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Activity of ZnO in the ternary system ZnO-CaO-SiO2 Fairweather, Michael John 1967

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THE ACTIVITY OF ZnO IN THE TERNARY SYSTEM ZnO-CaO-SiO,  by MICHAEL JOHN FAIRWEATHER  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER. OF APPLIED SCIENCE IN THE DEPARTMENT OF METALLURGY  We accept t h i s thesis as conforming to the standard required from candidates f o r the degree of MASTER OF APPLIED SCIENCE  Members of the Department of Metallurgy  THE UNIVERSITY OF BRITISH COLUMBIA February,  I967.  In p r e s e n t i n g t h i s t h e s i s  in p a r t i a l  f u l f i l m e n t of  requirements f o r an advanced degree at the U n i v e r s i t y of Columbia, for  I agree t h a t the L i b r a r y  r e f e r e n c e and s t u d y .  s h a l l make i t  freely  the  British available  I f u r t h e r agree that p e r m i s s i o n f o r  ex-  t e n s i v e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y purposes may be gran by the Heacl o f my Department o r by h i s  representatives.  understood t h a t c o p y i n g o r p u b l i c a t i o n of t h i s t h e s i s f o r cial  g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n  Department of  Metallurgy  The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date  F e b r u a r y 7,  1967  It  is  finan-  permission.  - i -  ABSTRACT  The  a c t i v i t y o f ZnO i n t e r n a r y Zno-CaO-SiO^ s l a g s h a s ; been measured  a t 1 3 0 0 C b y e q u i l i b r a t i o n w i t h copper r i c h b r a s s and low oxygen p o t e n t i a l gas u t i l i z i n g the f o l l o w i n g r e v e r s i b l e Pt I H ,H 0 2  2  galvaniccce.il:  || 0 . 8 5 Z r 0 - O . I 5 C a O 2  || 0  2 ( A i r )  |Pt  Thermodynamic d a t a on t h e component b i n a r i e s was employed t o c a l c u l a t e the excess f r e e energy o f t h e t e r n a r y system and t h e i s o a c t i v i t y p a t t e r n s o f the t h r e e components a t 1600 standard s t a t e s . ZnO.  C with respect t o the metastable  pure  liquid  An e s t i m a t e o f 6 E.U. was made f o r t h e e n t r o p y o f - f u s i o n iofu  The measured a c t i v i t i e s a r e i n good agreement w i t h t h e c a l c u l a t e d v a l u e s .  The  proposed  excess f r e e energy contours  tnoth&i'ZnOcCaQoSiOg  t e r n a r y a r e s i m i l a r i n shape t o those c a l c u l a t e d i n a s i m i l a r manner f o r t h e FeO~CaO~SiO„ system.  A l s o t h e c a l c u l a t e d z i n c oxide i s o a c t i v i t y f i g u r e  resembles  'c. the f e r r o u s oxide i s o a c t i v i t y diagram. weerds the lime o r t h o s i l i c a t e  composition.  T h i s z i n c oxide i s o a c t i v i t y p a t t e r n p r o j e c t s t o ThlS:. shape i s c h a r a c t e r i s t i c o f FeO,  'but i n t h e case o f ZnO the p r o j e c t i o n i s l e s s pronounced. are i n k e e p i n g w i t h t h e s l i g h t l y more b a s i c b e h a v i o u r  B o t h these  of zinc  oxide.  observations  ii  ACKNOWLEDGEMENT  The author would l i k e to extend his sincere thanks to his research director, Dr. C  S. Samis f o r his continued encouragement and guidance  throughout t h i s work.  The explanations and contributions by Dr. G. W. Toop  and Dr. W. G. Davenport are greatly appreciated.  The help and interest  shown by various members of the faculty, s t a f f and especially fellow graduate students i s warmly acknowledged. Appreciation i s expressed to the Defence Research Board and the National Research Council of Canada whose f i n a n c i a l support made t h i s work possible.  iii  TABLE OF CONTENTS Page I.  II.  INTRODUCTION A.  General  1  B.  Previous Work  1  C.  Scope of Present Investigation  2  D.  Experimental Method  3  THERMODYNAMIC . MEASUREMENT BY OXYGEN HALF-CELLS A.  B. III.  B.  3  Theory of Oxygen S o l i d E l e c t r o l y t e s  3  1.  Defect Structure  3  2.  Conduction Mechanism  ^ 6  C r i t e r i a for R e v e r s i b i l i t y  THERMODYNAMIC CALCULATIONS A.  IV.  1.  "  9  Binary Oxide Systems  9  1.  CaO-Si0  9  2.  ZnO-CaO  3.  ZnO-Si0  2  '  9 11  2  ZnO-CaO-Si0 Ternary  11  2  EXPERIMENTAL  18  A.  Equipment  18  1.  Oxygen C e l l Design  18  2.  Furnace  18  3.  Temperature Control  k.  Emf Measurement  18  5.  P u r i f i c a t i o n Train  23  6.  A i r Pump  23  .  18  iv  TABLE OF CONTENTS  (continued) Page  B.  C.  Materials  23  1.  Reagents  23  2.  Crucibles  23  3.  Oxygen C e l l s  23  k.  Electrodes  23  Procedure  2k  1.  Oxygen P o t e n t i a l  2k  a.  Oxygen P o t e n t i a l Range Available  2k  b.  Oxygen P o t e n t i a l Control  2k  c.  P u r i f i c a t i o n Train  d.  Duration of Run  2.  3.  V.  . .  25 25  Zinc A c t i v i t y  25  . . . :  a.  A l l o y Preparation  25  b.  Sampling  25  c.  Analysis  26  Slags  26  a.  Preparation  26  b.  Sampling  c.  Analysis  ' .  28 28  k.  Time f o r E q u i l i b r i a  28,  5.  R e v e r s i b i l i t y of the Oxygen Half C e l l . . . .  28  RESULTS  31  A.  Zinc Oxide A c t i v i t y  31  B.  S o l i d Zinc Oxide Saturation Line  3^  C.  Slag Analysis  3^  TABLE OF CONTENTS (continued) Page VI.  INTERPRETATION OF RESULTS A.  36  Calculation of a ZnO (Liquid Standard State) i n ZnO-CaO-Si0 Slags  36  2  B.  Comparison between Experimental G^^nO  ^ Calculated ZnO I s o a c t i v i t y Lines i n the ZnO-CaO-Si0 System  37  Comparison with Davenport's Calculated (X  <£ Q  an<  2  C.  Data f o r the ZnO-CaO-Si0  n  Ternary  2  37  6 D.  Comparison with Work by Azuma, Goto and Ogawa . .  40  E.  Comparison Between Zn0-Ca0-Si0 and Fe0-Ca0-Si0 Ternaries  hO  2  1.  Zn0-Si0 and Fe0-Si0  2.  Fe0-Ca0-Si0 Ternary  2  2  Binaries  2  2  kO k-2  VII.  SUGGESTIONS FOR FURTHER WORK  k2  VIII.  CONCLUSIONS  k6  IX.  REFERENCES  ^7  X.  APPENDICES I. II. III. IV. V.  Calculation: of I n f i n i t e l y Dilute Properties of Zinc i n the Copper-Zinc System  ^9  The System ZnO-Si0  53  2  Toop's Ternary Integration Technique  65  Oxygen P o t e n t i a l Limits  69  Free Energy of Formation of Zn SiO,  70  vi  LIST OF FIGURES  F i g . No-  Page  la.  Pure Z i r c o n i u m D i o x i d e  5  lb.  Z i r c o n i u m D i o x i d e w i t h Calcium Oxide A d d i t i o n  5  2.  Oxide C o n d u c t i v i t y as a F u n c t i o n o f Oxygen P a r t i a l Pressure- -^  3-  C o n d u c t i v i t y R e a c t i o n s a t Cathode and Anode i n an Oxygen  1  . Electrolyte k.  w i t h a Large C o n c e n t r a t i o n o f Oxygen Ion V a c a n c i e s  Excess Free Energy  .  8  of the CaO-SiOg B i n a r y a t l600°C Based on  the M e t a s t a b l e Pure L i q u i d  Standard S t a t e s ?  5.  Phase Diagram, ZnO-SiOg S y s t e m  6.  C a l c u l a t e d Excess Free Energy  7-  Calculated.AF  8.  C a l c u l a t e d I s o a c t i v i t y L i n e s f o r ZnO  9.  Calculated I s o a c t i v i t y Lines f o r S i 0  X S  7  10 12  1  i n the Zn0-Si02 B i n a r y a t l600°C  of the Z n 0 - C a 0 - S i 0  T e r n a r y a t l600°C  2  ...  Ik  15  a t l600°C 2  13  a t l600°C  -  16  10.  C a l c u l a t e d I s o a c t i v i t y L i n e s f o r CaO  11.  The E x p e r i m e n t a l Layout  19  12.  Schematic  20  13.  Oxygen C e l l  21  Ik.  Temperature P r o f i l e of Super K a n t h a l Furnace a t 1300°C . . .  22  - 15.  17  a t l600°C  Diagram of the E x p e r i m e n t a l Apparatus  S t a n d a r d i z a t i o n Curves  f o r the SP-90 Atomic A b s o r p t i o n U n i t  as a F u n c t i o n of the Zn t o Cu R a t i o i n the Standards  . . . .  16.  E x p e r i m e n t a l V a r i a t i o n i n A c t i v i t y o f ZnO  17.  C o n d u c t i v i t y o f O.85 Z r 0 - 0.15 CaO S o l i d E l e c t r o l y t e F u n c t i o n o f Oxygen P o t e n t i a l a t 1300°C  18.  Data from Runs I and K (ZnO S a t u r a t e d ) Together w i t h C a l c u l a t e d T h e o r e t i c a l L i n e f o r Z i n c Oxide S a t u r a t i o n . . . .  19-  as a F u n c t i o n o f Time  2  as a  29  30 35  Measured ZnO A c t i v i t y Values Compared w i t h the C a l c u l a t e d ZnO I s o a c t i v i t y L i n e s i n the Zn0-Ca0-Si02 T e r n a r y  20.  27  Comparison Between the I s o a c t i v i t y L i n e s f o r ZnO C a l c u l a t e d by Davenport-  5  and i n the P r e s e n t Study  38 a t l600°C 39  vii LIST OF FIGURES  (continued)  F i g . No21-  Page Comparison Between the Excess Free Energies of the Binaries Q  FeO-Si0  2  and Zn0-Si0  2  at 1600  C  ^1  22.  