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Sodium activity measurements in the sodium-aluminium system Mitchell, John Christopher 1965

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SODIUM A C T I V I T Y MEASUREMENTS  IN.THE SODIUM - A L U M I N U M SYSTEM  by JOHN CHRISTOPHER M I T C H E L L B.-Sc., The U n i v e r s i t y o f B r i t i s h Columbia, ;  1962  A T H E S I S SUBMITTED I N P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS FOR.THE DEGREE OF MASTER OF SCIENCE  i n t h e Department of METALLURGY  We a c c e p t t h i s  t h e s i s as conforming.to the  standard required  from candidates f o r t h e  d e g r e e o f MASTER.OF  SCIENCE  Members o f t h e D e p a r t m e n t of Metallurgy  THE U N I V E R S I T Y OF B R I T I S H COLUMBIA April,  1965  In presenting the  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f •  B r i t i s h Columbia, I agree that available  the L i b r a r y  f o r r e f e r e n c e and s t u d y *  s h a l l make i t f r e e l y  I f u r t h e r agree that  per-  m i s s i o n f o r extensive, copying of t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by his  representatives.  cation  I t i s understood that, copying or p u b l i -  of t h i s thesis f o r f i n a n c i a l gain  w i t h o u t my w r i t t e n  Department of  permission*  Metallurgy  The U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r 8, Canada Date  May  3.  1965  s h a l l n o t be a l l o w e d  ABSTRACT  : Sodium a c t i v i t y  d a t a has been o b t a i n e d f o r t h e sodium - aluminum = 25 x 10"^  and  A d d i t i o n a l .data has a l l o w e d t h e c a l c u l a t i o n o f a c t i v i t y  data  system f o r sodium c o n c e n t r a t i o n s i n aluminum between % 75 x 10"^.  fs  u p t o N • = 300  x 10"".  N a  J00  x 10"^  The c o n c e n t r a t i o n i n t e r v a l  %  a  a  = 25  x 10  6  to  e n c o m p a s s e s t h o s e s o d i u m c o n c e n t r a t i o n s n o r m a l l y f o u n d i n com-  mercial pot-line  The  operation,  sodium a c t i v i t y  d a t a has been c o l l e c t e d b y u s i n g a two-phase  distribution  equilibrationof  r i c h phase.  The s o d i u m - l e a d s y s t e m was u s e d a s a r e f e r e n c e f o r t h e d e t -  ermination of the a c t i v i t y  sodium between a - l e a d - r i c h and an aluminum-  o f sodium.  . The s o d i u m e x h i b i t s l a r g e p o s i t i v e d e v i a t i o n s f r o m i d e a l i t y i n the  sodium-aluminum system.  The s o d i u m a c t i v i t y  shows a s t r o n g  dependence  on t h e s o d i u m c o n c e n t r a t i o n o f t h e a l u m i n u m phase f o r s o d i u m c o n c e n t r a t i o n s below N = 100 Na  x  10" .  The a c t i v i t y  6  d a t a f o r aluminum i n t h e sodium-aluminum system  h a s b e e n o b t a i n e d b y t h e G i b b s - Duhem i n t e g r a t i o n o f t h e s o d i u m data. can  The d a t a f o r t h e a l u m i n u m i n d i c a t e s t h a t t h e a c t i v i t y  be c o n s i d e r e d e q u a l t o i t s mole f r a c t i o n  miscibility  o f t h e sodium-aluminum system.  over the e n t i r e  activity  o f aluminum range o f  ACKNOWLEDGEMENT  The a u t h o r would l i k e t o e x p r e s s h i s t h a n k s t o D r . C. S. Samis f o r h i s encouragement and guidance t h r o u g h o u t t h e p e r i o d o f t h i s work, and t o D r . E. W. Dewing, o f A l u m i n i u m L a b o r a t o r i e s , whose comments and s u g g e s t i o n s w i t h r e g a r d t o Appendix A were most  helpful.  Thanks a r e a l s o extended t o A l u m i n i u m L a b o r a t o r i e s and t h e Aluminum Company o f Canada f o r m a t e r i a l s and. i n f o r m a t i o n t h a t t h e y have so generously  provided. Acknowledgement i s made o f f i n a n c i a l a i d f r o m t h e N a t i o n a l R e s e a r c h  C o u n c i l o f Canada, under G r a n t A-IM-63, w h i c h made t h i s work p o s s i b l e .  . .TABLE OF CONTENTS  Page  INTRODUCTION . . '.  1  1) .. P r e v i o u s Work o n . t h e S o d i u m - A l u m i n u m - C r y o l i t e  . 1  System  2  a ) .. S o d i u m - A l u m i n u m - C r y o l i t e S y s t e m s b ) .. S o d i u m - A l u m i n u m - C r y o l i t e - L e a d S y s t e m s 2) . P u r p o s e 5).  4 6  of the Present Investigation  Method o f Measurement  k).-Region  .  6  .  9  of Investigation  10  .- EXPERIMENTAL .1).  10  Apparatus  2).  Materials  5).  Crucibles  10  •  10  k).. F u r n a c e  10  5) . T e m p e r a t u r e . C o n t r o l  10  6) . Gas S u p p l y  1  7) . E x p e r i m e n t a l P r o c e d u r e  2  12  . . .  8) .. E q u i l i b r a t i o n ' T i m e s  12  9) .. C h e m i c a l A n a l y s i s  12  • 10) .• S o u r c e s o f E r r o r  1^ 1^  a) . A n a l y s i s b) . C r u c i b l e s  1^15  c) . Temperature  16  RESULTS . 1)... E x p e r i m e n t a l 2).. C a l c u l a t i o n s  . .  •  16 .16  Table of Contents (Continued).  Page .27  DISCUSSION 1) . E x c e s s Thermodynamic P r o p e r t i e s  o f Sodium i n Sodium-Aluminum  2) . The A c t i v i t y o f Sodium  3Q  : 3). The A c t i v i t y - o f Aluminum  30  . h)..The P a r t i a l M o l a l Heat o f S o l u t i o n o f Sodium  3^  CONCLUSIONS  .36 37  RECOMMENDATIONS FOR .FURTHER.WORK APPENDIX- A: THE DETERMINATION OF THE ACTIVITY OF NaF AND A1F,- IN SODIUM FLUORIDE - ALUMINUM FLUORIDE'MELTS . . . . . . . . 1  A.  27  .  38  A c t i v i t y . ' D a t a f o r NaF and A l F j from t h e A c t i v i t y o f Sodium i n NaF - A1F  38  Melts  X  3 1) .. E v a l u a t i o n  of the E q u i l i b r i u m Constant  2) . . C a l c u l a t i o n o f l o g Y B.  Thermodynamic A n a l y s i s  N a F  /N|  44  and l o g i f r A l F j / ^ N a F  1 F 5  o f t h e Sodium F l u o r i d e  ^  - Aluminum  : F l u o r i d e System  46  1) . . C a l c u l a t i o n o f A c t i v i t i e s from t h e NaF - A l F j Phase Diagram k6 a) . The NaF - A l F ^ Phase Diagram  .48 50  b) . The E n t r o p y o f F u s i o n  2) . C a l c u l a t i o n o f log"t jj p-/ AlF5  f  3) . The C a l c u l a t i o n o f logY.AlFj  • *  w  r  o  a  C.  Discussion  • APFENDIX  t h e Phase Diagram . . .  APPENDIX C : . THE SODIUM - ALUMINUM SYSTEM . 'V  51 56  • • •  B: . THE SODIUM - LEAD SYSTEM  BIBLIOGRAPHY  m  59  64 73 78  LIST OF FIGURES Figure Number  Page  1.  S o d i u m - C o n c e n t r a t i o n o f L i q u i d Aluminum i n E q u i l i b r i u m w i t h NaF - A l F j M e l t s  2.  Sodium C o n c e n t r a t i o n i n L i q u i d Lead i n E q u i l i b r i u m  3  with 7  NaF - A l F ^ M e l t s 3.  C r o s s - s e c t i o n of E q u i l i b r a t i o n Apparatus  k.  Sodium D i s t r i b u t i o n between L i q u i d Aluminum a n d - L i q u i d Lead  5. 6.  s'^N /^Al ration  l o  11.  12.  i n  L i (  a  l  u i d  l o g V /N ration at  22  .  23  i n L i q u i d Aluminum as a F u n c t i o n o f C o n c e n t 1010 °C  28  ° s V ] i j / N ^ i n L i q u i d Aluminum as a F u n c t i o n o f Concent-, r a t i o n a t 1010-°C, f o r t h e Range o f C o m p o s i t i o n o v e r w h i c h Sodium.and Aluminum a r e M i s c i b l e a t 800 °C  29  A c t i v i t y o f Sodium i n L i q u i d Aluminum as a F u n c t i o n o f C o m p o s i t i o n a t 1010 °C  31  w  1  20  - Aluminum as a F u n c t i o n o f C o n c e n t -  P a r t i a l M o l a l Heat o f S o l u t i o n o f Sodium i n L i q u i d Aluminum as a F u n c t i o n o f C o n c e n t r a t i o n  8.  10.  17  •at Four E q u i l i b r a t i o n Temperatures Sodium A c t i v i t y i n L i q u i d Lead as a F u n c t i o n o f C o n c e n t r a t i o n a t Three Temperatures  7.  9.  11  . . . . . . . . .  a  A1  1  - A c t i v i t y o f Sodium i n L i q u i d Aluminum as a F u n c t i o n o f C o m p o s i t i o n a t 1010 °C, f o r t h e Range o f C o m p o s i t i o n over w h i c h Sodium and Aluminum a r e M i s c i b l e a t 800 °C  32  l o g y ^ - | _ / N j j i n L i q u i d Aluminum as a F u n c t i o n o f C o m p o s i t i o n a t 1010 "C, f r o m a Gibbs - Duhem I n t e g r a t i o n o f l ° g " ^ N / N ^ Values from F i g u r e 8  35  The A c t i v i t y o f Sodium i n L i q u i d Aluminum as a F u n c t i o n o f t h e NaF - A l F j r a t i o i n NaF - A l F j M e l t s . . . . . . . . .  .43  The V a l u e s o f l o g i N a F ^ A I F 5 SAlF3'/ NaF ° as a F u n c t i o n o f t h e C o m p o s i t i o n , f r o m t h e Computer R e s u l t s  bj  The Phase Diagram o f t h e NaF - A l F ^ B i n a r y System  1+9  a  a  A-l.  A-2.  h-3. A-k  a  l o  S^  / AiF N  N a F  a  t  1010  n  d  l o  N  a  t  1  0  1  0  c  °C,. D e r i v e d f r o m t h e NaF - A I F 3  B i n a r y Phase'diagram u s i n g W a g n e r ^ M e t h o d  .  57  L i s t of Figures  (continued)  Figure Number A-5.  A-6.  Page  2 *v 2 log"/ A l F j / % a F 1010- ° , D e r i v e d f r o m l o g • N a F / ^ A l F j v a l u e s i n F i g u r e A-k, U s i n g t h e Gibbs - Duhem I n t e g r a t i o n Technique . . 60 a  t  Comparison o f l o g ^ N / A l F ° Computer R e s u l t s o f E x p e r i m e n t a l Data f r o m F i g u r e A-2 and. t h e T h e o r e t i c a l R e s u l t s from: Wagner s Method ( F i g u r e N  V  a  l  u  e  s  a  t  1  0  1  0  f  o  r  t  h  e  a F  1  62  A-4)  2  k/  A-7.  B-l.  B^2.  C-l. C-2. C-3.  Comparison o f l ° g / /% V a l u e s a t 1010 °, f o r t h e Computer R e s u l t s o f F i g u r e A-2 and. t h e T h e o r e t i c a l R e s u l t s f r o m F i g u r e A-5 . . . . 63 P a r t i a l , M o l a l Heat o f S o l u t i o n o f Sodium i n L i q u i d Lead as a Function of Concentration . . . . . . . . . 11 A 1 F  ^Na^Fb a t kJ3 °C  l o s  i n  L i (  l  u i < i L e a d  a F  -  a s  a  Function of Concentration  72  Phase Diagram f o r t h e Sodium - Aluminum System,.Showing the Hypo-eutectic - Monotectic L i q u i d u s .  . . 7^  Phase Diagram .for t h e Sodium - Aluminum'System, Showing t h e S o l u b i l i t y L i m i t o f Sodium . .  -75  logN  N a  v s . 1/T from.Ransley  and N e u f e l d ' s ^ Data 2  ... . .  .77  L I S T OF TABLES  Page  Table  1.  • 5  2.  18  3.  . 19  k.  2k  5-  .25  6.  G i b b s - Duherri:; I n t e g r a t i o n o f t h e S o d i u m - A l u m i n u m B i n a r y -  A-l.  Sodium C o n t e n t o f Aluminum M e t a l under Sodium F l u o r i d e  -  A-2.  Sodium C o n t e n t o f Aluminum: M e t a l u n d e r S o d i u m : F l u o r i d e  -  •A-3.  Sodium .Content o f Aluminum M e t a l under S o d i u m ; F l u o r i d e  k-k. A-5.  .33 . 39 ko  -  Ml . S o d i u m C o n t e n t o f A l u m i n u m : M e t a l u n d e r Sodium. F l u o r i d e  -  D e t e r m i n a t i o n o f t h e A c t i v i t y : o f N a F by, I n t e g r a t i o n o f t h e  •53 • A-6.  .Determination of the A c t i v i t y  o f NaF b y I n t e g r a t i o n o f t h e  Aluminum  A-7.  Calculation of the A c t i v i t y  B-l.  Sodium A c t i v i t y ' D a t a f o r the-Sodium - Lead System  B-2.  Sodium A c t i v i t y Data f o r t h e Sodium - Lead System  B-3-  Sodium A c t i v i t y Data f o r t h e Sodium - Lead System  of  Fluoride by the  . . . . . . . . . . . .  .58 • 65 . 66 • 67 68  B-4. B-5.  C a l c u l a t i o n o f t h e A c t i v i t y o f Sodium i n Sodium - Lead A l l o y s a t 725°C, 775° a n d 825° . . .,  • 70  C-l.  P a r t i a l M o l a l Heat o f S o l u t i o n o f Sodium i n Aluminum  • 76  . . .  SODIUM A C T I V I T Y MEASUREMENTS I N THE SODIUM - ALUMINUM SYSTEM.  INTRODUCTION  Aluminum  i s produced commercially by the e l e c t r o l y t i c  of aluminum o x i d e d i s s o l v e d  i n molten c r y o l i t e .  reduction  There i s considerable  c o n t r o v e r s y o v e r t h e a c t u a l m e c h a n i s m s o f r e d u c t i o n , a n d much o f t h i s disagreement i s a t t r i b u t a b l e with cryolite..  Cryolite  to the experimental d i f f i c u l t i e s  i s o x i d i z e d i n a i r t o produce aluminum  which then dissolves i n the c r y o l i t e , on t h e phase diagram. / cell  i n working oxide,  causing the liquidus lines to s h i f t  I n a d d i t i o n , a t the operating temperature of the  0 .  ( a b o u t 950 C ) , c r y o l i t e  hydrogen  c a n h y d r o l y z e t o f o r m aluminum o x i d e and  fluoride. An e q u i l i b r i u m r e a c t i o n i n v o l v i n g sodium f l u o r i d e and aluminum  t o produce aluminum f l u o r i d e and sodium i s r e s p o n s i b l e f o r t h e p r e s e n c e o f sodium i n t h e aluminum phase.  A d d i t i o n a l sodium might r e s u l t from t h e  s i m u l t a n e o u s d e p o s i t i o n o f sodium and aluminum a t t h e cathode as a r e s u l t of an o v e r v o l t a g e . 1.)  P r e v i o u s work on t h e S o d i u m - A l u m i n u m - C r y o l i t e  System:  1 Grunert  h a d s u g g e s t e d t h a t sodium gas a t a t m o s p h e r i c  pressure 0  w o u l d b e t h e r e s u l t o f r e a c t i o n b e t w e e n c r y o l i t e a n d a l u m i n u m a t 1 0 0 0 C. S u b s e q u e n t i n v e s t i g a t i o n s h a v e shown t h a t p r o d u c t i o n o f s o d i u m a t a t m o s pheric  p r e s s u r e does n o t o c c u r .  