increasing  of  reaction +  mole were  taken.  iron takes  4  and  to  the  two  system sulfuric  occurs  as  shown  concentration.  immediately.  It  is  namely  H |g)  eq.(6.06)  2  s o l u t i o n pH  includes  adding  sulphate  place  occurs,  On  FeS0 .H20  d i s s o l u t i o n of  increase  that  up  final  reached  diffraction  confirms  5.17 at  equal  results  reprecipitation  believed  which  and  large  However,  Fe°  since  large  the  the  the  be  FeSC>4.H20 was  at  which with  Actually, experiments  (1965)  obtained  FeS04/kg  is  x-ray  and  i s added,  seems t o  concentration  precipitating solid,  4.52g  by  when w a t e r  Equilibrium  iron  concentration  et  but  quickly.  separate the  slowly,  towards  the  inital  value.  160  SECTION  6-4-1  6-4  : discussion.  : the ferrous sulphate  In  the runs  solubility vessel  a t 200°C,  with  therefore  FeS04/kg  iron  An  equal  i s  H2O  also  corresponding  Therefore (Fe)  t  t  introduced  into  (Fe)  t  2.92 in  this  would  respect  to  2  mole/kg s o l  = 2.923  10  - 2  mole/kg s o l  with  HFSu  errors.  The  using  mole/kg  above c o n d i t i o n s .  either  sol.  to  4  ( q)) a  unit 2.85  c l o s e t o -234  however, For  to  occur the  iron  concentration.  interpreted composition calculated  i s  likely  by  activity  10~  mole/kg  2  G°(HFSu)*s  200  as due t o was  water  The c o r r e s p o n d i n g  very  reaction  increase  sulphate  Since  the  likely  first  solution  4, b y a s s u m i n g  a r e both  Magnetite,  were  t h e G°(FeS0  equal  (1965).  results  2  by  way  the  elevated  t o be g i v e n i n  vessel,  slightly  -  (S04)t  10~  which  10  i n chapter =  i s  the  and s u l p h a t e i s  the results  the  eq.(6.06)  with  of iron  into  at  a l . ' s study  = 2.847  experimental calculated  allow et  to  equilibrium  method  would  the experimental  (SO4) at  concentration  sulphate  introduced  precipitates  as i n Bruhn  (thermodynamically), concentration  FeS04.H20  which  the ferrous  i s initially  2  and  expected,  out to determine  FeS04.7H 0  H 0, 2  temperature.  grams  carried  system.  then  Helgeson's and sol  for or to  calculated  cal/mole.  to precipitate  instance, the p r e c i p i t a t i o n  under the  o f Mag  at the  161  potential 4 This  Fe  of  2  the  '+  +  Fe°/Fe  4 H 0  = Fe 0  2  reaction  3  has  couple  2 +  A  a  +  4  is written  Fe°  G  +  8  H  lower  as eq.(6.07)  +  than  -10  kcal  in  both  calculations. When  the  experimental  eq.(6.07)  i s computed  between to  (Fe)t  and  as  lowers  relative  to  state  the  of  the  the  above  of  system  a A  is  data  points  G°(HFSu) with system  between on  and  magnetite cannot  described  from the  of  above  not  be  due  iron  concentration  and  (S0 )t  a  more  assumed  stable  less  a  q  because  of iron  is  interpreted used  the  )).  dependent,  and  The  1%  By  and  the  determined  leads  a  as  large  due  the  assuming  to  the  the  the  two  value  of  equilibrium  potential with  the  calculation,  solution,  provide both However  more  Therefore,  i n the  aqueous  the  (Fe)f  represents  200°C.  data  of  experimental errors  at  should  4  G°(FeS04 (  6-3-1.  be  a  experimentally  in section  difference  precipitation  o f G ° (FeSC>4 ( q ) ) .  value  is potential be  reaction  Mag  that  s t i l l  reaction  H F S u , Mag  ( F e ) ^ and  that  possible  thermodynamic  i n the  1%  which  calculated  i n the  the  s t u d y may  importance  with  kcal, a  may  relative  account  -2  G of  reached.  the  for  specifically  equilibrium  decreases  performed  than  kcal  uncertainties and  of  into  force  = -5.3  in this  result  with magnetite  and  take  G lower  driving A G  Fe°  to  Therefore  s u l p h a t e c o n c e n t r a t i o n so  calculation  sulphate  and  the A  used,  kcal.  I t may  pH  Equilibrium presence  -5.3  are  (S04)t observed  experimental errors.  which  to  results  the  of  the  set-up  162  Nevertheless The  an  interval  minimum p o t e n t i a l  i s given  by t h e F e ° / F e  by  H /H2(g)  maximum  potential  potential  i s not precisely  H  2 (g)  w  a  s  n  2 atm).  o  Fe 04 3  The  fugacity  limit  these  and  G° v a l u e s  As  a  two  Given  H  = 3 Fe  +  2 (g)  c  a  ^  n  e  presented  the  for  G 2  +  is  H /H (g)  likely  to  to  case i s  and  in  the  reaction eq.(6.08)  as u n i t y  to provide  The e q u i l i b r i u m to the solution  interval  yields  estimated  an.  a n d 1.7  a  high  computed composition  kcal/mole  for  set of  particles are a l l  the  about 4 ( a q  ) ).  values  surrounded  the potential  towards  the  of  G° ( F e S 0  the f i r s t  of magnetite,  increase  under  uncertainty  i n the system,  layer  equal  potential  of  the  of the  couple.  +  2  order  t o check  resulting  the  effect  G ° ' s , t h e same  (SC>4)t a r e r e d u c e d  change  eq.(6.07),  of  (6.03).  be more v a l i d , b u t i f t h e i r o n a relatively thick  maximun  former  + 4 H 0  leads  potential  o f Fe°  the  the  pressure  2  i n table  f o r G°(HFSu)  This  f o r the following  taken  and  approximately in  o f the system.  l i m i t i n g cases  the presence  system  and  + 6 H  conditions  1.5 k c a l / m o l e  In  of  result,  experimental  may  (g)  A G  a zero A  of the potential  in  by  2  ( i t was  estimated.  couple  2 +  the p a r t i a l  magnetite  a zero  by s e t t i n g  + H  since  c a n be  couple.  +  known  with  by s e t t i n g  case  the  measured  Equilibrium  calculated latter  accurately  t  for this potential  significantly  of  experimental  calculations  o r i n c r e a s e d by when  both  (Fe')t  errors  were performed 1%. and  The  on  the  when ( F e ) ^  G°*s  do  (SC>4)t a r e r e d u c e d  not or  163  increased,  but  (SC-4)  (Fe) .  and  t  cal/mole (Fe)  t  -  they  The  t  which 1%  to  the This  account  the  other  departure  accuracy  will  number o f  data  It  must be  the  +•'l%  t  interval  possible  at  to  to  the  difference  of of  sources from  reduces  emphasized  -238  about of  3.8  kcal  be  effect  that  of  treatment  random  i n a l l these  1%  and  take  into  errors,  determined  when a s t a t i s t i c a l  the  not  equilibrium.  can  for which  (Fe)t +  does  632  +  cal/mole  experimental  w h e n pH  Fe°/Fe2  for  +  between  f r o m -234  of  488  H /H2(g)  magnetite  obtained  200°C, and  potential to-  f  potential  1%.  be  sensitive  r e s u l t i n g G°(HFSu) s c a t t e r s  .(SO4)  (S04)t -  accurately  very  corresponds  and  corresponds  are  and  the  A  better  or  measured  on  a  large  errors.  calculations,  the  value  of G°(HFSu) remains value  {G (FeS0  within  of  )  o  -3580  an  4  ( a q )  +G°(H 0)} 2  interval  cal/mole.  of  440  cal/mole,  Therefore  the  above  refer  to  both  G°(HFSu) and  G° (FeSC>4 ( ) ) , a n d  of  of  them  leads  value  any  to  When s u l f u r i c dissolves  rapidly  sulphate  reprecipitates.  table  (6.03),  solution 1  hour  results  and  but  no  the  compositions  after  the  acid  corresponding  is  of  added  equilibrium By data can  using  other.  to  the  the  be  computed  the  second  Table set  G° in at  and  values table 20  of  G°  FeS04.H20 the  ferrous  obtained (6.02),  min,  (6.04)  average  determination  system,  i s reached,  presented  addition. to  the  an  uncertainties  the  a q  the  acid  around  30  min  presents  in table  in the and the  (6.03).  164  In  table  (6.04),  A G  precipitation.  refers  After  supersaturated  because  20 of  equilibrium  decreases  and  is  significant  obtained  with  0. 6 h i g h e r  In  the  chapter The  determined  f o r the  all  at  the  cases,  10%  (6.03),  (resp.  H /H2(g) +  the  6%)  (6.02),  respectively. when  ideal  diagrams dilute.  7,  set of  G°  of  solution  eq.(6.06),  after  E-pH  pH  but  is s t i l l  1 hour.  in table  two  by  With  between  FeSG"4.H20 is  the  already departure  slowly  Similar (6.03),  the  ( F e ) t and the  these a  solutions  17% With  figures  in  rising),  results  but  at  are  about  the are  region  assumed.  set  The  and  are of  lower G°  than  values  at  potential  also)  at  set  G°  4  3%)  of and  values  of  potential  G° 4% are  because  the  the in  the of  values  in  (resp.  6%)  preferred  r e s u l t i n g accuracy  i s good, mainly  In  represent  t  the  be  aqueous  above.  (S0 ) )  the  ideal can  the  (resp.  (resp.  last  assumption  (S04)t  second 3%  assuming  considered  data 17%  by  H F S u , Mag  (Fe)t  (resp.  r e s u l t , these are  this  first  experimental  and  plotted  potentials  differences  couple.  in this  incurred  calculated  the  As  are  limiting  data.  of  diagrams  equilibrium  couple,  Fe°/Fe2+  table  the  (although  errors  the  experimental table  min,  reaction  pH * s .  solutions.  solution  first  the  reaction  from  hardly  to  of  solution  the is  165  6-4-2  : the cupric  By  sulphate  using  the  between  Ten,  Ant  solution  composition  the  c a n be  aqueous  10~  4  mole/kg s o l  = 1.62  10  4  mole/kg s o l  =0.68  10~  4  mole/kg s o l  (HSO4-)  = 3.20  10  4  mole/kg s o l  pH = 3 . 7 7 .  The c o n c e n t r a t i o n s  (S04  lower salt  ))  )  2 -  than  10  - 6  -  -  mole/kg  the  equilibrium  the  following  computed  = 0.04 a q  for  solution,  (CuOH ) (CuS04(  m  ole/kg s o l  s o l .  of  the  other  The r e s u l t i n g G°'s  solutes  are  f o r the basic  and f o r t h e i o n p a i r a r e G°(CuSO4 (aq))  = ~  G°(Ant)  = -307 763  Contrary two  above  1%,  within  G°  The than  the  temperature  5  7  1  cal/mole  3  (aq) )  cal/mole.  o f G° (FeS04 (  comparatively  When  ( C u ) and t  varies  within  a q  ) ) and  not  (S04)t  G°(HFSu),  very  are  the  sensitive to  changed  ± 120 c a l / m o l e  within  and*G°(Ant)  cal/mole.  above figure data.  certainly  would  4  are  errors.  (CUSO4  ± 60  1  t o the case  figures  experimental  is  and  data  = 1 . 3 7 io-4  +  ±  experimental  (Cu +) 2  and  system.  G° f o r C U S O 4 ( q ) a  obtained However  erroneous  correspond  in this  since  i s about chapter  last  4  figure  2.4 k c a l / m o l e by e x t r a p o l a t i n g (-143 3 5 9  the experimental  to a system highly  lower  cal/mole)  ( C u ) and  supersaturated  t  with  low  ( 8 0 4 ) ^  respect  166  to  Ten ( A  occur Ten  i n t h e above and  system the  G > 1.2 k c a l / m o l e ) .  the  experiments.  aqueous  situation  First,  solution  i s made o f o n l y  reactions take  This  are fast,  Ten and s u l f u r i c  place  the  by d i s s o l v i n g  i s not likely to  reactions  secondly  acid  Ten  be e x p e c t e d particles,  removed  from  With generated can  which  by  assuming  (Cu)t  a n d (SC>4)tr  unit  water  When computed  activity, data.  data  and  (1929).  (SC>4)t This  more  model  Since ionic of  from  the  Ten  surrounding the solution i s  section,  the  ideal  CuO i s p r e s e n t  (dilute  6%  lower  the  coefficients  chapter than  i n such  high  errors activity  and  the  solution), the solution  and  the corresponding (concentrated  3% h i g h e r given  than t h e  by  Posnjak  same c o n d i t i o n s , t h e m o d e l o f  higher  model  Ant  present  a n d (SC"4)t  i n this  two times  solution  than  i s  water  ideal  i n m o l e / k g H2O)  Under used  an  lower  CUSO4.H2O  s t r e n g t h m u s t be a l r e a d y  solutions.  s o l u t i o n s and u n i t between  i s o b v i o u s l y wrong  the activity  dilute  to  t h e whole  equilibrium  (expressed  ideality than  in this  a r e 7% a n d 6%  (Cu)ti s only  Tunell  when  by assuming  When  experimental  departure  ideal  f o r the  solution.  solution),  of basic salt  c a n be o b s e r v e d  t h e two G°'s computed  experimental  respect  system  t h e v e s s e l a t 200°C.  be c a l c u l a t e d  aqueous  due t o t h e l a y e r  and hence  I f t h e above  was n o t i n e q u i l i b r i u m , a n u n d e r s a t u r a t i o n w i t h would  the i n i t i a l  solution,  Ten.  between  a  yields  ( C u ) ^ and  the experimental concentrated  provides enough  i s relatively  better  so t h a t  data.  solution.  results, the the logarithm  c l o s e 'to z e r o ,  as  i n  167  Section  6-4-3  The the be  : the  experimental  equilibrium expressed (Fe)  t  (S04)  t  These data  between  =  7.890 1 0  =  0.6975  can  be  is  following 3 +  )  (FeOH  0.64  +  )  =  7.875  -)  =  3.94  (HSO4-)  =  0.6184  pH  =  0.449.  200°C a r e  then  G°(FeS0  + 4  solution  for can  10~ 10"  free  energies  cal/mole.  pair,  the  G°  predicted  when t h e  value by  C (298,473) of p  ideal  solution  =  10  - 2  of  formation  at  -  is  Criss  are  mole/kg  simple  cations  method are  used  +  with  following sol  Cobble's  lower  FeS04 .  computed the  substantially and  c o e f f i c i e n t s of  concentrations  3.29  result  as  882  the  the  4  221  least  activity,  under  2  resulting  than  water  composition  - 4  = -  determining  t  (1922)  sol)  cal/mole  kcal/mole)  (Fe)  aqueous  solution  unit  620  (-3.8  assuming  the  169  ion  The  assuming  computed  the  at  Merwin  - 4  10  The  For  (1964)  the  and  sol  ) = -  G°(BFSu)  for  10  0.89  2  Posnjak and  to compute  ( i n mole/kg  =  4  BFSu  mole/kg  By  )  (S0  and  =  4  from  system.  mole/kg s o l .  2 +  (FeS0  data Hem,  - 2  used  conditions.  (Fe  sulphate  as  these the  ferric  the  above  data  by  168  (SO4)t Since  =  the  these  0.363  solution  data  However,  mole/kg s o l .  are  the  is relatively not  order  sufficient  very  of  when  only  SECTION  : conclusions.  for  the  (6.05) p r e s e n t s  Cu-Fe-S-H20  solubility  data  formation  G°.  literature  data  Debye  and  solution  The  value  lower that  than  high  the or  the  energy  temperatures,  results. which  in this  They of  were  are free  is  between accounts  on  energy  of  an  activity  chapter based  carried  calculations, the  acid,  semi-quantitative  i n terms  of  same,  generated  200°C  In  electrostatic  G°(Ant) errors  the  1978).  by  is  which  figure  provided  Scheuerman,  at  expression  experimental  200°C.  retrieved  in sulfuric  out  when  extended  coefficients  ionic  species,  f o r the  departure  ideality.  of  experimental  at  data  at  were m i s s i n g .  the  prevails  from  system are  the  remains  the  Experiments  Huckel  incorporating which  which  to  qualitative  i s needed.  Table  close  magnitude  information  6-5  concentrated  put a  not  very  makes  forward  i t by  Kennecott  I t must  be  noted  sensitive  to  possible  reliable.  