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

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SODIUM ACTIVITY MEASUREMENTS IN.THE SODIUM -ALUMINUM SYSTEM by JOHN CHRISTOPHER MITCHELL B.-Sc., ;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 , 1962 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR.THE DEGREE OF MASTER OF SCIENCE i n t h e Department o f METALLURGY We a c c e p t t h i s t h e s i s a s c o n f o r m i n g . t o t h e s t a n d a r d r e q u i r e d f r o m c a n d i d a t e s f o r t h e degree o f MASTER.OF SCIENCE Members o f t h e Department o f M e t a l l u r g y THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1965 I n p r e s e n t i n g 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 the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y of • B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study* I f u r t h e r agree t h a t p e r -m i s s i o n f o r extensive, c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that , c o p y i n g or p u b l i -c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n * Department of Metallurgy The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada Date May 3. 1965 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 s y s t e m f o r sodium c o n c e n t r a t i o n s i n aluminum between % a = 25 x 10"^  and 75 x 10" .^ 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 d a t a fs 6 up t o N N a•= 300 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 = 25 x 10 t o J00 x 10"^  encompasses t h o s e sodium 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-m e r c i a l p o t - l i n e o p e r a t i o n , The 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 d i s t r i b u t i o n e q u i l i b r a t i o n o f sodium between a - l e a d - r i c h and an aluminum-r i c h p h a s e . The s o d i u m - l e a d s y s t e m was used as a r e f e r e n c e f o r t h 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 sodium. . The sodium 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 sodium a c t i v i t y shows a s t r o n g dependence on t h e sodium c o n c e n t r a t i o n o f t h e aluminum phase f o r sodium c o n c e n t r a t i o n s below N = 100 x 10"6. - Na The a c t i v i t y d a t a f o r aluminum i n t h e sodium-aluminum s y s t e m has been o b t a i n e d by 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 sodium a c t i v i t y d a t a . The d a t a f o r t h e aluminum i n d i c a t e s t h a t t h e a c t i v i t y o f aluminum can 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 o v e r t h e e n t i r e range o f m i s c i b i l i t y o f t h e sodium-aluminum system. ACKNOWLEDGEMENT The author would l i k e t o express h i s thanks t o Dr. C. S. Samis f o r h i s encouragement and guidance throughout the p e r i o d of t h i s work, and to Dr. E. W. Dewing, of Aluminium L a b o r a t o r i e s , whose comments and suggestions w i t h regard t o Appendix A were most h e l p f u l . Thanks are a l s o extended t o Aluminium L a b o r a t o r i e s and the Alum-inum Company of 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 they have so generously provided. Acknowledgement i s made of f i n a n c i a l a i d from the N a t i o n a l Research C o u n c i l of Canada, under Grant A-IM-63, which 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 on.the Sodium - Aluminum - C r y o l i t e System . 1 a) .. S o d i u m - A l u m i n u m - C r y o l i t e Systems 2 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 Systems . 4 2) . P u r p o s e 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 6 5). Method o f Measurement . 6 k).-Region o f I n v e s t i g a t i o n 9 .- EXPERIMENTAL 10 .1). A p p a r a t u s 10 2). M a t e r i a l s • 10 5). C r u c i b l e s 10 k).. F u r n a c e 10 5) . Temperature. C o n t r o l 10 6) . Gas S u p p l y 1 2 7) . E x p e r i m e n t a l P r o c e d u r e . . . 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^  a) . A n a l y s i s 1^  b) . C r u c i b l e s 1^-c) . Temperature 15 RESULTS 16 . 1)... E x p e r i m e n t a l . 16 2).. C a l c u l a t i o n s . • .16 Table of Contents (Continued). Page DISCUSSION .27 1) . Excess Thermodynamic P r o p e r t i e s of Sodium i n Sodium-Aluminum 27 2) . The A c t i v i t y of Sodium 3Q : 3). The A c t i v i t y - of Aluminum 30 . h)..The P a r t i a l M o l a l Heat of S o l u t i o n of Sodium 3^  CONCLUSIONS .36 RECOMMENDATIONS FOR .FURTHER.WORK 37 APPENDIX- A: THE DETERMINATION OF THE ACTIVITY OF NaF AND A1F,- IN SODIUM FLUORIDE - ALUMINUM FLUORIDE'MELTS1. . . . . . . . . 38 A. Activity.'Data f o r NaF and A l F j from the A c t i v i t y of Sodium i n NaF - A1FX Melts 38 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 44 2) . . C a l c u l a t i o n of l o g Y N a F / N | 1 F 5 and l o g ifrAlFj/^NaF ^ B. Thermodynamic A n a l y s i s of the 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 of A c t i v i t i e s from the NaF - A l F j Phase Diagram k6 a) . The NaF - A l F ^ Phase Diagram .48 b) . The Entropy of Fusion 50 2) . C a l c u l a t i o n of log " t jjap-/wAlF5 f r o m the Phase Diagram . . . 51 3) . The C a l c u l a t i o n of logY.AlFj • * 56 C. D i s c u s s i o n • • • 59 • APFENDIX B: . THE SODIUM - LEAD SYSTEM 64 APPENDIX C : . THE SODIUM - ALUMINUM SYSTEM 73 BIBLIOGRAPHY . 'V 78 LIST OF FIGURES Figure Number Page 1. Sodium-Concentration of 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 3 2. Sodium Concentration i n L i q u i d Lead i n E q u i l i b r i u m w i t h NaF - A l F ^ Melts 7 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 . . . . . . . . . 11 k. Sodium D i s t r i b u t i o n between L i q u i d Aluminum and-Liquid Lead •at Four E q u i l i b r a t i o n Temperatures 17 5. Sodium A c t i v i t y i n L i q u i d Lead as a Function of Concent-r a t i o n at Three Temperatures 20 6. l os'^N a/^Al i n L i ( l u i d - Aluminum as a Function of Concent-r a t i o n 22 7. P a r t i a l M o l a l Heat of S o l u t i o n of Sodium i n L i q u i d Alum-inum as a Function of Concentration . 23 8. l o g V w /N A 1 i n L i q u i d Aluminum as a Function of Concent-r a t i o n a t 1010 °C 28 9. 1°sV] i j a/N^ 1 i n L i q u i d Aluminum as a Function of Concent-, r a t i o n a t 1010-°C, f o r the Range of Composition over which Sodium.and Aluminum are M i s c i b l e at 800 °C 29 10. A c t i v i t y of Sodium i n L i q u i d Aluminum as a Function of Composition at 1010 °C 31 11. - A c t i v i t y of Sodium i n L i q u i d Aluminum as a Function of Composition at 1010 °C, f o r the Range of Composition over which Sodium and Aluminum are M i s c i b l e a t 800 °C 32 12. logy^-|_/Njj a i n L i q u i d Aluminum as a Function of Composition at 1010 "C, from a Gibbs - Duhem I n t e g r a t i o n of l°g"^N a/N^ Values from Figure 8 35 A - l . The A c t i v i t y of Sodium i n L i q u i d Aluminum as a Function of the NaF - A l F j r a t i o i n NaF - A l F j Melts . . . . . . . . . .43 A-2. The Values of l o g i N a F ^ A I F 5 a n d l o S A l F 3 ' / N N a F a t 1 0 1 0 ° c as a Function of the Composition, from the Computer Re s u l t s bj h-3. The Phase Diagram of the NaF - A l F ^ B i n a r y System 1+9 A-k l o S ^ N a F / N A i F a t 1010 °C,. Derived from the NaF - AIF3 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 Page 2 *v 2 A-5. l o g " / A l F j / % a F a t 1010- ° , Derived from l o g • NaF/^AlFj values i n Figure A-k, Using the Gibbs - Duhem I n t e g r a t i o n Technique . . 60 A-6. Comparison of l o g ^ N a F / N A l F V a l u e s a t 1 0 1 0 ° f o r t h e Computer R e s u l t s of Experimental Data from Figure A-2 and. the T h e o r e t i c a l R e s u l t s from: Wagner1 s Method (Figure A-4) 62 k/ 2 A-7. Comparison of l ° g / A 1 F / % a F Values a t 1010 °, f o r the Computer R e s u l t s of Figure A-2 and. the T h e o r e t i c a l R e s u l t s from F i g u r e A-5 .... 63 B - l . P a r t i a l , M o l a l Heat of S o l u t i o n of Sodium i n L i q u i d Lead as a Function of Concentration . . . . . . . . . 11 B^2. l o s ^ N a ^ F b i n L i ( l u i < i L e a d - a s a Function of Concentration at kJ3 °C 72 C - l . Phase Diagram f o r the Sodium - Aluminum System,.Showing the Hypo-eutectic - Monotectic L i q u i d u s . . . 7^  C-2. Phase Diagram .for the Sodium - Aluminum'System, Showing the S o l u b i l i t y L i m i t of Sodium . . -75 C-3. l o g N N a v s . 1/T from.Ransley and N e u f e l d ' s 2 ^ Data ... . . . 7 7 L I S T OF TABLES T a b l e Page 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 Sodium - Aluminum Binary-. 3 3 A - l . S odium C o n t e n t o f Aluminum M e t a l u n d e r Sodium F l u o r i d e -. 39 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 -ko •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 -Ml k-k. . Sodium C o n t e n t o f Aluminum:Metal u n d e r Sodium. F l u o r i d e -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 by, I n t e g r a t i o n o f t h e •53 • A-6. . 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 o f t h e A-7. 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 Aluminum F l u o r i d e b y t h e .58 B - l . Sodium A c t i v i t y ' D a t a f o r t h e - S o d i u m - Lead System . . . . • 65 B-2. Sodium A c t i v i t y D a t a f o r t h e Sodium - Lead System . . . . . 66 B-3- Sodium A c t i v i t y D a t a f o r t h e Sodium - Lead System . . . . • 67 B-4. 68 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° and 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 ACTIVITY MEASUREMENTS IN THE SODIUM - ALUMINUM SYSTEM. INTRODUCTION Aluminum i s p r o d u c e d c o m m e r c i a l l y b y t h e e l e c t r o l y t i c r e d u c t i o n o f aluminum o x i d e d i s s o l v e d i n m o l t e n c r y o l i t e . There i s c o n s i d e r a b l e c o n t r o v e r s y o v e r t h e a c t u a l mechanisms o f r e d u c t i o n , and much o f t h i s d i s a g r e e m e n t i s a t t r i b u t a b l e t o t h e e x p e r i m e n t a l d i f f i c u l t i e s i n w o r k i n g w i t h c r y o l i t e . . C r y o l i t e i s o x i d i z e d i n a i r t o produce aluminum o x i d e , w h i c h t h e n d i s s o l v e s i n t h e c r y o l i t e , c a u s i n g t h e l i q u i d u s l i n e s t o s h i f t on t h e phase d i a g r a m . I n a d d i t i o n , a t t h e o p e r a t i n g t e m p e r a t u r e o f t h e / 0 . c e l l ( a b o u t 9 5 0 C ) , c r y o l i t e can h y d r o l y z e t o f o r m aluminum o x i d e and hydr o g e n f l u o r i d e . 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 m i g h t r e s u l t f r o m 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 c a t h o d e as a r e s u l t o f 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 G r u n e r t had 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 p r e s s u r e 0 woul d be t h e r e s u l t o f r e a c t i o n between c r y o l i t e and aluminum a t 1000 C. Subsequent i n v e s t i g a t i o n s have shown t h a t p r o d u c t i o n o f sodium a t atmos-p h e r i c p r e s s u r e does n o t o c c u r . 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 -v e n i e n t l y 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 sodium, aluminum, and c r y o l i t e , i n w h i c h t h e sodium c o n c e n t r a t i o n i n t h e aluminum was measured; 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 , t o g e t h e r w i t h l e a d , i n w h i c h t h e sodium a c t i v i t y was measured. - 2 -a.) Sodium, Aluminum, C r y o l i t e Systems: 2. Herman and Jander studied the r e a c t i o n : 3 N a F ( l ) + A l ( l ) *=± 3 ( N a ) ( d i l ) + A l F 3 ( l ) 0 at 1090 C i n alumina c r u c i b l e s under an atmosphere of dry, oxygen-free nitrogen. The equilibrium constant f o r the r e a c t i o n was expressed i n terms of concentration. Their r e s u l t s , which show an increase i n sodium content of the aluminum with the in c r e a s i n g NaF/AlF^ ratio- , are shown i n f i g u r e 1 . 