UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The activity of sodium in cryolite-aluminun melts Aylen, Peter Eric John 1962

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
[if-you-see-this-DO-NOT-CLICK]
UBC_1962_A7 A9 A2.pdf [ 6.04MB ]
Metadata
JSON: 1.0105803.json
JSON-LD: 1.0105803+ld.json
RDF/XML (Pretty): 1.0105803.xml
RDF/JSON: 1.0105803+rdf.json
Turtle: 1.0105803+rdf-turtle.txt
N-Triples: 1.0105803+rdf-ntriples.txt
Original Record: 1.0105803 +original-record.json
Full Text
1.0105803.txt
Citation
1.0105803.ris

Full Text

THE ACTIVITY OF SODIUM IN CRYOLITE-ALUMINUM MELTS by PETER- ERIC JOHN AYLEN A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE. REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of METALLURGY We accept this thesis as conforming to the standard required from candidates for the degree of MASTER OF APPLIED SCIENCE Members of the Department of Metallurgy THE UNIVERSITY OF BRITISH COLUMBIA August I962 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 o f the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y c f B r i t i s h Columbia,. I agree t h a t , t h e 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 s t u d y . 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 e x t e n s i v e c o p y i n g o f 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 g r a n t e d by t h e Head o f my Department o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f 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 o f M e t a l l u r g y  The U n i v e r s i t y o f B r i t i s h Columbia, Vancouver Canada. Date September 5, 1962 ABSTRACT Activities of sodium in alumina-saturated cryolite-aluminum melts have been measured by the equilibration of a three phase system of cryolite, aluminum and.lead. An approximate linear increase in the activity of sodium was noted on a log plot of activity as a function of NaF-AlF^ weight ratios over the range pertinent to commercial reduction cel l operation. Activities of sodium in cryolite-aluminum melts have been calculated by employing the equilibrium reaction between cryolite and aluminum metal and the thermodynamic data from-an analysis of the NaF-AlF^ phase diagram. Differences between the reversible deposition potential for aluminum and sodium at one atmosphere partial pressure were calculated from the measured equilibrium sodium activities. .The values obtained were of the order of . 15 to .kO volts, increasing with decreasing NaF-AlF, ratio. ACKNOWLEDGEMENT The author g r a t e f u l l y acknowledges Dr. C. S.Samis f o r h i s s u p e r v i s i o n and i n s t r u c t i o n during the course of t h i s work. Thanks are a l s o extended t o Mrs. A. M..Armstrong and Dr. E..peters f o r t h e i r h e l p f u l suggestions and t o the s t a f f of the computing centre who a s s i s t e d w i t h the mathematical i n t e r p r e t a t i o n and programming f o r one s e c t i o n of the t h e s i s . The author wishes t o thank the K a i s e r Aluminum and Chemical Cor p o r a t i o n , the Aluminum Company of Canada, L i m i t e d , and Aluminium L a b o r a t o r i e s L i m i t e d f o r supplying m a t e r i a l s and in f o r m a t i o n and c a r r y i n g out analyses. . The author i s g r a t e f u l t o the N a t i o n a l Research C o u n c i l of Canada f o r the f i n a n c i a l a s s i s t a n c e which made t h i s work p o s s i b l e . TABLE OF CONTENTS Page INTRODUCTION ' 1 1. Summary of Previous Work 2 (a) Activity of Sodium 2 (b) Dissociation of Cryolite h . (c) Effect of Additives 5 .' 2. Object and Scope of the Present Investigation 6 EXPERIMENTAL 8 1. Saturation of Cryolite with Alumina 8 (a) Materials 8 (b) Crucible 9 (c) Furnace . . . . . . 9 (d) Temperature Control • 9 (e) Procedure 9 2. Preparation of Lead Sodium Alloy 11 (a) Materials . . . . . . . . . . . 