Calculated A F  23.  Calculated I s o a c t i v i t y Lines f o r FeO at l600°C  2k-  Data  25-  Thermodynamic Data on the I n f i n i t e l y Dilute Free Energy of  X S  of the FeO-CaO-Si0 Ternary at l600°C. . . . 2  of Everett, Jacobs and Kitchener-^  43 kk  51  1  Zinc i n Copper  52  26.  ZnO-Rich Side of Zn0-Si02 B i n a r y  27.  Estimate of Enthalpy of Fusion f o r ZnO from the Liquidus Line  55  28-  Graphical Integration of the Liquidus Curve of Zn SiO^. . . .  59  29. 30.  5k  1  2  CX Plots f o r Zn0-Si0 Binary Comparison Between the Free Energy of the Zn0-Si0 Binary at l600°C as Given by Richardson and as derived i n the Present Study 2  62  2  31.  D e f i n i t i o n and Location of Terms Used i n Appendix I I I ^ .  32.  CX Plots f o r the Fe0-Si0  33.  0( Plots f o r the Ca0-Si0  1  ...  6^ 66  2  Binary  67  2  Binary  68  viii  LIST OF TABLES Table No-  Page  1.  Experimental Zinc Oxide A c t i v i t i e s  32  2.  A c t i v i t y of ZnO with respect to Metastable Pure Liquid ZnO at  3.  Calculation of A s  k.  A c t i v i t y of S i 0  5.  A c t i v i t y of ZnO from N  6.  Si0 -ZnO Binary Integration  7-  Excess Free Energy of Zh0-Si0  l600°C  2  f  ZnO  from N  36 %  Z n Q  = 0.235  = 1-0 to  S 1 0  = 1.0 to W  Zn0  = 0-5  58 60 6l  2  2  at l600°C  63  THE A C T I V I T Y  OF ZnO I N  THE TERNARY SYSTEM Z n 0 - C a 0 - S i O  2  INTRODUCTION  A.  General  Zinc lurgical  oxide bearing slags processes the  faming furnaces to are d i r e c t l y oxide  B.  Previous  in  In  this  utilize were to  2  taining zinc  one t o  vapour.  represented by  slags  zinc  these  slags  values.  activity  in  is  As t h e  a slag,  have a n economic  several  process the  slags  In  several  selectively fuming rates  studies  of  the  metal-  reduced of  in  zinc  activity  oxide of  justification.  to  solid  zinc  of  zinc  oxide  from an o p e r a t i n g l e a d b l a s t  furnaces  c o n t a i n i n g a maximum o f  + Al 02  Richards  its  data i n  particular  2  the  in  importance.  and Peters-^ c a l c u l a t e d the a c t i v i t i e s  done w i t h r e s p e c t  Si0  oxide  industrial  Work  plant  slags  to  various  B e l l , - Turner operating  recover  related  zinc  zinc  have  operate at  25  percent  oxide  approximately  ZnO.  and f o r  These  slags  of  from  furnace.  1200°C  and  calculations constant  CaO  ratio.  a n d Thorne^" e q u i l i b r a t e d F e 0 - C a 0 - S i 0 two They  percent  found that  a regular  energy between z i n c  ZnO i n  oxide  the  2  and F e 0 - S i 0  iron boats with a C0-C0 ternary  2  gas  system Z n 0 - F e 0 - S i 0  2  s o l u t i o n approximation i n which the and f e r r o u s  oxide  was a s s u m e d t o b e  2  melts  con-  containing c o u l d be  interaction zero.  - 2 -  The m o s t in  slags  containing  function remains urated  6  work, iron  b y Azuma e t . a l . ,  oxide,  of lime  content.  They  constant  a t about  1 with  state  t o 16.5 weight  from zero  oxide  contents,  used f o r zinc  oxide  reports  activities  of zinc  saturated and unsaturated w i t h s i l i c a ,  i n s i l i c a , ^ n O increases  content zinc  recent  that  for silica  f o r slags  not s a t -  f r o m 1.8 t o 3 . 1 w i t h a n i n c r e a s e percent.  Unfortunately  i n t h e CaO  information  the experimental temperatures and the entropy i s unavailable  at the present  as a  s l a g s , $£n0  saturated  increasing CaO, while  oxide  on t h e  of  fusion  time.  5 The most e x t e n s i v e mined a c t i v i t i e s  investigation  i n the ZnO-FeO-Si0  2  available ternary  i s by Davenport^  who d e t e r -  and Z n O - F e O - S i 0 - C a O  quaternary.  2  '7 He a l s o  calculated activities  information in  on t h e F e 0 - C a 0 - S i 0 2 s y s t e m .  t h e s y s t e m he u s e d a n i r o n  resulting range  Fe-FeO e q u i l i b r i a  of zinc  oxide  Scope o f P r e s e n t  The oxide  ternary  In order  saturated brass  available  using E l l i o t t  t o determine  held  i n an iron potential  was l i m i t e d .  It  s  the a c t i v i t y curcible.  of  The  a n d hence t h e  was f e l t  a means c o u l d b e f o u n d t o r e m o v e t h i s  that  this  limitation.  Investigation  ZnO-CaO-Si0  w i t h a wide  tween t h e f r e e  if  ternary  2  d e t e r m i n e d t h e oxygen  activity  work might be e x t e n d e d C.  i n the ZnO-CaO-Si0  range  energies,  is the simplest  2  s l a g system c o n t a i n i n g  of acid-base behaviour. with respect  zinc  B a s e d on t h e s i m i l a r i t y b e -  to the solid  standard  state,  o f t h e two  8 oxides  F e O a n d ZnO w i t h  ternary.  silica  The Z n 0 - C a 0 - S i 0  2  ,  this  ternary  system should resemble the F e 0 - C a 0 - S i 0  2  h a s a somewhat l i m i t e d a r e a w i t h a m e l t i n g  2 point  under  1300°C  .  It  i s proposed t o use t h e simple- e q u i l i b r i u m Zn  for  (  1  )  + l/20  2 ( g )  ^*r ZnO  ...(la.)  ( s )  which  -7 (9) K  1573°K  =  7-3x10  K  7  >  . ..(lb.)  zinc  -  3 -  to determine zinc oxide a c t i v i t i e s i n slags from t h i s ternary, primarily along the l i n e of s i l i c a saturation a t 1300°C.  D.  Experimental Method In order to thermodynamically  f i x the a c t i v i t y of zinc oxide i n a slag  i t i s necessary to measure the oxygen potential and the zinc a c t i v i t y . appendix I a discussion zinc binary. is  In  i s given of the available information on the copper-  For low concentration of zinc the following approximate expression  derived.  A.F £ "= -8200 + 2.58 T  . .. (2)  Z  Hence the a c t i v i t y c o e f f i c i e n t for zinc w i l l be less than unity.  I t i s also  possible to d i r e c t l y measure the oxygen potential of a gas phase using an oxygen s o l i d e l e c t r o l y t e of the type to be described i n section II.  The a c t i v i t y  of zinc oxide i n a slag may .be measured by the zinc content of a copper r i c h brass and the oxygen p o t e n t i a l of gas when both are i n equilibrium with a ZnO bearing slag.  THERMODYNAMIC MEASUREMENT BY OXYGEN HALF-CELLS A.  Theory of Oxygen S o l i d E l e c t r o l y t e s 1)  Defect  Structure  10 Hund  f i r s t showed that oxide mixtures containing  a predominance of valence  IV metallic ion with a small percentage of valence II or I I I metallic ion snould be capable of acting as s o l i d oxygen e l e c t r o l y t e s .  Due t o tne oxygen ion  mobility i n tne oxygen ion d e f i c i e n t l a t t i c e structure, under certain  conditions  -  k  -  (temperature and oxygen p a r t i a l pressure) oxygen ion transport i s the major 11  conduction mechanism.  Kuikkola and Wagner  made several of tnese oxide  mixtures at varying composition and showed that at certain conditions, many of these structures do conduct almost e n t i r e l y by oxygen ion transport. Zirconium dioxide forms an anion vacancy type of l a t t i c e .  This i s known  from measurements of conductivity and oxidation rate as a function of oxygen p a r t i a l pressure.  In the pure zirconia ionic l a t t i c e (Figure la) as oxygen  ions are removed, free electrons are formed.  In the pure material the con-  centration of these defects i s r e l a t i v e l y small.  The addition of a lower  valence impurity oxide such as lime or y t t r i a to t h i s structure w i l l cause a proportional increase i n the number of anion  defects to keep the cation to  anion charge balance within tne o r i g i n a l structure.  For every calcium ion that  enters the l a t t i c e on a zirconium ion s i t e there w i l l be an oxygen vacancy formed without increasing the number of free electrons.  (Figure l b ) .  2. Conduction Mechanism In a pure oxide of t n i s type (anion d e f i c i e n t ) at low oxygen p a r t i a l pressure the conduction reaction w i l l be: 1/2  0-2  0n  +  +  +  As the oxygen p a r t i a l pressure  k e~  0  ••• (3)  i s increased the oxide tends to approach  At high oxygen p a r t i a l pressure  stoichiometry.  oxygen ion i n t e r s t i t i a l s together with electron  holes w i l l be formed. 1/2  0  2  0  -«  =  +  2 ©  ...  Conductivity i s due to three charge c a r r i e r s i n any combination:  (k)  oxygen ions,  free electrons and p o s i t i v e electron holes ^  1/n =  where K , a  K, 2  ^ 'ion :  n and m are  +  K  iP°2  constants.  -l/m + K P0 2  2  (12)  ...