3 0 Pearson and Waddington performed s i m i l a r experiments at 1000 C over a range of sodium fluoride-aluminum f l u o r i d e melt compositions. Their r e s u l t s were i n agreement with those found by Herman and Jander. Their r e s u l t s were p l o t t e d i n f i g u r e L k Dewing and Hollingshead have measured the sodium content of aluminum as a f u n c t i o n of the NaF/AlF^ r a t i o n at 1025°C. Their r e s u l t s were i n agreement with those of Herman and Jander, and Pearson and Waddinton, and have been p l o t t e d i n f i g u r e 1 . Dewing'' measured the sodium content of the aluminum i n a re a c t i o n i n v o l v i n g the same reactants, sodium f l u o r i d e and aluminum: 6NaF ( s ) + A 1 ( i ) ^=± N a 3 A l F 6 ( s ) + 3 1 f e ( d l l ) There was, 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 r e a c t i o n and those discussed above, i n that there were now two s o l i d phases, NaF and Na^AlFg, and the l i q u i d aluminum phase present. 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 of sodium f l u o r i d e to aluminum f l u o r i d e . - 3 -o w -p <u o u (L) P-I -p •H 0. 015 — 0.010 — 0.005 o o o o o o o • o o A Dewing and Hollingshead'(1025°) • P e a r s o n and Waddington^ (1000°) O Herman and J a n d e r 2 (1090°) • 0.90 1.10 1.30 NaF - AUF-1.50 r a t i o 1.70 1.90 F i g u r e 1; Sodium 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 1 F 3 M e l t s . - k -of three phases and two components can only have one degree of freedom, and hence the sodium c o n c e n t r a t i o n of the aluminum was determined s o l e l y by the temperature. Dewing's measurements were over the temperature range 0 0 679 t o 896 , and the 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 Frank determined sodium a c t i v i t i e s by measuring the vapour pressure of sodium i n the fumes above a bath of molten c r y o l i t e and aluminum. A graphite c e l l c o n t a i n i n g the c r y o l i t e and aluminum was placed 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 the l i g h t path of a spectrograph passed through the c e l l , and the amount of sodium i n the vapours above the charge could be measured by the decrease i n the i n t e n -s i t y of the l i g h t r e a c h i n g the spectrograph. Experiments were done from 0 0 1100 down t o 700 C. By comparing the measured sodium vapour pressure above the b a t h a t any given temperature w i t h the vapour pressure of pure sodium at the same temperature, i t was p o s s i b l e t o c a l c u l a t e the 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 the sodium a c t i v i t y under c r y o l i t e melts having various NaF/AlF^ r a t i o s . The a c t i v i t y of the sodium was measured by m a i n t a i n i n g the aluminum and the c r y o l i t e melt i n e q u i l i b r i u m w i t h a l e a d phase. A separate study i n which the e.m.f. of the f o l l o w i n g e l e c t r o l y t i c c e l l : 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 | Na were measured gave the a c t i v i t y of sodium as a f u n c t i o n of the sodium con-c e n t r a t i o n i n the l e a d phase. E q u i l i b r a t i o n s t u d i e s f o r the sodium, aluminum, c r y o l i t e , l e a d system were c a r r i e d out at temperatures between TABLE 1. Dewing's Data"? • I Pemp. °C .11 wt <jo Na I I I % a x:l 0e IV A F (Kcal/mole) V aNa(T) VI ^Na(T) V I I L O S ? H a ( T ) -V I I I log TNa(lOlO) IX L O S ^NaaOlO) Nil X (^1010) 679 . 0.0111 128 16.45 O.O55I 450.5 2.634 2.087 2.087 0.0156 682 0.011 128 16.k2 O.O65O 437.5 2.641 2.101 2.101 0.0161 691 0.012 i4o 16.23 O.O583 416.4 2.620 2.100 2.100 0.0176 693 0.011 128 16.30 0.0591 461.7 . 2.664 2.148 2.148 0.0180 , 764 0.024 281 14.78 0.0914 325.3 2.512 2.140 2.140 0.0388 VJ, 765 0.022 257 14.83 0.0908 353.3 . 2.548 2.177 2.178 0.0586 . 766 0.022 257 14.75 0.0924 359,5 2.556 2.179 .2.180 0.0588 77H- 0.025 293 14.60 0.0964 329.0 2.504 2.145 2.146 0.C409 776 0.021 246 14.57 0.0972 395-1 2.597 2.242 2.245 0.0429 778 0.025 293 14.51 O.O986 335.0 2.526 2.175 2.176 0.01+58 781 0.024 281 •14.48 O.O998 355-2 2.550 2.207 2.208 0.0452 - 6 -9H-0° and 1010°C i n alumina c r u c i b l e s u s i n g alumina-saturated pure c r y o l i t e . An attempt was made t o approach e q u i l i b r i u m from the high-sodium as w e l l as the low-sodium s i d e . The sodium c o n c e n t r a t i o n was determined i n the l e a d phase only.. 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 the sodium:content of the l e a d phase increases w i t h an i n c r e a s i n g NaF/AlFj r a t i o . 8 Aylen e q u i l i b r a t e d mixtures of aluminum, c r y o l i t e and sodium-l e a d a l l o y s . The runs were done at 1010°C u s i n g alumina-saturated c r y o l i t e and alumina c r u c i b l e s . The NaF/AlFj 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 , which have been p l o t t e d i n f i g u r e 2 compare reasonably w e l l w i t h those obtained by F e i n l a b and P o r t e r a t s i m i l a r NaF/AlFj r a t i o s , although the sodium concentrations measured by-Aylen tended t o be lower than those reported by F e i n l a b and P o r t e r . . 2.) Purpose of the P r e s e n t . I n v e s t i g a t i o n : In the above-mentioned i n v e s t i g a t i o n s of the sodium-aluminum-c r y o l i t e system, with or without a l e a d phase being present, no data s u i t -able f o r the c a l c u l a t i o n of the excess thermodynamic p r o p e r t i e s of the sodium-aluminum system were rep o r t e d . The object of the present research was t o measure the sodium a c t i v i t y as a f u n c t i o n of composition i n sodium-aluminum a l l o y s and, i n so doing, t o o b t a i n thermodynamic data on the excess p r o p e r t i e s of sodium i n aluminum, and t o determine the p a r t i a l m olal heat of s o l u t i o n of sodium i n aluminum. 3.) Method of Measurement: The data on sodium a c t i v i t y i n the sodium-aluminum.system was obtained by a l l o w i n g sodium t o reach 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 -6.0 5.0 a o SH <D P-. -P •a •H 3.0 .2.0 1.0 o — — a*? — A A A * A A 4 A A A A 1 1 7 F e i n l a b and P o r t e r 1 (1010°) C (970°) 3 o (9^0°) Q ( ( Aylen°( l010°) ^ 0.90 1.10 1.30 1.50 1.70 1.90 NaF - A l F ^ r a t i o F i g u r e 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 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 sodium was known 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 s o d i u m - l e a d a l l o y s . T h e r e f o r e , b y m e a s u r i n g t h e sodium c o n t e n t o f t h e aluminum, i t was p o s s i b l e t o o b t a i n 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 t h e sodium-aluminum system. A d e t a i l e d a n a l y s i s o f t h e s o d i u m ^ l e a d s y s t e m was r e p o r t e d 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 r e a s o n s . I n t h e 9 f i r s t p l a c e , l e a d and aluminum a r e i m m i s c i b l e . Hansen r e p o r t e d t h a t t h e s o l u b i l i t y o f aluminum i n l e a d a t rJOO°C was l e s s t h a n 1.5 a t o m i c p e r c e n t and 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 aluminum a t t h i s t e m p e r a t u r e was o f t h e o r d e r o f 0.22 a t o m i c p e r c e n t . A t t h e s e low c o n e n t r a t i o n s i t might be e x p e c t e d t h a t t h e e f f e c t o f t h e i n t e r a c t i o n c o e f f i c i e n t s o f l e a d and aluminum on t h e a c t i v i t y o f sodium i n t h e aluminum and l e a d phases r e s -p e c t i v e l y w o u l d be s m a l l . A second c o n s i d e r a t i o n was tha'^ sodium-aluminum a l l o y s c o n t a i n o n l y v e r y s m a l l amounts o f sodium ( t h e maximum amount o f sodium t h a t can be d i s s o l v e d i n aluminum a t 800°C i s 0.J1 a t o m i c p e r c e n t ) w h i c h r e s t r i c t s t h e number o f s u i t a b l e methods by w h i c h t h e sodium-aluminum s y s t e m c o u l d be s t u d i e d . A t h i r d r e a s o n f o r s e l e c t i n g t h e sodium-aluminum-l e a d s y s t e m was t h e f a c t t h a t a c o n s i d e r a b l e amount o f r e s e a r c h has been 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 a l l o w 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 aluminum t o a c o n s i d e r a b l e degree o f a c c u r a c y . . I n a d d i t i o n , sodium 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 s o u r c e o f sodium, r a t h e r t h a n u s i n g c r y o l i t e as a s o u r c e o f t h e sodium, a v o i d e d t h e t e c h n i c a l p r o b l e m s t h a t w o u l d 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 of Investigation: Experimentally, i t was possible to e q u i l i b r a t e the sodium-aluminum-lead melts between sodium concentrations of N j ^ p ^ j = 0.080 to O.25O. For lower sodium concentrations, i t was d i f f i c u l t t o get 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 the sodium analysis of the aluminum phase using the flame-spectrophotometer because the sodium concentrations were of the order of 0.5 to 1 part per m i l l i o n . A maximum sodium l e v e l attainable was imposed by d i f f i c u l t i e s encountered i n handling lead samples containing sodium i n excess of N. . , . •= 0.250, f o r above t h i s amount, the a l l o y s became quite 1NSL f IT D j hydroscopic and the rate of moisture pick-up a f f e c t e d the accuracy of the sample weighings. In order to extend the range over which the sodium a c t i v i t y was 1 5 known as a function of i t s concentration i n the aluminum,. Dewing % y r e s u l t s for the rea c t i o n : 6NaF, . + A l «==*-' 3(Na) + Na A1F (s) ( l ) ' K ; ( d i l ) 3 6(B) were used. The free energy change f o r t h i s reaction at each of the temper-atures was' calculated, and from t h i s , the sodium a c t i v i t y as a function of i t s concentration was determined. - 10 -EXPERIMENTAL .1.) A p p a r a t u s : The a p p a r a t u s 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 f i g u r e 3• 2.) M a t e r i a l s : The aluminum u s e d 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 by t h e Aluminum:Company o f Canada,>Ltd. I t was " s u p e r - p u r i t y " g r a d e , a n a l y z i n g 99•997% aluminum, w i t h l e s s t h a n 0.001% by w e i g h t o f sodium p r e s e n t . B a k e r and Adamscn r e a g e n t grade sodium and l e a d were u s e d , as w e l l as A m e r i c a n S m e l t i n g and R e f i n i n g Company t e s t - l e a d . 3 .) C r u c i b l e s : The e q u i l i b r a t i o n s were c a r r i e d o ut i n a l u m i n a c r u c i b l e s . These were McDanel^AV30 c r u c i b l e s and M o r g a n i t e RR r e c r y s t a l l i z e d c r u c i b l e s . The t h e r m o c o u p l e p r o t e c t i o n t u b e s were M o r g a n i t e RR grade m a t e r i a l . The c r u c i b l e s were 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 f i t t e d w i t h a s t a i n l e s s s t e e l l i d . .k.) . F u r n a c e : A P h i l l i p s i n d u c t i o n u n i t , I70/55O V, 3-phase, 12 kw. o u t p u t was u s e d . 