11 (b) Crucible 11 (c) Furnace 11 (d) Temperature Control . 11 (e) Procedure 11 3. Equilibrium Studies 12 (a) Materials . ' 12 (b) Crucibles 12 (c) Furnace . . . . . . 12 (d) Temperature Control 12 Table.of Contents Continued Page (e) Procedure 15 (f) Chemical Analysis 15 (g) Determination of Activities of Sodium 15 (h) Equilibration Time . . . l 6 (i) Equilibration Temperature 18 RESULTS . 21 1. Displacement of Theoretical Activity Line by Dilution 22 2. Activity of Sodium in Contact with Alumina-Saturated Pure Cryolite . 22 3. Activity of Sodium in Contact with Commercial Reduction Cell Electrolytes 25 h. Effect of CaF2 Content on the Activity of Sodium in Contact with Alumina-Saturated Pure Cryolite . . 25 5. Effect of CaF2 Content on the Activity of Sodium in Contact with Commercial Reduction Cell Electrolyte 28 6. Discussion of Dilution F a c t o r . . . . . . . 28 7. Comparison of Activity Results . . . . . . . . . . . . 31 8. Determination of. Activity Data for NaF and AlF^ . . . 31 DISCUSSION 37 1. Comparison with Previous Work . 37 2. Effect of CaF2 Addition on Sodium Activity . . . . . 37 INTERPRETATION OF RESULTS IN TERMS OF COMMERCIAL OPERATION . kO CONCLUSIONS kk RECOMMENDATIONS FOR FUTHER WORK kf APPENDICES kQ A. Analysis of Pb-Na Binary System . . kQ B. . Calculation of K Equilibrium 6k C. Analysis of NaF-AlF„ Binary System 69 Table of Contents Continued Page D. Dilution, Calculations . . 86 E. Experimental Results . . . 92 F. Mathematical Analysis and Computer Data . 96 G. Analysis of Na-Al Binary System 102 BIBLIOGRAPHY Il6 LIST OF FIGURES Figure Page  Number 1. Sodium Content of Liquid Al in Equilibrium with Molten ' Mixtures of NaF and AlF^- Crossed circles from Jander and Hermann-'--'-, open circles from Pearson and Waddington-^. (Diagram from Grjotheim^) 3 2 . Construction Details of Experimental Furnace for Alumina Saturation 10 3- Experimental Setup and Furnace 13 k. Cross-Section of Experimental Setup Ik 5. Cross-Section of Experimental Setup for Temperature Check 19 6. Plot of *?Na vs. NaF-A1F3 Ratio. ' . . 23 7. Plot of 9S$& vs.. NaF-AlFo Ratio for Alumina-Saturated Pure Cryolite . . . . . . 5 . 2k 8. Plot of .*?Na vs. NaF-AlFo Ratio' for Commercial Reduction . Cell Electrolytes . 26 9 . Plot of ^Na vs. NaF-AlF^ Ratio for Alumina-Saturated Pure Cryolite containing CaFg . . . . . . . . . 27 10. Plot of fNa vs. NaF-AlF^ Ratio for Commercial Reduction Cell Electrolyte containing CaFg 29 11. Comparison of ^Na Curves for Pure Cryolite and Cryolite containing 22$> Diluent 30 12. Composite Plot of ^Na vs. NaF-AlF^ Ratio 32 13. Experimental and Theoretical Activity Data for NaF and AIF3 3^ Ik. Activity Data for NaF 35 15. Activity Data for AlF^. 36 16. Comparison of Activity Data 38 17. Difference Between Reversible Deposition Voltages of Na and Al as a function of NaF-AlF_ Ratio k2 Page A - l . . Significant Section of Pb-Na Binary ^ 9 A-2. Temperature Coefficient of EMF from Hauffe and Vierke's Data 5 2 A - 3 - Plot of Log.^vs. l /T from Feinleib and Pprter's Pb-Na Activity Data . 5 5 A-h. Plot of Log ^Na. vs. N^ . for Feinleib and Porter's and ( l - N N a ) 2 a Hauffe and Vierke's Data . . . . 5 7 A-5. Partial heats of solution of Pb-Na Alloy 6 0 A-6. Plot of Log t^Na V S . . . I / T for Na Data 6 l A-7- Activity of Na in Na-Pb Alloys as a Function of Concentration at 1 0 1 0 ° C 6 3 2 C-l NaF-AlF^ Phase Diagram (Diagram from Grjotheim ) 7 1 C-2. Plot of Log ^ NaF vs. N • 8 l N 2 AlF^ C-3. Plot of Log X A l F n vs. N„ 8 3 D-l . Liquidus Diagrams for Cryolite-Alumina with 5 > 1 0 , 1 5 and 2 0 $ 8 7 Aluminum Fluoride (Diagram from Fenerty and Hollingshead32) D-2. Liquidus Diagrams for Cryolite-Alumina with 5 , 1 0 , 1 5 and 2 0 $ Calcium Fluoride (Diagram from Fenerty and Hollingshead-^) 8 7 D-3. Liquidus Diagrams for Cryolite-Alumina-10$> Aluminum Fluoride with 5 , 1 0 , and 2 0 ^ Calcium Fluoride (Diagram from Fenerty and Hollingshead32) 8 7 F - l . Computer Program . . . 