(5)  +k  Zr., e  0 +k  0  Zr  0  0  l—l  Zr  Zr  +k  Figure l a .  Zr  +k  0  0  Zr =  0 g  =  -0 Zr  +h  Pure Z i r c o n i u m D i o x i d e .  0  o"  Ca  o"  0  Zr  +k  0  +2  0  Zr  0  0"  +U Zr  = 0 Zr  +k  +h  o" Figure l b . Zirconium Dioxide with .'. Calcium Oxide A d d i t i o n  With increasing oxygen p a r t i a l pressure  conductivity owing to p o s i t i v e hole  conduction,will increase and conductivity due t o electron conduction w i l l decrease (Figure 2 ) .  ,  Witn oxide mixtures of the z i r c o n i a - y t t r i a , z i r c o n i a - l i m e types, there are large numbers-of vacant oxygen sites, which are uncharged. then occur as i n figure 3. ..in, .. the  ;  Conductivity reactions  I f the^ contribution of charge c a r r i e d by the electrons  oxide i s n e g l i g i b l e with respect t o that c a r r i e d by oxygen ions  then the transport number f o r oxygen ions may be taken as unity.  Steele and  • 13 Alcock  indicate that both lime and y t t r i a s t a b i l i z e d z i r c o n i a would be useful  for the range of oxygen p o t e n t i a l t o be used i n the present  study.  \  B.  C r i t e r i a for Reversibility The determination  Nernst  of chemical p o t e n t i a l by emf .methods i s based on: the  equation. -nFE  = AF  This applies to a chemical reaction having a Gibbs free energy A F when carried out r e v e r s i b l y i n an electrochemical c e l l .  E i s the ^electromotive  force  generated, n i s the number of electrons transported by the reaction and F i s the Faraday constant.  The emf of the c e l l  Ft, 0 (/%) | 0.85Zn0-0.15CaO | 0 (yU ), Pt 2  2  2  2  i s given exactly by E Here t  2 Q  =  _1  ^  V /* 2 D  ... (7)  i s the transport number of oxygen ions i n the e l e c t r o l y t e . In  the simple case where t ~ n  2  = 1 equation 7 reduces t o  E = -i kF  (M  -/^l)  2  E = RT In a " II 5F I 2  0  ••• (  8 a  )  ... (8b)  - 8 -  Oxygen E l e c t r o l y t e High 0  2  0  2  +. 0  Q  +  2  Low Oo PP  PP  2e  0„  0  External  0"  2°2  +  °D  Circuit  Electrons.  F i g u r e 3C o n d u c t i v i t y R e a c t i o n s a t Cathode and Anode i n an Oxygen E l e c t r o l y t e w i t h a Large C o n c e n t r a t i o n o f Oxygen Ion V a c a n c i e s .  +  2 E  "  This means that the c e l l functions as a simple concentration c e l l f o r oxygen potential.  THERMODYNAMIC CALCULATIONS  Toop  has shown that a simple proportional combination of the excess  properties i n the component binaries may adequately describe the excess properties in the ternary system. Fe0-Ca0-Si02 ternary  He has successfully applied t h i s technique i n the to calculate the excess free energy at 1600 C based on  the pure l i q u i d metastable standard states. from the  CX plots (RTln o* i / ( 1-Ni )  2  I t i s shown (Appendix III) that  versus Ni) f o r each component i n i t s  binaries, the a c t i v i t i e s and excess free energies may be calculated. A.  Binary Oxide Systems 1. )  CaO-SiOg 7  Elliott  gives the excess free energy curve f o r the CaO-Si0 binary 2  based on the metastable pure l i q u i d s (Figure k).  Tangent intercepts were  taken from t h i s curve to determine the CX plots f o r the two components. 2. ) . ZnO-CaO No information i s available on the ZnO-CaO binary. i t i s assumed that the  curve f o r FeO-CaO  As an approximation  may be used for the ZnO-CaO  binary. CV  = RTln  ZnO = RTln j) CaO =  U-Nzno)  2  (i-Ncao)  -8580  cals mol"  3  8  This assumption gives the simplest shape f o r the excess free energy, a simple parabola.  - 11 3.)  ZnO-SlOg In  order t o derive suitable  &  plots for the ZnO-Si0  2  binary i t i s necessary  to know a c t i v i t i e s of the two components r e l a t i v e to the metastable pure l i q u i d s  1 at l600°C.  Bunting  has shown the phase diagram consists of a congruent  melting compound, zinc o r t h o s i l i c a t e , together with two simple eutectics (76-5  a n  d 50 mol fo ZnO ) and a two phase l i q u i d region at the s i l i c a  rich  side of the binary (Figure 5). A c t i v i t i e s may then be calculated from t h i s phase diagram using Chipman's melting point depression method  and Hauffe  and Wagner s congruent melting  19 compound technique The following thermodynamic information was used:  17 1. )  Entropy of fusion of s i l i c a  ( C r i s t o b a l i t e ) estimated at 1.8 E.U.  20 2. )  Kitchener and Ignatowitz s  estimated heat of fusion f o r zinc  ,26  o r t h o s i l i c a t e of 18.7 Kcals/mol " 1  An entropy of fusion zinc oxide ofcalculation 6 E.U. estimated from Elliott's a c t i v 3. i t y) diagram f o r the Z n 0 - S if0 o rbinary. This and the derivation 2  21  /N/  of mutually compatible  OC curves based on the Duhem Margules equation  is given i n appendix I I .  The excess free energy curve for the Z n 0 - S i 0 binary 2  i s shown i n figure 6. B.  Zn0-Ca0-Si0 Ternary 2  A Fortran computer program was written f o r processing the binary data according t o the equations developed i n appendix III on the University IBM 70^0 computer. The excess free energy of the Zn0-Ca0-Si0 ternary i s given i n figure 7 2  and the calculated i s o a c t i v i t y l i n e s for the three components ZnO, S i 0 are  presented i n figures 8, 9  a  n  d 10 respectively.  2  and CaO  1  - 12 -  10  20  30  40  50  60  70  8o  Mol io ZnO F i g u r e 5-  Phase Diagram, Z n O - S i 0  2  System?  90  loo  F i g u r e j£.  C a l c u l a t e d Excess F r e e Energy i n the ZnO-SiOp B i n a r y  at l600°C  Figure  9.  C a l c u l a t e d I s o a c t i v i t y Lines  for Si0  2  at l600°C.  Figure  10.  C a l c u l a t e d I s o a c t i v i t y L i n e s for f  CaO  at  l600°C.  - 18 EXPERIMENTAL  A  Equipment The experimental lay-out and apparatus are shown i n figures 11 and 1 2 . 1. )  Oxygen C e l l Design 22  A c e l l design similar to that of Fischer and Ackermann as the reference oxygen half c e l l was used (Figure 13).  employing a i r  Such a design avoided  any loading of the ceramic electrolyte and permitted i t s placement i n the best position relative to the temperature gradient of the furnace. (Figure Ik). 2. ) Furnace A v e r t i c a l Super Kanthal furnace was used. 1600°C  I t was capable of attaining  on a 1 3A" diameter cross section about three inches i n length. The  power input at the experimental temperature (1300°C) was 1.9 kilowatts. 3. )" Temperature Control Furnace temperature was measured with a Pt-Pt-10# Rh thermocouple. Maximum s e n s i t i v i t y of control was achieved by setting the voltage at a known level for the temperature desired and having continuous power into the furnace. In this way i t i s estimated that furnace temperature and control were accurate + to within - 10°C.  A Honeywell Brown Electronik controlling potentiometer was  available and acted as a maximum temperature cut-off device. k.)  Emf Measurement  The oxygen c e l l emf was measured with a Pye portable potentiometer. I t was found that this was as sensitive as a high impedance, vacuum tube voltmeter. At  1300°C  the emf could be measured to within - 1 mv.  - 19 -  I  Figure 11.  The E x p e r i m e n t a l  Layout.  Legend  1. Brass End Cap-Water Cooled 2. 0-Ring Seal 3. 0.85Zr0 -0.15Ca0 Impervious Tube 2  ( S o l i d Oxygen E l e c t r o l y t e ) Pt-Pt lOfoRh Thermocouple 5- Inner Platinum Electrode • 6. Outer Platinum Electrode 7- Crucible Containing melt 8. M u l l i t e Furnace Tube 9. F i r e c l a y Pedestal 10. V i t r e o s i l Pedestal Rod 11. 0-Ring Seal 12. Brass End Cap-Water Cooled 13. Anhydrite 14. Hot Copper Turnings 15. S i l i c a Gel 16. Ascarite 17- Deoxp Catalyst 18. S i l i c o n e Oil. Bubbler 19- Nitrogen Flow Meter 20. Needle Valve 21. Nitrogen,. Supply 22. Hydrogen Supply 23. Pye Potentiometer 24. C o n t r o l l e r and Variac. 25- A i r Supply  Figure 12.  Schematic Diag  F i g u r e 13•  Oxygen C e l l  Ik  13 12 11  I  10 X  (U  -p  a3 in a;  EH  9  Refers to the Position of the Thermocouple and Oxygen C e l l .  RXXXH Refers to the Position of the Crucible.  8 7 6 5 _L  _L  7  8  9  10  11  12  13  Ik  Inches From Top of the Furnace Figure lk.' Temperature P r o f i l e of Super Kanthal Furnace at 1300°C.  15  16  17  ro ro  X  Refers to the Position of the Thermocouple and Oxygen C e l l . Refers to the Position of the Crucible.  l  h  i  1  s  5  6  7  1  1 8  I  9  10  !  