veniently  These l a t e r i n v e s t i g a t i o n s c a n be c o n -  s e p a r a t e d i n t o two c a t e g o r i e s , t h o s e i n v o l v i n g s o d i u m , aluminum,  and c r y o l i t e ,  i n w h i c h t h e s o d i u m c o n c e n t r a t i o n i n t h e a l u m i n u m was m e a s u r e d ;  and t h o s e i n v e s t i g a t i o n s u s i n g sodium, aluminum and c r y o l i t e , lead,  i n w h i c h t h e s o d i u m a c t i v i t y was m e a s u r e d .  together  with  - 2 -  a.)  Sodium, Aluminum, C r y o l i t e  Systems:  2. Herman and J a n d e r 3NaF  ( l )  A l  +  s t u d i e d the r e a c t i o n : (  l  )  *=±  3(Na)  ( d i l )  +  AlF  3 ( l )  0 a t 1090  C i n alumina c r u c i b l e s under an atmosphere  nitrogen.  o f d r y , oxygen-free  The e q u i l i b r i u m c o n s t a n t f o r the r e a c t i o n was  terms o f c o n c e n t r a t i o n .  expressed i n  T h e i r r e s u l t s , which show an i n c r e a s e i n sodium  c o n t e n t o f the aluminum w i t h the i n c r e a s i n g NaF/AlF^ r a t i o - , a r e shown i n figure  1. P e a r s o n and Waddington  3  0  performed s i m i l a r experiments a t 1000 C  over a range o f sodium f l u o r i d e - a l u m i n u m f l u o r i d e m e l t c o m p o s i t i o n s . r e s u l t s were i n agreement  w i t h those found by Herman and J a n d e r .  r e s u l t s were p l o t t e d i n f i g u r e  Their  Their  L k  Dewing and H o l l i n g s h e a d have measured the sodium c o n t e n t o f aluminum as a f u n c t i o n o f the NaF/AlF^ r a t i o n a t 1025°C. were i n agreement  Their  results  w i t h those o f Herman and Jander, and Pearson and  and have been p l o t t e d i n f i g u r e  Waddinton,  1.  Dewing'' measured the sodium c o n t e n t o f the aluminum i n a r e a c t i o n i n v o l v i n g the same r e a c t a n t s , sodium f l u o r i d e and aluminum:  6NaF  ( s )  There was,  +  A  1  (  i  )  ^=±  Na AlF 3  6 ( s )  +  3 1 f e  (  d  l  l  )  however, a s i g n i f i c a n t d i f f e r e n c e between t h i s  and those d i s c u s s e d above, i n t h a t t h e r e were now Na^AlFg, and the l i q u i d aluminum phase p r e s e n t .  two s o l i d phases, NaF Any  system c o n s i s t i n g  'the NaF/AlF^ r a t i o i s used throughout t h i s paper as the weight r a t i o o f sodium f l u o r i d e t o aluminum f l u o r i d e .  reaction and  - 3 -  o o  0. 015 —  o w  -p <u o  u  (L)  0.010 —  o  P-I  -p  o  •H  o o  o  o 0.005  o  •  A  D e w i n g a n d Hollingshead'(1025°) P e a r s o n a n d W a d d i n g t o n ^ (1000°) Herman a n d J a n d e r (1090°) 2  0.90  1.10  1.30 NaF  1.50  1.70  • O  •  1.90  - AUF- r a t i o  F i g u r e 1; S o d i u m c o n c e n t r a t i o n o f l i q u i d A l u m i n u m i n E q u i l i b r i u m A1F Melts. w i t h NaF 3  - k -  of t h r e e phases and two components can o n l y have one degree o f freedom, and hence t h e sodium c o n c e n t r a t i o n o f t h e aluminum was d e t e r m i n e d s o l e l y by t h e t e m p e r a t u r e .  0  Dewing's measurements were o v e r t h e t e m p e r a t u r e range  0  679  t o 896 , and t h e r e s u l t s have been l i s t e d i n t a b l e 1.  6 Stokes and F r a n k  d e t e r m i n e d sodium a c t i v i t i e s b y m e a s u r i n g t h e  vapour p r e s s u r e o f sodium i n t h e fumes above a b a t h o f m o l t e n and aluminum.  cryolite  A g r a p h i t e c e l l c o n t a i n i n g t h e c r y o l i t e and aluminum was  p l a c e d i n s i d e an i n d u c t i o n c o i l i n such a way t h a t t h e l i g h t p a t h o f a s p e c t r o g r a p h p a s s e d t h r o u g h t h e c e l l , and t h e amount o f sodium i n t h e vapours above t h e charge c o u l d be measured by t h e d e c r e a s e i n t h e i n t e n s i t y o f t h e l i g h t r e a c h i n g t h e s p e c t r o g r a p h . E x p e r i m e n t s were done f r o m  0 1100  0 down t o 700 C.  B y comparing t h e measured  sodium vapour p r e s s u r e  above t h e b a t h a t any g i v e n t e m p e r a t u r e w i t h t h e vapour p r e s s u r e o f pure sodium a t t h e same t e m p e r a t u r e , i t was p o s s i b l e t o c a l c u l a t e t h e a c t i v i t y of  sodium a f t e r e q u i l i b r i u m had been a t t a i n e d . b.) Sodium, Aluminum, C r y o l i t e and Lead  Systems:  7 F e i n l a b and P o r t e r  s t u d i e d t h e sodium a c t i v i t y under  m e l t s h a v i n g v a r i o u s NaF/AlF^ r a t i o s .  cryolite  The a c t i v i t y o f t h e sodium was  measured by m a i n t a i n i n g t h e aluminum and t h e c r y o l i t e m e l t i n e q u i l i b r i u m w i t h a l e a d phase. electrolytic  A s e p a r a t e s t u d y i n w h i c h t h e e.m.f. o f t h e f o l l o w i n g  cell: Na(Fb) j e l e c t r o l y t e c o n t a i n i n g Na  were measured  gave t h e a c t i v i t y o f sodium as a f u n c t i o n o f t h e sodium con-  c e n t r a t i o n i n t h e l e a d phase. aluminum,  | Na  E q u i l i b r a t i o n s t u d i e s f o r t h e sodium,  c r y o l i t e , l e a d system were c a r r i e d o u t a t t e m p e r a t u r e s between  TABLE  1.  Dewing's Data"? • I  .11  IV  III  Pemp. ° C wt <jo Na% a x:l e 0  679 682 691 693 764 765 766 77H-  776 778 781  . 0.0111 0.011 0.012 0.011 0.024  0.022 0.022 0.025 0.021  0.025  0.024  128 128 i4o  128 281 257 257 293 246  293 281  A F (Kcal/mole)  16.45 16.k2  V a  Na(T)  O.O55I  14.75 14.60  O.O65O O.O583 0.0591 0.0914 0.0908 0.0924 0.0964  14.51 •14.48  O.O986 O.O998  16.23 16.30  14.78  14.83 14.57  0.0972  VI  ^Na(T)  450.5 437.5 416.4 461.7 325.3 353.3 359,5 329.0 395-1 335.0 355-2  VII L O  S  ?Ha(T)-  log  TNa(lOlO)  2.634 2.641 2.620  2.087 2.101 2.100  2.512  2.140 2.177 2.179  . 2.664  . 2.548  2.556 2.504 2.597 2.526 2.550  IX  VIII  2.148  2.145 2.242  2.175 2.207  L O  S  ^NaaOlO) Nil  2.087 2.101 2.100  2.148 2.140  2.178 .2.180 2.146 2.245  2.176 2.208  X  ^(1010) 0.0156 0.0161 0.0176 0.0180 , 0.0388 VJ, 0.0586 . 0.0588 0.C409 0.0429  0.01+58  0.0452  - 6 -  9H-0° and 1010°C i n a l u m i n a c r u c i b l e s u s i n g a l u m i n a - s a t u r a t e d pure c r y o l i t e . An a t t e m p t was made t o a p p r o a c h e q u i l i b r i u m f r o m t h e h i g h - s o d i u m as as t h e low-sodium s i d e .  well  The sodium c o n c e n t r a t i o n was d e t e r m i n e d i n t h e  l e a d phase o n l y . . The r e s u l t s , p l o t t e d i n f i g u r e 2 , show t h a t t h e sodium:content o f t h e l e a d phase i n c r e a s e s w i t h an i n c r e a s i n g N a F / A l F j ratio. 8 Aylen lead a l l o y s .  e q u i l i b r a t e d m i x t u r e s o f aluminum, c r y o l i t e and sodium-  The runs were done a t 1010°C u s i n g a l u m i n a - s a t u r a t e d  and a l u m i n a c r u c i b l e s .  cryolite  The N a F / A l F j r a t i o was v a r i e d between 1.07 and I.70.  The r e s u l t s , w h i c h have been p l o t t e d i n f i g u r e 2  compare r e a s o n a b l y w e l l  w i t h t h o s e o b t a i n e d by F e i n l a b and P o r t e r a t s i m i l a r N a F / A l F j r a t i o s , a l t h o u g h t h e sodium c o n c e n t r a t i o n s measured b y - A y l e n t e n d e d t o be l o w e r t h a n t h o s e r e p o r t e d by F e i n l a b and P o r t e r . . 2.)  Purpose o f t h e P r e s e n t . I n v e s t i g a t i o n : I n t h e above-mentioned i n v e s t i g a t i o n s o f t h e sodium-aluminum-  c r y o l i t e system, w i t h o r w i t h o u t a l e a d phase b e i n g p r e s e n t , no d a t a s u i t a b l e f o r t h e c a l c u l a t i o n o f t h e e x c e s s thermodynamic p r o p e r t i e s o f t h e sodium-aluminum s y s t e m were r e p o r t e d .  The o b j e c t o f t h e p r e s e n t r e s e a r c h  was t o measure t h e sodium a c t i v i t y as a f u n c t i o n o f c o m p o s i t i o n i n sodiumaluminum a l l o y s and, i n so d o i n g , t o o b t a i n thermodynamic d a t a on t h e e x c e s s p r o p e r t i e s o f sodium i n aluminum, and t o d e t e r m i n e t h e p a r t i a l m o l a l heat o f s o l u t i o n o f sodium i n aluminum. 3.)  Method o f Measurement: The d a t a on sodium a c t i v i t y i n t h e sodium-aluminum.system was  o b t a i n e d by a l l o w i n g sodium t o r e a c h a d i s t r i b u t i o n e q u i l i b r i u m between  - 7 -  o 6.0  5.0  —  a*?  — a o  SH <D P-. -P  3.0  A  —  A  A * A  •a  •H  4  A  A  .2.0 A  A  A  7  1.0  F e i n l a b and P o r t e r  1 0.90  (1010°) (970°) o (9^0°)  1  (  1.10  1.30 NaF  Figure  1  (  1.50  C 3 Q ^  Aylen°(l010°)  1.70  1.90  - AlF^ ratio  2; S o d i u m C o n c e n t r a t i o n i n L i q u i d L e a d i n E q u i l i b r i u m w i t h NaF - A l F ^ M e l t s .  - 8 -  l e a d and aluminum.  The a c t i v i t y  o f s o d i u m was  the  sodium c o n c e n t r a t i o n  the  sodium c o n t e n t o f t h e aluminum,  i n sodium-lead a l l o y s . i t was  excess p r o p e r t i e s o f t h e sodium-aluminum the  known a s a f u n c t i o n o f  s o d i u m ^ l e a d s y s t e m was  reported  Therefore,  by measuring  p o s s i b l e t o o b t a i n d a t a on t h e  system.  A detailed analysis of  i n A p p e n d i x B.  The a l u m i n u m - l e a d s y s t e m was  chosen f o r s e v e r a l reasons.  In the  9 f i r s t place, solubility  l e a d and aluminum a r e i m m i s c i b l e .  o f aluminum  i n l e a d a t JOO°C was r  Hansen  reported  l e s s t h a n 1.5  that the  atomic percent  a n d t h a t t h e s o l u b i l i t y o f l e a d i n a l u m i n u m a t t h i s t e m p e r a t u r e was order  o f 0.22  atomic percent.  A t these low c o n e n t r a t i o n s  expected that the e f f e c t of the i n t e r a c t i o n c o e f f i c i e n t s aluminum  on t h e a c t i v i t y  contain only very  i t might of lead  l e a d s y s t e m was  res-  s m a l l a m o u n t s o f s o d i u m ( t h e maximum amount o f atomic percent)  t h e number o f s u i t a b l e methods b y w h i c h t h e  s y s t e m c o u l d be s t u d i e d .  and  A s e c o n d c o n s i d e r a t i o n was tha'^ s o d i u m - a l u m i n u m  s o d i u m t h a t c a n be d i s s o l v e d i n a l u m i n u m a t 800°C i s 0.J1 which r e s t r i c t s  be  o f sodium i n the aluminum and l e a d phases  p e c t i v e l y w o u l d be s m a l l . alloys  of the  A t h i r d reason f o r s e l e c t i n g the  the fact that a considerable  sodium-aluminum sodium-aluminum-  amount o f r e s e a r c h  has  done on t h e a c t i v i t y o f s o d i u m , i n s o d i u m - l e a d a l l o y s , w h i c h w o u l d c a l c u l a t i o n of the a c t i v i t y  o f sodium i n aluminum t o a c o n s i d e r a b l e  been  allow degree  o f a c c u r a c y . . I n a d d i t i o n , s o d i u m e q u i l i b r a t i o n s done w i t h l e a d - s o d i u m a l l o y s as a source o f sodium, r a t h e r than u s i n g the  c r y o l i t e as a s o u r c e o f  sodium, a v o i d e d t h e t e c h n i c a l problems t h a t would have been e n c o u n t e r e d  had c r y o l i t e been u s e d .  - 9 h.)  Region o f I n v e s t i g a t i o n : E x p e r i m e n t a l l y , i t was p o s s i b l e t o e q u i l i b r a t e t h e sodium-  aluminum-lead m e l t s between O.25O.  sodium c o n c e n t r a t i o n s o f N j ^ p ^ j  =  0.080 t o  F o r lower sodium c o n c e n t r a t i o n s , i t was d i f f i c u l t t o g e t s a t i s f a c t o r y  r e p r o d u c i b i l i t y f o r t h e sodium a n a l y s i s o f t h e aluminum phase u s i n g t h e flame-spectrophotometer because t h e sodium c o n c e n t r a t i o n s were o f t h e order o f 0.5 t o 1 p a r t p e r m i l l i o n .  A maximum sodium l e v e l a t t a i n a b l e was imposed  by d i f f i c u l t i e s encountered i n h a n d l i n g l e a d samples c o n t a i n i n g sodium i n excess o f N. . , . •= 1NSL f IT D  0.250, f o r above t h i s amount, t h e a l l o y s became q u i t e  j  h y d r o s c o p i c and t h e r a t e o f m o i s t u r e p i c k - u p a f f e c t e d t h e a c c u r a c y o f t h e sample w e i g h i n g s . In o r d e r t o extend t h e range o v e r which t h e sodium a c t i v i t y was 1 known as a f u n c t i o n o f i t s c o n c e n t r a t i o n i n t h e aluminum,. Dewing %  5 y  results  f o r the r e a c t i o n : 6NaF,  .  (s) were used.  +  Al  «==*-'  (l)  3(Na) '  K  ;  (dil)  +  Na A1F 3  6(B)  The f r e e energy change f o r t h i s r e a c t i o n a t each o f t h e temper-  a t u r e s was' c a l c u l a t e d , and from t h i s , t h e sodium a c t i v i t y as a f u n c t i o n o f i t s c o n c e n t r a t i o n was determined.  - 10 -  EXPERIMENTAL  .1.)  