5•) Temperature C o n t r o l : A c h r o m e l - a l u m e l t h e r m o c o u p l e p l a c e d i n a h o l e d r i l l e d i n t h e 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 used t o measure t h e t e m p e r a t u r e . T h i s t h e r m o c o u p l e was a t t a c h e d t o an 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 i n m i l l i v o l t s . 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 and r e c o r d e r t o p r o v i d e a u t o m a t i c t e m p e r a t u r e c o n t r o l . The a c t u a l m e l t 5 mm. 0. D. V y c o r Tube. C o n t r o l Thermocouple. I n d u c t i o n C o i l s . A l u m i n a 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 Con-t a i n e r machined t o accommodate an a l u m i n a c r u c i b l e . •Measuring Thermo-c o u p l e . A l u m i n a R i n g . F i g u r e 3; C r o s s - s e c t i o n o f E q u i l i b r a t i o n A p p a r a t u s . - 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 t h e r m o c o u p l e c o n n e c t e d t o a 3 1 8 4 p o t e n t i o m e t e r m a n u f a c t u r e d by H': T i n s l e y and Company,. S t . Jerome, ,Quebec. 6. ) Gas S u p p l y : C o m m e r c i a l 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 u s e d . I t was d r i e d b y passage t h r o u g h s i l i c a g e l b e f o r e e n t e r i n g t h e a p p a r a t u s . 7. ) E x p e r i m e n t a l P r o c e d u r e : A l l o y s were p r e p a r e d by p l a c i n g a b out 30 grams o f aluminum, 50 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 between 0.5 and 2.5 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 h o u r . The t e m p e r a t u r e was 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 as p o s s i b l e by 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 and an a i r - j e t , i n o r d e r t o r e t a i n t h e e q u i l i b r i u m c o n d i t i o n s . The a l l o y s were removed f r o m 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 a n a l y s i s . 8. ) . E q u i l i b r a t i o n Times: .,. A y l e n 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 t i m e t o a t t a i n e q u i l i b r i u m i 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 - l e a d system. I n t h i s i n v e s t i g a t i o n t h e r u n s were done a t t e m p e r a t u r e s 200 t o 300° l o w e r t h a n A y l e n ' s work,.and a s e t o f r u n s a t v a r i o u s l e n g t h s o f t i m e i n d i c a t e d t h a t m a intenance o f t h e e q u i l i b r i u m t e m p e r a t u r e f o r f o u r hour's was adequate. 9. ) C h e m i c a l A n a l y s i s : As has been me 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 i n t o - 13 -t h e i r l e a d - and. aluminum-rich phases. The l e a d phase, which generally-weighed between 35 and kO grams, was d i s s o l v e d i n 25O mis of J.2N n i t r i c a c i d i n Pyrex beakers. ..Complete d i s s o l u t i o n took 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 then f u r t h e r d i l u t e d t o concentrations s u i t -a ble f o r a n a l y z i n g the sodium content u s i n g a flame spectrophotometry technique. . Each aluminum-rich phase was reduced t o tu r n i n g s and analyzed i n q u a d r u p l i c a t e . Each of the quadruplicate samples, which weighed about O.75 grams was d i s s o l v e d . i n 50 mis., of 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 " ) f i t t e d w i t h Teflon,watch-glass covers. A f t e r the aluminum t u r n i n g s had been d i s -s o l v e d , the s o l u t i o n s were evaporated almost t o dryness and then made up t o 50 mis w i t h d i s t i l l e d water, ready f o r a n a l y s i s on the flame spectrophoto-meter . In the sodium a n a l y s i s of the l e a d phase, i t was found convenient to a d j u s t the volume of the sample such t h a t the sodium c o n c e n t r a t i o n would be between 5 and.10 micrograms per m i l l i l i t r e of s o l u t i o n . Standards c o n t a i n i n g - 1 , 5* 10, 20 and 50 micrograms/ml. of sodium were used t o c a l i b r a t e the spectrophotometer by p l o t t i n g a graph of sodium c o n c e n t r a t i o n vs percent t r a n s m i s s i o n . I t was then necessary only t o measure the percent t r a n s m i s s i o n f o r any l e a d sample i n order t o determine the sodium c o n c e n t r a t i o n of th a t sample. A s i m i l a r procedure was fo l l o w e d i n the anal y s i s 1 .of the aluminum phase, except t h a t the standards used f o r c a l i b r a t i o n contained 0 . 5 , 1 , 2, 3 , 4, 5 and,10 micrograms of sodium/ml. of s o l u t i o n . In the a n a l y s i s of both the aluminum and l e a d , the r e s u l t s were adjusted such t h a t the reagent - 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 pick-up from ordinary beakers was a distinct possibility, so silica 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. How-ever, i t is felt 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 able t o maintain the d e s i r e d temperature t o w i t h i n -5° during.the run. .While temperature gradients i n a h o r i z o n t a l plane through the molten charge were not measured, the temp-erature p r o f i l e v e r t i c a l l y , through the center of the a l l o y s d i d not vary more than one degree from the bottom of the a l l o y , through the center and up t o the top s u r f a c e . - 16 -RESULTS 1. ) E x p e r i m e n t a l : F i g u r e 1+ i s a p l o t o f w e i g h t p e r c e n t sodium i n aluminum a g a i n s t w e i g h t p e r c e n t s o d i u m . i n l e a d a t f o u r t e m p e r a t u r e i n t e r v a l s . A t 725°C, th e l o w e s t t e m p e r a t u r e u s e d , t h e r e l a t i o n s h i p i s a p p r o x i m a t e l y l i n e a r f o r s o d i u m - l e a d a l l o y s i n w h i c h t h e sodium c o n t e n t d i d n o t exceed 3.5$. The l i n e a r r e l a t i o n s h i p , i s n o t as e v i d e n t f o r h i g h e r t e m p e r a t u r e i n t e r v a l s , b u t th e p o i n t s p l o t t e d do show t h a t an i n c r e a s e i n t e m p e r a t u r e i s accompanied by an 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 phase f o r a g i v e n s o d i u m - l e a d a l l o y . The d a t a p r e s e n t e d i n f i g u r e k i s t a b u l a t e d i n t a b l e s 2 and 3 . F o r p u r p o s e s o f c a l c u l a t i o n , t h e w e i g h t p e r c e n t s o d i u m . c o n c e n t r a t i o n s . r were c o n v e r t e d . t o sodium mole f r a c t i o n s f o r b o t h t h e aluminum and l e a d a l l o y s . The 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 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 B and p l o t t e d i n f i g u r e 5 f o r t h r e e t e m p e r a t u r e i n t e r v a l s , 725°, 7750 and 825°C. The-a c t i v i t y o f s o d i u m . i n t h e aluminum 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 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 b o t h t h e l e a d - and a l u m i n u m - r i c h phases,, and t h e sodium c oe f f TWSnlTS" and :the"i'r"To'garithms were d e t e r m i n e d 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 o f t h e sodium i n aluminum a t 1010°C. T h i s was a c c o m p l i s h e d b y . e x t r a p o l a t i o n o f t h e d a t a c o l l e c t e d a t 725, 775; a n d 8250, i n . a c c o r d a n c e w i t h t h e f o l l o w i n g r e l a t i o n s h i p s , d i s c u s s e d 10 by Chipman*. o.oo6o L— 0.0055 L_ 0.0050 0.00U5 L_ 0 . 0 0 4 0 L_ 0.0035 0.0030 0.0025 0.75 1.00 1.25 1.50 1-75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3-75 Weight P e r c e n t Sodium i n L i q u i d L e a d . F i g u r e h: Sodium D i s t r i b u t i o n between L i q u i d Aluminum and L i q u i d Lead a t F o u r E q u i l i b r a t i o n Temperatures. TABLE 2 . E x p e r i m e n t a l R e s u l t s : I Run No. I I o Temp. C I I I wt % Na, v... (Pb) IV N Na(Pb) V wt % Na ( A l ) V I 6 N x 10 N a ( A l ) V I I 2 a x 10 Na(T) V I I I ^Na(T) IX l i s TL T 15/t- 726 O.98 0.082 .0021 24 0.257 107 2.03 725 1.01 0.084 .0023 26 0.230 88.6 I.9A8 47/7 721 1.22 0.100 .0027 32 0.276 " 86:. 1, 1-935 W 7 725 1-33 0.108 .0027 32 0-304 95-0 1.978 48/7 722 I.36 0.110 .0027 32 0.309 96.8 1.986 3/8 726 1-73 0.137 .0030 35 0.423 121 2.082 V8 725 I.90 0.149 .0030 35 0.468 13* 2.127 5/8 724 I.91 0.149 .0031 36 0.472 131 2.117 6/7 726 2.59 0.193 •0035 41 0.782 191 2.281 2/7 724 2.64 O.I96 • 003M- 40 0.797 199 2.299 3/7 726 2.89 0.211 ' .0035 4 l i.o4o 25U 2.412 20/7 727 3-56 0.249 .0042 48 1.400 292 2.466 19/7 722 3-72 0.258 .0047 53 1.520 287 2.458 17/5 747 2.96 0.215 .0045 53 1.085 207 2.316 22/5 744 2.98 0.217 .0045 53 1.080 206 2.31k 21/5 7^ 7 3-11 0.224 .005U 63 1-195 190 2.279 23/5 7U6 3-^ 7 0.245 .0060 70 1.476 211 2.324 I 11 I I I Run-No. Temp. °C •wt: <$> Na./ 12/7 774 O.96 27/7 774 O.96 28/7 775 O.98 13/8 778 1.29 U9/7 771 1.34 6/8 775 I.78 8/8 775 1-79 7/8 776 1.80 43/7 823 0.87 44/7 823 O.87 45/7 825 0.86 2/8 827 •JU23 1/8 825 1-34 9/8 826 1.61 10/8 825 1.70 11/8 826 1-73 32/6 846 O.85 33/6 856 O.885 Pb) TABLE 3. E x p e r i m e n t a l . R e s u l t s : IV V V I % a ( P b ) w t # N a f A H % a ( A l ) x l ° 6 V I I V I I I IX a N a ( T ) x 1 q 2 ? N a ( T ) l Q g ^ N a ( T ) 0.080 .0025 29 O.278 96 1.982 0.080 .0025 29 0.278 96 1.982 0.082 .0025 29 0.325 112 2.049 0.105 .0032 37 O.374 101 2.004 0.109 .0031 36 O.385 107 2.030 0.140 .0033 38.$ 0.543 141 2.149 0.141 .O0Q4 40 V« 0.548 137 2.137 0.142 •0035 41 0.554 135 2.130 0.073 .0026 30.4 O.307 101 2.004 0.073 .0026 30.4 O.307 101 2.004 0.072 .0026 30.4 O.307 101 2.004 0.101 .0033 38.5 O.438 114 2.057 0.109 .0034 40 0.476 119 2.076 0.128 .0036 42 0.584 139 2.143 0.135 •0035 4l 0.684 158 2.199 0.137 .0036 42 0.655 156 2.193 0.072 .0030 35 0.329 ;94 1-973 0.074 .0029 34 0.346 102 2.008 - 20 -- 21 -F-, = RT Int ± ( I ) 1 d ( F f / T ) = Lid ( l / T ) ( I I ) so t h a t f o r t h e sodium - aluminum system: l o g T N a ( T i ) = L N a + l o S " * N a ( T p ) ( m ) and a t 1010°C: loS*Na(1010) = % a (°-779 - 1 ) + l°g ^ N a ( T ) ( I V ) 4.575 ^ 1 T2^ I n f i g u r e 6 , l o g YNa v s . N N a a t 725°, 775° and 825° was p l o t t e d . A t f i x e d v a l u e s o f % a , v a l u e s o f L j j a . w e r e d e t e r m i n e d b y re a r r a n g e m e n t o f e q u a t i o n ( I I I ) : % a = 4.575 T x T g ( logX N a ( T l ) - l o g y N a ( T 2 ) ) ( T 2 - T x ) ^ } u s i n g t h e t e m p e r a t u r e c o m b i n a t i o n s 825° and 775°; 825° and 725°; a n d 775°and 725° f o r T i and T 2 . The r e s u l t s were p l o t t e d as L N a v a l u e s a g a i n s t N i n f i g u r e 7 . The agreement between t h e t h r e e v a l u e s o f L a t ea c h Na Na N 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 f o r N„ l e s s t h a n k-0 x 10~°\ Na J Na Because o f t h e p o o r agreement o f t h e s e c a l c u l a t e d p a r t i a l m o l a l 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 L f r o m t h e i n c r e a s e i n t h e maximum ' Na s o l u b i l i t y o f sodium i n aluminum w i t h i n c r e a s i n g t e m p e r a t u r e . .The l i q u i d u s l i n e f o r l i q u i d sodium-aluminum a l l o y i n e q u i l i b r i u m w i t h p u r e m o l t e n sodium, shown i n f i g u r e C- l gave t h e r e l a t i o n s h i p between t h e maximum sodium s o l u b i l i t y and t e m p e r a t u r e . The p a r t i a l m o l a l h e a t o f sodium was c a l c u l a t e d as 9230 c a l o r i e s p e r mole. T a b l e s 4 and 5 c o n t a i n t h e v a l u e s o f logV^ a t t h e t e m p e r a t u r e s l i s t e d , as w e l l a s v a l u e s o f l o g 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 -Figure 7; P a r t i a l Molal Heat of Solution of Sodium i n L i q u i d Aluminum as a Function of Concentration. TABLE 4. Experimental Calculations; I II III . IV V VI VII Sun No. . Temp. °C % a x l o P log 2f N a ( T ) 1 0 6 * Na(1010) ^Na(lOlO) aNa(10] 15/7 726 24 2.03 1.586 38.55 .00092 14/7 725 26 1.948 1.499 31-55 .00082 47/7 721 32 1.935 1.477 30.00 .OOO96 ke/i 725 32 1.978 1.529 33-80 .00108 48/7 722 32 1.986 1.530 33.85 .00108 •3/8 726 35 2.082 1.534 43.10 .00151 4/8 725 35 2.127 I.678 47.60 .00167 5/8 724 36 2.117 I.665 46.26 .00166 6/7 726 4 l 2.281 1.833 68.10 .00279 2/7 724 4o 2.299 1.847 70.30 .00281 3/7 726 4 l 2.412 I.96O 91.20 .00374 -.20/7 727 48 2.466 2, 020 104.8 .OO503 19/7 722 53 2.458 2.002 100.5 .00533 17/5 7^ 7 53 2.316 1.911 83.50 .00442 22/5 744 53 2.314 1.903 80.00 .00424 21/5 7U7 63 2.279 1.874 74.80 .00471 23/5 746 70 2.324 1.917 82.60 .00578 Run Wo. I I Temp. I l l TABLE. 