I  I  1  J—  l l  12  13  Ik  15  Inches From Top of the Furnace Figure l U v  Temperature P r o f i l e of Super Kanthal Furnace at 1300°C.  - 23 5 . ) P u r i f i c a t i o n Train The gas p u r i f i c a t i o n t r a i n w i l l be discussed under oxygen p o t e n t i a l control in the section on procedure. 6. ) A i r Pump It was found necessary t o maintain a flow of a i r against the bottom of the c e l l to avoid the formation of an oxygen of the c e l l .  gradient from the top t o the bottom  A small v i b r a t o r pump supplied s u f f i c i e n t a i r pressure t o accomplish  this. B.  Materials 1. ) Reagents Baker and Adamson analysed granulated zinc, shot copper, powdered zinc  oxide and powdered calcium carbonate were used.  S i l i c a was standard commercial  grade. 2. ) Crucibles S i l i c a saturated slags were held i n 2f0 ml. V i t r e o s i l 97$ s i l i c a c r u c i b l e s . Non-silica saturated slags were contained i n y t t r i a stablized zirconia crucibles supplied by the Zircoa Corporation^  1 l/k" o.d.. x 3" long.  3. ) Oxygen C e l l s The oxygen c e l l s used were  0.85Zr0 - O.PpCaO impervious tubes 2  l/k" od  f i f t e e n inches long, closed one end, supplied by Zircoa Corporation. k.)  Electrodes  The inner electrode was simply the platinum lead from the thermocouple held i n e l e c t r i c a l contact against the s o l i d e l e c t r o l y t e by the thermocouple insulator.  The outer electrode was a piece of platinum wire wrapped around the  base of the c e l l immediately above the melt.  - 2k C.  Procedure A crucible containing  about ten grams of a l l o y together with f i f t e e n grams  of slag was loaded into the bottom of the furnace, at a temperature such that the brass would remain s o l i d . gas.  The system was purged with low oxygen p o t e n t i a l  When a suitable emf was reached the pedestal was raised t o bring the  crucible just below the c e l l and the variacset t o give the desired experimental temperature.  The metal phase was sampled at various oxygen p a r t i a l pressures  allowing time for equilibrium to be established at each p o t e n t i a l .  When a l l  the a l l o y was removed the furnace was cooled and the crucible withdrawn. 1.)  Oxygen Potential a. ) Oxygen Potential Range Available  At any given temperature and zinc oxide a c t i v i t y two considerations the range of oxygen potential a v a i l a b l e .  fix  The lower side i s determined  p r i n c i p l y by the b o i l i n g point of zinc i n the a l l o y .  At  1300°C with unit  a c t i v i t y of zinc oxide t h i s gives a lower oxygen p o t e n t i a l l i m i t of 2.0 x 10 atm.  (Appendix IV).  The highest oxygen p a r t i a l pressure i s fixed by the  limit  of d e t e c t a b i l i t y of zinc i n the brass and by the necessity of keeping copper from oxidizing into the slag.  Assuming that the oxidation of copper i s the  determining factor at 1300 C, the highest oxygen potential would be 1.1 x 10  atm.  (Appendix IV). b. ) Oxygen Potential Control The  oxygen potential was controlled by the water equilibrium constant i n  a flow of commercial grade nitrogen into which a small amount of hydrogen was bled through a s i l i c o n e o i l bubbler.  The oxygen potential was varied by  adjusting the needle valve on the nitrogen rates of the two gases.  flow meter t o change the r e l a t i v e flow  A t o t a l flow rate of about 100 cc's a minute was  - 25 sufficient  to  maintain equilibrium  c. ) The  gas t r a i n  potential percent  Purification  of  the  oxygen.  hydrogen  to  form water.  oxygen  oxygen  potential  Ascarite used t o  commercial grade  potential with  was u s e d t o reduce  the  d. )  of  time  potential the  flow  of  the  Zinc  2.)  powder the  amounts  of  the  at  serious b. )  of  help  reduce the  which p r o b a b l y  served to  copper a t  tne  combine most o f  temperature  the  of  tne  oxygen  as a f u r t h e r  of  and s i l i c a  oxygen  c o n t a i n e d about  s h o u l d be d e t e r m i n e d b y t h e  gas  content  the  two with  control  equilibrium  turnings..  g e l and a n h y d r i t e  were  gas.  Run  gases.  oxygen in  the it  The  potential furnace.  was a l a r g e In  order  was n e c e s s a r y t o  longest  to  factor keep the  continuously  r u n was e i g h t  in  the  oxygen  monitor  hours.  zinc  Preparation loss  it  furnace.  of  the  was  felt  inadvisable  Copper-rich  experiment  two m e t a l s w e r e The  brass  a s n o n e was sealed in  to  simply  l o a d premixed  ( N ^ ' f i * . 0.01) was p r e p a r e d readily  available.  evacuated quartz  composition gradient"of  the  at  Weighed  and melted i n  alloy  metal  was  slight  the and  limitation. Sampling  The m e t a l p h a s e was the  nitrogen  to  copper t u r n i n g s " s e r v e d  any l e v e l  Super K a n t h a l f u r n a c e . was n o  the  controlling  two  the  beginning  hot  devices  remove a n y CO2 p r e s e n t  water  Alloy  reduce into  of  furnace.  Activity  a. ) To  The  a r u n was k e p t  constant  of  catalyst  solid  Duration  The method o f length  deoxo  i n the  Train  consisted mainly  The  as the  conditions  melt and withdrawing  sampled by a pencil  of  inserting alloy  a 2 mm i . d .  quartz  quill  w i t h an a t t a c h e d a s p i r a t o r  into bulb.  .-26It was  found that the introduction of the tube only momentarily, lowered the oxygen  potential  and i t returned to i t s o r i g i n a l value within a minute of withdrawal. ' c.)  Analysis  '  Metal specimens were dissolved i n d i l u t e d 1:1  n i t r i c acid and the solution  analyzed for zinc using a Unicam SP-90 atomic adsorption spectrophotometer.  For  ! pure zinc the e f f e c t i v e s e n s i t i v i t y l i m i t of t h i s instrument was about 0.05  /Uo/ml of solution.  For a 0.1  found to be  gram sample dissolved i n the  minimum amount of n i t r i c acid and made up to 10 ml.', the minimum deiectable zinc i s about  0.'005 mol percent.  Pure copper has some'absorption at the  2139A l i n e used f o r zinc a n a l y s i s . One gram of copper i n f i f t y £ubic cen0  timeters of solution gives an absorption equivalent to one microgram per m i l l i l i t e of zinc. zinc.  This coincides with the s e n s i t i v i t y of the instrument  Hence the e f f e c t i v e s e n s i t i v i t y of the instrument  a copper r i c h brass i s 0.01 r a t i o was  mol percent*.  for pure  f o r detecting zinc i n  In a l l the specimens the  experimental  i n the order of one hundred parts of copper to one part of zinc.  t h i s range the exact proportion interfered, l i t t l e  (Figure 18).  A brass  standard containing one hundred parts of copper to one part of zinc was +  i n a l l the a n a l y s i s .  3.)  Accuracy was  In  used  ,  estimated at - yp.  Slags . *  a.)  Preparation  On i n i t i a l runs i t was  found that there was  considerable d i f f i c u l t y i n  melting the oxide powders to form a slag during a run at temperatures only s l i g h t l y higher than the estimated melting point of the slag".  Segnit and  23 Wolfe's  technique  f o r quenching prefused slags i n a platinum crucible  adapted f o r use i n the Super Kanthal furnace.  was  The furnace design was not very  suitable f o r t h i s work since a crucible had to be lowered on the pedestal and the pedestal furnace. removed Thus higher beforemelting the crucible point slags could could f a l l not into bea bucket r e a d i l y of made. cold water Mainlyunder  - 28  f o r . t h i s reason i t was  decided to work p r i n c i p l y along the  -  1J00 C s i l i c a 0  saturation l i n e . In addition the job of chipping only p a r t i a l l y glassy slags from the platinum crucible was b. )  somewhat laborious.  Sampling  Slags were sampled by a cold s t e e l rod with a notch cut into the lower c. )  end.  Analysis  Slag samples of about .0.5 gram were ground to minus 100 mesh and treated with a mixture of equal parts of concentrated hydrofluoric and p e r c h l o r i c acids in a platinum c r u c i b l e . metal chlorides.  The baked constant weight residue was weighed as  The difference was  assumed to be s i l i c a .  The  treated with b o i l i n g water to bring the chlorides into solution. was  then analyzed for zinc and' copper using the absorption  The difference was  again used to check the o r i g i n a l CaO  residue  was  The solution  spectrophotometer.  