Apparatus: The  figure  apparatus used  i n t h e e q u i l i b r a t i o n s t u d i e s i s shown i n  3•  2.)  Materials: The  aluminum used  i n t h e s e s t u d i e s was k i n d l y s u p p l i e d b y t h e  Aluminum:Company o f C a n a d a , > L t d .  I t was " s u p e r - p u r i t y " g r a d e ,  analyzing  99•997% a l u m i n u m , w i t h l e s s t h a n 0.001% b y w e i g h t o f s o d i u m p r e s e n t . B a k e r a n d Adamscn r e a g e n t g r a d e  sodium and l e a d were used, a s w e l l a s American  S m e l t i n g a n d R e f i n i n g Company t e s t - l e a d .  3 .)  Crucibles: The  e q u i l i b r a t i o n s were c a r r i e d o u t i n a l u m i n a c r u c i b l e s .  w e r e M c D a n e l ^ A V 3 0 c r u c i b l e s a n d M o r g a n i t e RR r e c r y s t a l l i z e d The  thermocouple  These  crucibles.  p r o t e c t i o n t u b e s w e r e M o r g a n i t e RR g r a d e m a t e r i a l .  The  c r u c i b l e s w e r e p l a c e d i n s i d e a s t a i n l e s s s t e e l s u s c e p t o r c r u c i b l e t h a t was fitted with a stainless steel l i d . .k.)  . Furnace: A Phillips  induction unit,  I70/55O V, 3 - p h a s e , 12 kw. o u t p u t was  used.  5•)  Temperature  Control:  A chromel-alumel thermocouple  placed i n a hole d r i l l e d  i n the  w a l l o f t h e s t a i n l e s s s t e e l s u s c e p t o r was u s e d t o m e a s u r e t h e t e m p e r a t u r e . This thermocouple in millivolts. and  was a t t a c h e d t o a n IMRA r e c o r d e r w h i c h r e a d t h e t e m p e r a t u r e  A PH-1653 r e g u l a t i n g u n i t was c o n n e c t e d t o t h e t h e r m o c o u p l e  recorder t o provide automatic temperature  control.  The a c t u a l  melt  5 mm. Tube.  Control  0. D.  Vycor  Thermocouple.  Induction  Coils.  Alumina Thermocouple P r o t e c t i o n Tube.  S t a i n l e s s S t e e l Cont a i n e r machined t o accommodate a n a l u m i n a crucible. • M e a s u r i n g Thermocouple.  Alumina  Figure  3;  Cross-section of Equilibration  Ring.  Apparatus.  - 12 -  t e m p e r a t u r e was  measured by a second c h r o m e l - a l u m e l thermocouple  t o a 3 1 8 4 p o t e n t i o m e t e r manufactured  connected  by H': T i n s l e y a n d Company,. S t . J e r o m e ,  ,Quebec.  6. )  Gas  Supply:  Commercial I t was  a r g o n f r o m t h e C a n a d i a n - L i q u i d A i r Company was  d r i e d by passage  7. )  through s i l i c a  used.  g e l before entering the apparatus.  Experimental Procedure: A l l o y s w e r e p r e p a r e d b y p l a c i n g a b o u t 30  grams o f l e a d and v a r i o u s amounts o f sodium,  u s u a l l y b e t w e e n 0.5  2.5  and  grams, i n a c r u c i b l e and p u r g i n g w i t h d r i e d a r g o n f o r h a l f an hour. t e m p e r a t u r e was  50  grams o f a l u m i n u m ,  The  t h e n r a i s e d t o t h e d e s i r e d l e v e l and m a i n t a i n e d t h e r e f o r  f o u r h o u r s . • A f t e r f o u r h o u r s t h e c r u c i b l e s were removed and quenched as r a p i d l y a s p o s s i b l e b y means o f a w a t e r - c o o l e d c o p p e r b l o c k a n d a n i n order t o r e t a i n the e q u i l i b r i u m c o n d i t i o n s .  The  air-jet,  a l l o y s were removed  from t h e c r u c i b l e s and t h e l e a d - and a l u m i n u m - r i c h phases were s e p a r a t e d f o r sodium  analysis.  8. ) . E q u i l i b r a t i o n .,. A y l e n  Times:  r e p o r t e d t h a t . t w o h o u r s a t 1010  C was  s u f f i c i e n t time t o  a t t a i n e q u i l i b r i u m i n the s o d i u m - a l u m i n u m - c r y o l i t e - l e a d system. i n v e s t i g a t i o n t h e r u n s were d o n e a t t e m p e r a t u r e s  200  to  300°  In  lower than  A y l e n ' s work,.and a s e t o f runs a t v a r i o u s l e n g t h s o f time i n d i c a t e d maintenance  9. )  o f the e q u i l i b r i u m temperature  Chemical  f o r f o u r hour's was  this  that  adequate.  Analysis:  As has been m e n t i o n e d  above,  t h e quenched a l l o y s were b r o k e n  into  - 13 -  t h e i r l e a d - and. a l u m i n u m - r i c h p h a s e s .  The l e a d phase, w h i c h generally-  weighed between 35 and kO grams, was d i s s o l v e d i n 25O mis o f J.2N n i t r i c a c i d i n P y r e x b e a k e r s . ..Complete d i s s o l u t i o n t o o k between t h i r t y and. f o r t y f i v e minutes.  The s o l u t i o n was t h e n f u r t h e r d i l u t e d t o c o n c e n t r a t i o n s s u i t -  a b l e f o r a n a l y z i n g t h e sodium c o n t e n t u s i n g a flame s p e c t r o p h o t o m e t r y technique.  . Each a l u m i n u m - r i c h phase was reduced t o t u r n i n g s and a n a l y z e d in quadruplicate. O.75  Each o f t h e q u a d r u p l i c a t e samples, w h i c h weighed  grams was d i s s o l v e d . i n 50 mis., o f 3.2N n i t r i c a c i d .  D i s s o l u t i o n , which  •took b t o 6 hours was performed i n 100$ s i l i c a beakers ( " V i t r o s i l " ) with Teflon,watch-glass covers.  about  fitted  A f t e r t h e aluminum t u r n i n g s had been d i s -  s o l v e d , t h e s o l u t i o n s were e v a p o r a t e d a l m o s t t o d r y n e s s and t h e n made up t o 50 mis w i t h d i s t i l l e d w a t e r , r e a d y f o r a n a l y s i s on t h e flame s p e c t r o p h o t o meter . I n t h e sodium a n a l y s i s o f t h e l e a d phase, i t was found c o n v e n i e n t t o a d j u s t t h e volume o f t h e sample such t h a t t h e sodium c o n c e n t r a t i o n would be between 5 and.10 micrograms p e r m i l l i l i t r e o f s o l u t i o n . c o n t a i n i n g - 1 , 5* 10, 20 and 50 micrograms/ml. the  Standards  o f sodium were used t o c a l i b r a t e  s p e c t r o p h o t o m e t e r by p l o t t i n g a graph o f sodium c o n c e n t r a t i o n v s p e r c e n t  transmission.  I t was t h e n n e c e s s a r y o n l y t o measure t h e p e r c e n t t r a n s m i s s i o n  f o r any l e a d sample i n o r d e r t o determine t h e sodium c o n c e n t r a t i o n o f t h a t sample.  A s i m i l a r p r o c e d u r e was f o l l o w e d i n t h e a n a l y s i s .of t h e aluminum 1  phase, e x c e p t t h a t t h e s t a n d a r d s used f o r c a l i b r a t i o n c o n t a i n e d 0 . 5 , 1 , 3 , 4, 5 and,10 micrograms  o f sodium/ml.  of solution.  2,  I n the a n a l y s i s of  b o t h t h e aluminum and l e a d , t h e r e s u l t s were a d j u s t e d such t h a t t h e r e a g e n t  - I V -  blank was the zero point. 10).  Sources of Error: a) . Analysis.:. The minimum sodium content of the aluminum was of the order of  0.0020 weight percent. The low levels meant that precautions had to be taken to avoid contamination of the samples.  As has been mentioned, be-  cause of the length of time required to dissolve the turnings, sodium pickup from ordinary beakers was a distinct possibility, so s i l i c a beakers were used.  These beakers and the Teflon watch-glasses were leached daily in  hot nitric acid.  As a check on the procedure, standard spectrographs  samples of sodium - aluminum alloys were obtained from Aluminium Laboratories, Arvida, and reduced to turnings, dissolved in nitric acid and analyzed on the flame spectrophotometer. The results agreed to within - 2.5% to the sodium content as reported by Aluminium Laboratories. b) . Crucibles: The alumina crucibles used in the experiments were slightly attacked by the alloys at the higher temperatures (825°C and over) used in certain of the runs. Wetting of the alumina was due only to the lead phase, and the alumina was unaffected by the aluminum phase.  The intensity  of the attack increased with increasing sodium content of the lead. However, i t i s f e l t that any loss of sodium was negligible because the attack was not severe, and therefore would have involved only a small amount of sodium.  - 15  c..)  -  Temperature:  The c o n t r o l thermocouple was a b l e t o m a i n t a i n t h e d e s i r e d temperature t o w i t h i n -5° d u r i n g . t h e r u n . .While t e m p e r a t u r e g r a d i e n t s i n a h o r i z o n t a l p l a n e t h r o u g h t h e m o l t e n charge were n o t measured, t h e tempe r a t u r e p r o f i l e v e r t i c a l l y , t h r o u g h t h e c e n t e r o f t h e a l l o y s d i d not v a r y more t h a n one degree from t h e bottom o f the a l l o y , up t o t h e t o p s u r f a c e .  t h r o u g h t h e c e n t e r and  - 16 -  RESULTS  1. )  Experimental: 1+ i s a p l o t  Figure weight  percent  sodium.in  the lowest temperature sodium-lead  alloys  o f weight percent  sodium i n aluminum a g a i n s t  lead a t f o u r temperature  used,  therelationship  A t 725°C,  intervals.  i s approximately linear f o r  i n which t h e sodium content d i d n o t exceed  l i n e a r r e l a t i o n s h i p , i s n o t as evident f o r higher temperature t h e p o i n t s p l o t t e d d o show t h a t a n i n c r e a s e i n t e m p e r a t u r e by a n i n c r e a s e i n t h e sodium c o n t e n t o f t h e a l u m i n u m - r i c h sodium-lead  3.5$.  The  intervals, but  i s accompanied phase f o r a g i v e n  alloy.  The  data presented  3 . F o r purposes  i nfigure  k  i stabulated i ntables  o fc a l c u l a t i o n , t h eweight  percent  2 and  sodium.concentrations  . r were c o n v e r t e d . t o sodium mole f r a c t i o n s The  activity  f o r b o t h t h e aluminum and l e a d  o fsodium as a f u n c t i o n o f t h e sodium c o n c e n t r a t i o n i n sodium-  l e a d a l l o y s was c o m p i l e d f r o m d a t a d i s c u s s e d i n A p p e n d i x figure  5  activity  alloys.  f o r three temperature  intervals,  725°, 775  0  B  and p l o t t e d i n  a n d 825°C. The-  o f s o d i u m . i n t h e a l u m i n u m a l l o y s was t h e r e f o r e e s t a b l i s h e d a s a  f u n c t i o n o f t h e sodium c o n c e n t r a t i o n i n both t h e l e a d - and aluminum-rich p h a s e s , , a n d t h e s o d i u m c oe f f TWSnlTS" a n d the"i'r"To'garithms w e r e :  determined  f o r sodium-aluminum a l l o y s vs. a f u n c t i o n o f t h e sodium c o n c e n t r a t i o n . 2. ) . C a l c u l a t i o n s : I t was d e s i r e d t o e s t a b l i s h t h e a c t i v i t y a t 1010°C.  725, 775;  a  T h i s was a c c o m p l i s h e d n  d  10 b y Chipman*.  825 , 0  o f t h e sodium i n aluminum  b y . e x t r a p o l a t i o n o fthedata c o l l e c t e d a t  in.accordance w i t h the following r e l a t i o n s h i p s , discussed  o.oo6o L—  0.0055 L_  0.0050  0.00U5 L_  0.0040  L_  0.0035  0.0030  0.0025 0.75  1.00 F i g u r e h:  1.25  1.50  1-75  2.00  2.25  2.50  Weight P e r c e n t Sodium i n L i q u i d Sodium D i s t r i b u t i o n b e t w e e n L i q u i d Aluminum and L i q u i d  2.75  3.00  3.25  Lead. Lead a t Four E q u i l i b r a t i o n  3.50 Temperatures.  3-75  TABLE 2 . Experimental R e s u l t s : I Run No.  II Temp.  III o C  IV  wt % Na, v... N (Pb) Na(Pb)  O.98 1.01 1.22 1-33 I.36 1-73 I.90 I.91 2.59  0.082 0.084 0.100 0.108 0.110 0.137  6/7 2/7 3/7 20/7 19/7  726 725 721 725 722 726 725 724 726 724 726 727 722  2.89 3-56 3-72  0.211  17/5 22/5 21/5 23/5  747 744 7^7 7U6  2.96 2.98 3-11 3-^7  15/t-  47/7 W7 48/7  3/8  V8 5/8  2.64  V wt % Na  VI (Al)  .0021 .0023 .0027 .0027 .0027 .0030 .0030 .0031 •0035  N  VII  6  Na(Al)  24 26 32 32 32 35 35 36  x 10  a  VIII  2  Na(T)  x 10  ^Na(T)  0.249  ' .0035 .0042  4l  0.472 0.782 0.797 i.o4o  .0047  53  1.520  107 88.6 " 86:. 1, 95-0 96.8 121 13* 131 191 199 25U 292 287  0.215 0.217  .0045 .0045  53 53 63 70  1.085 1.080 1-195 1.476  207 206 190 211  0.149 0.149  0.193  O.I96  0.258  0.224 0.245  • 003M-  .005U .0060  41 40  48  0.257 0.230 0.276 0-304 0.309 0.423 0.468  1.400  IX l i s TL T  2.03 I.9A8 1-935 1.978 1.986 2.082 2.127 2.117 2.281 2.299  2.316  2.412 2.466  2.458 2.31k  2.279 2.324  TABLE  3.  Experimental. Results: I Run-No.  11  III  Temp. °C •wt: <$> Na./P b )  IV %a(Pb)  V w  t  #  N  a  f A H  %a(Al)  x  l  °  6  a  Na(T)  x  VIII 1  q  2  ?Na(T)  IX l Q  g^Na(T)  •0035  29 29 29 37 36 38.$ 40 V« 41  O.278 0.278 0.325 O.374 O.385 0.543 0.548 0.554  96 96 112 101 107 141 137 135  1.982 1.982 2.049 2.004 2.030 2.149 2.137 2.130  0.073 0.073 0.072 0.101 0.109 0.128 0.135 0.137  .0026 .0026 .0026 .0033 .0034 .0036 •0035 .0036  30.4 30.4 30.4 38.5 40 42 4l 42  O.307 O.307 O.307 O.438 0.476 0.584 0.684 0.655  101 101 101 114 119 139 158 156  2.004 2.004 2.004 2.057 2.076 2.143 2.199 2.193  0.072 0.074  .0030 .0029  35 34  0.329 0.346  ;94 102  1-973 2.008  12/7 27/7 28/7 13/8 U9/7 6/8 8/8 7/8  774 774 775 778 771 775 775 776  O.96 O.96 O.98 1.29 1.34 I.78 1-79 1.80  0.080 0.080 0.082 0.105 0.109 0.140 0.141 0.142  .0025 .0025 .0025 .0032 .0031 .0033  43/7 44/7 45/7 2/8 1/8 9/8 10/8 11/8  823 823 825 827 825 826 825 826  0.87 O.87 0.86 •JU23 1-34 1.61 1.70 1-73  32/6 33/6  846 856  O.85 O.885  VII  VI  .O0Q4  - 20 -  - 21 -  F-,  1  d ( F f / T ) so  that  =  RT Int  =  Lid(l/T)  f o r t h e sodium - aluminum  l o  gTNa(Ti)  =  (I)  ±  (II)  system:  Na  L  +  l o  S"*Na(Tp)  (  )  m  a n d a t 1010°C: lo  S*Na(1010)  (°-779 - 1 ) + 4.575 ^ 2^ % a  =  1  In f i g u r e  6,  values o f %  log a  Y  vs.  