1 0 0 G-l . Na-Al Phase Diagrams from Data of Fink et a l . and Ransley and Neufeld 10k G-2. Plot of Log N vs. l /T for Ransley.and Neufeld's Data . . . 1 0 6 G-3« Sodium Content of Aluminum from Reduction Cells as a Function of NaF-AlF^ Ratio (from Hbllingshead23) . . . 1 0 9 G-k. Revised Na-Al Binary 1 1 0 G-5« Activity of Sodium as a Function of Concentration in Al Metal . Ill* G-6. Activity of Sodium as a Function of Weight Per Cent Na in Al Metal. . . 1 1 5 LIST OF .TABLES Table Page I. . . Analyses of Cryolite . . . . . . . . . • • • • 9 II. Analyses, of Lead-Sodium Alloys . . . . . . . 1 2 III. Equilibrium Time Data 1 7 ,IV. Equilibrium Temperature Data 2 0 V. Difference between Reversible Deposition Potentials of Na and Al (EL) kl A-I. Temperature - EMF Data for Pb-Na Alloys . . 5 1 ATII. Pb-Na Activity Data at 4-7 5°C . 5 6 A-III. Pb-Na Activity Data . . . . . . . . 5 8 A-IV. Composite Pb-Na Activity Data 6 2 C-I. Determination of ^NaF by Integration of ^  Compound NaoAlFg in NaF-AlF3 Phase Diagram 7 3 C-II. Determination of ^NaF by'Integration of Compound Na^Al^F]^ in NaF-AlF3 Phase Diagram . . . 7 7 C-III. Determination of ^MaF by Integration of Compound NaAlFi,. in NaF-AlF^ Phase Diagram 7 8 C-IV..' Determination of ^ l F ^ by Gibbs-Duhem Integration 7 9 C-V.. Activity, .Data, for NaF and AlF^. from Phase Diagram. . . . . 8k C-VI. Activities of Sodium from Phase Diagram 8 5 D-I. Sodium Activities for Cryolite (Dilution Factor . 8 8 ) . . . . 8 8 D-II. Sodium Activities for Cryolite (Dilution Factor . 8 2 5 ) . . . 8 9 D-III. Sodium Activities for Cryolite (Dilution Factor .84) . . . . 9 0 D-IV. Sodium Activities for Cryolite (Dilution Factor . 7 8 ) . . . . 9 1 E-I.'.. Sodium Activities (Alumina-.Saturated Pure Cryolite) . . . . 9 3 E - I I i Sodium Activities (Alumina-Saturated Reduction Cell Electrolyte) . . . . . . . . . . . 9k E-III. Sodium Activities (Pure Cryolite and Reduction Cell • Electrolyte with.7/0 CaF2 Addition) 9 5 F-I. Activity Data for NaF and A l l y . . . . . . . . 1 0 1 List of Tables • Continued Table Page G-I. Partial Heat of Solution Data for Na-Al Binary 105 G-II. Sodium Content of Aluminum from Reduction Cells as a Function of NaF/AlF3 Ratio (from Hollingshead23) . . . . . . . . 108 G-III. Determination of Sodium Activity from Revised Na-Al Binary . 112 THE ACTIVITY. OF SODIUM IN CRYOLITE -ALUMINUM MELTS INTRODUCTION Aluminum is produced commercially "by the electrolytic reduction of aluminum oxide dissolved in molten cryolite (Na^AlFg). The technical process is based on the independent discoveries of Hall (U.S.A.) and Heroult (France) in'1886. .... ' .Although the process is over. 70 years old there is s t i l l a great deal of controversy over the mechanisms of the reactions involved. Some of the unsolved problems include the identification of the structural constituents of the melt, the mechanisms of the anode and cathode reactions, the significance of the metal fog formed when metallic aluminum is added to molten fluorides, and the question of which of the metals, sodium or aluminum, is reduced directly in the electrolysis. The various theories.which have been proposed to explain the situation are reviewed by Pearson , Grjotheim and Foster . .v^ ~. ; -:" One of the major reasons for the scarcity of knowledge in this f ield is the electrolyte Involved. Molten cryolite Is one of the most corrosive materials known. It vapourizes with decomposition at the melting point and changes its constitution and freezing point. It oxidizes in air to form alumina which dissolves in the melt and hydrolyses at high temperature in the presence of water vapour. The corrosive nature of aluminum metal is also a factor in the difficulties inherent in any study of the process. Aluminum alloys with practically a l l metals. Platinum is one of the few metals which wil l - 2 - withstand the attack of cryolite, but i t cannot be used i f aluminum is present. One of the practical problems associated with the electrolytic production of aluminum is the low current efficiency of the ce l l . This has been attributed by many investigators to the formation of metallic h 5 6 7 8 sodium.'