to S i 0  2  r a t i o of the oxide  powders. )  Time f o r E q u i l i b r i a  The length of time required f o r equilibrium to be established was  arbitrarily  set at one h a l f hour to minimize the length of time during which the gas flows would require continuous monitoring. run of the actual over the average ZnO  In figure 16 a plot i s given from one a c t i v i t y as a function of time.  seen that although there i s considerable  scatter, the length of time between  readings had l i t t l e e f f e c t between one h a l f hour and four hours. that equilibrium was  It i s  It was  assumed  attained within one h a l f hour at each d i f f e r e n t l e v e l of  oxygen, p o t e n t i a l . 5.)  R e v e r s i b i l i t y of the Oxygen Half C e l l  The most important condition for oxygen c e l l r e v e r s i b i l i t y transference  number f o r oxygen ions be unity.  i s that the  As a further check that the  cell  - 29 -  o  id o d  0.5  0  100  200  Time i n Minutes A f t e r F i r s t F i g u r e 16.  300  1+00  Sample  Experimental V a r i a t i o n i n A c t i v i t y as a F u n c t i o n o f Time.  o f ZnO  -4.0  -3-5 o H  o  -3.0  -2-5  -7 Log Figure  17•  1 0  P0  2  Conductity of O.85 Zr0 -0.15 CaO S o l i d E l e c t r o l y t e as a Function of Oxygen Potential at 1300°C. 2  - 31 was measuring the true oxygen p o t e n t i a l of the system two b r i e f experiments were carried out.  Using a Bye potentiometer as a voltage source i t was  found that  a f t e r imposing a one v o l t emf across the c e l l i n either d i r e c t i o n , the resting p o t e n t i a l of the operating c e l l was c e l l was  not polarized.  unchanged.  A simple ohmmeter was  Thus i t was  concluded that the  used as a conductivity meter at  several d i f f e r e n t values of oxygen p a r t i a l pressure.  I t i s seen (Figure  17)  that the variations i n conductivity i s s l i g h t over a r e l a t i v e l y wide range of oxygen p a r t i a l pressure.  This indicates that oxygen ions are the major charge  carriers»  RESULTS A.  Zinc Oxide A c t i v i t y The experimental results are presented i n table 1.  of zinc oxide with respect to the s o l i d standard  The  state are  activities  measured at  the p a r t i c u l a r experimental temperature using the free energy expression given by Wicks and Block^. Reproducibility i s well within the calculated standard deviations which are admittedly  quite large.  Considering that t h i s work required a three  phase equilibrium at high temperature i t i s not unreasonable to such large standard  deviations.  find  -32 -  Table  Experimental Zinc  KEY  TEMP  a  Zn  °C  a ppo 2  EMF  PPOg  mv  xlO°  xlO  4.2  3.17  2  Zn  a  I  Oxide  ZnO  a  Activities  ZnO  7  SLAG ZnO  CaO  Si0  26.5  23  50.5  .48  24  21  55  .38  21  55  .23  21  55  • 36  Dl  1240 .00155 490  D3  1240 .00083 524 1.18  D4  1235 .00072 483 4.4  1.51  • 75  El  1310 .OOI89  5.45  • 733  E2  1300 .OOO96 507 4.71  2.1  .283  E3  1305 .00086 472 13.3  3-14  .4221  E4  1305 .OOO57 455  2.67  .36'  FI  1305 .0015  2.05  .275  F2  1305 .00129 494 6.96  3.4  • 457  F3  1320 .00154 499 7.5^  4.19  • 538 •519 24  F4A  1320 .ooi4i 494 8.37  4.07  .523  F4B  1320 .00189 494 8.37  5.45  •70  F6  1315 .00373 55^ 1.68  4.82  .620  G1A  1340 .00523 708  .021  • 755  GIB  1340 .00555 708  .021  .802  G2  1335 .00501 653  .094  1.54  • 759 .503 24  G3  1320 .00328 573  • 835  3-0  .39  490 8.37  22  536 1.88  .897  2  1.48  .44 .94  .45  • 364  -33 -  KEY  TEMP  <*Zn  °C  EMF  PPOg  mv  xlO  8  ^ZnO XlO  ZnO  SLAG CaO  Si0  1.11  42  22  36  1.00  42  22  36  .28  .405  14  27.5  58.5  • 13  Zn0  :  11  1365  .0019  409  149.  23.1  12  1365  .0022  383  348.  41.  13  1365  .0017  475  22.  l4  1365  .0030  475  22.  1.4  • 735  Jl  1330 .00345  501  8.36  9-93  .827  J2A  1325  .00238  480  1.38  8.85  • 737  J2B  1325  .00225  480  1.38  9.25  .772  J3  1330 .0028  460  2.65  14.4  1.2  J4  1330 .0039  463  2.2  18.3  1.52  J6  1345  .003  484  1.49  11.6  •97  Kl  1335  .0032  600  1.01  3-2  .263  K2  1365  .00305  477  24.  1.48  .78  K3  1345  .0033  ^29  80.  2.95  .209  K4  1345  .0012  480  I8.7  5-2  • 37  • 79  Q  2  1.21 '  2.15 .42  -34 B.  -  S o l i d Zinc Oxide Saturation Line ( Z n O = !) a  In figure 18 the results of two separate runs are plotted using a slag saturated i n both zinc oxide and zinc o r t h o s i l i c a t e (,22~CuO, .42 ZnO, -36 SiOg)-.  I t i s seen that the l i n e  calculated, from the assumption that 1/2  zinc oxide a c t i v i t y i s unity ( i . e . u^n x PP0 f i t s these points reasonably well.  2  = K ^ e(  w.r.t. s o l i d ZnO)  Hence i t i s concluded that at 1300°C  the transport number f o r oxygen ions i n the s o l i d e l e c t r o l y t e O.85 Zr.0 - 0.15 CaO over an oxygen p o t e n t i a l range of 2.3 x 10 ^ to 2  Q  8.4 x 10 C.  i s unity.  Slag Analysis Extensive slag analysis was done on one of the early runs and showed  that the v a r i a t i o n i n composition of the slag over a.six hour period was within f i v e percent of the o r i g i n a l f r a c t i o n of oxide powders.  This was  n e g l i g i b l e i n comparison with the v a r i a t i o n i n measured ZnO a c t i v i t y and hence i t was assumed for the other runs that the slag composition present was that given by the o r i g i n a l oxide mixture. The presence of large amounts of cuprous oxide i n the slag was evident from those runs i n which the controlled atmosphere was l o s t and copper was allowed to oxidize.  These slags were very dark brown i n colour and textured  rather than glassy.  In the analyzed slag samples which were clear or s l i g h t l y  green i n colour the maximum cuprous oxide content was less than one mole percent.  As long as the slag remained clear i t was assumed that the amount  of cuprous oxide present was n e g l i g i b l e .  Figure  18. Data f o r Runs I and_J. (ZnO S a t u r a t e d ) Together w i t h C a l c u l a t e d T h e o r e t i c a l L i n e f o r Z i n c Oxide S a t u r a t i o n .  - 36 •INTERPRETATION OF RESULTS A.  Calculation of a ZnO (Liquid Standard State) i n ZnO-CaQ-SiO  g  Slags  In order to compare the experimental results with those calculated hy  16 Toop's  method at l600°C i t i s necessary to recalculate these a c t i v i t i e s using  the pure metastable l i q u i d as the standard state. zinc oxide (6 E.U.) established from thermodynamic  The entropy of fusion for data (Appendix II) was  used together with the regular solutions theory temperature  adjustment.  results are given i n table 2. Table II A c t i v i t y of ZnO with respect to Metastable pure l i q u i d ZnO at l600°C Run D E F G I J K  a  (s)  M • 534 • 503  l.ll  1.00 .405  a  °l600°C  (1)T .21 .124 •15 •15 •35 .29 .12  • 792 .515 .623 .623 .833 .691 • 857  -.233 -.662 -.472 -.472 -.182 -.368 -.154  .828 •571 .669 .669 .853 .729 .875  ^1) i6oo°c .22 .14 .16 .16 • 36 • 31 .12  These  "37 B.  Comparison between Experimental  and Calculated ZnO  -  Isoactivity  Lines i n the ZnO-CaO-Si0 System 2  The a c t i v i t i e s from Table 2 are plotted i n Figure 19 together with the zinc oxide i s o a c t i v i t y l i n e s at l600°C from section I I I . The two points along the s i l i c a saturation l i n e at 1300°C check the upper shape of the l i n e Q_ Q = 0.1. ZN  The slag i n equilibrium with s o l i d ZnO and Z n S i 0 2  4  at 1300°C  gives an a c t i v i t y very close to the calculated a c t i v i t y at that point. I n s u f f i c i e n t work was done to validate t h i s t h e o r e t i c a l treatment but the slags studied produced several a c t i v i t i e s remarkably close to those calculated  16 from binary  data by Toop's method  .  I t should be remarked that these ZnO  a c t i v i t i e s were a c t u a l l y measured with reference to s o l i d zinc oxide at 1300°C.  It i s assumed that the regular solution theory temperature  adjustment  i s v a l i d and that the entropy of fusion of ZnO i s 6 E.U. i n the calculations comparing these a c t i v i t i e s with the calculated i s o a c t i v i t y lines i n Figure 12. C.  Comparison with Davenport's Calculated CL  Data f o r the Zn0-Ca0-Si0 Ternary 2  It i s d i f f i c u l t to make comparisons between t h i s work and work done previous to Davenport.  A l l these studies measured ZnO a c t i v i t i e s i n slags containing  a large percentage of FeO i n contact with Fe.  