This  value  Kwok a n d  Robins  is  (1973)  and  investigation  (Barner  and  that the  presented  value  in  169  table  (6.05)  study  concerning  and  i s consistent with  data  large  of the ion pair  for  G°(HFSu)  uncertainty.  (Fe)t- a n d  (S04)t  aqueous  solution  G ° (FeSO-4 ( q ) ) . determined sulphate and a  any  leads  no  to  between under  data  experimental  errors,  which  could  t h a t when  magnetite  A  about  1.7  are  very  increases  be  ferrous  leads  potential  for  the true  to  interval yields  an  G ° (FeSC>4 ( q ) )  and  a  sensitive  of  precipitates  conditions  kcal/mole  the  function  values  of  to  possible  u n c e r t a i n t y up  to  kcal/mole.  for  substantially  the  ion  lower  classical  These  t o 200°C,  experimental  These  by  shown  a  potential.  G°(HFSu).  G°  as  to a  and  pH  of  The  I t was  HFSu  e q u i l i b r i u m with magnetite  the  cations  the values  Assuming and  this  are subject  between  be known, b o t h  ambiguity.  uncertainty  4  ))  G°(HFSu)  could  are heated  pH d e c r e a s e s .  about  equilibrium  a q  system,  2  and w a t e r  estimated  in  a  In t h e FeS04-H2S04-H 0 for  with  relation  made  ( q).  CUSO4  a n d f o r G ° (FeSC-4 (  I f t h e pH  a  assumptions  the properties of the cupric hydrolytic  the presence  The  the  inability  free  energy  high  temperature  ( u p t o 3.8  extrapolation  ion pairs  The  pairs  data  seem of may  extremely the  in table  kcal/mole) methods  from  than  are a l l  predicted  low temperature  data.  temperatures.  methods f o r d e t e r m i n i n g  explain the d i f f i c u l t y  solutions.  (6.05)  those  stable at elevated  available  partly  aqueous  presented  of  their  modelling  170  It table  was  finally  (6.05),  chapter activity,  and can  experimental  the  shown E-pH  computed provide data.  that  diagrams by  assuming  reasonable  with  the  figures  presented ideal  in  the  solutions  approximations  of  and the  listed  in  following unit  water  available  171  TABLE Values for  of a j , "distance  several  ions  H+  9.  2+  6.  FeOH+  5.  S0  4.  2  _  4  HSO4-  3.  Fe3 +  9.  FeS0 Cu  :  + 1  °m  4.  + 4  6.  2 +  2  10  5.  + 2  5.  CU0H+ Cu  x  system.  6.  2 +  Fe(OH)  approach",  o f t h e Cu-Fe-S-H20  ai  FeOH  Note  of closest  Solutes  F e  Source  (6.01)  (OH)  6.  2 + 2  : B a r n e r and Scheuermari * = estimated  (1978).  by g r o u p i n g o f s i m i l a r  species.  172  TABLE Solution Initial  system  (6.02)  composition  : 500 c m  3  H2O  - 2  2  T=200°C  t=30  min  3.31  t=2  hours  3.13  Add  185 cm  + 0.6g  (S0 )  t  mole/kg s o l  t=0  3  time.  + 50g FeS04.7H 0  (Fe) 10  versus  4  10  - 2  t  mole/kg s o l  stable  hot water  t=6h30  (equilibrium)  t=tj  Add  t=ti  + 12 min  3.57  t=ti  + 22 m i n  3.585  4.211  t=ti  + 32  min  3.461  4.077  t=ti  + 60 m i n  3.164  3.603  Note  Fe°.  acid  : * = 104 mole  cm  2.847  2.923  *  3  H2SO4.  of  a  solution  containing  5.17  10  - 3  173  TABLE Equilibrium Solution  between  composition at  (6.03)  H F S u , Mag (mole/kg  and t h e aqueous  s o l ) and G° v a l u e s  two l i m i t i n g  (Fe)  (S0 ) 4  = 2.847 1 0  t  t  (cal/mole)  potentials. -  = 2.923 1 0  potential  solution.  mole/kg s o l  2  -  2  mole/kg s o l  Fe°/Fe  2 +  Potential  H+/H2( ) g  (fugacity  PH  4.700  Fe + 2  0.617  FeOH  +  FeS0 S0  2  4  (  a  q  )  _  4  HS0 " 4  G°(FeS0 G°(HFSu)  4 ( a q )  )  4.314  10~  2  0.222  10  -  2  0.022 1 0 ~  2  0.004  10  -  2  2.208 1 0 ~  2  2.621 l b "  2  0.543 1 0 ~  2  0.151  10  2  0.172 1 0 ~  2  0.151  10"  455  -183  160  -2 35 2 30  -236  774  -181  -  2  =  1)  TABLE System in  composition for  i  4  1  pH F e  FeOH  2  Note  :  G (cal)  t = 30 m i n  -  t=60 min  2  3. 4 6 1  lO"  2  3.164  10 -2  2  4. 0 7 7  lO"  2  3.603  10 -2  3.16  3.16 10-2  3.34  0. 6 3 1  10-2  0.488  10 -2  0.001  10 -2  2  0. 0 0 1  lO"  1 2.939 l O "  2  2. 8 2 9  10-2  2.675  10 -2  _  1  0.103 l O "  2  0. 100  lO  -  2  0.103  10 -2  -  1  1.169 l O  2  1. 148  lO  -  2  0.825  10 -2  *  1  -108  *  computed  4  (  a  q  )  4  G  (6.02).  -  4  HS0  A  1  +  FeS0 S0  t=20 min  1 0.645  2+  in table  FeS04.H20 p r e c i p i t a t i o n .  1 4.211 l O  t  addition  ( m o l e / k g s o l ) and A  1 3.585 l O -  t  (S0 )  acid  the run presented  Solution  (Fe)  after  (6.04)  0.001 l O  -  2  -72  by  -19  using  G ° ( F e S 0 ( q ) ) = -183 160  cal/mole  GO(HFSu)  cal/mole.  4  a  = - 2 3 6 774  TABLE G° v a l u e s obtained  (6.05)  (cal/mole)  a t 200°C  from s o l u b i l i t y  Compounds  data.  I  G ° a t 200°C  I  -307 763  FeS04.H 0  I  - 2 3 6 774  FeS0 OH  I  :-221 778  CuS0  I  - 1 4 5 713  FeS0 (aq)  I  -183 160  FeS0 +  I  - 1 6 9 510  CuS0 .2Cu(OH) 4  2  4  4  ( q)  4  4  a  2  176  CHAPTER  THE  D I A G R A M S OF THE  This diagrams on  chapter  generated computer  in  SYSTEM  2  presents  discussed  a  few  the  chapters  4  7-1  equilibrium presence  with  of  2  diagram  2  on three  Cu-S-0-H 0 2  the  determined  be  Cu-S-H 0  system  2  phase diagrams: quaternary,  the  procedure  G°  data  and t h e  diagram.  phase  first.  this  Their  the anhydrous  in  Because o f the  from  of a  The  can  be  fig.(7.01)  Cu-S-0  i n a three  the  classical  difference  a t 200°C.  represented  diagram  portion  distinguished  diagram.  a r e based  3 a r e used e x t e n s i v e l y .  2  compounds, must  The  Cu-Fe-S-0-H 0  has been  Cu-Fe-S-0 phase  illustrated represents  H 0  thermodynamic  2, a n d o n  phase  2  the  hydrated  Cu-Fe-S-0-H 0 anhydrous  of  (+H 0)  200°C.  These diagrams  6.  i n chapter  : t h e Cu-Fe-S-0  portion  to  AT  typical  i n chapter  programs d e s c r i b e d  The  the  CU-FE-S-H 0  o f t h e C u - F e - S - H 2 0 a t 200°C.  the assumptions  SECTION  7  ternary,  dimensional  177  tetrahedron,  and then  the  portion  of that  This  last  unit the  diagram,  water  C2Su.  HCSu  Cu-Fe-S  assemblage  last  solids,  distinct  once  of  can  the  be  stability  failure,  computed  f o r  t h e anhydrous  t e r n a r y by  t h e monohydrated  to this  last  Cu-S-0  (+H2O)  solid  (+H2O),  are  shown  i n  43  i n appendix  assemblages  and  extracted.  These  used  Cu-Fe-S-H20 s y s t e m  as  fig.(7.02).  90  2.  (+H2O) d i a g r a m . assemblages From  assemblages input  phase  diagram  of  t h e m , 109  different  two-solid  a r e computed  data  whenever  a  a t 200°C i s t o b e c o m p u t e d .  o c c u r s on t h e G°'s o f t h e s o l i d assemblages  (+H2O),  i srepresented with the  as a whole  listed  ternary.  Fe-S-0  i n t h eCu-Fe-S-0  involves  are  "hydrated"  compounds  compound  are  the unhydrated  cupric  of the  o f these  t h e whole  H2O.  r e p r e s e n t e d i n t h e E-pH d i a g r a m s  They  When a n y m o d i f i c a t i o n the  of  that  with  sulphate  diagram  and f o ra l l .  diagram  and  of  cupric  o f three  which  i nequilibrium  (+H2O) , h a s b e e n from  Cu-Fe-0  three-solid  assemblages  Cu-S-0  supersedes  fourth  phase  diagram  ternaries  (+H2O), a n d  o n t h e Cu-S-0 t e r n a r y ,  I tdiffers  a l l belong  four  corresponding  four  BCSu,  The assemblages  The  This  denoted  which  CU-S-H2O s y s t e m  Each  Cu-S-O-H2O  activity.  presence o f  sulphate  theprojection,  must  be  compounds,  checked,  must be computed  again.  and  on  178 S°  0  Ten  Cup  Cu°  H 0 2  0  Ten Cup  Cu°  S°  0  Three  phase and  Ten  Cup  Cu°  Fig.(7.01) diagrams r e p r e s e n t i n g , from t o p t o bottom, t h e Cu-S-0 t e r n a r y , t h e CU-S-O-H2O q u a t e r n a r y , t h e Cu-S-0 (H 0) p r o j e c t i o n d i a g r a m . 2  179  The  four  Fig.(7.02) t e r n a r i e s o f the Cu-Fe-S-0 p h a s e d i a g r a m a t 200°C.  (H2O)  180  S E C T I O N 7-2 '  : presentation  •  .  The  figure  presented at  in this  200°C (Fe)  The  =  0.3  computer  has two  solute  and  zones,  computed  with  unrealistic plotted  the  (Fe  and  FeS04 ,  2 +  into  predominate  The  over  Fe  chapter  6  HFSu  r e p r e s e n t s the  The 10  on  second  mole/kg  diagram  information  has  H 0,  an  2  level, is  one,  and  is  shown  the p l o t t e d  in  lines  is  output.  the  a l l the  two  complex  Fe-S-H 0 system 2  first  in certain  equilibria solutes at  plot.  regions of  occur  FeS04( q) a  200°C, a r e They  may  the diagram  and  not s t i l l this  FeS04( q)  in  a  i s present.  2.62  a  iron  of  I t was  given  aqueous  solutions  in table  (6.03)  of  as  '( F e S 0 4 ( q ) ) • =  The  (S)t =  resulting  this  maximum c o n c e n t r a t i o n when  (Fe)t  in  2 +  lines.  one  and  checked.  occurs  This  The  However,  account  first  lines,  r e p r e s e n t s _a c o n c e n t r a t i o n  considered i n the  +  The  in fig.(7.03a),  )-zone.  system  2  solid  condition  necessary  the diagram  in  m u s t be  extra  in  in dotted  in a separated printed  On  taken  diagrams.  lines.  The  the Fe-S-H 0  are  condition  the diagram  i s plotted  the  example,  the diagrams  2  extra  i n dashed  provided  the  t h e way  H 0.  high value,  f i g . (7.03a).  In this  under  plotted  superimposed  diagrams.  illustrates  chapter.  mole/kg  the  '  (7.03)  i s depicted  t  •  of  solute  =0.3 complex  then  mole/kg solute  10~  mole/kg  2  never  H 0 2  +  2  predominates  i s imposed  FeS04  H 0.  on  the  predominates  when  the  condition  system.  under  acid  and  oxidizing  2  -1  0  1  2  3  4  -2  - 1 0  pH  E-pH  pH  Fig.(7.03) o f t h e F e - S - H 0 s y s t e m a t 200°C f o r (Fe) = 0.3 j n o l e / k g H 0. computer o u t p u t . ' (b) f i n a l d i a g r a m .  diagram  2  t  (a)  I  2  2 . 3  182  -2  -I  0  I  2  3  4  5  6  7  PH  E-pH  diagram  Fig.(7.04) o f t h e F e - S - H 0 s y s t e m a t 200°C f o r (Fe) = 10-3 m o l e / k g H 0. 2  t  2  184  conditions. zone  diagram  (FeS04 )  =  +  and  The Two  then  0.3  mole/kg of  final  regions  region than stated  with  an  In  aqueous  of  which  the  practice, solution This  the  predominant  sulphur  an  region  is  is  Beyond  i s shown  no  sulphur  may  be  solid  plot  inside  an  iron  high  the  as  first  (  a q  assumptions  0.3  an  as  In  low  the  mole/kg on  as  labelled  aqueous  information  these  in equilibrium  only  ).  higher  under  be  blank,  in equilibrium with  and  The  concentration  H2S  The  concentration  erroneous  is left  as  fig.(7.03b).  phases.  p h a s e s may  s o l u t e , namely  be  solid  in  unrealistic.  region  hatched  equilibrium  and  no  with  includes nine  corresponding axes,  first  condition  by  second solution  H2O.  This  predominant  removed.  diagram in  can  with  is  concentration  is partly  solutes The  solids iron  diagram  diagram  H2O.  with  this  a calculated  mole/kg  no  the  the  +  0.3  region,  replaces  for  (FeS04 )-zone.  H2O,  to compute  conditions.  to  plotted  It  represented  mole/kg  in fig.(7.03a), i t s solute  -0.458. and  H2O.  stage  are  <  computed  the  corresponds 10  pH  is  boundaries  presented  as  > 0.693  diagram  the  the  i s determined E  A  In  to  with  Hem,  Mag  are  represented  these  boundaries  minerals  may  precipitate.  written  near  preceded  by  their  a +  zones  i n which  the  aqueous  and by  Fe°  the  inside The  are  sign.  mineral  The  zones  phase.  which  hatched  names o f  r e s p e c t i v e zones,  solid  perpendicular  lines the  a single  these  inside  bound  to  the  the  diagram.  region, these minerals the  plot  are  hatched  three then  region,  185  SECTION  7-3  : the diagrams.  Various Cu-Fe-S-H20  aspects  systems  of  the  Fe-S-H20,  a t 200°C a r e r e p r e s e n t e d  Cu-S-H^O, from  and  fig.(7.03)  to  fig.(7.16). Several  points  may  be  * The d i a g r a m s diagrams  of  f o r t h e Cu-Fe-S-H20  published  compatible  with  the system  constant  can  that  represent view.  most  They  they  often  may  easily  the  differences  point  and Robins chapter  constant  be  3,  t o economic  from  are  by  meaningful  since  the metal  only  (Cu)t  point  of  from  a  concentrations  i n a p l a n t , and because  restraints  on most  depends  imposed  the respective  and  authors  constant  a thermodynamic  more  to the  the  other  (Fe)t or  from  computed  a n d b y Kwok  they  so f a r  of the diagrams g r e a t l y  result  states  are similar  (1972)  and m o n i t o r e d  concentrations  and  on t h e s t a b l e  and f i g . ( 7 . 0 8 ) )  in  E-pH  temperature.  of view,  measured  aqueous  are the f i r s t  self-consistent  information  conditions  also  correspond  * The shape of  system,  programs published  valid  hydrometallurgical be  noted  However,  equally  can  by B i e r n a t  As  compute.  system  o f t h e F e - S - H ^ O a n d CU-S-H2O s y s t e m s  ( S ) t (fig.(7.05)  (1973).  diagrams  that  at the considered  diagrams published Robins  for  the available  * The d i a g r a m s for  noted.  upon  processes. the  values  on t h e system.  Major  importance  of  ion  pair  formation.  This  last  salient  point  examples.  c a n be e l a b o r a t e d  f u r t h e r by c o n s i d e r i n g  three  186  The  diagrams  (Fe)  =0.3  t  similar  of  the  mole/kg  when  H2O  no  and  complex  However,  when  cannot  i n equilibrium  be  (Fe)  presence  of FeS04( q)  (section  7-2).  region,  FeS04 ( q)  a  unrealistic  =  solids, a  example  Cu-Fe-S-H20  of  Hem  (Fe  2 +  pH  range  "iron  where  a  pair  presence  on can of  hence  ( F e ) t up  by  pH's  (S)t could be  10~3  a  >  i n the  (Fe) and  t  the boundary  HFSu the an  met. low  presence  of  formation  of  patterns  of  the  under  be  H2O  of  where  the  ( S ) f  condition  The  presence  a  can  a q  this  ion pair  (S)t <  (Fe)t  "iron  solute" In such  "sulphate 2 +  widely  enlarges  i s possible  fulfilled.  Fe  the  (FeS04 ( q ) ) - z o n e t h a n i n t h e  predominant not  fig.(7.10)  ( f i g . (7 . 0 9 ) ) , FeSC>4 ( )  predominant  mole/kg  the  the  the  and  different  C o n v e r s e l y , when a  level  actually  the  the d i f f e r e n t  the  and  which  maintained in  HFSu  I t reaches  is  under  a t two  solute",  be  be  solute,  region  represented  H2O,  t  that  o f what would  restricted  H2O,  because  drastically.  HFSu  be  mole/kg  2  are  account.  to at least  predominant  H2O  into  solution  a solid-aqueous equilibrium  cannot  condition  aqueous  i n fig.(7.09)  is  (S)  conditions.  FeSC>4 ( q )  (and  When  10~  mole/kg  3  for  fig.(7.04)).  