. ' ' . As a result, considerable interest has been shown in the estimation or determination of sodium in aluminum metal in contact with the electrolytic melts. Recently i t has been suggested that formation of mono valent aluminum compounds, which are reoxidized at the anode, account for Q 10 - the low current efficiencies .. . Most probably the loss in efficiency is due to a combination of factors involving these processes as well as side reactions. 1. Summary of Previous Work (a) . Activity of Sodium The equilibrium between sodium and aluminum in contact with fluoride melts has' been studied by Jander and Hermann1"1". They investigated the equil ibrium reaction ( 3 N a F ) ( D + M ( D — G = s W ) . + l A a 3 > M ( 1 ) at 1090°C. in alumina crucibles in an atmosphere of dry, oxygen-free nitrogen. The concentration of sodium in liquid aluminum in contact with molten mixtures of sodium fluoride and aluminum fluoride was determined. No attempt was made to measure activities and the equilibrium constant was expressed in concent rations. The resultsof their investigation are shown in Figure 1. 12 Pearson and Waddington determined the sodium content of liquid aluminum at 1000°C. in contact with fluoride melts whose composition was close to that of cryolite. Their results are also shown in Figure 1. and show a fair agreement with those of Jander and.Hermann. - 3 - 0.1 0.2 ! 03 Cryolite N A I F , ~ * ~ 0.4 Figure 1 . . Sodium Content of Liquid Al in Equilibrium with Molten Mixtures of NaF and AlF^. Crossed circles from Jander and Hermann''""'",, open circles from Pearson and Waddington-'-2. (Diagram from Grjotheim2). Feinleib and Porter measured the' activities of sodium in molten aluminum in contact with cryolite saturated with alumina in order to determine the difference in decomposition potential between sodium and aluminum. Their work was carried out in alumina crucibles over a temperature range of 9^0-1010GC. An attempt was made to obtain final cryolite ratios of 1.50 by adjusting the in i t i a l composition of the melts, but a wide variation occurred. Lead was used as an auxiliary phase in the melts for the deter mination of sodium concentration and activity. An independent study was carried out to determine the activity of sodium in"sodium-lead alloys at Ik high temperatures . . (b) Dissociation of Cryolite In order to carry out a thermodynamic analysis of the NaF-ALF^ system, i t is necessary to have some idea of the degree and type of dissoc iation involved when cryolite melts. The effect of alumina and calcium fluoride additions to the dissociation is also of significance. Many hypotheses have been advanced concerning various dissociation schemes. These 2 are discussed in detail by Grjotheim . The most recent dissociation calculations have been carried out 2 - 15 by Grjotheim and Frank and Foster . Grjotheim based his calculations on a cryoscopic study of the NaF-AlF^ system, while Foster and Frank developed their scheme on the basis of the density of NaF-AlF^ melts. Both arrived at the same dissociation scheme. Na3AlFg 3Na+ + AlFg = (2) A 1 F 6 5 5=£> M F k " + 2F~ (3) The recent review by Foster J suggested that 31 per cent .of the NaF present in the melt is dimerized. The latter refinement is an attempt - 5 - to correct the failure of the previous theory to account for the experimental shape of the NaF side of the eutectic on the NaF-AlF^ phase diagram and.the electrical conductance. Several reaction schemes for the dissolution