Na  N  N  a  at  725°, 775°  a  =  4.575 2  775°and 725° f o r T i a n d T . 2  i n figure 7  .  T T x  (  g  - T )  u s i n g the temperature combinations  Na  a n d 825° was p l o t t e d .  logX  -  Na(Tl)  lo y g  825°  a n d 775°;  825°  a n d 725°;  The r e s u l t s were p l o t t e d a s L  N  a  a  n  d  values  against  The agreement between t h e t h r e e v a l u e s o f L a t each Na J  f o r N„ Na  h e a t v a l u e s , i t was d e c i d e d t o c a l c u l a t e ' o f sodium i n aluminum w i t h  f o rl i q u i d  )  N a ( T 2 ) }  l e s s t h a n k-0 x  Because o f t h e poor agreement o f these c a l c u l a t e d  line  At fixed  ^  x  were o b s e r v e d t o be u n s a t i s f a c t o r y  solubility  )  I V  a  (T  N  (  , values o f Ljj .were determined b y rearrangement o f equation  %  Na  ^Na(T)  T  (III):  N  l°g  sodium-aluminum a l l o y  10~°\  partial  L from the increase Na  increasing  temperature.  i n equilibrium  with  molal  i n t h e maximum .The l i q u i d u s  pure molten  sodium,  shown i n f i g u r e C - l g a v e t h e r e l a t i o n s h i p b e t w e e n t h e maximum s o d i u m  solubility  and  9230  temperature.  The p a r t i a l  m o l a l h e a t o f s o d i u m was c a l c u l a t e d  as  c a l o r i e s p e r mole.  Tables  4  and 5  contain  l i s t e d , as w e l l as values o f l o g  the values of  logV^ a t t h e  temperatures  a t 1010°C, o b t a i n e d b y e x t r a p o l a t i o n  - 23 -  F i g u r e 7; P a r t i a l M o l a l Heat of S o l u t i o n o f Sodium i n L i q u i d Aluminum as a F u n c t i o n o f C o n c e n t r a t i o n .  TABLE 4. Experimental Calculations; I Sun No. 15/7 14/7 47/7 ke/i 48/7 •3/8  4/8 5/8 6/7 2/7 3/7 -.20/7 19/7 17/5 22/5 21/5 23/5  II  III  . Temp. °C % a 726 725 721 725 722 726 725 724 726 724 726 727 722 7^7 744  7U7 746  x  l o P  . IV log  2f  N  a  V (  T  )  1 0 6  VI  * Na(1010) ^Na(lOlO)  24  2.03  26 32 32 32 35 35 36 4l 4o 4l  1.948  53  2.458  2, 020 2.002  38.55 31-55 30.00 33-80 33.85 43.10 47.60 46.26 68.10 70.30 91.20 104.8 100.5  2.316 2.314 2.279 2.324  1.911 1.903 1.874 1.917  83.50 80.00 74.80 82.60  48  53 53 63 70  1.935 1.978 1.986 2.082 2.127 2.117 2.281 2.299 2.412 2.466  1.586 1.499 1.477 1.529 1.530 1.534 I.678 I.665 1.833 1.847 I.96O  VII a  Na(10]  .00092 .00082 .OOO96 .00108 .00108 .00151 .00167 .00166 .00279 .00281 .00374 .OO503  .00533 .00442 .00424  .00471 .00578  TABLE. 5. Experimental II R u n Wo.  IV  Ill  Temp.  log  12/7 27/7 28/7 15./8 49/7 6/8 8/8 7/8  774 774 775 778 771 775 775 776  29 29 29 37 36 38.  43/7 44/7 45/7 2/8 1/8 9/8 10/8 11/8  823 823 825 827 825 826 825 826  30.4 30.4 30.4 38.5  32/6 33/6  846 856  40 4l  Calculations:  y  V Na(T)  I.982 I.982 2.049 2.004  .2.030 21149 2.137 .2.130  log  VI  Ma (1010)  1.627 1.627 1.696 1.657 1.669 1.796 1.784 1.779  °Na(1010) 42.40 42.40  49.70 45.40 46.60 62.50 60.80 60.10  •VII a  Na(1010)  .00123 .00123 .00144 .00168 .00168 .00241  .00243 .00246 .00165 .00165 .00166  54.40 54.40  40 42 41 42  2.004 2.057 2.076 2.143 2.199 2.193  1.736 1.736 1.738 1.795 1.810 1.879 1.933 1.929  64.60  75.70 85.70 84.90  .00258 .00318 .00351 .00356  35 34  1.973 2.008  1.741 1.792  55.10 61.90  .00193 .00210  2.004 2.004  54.70 62.40  .00240  -  from t h e lower temperatures of  V  „  Na  and  a  conditions  -  using.equation  IV.  Also listed  are the values  1 0 1 0 ° .  at  . Na  As  26  was m e n t i o n e d u n d e r " R e g i o n o f I n v e s t i g a t i o n " , t h e e x p e r i m e n t a l  imposed.a r e s t r i c t i o n  t h a t t h e sodium-lead  alloys not contain  more s o d i u m t h a n N = O . 2 5 O , i n order t oavoid excessive moisture pick-up. Na The s o d i u m c o n c e n t r a t i o n i n t h e a l u m i n u m was t h e r e f o r e l i m i t e d a l s o , t o a maximum o f a b o u t N ••= 50-x-lQ Na  ^. . I n o r d e r t o e x t e n d ,  data,to  5  sodium c o n c e n t r a t i o n s g r e a t e r than t h i s , , Dewing s free  the a c t i v i t y  d a t a has been used.  The  energy for. t h e r e a c t i o n :  6NaF. .  +  (s)  A l  (1)  •*  fc-  >  3(Na) v  +  ( d i l )  N a A1F.  6(s)  3  ] 2  was from  c a l c u l a t e d u s i n g JANAF t a b l e s , a n d t h e a c t i v i t y t h e f r e e e n e r g y change o f t h e r e a c t i o n .  o f s o d i u m was o b t a i n e d  Dewing r e p o r t e d h i s r e s u l t s a s  weight p e r c e n t sodium i n aluminum f o r v a r i o u s temperatures, s o t h a t Y ^ and l o g Y a s a f u n c t i o n o f t h e mole f r a c t i o n o f sodium a t t h e s e temperatures JMa a  c o u l d be o b t a i n e d . converted  back t o Y  tabulated  Na i n t a b l e !•  The  v a l u e s were e x t r a p o l a t e d t o 1 0 1 0 ° a n d  T h e log"J(  present  Na anda . Na  The r e s u l t s  f o r Dewing's i n v e s t i g a t i o n  r e s e a r c h , and t h a t r e p o r t e d b y Dewing, f u r n i s h e d sodium -6  a c t i v i t y data from in  N N  a  ^  A  a sodium-saturated  1  ^  =  5 x 10  2  -6  t o3 0 0x 1 0  sodium-aluminum a l l o y  . . The s o d i u m  activity  i s unity, as t h i s a l l o y  e q u i l i b r i u m w i t h p u r e s o d i u m , a n d a t 8 0 0 ° C , t h e maximum s o l u b i l i t y N  Na(Al)  =  3150  x  -6 10  .  polation o f logYNa t o 1 which a  N  a  =  O.4896  were  e  at  Hence a t t h i s 0 1 0 °  1 0 1 0 °  concentration, logJ  b y e q u a t i o n : IV gave a v a l u e  was f o u n d .  T  ^  a  = 2 . 4 9 9 -  of2.192,  i s i n  i s at Extrafrom  - 27 -  DISCUSSION  Comparison o f the p r e s e n t work w i t h p r e v i o u s r e s e a r c h difficult  i n t h a t t h e r e was  the present research. content  a fundamental  Other  difference  i n v e s t i g a t i o n s determined  sodium i n the l e a d phase.  however, the a c t i v i t y  The  o f sodium i n aluminum, and  sodium  d i d show t h a t a s m o o t h t r a n s i t i o n h i s v a l u e s and examining  1).  those  Excess  x 10"^,  investigated  a  x 10  and  V  log J  c a l c u l a t i o n , and  ^.  The  A1  A  a  p l o t a p p e a r s t o be  2  /  Na.'^hl'  a s  comparisons  over the e n t i r e  is given i n figure  e q u a l t o 3157  research,  seen  between by  over the c o n c e n t r a t i o n l i n e a r f o r Njj  =  1-08.  ^ h i  s  (The  9  800°. -6 x.10  less  a  •  thermodynamic d a t a i s expressed  11  f u n c t i o n i s used i n the  o f a c t i v i t y d a t a c a n be  Gibbs-Duhem  conveniently  i n t h i s form.)  c o m p o s i t i o n range from Njj  a  =  The  0  The .  to  plot  3157  of  10"^  x  This f i g u r e c o n s i s t s of the data from f i g u r e  the a c t i v i t y data c a l c u l a t e d from the s o l u b i l i t y l i m i t  i n aluminum a t  results,  when e x t r a p o l a t e d t o l o w e r c o n c e n t r a t i o n , i n t e r s e c t s  made w i t h t h e t h e r m o d y n a m i c d a t a e x p r e s s e d a  in this  T h i s t r a n s i t i o n c a n be  i s a p l o t o f l o g " / | g / N i v s . N^  the ordinate a t logYNaA^Al  Yjj /N  o f Dewing's  Thermodynamic P r o p e r t i e s o f Sodium i n Sodium - Aluminum:  r a n g e ' N ^ a = 0 t o 300  form  have been measured.  10.  and  F i g u r e ..8  t h a n kO  thermodynamic  i n the a c t i v i t y values e x i s t e d  reported here.  8  figures  research,  the excess  a c t i v i t y d a t a o b t a i n e d from an a n a l y s i s  although at higher concentrations than  and  e i t h e r the  In the present  p r o p e r t i e s o f the sodium - aluminum system,  log  i n the object of  o f aluminum a t e q u i l i b r i u m w i t h c r y o l i t e m e l t s , o r measured  the a c t i v i t y . o f  i n the  was  p l o t a s y m p t o t i c a l l y approaches  of  2.206  8  sodium at  N^  a  F i g u r e 8: l o g / ^ /^AI  i  n  L  i  (  l  u  i  d  Aluminum as a F u n c t i o n o f C o n c e n t r a t i o n a t 1010°C  hO O H  ro  1.5 Data from Figure  8  Limit of Solubility  D a t 800°C  O  l.o  1  500  0 Figure  9; logY  1  2000  1000 % a  N  x  1  3000  2500  ^  /N?-, i n L i q u i d A l u m i n u m a s a F u n c t i o n  of Concentration  at  1010°,  for^the  C o m p o s i t i o n o v e r w h i c h S o d i u m a n d A l u m i n u m a r e M i s c i b l e a t 800  .  Range o f  - 30 -  2.)  The A c t i v i t y o f  Sodium:  The s o d i u m a c t i v i t y i n a l l o y s  containing l i t t l e  sodium i n c r e a s e s  F i g u r e 10 shows  c o n s i d e r a b l y w i t h i n c r e a s i n g sodium c o n c e n t r a t i o n .  that  the i n c r e a s e i s n o t as pronounced f o r sodium c o n c e n t r a t i o n s beyond N 50 x 10  .  A p l o t of sodium a c t i v i t y over the e n t i r e range from N  t o 3157  x 10  plotted  i n figure  3.)  ^ i s made i n f i g u r e 11,  b a s e d on t h e l o g ^ / N ^ . ] _ Na  was u s e d t o c a l c u l a t e l o g  1 1  the p l o t s of l o g y /N obtained from.figures 8 . Na Al  and 9  •j?Al =  log y A 1  =  - N  N a  N  A 1  logV  - \  N a  N Table 6 contains the r e s u l t s v s . Njg  a  e q u a l t o - 9125  a t N^  although log*5 i a  off for N  m  d  W  Al  N^i  =1  A 1  A 1  F i g u r e 12  is a  plot  2  .  I t i n d i c a t e s a maximum o f l o g V i / N N A  = hQ x 10"^.  a  I t s h o u l d be p o i n t e d o u t t h a t ,  A  on e i t h e r s i d e o f N • = kO x 10"°. A  ] _ / %  a  = -  a  For lower  N a  the f u n c t i o n e x t r a p o l a t e s t o l o g ^  5300,  p o i n t s d o n o t make f o r a r e l i a b l e e x t r a p o l a t i o n . A  F r o m t h e v a l u e s pf  log^f^l  calculate t h a t Y i  =  A  0.9999  the a c t i v i t y o f aluminum  The  curve  sodium  falls  levels,  a l t h o u g h o n l y two On t h e h i g h  s i d e , the p l o t a s y m p t o t i c a l l y approaches l ° g Y i / l %  mole f r a c t i o n .  o  , using the equation  causes a wide range o f v a l u e s f o r l o g y i / N § . N a  r  A1 Na  of the calculations.  a t 1010°  f  i s a s m a l l number, d i v i s i o n b y an even s m a l l e r number,  A  v i z ; N^ ,  a  a  N  log  ^  ~NAT  2  values  Aluminum:  The G i b b s - D u h e m t e c h n i q u e  A  =0 Na  9.  The A c t i v i t y o f  o f l o g Y ^/Njg  =  Na  c  -o  a  sodium  = - 6 a t N f [ = 3157 a  i n c o l u m n V I of t a b l e 6 , i t i s p o s s i b l e t o over the e n t i r e composition range.  Hence  i n t h e sodium - aluminum system i s e q u a l t o i t s  A s t h e s o l u b i l i t y o f s o d i u m i s 0.3  mole p e r c e n t ,  a  x  1  F i g u r e 10:  A c t i v i t y o f Sodium.in L i q u i d Aluminum as a F u n c t i o n o f Composition a t 1010°  - 32 -  h-0.6  are Miscible at 800°C.  6.'  TABLE  Gibbs-Duhem Integration of the Sodium-Aluminum Binary System: II  I % a  x  1  q  6  iogY 2  III N a  % a % l  x  1 q 5  TYT  N  0 20 30 4o 50 6o 70 80 90 100 120 14-0  160 180 200 225 250 275 300 U-00 500 750 1000 1500 2000 2500 3150  %a Al N  l o  S * Na 2 1\T N  A1  A1  1.08 1.40 1-59 1.78 1.892 1.960 2.000 2.030 2.053 2.071 2.098 2.120 2.129 2.l4l 2.155 2.165 2.175 2.180 2.183 2.188 2.190 2.195 2.200 2.202 2.204 2.206 2.206  IV  0 1.999 2.999 3-999 4.999 5-999 6.999 7-999 8.999 9-999 11.998 -13-998 15.997 17-997 19.996 22.495 24.994 27.492 29.991 39-984 49-975 74.944 99.900 149-775 199.60 249-37 314.70  0 2.80 4.77 7-12 9-46 11.76 14.00 16.24 18.47 20.71 25.17 29.67 34.06 38.53 43.09 48.70 54.36 59-93 65.47 87.48 109.44 164.50 219.78 329.80 439-92 550.12 694.23  N  x  10  5  A1  =  N  A1  - \ logt J  N  A 1  = 1  d N N  VI  V a  Al  N  x  1 C ) 5  - l o g / l x 10 A  5  -  iogir  2  2  T\T  Na  A 1  0 2.48 3.98 5.66 7.49 9-4i 11-39 13-41 15.45 17.51 21.68 25.80 30.05 34.32 38.61 43-99 48.42 53-85 59-30 81.16 103-05 157-86 212.79 322.84 432.99 543-24 688.17  VII  0 0.32 0-79 1.46 1-97 2-35 2.61 2.83 3-02 3-20 3.49 3.87 4.01 4.21 4.48 4.71 5.94 6.08 6.17 6.32 6-39 6.64 6.99 6.96 6-93 6.88 6.06  0 8000 8777 9125 7880 6528 5326  4422  3728 3200  2424  1974 1566 1299 1120 931 950 804  685 395 256 118 70 31 17 11 6  A 1  - 3b -  n e g l i g i b l y small error i s introduced  into calculations i f the a c t i v i t y  o f aluminum i s s e t e q u a l t o u n i t y . b.) The P a r t i a l M o l a l Heat o f S o l u t i o n o f Sodium: The  sodium, c o n c e n t r a t i o n o f t h e aluminum a l l o y s i s so low t h a t  i t . w o u l d be e x p e c t e d t h a t t h e p a r t i a l m o l a l heat o f s o l u t i o n would be independent o f c o n c e n t r a t i o n .  Figure  7 however, i n d i c a t e s t h a t L ^  d e c l i n e s from about 9300 c a l o r i e s / m o l e above Njy = W x 10 a  c a l o r i e s / m o l e a t Njj -= 30 x 10"^.  