i s shown  mole/kg  )-zone.  above  ion  can  occurs at higher  predominant  a  the  and  system  10~3  any  thereby explains  A  =  taken  increases  -  H2O  (fig.(7.03b)  t  are  conditions  diagrams  (Fe)  solutes  substantially  FeS04 ( q ) , w h i c h  second  10~  raise  before  mole/kg  are  (Fe)t =  the neighbourhood  the  10~3  will  computed  for  with  becomes  level  system  i s l o w e r t h a n 2.62  t  o f HSO4  Therefore (Fe)^  In a  concentration  Fe-S-H20  under  the the  since  the  a case,  this  solute",  region  a  (fig.(7.10)),  m a i n t a i n s t h e Hem  of the permitted  be  of the  but  the  formation diagram)  187  at  r e l a t i v e l y low  The  last  example  fig.(7.14), condition (S)  =  t  both  of  fig.(7;04),  wide  CuS0  at  range  The  -  sulphide  on  an  of  pH  =6.0  and  These of of  =  t  concentration,  the  mole/kg  - 2  l a s t two  Crerar  data  10  and  Such  which  results,  by  can  pH  Barnes  ( 1 9 7 6 ) , and  be  of Cu(HS)2~. made  the methods  thereby  i s p r e s e n t , and  The  available,  on  is  best in  in  This under  complex to  depicted  fig.(7.15),  the  conditions  7.20  diagrams  presented in this  occur  the  experiments  the evidence they  from  units.  i s very sensitive  i s shown  =  of  the s o l u b i l i t y  on  2.5  solubility  i s r e p r e s e n t e d under  H2O  BFSu.  ( f i g . (7 . 14 ) ) .  relation  in  solute",  formation  a diagram  are based  formation  =9.7  the  solute",  more t h a n  "window"  the  "sulphate  e q u i l i b r i a also  the  this  removes  +  ClFe  copper  from  diagrams  and  pH  important  of t h i s  as  by  aqueous  size  FeS04  which  solid  where t h e Cu-Fe-S-H20 s y s t e m (Cu)  at  with  t h e d i a g r a m , as  "copper  the diagram  results  E-p(S)t diagram.  as  At  ( f i g . (7 . 13 ) ) ,  t  from of  the  ( S ) f  in equilibrium  HFSu  and  under  different  (S)  formation  range  relatively  Cu(HS)2 .  low  i t predominates  between  conditions  At  be  predominates  a  (S)t =1,  alkaline  can  f i g . (7.13)  i s depicted  a t two  2  BFSu  ( qj  4  range  of  the  H 0,  removes  potential  "window"  solute  and  s i m i l a r l y the  t h e pH  Furthermore,  mole/kg  - 2  a  the  increasing  a  10  in fig.(7.12)  lowering  fig.(7.12),  t h e Cu-Fe-S-H20 s y s t e m  FeSC>4 ( q )  and  from  (fig.(7.12)).  fig.(7.13),  while  taken  HFSu  solution  formation  is  where  (Cu)t =  1,  aqueous  In  pH's.  stress  selected study.  the  provided amount  of  experimental  188  SECTION  7-4  : interpretation  Apparent resolved  by  system  diagrams.  at  The  =0.3  t  solute  of H2O  (Cu)t  formation  of  the  therefore  corresponds else  concentrations two  where C u  The  solid +  must  to  lower  fairly  diagram  mole/kg  H2O  interpreted  instance  -log(HSO4-))  the  cuprite and the  (Cu2+)-  and  the  corresponds  i s depicted predominant  as  in  copper  solute,  to  Given  the  fast  solution,  this  pattern  of  very  in  the  BCSu and  with  the  where one  the  HCSu a r e  140°C).  at  200°C This  in pair the and  for  diagram  coordinate (for  pH. equilibrium  perpendicular However,  this  ion  near  more  is  diagram  solution,  f i g . (7.07).  E and  this  where  where  diagram  concentrated  CU-S-H2O  a surface line.  the  above  +  a single  HCSu,  the  (Cu )-zones, to  of  complex  and  (for instance  to  the  c h a p t e r 6,  the  i s added  for  in  s t i l l  space  aqueous  equal  The  i s shown  the  is  temperatures  of  CU-S-H2O  solution  in  stable  as  in  solutions  l o w e r , but  be  In  to  account  be  the  fig.(7.06)  fulfilled.  200°C.  on  presence  sulphates in equilibrium  remains  0.3  at  into  only  diagrams  with  in  the  be  pairs  either  are  correct  (Cu)t =  cannot ion  illustrated  in  can  dimensional  take  discussed  meaningless  or  does not  a  as  which  (Cu)t i s imposed  CUSO4 ( q )  on  only  two be  diagrams.  occur  shown  However,  condition  copper,  T h i s can  H2O  CUSO4 ( a q ) •  mole/kg  then  these  diagram  mole/kg  concentration 3.10  often  200°C when a c o n s t a n t  solution. (Cu)  projection  discrepancies  interpreting  projection  as  when  equilibrium  involving  to the  diagram  CUSO4 ( q ) a  is  i s represented  Computer  Fig.(7.06) o u t p u t o f t h e E-pH d i a g r a m o f t h e C u - S - H 0 a t 2 0 0 ° C f o r ( C u ) = 0-3 m o l e / k g H 0. 2  t  2  system  190  pH  Final  Fig.(7.07) s t a g e o f t h e E-pH d i a g r a m o f t h e Cu-S-HoO a t 200°C f o r ( C u ) = 0 . 3 mole/kg H 0. t  2  system  191  E-pH d i a g r a m  Fig.(7.08) o f t h e C u - S - H 0 s y s t e m a t 200°C f o r (S) = 1 mole/kg H 0. 2  t  2  192  by  a portion of a plane  corresponding At  t h e boundary  simply of  to  The  the  part  I t  i s  limited When  (CuSO-4 ( q ) ) - z o n e value.  following  BCSu  by  the cuprite  i salso  lines BCSu}.  region  i s  inconsistency  represented  { T e n + BCSu}  (HSC>4~)  This  low  sulphate  i n c r e a s e s , t h e pH d r o p s  until the  and then  behavior  at  by a f o l d e d  rises  back,  c a n be understood  beyond  the  by w r i t i n g t h e  equations  CUSO4.2Cu(0H)2 CUSO4.  zone,  explains the apparent  i s reached,  a  two  thereby  involving  concentrations.  initial  {Cup + C c t } and {Cup +  (aq))  (CUSO4  and p a r a l l e l  o f the diagram.  equilibrium  plane.  two d i s t i n c t  equilibria  of the  folded, which  this  between  + 5 H  2Cu ( O H ) 2  + 2  +  = 3 Cu  H S O 4 -  + HS0  2 +  '+ 2 H  4  + 4 H 0  = 3 CuS0  +  eq.(7.01)  2  (  4  + 4  a q )  H 0 2  eq.(7.02) Here,  a(H20)  a(HS0 ~) increases  on r i s i n g  pH  range  represents two  pH Cup up  = 1,  Cup  s i d e down  for  (Cu)t  1.5  i s observed  i s  i s  also pH's,  with  BCSu,  constant, while  constant.  2 ) ,a point  with  i t  In  a  o f the diagram  corresponding  Cct.  H2O  Cct,  while  to  of are  (CUSO4  Near  a t higher pH's,  The C c t r e g i o n  of the  the conditions mole/kg  the chalcocite region.  on r e d u c i n g  a t t h e boundary  2  )  concentrations.  on o x i d i z i n g  = 10~  2 +  decreasing  and  equilibria  i s obtained  Therefore,  on  a  sulphate  i s obtained  a(Cu  pH's when a ( C u S 0 4 ( q ) )  (between  behavior  When  quickly  two d i s t i n c t  different  A similar  constant.  increases  4  small  remains  i s then  folded  (aq))-zone.  solid-aqueous represented  equilibrium in  the  space  193  (E  pH, PHSO4 ) a s a  complicated  -  f  line  pHS04~ = 1  fig.(7.07) on  an  itself,  the  cross  coordinate  plane.  I t  The  of  must  be  noted  that  1)  the  section of  representing  t  the  while  ( f o r pHS04~ <  p(S) )  t  of  surface,  i s a cross  ( E , pH, p ( C u ) ,  equilibria  concentration  this  surface  in fig.(7.07),  i n the space  solid-aqueous  section  o f the whole  represented  hypersurface  all  a  i s a projection  t h e ( E , pH)  surface  i s  surface.  CU-S-H2O s y s t e m  at  200°C.  SECTION  7-5  : discussion.  Thermodynamic system,  while  reactions. states under  which  provide  equilibrium  hydrometallurgists are mainly  This  can  diagrams  disagreement  be r e g a r d e d minerals  do  interested  i s s o l v e d whenever  as a c t u a l l i m i t s l e a c h , and those  states of  the  between under  the  in actual equilibrium  the conditions which  they  do  precipitate.  Fig.(7.09) at  constant  (Fe)t =  concentration 20g  Cu/dm3)  copper. conditions  fig.(7.11)  n  a  been  s  a  This  plotted  2  region which  any  be  2  and  each  various H 0  are  case.  more  interpreted solid  system  (S)j-.  A  (approximately  2  This  the corresponding  mineral  can  t h e Cu-Fe-S-H 0  mole/kg  in  i n which  any s o l i d  under  H 0  ( C u ) t = 0.3  region  with  present  10~3 m o l e / k g  line  circumscribes equilibrium  to  line  solutions i n  concentrated  in  as r e p r e s e n t i n g t h e  mineral  leaches  ,  when  194  (Cu)  = 0 . 3 mole/kg  t  Similarly,  when  containing remains agent  at potentials maintains  the  Hem  < 1 mole/kg  H2O,  copper  H2O  (fig.(7.09)) , a at  pH = 1  at  lower  agent  brings  solution  spontaneously I f  a  reducing  potentials,  FCct  t h e system  precipitate.  at  may  higher  Furthermore,  f o r  C p y i s u n s t a b l e a t pH = 1 a t a n y p o t e n t i a l (Cu)f  remains  H2O  0.32V a n d 0.63V.  system  may  a t any p r a c t i c a l  the  between  I f an o x i d i z i n g  potentials.  and  (HSO4-) = 1 m o l e / k g  ( C u ) t = 0.3 m o l e / k g  precipitate.  (S)^  H2O.  C p y may t h e n  i n solution  0 . 3 2 V , o r may r e p r e c i p i t a t e  leach,  at potentials  as c h a l c o c i t e  in  which  case  higher than  about  or digenite  at  lower  potentials.  When  these  "reactions",  1) for  two p o i n t s  The diagrams  several  represented under  diagrams  on such  where  t h e model,  adapted  to  consist ((Cu)  t  = 10  -  used  2  BCSu  mole/kg  H2O)  evolving  system  evolution  compute  on  i n  relation  between  section  7-4.  I t could  be  must  remain  these  of  i s t o be  take  constant.  Let  For  i s not  a  aqueous at  place  systems.  fig.(7.07). an  values  diagrams  closed  i n equilibrium  the  several  an  and  system,  plotting  constant  reactions  illustrated  terms  assuming  the  to  i n  by  these parameters  represent  of  interpreted  emphasized.  When  diagrams,  instance,  c a n be  be  a r e computed  parameters.  conditions  difficulty  must  are  This system  solution  200°C.  In  this  (HSO4-) a n d pH w a s d i s c u s s e d i n  depicted  (S)^-concentration  i n  even  lines  more on  detail  the  by  diagram.  195  However, adding such  fig.(7.07)  a solution a  system  solution  concentration and  present  i n  the final  directly  containing  contains  constant  cannot  no  sulphuric  i n  a  whole  (Cu)j- most states  acid  closed  copper,  the  represent  the  amount  remains  However  the  solution  probably varies,  and both  cannot  a case, fig.(7.07)  the  manner:  when s u l p h a t e s a l t s  which  for  i s present, additional  simultaneously  The Cu  BCSu  resulting  maintaining  CUSO4 ( q)  becomes  a  This  hydrometalurgical  open  copper  reactor,  to  c a n be i n t e r p r e t e d a r e added or alkali  to a i s  and i n c r e a s e s  the  case  of  where s i g n i f i c a n t  monitored.  the appropriate  system  be r e p r e s e n t e d on t h e in  system  required  ( C u ) t c o n s t a n t a n d BCSu  solute,  adapted  pH, E a r e a c t u a l l y  provides  initial  stable. when  a g a i n when  predominant.  r e a s o n n i n g i s more  (Cu)t,  the  pH d e c r e a s e s a t l o w s u l p h a t e c o n c e n t r a t i o n s ,  i s the predominant  2 +  acid  I f t h e added  copper  I n such  in  of  of  same d i a g r a m . following  effect  or sulphate salts to  autoclave.  system.  o f t h e system  the  diagrams  c a n be r e p r e s e n t e d as  a  continuous  parameters  The m o d e l  where  a  such as  presented  here  t h e b e h a v i o r o f such an  function  of  one  or  two  parameters.  2)  The  transformations;  precipitation) factors an  equilibrium  which the not  are  can only taken  state,  increases  system be  a  into  be  properly  account.  several  the practical  i s brought unique  of  ;  f a r from  a  system  interpreted  When a s y s t e m  transformations range  transformation  when  f o rwhich  kinetic  i s removed may  of the i n i t i a l  the equilibrium  (leaching,  not  occur,  state.  state,  there  substantial  from  When may  driving  196  forces (Cu)  t  exist.  mole/kg  H2O  0.32V  i f FCct  does n o t p r e c i p i t a t e .  -0.40V under  f o r which  force.  Several  Several at  generally actual  minerals  At  already  I f i t i s brought  predominates,  with  FCct  only  and  near  i s  the  shows t h e  the largest  precipitate  are available  such  f a s t and most  of  driving  remain  i n the  a high the  for  the  temperature,  diagrams  Cu-Fe-S-H20 reactions  are  reflect  the  should  o f the system. sulphide  1976)  state  phases.  200°C.  instance,  Peters,  may  containing  i n a metastable  However, t h e diagram  k i n e t i c data  behavior  {aq)  S  p r e c i p i t a t i o n occurs  as m e t a s t a b l e  system  w h e r e ^2  precipitate.  mineral  system  a t pH = 1 r e m a i n s  conditions  stable  For  i n f i g . (7.9) , a s o l u t i o n  =0.3  below  more  For instance  and  leach  minerals  chalcopyrite  relatively  including (Warren,  quickly  above  pyrite  1958;  ( B a i l e y and  Jones,  140°C  under  1974)  oxidizing  conditions. The  oxidation  does that  not  of elemental  take  place  temperature,  thereby 160°C  allows  and 190°C,  sulphur  into  a t any d e t e c t a b l e  the sulphur sulphur the  rings  SQ  oxidation.  reaction  may  sulphate rate  by  below  start  to  oxygen  gas  159°C.  Above  break,  which  A t some  temperature  become  explosive  between (Peters,  1980). The  crystallization  occurs and  at detectable  takes  Fregerslev, Concentrated  place  of  Hem,  rates  within  1968) solutions  a very  slow  over  a f e w week  two  hours  reaction period  a t 200°C  below above  100°C, 140°C,  (Christensen  and  ^ of sulphites  and t h i o s u l p h a t e s  can  remain  197  a  long  time  i n a metastable  thiosulphate No  sulphites  Prater  main  were  stable  pressure,  i n t h e absence  crystallization conditions,  reaction  allowing  "slow",  only  Such the  4 kcal/mole energy"  these  Cu-Fe-S-0  2 3 0 ° C , a n d SO2 i s t h e  t h e r e a c t i o n takes  are  enough  FDig  were  yields  and  diagram,  ternary  reported  as  i n  reactors  time.  be i n c o r p o r a t e d  has been  precipitation  Ida  specific  Also  aren e g l i g i b l e  f i g . (7.16)  The  crystallizations  computed  t o G°(Pyr) a n d G ° ( I d a ) , w h i c h  (+H2O) p h a s e  to being  slow.  very  never  Their  f a c t o r s c a n sometimes  conditions,  species  e t a l . , 1976).  of reaction  for the  place  water  known t o r e m a i n  hydrometallurgy.  For instance  200°C.  where c h a l c o p y r i t e i s  i s not  (Wikjord  so that  kinetic  "activation Under  i n  1960).  and oxygen.  Cub, FCct,  a few hours  diagrams.  adding  and  as Ida,  pH ( P r y o r ,  r e a c t i o n o f SO2, t h i s  reactions  a t 200°C  products  probably  a process above  temperature,  s o l u t i o n s near  o f P y r r e q u i r e s s e v e r a l days  even  compounds such  aqueous  there  o f water  several  A t high  a t high  However, s i n c e  i na dismutation  Conversely,  i n  H2SO4 s o l u t i o n  reaction product. atmospheric  even  put forward  by a strong  participate  are  i sfast  reported  e t a l . (1970)  oxidized  at  dismutation  s t a t e a t 25°C.  i s no  of  longer  and t h e  stands  these  after f o r an  minerals.  