of alumina in cryolite l 6 have been studied by Foster and Frank and interpreted in terms of their 15 cryolite dissociation scheme . The activities of the solvent were calculated for the proposed equilibria. If the ionic constituents present are represent ative of the true equilibrium a plot of In a vs l /T wi l l result, in a straight line the slope of which is the heat of fusion of cryolite. Foster and. Frank found the most likely mechanism to be 3F" + A1 20 3 3/2A102" + 1/2A1F6£ (k) The addition of calcium fluoride to cryolite melts would be expected to add calcium and fluoride ions in the following manner CaF2 * Ca + + + 2F" (5) (c) Effect of Additives Foreign ions of AlgOg and CaFV) added to cryolite may (i) act only as diluents in the melt, or ( i i ) affect the activity of sodium. Grube and Hantelmann^ found in their studies that the presence of AlgO^ did not affect the reactions between sodium or aluminum and NaF-AlF^ melts. From an ionic standpoint (considering equations ( l ) , (2), ( 3 ) , and (k) i t would appear that AlgO^ would act primarily as a diluent in the melt. On the other hand the addition of fluorine ions from the dissociation of CaJV) (see equation (5) might decrease the activity of sodium due to a reversal of the cryolite dissociation (equations ( l) , (2), and ( 3 ) -- 6 - 2. Object and Scope of the Present Investigation The object of the present investigation was to determine the activities of sodium in aluminum metal in contact with cryolite melts over a range of NaF-AlF^ weight ratios between 1.00 and 2.00.* These sodium activities could then be related to the difference in deposition potential between aluminum and sodium in order to evaluate the likelihood of simultaneous sodium and aluminum deposition in commercial cells. The activity measurements were carried out using two different grades of cryolite (pure laboratory grade and commercial electrolyte containing 7-8$ Cal^). In addition, 7$ CaF2 w a s added to both grades of cryolite in order to assess the affect of CaJV, content on the sodium activity. Activities were determined experimentally by the equilibration of a three phase system of cryolite, aluminum and lead. Aluminum and sodium are highly immiscible and thermodynamic data for the Al-Na.system has not been measured. Therefore, lead was used as a third phase. Sodium conc entrations can be measured easily in lead and activities can be calculated from a calibration of the lead-sodium system. The experiments were restricted to cryolite melts saturated with alumina. Any readily available crucible materials other than alumina would introduce components into the melt which could affect the activities. As * Throughout this paper NaF-AlF^ ratio is used to represent the weight ratios, e.g. the compound cryolite (SNaF.AlF^) has an NaF-AlF^ ratio of 3NaF _ 126 _ 1.50 AIF3 W - 7 - commercial electroytes contain dissolved alumina in varying concentrations, the experimental technique used here can "be compared with the commercial operation at one stage. Activities were also calculated by a thermodynamic analysis of the NaF-AlF^ and the Na-Al phase diagrams. Thermodynamic data for NaF and AlF^ were calculated from the experimental results. The sodium-lead system was investigated to provide a consistent extrapolation of activity data to high temperatures. - 8 - EXPERIMENTAL The experimental procedure involved the equilibration of cryolite (alumina-saturated) with, pure aluminum metal and a sodium-lead alloy. The reaction was carried out in alumina crucibles and the heat supplied by an induction furnace. At, the end of each run the crucible was air quenched to.preserve the equilibrium conditions, the phases separated and samples taken for analysis. As a preliminary step_. i t was necessary to adjust the composition of the starting materials. The cryolite was saturated with AlgO^ in order to prevent destructive attack of the crucibles and AlF^ and CaJV) were added to synthesize melts of a desired composition. Lead-sodium alloys were prepared and used in the runs. The use of induction heating made i t necessary to make a check of the temperature of the melt. Recorded temperatures were taken outside the reaction crucible and would therefore be slightly in error i f the melt were to act as a suseeptor. 