5. E x p e r i m e n t a l C a l c u l a t i o n s : IV V l o g y Na(T) l o g V I Ma (1010) °Na(1010) • V I I a N a ( 1 0 1 0 ) 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. 40 4 l I .982 I .982 2.049 2.004 .2.030 21149 2.137 .2.130 1.627 1.627 1.696 1.657 1.669 1.796 1.784 1.779 42.40 42.40 49.70 45.40 46 . 6 0 62.50 60.80 60.10 .00123 .00123 .00144 .00168 .00168 .00241 .00243 .00246 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 40 42 41 42 2.004 2.004 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 54.40 54.40 54 . 7 0 62.40 64.60 75 . 7 0 85.70 84 . 9 0 .00165 .00165 .00166 .00240 .00258 .00318 .00351 .00356 32/6 33/6 846 856 35 34 1.973 2.008 1.741 1.792 55.10 61.90 .00193 .00210 - 2 6 -f r o m t h e l o w e r t e m p e r a t u r e s u s i n g . e q u a t i o n I V. A l s o l i s t e d a r e t h e v a l u e s o f V „ and a a t 1 0 1 0 ° . Na . Na As was ment i o n e d u n d e r "Region 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 c o n d i t i o n s imposed.a r e s t r i c t i o n t h a t t h e s o d i u m - l e a d a l l o y s n o t c o n t a i n more sodium t h a n N = O . 2 5 O , i n o r d e r t o a v o i d e x c e s s i v e m o i s t u r e p i c k - u p . Na The sodium c o n c e n t r a t i o n i n t h e aluminum 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 about N ••= 50-x-lQ ^. . I n o r d e r t o e x t e n d t h e a c t i v i t y d a t a , t o Na , 5 sodium c o n c e n t r a t i o n s g r e a t e r t h a n t h i s , , Dewing s d a t a has been u s e d . The f r e e e n e r g y for. t h e r e a c t i o n : 6NaF. . + A l - fc- 3 ( N a ) + Na A1F. ( s ) ( 1 ) •* > v ( d i l ) 3 6 ( s ) ] 2 was c a l c u l a t e d u s i n g JANAF t a b l e s , and t h e a c t i v i t y o f sodium was o b t a i n e d f r o m 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 . Dewing r e p o r t e d h i s r e s u l t s as we i g h t p e r c e n t sodium i n aluminum f o r v a r i o u s t e m p e r a t u r e s , so t h a t Y ^ a and l o g Y as 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 t e m p e r a t u r e s JMa c o u l d be o b t a i n e d . The log"J( 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 ° and Na c o n v e r t e d back t o Y and a . 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 were Na Na e t a b u l a t e d i n t a b l e !• The p r e s e n t 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 - 6 a c t i v i t y d a t a f r o m N N a ^ A 1 ^ = 2 5 x 1 0 t o 3 0 0 x 1 0 . . The sodium a c t i v i t y i n a s o d i u m - s a t u r a t e d sodium-aluminum a l l o y i s u n i t y , as t h i s a l l o y i s i n e q u i l i b r i u m w i t h p u r e sodium, and a t 8 0 0 ° C , t h e maximum s o l u b i l i t y i s a t - 6 N = 3 1 5 0 x 1 0 . Hence a t t h i s c o n c e n t r a t i o n , l o g J T = 2 . 4 9 9 - E x t r a -N a ( A l ) ^ a p o l a t i o n o f logY N a t o 1 0 1 0 ° by e q u a t i o n : IV gave a v a l u e o f 2 . 1 9 2 , f r o m w h i c h a N a = O . 4 8 9 6 a t 1 0 1 0 ° was f o u n d . - 27 -DISCUSSION Compa r i s o n o f t h e 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 was d i f f i c u l t i n t h a t t h e r e was a f u n d a m e n t a l d i f f e r e n c e i n t h e 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 . O t h e r i n v e s t i g a t i o n s d e t e r m i n e d e i t h e r t h e sodium c o n t e n t 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 t h e a c t i v i t y . o f sodium i n t h e l e a d p h a s e . I n t h e p r e s e n t r e s e a r c h , however, t h e a c t i v i t y o f sodium i n aluminum, and 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 sy s t e m , have been measured. The a c t i v i t y d a t a o b t a i n e d f r o m an a n a l y s i s o f Dewing's r e s u l t s , a l t h o u g h a t h i g h e r c o n c e n t r a t i o n s t h a n i n v e s t i g a t e d i n t h i s r e s e a r c h , d i d show t h a t a smooth t r a n s i t i o n i n t h e a c t i v i t y v a l u e s e x i s t e d between h i s v a l u e s and t h o s e r e p o r t e d h e r e . T h i s t r a n s i t i o n can be seen by e x a m i n i n g f i g u r e s 8 and 10. 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: F i g u r e ...8 i s a p l o t o f l o g " / | g a / N A i v s . N^ a o v e r t h e c o n c e n t r a t i o n range'N^a = 0 t o 300 x 10 ^. The p l o t a p p e a r s t o be l i n e a r f o r N j j a l e s s t h a n kO x 10" ,^ and 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 t h e o r d i n a t e a t l o gY N a A ^ A l = 1-08. (The thermodynamic d a t a i s e x p r e s s e d V / 2 11 i n t h e f o r m l o g J Na.'^hl' a s ^ h i s f u n c t i o n i s u s e d i n t h e Gibbs-Duhem c a l c u l a t i o n , and c o m p a r i s o n s o f a c t i v i t y d a t a can be c o n v e n i e n t l y made w i t h t h e thermodynamic d a t a e x p r e s s e d i n t h i s form.) The p l o t o f l o g Yjja/NA1 o v e r t h e e n t i r e c o m p o s i t i o n range f r o m N j j a = 0 t o 3157 x 10"^  i s g i v e n i n f i g u r e 9 • T h i s f i g u r e c o n s i s t s o f t h e d a t a f r o m f i g u r e 8 and t h e a c t i v i t y d a t a c a l c u l a t e d f r o m t h e s o l u b i l i t y l i m i t o f sodium i n aluminum a t 800°. The p l o t a s y m p t o t i c a l l y a p p r o a c h e s 2.206 a t N^ a -6 e q u a l t o 3157 x.10 . Figure 8: l o g / ^ /^AI i n L i ( l u i d Aluminum as a Function of Concentration at 1010°C hO O H 1.5 l . o ro D a t a f r o m F i g u r e 8 D L i m i t o f S o l u b i l i t y a t 800°C O 1 0 500 1000 1 1 2000 2500 3000 % a x ^ F i g u r e 9; logYN /N?-, 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 a t 1010°, 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 . - 30 -2.) The A c t i v i t y o f Sodium: The sodium a c t i v i t y i n a l l o y s c o n t a i n i n g l i t t l e sodium i n c r e a s e s 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 . F i g u r e 10 shows t h a t t h e 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 = c Na -o 50 x 10 . A p l o t o f sodium a c t i v i t y o v e r t h e e n t i r e range f r o m N =0 Na t o 3157 x 10 ^ 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 a/N^.]_ v a l u e s p l o t t e d i n f i g u r e 9. 3.) The A c t i v i t y o f Aluminum: The Gibbs-Duhem t e c h n i q u e 1 1 was u s e d t o c a l c u l a t e l o g f r o m t h e p l o t s o f l o g y /N o b t a i n e d f r o m . f i g u r e s 8 and 9 , u s i n g t h e e q u a t i o n . Na A l •j?Al = N A 1 log y A 1 = - N N a N A 1 l o g V N a - \ log Na d W A l ~NAT ^ N^i N A 1 =1 A 1 T a b l e 6 c o n t a i n s t h e r e s u l t s o f t h e c a l c u l a t i o n s . F i g u r e 12 i s a p l o t 2 2 o f l o g Y A^/Njg a v s . Njg a a t 1010° . I t i n d i c a t e s a maximum o f l o g V A i / N N a e q u a l t o - 9125 a t N^ a = hQ x 10"^. I t s h o u l d be p o i n t e d out t h a t , a l t h o u g h l o g * 5 A i i s a s m a l l number, d i v i s i o n by an even s m a l l e r number, v i z ; N^ a, c a u s e s a wide range o f v a l u e s f o r l o g y A i / N § a . The c u r v e f a l l s o f f f o r N N a on e i t h e r s i d e o f N N a•= kO x 10"°. F o r l o w e r sodium l e v e l s , t h e 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 ^ A ] _ / % a = - 5300, a l t h o u g h o n l y two p o i n t s do 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 . On t h e h i g h sodium s i d e , t h e p l o t a s y m p t o t i c a l l y a p p r o a c h e s l ° g Y A i / l % a = - 6 a t Nf[ a = 3157 x 1 From t h e v a l u e s pf l o g ^ f ^ l i n column V I of t a b l e 6 , i t i s p o s s i b l e t o c a l c u l a t e t h a t Y A i = 0.9999 o v e r t h e e n t i r e c o m p o s i t i o n r a n g e . Hence th e a c t i v i t y o f aluminum i n t h e sodium - aluminum s y s t e m i s e q u a l t o i t s mole f r a c t i o n . As t h e s o l u b i l i t y o f sodium i s 0.3 mole p e r c e n t , a F i g u r e 10: A c t i v i t y o f S o d i u m . 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° - 32 -h-0.6 are Miscible at 800°C. TABLE 6.' Gibbs-Duhem Integration of the Sodium-Aluminum Binary System: I II III IV NA1 = NA1 V VI VII % a x 1 q 6 iogY N a % a % l x 1 q 5 % a N A l l o S * Na x 10 5 - \ logt N a d N A l x 1 C ) 5 - l o g / A l x 10 5 - i o g i r A 1 2 TYT 2 1\T J N 2 2 T\T NA1 NA1 N A 1 = 1 A 1 Na 0 1.08 0 0 0 0 0 20 1.40 1.999 2.80 2.48 0.32 8000 30 1-59 2.999 4.77 3.98 0-79 8777 4o 1.78 3-999 7-12 5.66 1.46 9125 50 1.892 4.999 9-46 7.49 1-97 7880 6o 1.960 5-999 11.76 9-4i 2-35 6528 70 2.000 6.999 14.00 11-39 2.61 5326 80 2.030 7-999 16.24 13-41 2.83 4422 90 2.053 8.999 18.47 15.45 3-02 3728 100 2.071 9-999 20.71 17.51 3-20 3200 120 2.098 11.998 25.17 21.68 3.49 2424 14-0 2.120 -13-998 29.67 25.80 3.87 1974 160 2.129 15.997 34.06 30.05 4.01 1566 180 2 . l 4 l 17-997 38.53 34.32 4.21 1299 200 2.155 19.996 43.09 38.61 4.48 1120 225 2.165 22.495 48.70 43-99 4.71 931 250 2.175 24.994 54.36 48.42 5.94 950 275 2.180 27.492 59-93 53-85 6.08 804 300 2.183 29.991 65.47 59-30 6.17 685 U-00 2.188 39-984 87.48 81.16 6.32 395 500 2.190 49-975 109.44 103-05 6-39 256 750 2.195 74.944 164.50 157-86 6.64 118 1000 2.200 99.900 219.78 212.79 6.99 70 1500 2.202 149-775 329.80 322.84 6.96 31 2000 2.204 199.60 439-92 432.99 6-93 17 2500 2.206 249-37 550.12 543-24 6.88 11 3150 2.206 314.70 694.23 688.17 6.06 6 - 3b -n e g l i g i b l y s m a l l e r r o r i s introduced i n t o c a l c u l a t i o n s i f the a c t i v i t y of aluminum i s set equal t o u n i t y . b.) The P a r t i a l M o l a l Heat of S o l u t i o n of Sodium: The sodium, c o n c e n t r a t i o n of the aluminum a l l o y s i s so low that i t . w o u l d be expected t h a t the 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 of con 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 ^ a 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 a = W x 10 t o 1500 c a l o r i e s / m o l e at Njj a-= 30 x 10" .^ i t i s obvious from; the s c a t t e r i n the 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. In f i g u r e 6 f o r N N a l e s s than 30 x 10" ,^ the p l o t s of l o g / j j a vs. N j j a a t each of the three temperatures appear t o merge. This i m p l i e s t h a t L ^ a i s equal t o zero, when the p l o t s meet. I t should be noted however, th a t the 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 of f i g u r e 6 i s of the same s i z e as L^ a i t s e l f and thus not too much r e l i a n c e can be place d on values of L ^ a c a l c u l a t e d from the d i s p o s i t i o n of the l i n e s . The s c a t t e r of the p o i n t s i s probably due t o the s e n s i t i v i t y of the c a l c u l a t i o n s t o smal l e r r o r s i n measuring N j j a , since the a c t i v i t y of sodium i s changing very r a p i d l y i n t h i s r e g i o n . 