present  assemblages  into  i n the  { C p y + S°}  { C p y + Cov} become p o s s i b l e .  It observed  must  be  i nnature,  noted  that  the  and i sa c t u a l l y  assemblage  {Cpy + Cov}  i s  i n t e r p r e t e d by m i n e r a l o g i s t s  198  as  a  metastable  crystallization the  main  elevated *  Cpy  in *  a  of  features  Pyr  of  large  as  pH  can  be  of  Cpy  to  *  oxidation  of  electrochemical  *  S.C. of  acid process  the  Cpy  *  the  140°C  acid  at  zone  under  low  oxidizing  (Jones  i n the  Berezowsky,  in  i f the  a  to  small  Cov,  of  and  a  Cpy  current 1973).  zone.  major  1978)  and  during  Peters,  sulphate  region  overvoltage  acidic  observed  solutions  visualized  under  was  and  H  of  Cpy  by  ( B i e g l e r , 1977; 2  (g)  of  high  0.1V,  1980)  solute  Cov  (Swinkels  reduction  reaction  at  to  Cpy  evolution  process.  as  solutions  step  i s shown  on  which  would  oxidation  was  of  the  the  tip  increase explicitly  account.  temperature  of  Furthermore  sulphate  i s represented  of  reaction  important  sulphate  i n the  leaching  region,  into  The  runs  i s also  substantially taken  1978).  slow  in fig.(7.16j .  phase  S°  Cpy  in sulphuric  reaction  The  the  range.  oxidizing conditions.  This  from  Craig, in  depicted  mildly  densities  and  leaching  a metastable  oxidation  The  resulting  (Vaughan  Cpy  temperature  i s shown  The  assemblage  has  Cpy  can  or  Hiskey occurs  Fig.(7.16)  the  Cu° and  thereby shows  theoretically  above  been  Fe°  successfully tested  studied  Wadsworth, reducing  that  take  potential  was  at  place of  at  the  i n the  1974)  the pH  at  low but  efficiency near  1,  the  potentials  H2 ( g ) / H . +  laboratory  Such  as a  (Peters,  .  Useful diagram.  information  However,  such  i s then a  provided  diagram  only  by  this  reflects  metastable a  specific  199  situation  where Cpy i s l e a c h e d  instance,  i t  contained  in a  would  need  the  a  a  large  t h e type  for  these  the  of  are  aspects  a t 200°C.  of the  able  variety  o f diagrams  conditions  o f a system  features of  free  entirely On  as complex  as  them  that can  energy  data  describe  the  the  in a clear  upon  the parameters  None  The  c a n be  involved,  the kinetic  to  For  diagram  purpose.  system.  to reveal,  t  Another  c o n d i t i o n s , upon  way  (S) .  leaching o f the Pyr  incorporate.  compact  equilibria  the  and  t  for this  Cu-Fe-S-R^O s y s t e m .  most  diagrams  to  (Fe)  concentrate.  and p l o t t e d  chooses  t h e whole  various  system  copper  for  i n t h e c o o r d i n a t e s , upon  solid-aqueous these  upon  stated  researcher  remain  the  pyritic  depending  represented  represent  account  conclusion,  values  the  not  t o be d e f i n e d  As plotted,  does  at constant  other  and u s e f u l the  hand, way,  Cu-Fe-S-H^O  200  201  -2  0  -I  I  '  2  3  4  5  pH  E-pH d i a g r a m (Fe) = 10-3 t  m  Fig.(7.10) o f the Cu-Fe-S-H 0 system / o and ( S ) = 1 0 ~ 2  o  l  e  k  g  H 2  t  4  a t 200°c f o r mole/kg H 0. 2  202  E-pH (Fe) t  Fig.(7.11) d i a g r a m o f t h e C u - F e - S - H 0 s y s t e m a t 200°C f o r = 1 0 " m o l e / k g H 0 and ( S ) = 10~6 m o l e / k g H 0. 2  3  2  t  2  283  0.2 -  1  1 0  1  2  -  1  I  I  i  2  ^  I  3  PH  Fig.(7.12) E-pH d i a g r a m o f t h e C u - F e - S - H 0 s y s t e m a t 200°C f o r ( C u ) = 1 0 - 2 m o l e / k g H 0 a n d ( S ) = 0.32 1 0 ~ m o l e / k g H 0. 2  2  t  2  t  2  "o >  . c • <u  o Q-  PH E-pH d i a g r a m (Cu) = l O -  t  Fig.(7.13) o f t h e C u - F e - S - H 0 s y s t e m a t 200°C f o r mole/kg H 0 and ( S ) = 1 mole/kg H 0. 2  2  2  t  2  O  205  5  6  7  8  9  10  pH  Fig.(7.14) E - p H d i a g r a m o f t h e C u - F e - S - H 0 s y s t e m a t 200°C f o r (Cu) = 10-2 o l e / k g H 0 and ( S ) = 1 m o l e / k g H 0, showing the e f f e c t o f the complex s o l u t e C u ( H S ) . 2  t  m  2  t  2  _  2  < 0)  Potential in Volts  I  o —. W  O — Crt  rt  QJ  II Q) M n o o> I 3 to  0  3  Hi  0  H rt CD D*iQ  \ a> • *•  O c • to I M O n> — cu cn 3 I  a  a  to T3 O  X  ii >•< CQ rt  to fD o 3 rt  to o o  0  O  i-h  0  to o  OA  207  0  Metastable for  (Fe)  computed  t  1  2  '  pH  E-pH d i a g r a m =  10-3  after  m  o  l  e  /  K  G  increasing  4  3  Fig.(7.16) o f the Cu-Fe-S-H 0 system 2  H O and  G°(ida)  (S)  t  =  3  10"2  a n d G°(Pyr)  m  o  at  i e / k g  by 4  200°c H 0, 2  kcal/mole.  208  C O N C L U S I O N  209  CHAPTER  S U M M A R I E S AND  A method  was d e v e l o p e d  semi-quantitatively used  and  The  water  phase  FURTHER  represent the  diagrams  WORK.  t o compute  i n h y d r o m e t a l l u r g y , even  ligands.  8  and p l o t  complex  those  C^  involving  are calculated  Cm  - H  2°  several  at constant  activity.  C o n d i t i o n s c a n be i m p o s e d  t h e form  of constant concentrations  i n  diagrams  on  which systems  m e t a l s and temperature  the  aqueous  o f one o r  several  components C j ' s . The  fundamentals  systems, However  the the  and  method  of  type  the  Such  the  conditions  automatically  published here  a specific  a procedure  may  method form  In  the  on  converted into  the  method  duplicated. to  o f computing  E-pH  of  Nerst  equation,  and t h e s o l u t e s  yields  a  presented  phase,  the appropriate  simple  adapted  by t h e s o l i d s  aqueous  for  be  well  automatically  i s caracterized  imposed  i s  and  i n handling the solids  diagram.  system  Pourbaix's,  The c l a s s i c a l  to solving  o f composite  study,  presented  no d i f f e r e n c e  the system.  to  already  systems.  i s tied  makes  similar  diagrams  multicomponent diagrams  are  specific in  this  p r e s e n t and by which  chemical  can  be  potentials  210  for  the  solutes  corresponding to  the  independently. flexible  types  diagrams.  of  a  result,  Pourbaix's extension  first and  t h e method  problem  generation diagrams  computes  generation  A  species  from  determine  Since  their a  of  different  but i t i s  as a computer  range  not  program.  to computing  an  of stability.  The  class  systems,  by s t r i c t l y  described  i t i s appropriate to identify  of  in  c l a s s e s o f diagrams,  The  equilibria,  specific  t h e program  different  of  the  I t provides  considered  diagrams obtained  Two  t h e method  second  composite applying  this  even  i t as  study  f o r very a  third  program.  study  presented.  are  s o l v e s an e x t e n s i o n o f  systems,  limited  Metal-Ligands-H20  systems,  makes  a large variety  implemented  programs were  and p l o t s  corresponding,  components  indepedence  here  equations  method.  was  method.  The  and those  given  presented  programs determine for  Pourbaix's  complex  not  of  to multicomponent  method  generation could  This  f o r generating  of Pourbaix's  The  of solids,  concentrations  extremely  As  region of the diagram.  to the presence  constant  generated  i n each  a  been  system  consistent  in this  in this  approaches have  Cu-Fe-S-B^O  system,  set  of  a t 200°C w a s G°'s  for  then every  and a d i s c u s s i o n o f s e v e r a l  way.  followed to generate  the  data  missing  the l i t e r a t u r e .  First,  an  extension  of the lever-arm  method  to ternary  systems  211  has  been d e v e l o p e d ,  contained thereby  in  ternary  generated,  free  energy data  the  ternary  Kullerud  providing  are  when  solution  were  in  digenite,  Secondly,  way  and  the  Huckel  basic  ferrous FeSC>4 . +  was  cupric  and  lower  extrapolation  methods  the  for  effects the  this  main  the  of  and  the  Yund  and that  available These  the  phases.  solid  Data  idaite, rich  and  shown  were  cubanite,  boundaries  The  of  pairs  for  the  ion  features  equilibrium  from  New  CuS0  4  (aq) r  of  were  with were  of  the  provided  monohydrated F  e  S  experimental predicted  to  extended  ideality  data  0  4 (aq)  results by  a n d  are  classical  data.  were p r e s e n t e d . pair  An  sulphate,  temperature  diagrams  i n order  r e s u l t i n g data  departure  those  low  in  formation.  ferric  ion  account  of  was  were c a r r i e d out  purpose.  basic  from  the  considering  minerals  energy  than  thermodynamic  important  account  for  G°' s w h i c h  substantially  Selected  for  to  considered.  digenite  200°C.  f o r the  sulphate,  sulphate, The  used  diagram  iron  missing  a v a i l a b l e data  It  composition at  free  model  the  is  phases.  assemblages  Debye  inequalities  applied  for  information  which  phases were  the  of  of  the  explicitly  for  phase  i n terms of  aqueous phase  by  both  phase  experiments  interpreted  set  200°C.  p y r r h o t i t e and  aqueous  solid  and  at  this  chalcocite  A  been  c h a l c o c i t e and  solubility  determine several  this  monoclinic  digenite  with  I t has  resolved the  retrieval  range w i t h i n  stoichiometric  range of  provided  for  a  consistent  a r i s e between  only  the  phase diagrams.  Cu-Fe-S phase d i a g r a m  discrepancies  the  allows  phase diagram.  discrepancies data  which  They p o i n t  formation chalcopyrite  at  out  200°C,  and  leaching  at  212  elevated  temperature.  For succeeded diagram  the  engineers.  of As  often  the tried  last  be d e s c r i b e d  of  i . e . Metal-H20,  them  by  a  twenty  data  y e a r s , h y d r o m e t a l l u r g i s t s and  The s t u d y p r e s e n t e d h e r e  makes  such  by a s i n g l e  composite  f o r corrosion  with  system  Pourbaix  single  t o a c h i e v e t h e same g o a l  multicomponent  t h e complex i t  clear  a s t h e CU-F6-S-H2O  diagram,  n o t even  system  by a s m a l l s e t  plots. a matter  of fact,  corresponds solution  depicted  such  a s P,  Even on ( 2  corresponding which  remain  greatly  and  restricted  data  which  a(H20),  one  framework,  diagram  the  rate  a complete  classes  of  parameters  more Cm  - H  already ofthe  (CjJt's 2°  diagrams,  the  respective  remain  system  c a n be  each  class  diagrams  differ  values of the constant  data, their  become more c o m p l e x ,  very  allows  a  study  kind  of  validity  information, i s even  more  cases.  c a n be d i s p l a y e d  i s the only  or  provides a specific  incorporate  system  several  W i t h i n one c l a s s ,  upon  to specific  comparatively  system.  where  i n this  a g i v e n s e t o f components, t h e composition o f  constant.  t h e systems  developed  systems  + 1) d i s t i n c t  to  Each  when t h e y  When  m  T,  i n this  depending  (Ci)t's.  t h e method  to specific  constant.  the  each  systems,  together a l l the useful  they handled.  a  cannot  brought For  geologists  that  simple  i n describing  which  systems  most  i n a two  small.  The  self-consistent description  the fraction dimensional  free piece  energy of  of available plot  becomes  function  ofthe  information  which  of a l l the possible  equilibria  of  213  The  changing  confirmed. when  Diagrams  the systems  described  by  a  exhaustive  systems  valuable well  first generate  This  the  of  the  the  inaccuracy  free are  t h e way  system  formation  predominance  solutions In  available of be  at elevated  the near  future, and  thermodynamic  on  on  solve  equations.  model  room  a l l  be  the  the  resulting  showed  i n which  the and high data.  inadequacy  studies  carried  for  purposes.  temperature  and  of  of  aqueous  on.  electrolytes  the aqueous  rigorously The  to  temperatures,  them, s y s t e m a t i c  within  which  200°C  the chemical p o t e n t i a l s  XJ  enough  possible;  available  of these species  adequate  provide  to  from  t e m p e r a t u r e s must  an  the concentrations possible  at  o f the methods p r e s e n t l y  information  under  twofold:  as  at elevated  Given  available  of more  problems  for hydrometallurgical  data are extrapolated  the  be  based.  temperature the  cannot  even  flexible  data  on  complexity  is therefore  energy  atlas,  focussed  become  specific  facilities  Cu-Fe-S-H20  ion pair  the  t o a s many p r o b l e m s  calculations  of  importance  adapted  of  diagrams  trend  computer  s t u d y opens  case  The  is  is  completely  a s e t of diagrams  engineers to solve  improve  thermodynamic  these  t o be  research  which  diagrams  f o r m o f an  enough  However, because  study,  develop diagrams  i n the  simple  Current for  conditions.  secondly  The  longer.  i n helping  defined  published  plots.  under  thermodynamic  s t u d y were  systems,  any  of  were  under  few  multicomponent  the  status  UJ as  a  may  be  function  phase.  It will  then  whole  system  of  thermodynamic  diagrams  214  will will  be much take  more a c c u r a t e t h a n into  account  true  a c t i v i t y of water,  with  no.arbitrary  their  activity  the present ones,  the electrolyte  and t h e c o n d i t i o n s  assumptions  coefficients.  on  because  electroneutrality, imposed  predominant  they the  on t h e system  species  and  on  215  NOTATIONS  GOTHIC : Aj< A ,k E v e  c h e m i c a l a f f i n i t y o f r e a c t i o n k. electrochemical a f f i n i t y of reaction electric field. variance o f t h e system.  k,  C A P I T A L ROMAN : A denotes any s p e c i e s , s o l u t e o r s t o i c h i o m e t r i c compound, o f t h e s y s t e m . Aj r e f e r s more s p e c i f i c a l l y t o a p r e d o m i n a n t s o l u t e , Bi stands f o r the reference species considered i n the s y s t e m , one p e r i n d e p e n d e n t component C j . C t o t a l number o f i n d e p e n d e n t c o m p o n e n t s o f t h e system. Cj denotes any independent component o f t h e system. E or E electrochemical potential of a solid-aqueous system, d e f i n e d i n eq.