t o 1500  i t i s obvious from; t h e s c a t t e r i n t h e  a  p o i n t s t h a t agreement of•• L j j  a  p l o t s i n f i g u r e 7 i s poor.  a  In f i g u r e 6 f o r N  N a  l e s s t h a n 30 x 10"^, t h e p l o t s o f l o g / j j  v s . N j j a t each o f t h e t h r e e t e m p e r a t u r e s appear t o merge. a  t h a t L ^ i s e q u a l t o z e r o , when t h e p l o t s meet. a  This  a  implies  I t s h o u l d be n o t e d  however, t h a t t h e s c a t t e r i n i n d i v i d u a l p o i n t s o f f i g u r e 6  i s o f the  same s i z e a s L ^ i t s e l f and t h u s n o t t o o much r e l i a n c e can be p l a c e d on a  v a l u e s o f L ^ c a l c u l a t e d from t h e d i s p o s i t i o n o f t h e l i n e s . a  of the p o i n t s i s probably  The s c a t t e r  due t o t h e s e n s i t i v i t y o f t h e c a l c u l a t i o n s t o  s m a l l e r r o r s i n measuring N j j , s i n c e t h e a c t i v i t y o f sodium i s changing a  very r a p i d l y i n t h i s region.  Above l %  a  = bo x 10 ^, p a r t i a l m o l a l heats  of s o l u t i o n c a l c u l a t e d on t h e b a s i s o f e q u a t i o n I I I and f i g u r e 7 a r e i n f a i r l y c l o s e agreement, and'-L  =  9300 c a l o r i e s / m o l e i s p r e d i c t e d .  T h i s v a l u e d i f f e r s b y o n l y 0.76$ from t h a t c a l c u l a t e d from t h e maximum s o l u b i l i t y o f sodium i n aluminum (see f i g u r e C - 1 ) , and so e x t r a p o l a t i o n s u s i n g • L j j • = 9230 c a l o r i e s / m o l e , independent o f c o n c e n t r a t i o n , would a  appear t o be j u s t i f i e d .  -1.0  F i g u r e 12:  l o g y / N § i n L i q u i d A l u m i n u m a s a F u n c t i o n o f C o m p o s i t i o n a t 1010 , f r o m a G i b b s - Duhem I n t e g r a t i o n o f l o g OsJlS^j. V a l u e s f r o m F i g u r e 8. A 1  a  - 36 -  CONCLUSIONS  1)  .  The a c t i v i t y  o f sodium i n aluminum a t  1010°C h a s b e e n e s t a b l i s h e d  by a two phase d i s t r i b u t i o n e q u i l i b r i u m technique.  The a c t i v i t y o f  s o d i u m h a s b e e n f o u n d t o show l a r g e p o s i t i v e d e v i a t i o n s  2) .  The s o d i u m a c t i v i t y  shows a s t r o n g  dependence  from  on  ideality.  concentration  for  sodium,- aluminum a l l o y s i n w h i c h t h e sodium c o n c e n t r a t i o n  N  =  N a  100  3) .  x IO  - 6  .  The a c t i v i t y  d a t a f o r aluminum i n t h e sodium - aluminum system,  c a l c u l a t e d b y t h e G-ibbs - Duhem m e t h o d f r o m t h e s o d i u m a c t i v i t y shows t h a t t h e a c t i v i t y of composition, can  be assumed  i s below  c o e f f i c i e n t o f aluminum i s  N j ^ = 0 t o 3157 a  x 10"  0.9999  over t h e range  , so that the a c t i v i t y  t o be u n i t y over t h e e n t i r e range o f  data,  o f aluminum  compositions.  - 37 -  RECOMMENDATIONS FOR .FURTHER WORK  1) .  The a c t i v i t y o f sodium i n aluminum f o r c o n c e n t r a t i o n s between  N. =100 Na  x 10 ^ and t h e l i m i t o f s o l u b i l i t y o f sodium c o u l d be s t u d i e d  T  i f some s u i t a b l e e x p e r i m e n t a l t e c h n i q u e c o u l d be d e v e l o p e d . aluminum - sodium system c o u l d p r o b a b l y be adapted f o r t h i s  The l e a d investigation  by u s i n g d r y - b o x t e c h n i q u e s t o m i n i m i z e t h e t e c h n i c a l problems a s s o c i a t e d :  w i t h h a n d l i n g l e a d a l l o y s c o n t a i n i n g h i g h sodium c o n c e n t r a t i o n s . 2) .  The e f f e c t s o f t h e p r e s e n c e o f o t h e r elements i n t h e sodium -  aluminum, system.on t h e a c t i v i t y o f sodium i n t h i s system would be o f interest. 3) .  D e t e r m i n a t i o n o f t h e p a r t i a l m o l a l heat o f s o l u t i o n o f sodium  i n aluminum, by use o f a c t i v i t y measurements, would be u s e f u l f o r . t h e e x t r a p o l a t i o n of a c t i v i t y data t o higher temperatures.  - 38 -  APPENDIX A  THE DETERMINATION OF THE ACTIVITY QF NaF AND A l F ^ I N SODIUM . FLUORIDE-ALUMINUM- FLUORIDE MELTS A.  A c t i v i t y D a t a . f o r NaF and A l F ^ from t h e A c t i v i t y o f Sodium i n NaF  -AlF^  Melts.  Under t h e h e a d i n g " P r e v i o u s Work on t h e Sodium - Aluminum C r y o l i t e System", v a r i o u s  s t u d i e s were c i t e d t o show t h a t t h e sodium  c o n t e n t o f t h e aluminum i s t h e r e s u l t o f an e q u i l i b r i u m . r e a c t i o n between sodium f l u o r i d e and aluminum t o produce sodium and aluminum f l u o r i d e . 2,3,1+,  The  reported  are t a b u l a t e d  6,7,8  results  were p l o t t e d i n f i g u r e s 1 and 2, and  i n t a b l e s A - l throughA-l+.  The sodium c o n c e n t r a t i o n s  i n t h e s e e x p e r i m e n t s have been c o n v e r t e d t o sodium a c t i v i t i e s ,  reported  using  the r e s u l t s o f t h e p r e s e n t i n v e s t i g a t i o n , and,the a c t i v i t i e s so o b t a i n e d were p l o t t e d a g a i n s t t h e NaF/AlF^ r a t i o , . a s shown i n f i g u r e A - l .  The  reaction taking place i s : 3[NaF  ( 1 )  ]  .+  A l  (  1  )  «  »  3(Na'  (1)  ) .+  [A1F  5 ( 1 )  ]  f o r which the e q u i l i b r i u m constant i s :  3 ( Na) a  k  =  ^AlFjl  x  (a )  x:[a  A 1  N a F  ]^  3 ( Na)  x  (a )  x  a  A 1  The  e x t r e m e l y low c o n c e n t r a t i o n  [  *A1F  [f  x 5  NaF  x  N  A1F  N  ] 3  N a F  P  o f sodium i n aluminum meant t h a t t h e  a c t i v i t y - o f aluminum c o u l d be t a k e n as u n i t y , and s i n c e t h e sodium a c t i v i t y was known as a f u n c t i o n o f t h e NaF/AlF^ r a t i o from f i g u r e A - l i t was t h e r e f o r e p o s s i b l e t o e v a l u a t e  t h e two unknowns, V ^  a F  and^^jj,  TABLE A - l . Sodium Content o f Aluminum M e t a l under S o d i u m ; F l u o r i d e - A l u m i n u m : F l u o r i d e M e l t s (Data from Herman and J a n d e r ) 2  • I In  . II  III  . IV  V  VI  Slag  %A1  %Na  foAlF^  %NaF  1 8 . 7  2 2 . 8  5 8 . 2 0  41.51  .005  .715  58  1.855  7 1 . 6  1 6 . 2  2 7 . 1  5 0 . 3 9  49.46 ;  .004  .981  47  1.770  5 8 . 8  .0028  15.4  28  27.87  51.86  .OO55  1.083  64  1.890  77-6  .0050  1 3 . 5  3 1 . 7  4 1 . 9 9  5 7 . 8 2  .0042  49  1.795  62.4  .0031  1 2 . 8  3 2 . 8  3 9 . 8 1  59.88  .019  233  2 . 0 8 0  120.5  .0281  8.7  41.5  27.04  75.79  .028  6 . 5  4 3 . 8  20.24  79-99  .028  5 . 0  46.2  15.54  84.36  .033  3 . 0  49.3  9.32  90.03  .043  1.9  5 1 . 6  5.88  94.22  .051  0.9  5 3 . 2  2.77  97.12  .063  A  wt % W a  ( A 1 )  •NaF/AlFj r a t i o  N  x.l0  N a  1 . 3 7 7 : •.1.504  6 l  o  (Data from Dewing and H o l l i n g s h e a d I  wt * N a  II m )  NaF/AlF^  ^Na(1090)  IV  N Na  1 0  ^ ( 1 0 9 0 ) .0041  )  III ratio  ^Na(1010)  g  V  VI  6 l  0  g  ^Na(1025)  *Na(1025)  a  Na(1025)  .0190  1.50  222  2 . 1 4 9  .0126  1.46  148  2.106  127.8  .0189  .0092  1.42  108  2.063^  115.8  .0125  104.3  .0070  1.38  82  2.018  .0054  1.34  63  1.954  .141  .0313  .0085  9 0 . 0  .0057  .0044  1.30  50  1.875  7 5 . 0  .0037  .0034  1.26  40  1.767  58.4  .0023  .0027  1.22  32  1.627  42.3  .0013  .0022  1.18  26  1.487  3 0 . 7  .0008  TABLE A - 2 . Sodium Content of Aluminum Metal under Sodium Fluoride-Aluminum Fluoride Melts (Data from Waddington • ) I  ..II  NaF/AlF^ ratio  wt $  III Na  (A1)  N .x 1 0 Na  IV 6  l  o  g  ' Na(1000)  V ^Na(lOOO)  VI a  Na(1000)  1.50  .OI65 .0155 .0120 .0080 .0070  193 181 140 93 82  2.176 2.157 2.134 2.074 2.050  150 143.6 136 118.7 117  .0289 .0260 .0190 .0110 .0092  1.273  .0130 .0115 .0100 .0090  152 134 117 105  2.140  138 134 127.7 124  .0209 .0179 .0130  .0070 .0060  82 70  2.050 2.014  .0040  46  112 103.2 73.1 51.8  .0092 .0072 .0034 .0018  .'.  •  0.887  .0030  35  2.128 2.106 2.094'  1.864 1.714  .0149  - 41 -  •  /  TABLE A - 3 . Sodium Content of Lead Metal under Sodium Fluoride-Aluminum Fluoride Melts Q  (Data from Aylen ° ) I  II  III  NaF/AlF ratio wt <f> Na(Pb) N 1.68 ' 4.78 0,312 1.68 4.58 0,302 1.68 I+.58 0.302 4.38 0.292 1.70 1.66 4.28 0.286 4.90 O.316 I.67 1.66 4.88 O.316 5-20 1.68 0,330 1.60 . 4.18 O.282 4.00 O.272 1.63 1.67 4.30 0.288 1.65 4.20 0.282 4.40 1.70 0.293 4.70 0.308 1.70 I.70 4.50 0.298 4.60 0.303 1.70 1.70 4.80 0.312 4.90 O.316 I.67 1.67 4.30 0.288 1.68 4.20 0.282 4.80 0.312 1.63 0.224 3-10 1.51 5  N a ( p b )  IV l°gy .37 .345 .345 .318 .305 .380 .380 .410 .290 .268 .307 .290 .319 .358 .334 .346 •370 -. .380 .307 .290 .370 .143 -  V N a (  l l 1 1 1 1 1 1 1 1 l 1 1 1 l l 1" 1 l 1 1 1  iQ  1 0  )  VI  > (101Q) ^aflQlO) .234 .073 .221 .067 .221 .067 .208 .061 .202 .058 .240 .075 .O76 .240 .085 .257 .195 .055 .185 .050 ,203 .058 .055 .195 .208 .061 .228 .070 .216 .064 .222 .067 .073 .235 .076 .240 .203 .058 .195 .055 .073 .235 .031 • 139 Ha  - 42 -  TABLE A-4. Sodium Content of Lead Metal under Sodium Fluoride-Aluminum Fluoride Melts (Data from Feinlab and Porter ^ ) I NaF/AlF ratio J  II wt # Na,_ " (Pb) r  .1.50 1.42 1.89  5.78 5.87 6.05  1.67 1.60 1.71 1.66 1.54 I.58 1.60 1.60  5.65 .5.06 6.46 5.02 3.8O 3.89 4.26 3.98,  I.65 1.54  5.08 5.81  III log / ° '. Na(T) 1010 °C  970 °C  940 °C  IV Na(T)  V a.  Na(T)  0.46 - 1 0.45 - 1 0.47 - 1  .288 .282 .295  .102 .101 -108  0.43 - 1 0.J4 - 1 0.45 - 1 O.33 - 1 O.17-I 0.17-1 0.24 - l 0.21-1  .269 .219 .282 .214 .148 .148 .174 .162  .094 .0719 .108 .0689 .0388 .0395 .0497 .0441  0.30 - 1 0.37 - l  ,199 .234  .0646 .0838  - 4  3  -  9 4 0 °  I 0.90  I 1.10  I 1.30  I 1.50  I 1.70  Q  I 1.90  NaF - AlF^ ratio Figure A - l : The Activity of Sodium in Liquid Aluminum as a Function of the NaF - A1F, ratio in NaF - A1F, Melts.  -  kk  -  as a f u n c t i o n o f the A I F 3 c o n c e n t r a t i o n by s o l v i n g two  simultaneous  e q u a t i o n s , namely: .1). 2).  The e q u i l i b r i u m c o n s t a n t , k. The Gibbs - Duhem r e l a t i o n s h i p , u s e d . f o r c a l c u l a t i o n  o f the a c t i v i t y o f one component i n a b i n a r y system when the n e c e s s a r y a c t i v i t y d a t a i s a v a i l a b l e f o r the second component. 1).  E v a l u a t i o n o f the E q u i l i b r i u m , C o n s t a n t . In d e t e r m i n i n g the e q u i l i b r i u m c o n s t a n t f o r a r e a c t i o n  from  the.-free energy changes a s s o c i a t e d w i t h t h a t r e a c t i o n , i t i s convenient t o s p e c i f y the s t a n d a r d s t a t e s f o r the r e a c t i n g s p e c i e s and the p r o d u c t s . F o r aluminum, sodium, and sodium f l u o r i d e , the s t a n d a r d s t a t e s a t were taken t o be the pure l i q u i d m a t e r i a l .  1010°  However, pure l i q u i d aluminum  f l u o r i d e i s m e t a s t a b l e w i t h r e s p e c t t o the vapour s t a t e , and s o l i d aluminum f l u o r i d e sublimes a t 1281°C.  No thermodynamic d a t a i s a v a i l a b l e  on m e t a s t a b l e l i q u i d aluminum f l u o r i d e . f o r the NaF  E x a m i n a t i o n : o f the phase diagram  - A l F j s y s t e m ( f i g u r e A - 3 ) shows t h a t a t 1010°, pure  aluminum f l u o r i d e i s i n e q u i l i b r i u m w i t h a m e l t c o n t a i n i n g 55  solid atomic  p e r c e n t aluminum f l u o r i d e , hence the a c t i v i t y , o f aluminum f l u o r i d e i n a melt o f t h i s c o m p o s i t i o n and temperature  i s the same as t h a t f o r pure  s o l i d aluminum f l u o r i d e , which can t h e r e f o r e be used as the s t a n d a r d s t a t e f o r the aluminum f l u o r i d e .  The  thermodynamic d a t a f o r these m a t e r i a l s i n t h e i r s t a n d a r d  12 s t a t e s was  taken from JANAF  t a b l e s , a t 1010°:  - 45 -  F°  - H° _ , , / , . A H ° 298 ( c a l / m o l e ) f(298)  v  ( k c a l / m o l e; )  '  NaF^  26.597  Al  13.87  2.40  18.888  0.575  • (1) Na (1) AlF  -129.885  31.17  v  -358-00  3(s) The f r e e e n e r g y c h a n g e f o r t h e r e a c t i o n w a s : AG° giving an equilibrium  -)  38.45  kcal  constant: k  2  =  Computation o f l o g j  =2.8 / N^  x  10"^ andl o g ^  1 F  A  i  /^ '-  F  3  a F  5  The G i b b s - D u h e m e q u a t i o n a n d t h e e q u i l i b r i u m c o n s t a n t w e r e u s e d t o s o l v e t h e two unknowns, l o g  Yjg  aF  and  1°ST-J_F '  A S A  A  *' ' ' UNC  T  ION O F T L I E  3 aluminum f l u o r i d e c o n c e n t r a t i o n , over t h e c o m p o s i t i o n range N = 0.223 AlFj t o 0.321. T h e logY . „ a n d logY v a l u e s were o b t a i n e d b y u s i n g a NaF AlFj c o m p u t e r programme a n d t i e p o i n t o n a n I B M  "JOkO  computer.  13 The c o m p u t e r programme d e v e l o p e d b y A y l e n a n d S a m i s f o r the present computations.  