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 the b a s i s of equation I I I and f i g u r e 7 are 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 . This value d i f f e r s by only 0.76$ from t h a t c a l c u l a t e d from the maximum s o l u b i l i t y of sodium i n aluminum (see figureC - 1 ) , and so e x t r a p o l a t i o n s using•Ljj a•= 9230 c a l o r i e s / m o l e , independent of co n c e n t r a t i o n , would 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 A 1 / N § a 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 , 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. - 36 -CONCLUSIONS 1) . The a c t i v i t y o f sodium i n aluminum a t 1010°C has been e s t a b l i s h e d b y 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 t e c h n i q u e . The a c t i v i t y o f sodium has been 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 f r o m i d e a l i t y . 2) . The sodium a c t i v i t y shows a s t r o n g dependence on c o n c e n t r a t i o n f o r 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 i s below N N a = 100 x I O - 6 . 3) . 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 method f r o m t h e sodium a c t i v i t y d a t a , shows t h a t t h e a c t i v i t y c o e f f i c i e n t o f aluminum i s 0.9999 o v e r t h e range o f c o m p o s i t i o n , Nj^ a = 0 t o 3157 x 10" , so t h a t t h e a c t i v i t y o f aluminum can be assumed t o be u n i t y o v e r t h e e n t i r e range o f c o m p o s i t i o n s . - 37 -RECOMMENDATIONS FOR .FURTHER WORK 1) . The a c t i v i t y of sodium i n aluminum f o r concentrations between N.T =100 x 10 ^ and the l i m i t of s o l u b i l i t y of sodium could be studi e d Na i f some s u i t a b l e experimental technique could be developed. The lead -aluminum - sodium system could probably be adapted f o r t h i s i n v e s t i g a t i o n by u s i n g dry-box : techniques t o minimize the t e c h n i c a l problems a s s o c i a t e d w i t h handling l e a d a l l o y s c o n t a i n i n g high sodium concentrations. 2) . The e f f e c t s of the presence of other elements i n the sodium -aluminum, system.on the a c t i v i t y of sodium i n t h i s system would be of i n t e r e s t . 3) . Determination of the p a r t i a l m olal heat of s o l u t i o n of sodium i n aluminum, by use of 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 ^ IN SODIUM . FLUORIDE-ALUMINUM- FLUORIDE MELTS A. A c t i v i t y Data.for NaF and A l F ^ from the A c t i v i t y of Sodium i n NaF - A l F ^ M e l t s . Under the heading "Previous Work on the Sodium - Aluminum -C r y o l i t e System", va 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 the sodium content of the aluminum i s the r e s u l t of 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+, 6,7,8 The reported r e s u l t s were p l o t t e d i n f i g u r e s 1 and 2, and are t a b u l a t e d i n t a b l e s A - l throughA-l+. The sodium concentrations reported i n these experiments have been converted t o sodium a c t i v i t i e s , u s i n g the r e s u l t s of the present 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 obtained were p l o t t e d against the NaF/AlF^ r a t i o , . a s shown i n f i g u r e A - l . The r e a c t i o n t a k i n g place i s : 3 [ N a F ( 1 ) ] .+ A l ( 1 ) « » 3(Na' ( 1 )) . + [ A 1 F 5 ( 1 ) ] f o r which the e q u i l i b r i u m constant i s : 3 k = ( aNa) x ^ A l F j l ( a A 1 ) x : [ a N a F ] ^ 3 ( aNa) x [ * A 1 F 5 x N A 1 F 3 ] ( a A 1 ) x [fNaF x N N a F P The extremely low con c e n t r a t i o n of sodium i n aluminum meant th a t the a c t i v i t y - o f aluminum could be taken as u n i t y , and since the sodium a c t -i v i t y was known as a f u n c t i o n of the 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 evaluate the two unknowns, V ^ a F a n d ^ ^ j j , TABLE A - l . Sodium Content of Aluminum Metal under Sodium;Fluoride-Aluminum:Fluoride Melts (Data from Herman and Jander 2) • I . II I I I . IV V VI In Slag %A1 %Na foAlF^ %NaF wt %Wa ( A 1 ) •NaF/AlFj r a t i o N N a x . l 0 6 l o g ^ N a ( 1 0 1 0 ) ^ N a ( 1 0 9 0 ) ^ ( 1 0 9 0 ) 1 8 . 7 2 2 . 8 5 8 . 2 0 4 1 . 5 1 . 0 0 5 . 7 1 5 5 8 1 . 8 5 5 7 1 . 6 .0041 1 6 . 2 2 7 . 1 5 0 . 3 9 4 9.46 ; .004 . 9 8 1 4 7 1 . 7 7 0 5 8 . 8 . 0 0 2 8 1 5 . 4 2 8 A 2 7 . 8 7 5 1 . 8 6 .OO55 1 . 0 8 3 64 1 . 8 9 0 7 7 - 6 . 0 0 5 0 1 3 . 5 3 1 . 7 4 1 . 9 9 5 7 . 8 2 .0042 1 . 3 7 7 : • - 4 9 1 . 7 9 5 6 2 . 4 . 0 0 3 1 1 2 . 8 3 2 . 8 3 9 . 8 1 5 9 . 8 8 . 0 1 9 . 1 . 5 0 4 2 3 3 2 . 0 8 0 1 2 0 . 5 . 0 2 8 1 8 . 7 4 1 . 5 2 7 . 0 4 7 5 . 7 9 . 0 2 8 6 . 5 4 3 . 8 2 0.24 7 9 - 9 9 . 0 2 8 5 . 0 4 6 . 2 1 5 . 5 4 8 4 . 3 6 . 0 3 3 3 . 0 4 9 . 3 9 . 3 2 9 0 . 0 3 . 0 4 3 1 . 9 5 1 . 6 5 . 8 8 9 4 . 2 2 . 0 5 1 0 . 9 5 3 . 2 2 . 7 7 9 7 . 1 2 . 0 6 3 (Data from Dewing and Hollingshead ) I II I I I IV V VI wt * N a m ) NaF/AlF^ r a t i o N 1 0 6 Na l 0 g ^ N a ( 1 0 2 5 ) * N a ( 1 0 2 5 ) a N a ( 1 0 2 5 ) . 0 1 9 0 1 . 5 0 2 2 2 2 . 1 4 9 . 1 4 1 . 0 3 1 3 . 0 1 2 6 1.46 1 4 8 2 . 1 0 6 1 2 7 . 8 . 0 1 8 9 . 0 0 9 2 1.42 108 2 . 0 6 3 ^ 1 1 5 . 8 . 0 1 2 5 . 0 0 7 0 1 . 3 8 8 2 2.018 104 . 3 . 0 0 8 5 . 0 0 5 4 1 . 3 4 6 3 1.954 9 0 . 0 . 0 0 5 7 . 0 0 4 4 1 . 3 0 5 0 1 . 8 7 5 7 5 . 0 . 0 0 3 7 . 0 0 3 4 1 . 2 6 4 0 1 . 7 6 7 5 8 . 4 . 0 0 2 3 . 0 0 2 7 1 . 2 2 3 2 1 . 6 2 7 4 2 . 3 . 0 0 1 3 . 0 0 2 2 1 . 1 8 2 6 1 . 4 8 7 3 0 . 7 . 0 0 0 8 TABLE A -2 . Sodium Content of Aluminum Metal under Sodium Fluoride-Aluminum Fluoride Melts (Data from Waddington • ) I ..II III IV V VI NaF/AlF^ ratio wt $ Na(A1) N N a .x 1 0 6 l o g ' Na(1000) ^Na(lOOO) aNa(1000) 1.50 .OI65 193 2.176 150 .0289 .0155 181 2.157 143.6 .0260 .0120 140 2.134 136 .0190 .0080 93 2.074 118.7 .0110 .0070 82 2 .050 117 .0092 1.273 .0130 152 2.140 138 .0209 .0115 134 2.128 134 .0179 .'. • .0100 117 2.106 127.7 .0149 .0090 105 2 . 0 9 4 ' 124 .0130 0.887 .0070 82 2 .050 112 .0092 .0060 70 2.014 103.2 .0072 .0040 46 1.864 7 3 . 1 .0034 .0030 35 1.714 51 .8 .0018 - 41 -• / TABLE A - 3 . Sodium Content of Lead Metal under Sodium Fluoride-Aluminum Fluoride Melts Q (Data from Aylen ° ) I II III IV V VI NaF/AlF5 ratio wt <f> Na(Pb) N N a ( p b ) l ° g y N a ( i Q 1 0 ) >Ha(101Q) ^aflQlO) 1.68 ' 4.78 0,312 .37 - l .234 .073 1.68 4.58 0,302 .345 - l .221 .067 1.68 I+.58 0.302 .345 - 1 .221 .067 1.70 4.38 0.292 .318 - 1 .208 .061 1.66 4.28 0.286 .305 - 1 .202 .058 I.67 4.90 O.316 .380 - 1 .240 .075 1.66 4.88 O.316 .380 - 1 .240 .O76 1.68 5-20 0,330 .410 - 1 .257 .085 1.60 . 4.18 O.282 .290 - 1 .195 .055 1.63 4.00 O.272 .268 - 1 .185 .050 1.67 4.30 0.288 .307 - l ,203 .058 1.65 4.20 0.282 .290 - 1 .195 .055 1.70 4.40 0.293 .319 - 1 .208 .061 1.70 4.70 0.308 .358 - 1 .228 .070 I .70 4.50 0.298 .334 - l .216 .064 1.70 4.60 0.303 .346 - l .222 .067 1.70 4.80 0.312 •370 -. 1" .235 .073 I .67 4.90 O.316 .380 - 1 .240 .076 1.67 4.30 0.288 .307 - l .203 .058 1.68 4.20 0.282 .290 - 1 .195 .055 1.63 4.80 0.312 .370 - 1 .235 .073 1.51 3-10 0.224 .143 - 1 • 139 .031 - 42 -TABLE A-4. Sodium Content of Lead Metal under Sodium Fluoride-Aluminum Fluoride Melts (Data from Feinlab and Porter ^ ) I II III IV V NaF/AlF ratio wt # Na,_ log / a. J r" (Pb) ° '. Na(T) Na(T) Na(T) 1010 °C .1.50 5.78 0.46 - 1 .288 .102 1.42 5.87 0.45 - 1 .282 .101 1.89 6.05 0.47 - 1 .295 -108 970 °C 1.67 5.65 0.43 - 1 .269 .094 1.60 .5.06 0.J4 - 1 .219 .0719 1.71 6.46 0.45 - 1 .282 .108 1.66 5.02 O.33 - 1 .214 .0689 1.54 3.8O O . 1 7-I .148 .0388 I.58 3.89 0 . 1 7 - 1 .148 .0395 1.60 4.26 0.24 - l .174 .0497 1.60 3.98, 0 . 2 1 - 1 .162 .0441 940 °C I.65 5.08 0.30 - 1 ,199 .0646 1.54 5.81 0.37 - l .234 .0838 - 4 3 -9 4 0 ° Q I I I I I I 0 . 9 0 1 . 1 0 1 . 3 0 1.50 1 . 7 0 1 . 9 0 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 function of the AIF3 concentration by solving two simultaneous equations, namely: .1). The eq u i l i b r i u m constant, k. 2). The Gibbs - Duhem r e l a t i o n s h i p , used.for c a l c u l a t i o n of the a c t i v i t y of one component i n a binary system when the necessary a c t i v i t y data i s a v a i l a b l e f o r the second component. 1). Evaluation of the Equilibrium, Constant. In determining the eq u i l i b r i u m constant f o r a reaction from the.-free energy changes associated with that reaction, i t i s convenient to s p e c i f y the standard states f o r the rea c t i n g species and the products. For aluminum, sodium, and sodium f l u o r i d e , the standard states at 1010° were taken to be the pure l i q u i d m aterial. However, pure l i q u i d aluminum f l u o r i d e i s metastable with respect to the vapour state, and s o l i d alum-inum f l u o r i d e sublimes at 1281°C. No thermodynamic data i s a v a i l a b l e on metastable l i q u i d aluminum f l u o r i d e . Examination:of the phase diagram f o r the NaF - A l F j system(figureA-3) shows that at 1010°, pure s o l i d aluminum f l u o r i d e i s i n eq u i l i b r i u m with a melt containing 55 atomic percent aluminum f l u o r i d e , hence the a c t i v i t y , of aluminum f l u o r i d e i n a melt of t h i s composition and temperature i s the same as that f o r pure s o l i d aluminum f l u o r i d e , which can therefore be used as the standard state f o r the aluminum f l u o r i d e . The thermodynamic data f o r these materials i n t h e i r standard 12 states was taken from JANAF ta b l e s , at 1010°: - 45 -F° - H° _ , , / , . A H ° ( k c a l / m o l e ) 298 ( c a l / m o l e ) f(298) v ' ; N a F ^ 26.597 -129.885 A l 13.87 2.40 • (1) Na 18.888 0.575 (1) A l F v 31.17 -358-00 3(s) The f r e e e n e r g y change f o r t h e r e a c t i o n was: A G ° = 38.45 k c a l g i v i n g an e q u i l i b r i u m c o n s t a n t : k =2.8 x 10"^  2 - ) C o m p u t a t i o n o f l o g j / N ^ 1 F and l o g ^ A i F /^ a F'-3 5 The Gibbs-Duhem e q u a t i o n and t h e e q u i l i b r i u m c o n s t a n t were u s e d t o s o l v e t h e two unknowns, l o g YjgaF and 1°STA-J_F ' A S 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 , o v e r t h e c o m p o s i t i o n range N = 0.223 A l F j t o 0.321. The logY . „ and 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 A l F j computer programme and t i e p o i n t on an IBM "JOkO computer. 13 The computer programme d e v e l o p e d by A y l e n and Samis was m o d i f i e d f o r t h e p r e s e n t c o m p u t a t i o n s . The t i e p o i n t u s e d i n t h e programme was a t ' N ^ e q u a l t o 0.223. The 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, (where Y = logY ) and was o b t a i n e d f r o m figure.A - 4 , c o n v e r t i n g t h e v a l u e NaF o f l o g / N a F / N A 1 F ^ a t N M F = 0.223 t o l o S ^ N a F - T h e o t h e r changes made i n t h e programme were 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 computer programme i s r e p r e s e n t e d b y t h e symbol C ) , k = 2.8 x 10 and new v a l u e s o f t h e sodium a c t i v i t y (ANA) a t each o f t h e t e n aluminum f l u o r i d e \ - 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. These new sodium a c t i v i t y v a l u e s l i e on t h e l i n e drawn on f i g u r e A - l . The computer o u t p u t gave v a l u e s o f l o g Y „ „ and l o g Y 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 6 NaF s > 9 A l F j 1010°C. These r e s u l t s were c o n v e r t e d t o l o g Y fw and logY /N „ NaF A l F j A l F ^ NaF r e s p e c t i v e l y and p l o t t e d i n f i g u r e A-2 a g a i n s t N o v e r t h e c o m p o s i t i o n AIF3 range-N = 0.223 t o 0.321. 