(2.15) Ei i n t e r f a c e p o t e n t i a l between two phases. Eh electrode potential. F Faraday constant. Gj f r e e energy f u n c t i o n ( o r model) o f phase j . G°(i) standard free energy o f formation o f species i . G , G r e s p e c t i v e l y , t h e n e u t r a l and e l e c t r o s t a t i c c o n t r i b u t i o n t o t h e free energy o f a system. J t o t a l number' o f p h a s e s o f t h e s y s t e m . K c o n s t a n t v a l u e imposed on t h e a c t i v i t y o f a solute i . Mj t o t a l number o f moles o f phase j . N t o t a l number o f s p e c i e s c o n s i d e r e d i n a s y s t e m . Nj t o t a l number o f s p e c i e s i n phase j . Ns number o f s o l i d p r e s e n t i n a s y s t e m a t equilibrium. Nc number o f c o n d i t i o n s imposed o n t h e s y s t e m . P t o t a l pressure o f t h e system. {P)r {Q} denote t h e e q u i l i b r i a c o n s i d e r e d i n t h e system. Q ( A ) , Q (A) constant c o e f f i c i e n t s o f Nernst type equations such as eq.(2.37) o r eq.(2.42) c o r r e s p o n d i n g t o s p e c i e s A. R universal gas constant. S entropy o f t h e system. Si r e f e r s t o a s o l i d present i n t h e system a t equilibrium. T asolute temperature o f t h e system. V volume. X c o n s t a n t d e f i n e d by e q . ( 2 . 3 8 ) . c  e  n  n  n  S M A L L ROMAN : a(A) activity of a solute. ik k ( i ) stoichiometric coefficient i n r e a c t i o n k. c  o  r  c  of species  i (or Bj)  216  C i (A)  e i h(A)  stoichiometric c o e f f i c i e n t of species A with r e s p e c t t o a r e f e r e n c e s p e c i e s Bi« denotes the e l e c t r o n , d e n o t e s any s p e c i e s . stoichiometric c o e f f i c i e n t of species A with respect to H i n any g i v e n r e a c t i o n , e x t e n t o f r e a c t i o n k. number o f i n d e p e n d e n t c o m p o n e n t s , o t h e r t h a n 0 a n d H, i n a n s o l i d - a q u e o u s system. number o f moles o f component C i i n a c l o s e d system. stoichiometric c o e f f i c i e n t of species A with r e s p e c t t o t h e e l e c t r o n i n any g i v e n r e a c t i o n , t o t a l number o f c o n s t i t u e n t i i n t h e s y s t e m (chapter 1 o n l y ) . number o f mole o f c o n s t i t u e n t i i n phase j . d e f i n e d by a n a l o g y w i t h pH, a s - l o g ( a ( A ) ) . T h i s d e f i n i t i o n e x t e n d s , i n t h i s t e x t , t o any s p e c i e s A considered i n the system . p a r t i a l pressure of a gaseous s p e c i e s i . charge of a species i . number o f i n d e p e n d e n t r e a c t i o n s i n t h e s y s t e m . number o f a t o m s o f c o m p o n e n t h i n a m o l e c u l e o f species i . number o f c h a r g e o f s p e c i e s i ( o r B i ) . stoichiometric coefficient of species A with r e s p e c t t o H2O i n any g i v e n r e a c t i o n , c o n c e n t r a t i o n o f s p e c i e s i i n p h a s e j . The m e n t i o n o f t h e p h a s e may b e o m i t t e d . +  Ik m ItliO  n(A)  pA  Pi  th(i) Zi  w(A) Xij  or  GREEK dTT Pij crij  XJ  ( i)  :  °r P j ( i ) or O i ( i )  <*i  non c o m p e n s a t e d h e a t due t o i r r e v e r s i b i l i t i e s i n any t r a n s f o r m a t i o n o f t h e s y s t e m , chemical p o t e n t i a l o f s p e c i e s i i n phase j . a c t i v i t y c o e f f i c i e n t o f spe'cies i i n phase j . electrostatic potential. value of the e l e c t r o s t a t i c p o t e n t i a l at the point where s p e c i e s i i s l o c a t e d .  ABBREVIATIONS t o t a l c o n c e n t r a t i o n o f component C i i n the aqueous phase. (g-x) diagram molar free energy versus composition diagram, mole r e f e r s t o gram mole. { P } , {A+B} s t a b l e e q u i l i b r i u m , s t a b l e assemblage, RPS p o t e n t i a l r a n g e o f s t a b i l i t y o f an e q u i l i b r i u m , resp. stands for " r e s p e c t i v e l y " . (Ci)  t  SYMBOLS FOR BCSu BFSu Bnt Cct  THE  S O L I D COMPOUNDS OF THE C U - F E - S - H 0 b a s i c copper sulphate. basic iron sulphate. bornite. chalcocite. 2  SYSTEM  217  Cov Cpy Cub Cup C2Fe ClFe Dig FCct FDig F2Su F3Su Hem HCSu HFSu Ida Mag MPyh Pyr Ten Tro  covellite. chalcopyrite. cubanite cuprite. cupric ferrite. cuprous f e r r i t e . digenite. iron-rich chalcocite. iron-rich digenite. ferrous sulphate. ferric sulphate. hematite. monohydrated copper s u l p h a t e . monohydrated f e r r o u s s u l p h a t e . idaite. magnetite. monoclinic pyrrhotite. pyrite. tenorite. hexagonal p y r r h o t i t e phase w i t h t h e s t o i c h i o m e t r i c composition FeS.  OTHER C O N V E N T I O N S  :  U n d e r s c r i p t w o r (aq) r e f e r t o t h e aqueous p h a s e . U n d e r s c r i p t (g) and (c) r e f e r t o t h e g a s and t o t h e s o l i d state. 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Mineralog.,  229  A P P END  I C E S  APPENDIX I  This appendix I l i s t s the a v a i l a b l e data w i t h t h e i r sources i n t h e i r o r i g i n a l l y published form a l o n g w i t h t h e main s t e p s l e a d i n g t o t h e G°'s a t 200°C. The s o u r c e s and t h e methods a r e d i s c u s s e d i n c h a p t e r 4.  231  SECTION I-A : t h e c o n s t a n t s . 1 c a l = 4.184 j o u l e s R = 8 . 3 1 4 joules/K F = 9 6 484 coulombs  SECTION I-B : t h e e l e m e n t s . * D a t a p r o v i d e d by H u l t g r e n e t a l . (1973)  T  |  Elements K Fe°  S°  Cu°  |  1  0.5 0 ( g ) 2  0.5 H ( g ) 2  Note:  1  C  s  P  - S  |  s t  H -  1cal/mole.K cal/mole.KI  H  '  s t  s  s t  c a l / m o l e 1cal/mole.K  298. 15 500  1 1  5.97 7.10  0. 3.354  0 1319  1  |  6.52  298. 15 480 500  1 1 1  5.430 9.432 9.095  0. 4.922 5.292  •1 | |  0 1863 2049  1  7.60  298. 15 500  1  5.840 6.192  0. 3.109  0 1217  1  7.923  298 500  1 1  3.511 3.716  0. 1.858  |  0 727  298 500  1 1  3.446 3.497  0. 1.799  | |  0 703  * = practical  1  1  1  I 1  1 24.502 1 15.604 *  scale.  * D a t a p r o v i d e d b y C r i s s and C o b b l e (1964): H+ : C ( 2 9 8 , 4 7 3 ) = 35 c a l / m o l e . K abs s  p  =  -  cal/mole. K  5  * R e s u l t i n g f r e e e n e r g y changes:  I 473 ) dG 298 p  ,473 ) dG 500 Note:  *  |  S°  ( l i q )  |  Cu°  I  I  I  I -1414  | -1796  I -1645  I I =  Fe°  V  2 ( g )  |0.5 H g)| 2 {  I  I  I -4443  |  2881  |  |  |  465  |  H+  I 648  I 260  |  I  335 * |  292  I . I  between 460 K and 480 K, p = 21.264 - 0.02465 T.  c  10.5 O  705  linear  I  I  extrapolation  of  232  SECTION I-C : t h e s o l i d  compounds.  A v a i l a b l e d a t a a t 500 K  G° 473.15 K  Compounds Source  CuO CU2O  Fe 0 Fe 0 FeS Fei.ooS CuFeS CU5FeS4 * CUSO4 FeS04 Fe (S0 ) CuFe204 CuFe0 CUSO4.H 0 2  3  3  4  2  2  2  4  3  2  2  Note: * = Source a b c  a a b b c c a a a b b a a a  I  G° Cp S° cal/mole.K cal/mole.Kl cal/mole  I  11.769 17.015 31.500 45.980 17.32 17.40 26.690 66.254 30.290 30.810 81.090 45.320 22.597 38.0  15.888 30.356 35.469  I -26 1 -31 1 -164 55.555 I -266 -35 21.06 23.775 I -24 42.780 I -45 116.892 I -95 40.180 I -139 ! 43.085 I -180 ! 110.809 I -488 1 55.988 I -189 1 32.093 I -101 I 52.648 | -191  I  153 679 681 772 816 139 228 167 816 178 343 399 457 154  cal/mole  1  1  -26 -32 -166 -228 -36 -24 -45 -95 -142 -182 -495 -191 -102 -194  732 165 387 914 193 108 321 137 206 459 412 561 574 850  d a t a a t t r a n s i t i o n t e m p e r a t u r e 485 K. = Gedansky e t a l . (1970) = JANAF S e l e c t i o n ( S t u l l and P r o p h e t , 1971) = M i l l s (1974)  * Data provided by P o t t e r CuS  (1977):  (388.36 K - 717.73 K) G°(T) = -13 548 + 1.587 T  cal/mole ( e r r o r < 50 c a l / m o l e )  Cu^  (376.65 K - 708.15 K) G°(T) = -18 386 - 6.01, T - 0.000941 T cal/mole ( e r r o r < 300 c a l / m o l e ) 2  and t h u s a t 200°C G°(Cov) = -12 797 c a l / m o l e G°(Cct) = -21 440 c a l / m o l e  233  SECTION I-D : d a t a f o r s o l u t e s .  * 2°(liq) H  :  d  a  t  a  f  r  o  m  U  S  B  S e c t i o n (Wicks and B l o c k , 1963) a t 200OC GO(H 0) = -50 190 c a l / m o l e .  M  2  *H S(q):  data selected 298 K: AH° S 500 K: C H - H S - S and hence a t 473.15 K 2  s t p  s t s t  b y M i l l s (1974) = -4.90 k c a l / m o l e = 49.15 c a l / m o l e . K = 9.11 c a l / m o l e . K = 1753 c a l / m o l e =4.47 cal/mole. K G°(H S( )) = -9395 c a l / m o l e . 2  * 2S (aq)  Helgeson H2S(g) = H S thus A G ° = 3334 c a l  H  :  d  a  t  a  fr  o  m  2  and  ( a q )  g  (1967) a t 200°C pK = 1.54 G°(H S( 2  a q )  ) = -6061 c a l / m o l e .  * HS :  d a t a s e l e c t e d b y Rao and H e p l e r (1977) H2S = HS" + H+ 167°C : p K i = 6.92 228°C : pK! = 7 . 4 4 by l i n e a r e x t r a p o l a t i o n a t 200°C pK]_ = 7.20 A G ° = 15 587 c a l G°(HS ) = 9526 c a l / m o l e . -  { a q )  _  * S  d a t a from G i g g e n b a c h (1971) a t 200°C HS" = S + H+ p K > 12.5 by u s i n g p K = 12.5, A G ° = 27 061 c a l G°(S ") = 36 587 c a l / m o l e . 2 _  :  2 -  2  2  2  * Cu(HS) ~: d a t a from C r e r a r and B a r n e s (1976) a t 200°C 0.25 C u F e S 4 + HS" + 0.5 H S = ,0 =.02. 255 C C u FFe S + C u ( H S ) " Log K = -2.3 and t h u s A G ° = 4979 c a l . G°(Cu(HS) -) = -2646 c a l / m o l e . 2  5  2  2  2  * OH : -  d a t a from Sweeton e t a l . (1974) a t 200°C 2°(liq) = H + OH" l o g K = -11.302 thus A G ° = 24 467 c a l H  +  w  and  G ( 0 H ~ ) = -25 723 c a l / m o l e . O  d a t a from L i e t z k e e t a l . (1961) a t 200°C  * HSO4-:  HSO4- = H+ + S O 4 2  A G° = 9757 c a l / m o l e and  thus G ° ( H S 0 - ) = G ° ( S 0 - ) - 9757 c a l / m o l e 2  4  4  2  234  SECTION I-E : t h e f e r r o u s  solutes.  * d a t a p r o v i d e d b y Sweeton and Baes (1970) f o r t h e e q u a t i o n s 1/3 F e 0 4 + 2 H  +  3  + 1/3 H ( ) = F e 2  + 4/3 H 0  2 +  g  eq.(a) eq.(b) eq.(c) eq.(d)  2  * Data a t 200°C. A v a i l a b l e data Equations  AG°  I I 1 1  eq.(a) eq.(b) eq.(c) eq.(d)  A H° | A S° cal/mole Ical/mole.K  cal/mole  I | | | |  -12 392 311 15 781 32 419  -22 -10 4 9  234 146 615 045  -20.8 -22.1 -23.6 -49.4  G°(solutes)  Solutes  cal/mole -21 -59 -93 -127  777 264 983 536  2+ FeOH+ Fe(OH) F e  2  Fe(OH)3-  * Data a t 25°C.  A v a i l a b l e data Equations  |  Data f o r s o l u t e s AG°  AH° I A S° I c a l / m o l e |cal/mole.K| c a l / m o l e I -23 950 I -10 732 | 9 045 I  eq.(a) eq.(b) eq.(d)  -25.3 -23.6 -49.4  I / /. I -16 407 | -3 696 \- 23 774  N o t e : d a t a used f o r t h e c a l c u l a t i o n s a t 25°C G°(H 0) = -56 688 c a l / m o l e G°(Mag) = -243 191 c a l / m o l e 2  G° cal/mole  I S° |cal/mole.K  I -21 886 I -25.60 -65 863 I -7.19 -151 770 | 0.43  S°(H 0) = 16.71 c a l / m o l e . K S°(Mag) = 34.72 c a l / m o l e . K 2  235  * C r i s s and C o b b l e e x t r a p o l a t i o n  1  Ions  s  1  1 Cp  abs  (1964)  |  2+ FeOH+ HFe02  _  1 1 1  -35.60 ! 72.43 ! -12.19 1 57.68 | -11.28 | -199.83 I  dG  G  °exp  1  -G°call  1 (cal.) | (exp.) | 473 K I Ical/mole.KIcal/mole.K| cal/mole c a l / m o l e | c a l / m o l e | cal/mole I F e  298 K  4 7 3  J  I (298,473)1 | |  I  1 G° | G°473 1 1 - G°2981 - G°2981  e  I  1  I  3 079 -376 10 668  27 1  6 129 26 082  |  I  |  109 6 599 17 736  I I I  82 470 -8 346  | |  I  Note : t h e G°(HFe02~) i s c a l c u l a t e d by assuming a z e r o A G ° f o r t h e r e a c t i o n Fe(OH) = HFe0 + H 0 AG° = 0 and t h u s a t 25°C : G°(HFe0 ) = -95 082 c a l / m o l e a t 200°C : G°(HFe02 ) = -77 346 c a l / m o l e -  _  3  2  2  _  2  * D a t a s e l e c t e d by L a t i m e r (1952) a t 25°C. E ° ( F e / F e ) = 0.771V and t h u s G ° ( F e ) = G ° ( F e ) + 17 779 = -4107 c a l / m o l e i n s t e a d o f G ° ( F e ) = -1.1 k c a l / m o l e p r o v i d e d by t h e NBS s e l e c t i o n (Wagman e t a l . , 1969) 3+  2+  3+  2+  3+  A s a r e s u l t , t h e G°'s -3000 c a l / g . f e r r i c i o n .  at  25°C  of  a l l f e r r i c s o l u t e s a r e c o r r e c t e d by  SECTION I - F : t h e i o n p a i r s . * D a t a from I z a t t e t a l . (1969) a t 25°C  A v a i l a b l e d a t a a t 25°C. Equations  I  A H° ./ A S° | c a l / m o l e , |cal/mole.KI 2+ + S0 2- = F e S 0 C u ^ + S 0 ^ = C u S 0 ( q) F e  4  4 ( a q )  -  4  AG  0  4  a  560 1220  I  12.0 14.6  I  A G° cal/mole  -3018 -3133  a t 200°C o b t a i n e d by e q . (4.09) from H e l g e s o n (1967) A G°473 = A H°298 " 575.09 A S° 98 2  A G °  200°C cal/mole -6341 -7176  236  SECTION  I-G : C r i s s and C o b b l e e x t r a p o l a t i o n f o r i o n s .  Ions  G°  s  298.15 K cal/mole Cu+ Cu2+ CUOH+ Cu (OH) C113 (OH) 3+ 2  12 15 -30 -67 -150 -4 -57 -107 -117 -187 -111 -116 -177 -124 -129 -126 20 18 15 16 -61 -43  2 + 2 2  +  2  F e  FeOH Fe(OH) + F e (OH) FeSO/" " Fe04 2 +  2  2  A  +  2  1  2 _  so f 3  S04 : S203 HS203" HSO32  2  S3 2  s?" S5 " HCuO Cu0 2  2  Source  a c d f h aa  000 700 468 326 512 100 800 700 650 700 700 300 970 000 500 150 330 420 790 030 312 624  a a b  1  I 1  I I  b b cc| cc| cc| cc| cc| h c c g h c  I  G  G°  °298  (298,473) 298.15 K + J dG cal/mole K cal/mole cal/mole K 4.8 a 46.98 1 9 116 -33.6 a 71.17 1 18 484 -18.89 b 61.90 1 29 8 5 5 -36.78 b 73.17 1 -64 073 -24.96 b I 65.72 1 -149 004 -90.5 c 107.02 1 7 081 -44. a 77.72 1 -53 481 -17.1 e 60.77 1 -107 352 -105. 1 -104 328 c 1 116.15 -36. c 1 72.68 1 -184 562 (20) e j -94.4 1 -111 093 3. -137.41 c -110847 14.8 c 1 -107.56 -175880 18. -99.46 g -122823 (21) 1 130 436 d 1 -62.96 38.4 c 10.82 1 -133 341 12.39 -65.50 1 21 011 j 27.22 -66.09 1 16 532 I 35.12 -66.40 1 12 533 34.40 -66.38 1 12 898 15. f I -88.40 1 -60 091 23. f | -86.81 1 -43 872  I I I  1  1 1 1 1  iI i| iI iI aa| aa|  CP  abs  i i i i  473.15 K cal/mole  1  8 528 15 663 -23 119 -50 601 -119 239 1 796 -49 209 -93 523 -95 784 -165813 -87 441. -91 256 -151 846 -101 436 -108 401 -113 102 29 069 26 386 24 183 26 344 -44 446 -28 875  = = = = = =  Gedansky e t a l . (1970) b = A r e n a e t a l . (1976) NBS S e l e c t i o n (Wagman e t a l . ,1969) B i e r n a t and R o b i n s (1969) e = B i e r n a t and R o b i n s (1972) Kwok and R o b i n s (1973) g = L a t i m e r (1952) P o u r b a i x (1963) G e d a n s k y e t a l . (1970) f o r Cu(OH)3~ and C u ( O H ) 4 , a d a p t e d b y u s i n g G°(H20) = -56 688 c a l / m o l e . c c = NBS S e l e c t i o n (Wagman e t a l . , 1 9 6 9 ) , c o r r e c t e d by -3000 c a l / g f e r r i c i o n . i i = G i g g e n b a c h (1974) w h i c h p r o v i d e s a t 25°C : 2_  I G° S°  (kj/mole)  S  2 2  ~  I S3  2  -  IS  ~  I  66  |  2 4  I  85  I  77  I  (j/mole. K ) |  10  I  72  | 105  s  2 5  -  67  I 102  0  APPENDIX I I  T h i s appendix l i s t s t h e data used i n t h i s s t u d y on the Cu-Fe-S-H20 system a t 200°C. The f o u r phase assemblages o f t h e c o r r e s p o n d i n g Cu-Fe-S-H20 phase diagram are also provided. These d a t a d i f f e r i n some c a s e s from t h o s e i n A p p e n d i x I a s a consequence of new d a t a e v a l u a t e d by methods d e s c r i b e d i n c h a p t e r 6.  