The presence of t h i s FeO  tends to complicate the effect of the increasing CaO to S i 0  2  r a t i o on the  a c t i v i t y of ZnO. The agreement between t h i s work and Davenport's rather poor (Figure 20).  calculated data i s  Several reasons may be given by way of explanation.  The entropy of fusion f o r zinc oxide used i n the present study was 6 E.U. Davenport estimated a value of 2.85  E.U.5  , The excess free energy of the  Zn-Cu system was found to have the following temperature dependence A C  =  -  8  2  0  0  +  2.58T  CaO  Mol  f>  ZnO  -~  Figure 20. Comparison Between the I s o a c t i v i t y Lines f o r ZnO at l600°C Calculated by Davenport 5 and i n the Present Study.  ^ i  .  .  at low zinc composition. energy of 755^ cals mol  -  .  40 -  Davenport assumed complete r e g u l a r i t y with an interaction  1 }  5 . Different methods of combining tne a u x i l i a r y data  were used i n tne two investigations.  The present study used Toop's ternary  integration technique based on the regular solution theory;  Davenport used  Schumann's ternary i n t e g r a t i o n ^ and tangent intercept techniques'^  Both are  2  based..on the Gibbs Duhem relationship and hence should be compatible.  It i s  quite obvious that tne two studies measured a c t i v i t i e s i n slags of widely d i f f e r e n t composition and i t may well be tnat a s l i g h t l y d i f f e r e n t t h e o r e t i c a l treatment might bring both closer i n t o agreement. 6  D.  Comparison with Work by Azuma, Goto and Ogawa In keeping with t h e i r results i t i s seen that an increase i n lime content  to move the slag composition away from the l i n e of s i l i c a saturation increases the a c t i v i t y c o e f f i c i e n t of zinc oxide i n the slag, i  E.  Comparison Between Zn0-Ca0-Si0 and Fe0-Ca0-Si0 2  1.)  ZnO-SiOg and Fe0-Si0  2  2  Ternaries  Binaries  In figure 21 tne excess free energy of the Zn0-Si0  '  ' •  together with E l l i o t t  binary i s replotted  2  ,  s curve f o r the excess free energy of Fe0-Si0  1 2  . The  seemingly large difference between the two curves i s attributed to the fact that the Fe0-Si0 Zn0-Si0  2  2  binary has s l i g n t positive deviation from i d e a l i t y whereas the  binary has s l i g h t l y greater negative deviation.  them, i s never much greater tnan two k i l o c a l o r i e s .  The difference between  When based on tne s o l i d  8 standard states both curves are r e l a t i v e l y close to i d e a l .  - kl -  2500 2000 1500 1000 500 f-  03  o .fa  -500 1000  \  -1500 -2000 -2500  Fe0-Si0  2  Zn0-S10  2  7  Difference  _J .6  .1  .7  'Mo Figure 21.  Comparison Between the Excess Free Energies of the Binaries F e 0 - S i 0 and ZnO-SiOg t l600°C. 2  a  - k2  2.)  -  FeO-CaO-S10 Ternary 2  The excess free energy contours and the i s o a c t i v i t y lines f o r FeO are shown In figures 22 and 23 respectively.  Figure 22 shows a somewhat  larger area with a positive excess free energy than does the corresponding figure f o r zinc oxide (Figure 7), but otherwise tne shape of the contours i s quite similar over most of the diagram.  The i s o a c t i v i t y l i n e s f o r  FeO have a c h a r a c t e r i s t i c projection extending further towards the lime o r t h o s i l i c a t e composition than does tne c h a r a c t e r i s t i c projection f o r the zinc oxide i s o a c t i v i t y l i n e s (Figure 8).  This i s i n keeping with the  s l i g n t l y more basic behaviour of ferrous  oxide.  SUGGESTIONS FOR FURTHER WORK The most important l i m i t a t i o n was the e f f e c t i v e r e s t r i c t i o n on slag melting point because of the technique used f o r slag preparation.  I f an  induction furnace had been available, slags could have been prefused i n a i r using a platinum crucible as a susceptor.  The crucible could tnen have  been immediately quenched i n water on removal from the c o i l s . At 1600  °C, for unit a c t i v i t y of zinc oxide: [Zn](P0 )2 2  At t h i s temperature approximately 0.01  = 8.7 x 10"  5  ( 9 )  ...(9)  the zinc-copper a l l o y b o i l s at a zinc a c t i v i t y of (Appendix IV).  From the thermodynamics of tne copper-  oxygen equilibrium, this w i l l result i n an a c t i v i t y of about 0.2  for cuprous  oxide i n the slag, wnich i s no longer n e g l i g i b l e . Further work might be done using a modification of the technique used by Richards and Thorne^ . Using a horizontal bed furnace, i t would  io  20  30  4o  50 Mol  Figure 23.  <fo  60 .FeO  70  >-  Calculated I s o a c t i v i t y Lines f o r FeO at l600°C.  80  90  - 4  5  -  be r e l a t i v e l y simple to use a zinc source to e s t a b l i s h a zinc p a r t i a l pressure i n the incoming low oxygen potential gas. would be completely avoided.  Slag zinc loss  Slags could be equilibrated with t h i s  gas  in a platinum boat, circumventing the problem of containment f o r a slagmetal equilibrum melt.  Zinc a c t i v i t y could then be determined by measuring  the zinc p a r t i a l pressure of the equilibrium gas. could be measured The  The  oxygen potential  using an oxygen h a l f - c e l l as i n the present study.  slag could be sampled once equilibrium conditions were established.  CONCLUSIONS A c t i v i t i e s of ZnO.in ZnO-CaO-Si0 slags have been measured at 1300°C 2  by a slag-metal-gas equilibrium technique.  The experimental zinc oxide  a c t i v i t i e s agree c l o s e l y with the i s o a c t i v i t y l i n e s calculated on tne basis of Toop s ternary  integration technique  and an estimated entropy of  fusion for zinc oxide of 6 E.U. The calculated excess free energy contours for the ZnO-CaO-Si0  2  ternary are similar i n shape to those calculated" i n a similar manner 7  for the FeO-CaO-Si0  2  system using E l l i o t t ' s data on the component binaries .  Also the calculated zinc oxide i s o a c t i v i t y figure oxide i s o a c t i v i t y diagram.  i s similar to the ferrous  The zinc oxide i s o a c t i v i t y pattern  projection towards the lime o r t h o s i l i c a t e composition. c h a r a c t e r i s t i c of FeO^but i n the case of ZnO pronounced.  shows a  This shape i s  the projection i s not so  Both these observations are i n keeping with the s l i g h t l y more  basic behaviour of zinc oxide. It i s f e l t that the estimated entropy of fusion for zinc oxide i s reasonable based on the close agreement between the calculated i s o a c t i v i t y l i n e s and the measured a c t i v i t i e s and on the s i m i l a r i t y between the two ternaries, ZnO-CaO-Si0 and FeO-CaO-Si0 . 2  2  In addition, the calculated  free energy curve for the ZnO-Si0 binary agrees quite closely with the 2  8 free energy curve given by Richardson  f o r t h i s binary based on s o l i d  standard states for the two components. It was found that the s o l i d oxygen e l e c t r o l y t e O.85 Z r 0  2  - 0.15 CaO  -6 behaves reversibly at 1300°C over an oxygen potential range of 2.3 x 10  -8 to 8.4 x 10  atmospheres.  - 47 REFERENCES  1.  E. N. Bunting, J . Am. Ceram. S o c ; 13,  1  2.  E. R. Segnit, J . Am. Ceram. S o c ; 37,  3-  R. C  4.  A. W. Richards and D. J . Thorne, "Physical Chemistry of Process Metallurgy - Part 1", Interscience, New York, (1961) p. 277.  5.  W. G. Davenport,  6  8 (1930). 274 (1954).  B e l l , G. H. Turner and E. Peters, J . Metals; 6, 472  (1955).  "The A c t i v i t y of Zinc Oxide i n Multi-component Slags",  M.A.Sc. Thesis, University of B r i t i s h Columbia,  i960.  6.  K. Azuma, S. Goto, 0. Ogawa, Nippon Kogyo K a i s h i ; 8l, l8 (1965).  7-  J . F. E l l i o t t , J . Metals; 6, 485 (1955).  8.  F. D. Richardson, "Physical Chemistry of Melts", Inst. Min. London,  9.  Met.,  (1953) P- 86.  C. E. Wicks and F. E. Block, U. S. Bureau of Mines B u l l e t i n 605  10.  F. Hund, Z. physik. Chem.; 199,  11.  K. Kiukkola and C. Wagner, J . Electrochem. S o c ; 104,  12.  S. P. M i t t o f f , J . Chem. Phys.;  13.  B. C. H. Steele and C  14.  R. Littlewood, Can. Met. Quarterly; 5, 8 (1966).  15.  N. J . Olson and G. W. Toop, Trans. A.I.M.E.; 236,  16.  G. W. Toop, Trans. A.I.M.E.; £33,  17.  F. D. Richardson, "The Physical Chemistry of Melts", Inst. Min. London,  142  (1963).  (1952). 379 (1957).  36, I383 (1962).  B. Alcock, Trans. A.I.M.E.; 233,  1359  (1965)•  590 (1966).  850 (1965). Met.,  (1953) P- 93-  18.  J . Chipman, Discussion Faraday S o c ; 4, 23 (1948).  