3 B. Thermodynamic A n a l y s i s o f t h e 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 System. 1.) C a l c u l a t i o n o f A c t i v i t i e s f r o m t h e NaF - A1F., Phase Diagram: 2 I n t h e p r e c e e d i n g s e c t i o n , l o g 7 j j a F ^ A l F & n d ' l 0 g ^ A1F ^ a F were o b t a i n e d by s o l v i n g two s i m u l t a n e o u s e q u a t i o n s , v i z ; t h e e q u i l i b r i u m c o n s t a n t and t h e Gibbs-Duhem r e l a t i o n s h i p . A n o t h e r method w i l l now be d e s c r i b e d whereby v a l u e s o f l o g V^p/^ 2 a n < i l°g X^JJ ^ N a F 1 3 6 0 D ' t a i n e d 3 f r o m 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 d i a g r a m . 14 .Wagner has d e v e l o p e d an e x p r e s s i o n t o o b t a i n a c t i v i t i e s o f th e components f r o m t h e phase diagram, o f a b i n a r y s y s t e m e x h i b i t i n g compound f o r m a t i o n b y s u c c e s s i v e n u m e r i c a l i n t e g r a t i o n s o f t h e compounds i n t h e b i n a r y s y s t e m . The e q u a t i o n i s : RT I n a 2 = A H F J (1 - N 2 ) A T + (1 --Xg) ( A T d N 2 T m I N 2 - X 2 j ( N 2 - X 2 ) 2 where: AH^, = t h e h e a t o f f u s i o n o f t h e compound. . T = t h e m e l t i n g t e m p e r a t u r e o f t h e compound. -••Nj> N 2 = t h e mole f r a c t i o n s o f aluminum f l u o r i d e and sodium f l u o r i d e r e s p e c t i v e l y . -2k. 0 -22.0 -20.0 l o s V N a F / ^ i F 3 -18.0 -16.0 -lk.0. -12.0 0.200 TT -O. 0.250 0.300 N A1F~ lU.O -12.0 log V A 1 F 3/N| a F ( -p--10.0 -8.0 - 6 . 0 0.350 Figure A - 2.: The Values of log ^ a F / ^ 3 *nd 1°S^AiF^^NaF a s a F u n c t i P n ' of the Composition from the Computer Results. - 48 -X^, Xg = the 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 corresponding t o the compound. I t can be seen from.the equation 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 w i l l depend • on • two f a c t o r s . These are,' being able t o obta i n an accurate p l o t of the l i q u i d u s l i n e ( i . e . , temperature vs. composition), and e v a l u a t i o n of the entropy of f u s i o n of the compounds th a t e x i s t in-the•system. These 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 some d e t a i l . a..) The NaF. - A l F ^ Phase Diagram: Three recent papers have been published on the sodium f l u o r i d e -aluminum.fluoride phase diagram. These papers.are by Grjotheim, who .16 i n v e s t i g a t e d the reg i o n from-N = 0 . 0 0 0 .to O.5OO,.Hollingshead, who 3 17 i n v e s t i g a t e d the .same r e g i o n , and'Rolin, who st u d i e d the range between NA,_, = 0.250 t o the e u t e c t i c a t N = 0 . 4 6 5 . - A composite of these • A1F, ^ , A1F, 3 3 • i n v e s t i g a t i o n s was used t o construct the phase diagram shown i n f i g u r e A-3» The r e s u l t s show good agreement f o r - r e g i o n s r i c h in-sodium f l u o r i d e , but serious, errors-become apparent above N ^ = 0.400. ..The- l i q u i d u s 3 curve f o r melt 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 ( N a ^ A l ^ F ^ ) as determined by Ho l l i n g s h e a d . i s some 10 t o 15 degrees higher than the l i q u i d u s found by R o l i n . The temperature and composition of the e u c t e c t i c between c h i o l i t e and sodium aluminum t e t r a f l u o r i d e are reported t o be: i . ) Grjotheim . N A 1 F = 0.1+70 . T = 690°C 3 i i . ) H o llingshead = 0.1+70 = 693 i i i . ) R o l i n = 0.465 = 681+ G r j o i h e i m reported t h a t 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 me l t i n g . p o i n t - of 731°• He a l s o claimed than 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 = O.5OO, but rather 3 R that at N = 0.500, the liquidus temperature was in fact 860°. Dewing'-s AlFj • work on vapour pressure measurements substantiates Hollingshead's findings, and suggests that beyond .the euctectic at N = 0.465, the-liquidus Air _ 3 line rises very steeply and in.fact that along this line, the liquid-melt is in 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 to apply Wagner's equation. For sodium fluoride, this i s no problem, . since the entropy of fusion at the melting point is simply the heat of fusion divided by the melting temperature and reliable values are reported 12, 18 in the literature. However, the situation is more complex with regard to the entropy of fusion- of cryolite, because of the fact that cryolite dissociates on melting. The experimentally measured heat of fusion is actually the sum. of the true heat of fusion plus the heat of dissociation. 15, 19,. 20, 21, 22 Several pieces of work have been done on various dis-sociation schemes, and the proposed reaction of: Na^AlFg - — » 2NaF + WaAlF^ gives the best agreement with experimental evidence provided by x-ray diffraction, transport studies, cryoscopic studies and NaF - AlF^ melt density measurements. • Assuming that the species in the molten state are completely ionic, and using.Temkin's ionic theory, the equilibrium con-stant for the above reaction can be expressed as a function of the degree of dissociation, o( : 51 D (1 - )(2cA + l ) 2 23 F o s t e r and F r a n k e s t a b l i s h e d v a l u e s f o r v a r i o u s t e m p e r a t u r e s u s i n g m e l t d e n s i t y s t u d i e s , and a p l o t o f l o g v s . . l / T gave a v a l u e f o r t h e hea t o f d i s s o c i a t i o n o f 22.5 K c a l / m o l e . . The t r u e h e a t o f f u s i o n c o u l d t h e r e f o r e be c a l c u l a t e d f r o m : A H F = A H F + C ^ A H ^ where: A R _ = 26.6 k c a l / m o l e , . t h e c r y o s d o p i c h e a t o f f u s i o n , r A H ^ = 22.5 k c a l / m o l e , t h e h e a t 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 degree o f d i s s o c i a t i o n a t 1010°C. The t r u e h e a t o f f u s i o n - o f c r y o l i t e t o p u r e , u n d i s s o c i a t e d m o l t e n c r y o l i t e was c a l c u l a t e d t o be 18.73 k c a l / m o l e , w h i c h c o r r e s p o n d s t o an e n t r o p y o f f u s i o n 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 o f l o g T f w a p / N 2 f r o m t h e Phase Diagram: 3 The a c t i v i t y o f e i t h e r o f t h e components i n a b i n a r y s y s t e m can be d e t e r m i n e d , f r o m t h e phase d i a g r a m b y using-Wagner's e q u a t i o n . . The a c t i v i t y so c a l c u l a t e d i s a t t h e t e m p e r a t u r e and c o m p o s i t i o n o f t h e l i q u i d u s , and w o u l d be 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 i s . assumed t o be u n i t y f o r t h e c a l c u l a t i o n . E x a m i n a t i o n o f t h e phase d i a g r a m ( f i g u r e A-3 ) shows t h a t m e l t s -•52 -with c o m p o s i t i o n s . b e l o w - = 0.137 are i n equilibrium with sodium fl u o r i d e , melts between N = 0.137 and 0.407 are in-equilibrium-with ' A1F X 3 c r y o l i t e , , and melts for N^ -^ , greater than 0 .407-are i n equilibrium with 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 fusion i s not known for c h i o l i t e , sodium aluminum tetrafluoride,- or aluminum.fluoride,-melts whose compositions are above N^ -^ , = 0.407 w i l l not be considered further. The a c t i v i t y of sodium fluoride for melts whose compositions were between-N^p = O.and 0.137 were calculated and .tabulated in. table A-5 3 For convenience, the a c t i v i t y data was presented i n the form, l o g ! at selected melt compositions,.and l i s t e d . i n column-XIV of table A-5. The l a s t . entry i n column-XIV i s the value of log X-^a-p at "the temperature and composition of the eutectic. This point i s used-as-the t i e point i n the calculation of log)f „ values, at higher aluminum fluoride concentrations, NaF as w i l l be explained i n the following paragraph. Melts having a temperature and composition that l i e on the liquidus between J ^ j , = 0.137 a n d 0.407-were i n equilibrium with c r y o l i t e . The log Tf values l i s t e d i n column XIV of table A-6 were calculated r e l a -NaF tiv e to t h i s compound.. The eutectic was used as a t i e point to.correct this a c t i v i t y data to that of pure sodium f l u o r i d e . The correction.factor was - 1 . 5 l 8 , and was added to the log _ values of column XIV. ' ' NaF Each of'the"logY values l i s t e d i n column XV of tables A-5 NaF .and A-6 was adjusted to a common temperature, 1010°C. The temperature adjustment was done using regular solution formula. 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 by I n t e g r a t i o n o f t h e Compound NaF i n t h e N a F - A l F ^ B i n a r y I . I I . I l l IV . V V I V I I V I I I IX w N a F % a F N A 1 F T ( ° K ) A T N A 1 F A T X A 1 F A T C X A 1 F A T d N (V + V I I ) ( V I I I ) x 6.35 3 5 3 _ 2 \ 3 2 % a F " x N a F ( % a F - XNaF^ J WNaF ~~ XNaF) X N a F  1.000 0.000 1267 0 0 .0 0 0 0 O.995 0.005 1264 3.0 - 3.0 0 0 - 3.0 - 19.0 O.987 0.013 1260 7.0 - 7.0 0 0 - 7.0 - 44.4 O.976 0.024 1254 13.0 - 13.0 0 0 13.0 - 82.5 O.949 0.051 1238 29.0 .- 29.0 0 0 29.0 -184.2 0.926 0.074 1225 43.0 - 43.6 0 0 43.0 -273.0 0.907 0.093 1207 60.0 - 60.0 0 0 - 60.0 -381.0 0.900 0.100 1200.5 66.5 -66.5 0 0 -66.5 -422.3 0.883 0.117 1180.5 86.5 - 86.5 0 0 86.5 -549.2 0.863 0.137 1155 112.0 -112.0 0 0 -112.0 -711.0 X X I • X I I X I I I XIV XV XV I X V I I % a F 4.575 x T l 0 g a N a F l 0 g N N a F l 0 g * N a F l G g V NaF l 0 g y NaF l 0 g ^ NaF (T) (1285) 2 N A l F ^ 1.000 .5796.6 0 0 0 0 0 0 0.995 5782.8 -0.003 -0.002 -0.001 -0.001 -0.001 -40.00 O.987 5764.5 -0.007 -0.006 -0.001 -0.001 -0.001 - 5-88 0.976 5737-0 -0.014 -0 .010 -0.004 -0.004 -0.004 - 7-00 0.949 5663.8 -0.032 -O.O23 -0.009 -0.009 -0.009 - 3.46 0.926 5599-9 -0.049 -0.033 -0.016 -0.016 -0.015 - 2.73 0.907 5522.0 -0.069 -0.042 -0.027 -0.027 -0.025 - 2.91 0.900 5492.3 -0.077 -0.046 -0.031 -0.031 -0.029 - 2.90 0.883 5400.8 -0.102 -0.054 -0,048 -0.. 048 -0,044 - 3.21 0.863 5284,1 -0.132 -0.064 -0.068 -0.068 -0.061 - 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 - AlF^ Binary I I - I I I IV VI V I I V I I I IX NNaF ^AlF, T(°K) A T N A T A1F, 5 N NaF NaF A l F j ?NaF XA1F ^ T ' W ^ + V I 1 ^ ( y i 1 1) x 1 4 - 6 7 (N - X r \(N - X )' NaF NaF , J NaF NaF %aF 0 . 8 6 3 0 . 1 3 7 1155 127 1 5 3 . 9 8 . 2 4 8 0 3 4 5 . 2 3 4 9 9 . 2 1 7 3 2 3 . 4 0 . 8 5 7 0 . 1 4 3 1163 119 1 5 8 . 8 8 2 6 1 0 3 2 9 . 9 6 488.84 7 1 7 L 3 0 . 8 5 0 0 . 1 5 0 • 1183 99 1 4 8 , 5 0 2475 3 1 2 . 1 7 4 6 0 . 6 7 6758.O 0 . 8 4 2 - 0 . 1 7 6 1223 5 9 1 4 0 . 2 7 2682 2 4 5 . 1 3 3 8 5 . 4 0 5 6 5 3 . 8 0 . 8 0 9 0 . 1 9 1 1242 40 1 2 9 . 4 9 2857 2 0 3 . 5 9 3 3 3 . 0 8 4886.3 O.789 9 . 2 1 1 1262 2 0 1 1 0 . 0 0 3 2 8 9 142.13 2 5 0 . 3 8 3 6 7 3 . 1 0 . 7 8 0 0 . 2 2 0 1267 15 1 0 8 . 2 5 4167 IO8.58 2 1 8 . 5 8 3 2 0 6 . 6 0 . 7 7 7 0 . 2 2 3 1272 10 8 2 . 5 9 3 4 2 4 . 6 9 7 . 1 9 1 7 9 . 7 8 2 6 3 7 . 4 0 . 7 6 8 0 . 2 3 2 1 2 7 7 . 5 4 . 5 5 8 . 0 0 3 5 1 3 . 4 6 5 . 9 7 1 2 3 . 9 7 1 8 1 8 . 6 0 . 7 5 9 0 . 2 4 1 1281 1 , 0 2 6 . 7 8 3125 3 6 . 0 9 6 2 , 8 7 9 2 2 . 3 0 . 7 5 4 0 , 2 4 6 1 2 8 1 . 6 0.4 24.60 5 0 0 0 2 0 . 0 0 4 4 . 6 0 6 5 4 . 3 O.75O 0 . 2 5 0 1282 0 0 0 0 0 0 O.745 0 . 2 5 5 1 2 8 1 . 7 0 , 3 - 1 5 . 3 3 0 0 0 - 1 7 - 5 - 3 2 . 8 - 4 8 1 . 2 O.740 0 . 2 6 0 1281 1 . 0 - 2 6 . 0 2 5 0 0 - 3 1 . 2 - 5 7 - 2 - 8 3 9 . 1 0 . 7 3 5 0 . 2 6 5 1 2 8 0 . 1 1-9 - 3 3 . 5 6 2111 - 4 2 . 7 - 7 6 . 2 6 - 1 1 1 8 . 7 O.730 0 . 2 7 0 1 2 7 9 . 2 2.-8 - 3 7 . 8 0 1750 - 5 2 . 4 1 - 9 0 . 2 2 - 1 3 2 3 . 5 0 . 7 2 5 0 . 2 7 5 1277 5 - 5 5 , 0 0 2 0 0 0 - 6 1 . 7 9 - 1 2 6 . 7 9 - 1 8 6 0 . 0 0 . 7 2 0 0 . 2 8 0 1275 7 - 6 5 . 3 3 1944 - 7 1 . 