238  TABLE  (A2.01)  The s o l i d compounds c o n s i d e r e d i n t h e C u - F e - S - H ^ s y s t e m a t 200°c. Symbols  Cu° Fe° S° Cup Ten Cct Dig Cov Mag Hem Tro Mpyh Pyr Cpy Bnt FDig FCct Ida Cub C2Su F2Su F3Su C2Fe ClFe HCSu HFSu BCSu BFSu  Formulas  G° cal/mole  Cu° Fe° S° -  CU2°  CuO  CU2S  Cu S CuS 3°4 Fe20 FeS 1 > 8  F e  3  0.875 FeS2 CuFeS2 Cu5FeS4 F e  s  Cui.58 0.1 ^1.92^0.04 F e  CuFe S3 CuS0 ( ) FeS0 / Fe (S0 ) CuFe 0 CuFe02  s  s  2  4  c  4  c )  2  4  2  4  3  CUSO4.H2O  FeS0 .H20 CuS0 .2(OH) / FeS0 OH 4  4  4  2  32 26 21 21 12 - 228 - 166 - 24 - 23 - 36 - 45 - 95 - 23 - 23 - 106 - 69 - 142 - 182 - 495 - 191 - 102 - 194 - 236 - 307 - 221  0 0 0 165 732 440 100 797 914 387 108 100 193 321 137 450 500 350 700 206 459 412 561 574 850 774 763 778  TABLE  (A2.02)  The s o l u t e s c o n s i d e r e d i n t h e C u - F e - S - H ^ s y s t e m a t 200°C.  Formulas cal/mole H+ Cu2+ Fe + S2" 2° H (g)  0 663 777 587 190 0 0 8 528 - 23 119 - 50 601 - 119 239 - 94 636 - 129 255 - 59 264 - 93 983 - 127 536 1 796 - 49 209 - 93 523 - 95 784 - 87 441 - 1 6 9 510 - 6 061 9 526 29 069 26 386 24 183 26 344 - 161 603 - 151 846 - 113 102 - 91 256 - 108 401 - 101 436 - 145 713 - 183 160 - 2 646 15 - 21 36 - 50  2  H  2  CuOH+ Cu (OH) Cu (OH) 2+ Cu (OH) " Cu (OH) 2Fe (OH) + Fe(OH) Fe(0H)3 Fe Fe ( O H ) Fe (OH) + F e ( 0 H ) ,2+ Fe0 ~ FeS0 2 +  2  2  3  4  3  :  4  2  3 +  2 +  2  2  2  2  4  +  4  HSO/-  so "4  S0 ' HS2O3S2O32CuS0 3  4 ( a q )  4(ag) Cu(HS) F e S 0  2  TABLE (A2.03): f  Four-phase e q u i l i b r i a o f t h e Cu-Fe-S-0 (+H2O) phase d i a g r a m a t 200°C. Cu° Cu° Cu° Mag Mag Mag Mag Mag Mag Pyr Cov Cov S© Mag Hem Dig Cct Dig Cu° S° Dig Dig Cup Cup Hem Cup Ten S° F3Su Hem Hem Mag Mag Hem Cu° Cu° Cu° Cup Cup HCSu Hem Mag Cup  Fe° Mag Mag Tro Cpy Tro Mpyh Mpyh Bnt FDig FDig Pyr Cov Cpy Pyr Cov Dig FDig Cup Cov Cov FCct Cct ClFe ClFe Ten Hem F3Su HCSu Pyr FDig Hem Hem HFSu Mag Hem Cup FCct FCct HFSu FCct Hem HCSu  Mag Tro Bnt Bnt Bnt Mpyh Cpy Pyr FDig Ida Ida Ida Pyr Bnt Cpy FDig FCct FCct Cct HCSu HCSu HCSu FCct HFSu HFSU ClFe ClFe HCSu HFSU FDig FCct Pyr Cpy /. BCSu Hem FCct FCct ClFe HCSu BCSu ClFe FDig HFSu  Tro Bnt FCct Cub Cub Cub Cub Cpy FCct HFSu HFSu' HFSu HFSu FDig FDig HFSu HCSu HFSu FCct HFSu HFSu HFSu HCSu BCSu BCSu BCSu BCSu HFSu BFSu HFSu HFSU Cpy FDig BFSu FCct ClFe ClFe HFSu HFSu BFSu HFSu FCct BCSu  APPENDIX I I I  T h i s a p p e n d i x d e s c r i b e s and e x p l a i n s how to use t h e program w h i c h h a s computed and p l o t t e d t h e . Eh-pH d i a g r a m s shown i n c h a p t e r 7 f o r t h e C u - F e - S - H ^ system. The u s e r i s r e f e r r e d to c h a p t e r 2 f o r t h e t h e o r e t i c a l ground and to c h a p t e r 3 f o r t h e methods on w h i c h t h e program i s b a s e d .  242  SECTION I I I - A  :  presentation.  The computer p r o g r a m d e s c r i b e d here p l o t s Eh-pH diagrams f o r systems with a maximum o f t h r e e i n d e p e n d e n t o o m p o n e n t s ( b e s i d e s H " a n d H2O) : C1-C2-C3-H2 . I t c a n b e e x t e n d e d b o a n y n u m b e r o f c o m p o n e n t s b y i n c r e a s i n g the s i z e o f a few matrices. 4  0  The i n p u t d a t a i n c l u d e , f o r each c h e m i c a l s p e c i e s c o n s i d e r e d i n t h e s y s t e m , i t s name, i t s G ° v a l u e a t t h e c o n s i d e r e d temperature, and its stoichiometric coefficients. The i n p u t d a t a a l s o i n c l u d e t h e l i s t o f s o l i d assemblages i n e q u i l i b r i u m w i t h H2O i n t h e p h a s e diagram C -C -C -0-H 0. 1  2  3  2  Two t y p e s o f conditions are considered. C o n d i t i o n s such as constant ( C i ) tare designated by TO. C o n d i t i o n s such as / constant activity o f a s o l u t e a r e d e s i g n a t e d b y P K . When c o m p u t i n g t h e s o l u t e zones corresponding t o c o n d i t i o n s TO, t h e program e l i m i n a t e s a l l complex solutes. The d i a g r a m i s then p l o t t e d without taking these complexes into account. F o r each complex solute, a d i a g r a m must be computed separately by using the appropriate c o n d i t i o n PK. The boundaries o f the s o l u t e zones must a l s o be computed s e p a r a t e l y , and these zones a r e s u p e r i m p o s e d o n t h e i n i t i a l d i a g r a m i n s i d e t h e i r s t a b l e b o u n d a r i e s when they e x i s t . A c o m p l i c a t e d diagram c a n be p l o t t e d i n l e s s than h a l f an hour.  The computer following effects:  program i s d i v i d e d i n t o four p a r t s , 1) R e a d i n p u t d a t a a n d w r i t e t h e  which have t h e  heading  of  the  print-out.  2) D e t e r m i n e t h e s o l u t e z o n e s c o r r e s p o n d i n g t o t h e Nc c o n d i t i o n s imposed o n t h e system. 3) C o m p u t e , i n each solute zone, the e q u i l i b r i a w i t h one degree o f freedom and determine t h e i r s t a b i l i t y ranges. 4) W r i t e t h e p r i n t - o u t a n d p l o t t h e d i a g r a m . Two s u b r o u t i n e s a r e u s e d . The f i r s t subroutine FRIEND equilibrium with one degree o f freedom and determines range. The s e c o n d s u b r o u t i n e PETERS i n v e r t s t h e m a t r i c e s s u b r o u t i n e FRIEND.  computes any its stability involved i n  A second computer program h a s been w r i t t e n w h i c h s i m p l y computes e q u i l i b r i a and determines t h e i r s t a b i l i t y . I t i s used t o compute once and f o r a l l the s o l i d a s s e m b l a g e s o f t h e C1-C2-C3-O (+H2O),phase diagram, a n d , f o r each diagram, t h e boundaries o f i t s complex solute zones. This p r o g r a m u s e s s u b r o u t i n e s F R I E N D a n d P E T E R S e x t e n s i v e l y . It i s s t r a i g h t f o r w a r d , and i s n o t described here.  243  SECTION III-B : description of the program.  III-B-1 : subroutine PETERS.  It computes the solutions equations by inverting a matrix. The Gauss-Jordan reduction method strategy (Carnahan et al., 1969).  of a system of simultaneous linear i s used  with  the maximum  pivot  ORDER  number of linear equations of the system.  A  matrix formed i n MAIN with the coefficients of the linear equations.  B  matrix actually inverted. Matrix A i s copied into B at the beginning of the subroutine.  PIVOT  coefficient of trie largest absolute value in the f i r s t ORDER rows and columns of the matrix being inverted, at each stage o f the inversion.  TROW, JCOL  coordinates of the actual pivot.  DETER  determinant value  EPS  minimum pivot set i n input data; when the absolute value of a pivot i s smaller than EPS, the matrix i s considered singular, and DETER=0. i s returned.  SOL  matrix to be returned to MAIN. I t contains the solution of the system of equations.  III-B-2 : subroutine FRIEND.  It computes any equilibrium {P} with one degree of freedom and determines i t s s t a b i l i t y range. The subroutine f i r s t forms matrix A with the coefficients of the linear equations corresponding to the conditions and to the compounds involved in {p}. Subroutine PETERS then computes {pj. When fp} i s represented by a vertical line i n the Eh-pH diagram (constant pH), the determinant of the matrix calculated by PETERS i s equal to zero. Therefore, when a zero determinant i s f i r s t returned, the columns corresponding to Eh and pH are changed i n matrix A, and subroutine PETERS i s called again. If a  244  z e r o d e t e r m i n a n t i s r e t u r n e d f o r t h e second t i m e , {p} i s i g n o r e d . When {P} h a s been s u c c e s s f u l l y computed, i t s s t a b i l i t y i s f i n a l l y checked by a s i m p l e x p r o c e s s d e s c r i b e d i n c h a p t e r 3. ISIZE  number o f components C ± , C {p}., •;. .  NCOND  number o f c o n d i t i o n s i n v o l v e d i n {p}.  'HCOND  matrix containing linear equations conditions.  2  o r C3  involved i n  the c o e f f i c i e n t s o f the corresponding t o the  COMOD  matrix containing the coefficients o f the l i n e a r equations corresponding t o the borders o f t h e d i a g r a m , and t o a l l t h e s p e c i e s ( s o l i d o r s o l u t e ) i n v o l v e d i n {p} o r a f f e c t i n g i t s stability.  NCP  number o f rows o f m a t r i x COMOD.  EQUIL  m a t r i x c o n t a i n i n g t h e a d d r e s s e s i n COMOD o f t h e s o l i d compounds i n v o l v e d i n {P} .  REFPOT  p o t e n t i a l o f the r e f e r e n c e e l e c t r o d e .  X  c o n s t a n t e q u a l t o (Ln(10) R T / F ) , i n w h i c h T i s t h e temperature, R the p e r f e c t gas constant and F t h e Faraday. X i s calculated i n MAIN (158)  SOLI  m a t r i x e q u a l t o z e r o when {p} i s n o t s t a b l e , and o t h e r w i s e c o n t a i n i n g t h e a d d r e s s e s i n COMOD of t h e two " s p e c i e s " which form stable e q u i l i b r i a w i t h {p}.  SOLR  S0LR(1) i s e q u a l t o 1. when f o r {P}, E h i s expressed a s a f u n c t i o n o f pH. I n t h i s case, the c o e f f i c i e n t s o f t h i s f u n c t i o n are s t o r e d i n SOLR(2) a n d SOLR(3). SOLR(l) i s equal t o - 1 . when f o r { p } , t h e pH i s c o n s t a n t . I n t h i s c a s e , t h i s pH v a l u e i s s t o r e d i n SOLR(2). The c o o r d i n a t e s (Eh a n d pH) o f t h e two p o i n t s l i m i t i n g t h e s t a b i l i t y r a n g e o f {P} a r e s t o r e d i n SOLR(4) t o SOLR(7).  NBSTAB  c o u n t e r : number o f " s p e c i e s " e q u i l i b r i a w i t h {p}.  forming s t a b l e  245  I I I - B - 3 : main program - p a r t 1 (1.59 t o 1.209).  I t reads i n p u t d a t a from three d i f f e r e n t f i l e s . These f i l e s a r e made f o r t h e C2-C2-C3-H2O system, b u t a r e e q u a l l y v a l i d f o r subsystems s u c h a s t h e C3-C3-H2O. I n each c a s e , t h e program s e l e c t s t h e compounds and t h e s o l i d assemblages w h i c h b e l o n g bo t h e s y s t e m t o be c o n s i d e r e d . The program a l s o s e l e c t s t h e s o l i d ; assemblages w h i c h , g i v e n t h e number o f c o n d i t i o n s , r e s u l t i n e q u i l i b r i a w i t h o n e d e g r e e o f freedom. Then i t computes t h e c o e f f i c i e n t s o f t h e l i n e a r e q u a t i o n s c o r r e s p o n d i n g t o t h e b o r d e r s o f t h e d i a g r a m , and t o a l l t h e s o l i d and s o l u t e compounds o f t h e system. F i n a l l y , i t w r i t e s t h e h e a d i n g o f t h e p r i n t e d o u t p u t . T NCPS, NCPI  temperature. number o f s o l i d , and s o l u t e l 2~ 3 2 system.  C  CNAME(I,K) , GFOR(I,K), EQCO(I,K,J)  - C  c  - H  compunds  o f the  0  m a t r i c e s f o r t h e names, t h e G°'s a t t e m p e r a t u r e T, and t h e 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 s o f a l l the compounds I o f t h e C i - C 2 3 2 system. K = l f o r s o l i d compounds and K=2 f o r s o l u t e s . - C  _ H  0  TITL1  t i t l e o f the p l o t t e d Output.  TITL2  t i t l e f o r theprinted output.  IWORK  number o f diagrams t o be computed.  NWORK  c o u n t e r : number o f d i a g r a m s a c t u a l l y computed.  INDEX  matrix l 2 3 C  - C  - C  - H  specifying t h e subsystem 2 ^ considered. 0  o f the  to  BOOK  a d d r e s s e s i n t h e m a t r i c e s CNAME, GFOR o r EQCO of t h e compounds i n v o l v e d i n the considered subsystem.  NCPI, NCP2  Number o f s o l i d and s o l u t e s u b s y s t e m bo be c o n s i d e r e d .  MCOND  number o f c o n d i t i o n s s o l u t i o n (Nc).  MCONC  number o f c o n c e n t r a t i o n l e v e l s t o be on t h e d i a g r a m .  IBQRN, BORN  t y p e s (1 f o r Eh and 2 f o r pH) and v a l u e s o f t h e b o r d e r s o f t h e diagram.  PH20  c o n s t a n t e q u a l to - l o g ( w a t e r a c t i v i t y ) .  TYCOND, NACOND, V7ACOND  m a t r i c e s d e f i n i n g t h e c o n d i t i o n s imposed on t h e  compounds  imposed  o f the  o n t h e aqueous  depicted  246  solution. F o r : each one, i t s t y p e (TO o r P K ) , the a d d r e s s o f t h e c o r r e s p o n d i n g s o l u t e i n EQCO and t h e v a l u e s t a t e d f o r t h e - l o g o f t h e s o l u t e activity ( c o n d i t i o n PK) o r that o f the c o r r e s p o n d i n g ( C i ) ( c o n d i t i o n TO). t  NEEKIL  number Cl-^-Cs  - 0  of solid assemblages ( 2°) Phase d i a g r a m .  the  in  +H  EOUU,  matrix f o r assemblage.  NFREED  number o f d e g r e e s o f freedom c o r r e s p o n d i n g to a solid assemblage, given t h e number of conditions.  NEKIL(J)  number o f s o l i d V assemblages w h i c h a r e t a k e n i n t o account. Two c a s e s a r e c o n s i d e r e d : J = l c o r r e s p o n d s to MCOND c o n d i t i o n s , i . e . to t h e assemblages needed to compute t h e d i a g r a m i t s e l f . J=2 c o r r e s p o n d s to MCOND+1 c o n d i t i o n s , i . e . to t h e assemblages needed to d e t e r m i n e t h e concentration lines.  BQUTLI  matrix i n which the assemblages a r e stored;,  DIM1, DIM2  s i z e o f t h e d i a g r a m (Eh and pH c o o r d i n a t e s ) .  NOWRIT  c o n s t a n t w h i c h must be d i f f e r e n t f r o m z e r o when no p r i n t e d o u t p u t i s to b e g e n e r a t e d .  NODRAW  c o n s t a n t w h i c h must be d i f f e r e n t f r o m z e r o when no p l o t t e d o u p u t i s to be g e n e r a t e d .  CO  constant c o e f f i c i e n t s o f the l i n e a r equations.  temporary  storage  of  considered  a  solid  solid  I I I - B - 4 : main p r o g r a m - p a r t 2 (1.211 to 1.381).  I t d e t e r m i n e s t h e s t a b l e s o l u t e zones c o r r e s p o n d i n g to t h e c o n d i t i o n s imposed o n t h e system, and f o r each zone, t h e n e i g h b o u r i n g predominant s o l u t e s . I t a l s o determines t h e i r boundaries which a r e p l o t t e d o n the diagram. I n t h e f i r s t p a r t (1.237 to 1.308), t h e s o l u t e zones a r e computed f o r each r e s p e c t i v e c o n d i t i o n such a s c o n s t a n t { C £ ) ( t y p e TO c o n d i t i o n ) . For t h a t p u r p o s e , s u b r o u t i n e FRIEND i s used w i t h ISIZE=1 and NCOND=0, with COMOD containing the c o e f f i c i e n t s o f the l i n e a r equations c o r r e s p o n d i n g to t h e b o r d e r s o f t h e diagram, and to a l l t h e s o l u t e s , o f the c o r r e s p o n d i n g Cj-HoO system. EQuTL s c a n s t h e d i f f e r e n t p a i r s o f these s o l u t e s . I n t h e second p a r t (1.320 to 1.381), used when a t l e a s t two t y p e TO t  247  conditions are involved, two sets of solute zones are combined to form a single consistent set. For that purpose, subroutine FRIEND i s used with ISIZE equal bo the number of components involved, with NCOND=0, and with COMOD containing the coefficients of the linear equations corresponding to the diagram borders and to a l l the predominant solutes involved i n the two sets of solute zones which are combined. In both cases, since solute zone boundaries are computed, the constant coefficients of the linear equations (stored in CO) are corrected to take into account only half the concentration value set by the corresponding VACOND. LSIZE  counter : number considered in calculated.  