was m o d i f i e d  T h e t i e p o i n t u s e d i n t h e programme was  at'N^ e q u a l t o 0.223. T h e new v a l u e o f t h i s t i e p o i n t i s Y =-2.183, ( w h e r e Y = logY ) a n d was o b t a i n e d f r o m f i g u r e . A - 4 , c o n v e r t i n g t h e v a l u e NaF of l o g /  N a F  /N  A 1 F  ^ atN  M  F  =  0.223  to S^ l o  N a F  -  T  h  e  o t h e r c h a n g e s made  i n t h e programme w e r e t h e e q u i l i b r i u m c o n s t a n t , u ( w h i c h i n t h e c o m p u t e r programme i s r e p r e s e n t e d b y t h e s y m b o l of t h e sodium a c t i v i t y  C ) , k = 2.8  x 10  (ANA) a t e a c h o f t h e t e n a l u m i n u m  a n d new v a l u e s fluoride  - 46 -  \  c o n c e n t r a t i o n s u s e d i n t h e programme. lie  on t h e l i n e drawn on f i g u r e A - l .  l o g Y „ „ and l o g Y NaF AlFj 6  s > 9  1010°C.  T h e s e new s o d i u m a c t i v i t y  values  The computer o u t p u t gave v a l u e s o f  a t t h e t e n aluminum f l u o r i d e c o n c e n t r a t i o n s , a t  Y  These r e s u l t s were c o n v e r t e d t o l o g  r e s p e c t i v e l y and p l o t t e d  fw  a n d logY /N „ AlFj A l F ^ NaF over t h e composition  NaF i n f i g u r e A-2 a g a i n s t N  AIF3 range-N  = 0.223 t o 0.321.  3 B.  Thermodynamic A n a l y s i s  1.)  o f the Sodium.Fluoride-Aluminum Fluoride  Calculation ofActivities  System.  f r o m t h e N a F - A1F., P h a s e D i a g r a m :  2 In the preceeding  section, log 7jjaF^AlF  were o b t a i n e d b y s o l v i n g t w o s i m u l t a n e o u s  2  n  '  d  l  0  g  ^ A1F ^ a F  equations, v i z ; the equilibrium  c o n s t a n t a n d t h e Gibbs-Duhem r e l a t i o n s h i p . d e s c r i b e d whereby v a l u e s o f l o g V^p/^  &  a n  Another  m e t h o d w i l l now b e  < i l°g X^JJ  ^NaF  1 3 6  0 D  '  t a i n e d  3 from t h e sodium f l u o r i d e - a l u m i n u m f l u o r i d e phase  diagram.  14 .Wagner  hasdeveloped  an expression t o obtain a c t i v i t i e s o f  the components f r o m t h e phase diagram, o f a b i n a r y system formation by successive numerical integrations b i n a r y system.  e x h i b i t i n g compound  o f t h e compounds i n t h e  The e q u a t i o n i s : RT I n a  2  = A H T  m  F  J (1 - N ) A T 2  I  N  2  - X  +  (1 --Xg) (  j  2  A TdN (N  2  where: AH^, = t h e h e a t .T -••Nj> N  offusion  o f t h e compound.  = the m e l t i n g temperature 2  o f t h e compound.  = t h e mole f r a c t i o n s o f aluminum f l u o r i d e a n d sodium fluoride  respectively.  2  - X  2  )  2  -2k. 0 -22.0  -O.  TT  lU.O  -20.0 l o  sV  N a F  /^iF  3  -12.0  -18.0  log V -10.0  -16.0  -8.0  -lk.0.  -6.0  -12.0 0.200  0.350  0.300  0.250 N  A1F~  Figure A - 2.: The Values of l o g ^ / ^ *nd 1 ° S ^ A i F ^ ^ N a F ' of the Composition from the Computer Results. a  F  3  a  s  a  F u n c t i  P  n  A 1 F 3  /N|  -pa F  (  - 48 -  X^, Xg = t h e more f r a c t i o n s of. aluminum f l u o r i d e and sodium f l u o r i d e c o r r e s p o n d i n g t o t h e compound. I t c a n be seen from.the e q u a t i o n t h a t i t s s u c c e s s f u l a p p l i c a t i o n depend • on • two f a c t o r s .  will  These are,' b e i n g a b l e t o o b t a i n an a c c u r a t e p l o t  o f t h e l i q u i d u s l i n e ( i . e . , t e m p e r a t u r e v s . c o m p o s i t i o n ) , and e v a l u a t i o n of t h e e n t r o p y o f f u s i o n o f t h e compounds t h a t e x i s t i n - t h e • s y s t e m . two  f a c t o r s w i l l now be d i s c u s s e d . i n  a..)  These  some d e t a i l .  The NaF. - A l F ^ Phase Diagram:  Three r e c e n t papers have been p u b l i s h e d on t h e sodium f l u o r i d e a l u m i n u m . f l u o r i d e phase diagram.  These p a p e r s . a r e b y G r j o t h e i m ,  who .16  = 0 . 0 0 0 . t o O.5OO,.Hollingshead, who 3 17 i n v e s t i g a t e d t h e .same r e g i o n , a n d ' R o l i n , who s t u d i e d t h e range between  investigated  the region  from-N  N ,_, = 0.250 t o t h e e u t e c t i c a t N = 0 . 4 6 5 . - A composite o f t h e s e • A1F, ^ , A1F, 3 3 • i n v e s t i g a t i o n s was used t o c o n s t r u c t t h e phase d i a g r a m shown i n f i g u r e A - 3 » A  The but  r e s u l t s show good agreement f o r - r e g i o n s  s e r i o u s , errors-become apparent above N ^  r i c h in-sodium f l u o r i d e ,  = 0.400. ..The- l i q u i d u s 3  curve f o r m e l t i n e q u i l i b r i u m , w i t h c h i o l i t e Hollingshead.is Rolin. and  ( N a ^ A l ^ F ^ ) as d e t e r m i n e d by  some 10 t o 15 degrees h i g h e r t h a n t h e l i q u i d u s found b y  The temperature and c o m p o s i t i o n o f t h e e u c t e c t i c between c h i o l i t e  sodium aluminum t e t r a f l u o r i d e a r e r e p o r t e d t o be: i.) Grjotheim . N = 0.1+70 3 A  ii.) iii.)  1  F  . T = 690°C  Hollingshead  = 0.1+70  = 693  Rolin  = 0.465  = 681+  Grjoiheim reported that  sodium aluminum t e t r a f l u o r i d e e x i s t e d as a, s t a b l e  compound, w i t h a m e l t i n g . p o i n t - of 731°•  He a l s o c l a i m e d t h a n an e u t e c t i c  - 50 -  existed at N  A 1 F  = O..537 and 70k° .  This work was contradicted by that of  Hollingshead,,who reported no eutectic above  3  = O.5OO, but rather  that at N = 0.500, the liquidus temperature was i n fact 860°. AlFj •  Dewing'-s  R  work on vapour pressure measurements substantiates Hollingshead's findings, = 0.465, the-liquidus  and suggests that beyond .the euctectic at N Air _  3 l i n e r i s e s very steeply and i n . f a c t that along t h i s l i n e , the liquid-melt i s i n equilibrium with pure solid• A1F,.  3 b.)  The Entropy of Fusion:  The entropy of fusion of each of the compounds must be evaluated in order t o apply Wagner's equation.  For sodium f l u o r i d e , t h i s i s no problem,  . since the entropy of fusion at the melting point i s simply the heat of fusion divided by the melting temperature and r e l i a b l e values are reported  12, 18 in the l i t e r a t u r e .  However, the s i t u a t i o n i s more complex with regard  to the entropy of fusion- of c r y o l i t e , because of the fact that c r y o l i t e dissociates on melting.  The experimentally measured heat of fusion i s  a c t u a l l y the sum. of the true heat of fusion plus the heat of d i s s o c i a t i o n .  15, 19,. 20, 21, 22 Several pieces of work  have been done on various d i s -  sociation schemes, and the proposed reaction of: Na^AlFg  -—»  2NaF  +  WaAlF^  gives the best agreement with experimental evidence provided by x-ray d i f f r a c t i o n , transport studies, cryoscopic studies and NaF - AlF^ melt density measurements. • Assuming that the species i n the molten state are completely i o n i c , and using.Temkin's i o n i c theory, the equilibrium constant f o r the above reaction can be expressed as a function of the degree of d i s s o c i a t i o n , o( :  51  D  (1 -  + l)  )(2cA  2  23 Foster and Frank  established  melt d e n s i t y s t u d i e s , and a p l o t h e a t o f d i s s o c i a t i o n o f 22.5 t h e r e f o r e be c a l c u l a t e d  values f o r various temperatures of log  using  v s . . l / T gave a v a l u e f o r t h e  K c a l / m o l e . . The  t r u e heat o f f u s i o n  could  from: AH  =  F  A H  F  + C^AH^  where:  A R _ = 26.6 r  kcal/mole,. the cryosdopic heat o f f u s i o n ,  A H ^ = 22.5  kcal/mole, t h eheat o f d i s s o c i a t i o n .  A H ^ = t h e t r u e heat- o f f u s i o n o f c r y o l i t e .  ck  = 0.353, t h e d e g r e e o f d i s s o c i a t i o n a t 1010°C.  The  true heat o f f u s i o n - o f c r y o l i t e t o pure, undissociated molten  was  c a l c u l a t e d t o b e 18.73  fusion  cryolite  kcal/mole, which corresponds t o an entropy o f  o f lh .61 e n t r o p y u n i t s .  2.)  C a l c u l a t i o n of logTfwap/N  f r o m t h e Phase  2  Diagram:  3 The  activity  of either  be d e t e r m i n e d , f r o m t h e p h a s e activity  so c a l c u l a t e d  o f t h e components i n a b i n a r y s y s t e m c a n  diagram b y using-Wagner's  e q u a t i o n . . The  i s a t t h e temperature and composition o f t h e l i q u i d u s ,  a n d w o u l d b e r e l a t i v e t o t h e compound, w i t h w h i c h t h e m e l t i s i n e q u i l i b r i u m . The  a c t i v i t y - o f t h e compound a t i t s m e l t i n g p o i n t  is. assumed t o be u n i t y  for the calculation. E x a m i n a t i o n o f t h e phase  diagram  ( f i g u r e A-3 ) shows t h a t  melts  -•52 -  w i t h c o m p o s i t i o n s . b e l o w - = 0.137  are i n e q u i l i b r i u m w i t h sodium  f l u o r i d e , melts between N = 0.137 ' A1F  and 0.407 are i n - e q u i l i b r i u m - w i t h  3  X  greater than 0.407-are i n e q u i l i b r i u m w i t h  c r y o l i t e , , and melts f o r N^-^, 3  c h i o l i t e , sodium aluminum tetrafluoride or aluminum, f l u o r i d e , depending :  on the melt composition.  Because the entropy- of f u s i o n i s not known f o r  c h i o l i t e , sodium aluminum t e t r a f l u o r i d e , - or aluminum.fluoride,-melts  whose  = 0.407 w i l l not be considered f u r t h e r .  compositions are above N^-^,  The a c t i v i t y of sodium f l u o r i d e f o r melts whose compositions = O.and 0.137  were between-N^p  were c a l c u l a t e d and .tabulated in. t a b l e A-5  3  For convenience, the a c t i v i t y data was presented i n the form, l o g ! selected melt compositions,.and  l i s t e d . i n column-XIV of t a b l e A-5.  at The  l a s t . entry i n column-XIV i s the value of l o g X-^ -p at "the temperature and a  composition of the e u t e c t i c .  This point i s used-as-the t i e point i n the  c a l c u l a t i o n of log)f  „ values, at higher aluminum f l u o r i d e concentrations, NaF as w i l l be explained i n the f o l l o w i n g paragraph. Melts having a temperature and composition that l i e on the l i q u i d u s between J ^ j ,  = 0.137  a n d  0.407-were i n e q u i l i b r i u m w i t h c r y o l i t e .  The l o g Tf  values l i s t e d i n column XIV of t a b l e A-6 were c a l c u l a t e d r e l a NaF t i v e t o t h i s compound.. The e u t e c t i c was used as a t i e point t o . c o r r e c t t h i s  a c t i v i t y data t o that of pure sodium f l u o r i d e .  The c o r r e c t i o n . f a c t o r was  - 1 . 5 l 8 , and was added t o the l o g _ values of column XIV. ' ' NaF Each o f ' t h e " l o g Y  NaF  values l i s t e d i n column XV of t a b l e s A-5  .and A-6 was adjusted t o a common temperature, 1010°C. adjustment was done using regular s o l u t i o n formula.  The temperature This was at best only  TABLE A - 5 . D e t e r m i n a t i o n o f t h e A c t i v i t y o f NaF b y I n t e g r a t i o n I  .I I  .I l l  IV  . V  o f t h e Compound N a F i n t h e N a F - A l F ^ B i n a r y  VI  VII w  %aF  N  A1F  T  (° ) K  A  T  N  A1F  3  A  T  X  A 1 FA  5 %aF  C  T  3 _  " NaF  -  X  X  1.000 O.995 O.987 O.976 O.949 0.926 0.907 0.900 0.883 0.863 X %aF  0.000 0.005 0.013 0.024 0.051 0.074 0.093 0.100 0.117 0.137  1267 0 1264 3.0 1260 7.0 1254 13.0 1238 29.0 1225 43.0 1207 60.0 1200.5 66.5 1180.5 86.5 1155 112.0 XI  4.575 x T  0 - 3.0 - 7.0 - 13.0 .- 29.0 - 43.6 - 60.0 -66.5 - 86.5 -112.0  • XII l  0  g  a  NaF  0  g  1  F  N  NaF  T  .5796.6 5782.8 5764.5 5737-0 5663.8 5599-9 5522.0 5492.3 5400.8 5284,1  0 -0.003 -0.007 -0.014 -0.032 -0.049 -0.069 -0.077 -0.102 -0.132  0 -0.002 -0.006 -0.010  -O.O23  -0.033 -0.042 -0.046 -0.054 -0.064  0  -0.001 -0.001 -0.004  -0.009 -0.016 -0.027 -0.031 -0,048  -0.068  2  NaF  0 3.0 7.0 13.0 29.0 43.0 - 60.0 -66.5 86.5 -112.0  l G g  V NaF  0 - 19.0 - 44.4 - 82.5 -184.2 -273.0 -381.0 -422.3 -549.2 -711.0  -  XV  XVI  y  l 0 g  XVII NaF  (1285)  (T)  1.000 0.995 O.987 0.976 0.949 0.926 0.907 0.900 0.883 0.863  6.35  (VIII) x  X  0 0 0 0 0 0 0 0 0 0  *NaF  (V + V I I )  ~~ NaF)  W  XIV l 0 g  A dN  3  .0 0 0 0 0 0 0 0 0 0  XIII l  A  J NaF X  IX  NaF  \  2  ( % a F NaF^  x  VIII  0 -0.001 -0.001 -0.004 -0.009 -0.016 -0.027 -0.031 -0.. 048 -0.068  0  -0.001 -0.001 -0.004 -0.009 -0.015 -0.025 -0.029 -0,044 -0.061  l  0  ^ NaF  g  2  N AlF^  0 -40.00 - 5-88 - 7-00 - 3.46 - 2.73 - 2.91 - 2.90 - 3.21 - 3.21  TABLE A-6 Determination of the A c t i v i t y of NaF by Integration of the Compound. Na^AlFg i n the NaF - A l F ^ Binary II  - III  IV  ^ A l F , T(°K)  AT  VI  VII  VIII  IX  ?NaF N  NaF  N  AT  AlFj  A1F,  5  N  127 0.863 0.137 1155 0.143 1163 119 0.857 0.850 0 . 1 5 0 • 1183 99 0 . 8 4 2 - 0 . 1 7 6 1223 59 0.809 1242 40 0.191 1262 20 O.789 9 . 2 1 1 0.780 0.220 1267 15 0.223 1272 10 0.777 0.768 0.232 1277.5 4.5 0.241 1,0 1281 0.759 0.4 0,246 1281.6 0.754 0 O.75O 0 . 2 5 0 1282 1281.7 O.745 0 . 2 5 5 0,3 1.0 O.740 0 . 2 6 0 1 2 8 1 1280.1 0.265 0.735 1-9 1279.2 2.-8 O.730 0 . 2 7 0 0.725 0.275 1277 5 0.720 0 . 2 8 0 1275 7 1272 10 0.285 0.715 0 . 2 9 0 1269 O.710 •13 0.700 0 . 3 0 0 1261 .21 0 . 3 2 5 1233 0.675 49 1187 O.650 0 . 