6 7 - 1 3 7 . 0 0 - 2 0 0 9 . 8 0 . 7 1 5 0 . 2 8 5 1272 10 - 8 1 . 4 3 2041 - 81.63 - 1 6 3 . 0 6 - 2 3 9 2 . 1 O.710 0 . 2 9 0 1269 •13 - 9 4 . 2 5 2 0 3 1 - 9 1 . 0 0 - 1 9 6 . 0 5 - 2 8 7 6 . 0 0 . 7 0 0 0 . 3 0 0 1261 .21 - 1 2 6 . 0 0 2 1 0 0 -112.46 -238.46 - 3 4 9 8 . 2 0 . 6 7 5 0 . 3 2 5 1233 49 . - 2 1 2 . 3 3 2 1 8 7 . 5 -166.06 - 3 7 8 . 3 9 - 5 5 5 1 . 0 O.650 0 . 3 5 0 1187 95 - 3 3 2 . 5 0 2375 - 2 2 2 . 1 1 - 5 5 5 . 6 1 - 8 1 5 0 . 8 0 . 6 2 5 0 , 3 7 5 1123 159 - 4 7 7 . 0 0 2548 - 2 8 4 . 1 6 - 7 6 1 . 6 3 - 1 1 1 7 3 . 1 0 . 6 0 0 • 0 . 4 0 0 1044 - 238 - 6 3 4 . 6 7 2644 - 3 5 0 . 7 3 - 9 8 5 , 4 0 - 1 4 4 5 5 . 8 0 , 5 9 3 0 . 4 0 7 1012 270 - 7 0 0 . 0 0 2 7 4 0 - 3 6 8 . 9 1 - 1 0 6 8 . 9 1 - 1 5 6 5 0 . 0 - 55 -H LTN oo oo CM oo-d- vo L T N J - C O OA oo 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 HHrHrHrHCMCMOJCMCMCMOJCMCMCMCM 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 - roj- 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 UA t— C— ON OO-d- O N H OJ ON CM H VO O ON CM VO f - LTN LTN OA J - CO OA C— OO C— O OA H CO VO VO OO C O C O CM C— O H H L f A ^ - C O ON O CM CM r O J - UA U A V O VO t - f - C O OA 0OC0 -d" OOVO O O O O O O O O H H r H H H i H H H H H H H H W ^ 1 j i i | i I i i I I I i i i i i I l i ' ' • ' 1 ' O U N 0 4 OI ON H CMVOt-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" UAH 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 d d d o o H H C M o o I I I I I I I I I I I i I -dr t— H -d- CM OOCO ONIAO OOUACO H -dr tr- OA OOVO O M A H t--d" CM VOVO Ir—CO ONO 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 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 i t i i i i i i i i i V Q C O O A O O V O O O O O H I r — H Cv) OO H MD CO J - H UAVO -d" rH UAVO O CO_d-_d-rHV0OOLr\uArHUArH c O d O N W H d H O N O C O O t ^ O J C O OOOOCMOCOVOUA -d-OOHrH 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 ' • 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 !r- r H O UA t — oo O -d" O CM UA CM OOVO ON-dr O 0OUA0OOVO CM CM O O O A U A O A r H O Ir - VO O CO CM rH ON CO t r — O N r H - d - V O V O V O V O V Q UA U A-d O O r H O V O - d " OO OO Ir—CO CM OO U A V O 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— UA 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 U A U A U A U A UA J " -d OOND— O - d O N O N O l ^ C O ON-d - O U A O U A O U A O U A O O U A O U N O on VO.UAUACM 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 , as t h e NaF - A1F s y s t e m was n o t a . r e g u l a r s o l u t i o n . 3 The v a l u e s o f l o g / /NT,- a t 1010eC were a l s o l i s t e d i n t a b l e s A-5 & v NaF . A l F ^ and A-6 and p l o t t e d 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,„. A l F j NaF A1F.3 a t = 0.223 w a s used f o r t h e t i e p o i n t i n . t h e computer programme 3 d i s c u s s e d e a r l i e r . . 3.) The C a l c u l a t i o n o f l o g Y : A l F ^ The a c t i v i t y d a t a f o r sodium f l u o r i d e f r o m a thermodynamic a n a l y s i s o f t h e NaF - A l F ^ phase d i a g r a m has been d e s c r i b e d above. .The Gibbs-Duhem 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 = " N A 1 F % a F l o e * N a F + \ l o § * N a F ^ A 1 F 3 3 \ 5 N ! l F 5 \ N A 1 F 3 N A 1 F , = ° 3 The v a l u e s o f l o g J / N 7 , „ a t v a r i o u s c o n c e n t r a t i o n s were t a k e n f r o m s NaF A 1 F 5 f i g u r e A-4 f o r use 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 v c o u l d n o t A l F j be c a l c u l a t e d b y t h i s method beyond N^ . = 0.407 s i n c e t h e p l o t o f l o g Y^  p / ^ A i p c o u l d n o t be made beyond t h i s p o i n t . Hence v a l u e s o f v a ^ l°g 0AIF 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 r e l a t i v e , because t h e 3 c o n t r i b u t i o n o f t h e i n t e g r a l t e r m between-N = 0.407 and 1.00 was A l F j m i s s i n g f r o m t h e r i g h t hand s i d e o f t h e Gibbs-Duhem e q u a t i o n . . These r e l a t i v e l o g YAQ_F 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 3 I n 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 w i t h r e s p e c t t o a s t a n d a r d s t a t e o f t h e pur e s o l i d m a t e r i a l a t 1010°, i t 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 t some p o i n t between A i r 3 TABLE A-7-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 Aluminum F l u o r i d e b y t h e Gibbs-Duhem T e c h n i q u e I I I I I I IV V VT V I I V I I I I X N = N I* A l F o A1F l o g T dN 3 (-V+VT) (VII:. + 6.452) l o g V NaF A I F 3 A I F 3 A L F 3 NaF N A 1 F 3 = ° ' k 0 1 0.593 0.407 -22.32 0.600 0.400 -22.00 O.625 0.375 -21.65 0.650 0.350 :21.40 0.675 0.325 -21.20 0.700 0.300 -21.55 0.725 0.275 -22.15 0'.745 0.255 -22.62 0.750 0.250 -22.30 0.775 0.225 -19.10 0.800 0.200 -16.00 0.825 0.175 -13.10 O.85O 0.150 -8.00 O.863 0.137 -3.21 O.875 "0.125 -3.15 0.900 0.100 -2.95 O.925 0.075 -2.80 0.950 0.050 -2.45 0-975 0.025 -2.20 1.000 0.000 -2.00 0.242 - 5.40 0.240 - 5.28 0.234 - 5.05 0.227 -4.86 0.219 - 4.64 0.210 - 4.52. 0.199 - 4 .4l 0.190 - 4.30 0.187 - 4.17 0.174 - 3.32 0.160 - 2.56 0.144 - 1.87 0.127 - 1.02 0.118 - O.38 0.109 - 0.34 0.090 - 0.26 O.069 " 0.19 0.047 - 0.11 0.024 ~ 0.05 0 0 - 0, 5-400 -0.155 5.125 - 0.701 4.349 -1.-239 3.621 -1.771 2.869 "2.313 2.207 -2.874 1.536 -3.330 0.970 -3.443 0.727 -3.884 0-564 - 4.328 I.768 -4.660 2.790 -4.924 3-904 - 4.969 4.589 -5.007 4.667 -5.083 4.823 - 5.155 4.965 -5-220 5-110 -5.278 5.228 -5.330 5.330 -I.052 -2.992 -1.327 -3-686 -2.103 -5-384 -2.831 -6.700 -3-583 -7.865 -4.245 -8.663 -4.916 -9.353 -5-482 -9.877 -5.725 -IO.187 -7.016 -11.682 -8.220 -12.844 -9.242 -13.579 -10.356 -14-333 - i l . o 4 i -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 -rlAlF = 0 and 0 . 4 0 7 , and a p p l y a c o r r e c t i o n f a c t o r t o t h e v a l u e s o f logY 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 t i e p o i n t A 1 F 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 ^ = 0.223, s i n c e t h e r e s u l t s o f t h e computer programme gave a . v a l u e o f l o g ^ A ^ F a t "thi s p o i n t . The c o r r e c t e d >3 logY. v a l u e s a p p e a r i n column V I I I o f t a b l e A-7 and t h e c o r r e s p o n d i n g A l F j v a l u e s o f log'if /N„, „ a p p e a r i n column I X . ° " AlH ' NaF 3 F i g u r e A-5 i s a p l o t o f logY / l C _ a g a i n s t N . The p l o t • A l F j NaF A 1 F 5 c o n s i s t s o f two s t r a i g h t l i n e segments m e e t i n g a t N = 0 .137 ' . The • Air 3 e x t r a p o l a t i o n o f t h e s t r a i g h t l i n e s e c t i o n between N^^, = 0 . 1 3 7 and 0 . 4 0 7 3 2 t o h i g h e r a l u m i n u m . f l u o r i d e c o n c e n t r a t i o n s g i v e s 1°sY'A1F / N N a F = 1 , 9 a - t W A 1 F = °'55 0 , T h e P h a s e 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 t h i s c o m p o s i t i o n 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 , so t h a t t h e a c t i v i t y o f t h e alumnium f l u o r i d e i s u n i t y h e r e , and hence l o g / , /N„ „ J A l F j NaF e q u a l s 1.3, w h i c h a g r e e s r e a s o n a b l y w e l l w i t h t h e e x t r a p o l a t e d v a l u e . C. D i s c u s s i o n : I n s e c t i o n s A and B o f t h i s a p p e n d i x , two i n d e p e n d e n t 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 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, t h i s a c t i v i t y d a t a was c a l c u l a t e d f r o m a knowledge o f t h e a c t i v i t y , o f .sodium i n NaF - A l F j 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 sodium a c t i v i t y v a l u e s used i n t h e computer programme l i e on t h e l i n e drawn i n f i g u r e A - l . I t i s i ,4 o b s e r v e d 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 H o l l i n g s h e a d s d a t a a g r e e w e l l w i t h t h e s e l e c t e d l i n e o v e r t h e e n t i r e c o m p o s i t i o n r a n g e . The computed, r e s u l t s f o r l o g ^ N A F / N ^ 1 F and l o g Y A 1 F . / N ^ A R E P L O T T E D A S 3 3 - 61 -open c i r c l e s and open . t r i a n g l e s i n f i g u r e s A-6 andA-7 r e s p e c t i v e l y . I n s e c t i o n B, 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 aluminum 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 d i a g r a m f o r t h i s s y stem, t h e c a l c u l a t i o n s bang done by use o f Wagner's. method. The a c t i v i t y d a t a a r e p l o t t e d as l o g Y ^ p / N 2 ^ a n d l o g Y A 1 p / N N a F ( c l o s e d . c i r c l e s and t r i a n g l e s ) 3 3 i n . f i g u r e s A-6 and A-7 r e s p e c t i v e l y . The r e s u l t s f o r l o g / /Nt n i-, f r o m s e c t i o n B were used, t o NaF A l F ^ e s t a b l i s h t h e t i e p o i n t f o r s e c t i o n A, and so b o t h c u r v e s o f f i g u r e A-6 i n t e r s e c t a t N ^ p = 0.223. A t a l l o t h e r p o i n t s 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 in d e p e n d e n t methods o f s e c t i o n s A and B. Agreement w i t h r e s p e c t t o d i s p o s i t i o n and shape i s s a t i s f a c t o r y and.the s m a l l peak o b s e r v e d i n t h e g r a p h d e r i v e d f r o m s e c t i o n B i s a t t r i b u t a b l e t o t h e s e n -s i t i v i t y o f t h e f i g u r e s i n column V I o f t a b l e A-6 t o s l i g h t , e r r o r s i n t h e 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 c u r v e n e a r t h e c r y o l i t e compos-i t i o n . I n f i g u r e A-7, t h e r e s u l t s o f l°sV^p A^aF f r o m s e c t i o n A were u s e d . t o e s t a b l i s h ' t h e t i e p o i n t a t N ^ p = 0.223 f o r t h e l 0 S ^ A ^ p v a l u e s 3 3 c a l c u l a t e d by 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 B. A g a i n t h e d i s -p o s i t i o n and shape o f t h e two c u r v e s i s s a t i s f a c t o r y . oo -24.0 -20.0 -l6.0 1 -12.0 tt> o H -8.0 -4.0 0.0 from Figure A - 2 O from Figure A - 4 • ro 0.1 0.2 0.3 0.4 0.5 W, A1F, Figure A - 6 ; Comparison of l o g Y N a F / N | 1 F 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 oo fe H <; O -16.0 -12.0 -8.0 ON (jo 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 F o u r p a p e r s have appe a r e d i n t h e l i t e r a t u r e c o n c e r n i n g t h e a c t i v -i t y o f sodium i n sodium - l e a d a l l o y s . The sodium 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 b a s e d on t h e c e l l : . Na e l e c t r o l y t e c o n t a i n i n g N a + | Na(Fb) w h e r e i n t h e sodium a c t i v i t y , i s r e l a t e d t o t h e e.m.f. a s : E = - ^575 T l o g a N a ( p b ) n f 2k H a u f f e and V i e r k e s t u d i e d t h e c o m p o s i t i o n i n t e r v a l between N N a = 0 , 33 6 t o °*935 a t k25° and 475°. M o r a c h e v s k i i 2 5 s t u d i e d a l l o y s r a n g i n g between N N & = 0.131 and 0.851, a t 375° and 475°, and L a n t r a t o v 2 ^ f o r c o m p o s i t i o n s between N N a = 0.05 and 0.90, a t 400°, 500° and 600°. 