SWITCH  = 1 when the diagram i s computed; = 2 when concentration lines are determined.  STORE, ISTO  matrices where the two sets of solute zones to be combined are stored.  IND  refers to the component C]_, C r or C3 considered at any stage of the calculation.  NAION  stores the addresses of the solutes at any stage of the calculation.  NBION  number of rows in NAION.  NCP  = NBION + 4 = number of rows (including the diagram borders)  NSTAB  counter : number of stable solute zones.  NBLIM  counter : number of stable given solute zone.  IONLIM  counter : number o f stable boundaries non including the diagram boundaries (neighbouring predominant solutes).  LIMTOT  number of solute zone boundaries to be plotted  DROLIM  coordinates (Eh and pH) of the two points limiting each solute zone boundary.  N0DR01  switch used to avoid the same solute boundaries to be plotted several times.  COUPLE  matrix where the solute zones are stored; the three f i r s t columns are set for the predominant solutes in each zone, the subsequent columns for the neighbouring predominant solutes..  NBCOP  number  of the  components actually solute zones actually  2  considered  i n COMOD  boundaries o f a  zone  of rows in COUPLE, equal to the number  248  of stable solute zones.  I I I - B - 5 zmain  program - part 3 (1.383 to 1.523).  I t computes l i n e a r Eh-pH d i a g r a m s i n each s o l u t e zones, b y d e t e r m i n i n g t h e e q u i l i b r i a w i t h one degree o f freedom, and t h e i r s t a b i l i t y r a n g e s when t h e y e x i s t . The c o e f f i c i e n t s o f t h e l i n e a r e q u a t i o n s c o r r e s p o n d i n g to t h e c o n d i t i o n s a r e s t o r e d i n HCOND once and f o r a l l i n each s o l u t e zone. COMOD c o n t a i n s t h o s e c o r r e s p o n d i n g to t h e d i a g r a m b o r d e r s , to t h e n e i g h b o u r i n g p r e d o m i n a n t s o l u t e s and to a l l t h e s o l i d compound c o n s i d e r e d i n t h e system. NCOND i s e q u a l to MCOND. F i n a l l y , t h e program w r i t e s t h e p r i n t - o u t and p l o t s t h e diagram. F o r each r e q u i r e d c o n c e n t r a t i o n l i n e , a t y p e TO c o n d i t i o n t h e MCOND c o n d i t i o n s and a new d i a g r a m i s computed.  i s added  to  The w h o l e p r o c e d u r e i s r e p e a t e d u n t i l NWGRK r e a c h e s IWORK, t h e r e q u e s t e d number o f d i a g r a m s .  SECTION III-C : how to use the program.  T h i s s e c t i o n l i s t s t h e i n p u t d a t a needed to r u n t h e program. The i n p u t d a t a h a s been d i v i d e d i n t o t h r e e d i f f e r e n t f i l e s . The two f i r s t f i l e s depend o n t h e C - C - C 3 - H 0 s y s t e m and a r e c r e a t e d once and f o r all. The l a s t f i l e d e f i n e s t h e d i a g r a m s to be computed and must be s p e c i f i e d f o r each j o b . 1  2  2  III-C-1 : f i l e 1.  C  l  - C  2  - C  It mainly contains 3 - 2 ° system. H  data  on  the  chemical  species  of °  the  The f i r s t row (FORMAT(F6.2,21.3,E7.1)), contains T, NCPS, NCPI, and EPS. The temperature i s expressed in K. Then (NCPS + NCPI) rows, one for each chemical species, a l l read with the same FORMAT(A4,4X,F8.0,2X,F6.4,8F7.4), contain CNAME, GFOR, and EQCO. The free energy of formation G° i s expressed i n calories at temperature T. EQCO contains the coefficients of a mass balance equation balancing each chemical species with three independent  249  reference species B]_, B , and B3, with HoO, H+ and the electron. The same reference species must be used for a l l compounds o f the C1-C2-C3-H2P system, but i n so far as they are independent and not complexed, they can be chosen a r b i t r a r i l y . 2  In a row, EQCO i s read i n the following order : the coefficient o f the electron (always positive), the coefficient of H*, the coefficient o f the chemical species i n question, the coefficients o f the three B^, B , and B3, and f i n a l l y the coefficient o f H-p. 2  The NCPS solid compounds come f i r s t (K=l). The order i s o f no consequence but for the f i r s t three : their names are used i n the t i t l e , and the pure components are generally preferred (Cu°, Fe°, S° for instance). The f i r s t solute must be H", then the reference species B p B , and B3 in that order, then H 0 and ^2(g)' order o f the other solutes i s of no consequence. 4  2  2  The last row of the f i l e i s a t i t l e such as "THERMODYNAMICS OF THE -H20 SYSTEM AT The blanks are f i l l e d by the computer.  OK".  III-C-2 : f i l e 2.  It contains phase diagram.  a l l the solid assemblages of the Ci~C -C3-0 (+H2O) 2  The f i r s t row (FORMAT(13)) provides NBEKIL, and NBEKIL rows follow (FORMAT (513)), one for each solid assemblage. The assemblages must a l l be considered from Ns=l to Ns=4. The solids are referred to by their ranks i n the l i s t of solid compounds in f i l e 1. III-C-3 : f i l e 3.  It defines the specific problem to be solved. The f i r s t row (FORMAT(12)) contains IWORK. The second row (FORMAT(311,213,4(Il,F7.3) ,F7.3)), includes INDEX, MCOND, MCONC, (IBORN and BORN) for the four diagram borders, and f i n a l l y PH20. The INDEX i s zero i n the column corresponding to a component C^, C , or C3 which i s omitted i n the particular run. For instance, when F i l e 1 i s written for the Cu-Fe-S-H^ system, then INDEX = 1 1 1 corresponds to the Cu-Fe-S-H20 system 2  INDEX = 1 0 0  corresponds to the Cu-HoO system  INDEX = 0 1 1 corresponds to the F e - S - H 2 P system. . >\ The. borders can be written i n any order as long as the proper code IBORN  250  (1 f o r Eh, 2 f o r pH) i s used.  P o t e n t i a l s are expressed i n V o l t s .  Then MCOND + MCONC rows f o l l o w , one f o r each c o n d i t i o n , containing TYGOND, NACOND and VACOND (FORMAT(A2,I3,1X,F7.3)). F o r t y p e PK c o n d i t i o n s , NACOND may r e f e r t o a n y s o l u t e ( e x c e p t H+, H ^ r 2(g)'°2(g))• p o t e n t i a l remains c o n s t a n t t h r o u g h o u t t h e d i a g r a m t o B e p l o t t e d . F o r t y p e TO c o n d i t i o n s , NACOND r e f e r s t o a component C^, t h e c o n c e n t r a t i o n o f w h i c h remains c o n s t a n t i n t h e aqueous s o l u t i o n . NACOND c a n n o t r e f e r t o a complex s o l u t e i n t h i s c a s e , b u t any s p e c i e s o f t h e C3-H2O s y s t e m c a n be used w i t h t h e same r e s u l t . When b o t h t y p e o f c o n d i t i o n s a r e i n v o l v e d , t h e t y p e TO c o n d i t i o n s must come f i r s t , t h e n t h e t y p e PK c o n d i t i o n s f o l l o w , and f i n a l l y t h e MCONC c o n c e n t r a t i o n c o n d i t i o n s which a r e o f t y p e TO i n o r d e r t o be i n t e r p r e t e d as concentration l e v e l s . H  I  t  s  A l a s t row (FORMAT (F5.1,211))  i n c l u d e s D I M l , DIM2, NOWRIT arid NODRAW.  As a whole, t h e r e a r e MCOND + MCONC + 3 rows i n f i l e 3.  The program i s c a l l e d a s u s u a l by a $RUN command, t y p e d (or punched) a s f o l l o w s $RDN CEHPHl 3= F i l e 3 4= F i l e 2 5= F i l e l 6=*PRINT* 9=PL0T CEHPH1 i s t h e f i l e c o n t a i n i n g t h e c o m p i l e d program, a n d t h e f i l e PLOT w i l l s t o r e the d a t a f o r p l o t t i n g .  The n e x t page shows a a t y p i c a l p r i n t - o u t o f t h e program. The h e a d i n g r e c a l l s t h e c o n d i t i o n s under w h i c h t h e d i a g r a m i s computed ( t h e system, t e m p e r a t u r e , c o n d i t i o n s on aqueous s o l u t i o n s and t h e c o n s i d e r e d s p e c i e s ) . F o r each p l o t , t h e l i s t o f s o l u t e zones i s p r i n t e d o u t . F o r each o f them, t h e s t a b l e e q u i l i b r i a w i t h one d e g r e e o f freedom, t h e i r e q u a t i o n s i n t h e Eh-pH d i a g r a m s , and t h e name and c o o r d i n a t e s (Eh and pH) o f the boundaries o f t h e i r s t a b i l i t y f i e l d . The name BORD corresponds t o a border o f the diagram. The l i s t i n g o f t h e program i s a v a i l a b l e t h e r e a f t e r .  EH-PH DIAGRAM FOR THE CO- FE- S - H20 SYSTEM AT 473.15 OK SOLID PHASES  :  IONIC SPECIES t  CU-  FE- S -  CUP  TEN CCT  DIG  COV  MAG  HEM  TRO  MPYH PYR  CPY  BNT  FDIG FCCT IDA CUB  ll SS S" S" H20? 25° 02G° S5 COH C2H C3H+ CH3- CH4- F2H F2H2 FH3- FE3 F04rr FSO+ H2SA HS- S22- S32- S42- S52- HS04 S04 HS03 S03 HS20 S20 CUSU FESU CUHS SV  +  NUMBER OF EQUILIBRIA CONSIDERED  90  CONDITIONS ON AQUEOUS PHASE  PK H20 = TO FE2+ «= TO S2- •=  BORDERS OF THE DIAGRAM :  AND THEN :  -0.700 3.000  E PH  +  +  C2SU  FEH1 FEH2 FE2H  +  0  0.0 3.000 4.000 0.0 5.000  AND AND  EQUILIBRIA OF THE SOLID PHASES : FE2+ -H2SA FECUTRO CUBNT CUTRO •', BNT FCCT CUFCCT BNT CUB ' TRO •; CUB BNT . CPY .' V • MAG BNT CPY CUB CPY CUB ' MPYH CPY : MPYH CPY : PYR FDIG • • BNT FCCT "• • FDIG FDIG PYR FDIG . CPY FE2+ -HS04 . FDIG - FCCT PYR - FDIG HEM -r FDIG HEM - FCCT FE2+ -S04 :  4  E PH E = PH E = E = PH E = E = E = PH E •= E = E= E= E= E= E« E E E E  * ' « '  -0.613 4.361 -0.058 4.,361 -0.173 0. 518 4.,361 1.767 1.229 0.758 4.299 2.837 2.837 0. 467 1. 527 0.077 0.467 0.812 0.276 0.213 0.883 0.883  -  PH  BORD FETRO CUBNT CUBNT TRO MPYH CUB BNT TRO CUB MAG FCCT BNT CPY BNT  0.097 PH 0.094 PH 0.282 PH 0.282 PH  HEM HEM PYR FDIG  0.125 PH 0.098 PH 0.262 PH 0.516 PH 0.376 PH 0.282 PH 0.751 0.751 0.188 0.516 0.151 0.188 0.298  PH PH PH PH PH PH  -0.613 -0.613 -0.604 -0.604 -0.584 -0.584 -0.485 -0.485 -0.380 -0.452 -0.452 -0.438 -0.391 -0.295 -0.523 -0.523 -0.121 -0.164  PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH=  3.000 4.361 4.361 4.361 4.202 4.202 4.361 4.361 4.285 4.299 4.299 4.361 4.299 4.058 3.969 3.969 3.132 3.274  E=-0.044 E=-0.121 E=-0.121 E= -0.044  PH= PH= PH= PH=  3.292 3. 566 3. 566 3.292  E= E= E= E= E= E= E= E= E= E= E= E= E= E= E= E= E= E=  : : : :  TRO : E= -0.613 BNT : E= -0.604 FCCT : E= -0.584 --CUB : i E= -0.485 BORD ! E= -0.466 FDIG • E= -0.523 E= -0.438 MPYH E= -0.452 CPY E= -0.295 PYR E= -0.164 FDIG MPYH . E= -0.391 E= -0.391 CPY . E= -0.380 MAG FDIG : E= -0.121 ! E= -0.164 CPY BORD : E= -0.376 BORD : E= -0.097 : E= -0.121 PYR  PH=» PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH= PH=  4.361 4.361 4.202 4.361 3.000 3.969 4.361 4.299 4.058 3.274 4.299 4.299 4.285 3.132 3.274 3.000 3.000 3.132  -0.016 -0.068 -0.044 -0.000  PH= PH= PH= PH=  3.000 3.000 3.292 3.135  BORD BORD FCCT BORD  : : : :  ********************************************************************************************************  Fig.  (A3.01).  Typical  print-out  o f t h e computer  program.  E= E= E= E=  252  C C  c  THERMODYNAMICS OF THE C1-C2-C3-H20 SYSTEM. PROGRAM TO COMPOTE AND PLOT EH-PH DIAGRAMS. ~  -  >-•••  • -  REAL*8 . DETER, SOL,EPS, X, CO,EQCO, HCOND, COMOD, SOLR, BORN,VAGOND, XBORN B, REFPOT, DABS, DLOG, PH20, T, GFOR, DELG INTEGER EQUIL,EQUILI,ORDRE, ISIZE, INDEX, E<XDK,COUPI£,EKITOT,CONTOT, BSOLI,SWITCH,STORE INTEGER*2 TOTL,TYCOND REAL CNAME,BNAME,BORDER DIMENSION aOr^(40,2),GFOR(40,2),EOCO(40,2,9),EOUIL(5) OT BNDEX(6),IMDEX(6),BOOK(40,2),NACOND(9),TYCOND(9),VACOND(9),HCOND(3, B6),EQUILI (2,100, 5) ,NEKIL(2),COMOD(60,6),SOLR(7),SOLI (2),ISTO(15,15 B), IBORN (4),BORN (4),COUPLE (30,20), IND(10) ,NAION (20), STORE (20,20), BTITL2(3),DROLIM(100,2,2),DROEKI(200,2,2) ,DROCON(100,2,2),TITLl(16) DATA PMINUS/ - API^/HVrTOTL/ TO /FFIN/ ' ABORDFJR/'BORD /,BIAN BK/ 'ANLIM/0ANEKI/0/,NCON/0/ COMMON X,EPS,REFPOT f  ,  ,  ,  ,  ,  1  1  C. 900 FORMAT(F6.2,213,E7.1) 902 FORMAT(311,213,4(II,F7.3),F7.3) 903 FORMAT(12) 905 FORMAT(A4,4X F8.0,2X,F6.4,8F7.4) 910 F0RMAT(A2,I3,1X,F7.3) 912 FORMAT('0','CHECK MINERAL ',13,» 915 FORMAT(13) 917 FORMAT(513) 920 FORMAT(2F5.1,211) 922 FORMAT(20A4) C. f  925 927 928 930 931 932 935 937 C 950 952 954 955 956 957 958 959 960 965 C 970  ON CONDITION  \ II)  FORMATCl', 'EH-PH DIAGRAM FOR THE ',3A4, 'H20 SYSTEM AT ',F6.2, ' OK B.') FORMAT('0','SOLID PHASES : »,T20,20 (A4,lX)/' ',T20,20 (A4,1X)) FORMATC ','IONIC SPECIES : ',T20,20 (A4,1X)/' ',T20,20 (A4,1X)) FORMAT('0','CONDITIONS ON AQUEOUS PHASE : ',5X,'PK H20 = ',F7.3) FORMAT('+',3(Al/ ',T37,A2,1X,A4,' = ',F7.3,8X)) FORMATC ', 'CONCENTRATION LIMITS : ',4X,A1,A2,1X,A4, ' = ', BF7.3,9(A1/' ',T37,A2,1X,A4, ' = ',F7.3)) FORMAT (' ', 'NUMBER OF EQUILIBRIA CONSIDERED : ',13,' AND THEN : ' B,I3) FORMAT('0','BORDERS OF THE DIAGRAM : E = ',F7.3,4X,'AND',4X,F7. B3/' ',27X,'PH = ',F7.3,4X,'AND',4X,F7.3) 1  FORMAT('0','EQUILIBRIA OF THE SOLID PHASES :') FORMAT ('0','CONCENTRATION LIMITS FOR ',A2,1X,A4, = FORMATC ',A1,3 (A4,A1, '-')) FORMATC ', 5X,Al, 4 (A4,Al,'- »')) FORMAT(' + ',T35,'E = ',F7.3) FORMAT(' + ',T48,Al, 1X,F7.3, ' PH') FORMAT(' + ',T35, 'PH = \F7.3) FORMAT('+',T65,A4,' : E=',F7.3,3X,'PH=\F7.3) . FORMAT('+',T100,A4,' : E=',F7.3,3X,'PH=',F7.3) FORMAT(*0*,'NO STABLE EQUILIBRIA')  \r7.3 : )  1  ,  ,  t  FORMAT('0','TOTAL NUMBER OF IONIC BOUNDARIES :\l3/ \16X, 'SOL BID EQUILIBRIA :',13/' *,16X,'CONCENTRATION LINES :',I3) 980 FORMAT('0','****************************************************** %  253  g**************************************************ij Q  * * * * * * * * * * * * * *  C  * READ DATA. *  Q  * * * * * * * * * * * * * *  C :, C READ PROPERTIES OF ALL THE SPECIES OF THE C1-C2-C3-H20 SYSTEM. 100 READ(5,900) T,NCPS,NCPI,EPS <' NCP=NCPS DO 105 K=l,2 DO 103 1=1,NCP READ(5,905) CNAME(I,K) ,GFOR(I,K), (EQCO(I,K,L) ,L=1,9) 103 CONTINUE 105 NCP=NCPI C C READ THE NUMBER OF DIAGRAM TO BE COMPUTED. READ(3,903) IWORK NWORK=0 C FOR EACH DIAGRAM, READ ITS DEFINITION. 108 NWORK=NWORK+1 110 READ(3,902) (INDEX(I),1=1,3) ,MCOND,MCONC,(IBORN(I),BORN(I),1=1,4), BPH20 C SELECT COMPOUNDS WHICH BELONG TO THE CONSIDERED SYSTEM (INDEX). 112 NCP=NCPS DO 118 K=l,2 N=0 DO 116 1=1,NCP DO 114 L=l,3 IF(INDEX(L).EQ.0.AND.EOCO(I K,L+3).NE.0.) GO TO 116 114 CONTINUE N=N+1 BOOK(N,K)=I 116 CONTINUE IF(K.EQ.l) NCP1=N NCP2=N 118 NCP=NCPI C C READ THE CONDITIONS ON THE AQUEOUS PHASE AND THE CONCENTRATION C LINES TO BE PLOTTED. 120 MTOT=MCOND+MCONC IF(MTOT.EQ.O) GO TO 130 DO 128 I=l,MTOT READ(3,910) TYCOND(I),NACOND(I),VACOND(I) IF(NACOND(I).EQ.BCOK(l,2)) GO TO 125 DO 123 K=2,NCP2 IF(NACOND(I).EQ.B0OK(K,2)) GO TO 128 123 CONTINUE 125 WRITE(6,912) NACOND(I),I GO TO 1000 128 CONTINUE C C RESET MATRIX INDEX. 