19. 20. 21.  Hauffe and Wagner, Z. Elektrochem.; 46, 160 (1940). J . A. Kitchener and S. Ignatowitz, Trans Faraday S o c ; 4j_, 1278 L. S. Darken and R. W. Gurry, "Physical Chemistry of Metals", McGraw-Hill, New York, (1953) P- 264.  22.  W. A. Fischer and W. Ackermann, Archiv. f . d. Eisenhutt.; 9_, 643 (1965).  (1951).  - 48 23-  E. R. Segnit and J . D. Wolfe, Chem. Eng. Mining Rev.; 45, 215 (1953)-  24.  R. Schuhmann, J r . , Acta Met.; 3, 223 (1955)-  25-  R• Schuhmann, J r . , Acta Met.; 3, 220 (1955).  26.  J . F. E l l i o t t , M. Gle i s e r and V. Ramakrishna, "Thermochemistry f o r Steelmaking, Volume I I " , Addison-Wesley, Reading, Massachusetts,  (1963) p. 578.  27-  R- Hargreaves, Journal Institute of Metals; 6k,  .28.  W. Leitgebel, Z. anorg. Chem.; 202, 305 (1931).  29.  A. Schneider and H. Schmid, Z. Elektrochem.; 48, 627 (1942).  30.  A. W. Herbenar, C. A. Siebert and 0. S. Duffendack, J . of Metals; 2, 323  115 (1939).  (1950). 31.  L. H. Everett, P. W. M. Jacobs and J . A. Kitchener, Acta Met; 5, 28l (1957).  32.  0. Kubaschewski and E. LL. Evans, "Metallurgical Thermochemistry", Pereamon, London, (1965) p. 177J- Lumsden, "Thermodynamics of A l l o y s " , Institute of Metals, Clowes and Sons, London, (1952) p. 272.  3334.  0. Kubaschewski and J . A. C a t t e r a l l , "Thermochemical Data of A l l o y s " , Pergamon, London, (1956) P- 69.  35-  Kleppa and King, "Metallic S o l i d Solutions", W. A. Benjamin Inc.,  36.  L. Guttman, Trans. A.I.M.E.; 175, 178 (1948).  37-  K. K. Kelly, U. S. Bureau of Mines B u l l e t i n  38.  A. Glassner, A.N.L. -  39-  M. J . N. Pourbaix and C. M. Rorive-Boute, Discussion Faraday S o c ; 4,  Mew York, (1965).  140 (1948).  393'(1936).  5750, (1959)-  -  49 -  APPENDIX I Calculation of I n f i n i t e l y Dilute Properties of Zinc i n the Copper-Zinc System A.  Hargeaves Datsfr?  , Zn  .052 .144  • 195 . .255 • 373 .453  -5300  .OJOl  .O545  -568O -5430  .134  -5150  -5720 -5520  -5410  .200  .481 .504  LeitgebeJ  .0045  .0086 .OI85  .094  B,  G(Zn  ^Zn  N  .246  -4920  .291  -4410  28  AF  T°K  1*188 1198  -200 -440  1246  -1570  Zn  <*Zn  0.883  +7930 + 338  0.828 O.7O7 O.577  :  1283  -2440  1337 1373  -3710  0.441  -8280 -5810-4900  -4540  O.38I  -6O5O -7920  -5000  0.273  -13790  0.063  -4440 -4480 -4630  a zn  «Zn  1438  1518 1773  0.191  C . Schneider and Schmid 9 2  T°K 973 973 973 973 973 1123 7123 1123 1123 1123  N  Zn  0  O.798  0.80  0.714 0.664  0.57 0.48 0.35 0.14 0.795  -5370  O.580  0.531 0.398  0.428  0.184  -4340 -4780 -5750  0.580  0.428 O.798 0.714  0.664  0.612  -5570 -5570 -6600  -2440 -4150  ,  - 50 -  D.  Herbenar et. a l  30 1073°K  Temp. N  1198°K  O^Zn  ^Zn  0u  .9^65  -5920  -56OO  .8895 .8382 . 8001 • -7^97 .7105 E.  ll48°K  -5570 -5700 -585O -5530  ''  -5100 -5230 -514 0 -5230 -5270 -1+880  -it-780 -5030 ' -^750 -4840  EveYett, Jacobs and Kitchener31 The data of'Everett, Jacobs and .Kitchener-^ i s presented in.figure 24. 1  On t h i s figure are drawn the regular solution l i n e used by Davenport and a.sloping l i n e which f i t s the data somewhat better.  F.  Kubaschewski  and E v a n s ^  Their book gives a curve f o r the i n t e g r a l heats of formation of Cu-Zn alloys based on several techniques. at Zn=0 gives A H  Taking the slope of this l i n e  . From this must be subtracted the heat of fusion  of zinc, I76O cals/gm atom.  This gives: , -1 ^ \-\ = -916O cals atom  G.  Excess Free Energy Expression Results from a l l available sources i s given i n figure 24. The  equation of the l i n e drawn f o r the excess free energy i s : "AFz  n  = -8200 +2.58 T.  A A  -8500 A  -8000 -7500  ~A  A  -7000  A  -6500 -6000  " A  A A  -5500  Improved F i t Line  -5000  O r i g i n a l F i t Line  -4500 -4000 A  .6 N,Zn Figure 2k.  31  Data of Everett, Jacobs and Kitchener  - 52  1000  -  1200  Temperature °K Figure 2\  thermodynamic Data on the I n f i n i t e l y Dilute Free Energy of Zinc i n Copper.  - 53 APPENDIX II The System ZnO-SiOp A.  Previous Work 1. ) K.K.  K e l l y 37  From Bunting's d a t a , K e l l y plotted RlnN^nO 1  temperature  a s  a function of r e c i p r o c a l  and derived a value f o r AH-p from the slope of t h i s l i n e of  4480 cals m o l  ^37) _ F  - 1  r o m  figure 26 i t i s seen that Bunting's measured  compositions do not l i e exactly on a l i n e j o i n i n g the eutectic at "76.5 ZnO with pure ZnO.  In fugure 27 values from the l i n e a r plot and Bunting's  actual values are plotted.  Kelly's value l i e s i n between.  l i e s i n the f a c t that the range of temperature the temperature eutectic.  The error probably  covered i s only 22 percent of  difference between the melting point of, pure ZnO and the  Kelly's value gives an entropy of fusion f o r ZnO of 1-99  \ 2. )  mol $  E.U. 37  4 Richards and Thorne  Richards and Thorne used an entropy of fusion of 5 E.U.'^  There was  no reference' given as to the source of t h i s value. 3-)  G-lassner  3 8  Glassner gives a difference i n enthalpy between s o l i d and l i q u i d zinc oxide at 2248°K of 8600 cals'3 . 8  This value i s presumably calculated from  heat capacity considerations. This enthalpy gives an entropy of fusion f o r ZnO of 3-8 k.)  E.U. Davenport 5  Based on a somewhat a r b i t r a r y closure of his Otplot f o r SiOg i n the Zn0-Si02 binary 5 ZnO of 2.85  E.U.5  present study.  }  Davenport derived a value f o r the entropy of fusion f o r He used much the same technique as was used i n the  - 55 -  Figure  27-  Estimate of Enthalpy of Fusion f o r ZnO from the Liquidus Line.  -  B.  Estimation of A s Elliott ^ 2  curve  8  f  56 -  ZnO  has plotted a c t i v i t i e s calculated from Richardson's free energyThese a c t i v i t i e s from Nz n = O . 7 6 5 (the eutectic  f o r the ZnO-SiC>2 binary.  n  between Z^SiOlj. and ZnO) to saturation at l 6 0 0 ° C may be used together with Bunting's phase diagram^ to s a t i s f y the formula used i n Chipman's melting point depression expression fusion f o r ZnO.  to derive am average value f o r the entropy of  This i s shown i n table 3-  The f i r s t composition (N^nO  =  i s not very useful as the liquidus i s not well established at t h i s point. The average of the other two points i s taken as 6 E.U.  Table I I I  Calculation of A S f ZnO Chipman s Liquidus Curve Expression : 1  As  f  1  8  = -RTlnaZnO • T-TmznO  NZnO  AT  .807 18 .783 55 •772 75  C.  4l6oo°C*  a  °1600OC  1.188 1.16  .96 •91 .85  1.10  T  lnOlT  AF  I.I89 •96 -.0407 -151 I.I65 .912 -.O918 -331 -442 l.lkk .883 -.124  Calculation of A c t i v i t y f o r S i l i c a  AS  f  8-3  6.02  5-9  to Ns-jnp = 0-235  S i l i c a a c t i v i t y may be calculated from the phase diagram using the techniques developed by Chipman  *From E l l i o t t '  18  and Hauffe and Wagner-*-9(Table 4 ) .  O.807)  - 57 "  T a b l e IV  A c t i v i t y of Si0  1.  2  from N  = 1.0 t o N s i o  S i 0 2  = 0.235  2  Congruent m e l t i n g Compound M e t h o d ^ 1  Symbols: x x  N  ZnO>  N  Z n 0  Hf = Heat o f f u s i o n o f Z ^ S i O ^ = 18.7 k c a l s m o l " 0 = M e l t i n g P o i n t o f Z ^ S i O ^ = 1784°K = 0.666 M q 1f r a c t i o n s i nZ n S i Q  SiO? T Si02  II RTlnCLsi0  =  =  0  -  3  3  = L i q u i d u s temperature P° tion C o m  I 2  3  1  = RTlnaSi0  2  s i  AHj  e  + x  NZnO(Q-T)  Z n 0  Nsi02" Si02  [ (Q-T) I  X  dNsiOc  I^0(FSi02 1  Nsi02 • 50 •45 .4o •38 •36 •32 •30 .28 .26 •235  T°K 1705 1751 1775 1780 1783 1784.5 1783.5 1782.5 1781.5 1780  •(Q-T)  (N-X)  (9-T)/(N-X)  80 34 10 5 2 •5 1-5 2-5 3-5 5  .166 .116 .066 .046 .026 -.013 -.033 -.053 -.073 -.098  2900 2520 2290 2360 2940 2960  2  XznOjC J d N s i 0 A 293 204 124 93 58 -29 -59 -74 -85  l46o  890 650 520  The g r a p h i c a l i n t e g r a t i o n o f (Q-T)/(Ef-X) f i g u r e 28.  [Parti]  2  241 161 90 67 49 -26 -32 -3^ -36 -39  -95  2  a g a i n s t N,S i 0  2  i  s  1 r  AH, e 5600 3830 2240 1680 1120 -580 -950 -1120 -1270 -1400  ^ven in  L  l J  - 58 " 2.  Liquidus Curve Method  -i Q  InCL = T-TraASf T R  As  f  2  = 1.8 E.U.  N i02  T°K  T-Tm/T  In a  •975 • 95 .90 .85 .80 •75 • 70 .657 •65 .60 • 55 • 50 .45  1968 "  . -.00913 " " "  -.OO83  S  .40  • 36 • 30 .26 .235 D.  = Entropy of Fusion of S i 0  "  " " " 1951 1853 1773 1705 1751 1775 1783 1783.5 1781.5 1780  " " " -•0179 -.0718 -.1200 -.165  "  17  a .992 "  "  " "  " " -.0163 -.0652 -.1093 -.150 -•705 -1.172 -1.492 -2.065 -2.17 -2.207  " " .984 .937 .896 .86 .493 .309 .223 .126 •113 .109  CVsi0  2  1.018 1.044  1.102 1.166 1.241  1.321 1.418 1.51 1.51 I.56 I.63 1.72 1.095 •773 .62 .420 .435 .464  111000 67200 37800 26600 21100 17400  15100 13600 12900 10200 8480 7330 1040  -2510 -4080 -6230 -5330 -4590  Calculation of A c t i v i t y f o r ZnO to N r ^ y = O.50 The same techniques may be used to calculate a c t i v i t i e s f o r ZnO from  the phase diagram u t i l i z i n g the estimated entropy of fusion of 6 E.U.  - 59 -  - 6o Table V  Activity  1.  Congruent M e l t i n g  o f ZnO f r o m N^nO = 1.0  Compound. M e t h o d  to N  Z  n  =0.5  0  1 9  NT K  T°K  Zn0  • 765 •74 •72 • 70 .68 .64 .62 .60 •55 • 50  1780 1781.5 1782.5 1783.5  (Q-T)  5  3-5 2-5 1-5 •5 2  1784.5 1783.5 1780 5 10 1775 3k 1751 80 1705  2 ..  Liquidus  NznO  T°K  • 95  2148 2048 1948 1848  .90 • 85 .80 • 765 .Ik  .70 ,6k  .60 • 55 • 50  (N-X)  .098 •073 •053 •033 .013 -.026 -.046 -.066 -.116 -.166  Curve  I78O 1781.5 1783.5 1783.5 1Y75 1751 1705  (Q-T)/(N-X)  2  x  Si0 ^C J dN  520 654 890 1460 2960 2940 2360 2290 2520 2900  2  Z n 0  [Part  47 42  12 12  37 30 15 -29  14 14 12  -28 -41 -60 •132 •24l  -kl  -62 -102 -147  I]  AH Q  rn f  618 566 524 46l 283 -597 -922 -1280 -2450 -4070  Method  T-Tm/T  -.0465 -.0977 -.1540 -.2170 -.2630  in  a  -...141  -  .296 .467 .657 .797 .812 .842  -1.141  -1.336 -I.678  -2.176  a .868 .743 .626 .517 .45 .458 • 43 • • 351 .261  .I85 .112  CX ZnO .913 .825 • Y37  .647 .588 .62  .615 • 55 • 435 • 337 .224  -IbOOOO  -78OOO -52200 -39700 -33600 -24700 -19000 -16100 -18200 -18500 -17400  E\  Gibbs Duhem Integration  The Duhem-Margules Equation^! may be written as:  or ZnO  rtdN&io - ^sPiXsio 2  %i0  2  2  Table VI SiOo-ZnO Binary  %i0  2  .02 •05 .10 •15 .20 •25 •30 •35  - .40  •45  • 50 .60 • 70 .80 • 90 •95  •  Integration  ^Si02  Part I  Part I I  °^Zn0  -24400  -1400000  -460000 -178000 -99200  -1195000 -300000 -99000 -45200  -205000 -160000 -78400  -46ooo  -18000  -15800 -11000 -8000 -6000 -6000 "-6000 -5000 -3000 1000 .4000  10000 14000  21000 38000 67OOO  -64500  -35400 -27800 -22700 -18200  -14000  -7850 -3310 195 3550 6100  -24,000  -54000 -40500  -14000  -21400 ••:  - 9250 - 4500 1100 4000  6670 6000 5250 4230  3530  -28OOO .  -I855O -18200 -19300 -18300 -14500  -9300 -5050 -680 2570  *From Table V. The r e s u l t i n g C^plots are given i n figure .29-  °<Zn0*  -205000' -160000 -78000 -52000 -40000  -28000 -20000 -17000 -18000 -18000 -18000  NznO .98 •95 ' .90 • 85 .80 • 75 •70 •65 .60 •55 •50 .40  •30 .20 .10 •05  - 62 -  - 63 F.  . Excess Free Energy  Curve Table V I I  Excess Free Energy  of Z n 0 - S i 0 2 a t l600°C  NZnO  AF  •05 .10 •15 .20 • 25 •30 •35  227 280 155 -37 -265 -555 -892 -1260 -1593 -1750 -1927 -2064 -2064  AO  •45 • 50 •55 .60 •65 •70 •75 .80 •85 •90 •95  X S  -2048  -2257 -2166 -1781 -1584 -408  Based on the m e t a s t a b l e l i q u i d s t a n d a r d s t a t e s and c a l c u l a t e d from the (X curves by the method shown i n Appendix I I I .  G.  Comparison w i t h R i c h a r d s o n ' s F r e e Energy  Curve  0  R i c h a r d s o n ' s f r e e energy curve f o r the b i n a r y Z n 0 - S i 0 2 w i t h r e s p e c t t o the s o l i d  s t a n d a r d s t a t e s o f the two  components  8  i s shown i n f i g u r e  In the same f i g u r e the s t a n d a r d s t a t e s are changed t o the two pure  30-  liquids  and the r e s u l t i n g curve compared t o t h a t c a l c u l a t e d i n the p r e v i o u s s e c t i o n . The agreement i s q u i t e good.  - 65 APPENDIX I I I  Toop's Ternary I n t e g r a t i o n Technique  The  l o c a t i o n and d e f i n i t i o n o f terms used i n t h i s d e r i v a t i o n a r e shown  in figure 31.  Toop g i v e s the f o l l o w i n g e x p r e s s i o n  f o r the excess f r e e energy  within the t e r n a r y : ^ 1  The  excess f r e e energy i n a b i n a r y  AF  XS  = RT(Nj_ln #2.(2)  system i s g i v e n b y : N ln^2(l))  +  2  = ^(1-^)^X1(2) = %N (N CXi( ) 2  2  Thus by u s i n g t h e v a l u e s  + N (l-N ) tf 2  2  2  2 ( l )  + Nitf (i))  2  2  of a l l three ordinates  o f any one p o i n t , the  excess f r e e energy a t t h a t p o i n t may be c a l c u l a t e d by u s i n g t h e b i n a r y CX p l o t s . The  l o g ofJ t h e " a c t i v i t y c o e f f i c i e n t o f a component w i t h i n a t e r n a r y i s  g i v e n by t h e f o l l o w i n g Log^ ( ern) = 2  expression  L o g *  t  2  (l) +  'M  L°S* (tern) 2  RT \ ^  + (1-N )  ^ L o g »  2  a u ,  2  2  / x - w„« 2(tern) = 2  The CX p l o t s o f t h e b i n a r y  3  ) ]  [*iU-N )« (l)  ^3(^0(3(1)  2  2  (  N  e  3  2  1-J  2  ^  ^  Ni/N^) •  ^2(tern) ' v  systems CaO-SiOg and F e O - S i 0  ( F i g u r e s 32 and 33 r e s p e c t i v e l y ) .  A F  N (l-N )CX (3)]  +  + N g O f ! ^ ) )]  L o s  [  "  2  are included  3  -  65  -  APPENDIX I I I  loop's  Ternary I n t e g r a t i o n  Technique  The l o c a t i o n and d e f i n i t i o n o f terms used i n t h i s d e r i v a t i o n a r e shown i n f i g u r e 31*  Toop g i v e s t h e f o l l o w i n g e x p r e s s i o n  f o r t h e excess f r e e energy  within the ternary: -' 1  a»5»  *  - u V C^-J  t -"!) 1  The excess f r e e energy i n a b i n a r y AF  X  - RT(N ln? ( )  S  1  1  2  N /N 2  <*-%>  +  3  2  [^h] w  system i s g i v e n b y :  +  N  2  2  ^2(l))  l n  = Ni(l-N1)^Xi(2) + N ( l - N ) t f 2  2  = N^NaQfi^) Thus b y u s i n g the v a l u e s  2  2 ( l )  + NiCV (l)) 2  of a l l three ordinates  o f any one p o i n t , t h e  excess f r e e energy a t t h a t p o i n t may be c a l c u l a t e d by u s i n g the b i n a r y Of p l o t s . The l o g of.,:the " a c t i v i t y c o e f f i c i e n t o f a component w i t h i n a t e r n a r y i s given by the f o l l o w i n g Lo« ^ 2 ( t e r n ) = v  L o  L  L  l-N  expression: ^ 1  6 * 2(1) +  Log8  2  3  I-N2  2  1  ( ) J  N  - (l-N )  [AFjfJ  2  2  L g  ^r'  i  J  Ni/N3  °S^2(tern) 1-N )C< ( ) + 2  + (1-N ) 2  2  2  ^3(^0(3(1)  +  CL/*. \ - Mo ^2(tern) - 2 N  The CX p l o t s o f the b i n a r y  e  1  3  ^ (  systems C a O - S i 0  ( F i g u r e s 32 and 33 r e s p e c t i v e l y ) .  2  v  2  2  3  N 0fK3) )]  L o s e  N (l-N )a ( )]  t e  Nl  2  3  ^  /N^> •  ^) '  and F e 0 - S i 0  2  are included  - 66 -  Figure 31.  D e f i n i t i o n and Location of Terms Used i n Appendix I I I . ^  - 67 -  F i g u r e 32..  CX P l o t s f o r the FeO-Si0  2  Binary.  -  68  -  69 APPENDIX IV  Oxygen P o t e n t i a l  A.  Limits  1300 C o  1.)  Lover L i m i t Z n  0  (l)  —  Z  n  ( g )  = -6275 + 5-33 - Log P  3 9 Z n  T  flzn(g) a  =  22  Zn(l) Zn(l)i0-0^55  0 1  G ^ z J ( 0 )^ = 7.3=  •7 (9)  p  2  PQ  2.)  1  £2,6 x 10  2  0  -10  Upper L i m i t 2Cu + -gQ2  For u n i t a c t i v i t y of  AFQ^^^OK  Cu 0 2  Cu 0 2  at  =  -14200 c a l s .  1300°C  PP  B.  x  0  = 1.1 x 10"^  2  l600°C ^Zn(g)  = 78  TK  Qzn(l) P0  2  2- U.5 x 10-5  C9) kCu + 0 —*-2Cu 0 2  2  K  i873°K  Cu 0> 2  = 1 ,  0.18  3  8x 1  0  -  3  70 APPENDIX V Free Energy o f F o r m a t i o n o f Z n S i 0 k 2  The s l a g used i n runs I and J was  s a t u r a t e d i n b o t h ZnO and  Zn SiO^. 2  T h i s i n d i c a t e s t h a t t h i s s l a g may be used t o determine the f r e e energy of f o r m a t i o n o f Zn Si0ij. a t 1300  C.  2  The c a l c u l a t e d v a l u e f o r the s i l i c a a c t i v i t y a t t h i s p o i n t i s a p p r o x i m a t e l y Q-g Q^ = 0.2.  The s t a n d a r d s t a t e may be changed  i  from l i q u i d t o  s o l i d by the f o l l o w i n g e x p r e s s i o n based on an entropy o f fusibar, f o r S i 0  1.8  = 1560  dZnO(s) hence  a  s i 0 2  ( ) 1600 s  C  - 0.91  T =  .22  S i 0 ( s ) 1300 C = .2:0 u s i n g the r e g u l a r s o l u t i o n t h e o r y temperature n  d  of  E.U.:  .gzao(i)  a  2  Q  2  adjustment.  F o r the f r e e energy o f f o r m a t i o n o f Zn^SiO^ K = [ Z n O ] f SiO ] 2  g  = 0.2  [zn SiO^] 2  A F  1300 C = (1.98)(1573) I n (-20)  = -5000  cals.  K i t c h e n e r and Ignatowicz  20  g i v e the f o l l o w i n g e x p r e s s i o n f o r the f r e e energy o f  f o r m a t i o n o f ZngSiO^. A F = -7129 + 0.23 T AF1300 C = -6800 c a l s .  I n view of the r a t h e r l a r g e estimate-, o f e r r o r i n A H °  and  A S ° quoted i n  K i t c h e n e r and Ignatowicz's paper, the agreement i s q u i t e good.  

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