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 on a s o l i d e l e c t r o l y t e c o n s i s t i n g o f g l a s s w i t h a h i g h Na 2 0 c o n t e n t . The f o u r t h p a p e r , b y F e i n l a b and P o r t e r J u s e d as a s o l i d e l e c t r o l y t e a l u m i n a b r i c k s a t u r a t e d w i t h NagCO^. T h i s l a s t i n v e s t i g a t i o n c o v e r e d t h e a l l o y c o m p o s i t i o n between N j j a = 0.151 t o 0.401 f o r v a r i o u s t e m p e r a t u r e s between 500° and 800°. The r e s u l t s o f t h e s e e x p e r i m e n 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 i n t e r v a l s i n t a b l e s B - l t h r o u g h B -4 r e s p e c t i v e l y . A c o m p o s i t e p l o t o f l o g Y ^ / N ^ v s . N j j a f r o m t h e above d a t a was p r e p a r e d a t 475°- 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°> 775° and 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 the Sodium-Lead System (from Hauffe and V i e r k e ^ ) I I I I I I IV V VI V I I NNa(Fb) aNa ^Na -l o g y N a NPb 4 - i o g y j ] 475 c C 3 3 6 0.007 0.021 1.682 0.664 0.441 3-81 0.392 0.011 0.028 1.551 0.608 0.370 4.20 0.444 0.020 0.046 1-347 0.556 O.309 4.36 0.470 O.O38 0.031 "I.O92 0.530 O.281 3.89 0.562 0.074 0.132 0.881 0.438 0.192 4.59 0.567 0.090 0.159 0.799 0.433 0.187 4.26 0.625 0.135 0.216 O.665 0-375 0 . l 4 l 4.73 O.678 0.215 0.317 0.499 0.322 0.104 4.81 0.705 0.246 0.349 0.457 0.295 O.087 5-25 0.757 0.363 0.470 0.320 0.243 0.059 5.42 O.794 0.515 0.649 0.188 0.206 0.042 4.43 0.815 0.710 0.871 0.060 O.185 0.034 1-75 0.873 0.840 0.962 0.017 0.127 0.016 1.04 0-935 O.925 0.989 0.005 O.065 0.004 1.14 •425 °C 0.336 0.005 0.015 1.824 0.392 0.008 0.020 1-699 0.444 0.015 0.034 1.469 0.470 O.029 0.062 •1.208 O.562 O.060 0.107 0.971 0.567 0.074 0.130 0.886 O.625 0.113 0.182 0.740 O.678 0.188 0.277 O.558 0.705 0.215 0.305 O.516 0.757 O.326 0.431 O.366 0.794 0.487 0.613 0.213 O.815 0.681 0.836 0.078 O.873 O.865 0.991 0.004 0-935 0.920 0.984 0.007 TABLE B - 2 . Sodium A c t i v i t y D a t a 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 ) I I I I I I : IV V V I V I I N N a ( P b ) a N a ^Na - l o e * N a Nib -logVi I 475 °c 0.131 0.0008 O.OO59 2.231 0.869 O.755 2.954 0.14-9 0.0008 0.0052 2.286 0.851 0.724 3.157 0.177 0.0013 0.0071. 2.147 0.823 0.6773 3.171 0.200 0.0017 O.OO87 2.060 0.800 o.64o 3.219 0.205 0.0019 0.0091 2.040 0.795 0.632 3.228 0.222 0.0025 0.0113 1.946 0.778 0.605 3.216 0.300 0.0054 0.0181 1.743 0.700 0,490 3.557 0.354 0.010 0.0282 1.549 0.646 0.417 3.712 0.402 0.0166 0.0413 1.384 0.598 O.358 3.871 0.409 0.0184 0.0450 1.347 0.591 O.349 .3.856 0.500 O.O518- 0.1036 0.984 0,500 O.250 3.939 0.503 0.053 0.1054 0.977 0.497 0.247 3.956 O.598 . 0.131 0.219 0.659 . 0.402 0.162 4.080 0.700 0.284 0.4057 0.392 - . 0.300 0,090 4,353 0.734 0.341 0.465 0.333 0,266 O.071 4.716 0.800 O.58O 0.725 o.i4o 0.200 o.o4o 3.491 O.85I 0.740 0.870 0.061 0.149 0.022 2.733 TABLE B - 3 . 26 Sodium A c t i v i t y Data f o r the Sodium-Lead -System. (from Lantratov ) I I I I I I IV V VI VII a(Pb) aNa . / N E " l o g ^Na NPb 4b " l o S * Na N P b 475 °C 0.05 0.0002 0.0046 2,357 0.95 0.902 2.589 0.10 0.0005 0.0054 2.268 0.90 0.810 2.799 0.20 0.0019 O.OO95 2.022 0.80 o.64o 3.160 0.30 0.0050 0.0168 1.775 0.70 0.490 3.622 0.40 0.0132 0.0330 1.481 0.60 0.360 4.115 0.50 0.0445 0.0890 1.051 0.50 0.250 4.202 0.60 0.1230 0.2050 0.688 0.4o 0.160 4.302 0.70 0.2570 0.3670 0.435 0.30 0.090 4.837 0.80 0.5750 0.7187 0.143 0.20 0.040 3.586 0.90 0.8400 0.9333 0.030 0.10 0.010 2.998 VIII IX X XI XII XIII XIV XV XVI XVII WNa(Pb) aNa ^Na " L O S *Na aNa • • Na - 1 O S ?Na aNa ^Na " l osY N a 400;°c 500 °C 600 °C 0.05 0.0001 0.002 2.627 0.0003 0.0062" 2.210 0.0006 O.OI30 1.886 0.10 0.0003 0.0028 2.556 0.0007 0.0070 2.152 0.0014 0.0144 1.842 0.20 0.0010 0.0049 2.307 0.0024 0.0121 1.917 0.0049 . 0.0243 1.614 0.30 O.OO27 0.0090 2.045 0.0066 0.0219 1.660 0.0130 0.0433 1.363 0.40 0.0079 0.0190 1.719 0.0164 0.0410 1.387 0.0287 0.0719 1.143 O.5O 0.0301 0.0602 1.220 O.O518 0.104 0.983 O.O787 0,157 0.804 0.60 O.952 O.I587 0.799 0.137 0.229 o.64o 0.188 0.305 O.516 0.70 0.315 0.307 0.5123 O.276 0.394 o.4o4 0.334 0.478 0.321 0.80 0.533 0.622 0.206 O.587 0.733 0.135 0.614 0.767 0.115 0.90 0.828 0.921 0.036 0.841 0.935 0.029 0.853 0.947 0.024 N Na(Fb) TABLE B - 4 . 7 Sodium A c t i v i t y D a t a f o r t h e Sodium-Lead System ( f r o m F e i n l a b and P o r t e r 1 ) I I I I I IV V V I Na Na - l o g y Na N Pb N 2 Pb V I I - l o g ft Na N 2 Pb 475 °C V I I I N„. 0.151 0.0012 0.0082 2.085 0.849 0.729 .2.860 0.212 0.0020 0.0097 2.014 0.778 0.621 3-245 0.225 0.0029 0.0130 1.886 0.777 o.6o4 3.124 0.295 0.0068 O.O232 1.634 0.707 0.500 3.270 0.358 0.0115 0.0321 1.493 0.642 0.412 3.623 0.361 O.OO78 0.0216 1.665 0.639 o.4o8 4.079 0.401 0.0140 0.0349 1.457 0.599 0.359 4.061 I X X X I X I I - X I I I XIV XV X V I X V I I ^ a ^ N a - l o g *Na ^ a ^ N a - l o g y N a . ^ a ^Na " l o g * Na 500 °C 600 °C 700 °C 0.151 0.212 0.223 0.293 0.358 O.36I o.4oi 0.0015 0.0023 0.0033 0.0074 0.0119 0.0089 0.0164 0.0098 0.0110 0.0149 0.0252 .0.0332 0.0246 0.0409 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 0.0194 0.0205 0.0269 0.0427 0.0581 0.0446 0.0723 1.712 1.688 1.570 1,370 1.236 1.351 l . l 4 i O.OO54 O.OO78 0.0108 0.0210 0.0345 0.0292 0.0507 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 -l e a d a l l o y s a t t h e s e h i g h e r t e m p e r a t u r e s . I n o r d e r t o a c c o m p l i s h t h i s e x t r a p o l a t i o n , i t was n e c e s s a r y t o e v a l u a t e t h e 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 sodium i n l e a d , 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 . L.T can be ' Na e v a l u a t e d b y p l o t t i n g logYj j a v s . l / T f o r f i x e d c o m p o s i t i o n s , w h i c h w i l l 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 ^ . The d a t a o f F e i n l a b and P o r t e r , and L a n t r a t o v , was used t o c a l c u l a t e t h e L j j a v a l u e s , as t h e s e i n v e s t i g a t i o n s c o v e r e d t h e w i d e s t t e m p e r a t u r e r a n g e s , t h e r e b y g i v i n g t h e most a c c u r a t e v a l u e s o f l o g t ^ & a t v a r i o u s t e m p e r a t u r e s . S i n c e t h e r e -s u l t i n g p l o t s were l i n e a r , t h e method o f l e a s t s q u a r e s was us e d t o c a l c u l a t e t h e b e s t l i n e s and g r a d i e n t s f r o m t h e d a t a . 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 ^ a i n f i g u r e B - l . F i g u r e B-2 was t h e c o m p o s i t e o f t h e ^-°gf ^ /^p^ d a t a f r o m a l l f o u r p a p e r s . The l o g Y ^ a v a l u e s c a l c u l a t e d f r o m t h i s p l o t were a d j u s t e d t o t h e h i g h e r t e m p e r a t u r e s u s i n g L^a v a l u e s t a k e n f r o m f i g u r e B - l , i n a c -cor d a n c e w i t h t h e f o r m u l a : ^ N a t T - L ) = % a ( 1 - 1 ) + l o S Y N a ( T 2 ) U.575 ( T x T 2 ) The r e s u l t i n g l ° g ^ u a ( [ T j ) ^ ^ N a ( T ) a n d a N a ( T ) v & l u e s a^ s e * c o n c e n t r a t i o n 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 i n t a b l e B-5- F i g u r e 5 w a s c o m p i l e d f r o m t h e d a t a i n t h i s t a b l e . U s i n g t h i s same t e c h n i q u e , t h e sodium a c t -i v i t i e s a t 940°C, 970° and 1010° were 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 of the A c t i v i t y of Sodium i n Sodium-Lead A l l o y s a t 725, 775, and 825 °C. I 11 I I I IV V V I 725 °C ^Na(Pb) " L Na - l 0 s Y N a ( 4 7 5 ) l 0 g y N a ( 7 2 5 ) y Na(725) V ( 7 2 5 ) 0.05 9950 2.310 0 . 4 l 8 - 2 0.0262 .0013 0.10 9625 2.260 0.444 - 2 0.0278 .0028 0.15 9450 2.190 0.502 - 2 0.0318 .0048 0.20 9320 2.050 0.632 - 2 0.0428 .0086 0.25 9150 1.910 O.76O - 2 0.0575 .0144 0.50 8890 1.750 0.901 - 2 O.O796 .0239 0.35 85OO 1,590 0.032 - 1 0.1070 .0374 0.40 7750 1.420 0.147 - 1 0.1400 .0560 0,45 6750 1.240 0.254 - 1 O .I79O .0805 0.50 56OO 1.080 0.330 - 1 0.2140 .107 V I I V I I I IX X X I X I I X I I I 775 °C 825 °C %a(Pb) lo§ Y Na(775) / Na(775) a Na(775) l 0 g r N a ( 8 2 5 ) yNa(825) a Wa(825) 0.05 0.523 - 2 0.0333 .0017 0.616 - 2 0.0413 .0021 0.10 O.5I+6 - 2 0.0351 .0035 0.636 - 2 0.0432 .0043 0.15 0.601 - .2 O.O399 .0060 O.69O - 2 0.0490 .0073 0 .20 0.730 - 2 0.0537 .0107 O.818 - 2 O.O658 .0132 0.25 O.856 - 2 O.O718 .0179- 0.942 - 2 0.0875 .0219 0 .30 O.99I+ - 2 O.O986 .0296 O.O78 - . 1 0.1200 .0360 0.35 0 . 1 2 1 - 1 0.1320 .0462 0.201 - 1 O .I59O .O556 o.4o 0.229 - 1 0.1690 .0676 0 . 3 0 1 - 1 0.2000 .0800 0.45 0.325 - 1 0.2110 .0949 0.388 - 1 0.2440 .IO98 0.50 O.389 - 1 0.2450 .1225 0.441 - -1 O.276O .1380 F i g u r e B - 1: 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 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 L i t t l e 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 d i a g r a m . F i n k e t a l . 2 ? i n v e s t i g a t e d t h e s y s t e m u s i n g d i r e c t and d i f f e r e n t i a l t h e r m a l a n a l y s i s , and 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 w e i g h t p e r c e n t sodium 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 t h e 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. They a t t e m p t e d t o d e t e r m i n e t h e s o l i d s o l u b i l i t y by r e s i s t i v i t y measurements, b u t were n o t s u c c e s s f u l i n t h i s 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 , however, t h e y c o n c l u d e d t h a t t h e s o l u b i l i t y o f sodium was l e s s t h a n 0.003 p e r c e n t a t a l l t e m p e r a t u r e s below t h e m o n o t e c t i c . ?8 . R a n s l e y and N e u f e l d i n v e s t i g a t e d t h e l i q u i d - m i s c i b i l i t y bound-a r y b y f u s i o n o f aluminum i n t h e p r e s e n c e o f e x c e s s sodium, f o l l o w e d b y r a p i d q u e n c h i n g o f t h e m e l t and a n a l y s i s o f t h e a l u m i n u m - r i c h l a y e r . The r e s u l t s 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 sodium, and i n d i c a t e d t h a t t h e s o l u b i l i t y i n c r e a s e d r e g u l a r l y w i t h t e m p e r a t u r e . The d a t a f r o m t h i s 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 u s e d t o c o n -s t r u c t t h e phase d i a g r a m s , f i g u r e s C - l and C - 2 . . R a n s l e y and N e u f e l d ' s d a t a on t h e s o l u b i l i t y o f sodium i n t h e l i q u i d phase was p l o t t e d as l o g N^ a a g a i n s t I / T i n f i g u r e C - J . The s l o p e o f t h e l i n e y i e l d s a v a l u e o f t h e 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 sodium i n aluminum o f 92J0 c a l o r i e s / m o l e . 1 1 1 1 660.5 v A 660.0 1 Temperature,.°C 659.5 659.O ..Fink e t a l . 2 ? 28 R a n s l e y and N e u f e l d 658.5 1 1 1 1 I I 1 1 1 0 0.02 0.0U 0.06 0.08 0.10 0.12 0.l4 0.16 0.18 0.20 Weight P e r c e n t Sodium : F i g u r e C - 1: 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 . - 75 -Figure 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 of Sodium. - 76 -TABLE C - l . Partial:.Molal- Heat of Solution of Sodium in Aluminum. (Ransley and Neufeld 2 8). Wt. Percent Sodium N^ a T(°C) T(°K) l /T x 1 0 5 0.l4 0.001643 665 938 1.066 0.15 O.OOI76I 670 943 1.060 0.15 O.OOI76I 670 943 1.060 0.18 0.002112 700 973 1.028 0.22 0.002582 725 998 1.002 0 .20 0.002347 725 998 1.002 0.23 O.OO2699 750 1023 0.977 0.22 0.002582 750 1023 0.977 0.25 0.002934 775 1048 O.952 - 78 -- BIBLIOGRAPHY 1 . • Grunert,,E.,; Z.. Electrochem. . 48, .393 (194-2). 2. Jander, ,W. ,. and Herman,. H. ,•Z. anorg. allgem. Chem. 239_, 65 (1938). 3. Pearson,..T. G.,. and Waddington, J . , . D i s c u s s i o n s of the Faraday .. Society,. 1, 307 (194 -7) . 4. Hollingshead,. E.•A., p r i v a t e communication. 5 - - Dewing,,E. W.,.private communication. 6. Stokes, J . J . J r . , and-Frank,. W. • B., "Spectroscopic I n v e s t i g a t i o n of the Occurrence of' Sodium i n the Fumes above Molted C r y o l i t e " , i n "International.Symposium on the E x t r a c t i v e M e t a l l u r g y of Aluminum", ed: G. • Gerard,. I n t e r s c i e n c e (I963). 7. Feinlab,. 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