130 MSIZE=0 DO 134 1=1,3 ^ TF(INDEX(I) .EQ.0) GO TO 134 MSIZE=MSIZE+1 r  INDEX (3+MSIZE) =3+1 134 CONTINUE DO 136 1=1,3 136 INDEX(I)=1 MSIZE3=MSIZE+3  C C READ SOLID ASSEMBLAGES. 140 REWIND 4 READ(4,915) NBEKIL NB=2 IF(MCONC.EQ.O) NB=1 DO 141 1=1,2 141 NEKIL(I)=0 DO 148 1=1,NBEKIL READ(4,917) (EQUIL(J),J=l,5) ORDRE=0 DO 144 J=l, 5 IF(EQUIL(J).EQ.O) GO TO 145 ORDRE=ORDRE+l DO 142 K=1,NCP1 IF(EQUIL(J).EQ.BOOK(K,l)) GO TO 143 142 CONTINUE GO TO 148 143 EQUIL(J)=K 144 CONTINUE 145 NFF^D=MSIZE+2-MCOND-ORDRE IF(NFREED.NE.l.AND.NFREED.NE.NB) GO TO 148 NEK TL (NFREED)=NEKIL(NFREED)+1 DO 146 J=l,5 146 EQUILI (NFREED, NEKIL (NFREED), J) =EQUIL (J) 148 CONTINUE IF(NEKIL(2).EQ.O) MCONC=0 MTOT=MCCND+MCONC C C READ SPECIFICATIONS OF JOB. 150 READ(3,920) DIML,DIM2, NOWRIT,NODRAW IF(NWORK.EQ.l) READ(5,922) (TITLl (I), 1=1,15) DO 152 1=1,3 152 TITL2(I)=BIANK DO 155 I=1,MSIZE 155 TITL2 (4-1)=CNAME(INDEX(MSIZE+4-I)-3,1) C ; . C ! : • ; . : ;  ;  c  C 160  162 164 166 168  COMPUTE X, MATRIX CO AND REFERENCE POTENTIAL. X=(2.3026D+00*8.314D+00*T)/9.6484D+04 NCP=NCPS DO 166 K=l,2 DO 164 1=1, NCP DELG=+EQCO (I,K, 3) *GFOR (I,K) +EQCO (I,K, 2) *GPCR (1,2) DO 162 J=2, 5 DE^DFiG+FX3CO(I,K,J+2)*GFOR(J,2) OO(I,K)=+(4.184D+00*DFlX3/9.6484D+04)-EQCO(I,K,7)*X*PH2O NCP=NCPI REFPOT=0.5D+00*CO(6,2)  255  C SET BOUNDARIES IN ORDER AND C FILL OUT THE CORRESPONDING LINES OF MATRIX COMOD. 170 DO 172 I=l 4 DO 172 J=l,6 172 COMOD(I,J)=0.0D+00 XBORN=l.0D+00 DO 176 1=1,2 IF(I.EQ.2) XBORN=X NAX=0 COMOD(2*1-1,I)=-1.OD+00/XBORN COMOD(2*1,I)=1.0D+00/XBORN DO 176 J=l,4 IF(IBORN(J) .NE.I) GO TO 176 NAX=NAX+1 IF(NAX.EQ.2) GO TO 174 COMOD (2*1-1,3)=-BORN(J) GO TO 176 174 IF(BORN(J) .LT.-COMOD(2*I-1,3)) GO TO 175 COMOD (2*1,3)=BORN(J) GO TO 176 175 CC*OD(2*I,3)=-COMOD(2*I-1,3) COMOD (2*1-1,3)=-BORN (J) 176 CONTINUE Wl=-COMCD(l,3) W2=COMOD(2,3) W3=-COMOD (3,3) COMOD(1,3)=COMOD (1,3)-REFPOT COMOD(2,3)=COMOD(2,3)+REFPOT C C WRITE INPUT DATA. 180 WRITE(6,925) (TITL2 (I), 1=1, 3) ,T WRITE(6,927) (CNAME(BOOK(1,1),1), I=l,NCPl) WRITE(6,928) (CNAME(BOOK(1,2),2),I=1,NCP2) WRITE(6,935) NEKIL(1),NEKIL(2) WRITE(6,930) PH20 IF (MCOND.NE. 0) WRITE (6,931) (FIN,TYCOND (I),CNAME (NACOND (I), 2), VACOND B (I), 1=1, MCOND) IF (MCONC.NE. 0) WRITE (6,932) (FIN, TYCOND (MCOND+I), CNAME (NACOND (MCOND+ BI), 2), VACOND (MCOND+I), 1=1,MCONC) WRITE(6,937) Wl,W2,W3,COMOD(4,3) WRITE (6,980) C / ; f  ;  Q  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  C  * COMPUTE THE SOLUTE ZONES. *  Q  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  C 200 NBCOP=l LSIZE=0 SWTTCH=1 LIMTOT=0 CONTOT=0 EKITOT=0 DO 202 J=l,3 202 IMDEX(J)=J IF(MCOND.EQ.O) GO TO 300 COUPLE(1,4)=0  !  256  C 203 LSIZE=LSIZE+1  c• C  >• '  . •  CASE OF THE TYPE PK CONDITIONS. IF (TYCOND (LSIZE). EQ.TOTL.CR. SWITCH. EQ. 2) GO TO 210 DO 205 J=l NBCOP 205 COUPLE(J,LSIZE)=NACOND(LSIZE) CO(NACOND(LSIZE),2)=00(NACOND(LSIZE),2)/EQCO (NACOND(LSIZE) ,2,3)-X* BVACOND (LSIZE) IF(LSIZE.EQ.MCOND) GO TO 300 GO TO 203 C C CASE OF THE TYPE TO CONDITIONS : C COMPUTE THE SOLUTE ZONES OF THE CORRESPONDING CI-H20 SUBSYSTEM. 210 NODRO2=0 DO 212 J=l,3 IF(EQCO(NACOND(LSIZE) ,2,J+3) .NE.0.0D+00) GO TO 213 212 CONTINUE 213 IND(LSIZE)=J 215 IMDEX(4)=IND(LSIZE)+3 NAION(1)=NACOND(LSIZE) NBION=l DO 216 J=l,4 216 COMCD(5,J)=EQCD(NAION(l),2,IMDEX(J))/EQCO(NAION(l),2,3) COMOD (5,3) =00 (NAION (1), 2) /EQCO (NAION (1), 2,3) -X*VACOND (LSIZE) -X*DLO BG (2.0D+00*DABS (EQCO (NAION (1), 2, IMDEX (4)))) DO 220 K=1,NCP2 IF (BOOK (K, 2) .EQ.NAION (1) .OR.EOCO (BOOK (K, 2), 2,3+IND (LSIZE)) .EQ. 0.0D B+00) GO TO 220 DO 217 J=l,3 IF(J.EQ.IND(LSIZE)) GO TO 217 IF(EQCO(BOOK(K,2), 2,J+3).NE.0.0D+00) GO TO 220 217 CONTINUE NBION=NBION+l NAION (NBION)=BOOK(K,2) DO 218 J=l,4 218 COMOD(NBION+4,J)=EQCO(BOOK(K,2),2,IMDEX(J))/EQCO(BOOK (K,2),2,3) COMOD (NBION+4,3) =00 (BOOK (K, 2), 2) /EQCO (BOOK (K, 2), 2,3) -X*VACOND (LSIZ BE)-X*DLOG(2.0D+00*DABS(EQCO (BOOK(K,2),2,IMDEX(4)))) 220 CONTINUE NCOND=0 ISIZE=1 NCP=NBION+4 225 NSTAB=0 DO 240 K=l,NBION EQUIL(l)=K+4 NBLIM=0 IONLIM=0 DO 235 J=1,NCP NODROl=0 IF(J.LE.4.0R.J.GT.K+4) GO TO 229 IF(NSTAB.EQ.0.OR.J.EQ.K+4) GO TO 235 DO 227 L=l,NSTAB IF (NAION (J-4) .EQ.COUPLE (L, 1)) GO TO 228 227 CONTINUE V GO TO 235 f  257  228 N0DR01=1 229 EQUIL(2)=J CALL FRIEND(ISIZE,EQUIL,NCCW,HCOND,NCP,CCMCD,SOIR,SOLI) IF (SOLI (1) .EQ.O) GO TO 235 NBLIM=NBLIM+1 IF (NBLIM.GE. 2) GO TO 230 NSTAB=NSTAB+1 COUPLE(NSTAB,1)=NAION(K) COUPLE(NSTAB,2)=0 COUPLE (NSTAB,3)=0 230 IF(J.LE.4) GO TO 235 IONLIM=IONLIM+l COUPLE(NSTAB,IONLIM+3)=NAION(J-4) IF(NODR01.FjQ.l.CR.SWrTCH.EQ.2) GO TO 235 LIMTOT=LIMTOT+1 DO 232 1=1,2 DO 232 M=l,2 232 mOLIM(LT3irOT,L,M)=SOLR(2*L+M+l) 235 CONTINUE IF (NBLIM.NE. 0) COUPLE (NSTAB, IONLIM+4) = 0 240 CONTINUE NBCOP=NSTAB DO 243 J=l,NBION 243 CO (NAION (J), 2) =00 (NAION (J), 2) /EQCO (NAION (J), 2,3) -X*VACOND (LSIZE) -X B*DLOG(DABS (EQCO (NAION (J), 2, IMDEX (4)))) IF (MCOND.EQ.l. AND.SWITCH.EQ.l.CR.MOT 2) GO TO B 300 IF(LSIZE.GT.1.0R.SWITCH.EQ.2) GO TO 260 C C STORE SET OF SOLUTE ZONES. 250 DO 255 I=l,NBCOP DO 253 J=l,20 STORE(I,J)=COUPLE(I,J) IF(COUPLE(I,J).EQ.0.AND.J.GE.4) GO TO 255 253 CONTINUE 255 CONTINUE 257 NBSTO=NBCOP ' GO TO 203 C C COMBINE SETS OF SOLUTE ZONES. 260 ISIZE=LSIZE IF(SWITCH.EQ.2) ISIZE=MCOND+l , NCOND=0 DO 263 J=l,NBCOP DO 262 K=l, 15 ISTO (J,K)=COUPLE(J,K) IF(COUPLE(J,K).EQ.0.AND.K.GE.4) GO TO 263 262 CONTINUE 263 CONTINUE DO 265 K=l,ISIZE 265 EQUIL (K)=K+4 NSTAB=0 DO 288 I=l,NBSTO DO 266 K=2,ISIZE 266 NAION (K-1) =STORE (I, K-1) DO 268 K=l, 20  IF(ST0RE(I,K+3).EQ.O) GO TO 270 268 NAION (K+ISIZE) =STORE (I K+3) 270 NCPINT=K+ISIZE+3 DO 287 J=l,NBCOP NAION(ISIZE)=ISTO (J 1) DO 272 K=l, 20 IF(ISTO(J K+3) .EQ.O) GO TO 275 272 NAION (NCPINT+K-4) =ISTO (J, K+3) 275 NCP=NCPINT+K-1 DO 277 K=2,ISIZE 277 IMDEX(K+2)=3+IND(K-l) IMDEX(ISIZE+3)=3+TND(LSIZE) ISIZE3=ISIZE+3 DO 281 K=5,NCP DO 280 L=1,ISIZE3 280 COMOD (K, L) =EQCO (NAION (K-4), 2, IMDEX (L)) /EQCO (NAION (K-4) ,2,3) 281 COMOD (K 3)=00(NAION (K-4), 2)-X*DLOG(2.0D+00) NBLIM=0 IONLIM=0 DO 285 K=1,NCP DO 282 L=l,ISIZE IF(K.EQ.L+4) GO TO 285 282 CONTINUE EQUIL(ISIZE+1)=K CALL FRIEND (ISIZE, EQUTL, NCOND, HCOND,NCP, COMOD, SOLR, SOLI) IF(SOLI(l).EQ.0) GO TO 285 NBLIM=NBLIM+1 IF (NBLIM.GE.2) GO TO 284 NSTAB=NSTAB+1 COUPLE(NSTAB,ISIZE)=NAION(ISIZE) TF(ISIZE.EQ.3) GO TO 284 DO 283 L=ISIZE3,5 283 COUPLE(NSTAB,L-2)=0 284 IF(K.LE.4) GO TO 285 IONLIM=IONLIM+l COUPLE (NSTAB, IONLIM+3) =NAION (K-4) 285 CONTINUE IF(NBLIM.EQ.O) GO TO 287 DO 286 L=2, ISIZE 286 COUPLE(NSTAB,L-l)=NAION(L-l) COUPLE (NSTAB,IONLIM+4)=0 287 CONTINUE 288 CONTINUE NBCOP=NSTAB 290 IF (LSIZE. LT.MCOND) GO TO 250 C f  f  f  f  Q  C C  c  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  * COMPUTE THE DIAGRAMS AND WRITE THE DATA. * ********************************************  C COMPUTE EQUILIBRIA WITH THE SOLID PHASES. 300 ISIZE=MSIZE IF(SWITCH.EQ.1.AND.NEKIL(1).EQ.0) GO TO 355 ISIZE3=ISIZE+3 NCOND=MCOND-l+SWTTCH DO 306 1=1,NCPI  259  DO 305 L=l,ISIZE3 305 COMOD (I+4,L)=EQCO(BCOK(I,l) ,1,INDEX(L))/EQCO (BOOK(I l),1,3) 306 COMCD(I+4 3)=CO(BOOK(I,l),l)/FjQCO(BCOK(I,l) l 3) IF(NOWRIT.EQ.O.AND.SWITCH.EQ.l) WRITE(6,950) IF(NOWRIT.EQ.0.AND.SWITCH.EQ.2) WRITE(6,952) TYCOND(LSIZE),CNAME(N BACOND (LSIZE), 2), VACOND (LSIZE) NSTAB=0 NCP=NCPl+4 C C IN EACH SOLUTE ZONE, COMPUTE A LINEAR DIAGRAM. DO 350 I=l,NBCOP IF(NOOND.EQ.O) GO TO 323 IF(NOWRIT.EQ.O) WRITE (6,954) (FTN,CNAME(COUPLE (I, J), 2), J=l,NCOND) DO 310 J=l,NCOND DO 308 L=1,ISIZE3 308 HCOND (J,L) =EQCO (CCOTLE (I, J), 2, INDEX (L)) /EQCO (COUPLE (I, J) 2,3) 310 HCDND(J,3)KX)(COUPLE(I,J),2) DO 320 J=l,20 IF(COUPLE(I,J+3).EQ.O) GO TO 322 DO 315 L=1,ISIZE3 315 COMOD(NCP1+J+4,L)=EQCO(COUPLE(I,J+3), 2, INDEX(L))/EQCO (COUPLE(I,J+3 B),2,3) 320 Cn^(NCPl+J+4,3)=CO(COUPLE(I,J+3),2) 322 NCP=NCPl+J+3 323 ISIZEl=ISIZE+l-NCOND NSW=NEKIL (SWITCH) DO 340 K=1,NSW DO 325 L=1,ISIZE1 325 EQUIL (L) =EQUILI (SWITCH,K,L) +4 CALL FRIEND (ISIZE,F^UILjNCX^^^CONDjNCP,COMOD,SOLR, SOLI) IF(SOLI(1).EQ.O) GO TO 340 NSTAB=NSTAB+1 IF (SWITCH.EQ. 2) GO TO 330 DO 328 J=l,2 DO 328 L=l,2 328 DROEKI (NSTAB, J, L) =SOLR (2*J+L+1) GO TO 335 330 DO 333 J=l,2 DO 333 L=l,2 333 DROCON (NSTAB+CONTOT,J,L)=SOLR(2*J+L+1) C C PRINT THE DATA. 335 IF(NOWRIT.EQ.l) GO TO 340 WRITE(6,955)(FIN,CNAME(BOOK(EQUIL(L)-4,1), 1), L=l,ISIZEl) IF(SOLR(l).EQ.-l.0D+00) GO TO 337 WRITE(6,956) SOLR(2) SGE=PMTNUS IF(SOLR(3) .EQ.O.OD+00) GO TO 338 IF (SOLR(3) .GT.0.0D+00) GO TO 336 SGE=PLUS SOLR(3)=-SOLR(3) 336 WRITE(6,957) SGE,SOLR(3) GO TO 338 337 SOLR(2)=SOLR(2)/X WRITE(6,958) SOLR(2) 338 DO 339 J=l,2 r  f  f  r  r  260  IF(SOLI(J).EE.4) BNAME=BORDER TP (SOLI (J) .GE. 5.AND.SOLI (J) .LE.NGPl+4) BNAME=CNAME (BOOK (SOLI (J) -4, Bl),l) IF(SOLI(J).GT.NCPl+4) BNAME=CNAME(COUPLE(I,SOLI(J)-NCPl-l),2) IF(J.EQ.l)WRITE(6 959) BNAME,SOLR(4), SOLR (5) IF(J.EQ.2)WRITE(6,960) BNAME,SOLR(6),SOLR(7) CONTINUE CONTINUE CONTINUE IF(NOWRIT.EQ.O.AND.NSTAB.EQ.O) WRITE(6,965) WRITE (6,980) IF(SWITCH.EQ.l) EKITOT=NSTAB IF(SWTTCH.EQ.2) CON^OT=CO^r^OT+NSTAB IF (LSIZE.EQ.MTOT) GO TO 400 SWITCH=2 TP (MCOND.EQ.LSIZE. AND.MCOND.NE. 0) GO TO 250 GO TO 203 r  339 340 350  355  C C C  400  PLOT THE DIAGRAM. IF(NODRAW.EQ.l) GO TO 1000 PLOT AXIS. XMl=-COMCD (1, 3) XM2=-COMOD(3,3) DX1=(COMOD (2,3)+COMOD(1,3)) /DIML DX2=(COMOD(4,3)+COMCD(3,3))/DIM2 CALL AXIS(0.,0.4,•POTENTIAL IN VOLT*,17,DIM1,90.,XM1,DX1) V CALL AXIS(0.,0.4, PH ,-2,DTM2,0.,XM2,DX2) PLOT TITLE. CALL SYMBOL(0.,-0.2,0.14,TITL1,0.,60) CALL SYMBOL(2.64,-0.2,0.14,TITL2,0.,12) CALL NUMBER(5.76,-0.2,0.14,T,0.,2) IF(MCOND.NE.0) GO TO 405 CALL SYMBOL(0.,-0.4,0.14,'NO CONDITION',0., 12) GO TO 413 DO 410 1=1,MCOND SX=I CALL SYMBOL(2.4*(SX-l.),-0.4,0.14,TYCOND(I) ,0.,2) CALL SYMBOL(2.4*(SX-1.)+0.24,-0.4,0.14,CNAME(MCOND(I),2),0.,4) CALL SYMBOL(2.4*(SX-1.)+0.84,-0.4,0.14,'=',0.,1) CALL NUMBER(2.4*(SX-1.)+1.08,-0.4,0.14,VACOND(I), 0.,3) CONTINUE PLOT IONIC REGIONS. IF (LIMTOT.EQ. 0) GO TO 420 CALL DASHLN (. 04,. 04, .04, .04) DO 415 I=l,LIMTOT CALL PLOT((DROLIM(I,l,2)-XM2)A>X2, (DROLIM(I,l,l)-XMl) A>Xl+0.4,3) CALL PL0T((mOLIM(I,2,2)-XM2)/DX2, (DROLIM(I,2,l)-XMl)/TJXl+0.4,4) CONTINUE PLOT EQUILIBRIA BETWEEN SOLID PHASES. TP (EKITOT.EQ.0) GO TO 430 DO 425 I=1,EKIT0T CALL PLOT((DROEKI(I,l,2)-XM2)/bX2, (DROEKI (I,l,l)-XMl)/DXl+0.4,3) CALL PLOT( (DROEKI (1,2,2)-XM2)/DX2, (DROEKI(1,2,1)-XMl)/DXl+0.4,2) CONTINUE PLOT CONCENTRATION LIMITS. IF(CONTOT.EQ.O) GO TO 440 ,  C  405  410 C 413  415 C 420  C  425 430  ,  261  CALL DASHLN (. 36,. 06,. 04,.06) DO 435 I=l OONTOT CALL PLOT((r«OCON(I lf2)-XM2)A>X2, (H<OCON(I,l l)-XMl)/DXl+0.4,3) CALL PLOT((DROCON(I,2,2)-XM2)/bX2, (mOCON(I,2,l)-XMl)/DXl+0.4,4) 435 CONTINUE f  r  440  f  NLIMFNLIM+LIMTOT  NEKI=NEKI+EKITOT NCON=NCON4CONTOT C  C  GO AND COMPUTE NEXT DIAGRAM, OR END T H E PLOT. IF(NWORK.EQ.IWORK) GO T O 445 C A L L PLOT(DIM2+3. 0.,-3) GO T O 108 C A L L PLOTND f  445 C C  E N D OF  T H E PROGRAM.  WRITE(6,970) NLIM,NEKI,NOON 1000  STOP  END  C C Q  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  C C  * SUBROUTINE "FRIEND' TO COMPUTE EQUILIBRIA, AND * * DETERMINE THEIR STABILITY RANGE I N T H E DIAGRAM. *  Q  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  C  SUBROUTINE FRIEM) (ISIZE, EQUIL, NCOND,HCOND,N<^ IMPLICIT REAL*8(A-H,0-Z) INTEGER ORDRE, EQUIL, SOLI DIMENSION ECjUIL(5),HCOND(3,6),A(5,6),COMOD(60,6),SOL(5,5),SOLR(7), BSOLI (2), BX (2, 5), POTEQ (2) COMMON X,EPS,REFPOT  C 1  C C  ORDRE=ISIZE+l DO 3 K=l,2 3 SOLI(K)=0 DO 5 J=l,5 DO 5 K=l,6 5 A(J,K)=0.0D+00  6 7 8 10 12 13 15  COMPUTE MATRIX A . IF(NCOND.EQ.O) GO TO 10 DO 8 J=l,NCOND DO 6 L=l, ISIZE A(J,L)=HCOND(J,L+3) DO 7 1=1,3 A(J,ISIZE+L)=HCOND(J,L) CONTINUE NlCOND=NCOND+l DO 15 J=N100ND,ORDRE DO 12 1=1,ISIZE A (J,L)=COMOD(EQUIL(J-NCOND), L+3) DO 13 L=l,3 A(J,ISIZE+L)=COMOD (EQUIL(J-NCOND),L) CONTINUE  262  C  C C C C  C C  COMPUTE EQUILIBRIUM. SOLR(1)=-1.0D+00 20 SOLR(l)=-SOLR(l) CALL PETERS(A, ORDRE,SOL,DETER) IF(DETER.NE.0.0D+00.AND.SOLR(l) .EQ.l.OD+00) GO TO 28 IF(DETER.EQ.0.0D+00.AND.SOLR(l) .EQ.-1.0D+00) GO TO 80 DO 25 J=l, 5 APRIME=A(J, ISIZE+1) A (J,ISIZE+1)=A(J,ISIZE+2) 25 A(J,ISIZE+2)=APRIME IF(SOLR(l).EQ.l.OD+00) GO TO 20 SOLR(2)=SOL(ISIZE+1,2) GO TO 30 28 SOLR(2)=SOL(ISIZE+1,2)-REFPOT SOLR(3)=SOL(ISIZE+1,1)*X STABILITY RANGE OF THAT EQUILIBRIUM. DETERMINE TWO STARTING POINTS BY INTERSECTING WITH AXES. 30 NBSTAB=0 NORDRE=ORDRE QRDRE=ORDRE+l DO 40 K=l,4 DO 32 L=NlCOND,NORDRE IF (EQUIL (L-NCOND) .EQ.K) GO TO 40 32 CONTINUE EQUIL(ORDRE-NCOND)=K DO 35 L=l, ISIZE 35 A(ORDRE,L)=COMOD(K, L+3) DO 37 L=l,3 37 A(CmiE,ISIZE+L)=COMOD(K,L) CALL PETERS(A,ORDRE,SOL,DETER) IF(DETER.EQ.0.0D+00) GO TO 40 NBSTAB=NBSTAB+1 SOLI(NBSTAB)=K ISIZE2=ISIZE+2 DO 39 L=1,ISIZE2 39 BX(NBSTAB,L)=SOL(L,l) IF (NBSTAB.EQ. 2) GO TO 50 40 CONTINUE SCAN ALL COMPOUND, AND CHECK FOR STABILITY. DO 70 K=1,NCP DO 52 L=N1C0ND,NORDRE IF(EQUIL(L-NCOND).EQ.K) GO TO 70 52 CONTINUE IF(K.EQ.SOLI(l).OR.K.EQ.SOLI(2)) GO TO 70 DO 55 L=l,2 POTEQ (L) =COMOD (K, 3) -COMOD (K, 2) *BX (L, ISIZE+2) -COMOD (K, 1) *BX (L, ISIZE B+l) DO 55 J=l,ISIZE 55 POTEQ (L)=POTEQ(L)-COMOD (K, J+3) *BX(L,J) IF(POTFX3(1).GT.O.OD+OO.AND.POTEQ(2).GT.O.OD+O0) GO TO 70 IF(PCOEQ(l)*POTEQ(2).LT.0.0D+00) GO TO 58 SOLI(1)=0 GO TO 80 50  58 N=l IF(P0TEQ(1) .GT.O.OD+00) N=2 EQUIL(ORDRE-NCOND)=K DO 60 L=l ISIZE 60 A(ORDRE,L)=COMOD(K,L+3) DO 62 L=l 3 62 A (ORDRE, ISIZE+L) =COMOD(K,L) CALL PETERS (A,ORDRE,SOL,DETER) SOLI(N)=K DO 65 L=l,ISIZE2 65 BX(N,L)=SOL(L,l) 70 CONTINUE DO 72 L=l,2 SOLR(2*L+2)=BX(L ISIZE+1)-REFPOT 72 SOLR(2*L+3)=BX(L,ISIZE+2)/X f  f  f  C  80  RETURN END  C  c fj  ******************************************  C C  * SUBROUTINE "PETERS" TO COMPUTE SOLUTIONS OF SIMULTANEOUS * * LINEAR EQUATIONS BY THE MAXIMUM PIVOT STRATEGY.*  Q  * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *  C  1 3 5 6  8 9  11 12 13  SUBROUTINE PETERS (A,ORDRE,SOL,DETER) IMPLICIT REAL*8(A-H,0-Z) INTEGER ORDRE DIMENSION A(5,6),B(5,6), SOL (5, 5), TROW (5), JCOL (5) COMMON X,EPS,REFPOT DO 3 Ll=l,5 DO 3 L2=l,6 B(L1,L2)=A(L1,L2) CONTINUE DETER=1.0D+00 DO 18 K=l,ORDRE KM1=K-1 PIVOT = 0.0D+00 DO 11 1=1,ORDRE DO 11 J=l,ORDRE IF(K.EQ.l) GO TO 9 DO 8 ISCAN =1,KM1 DO 8 JSCAN =1,KM1 IF(I.EQ.IROW(ISCAN)) GO TO 11 IF(J.EQ.JCOL(JSCAN)) GO TO 11 CONTINUE IF(DABS(B(I,J)).LE.DABS(PIVOT)) GO TO 11 PIVOT = B(I,J) IROW(K)=I JCOL(K)=J CONTINUE IF (DABS (PIVOT) .GT.EPS) GO TO 13 DETER = 0.0D+00 RETURN DETER=DETER * PIVOT DO 14 J=l,6  14 B(IROW(K), J)= B(IROW(K), J)/PIVOT 15 DO 18 1=1,ORDRE IF(I.EQ.IROW(K)) GO TO 18 BICOLK=B (I, JCOL (K)) DO 17 J=l,6 B(I,J)= B(I, J)-B(IROW(K),J)* BICOLK 17 CONTINUE 18 CONTINUE 19 IORDRE=ORDRE+l DO 21 1=1, ORDRE DO 20 J=IORDRE,6 20 SOL (JCOL (I), J-ORDRE) =B (IROW(I), J) 21 CONTINUE DETER=DABS(DETER) RETURN END  


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