3 5 0 95 0.625 1123 159 0,375 0 . 6 0 0 • 0 . 4 0 0 1044 - 238 0 . 4 0 7 1012 270 0,593  NaF  NaF  153.98 158.88 148,50 140.27 129.49 110.00 108.25 82.59 58.00 26.78  24.60 0 - 15.3 - 26.0 - 33.56 - 37.80 - 55,00 - 65.33 - 81.43 - 94.25 -126.00 . -212.33 -332.50 -477.00 -634.67 -700.00  (N  NaF  .  X  A1F  ^  T  '  W  ^  +  V I 1  ^  (  y i 1 1  ) 14-67 x  -X r \(N - X )' NaF , J NaF NaF %aF  2480 2610 2475 2682 2857 3289 4167 3424.6 3513.4 3125 5000 0 3000 2500 2111 1750 2000 1944  2041 2031 2100 2187.5 2375 2548 2644 2740  345.23 329.96 312.17 245.13 203.59  142.13  IO8.58 97.19 65.97 36.09 20.00 0 - 17-5 - 31.2 - 42.7 - 52.41 -  61.79 71.67  81.63  91.00  -112.46 -166.06 -222.11 -284.16 -350.73 -368.91  499.21  488.84 460.67 385.40 333.08 250.38 218.58 179.78 123.97 62,87 44.60 0 - 32.8 - 57-2 - 76.26 - 90.22 -126.79 -137.00 -163.06 -196.05  -238.46 -378.39 -555.61 -761.63 -985,40 -1068.91  7323.4 717L3  6758.O 5653.8  4886.3 3673.1 3206.6 2637.4 1818.6 922.3 654.3 0 - 481.2 - 839.1 -1118.7 -1323.5 -1860.0 -2009.8 -2392.1 -2876.0 -3498.2 -5551.0 -8150.8 -11173.1 -14455.8 -15650.0  - 55 -  H LTN o o o o CM oo-d- v o L T N J - C O OA o o H H O M A O C O J - CM OO O C O O N O CM VO CA) O CM -d" VD ON H ro OO CM VO VO -d" OA 0O00 c— ON UN CM -d" ON CM 00-d" 00 C O l A C - t — C O O H H C v l C A I W C v l H a i H r l r l r l r l H H H W H H r H r H r H C M C M O J C M C M C M O J C M C M C M C M CM CM CM CM CM CM CM  H OO H -d" CO l>- t~-CO CO H r O P O r l ON OO OO O ON ON UA f - CM CO VO ON O \D ONCO O J - V O J - 4 - C O J - c O O \ t - C V I t - 0 0 \ O V O J - r o j - W 1A H CO O O H -d" UA f-CO ON O CM CM OO-d" LfN UA VO VO [>- C—CO ON CM VO O UAVO O O o d d o O O r H r H ^ r H r H r H ^ r H r H ^ r H ^ r H ^ C M C O O O O O  CO C O C O -d" VO ON t — V O CM rH _d OO CM O U A t — C— ON OO-d- O N H OJ ON CM H VO O ON CM V O f - LTN LTN OA J - CO OA C— OO C— O OA H CO V O V O OO C O C O CM C— O H H L f A ^ - C O ON O CM CM r O J - U A U A V O V O t - f - C O OA 0OC0 -d" O O V O  O1 Oj Oi O i O | O iO IO H Hi rI HI HI H i i iH iH iH H HI Hl Hi H' W ' ^ i i  •  '  '  1  O U N 0 4 OI ON H C M V O t - J - UAVO CM C— ON CA H UAVO H OO -d" H -4" OO LCA i—I CM ON UA OOVO VO CM OO CM -d H UACO C— O VO -d" U A H H t— O UTN OO O OA E—VQ UA J - C M C M H O O O O H C M C M OO CO OO OACO H -  H  H  H  H  o  o  o  d  d  d  o  d  d  d  o  d  o I  I  d d I I  d o o I I  H  I  H C M o o I I I I i I  -dr t — H -d- CM OOCO O N I A O OOUACO H -dr tr- OA OOVO O M A H t--d" CM VOVO Ir—CO O N O O O H CM CM CM CM OO OO OO 0O-d" -d" UAt-CO O CM CM O O O O O H H H H H H H H H H H H H ' H H H H H O J O J C M o  i  o d o d d d o d d o d d o d d d d d d d d d d d d i • i i i i i i i i i i i i i t i i i i i i i i i  VQCOOAOOVOOOOOHIr— H CO_d-_d-rHV0OOLr\uArHUArH OOOOCMOCOVOUA-d-OOHrH  Cv) OO H MD CO J - H UAVO -d" rH UAVO O c O d O N W H d H O N O C O O t ^ O J C O O H H O J f n M 4 4 U 3 ( J M A H O n  H r H r H H o d d o d d d o d d d d d d d d d d r H C M o o o o •  I  I  I  i  i  i  H  Ir- CXI CM r H V O U A U A V O V O CO H CO VO -d" r o m H d  -d" CO CM UA  O CM U A CM CM r H ON CO OO UAVO UAUAUAUA  '  •  i  i  i  i  i  !r- r H O U A t — oo O  O O V O ON-dr O 0 O U A 0 O O V O CM CM O O O A U A O A r H O I r - V O O t r — O N r H - d - V O V O V O V O V Q U A U A - d O O r H O V O - d " OO OO Ir—CO tr— t - C O C O C O C O C O C O C O C O C O C O C O C O C O Ir—VO -d" H Ir— U A U A U A U A U A U A U A U A U A U A U A U A U A U A U A U A U A U A U A UA J " -d  OOND— O - d O N O N O l ^ C O O N - d O U A O U A O U A O U A O O U A O U N O on V O . U A U A C M O C O C O Ir— VO U N U M A d d 0O0OCM CM rH rH O tr- UN CM O ON CO ,00 CO CO CO — t — t — C-— C— D— C-— — Ir— I r — t ^ - t r - l r — I r - l r - l r - V O V O V O V O U"N -  - 56 -  an  a p p r o x i m a t i o n , a s t h e NaF - A 1 F  s y s t e m was n o t a . r e g u l a r  solution.  3 The  values of l o g / /NT,- a t 1010 C w e r e a l s o l i s t e d NaF . A l F ^  and  A-6 a n d p l o t t e d  i n tables  e  &  v  i n f i g u r e A-k a g a i n s t  N  . . The v a l u e o f l o g / /N7,„. NaF A1F.  AlFj at  =  3  discussed  . 3.)  0.223  w  a  used f o r t h e t i e p o i n t  s  3  in.the  c o m p u t e r programme  earlier.  The C a l c u l a t i o n  The analysis  A-5  of log Y : AlF^  a c t i v i t y d a t a f o r sodium f l u o r i d e from a thermodynamic  o f t h e NaF - A l F ^ p h a s e d i a g r a m h a s b e e n d e s c r i b e d  above.  .The  G i b b s - D u h e m r e l a t i o n s h i p was u s e d . t o c a l c u l a t e t h e a c t i v i t y d a t a f o r aluminum f l u o r i d e , s i n c e :  logY'AiF 3  =  " A1F % a F N  l o  3  e* N  \  +  N a F  !lF  § *  l o  \  5  N  N  The  values of l o gJ s  NaF  / N 7 , „ at various A1F  N  \  a  A1F  A1F,  concentrations  F  3  ^  A  1  F  5  3  = °  were t a k e n  from  5  v could not AlFj the plot of  f i g u r e A-4 f o r u s e i n . t h i s i n t e g r a t i o n . . The v a l u e o f l o g Y be  c a l c u l a t e d b y t h i s method b e y o n d N^  l o g Y^  p/^Aip  v l°g 0AIF  could  n o t be made b e y o n d t h i s p o i n t .  c a l c u l a t e d b y t h i s t e c h n i q u e were o n l y  3 contribution  Hence v a l u e s o f  log  In  r e l a t i v e , because t h e  = 0.407 a n d 1.00 was AlFj o f t h e Gibbs-Duhem e q u a t i o n . . These  o f t h e i n t e g r a l t e r m between-N  m i s s i n g f r o m t h e r i g h t hand s i d e  with  0.407 s i n c e  ^  a  relative  .=  YAQ_F 3  v a  l  u e s  were l i s t e d  i n column V I I o f t a b l e  A-7  o r d e r t o e s t a b l i s h t h e a c t i v i t y 'data:;!for--»a-iuminum f l u o r i d e  respect t o a standard state  o f t h e pure s o l i d m a t e r i a l  was n e c e s s a r y t o e s t a b l i s h t h e v a l u e o f l o g Y* A i r  at  a t some p o i n t  3  1010°, i t between  TABLE Calculation I  II  I I I  A-7-  o f t h e A c t i v i t y o f Aluminum F l u o r i d e IV  V  I  VT  N  0.407 0.400 0.375 0.350 0.325 0.300 0.275 0.255 0.250 0.225 0.200 0.175  O.863 O.875 0.900 O.925 0.950 0-975 1.000  0.137 "0.125 0.100 0.075 0.050 0.025 0.000  O.85O 0.150  -22.32 -22.00 -21.65 21.40 -21.20 -21.55 -22.15 -22.62 -22.30 -19.10 -16.00 -13.10  :  -8.00  -3.21 -3.15 -2.95 -2.80 -2.45 -2.20 -2.00  0.242 0.240  0.234 0.227 0.219 0.210 0.199 0.190 0.187 0.174 0.160 0.144 0.127 0.118 0.109 0.090 O.069 0.047 0.024 0  - 5.40 - 5.28 - 5.05 -4.86 - 4.64 - 4.52. - 4.4l - 4.30 - 4.17 - 3.32 - 2.56 - 1.87 - 1.02 - O.38 - 0.34 - 0.26 " 0.19 - 0.11 ~ 0.05 0  VII  VIII  IX  = N  *AlFo  A1F  log T  dN  N  0.593 0.600 O.625 0.650 0.675 0.700 0.725 0'.745 0.750 0.775 0.800 0.825  b y t h e Gibbs-Duhem T e c h n i q u e  NaF ALF  A1F  3  3  (-V+VT) ( V I I : . + 6 . 4 5 2 ) l o g V  AIF3  AIF3 NaF  3  = °'  - 0, -0.155 - 0.701 -1.-239 -1.771 "2.313 -2.874 -3.330 -3.443 -3.884  - 4.328 -4.660 -4.924 - 4.969 -5.007 -5.083 - 5.155 -5-220 -5.278 -5.330  k 0 1  5-400 5.125 4.349 3.621 2.869 2.207 1.536 0.970 0.727 0-564 I.768 2.790 3-904 4.589 4.667 4.823 4.965 5-110 5.228 5.330  -I.052 -1.327 -2.103 -2.831 -3-583 -4.245 -4.916 -5-482 -5.725 -7.016 -8.220 -9.242 -10.356 -il.o4i  -2.992 -3-686 -5-384 -6.700 -7.865 -8.663 -9.353 -9.877 -IO.187 -11.682 -12.844  -13.579 -14-333 -14.824  -11.119; -14.516 -11.275 -13.920 -11.417 . .. . -13-344 -11.562 -12.811 -11.680 '12.287 -11.782 -II.782  - 59 -  = 0 and  rlAlF logY  A1F  0.407,  and  apply a c o r r e c t i o n f a c t o r t o the values  c a l c u l a t e d f r o m t h e Gibbs-Duhem e q u a t i o n .  The  of  t i e point  5  s e l e c t e d f o r t h i s p u r p o s e was  a t - N ^  c o m p u t e r programme g a v e a . v a l u e  0.223,  =  of l o g ^ ^ A  since the r e s u l t s  a t "this p o i n t .  F  of  The  the  corrected  >3 logY. v a l u e s appear i n column V I I I AlFj v a l u e s o f log'if  ° " AlH  3  /N„, „ a p p e a r i n c o l u m n ' NaF  A-5  Figure  o f t a b l e A-7 a n d  i s a plot  the  corresponding  IX.  logY  of  /lC _ against N . The p l o t • AlFj NaF A1F segments m e e t i n g a t N = 0.137'. The •Air 5  consists  o f two  straight  line  3 e x t r a p o l a t i o n of the s t r a i g h t l i n e  = 0.137  s e c t i o n b e t w e e n N^^, 1  °sY'  3  2  to higher aluminum.fluoride concentrations gives A1F / N a F A1F °'55 P d i a g r a m • shows, t h a t a t 1 0 1 0 ° , a m e l t o f =  W  0,  composition  T h e  h  a  s  a c t i v i t y of the alumnium f l u o r i d e J  equals  C.  1.3,  N  which  =  agrees  i s u n i t y h e r e , and  9  1 ,  a-t  this  e  i s i n e q u i l i b r i u m w i t h s o l i d aluminum f l u o r i d e ,  0.407  and  so t h a t  hence l o g /  the  , /N„ „ AlFj NaF  reasonably w e l l w i t h the e x t r a p o l a t e d value.  Discussion:  I n s e c t i o n s A and  B of t h i s appendix,  two  independent  and  a l t e r n a t i v e methods f o r t h e d e t e r m i n a t i o n o f a c t i v i t y d a t a f o r sodium f l u o r i d e and d a t a was  aluminum f l u o r i d e were d i s c u s s e d .  I n s e c t i o n A,  this  activity  c a l c u l a t e d f r o m a k n o w l e d g e o f t h e a c t i v i t y , o f .sodium i n NaF  m e l t s as a f u n c t i o n o f t h e m e l t  c o m p o s i t i o n . . The  - AlFj  sodium a c t i v i t y  values  u s e d i n t h e c o m p u t e r programme l i e on t h e l i n e d r a w n i n f i g u r e A - l .  It is  ,4  i observed  t h a t t h e a c t i v i t y v a l u e s c a l c u l a t e d f o r Dewing s and  data agree w e l l w i t h the The  computed, r e s u l t s  selected line  for log ^  N A F  /N^  over the e n t i r e and  1 F  3  logY  A 1 F  composition  ./N^  3  Hollingshead s  A R E  P  L  O  range. T  T  E  D  A  S  - 61 -  o p e n c i r c l e s a n d o p e n . t r i a n g l e s i n f i g u r e s A-6 a n d A - 7  In section  B, a c t i v i t y d a t a f o r s o d i u m f l u o r i d e a n d a l u m i n u m  f l u o r i d e were c a l c u l a t e d  u s i n g t h e phase  diagram f o r t h i s  c a l c u l a t i o n s b a n g d o n e b y u s e o f Wagner's. m e t h o d . plotted  as l o g Y ^ p / N ^  andlogY  2  A 1  p  3  results for log /  e s t a b l i s h the t i e point intersect at N ^ p  =  /N  N a F  The a c t i v i t y  /Nt -, f r o m s e c t i o n NaF A l F ^  B were used, t o  ni  f o r s e c t i o n A, a n d s o b o t h c u r v e s o f f i g u r e  0.223.  At a l l other points  r e s p e c t t o d i s p o s i t i o n a n d shape  observed i nthe graph derived sitivity  o f the figures  dataa r e  ( closed . c i r c l e s and t r i a n g l e s )  A-6  t h e two c u r v e s were  e s t a b l i s h e d . b y . t h e two i n d e p e n d e n t methods o f s e c t i o n s with  system, t h e  3  i n . f i g u r e s A-6 a n d A-7 r e s p e c t i v e l y .  The  respectively.  A a n d B.  i ss a t i s f a c t o r y and.the  Agreement  small  peak  from s e c t i o n B i s a t t r i b u t a b l e t o the  sen-  i n c o l u m n V I o f t a b l e A-6  measurement o f t e m p e r a t u r e o f t h e l i q u i d u s  t o slight, errors  curve near the c r y o l i t e  i n the compos-  ition. In f i g u r e  A-7,  used.to establish'the  the results of  t i e point  l°sV^p  atN^p  =  0.223  A^aF  f  b y t h e Gibbs-Duhem i n t e g r a t i o n . i n s e c t i o n  p o s i t i o n a n d shape  o  s e c t i o n A were  m  f o r the l S ^ ^ p 0  A  3 calculated  r  o f the two curves i s s a t i s f a c t o r y .  values  3 B.  Again the  dis-  -24.0  -20.0  oo  1 tt> o  -l6.0  ro  -12.0  H  -8.0  from Figure A - 2  O  from Figure A - 4  •  -4.0  0.0  0.1 Figure A - 6 ;  0.2  Comparison of l o g Y  N a F  /N|  WA, 1 F , 1 F  0.3  0.4  0.5  Values at 1010°C for the Computer Results of Experimental Data  (Figure A - 2 ) and the Theoretical Results from Wagner's Method (Figure A - 4).  -20.0  -16.0  -12.0 oo fe  H <;  ON  -8.0  (jo  O  Fi gure A - 1  Comparison of log X  A  1  F  /NfaF Values at 1010°C for the Computer Results of Experimental Data  from Figure A - 2 ,  and the Theoretical Results from Figure  A-5.  - 64 -  APPENDIX B  THE SODIUM - LEAD SYSTEM  Four papers  have appeared  i n the l i t e r a t u r e concerning the activ-  i t y o f sodium i n sodium - l e a d a l l o y s .  The s o d i u m a c t i v i t y was o b t a i n e d  by e l e c t r o m o t i v e f o r c e measurements based  electrolyte containing Na  Na  wherein  on t h e c e l l : .  t h e sodium a c t i v i t y , E  =  |  +  Na(Fb)  i s r e l a t e d t o t h e e.m.f. a s : ^575  -  T log  a  N  a  (  p  b  )  nf 2k Hauffe N  Na  =  0,  33  6  t  o  and Vierke  °*935  r a n g i n g between N  N  k25° a n d 475°.  a t  &  s t u d i e d t h e composition i n t e r v a l between  =  0.131  f o r compositions between N  N  and a  =  Morachevskii  0.851,  0.05  375°  studied alloys  a n d 475°, a n d L a n t r a t o v ^ 2  a n d 0.90, a t 4 0 0 ° ,  These t h r e e i n v e s t i g a t i o n s were b a s e d o f g l a s s w i t h a h i g h Na 0 c o n t e n t .  at  2 5  500°  on a s o l i d e l e c t r o l y t e  a n d 600°. consisting  The f o u r t h p a p e r , b y F e i n l a b a n d  2  P o r t e r J used as a s o l i d e l e c t r o l y t e alumina b r i c k  s a t u r a t e d w i t h NagCO^.  This l a s t i n v e s t i g a t i o n covered t h e a l l o y composition between Njj to  0.401  f o r v a r i o u s temperatures  of these experiments i n t a b l e s B - l through A composite was  775°  prepared a t  475°-  between  500°  a n d 800°.  =  0.151  The r e s u l t s  were r e c o r d e d a t c o n v e n i e n t t e m p e r a t u r e B-4  a  intervals  respectively.  plot of logY^/N^  v s . Njj  a  f r o m t h e above d a t a  I t was n e c e s s a r y t o a d j u s t t h i s d a t a t o 725°>  a n d 825° i n o r d e r t o d e t e r m i n e  t h e a c t i v i t y o f sodium i n t h e sodium -  TABLE B - l . Sodium A c t i v i t y Data f o r t h e Sodium-Lead System ( f r o m H a u f f e and V i e r k e ^ ) II  I N  Na(Fb)  a  Na  III ^Na  IV -log y  N  a  N  V  VI  VII  Pb  4  -iogyj ]  C336  0.392 0.444 0.470 0.562 0.567 0.625 O.678 0.705 0.757 O.794 0.815 0.873 0-935 0.336 0.392 0.444 0.470 O.562 0.567 O.625 O.678 0.705 0.757 0.794 O.815 O.873 0-935  0.007 0.011 0.020 O.O38  0.074 0.090 0.135 0.215 0.246 0.363 0.515 0.710 0.840 O.925 0.005 0.008 0.015 O.029 O.060 0.074 0.113 0.188 0.215 O.326 0.487 0.681 O.865 0.920  0.021 0.028 0.046 0.031 0.132 0.159 0.216 0.317 0.349 0.470 0.649 0.871 0.962 0.989 0.015 0.020 0.034 0.062 0.107 0.130 0.182 0.277 0.305 0.431 0.613 0.836 0.991 0.984  475 c 1.682 1.551 1-347 "I.O92 0.881 0.799 O.665 0.499 0.457 0.320 0.188 0.060 0.017 0.005 •425 °C 1.824 1-699 1.469 •1.208  0.971 0.886 0.740 O.558 O.516 O.366 0.213 0.078 0.004 0.007  0.664 0.608 0.556 0.530 0.438 0.433 0-375 0.322 0.295 0.243 0.206 O.185 0.127 O.065  0.441 0.370 O.309 O.281 0.192 0.187 0.l4l 0.104 O.087 0.059 0.042 0.034 0.016 0.004  3-81 4.20 4.36 3.89 4.59 4.26 4.73 4.81 5-25 5.42 4.43 1-75 1.04  1.14  TABLE B - 2 . Sodium A c t i v i t y Data f o r t h e Sodium-Lead System, ( f r o m M o r a c h e v s k i i II  I N  Na(Pb)  a  Na  III ^Na  : IV -  l o  V  ) VI  Nib  e*Na  VII  -logVi I  475 0.131 0.14-9  0.177 0.200 0.205 0.222 0.300 0.354  0.402 0.409 0.500 0.503 O.598 0.700 0.734 0.800 O.85I  0.0008 0.0008 0.0013 0.0017 0.0019 0.0025 0.0054 0.010 0.0166 0.0184 O.O518-  0.053 . 0.131 0.284 0.341 O.58O 0.740  O.OO59 0.0052 0.0071. O.OO87  0.0091 0.0113 0.0181 0.0282  0.0413  0.0450 0.1036 0.1054 0.219 0.4057 0.465 0.725 0.870  °c  2.231 2.286 2.147 2.060  2.040 1.946 1.743 1.549  1.384  1.347 0.984 0.977 0.659 0.392 0.333 o.i4o 0.061  0.869 0.851 0.823 0.800 0.795 0.778 0.700  0.646  0.598 0.591 0,500 0.497 . 0.402 . 0.300 0,266 0.200 0.149  O.755 0.724 0.6773  o.64o 0.632 0.605 0,490 0.417 O.358 O.349 O.250  0.247 0.162 0,090 O.071 o.o4o 0.022  2.954 3.157 3.171 3.219 3.228 3.216 3.557 3.712 3.871 .3.856 3.939 3.956 4.080 4,353 4.716 3.491 2.733  TABLE B - 3 . Sodium A c t i v i t y Data f o r t h e Sodium-Lead -System. ( f r o m L a n t r a t o v  I  II  a(Pb)  a  Na  III .  IV "  / N E  l o g  26  V  ^Na  N  )  VI 4b  Pb  VII " S * Na l o  N  Pb  475 °C 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90  0.0002 0.0005 0.0019 0.0050 0.0132 0.0445 0.1230 0.2570 0.5750 0.8400  VIII W  Na(Pb)  a  IX  X  Na  ^Na  0.0046 0.0054 O.OO95 0.0168 0.0330 0.0890 0.2050 0.3670 0.7187 0.9333 XI "  L O  S  *Na  2,357 2.268 2.022 1.775 1.481 1.051 0.688 0.435 0.143 0.030 XII  XIII  Na  • • Na  a  O.5O  0.60 0.70 0.80 0.90  0.0001 0.0003 0.0010 O.OO27  0.0079 0.0301 O.952 0.315 0.533 0.828  0.002 0.0028 0.0049 0.0090 0.0190 0.0602 O.I587  0.307 0.622 0.921  XIV -  1 O  S  ?Na  XV a  Na  500 °C  400;°c 0.05 0.10 0.20 0.30 0.40  0.902 0.810 o.64o 0.490 0.360 0.250 0.160 0.090 0.040 0.010  0.95 0.90 0.80 0.70 0.60 0.50 0.4o 0.30 0.20 0.10  2.627 2.556 2.307 2.045 1.719 1.220 0.799 0.5123 0.206 0.036  0.0003 0.0007 0.0024 0.0066 0.0164 O.O518 0.137 O.276 O.587 0.841  0.0062" 0.0070 0.0121 0.0219 0.0410 0.104 0.229 0.394 0.733 0.935  2.589 2.799 3.160 3.622 4.115 4.202 4.302 4.837 3.586 2.998 XVI  ^Na  XVII  " sY lo  Na  600 °C 2.210 2.152 1.917 1.660 1.387 0.983 o.64o o.4o4 0.135 0.029  0.0006 0.0014 0.0049 0.0130 0.0287 O.O787  0.188 0.334 0.614 0.853  O.OI30 0.0144 . 0.0243 0.0433 0.0719 0,157 0.305 0.478 0.767 0.947  1.886 1.842 1.614 1.363 1.143 0.804 O.516 0.321 0.115 0.024  TABLE  B-4.  Sodium A c t i v i t y Data f o r t h e Sodium-Lead System ( f r o m F e i n l a b II N  I I I  Na  Na(Fb)  IV  V  -logy  Na  and P o r t e r  N  Na  7  1  ) VII  VI N  Pb  2  - l o g ft Na N Pb  Pb  2  475  N„.  ^ a  ^Na  O.36I  o.4oi  0.0015 0.0023 0.0033 0.0074 0.0119 0.0089 0.0164  XII  XI  X  IX  500 0.151 0.212 0.223 0.293 0.358  0.0321 0.0216 0.0349  0.0140  -  l o g  *Na  ^ a  0.849  1.886 1.634 1.493 1.665 1.457  0.778 0.777 0.707 0.642 0.639 0.599 -XIII ^Na  600  °C  0.0098 0.0110 0.0149 0.0252 .0.0332 0.0246 0.0409  2.085  2.014  O.O232  O.OO78  0.401  VIII  0.0082 0.0097 0.0130  0.0012 0.0020 0.0029 0.0068 0.0115  0.151 0.212 0.225 0.295 0.358 0.361  °C  2.009 1.959 1.827 1.599 1.479 1.610 .1.388  0.0029 0.0043 0.0060 0.0125 0.0208 0.0161 0.0290  0.729 0.621 o.6o4 0.500 0.412 o.4o8 0.359 XV  XIV -  l  o  g  y  Na  . ^ a  0.0446 0.0723  XVI ^Na  700  °C  0.0194 0.0205 0.0269 0.0427 0.0581  .2.860 3-245 3.124 3.270 3.623 4.079 4.061  1.712 1.688 1.570 1,370 1.236 1.351 l.l4i  O.OO54 O.OO78  0.0108 0.0210 0.0345 0.0292 0.0507  XVII "  l  o  g  * Na  °C  0.0358 0.0368 0.0484 0.0717 0.0964 O.0809 0.1264  1.446 1.434 1.315 1.145 1.016 I.092 O.898  - 69 lead a l l o y s a t these higher temperatures. extrapolation,  i t was n e c e s s a r y  I n order t o accomplish  t o evaluate t h ep a r t i a l m o l a l heat  o f sodium i n l e a d , a s a f u n c t i o n o f t h e sodium c o n c e n t r a t i o n . ' evaluated by p l o t t i n g  logYjj  a  L. Na  T  i n v e s t i g a t i o n s covered the widest temperature  most  accurate values of l o g t ^  s u l t i n g p l o t s were l i n e a r ,  can be  ranges,  a  values, as  thereby  a t various temperatures.  &  will  The d a t a o f  F e i n l a b a n d P o r t e r , a n d L a n t r a t o v , was u s e d t o c a l c u l a t e t h e L j j  the  of solution  v s . l / T f o r f i x e d compositions, which  g i v e s t r a i g h t l i n e s , whose s l o p e s a r e p r o p o r t i o n a l t o L ^ .  these  this  giving  Since the r e -  t h e m e t h o d o f l e a s t s q u a r e s was u s e d t o c a l c u l a t e  the b e s t l i n e s and g r a d i e n t s from the data. The v a l u e s o f L„ c a l c u l a t e d ° Na i n t h i s manner were p l o t t e d a g a i n s t N ^ i n f i g u r e B - l . a  F i g u r e B-2 was t h e c o m p o s i t e four papers. to  The  logY^  values c a l c u l a t e d from  a  the higher temperatures  cordance  o f t h e ^-°gf ^/^p^  u s i n g L^  t h i s p l o t were a d j u s t e d  values taken from f i g u r e B - l , i n a c -  a  w i t h the formula:  ^NatT-L)  % a  =  (  1  -  U.575 ( T The r e s u l t i n g  l°g^u ([Tj)^ a  ^Na(T)  a  n  d  a  from the data i n t h i s t a b l e . at  940°C, 970°  and  +  l o  S Na(T ) Y  2  T ) 2  v  &  l  u  e  s  ^  a  i n t a b l e B-5-  Using this  1010° w e r e  )  1  x  Na(T)  i n t e r v a l s were c a l c u l a t e d and l i s t e d  ivities  data from a l l  s e  * concentration  Figure 5  w  a  s  compiled  same t e c h n i q u e , t h e s o d i u m a c t -  c a l c u l a t e d f o r use w i t h F e i n l a b and  P o r t e r ' s d a t a i n f i g u r e A - l o f A p p e n d i x A.  TABLE B-5. C a l c u l a t i o n o f t h e A c t i v i t y o f Sodium i n Sodium-Lead A l l o y s a t 725, 775, I  11  ^Na(Pb)  " Na  VIII  0.35  o.4o 0.45 0.50  lo  § Y Na(775) 0.523  l 0 s Y  IV  Na(475)  l  - 2  O.5I+6 - 2 0.601 - .2 0.730 - 2 O.856 - 2  O.99I+ - 2 0.121-1 0.229 - 1 0.325 - 1 O.389 - 1  0.0333 0.0351 O.O399 0.0537 O.O718 O.O986 0.1320 0.1690 0.2110 0.2450  g  y  Na( 25)  0.4l8 0.444 0.502 0.632 O.76O 0.901 0.032 0.147 0.254 0.330 X  IX 775 °C / Na(775)  0  a  Na(775) .0017 .0035 .0060 .0107 .0179.0296 .0462 .0676 .0949 .1225  XI  V  VI  y Na(725)  V(725)  725 °C 7  2.310 2.260 2.190 2.050 1.910 1.750 1,590 1.420 1.240 1.080  9950 9625 9450 9320 9150 8890 85OO 7750 6750 56OO  VII  0.05 0.10 0.15 0.20 0.25 0.30  -  L  0.05 0.10 0.15 0.20 0.25 0.50 0.35 0.40 0,45 0.50  %a(Pb)  III  and 825 ° C .  -  2 2 2 2 2 2 1 1 1 1  XII 825 °C  Na(82 )  yNa(825)  0.616 - 2 0.636 - 2 O.69O - 2 O.818 - 2 0.942 - 2 O.O78 - . 1 0.201 - 1 0.301-1 0.388 - 1 0.441 - -1  0.0413 0.0432 0.0490  l 0 g r  .0013 .0028 .0048 .0086 .0144 .0239 .0374 .0560 .0805 .107  0.0262 0.0278 0.0318 0.0428 0.0575 O.O796 0.1070 0.1400 O.I79O 0.2140  5  O.O658 0.0875 0.1200 O.I59O 0.2000 0.2440 O.276O  XIII a  Wa(825) .0021 .0043 .0073 .0132 .0219 .0360 .O556 .0800 .IO98 .1380  F i g u r e B - 1: P a r t i a l M o l a l H e a t o f S o l u t i o n o f S o d i u m i n L i q u i d L e a d as a F u n c t i o n o f C o n c e n t r a t i o n .  - 73 APPENDIX C  THE SODIUM - ALUMINUM SYSTEM  Little  i n f o r m a t i o n has been p u b l i s h e d c o n c e r n i n g . t h e sodium. -  aluminum'phase diagram. and d i f f e r e n t i a l  to  2  c o n c e n t r a t i o n , a t 659°C.  They a l s o r e p o r t e d . t h a t  sodium e x h i b i t e d r e t r o g r a d e s o l u b i l i t y , i n t h e system. determine t h e s o l i d  successful i n this  They  attempted  s o l u b i l i t y b y r e s i s t i v i t y measurements, b u t were n o t  endeavour.  •On t h e b a s i s o f m i c r o g r a p h i c s t u d i e s ,  they concluded that the s o l u b i l i t y at  i n v e s t i g a t e d t h e system u s i n g d i r e c t  t h e r m a l a n a l y s i s , a n d f o u n d a m o n o t e c t i c p o i n t a t 0.18  weight p e r c e n t sodium the  Fink et a l . ?  a l l temperatures below  o f s o d i u m was l e s s t h a n  0.003  however,  percent  the monotectic.  ?8 .Ransley and Neufeld ary  investigated the l i q u i d - m i s c i b i l i t y  b y f u s i o n o f aluminum i n t h e presence  rapid quenching results  o f excess sodium,  bound-  followed by  o f the melt and a n a l y s i s o f the aluminum-rich l a y e r .  The  s u g g e s t e d t h e m o n o t e c t i c c o m p o s i t i o n was O.lk p e r c e n t s o d i u m , a n d  indicated that the s o l u b i l i t y increased r e g u l a r l y w i t h temperature. data from t h i s  The  i n v e s t i g a t i o n has b e e n . t a b u l a t e d i n t a b l e C - l .  The r e s u l t s  o f t h e above i n v e s t i g a t i o n s have been used  s t r u c t t h e phase diagrams, d a t a on t h e s o l u b i l i t y  f i g u r e s C - l and C-2. . Ransley and Neufeld's  o f sodium  against I / T i n figure C - J .  t o con-  i n t h e l i q u i d p h a s e was p l o t t e d a s l o g N ^  The s l o p e o f t h e l i n e  p a r t i a l m o l a l heat o f s o l u t i o n o f sodium  yields a value o f the  i n a l u m i n u m o f 92J0 c a l o r i e s / m o l e .  a  1 1  1  1  660.5  v A  1  660.0 Temperature,.°C  659.5  659.O ..Fink e t a l . ? 2  28 Ransley andNeufeld  658.5 0  1  1  1  0.02  0.0U  0.06  1  0.08  I  0.10  Weight Percent :  F i g u r e C - 1:  I  1  0.12  0.l4  1  1  0.16  0.18  Sodium  Phase Diagram f o r t h e Sodium - Aluminum System, Showing t h e H y p o - e u t e c t i c - M o n o t e c t i c L i q u i d u s .  0.20  - 75 -  F i g u r e C - 2:  Phase Diagram f o r the. Sodium - Aluminum System,.Showing- S o l u b i l i t y L i m i t o f Sodium.  - 76 -  TABLE C - l . Partial:.Molal- Heat of Solution of Sodium in Aluminum. (Ransley and Neufeld ). 28  Wt. Percent Sodium  0.l4 0.15 0.15 0.18 0.22 0.20 0.23 0.22 0.25  N^  a  0.001643 O.OOI76I O.OOI76I 0.002112 0.002582 0.002347 O.OO2699 0.002582 0.002934  T(°C)  T(°K)  665 670 670 700 725 725 750 750 775  938 943 943 973 998 998 1023 1023 1048  l/T x 10 1.066 1.060 1.060 1.028 1.002 1.002 0.977 0.977 O.952  5  - 78 - BIBLIOGRAPHY  1.  2. 3. 4.  • Grunert,,E.,; Z.. E l e c t r o c h e m . . 48, .393  (194-2).  J a n d e r , ,W. ,. and Herman,. H. ,•Z. a n o r g . a l l g e m . Chem. 239_, 65 (1938). Pearson,..T. G.,. and Waddington, J . , . D i s c u s s i o n s of the Faraday .. S o c i e t y , . 1, 307 ( 1 9 4 - 7 ) . H o l l i n g s h e a d , . E.•A., p r i v a t e communication.  5-  - Dewing,,E. W . , . p r i v a t e communication.  6.  S t o k e s , J . J . J r . , and-Frank,. W. • B., " S p e c t r o s c o p i c I n v e s t i g a t i o n o f the Occurrence of' Sodium i n the Fumes above M o l t e d C r y o l i t e " , i n " I n t e r n a t i o n a l . 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E., C  175, 36k (19^8). 28.  •Ransley,,C. E., and N e u f e l d , . H . , J . I n s t . M e t a l s , j8, 25 ( I 9 5 O - 5 I ) .  

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