1. Saturation of Cryolite with Alumina (a) Materials Cryolite samples were kindly supplied by the Kaiser Aluminum and Chemical Corporation, Spokane, Washington and by Aluminium Laboratories Limited, Arvida, Quebec. Analyses of the three materials used are shown in Table I. - 9 - TABLE I. Analysis of Cryolite Material Pure Cryolite Reduction Cell Electrolyte Reduction Cell Electrolyte The alumina used was Alcoa A-10 and the aluminum fluoride was supplied by Aluminium Laboratories. This material was 89.8$ grade, with the major impurity alumina. Sodium fluoride and calcium fluoride were Baker and Adamson reagent grade. (b) Crucible A standard form 300 cc-Engelhard Platinum evaporating dish, No. 202, was used as the container for the preparation of the saturated cryolite. (c) Furnace A simple glo-bar furnace was used. Construction details are shown in Figure 2. The source of power was a kva transformer. (d) Temperature Control Temperature control was maintained by a platinum, platinum 10$- rhodium thermocouple attached to a "Wheelco" mercury switch controller. (e) Procedure Saturated cryolite was prepared in batches of 200 to 350 grams. Alumina, AlF^, NaF and CaF2 were added in varying proportions in order to produce saturated cryolite of different NaF-AlF^ ratios and CaF2 contents. The batches were mixed and placed in the furnace. The temperature was raised to 1100°C. and reduced to 1000°C. after the material became molten. N'aF-AlF^ Ratio CaFP Free Alp03 1.52 - 0.25$ 1.55 7.6$ h.O i 1.39 8.2$ 5-6 $ - 10 - Figure 2 . Construction Details of Experimental Furnace for Alumina Saturation. - 11 - The mixture was stirred with a Morganite recrystallized alumina rod (see Figure 2) for 30 minutes and then removed from the furnace and air- cooled to prevent segregation of the melt. 2. Preparation of Lead-Sodium Alloy (a) Materials American Smelting and Refining Company Test Lead, high purity lead f o i l and Baker and Adamson reagent grade sodium were used. (b) Crucible. The materials were melted in a graphite crucible. (c) Furnace A small 230 volt, 3600 watt "Multiple Unit" electrical resistance, muffle furnace was used for the melting operation. (d) . Temperature Control Temperature control was maintained by a chrome1-alumel thermo couple attached to a Hoskins hunting device controller. (e) Procedure Three batches of Pb-Na alloy were prepared in the following manner. Test lead was melted in the graphite crucible at 600°C. in the muffle furnace. Sodium metal was cleaned of oxide material and wrapped in lead f o i l . The lead-covered sodium was immersed in the molten lead, using a hollowed graphite rod. When sufficient sodium had been added to the molten lead the slag was skimmed and the metal poured into a stainless steel tray. After cooling, the metal was kept in a vacuum desiccator until used. An analysis of the three batches is shown in Table II. - 12 - TABLE II. Analyses^of Lead-Sodium Alloys •No. Na Content (wt.$) 1 . 8 . 6 $ 2 • 6.6 $ 3 2.8 $ 3. Equilibrium Studies (a) Materials The materials used for these studies included those prepared in Parts 1 and 2 of this section. Other materials used included super-purity Alcan aluminum. (99-99$) and the alumina, AlF^, NaF and Pb which have been discussed in the last two sections. (b) Crucibles The experimental equilibration measurements were carried out in McDanel vitrif ied alumina crucibles. Covers for the crucibles were fabri cated from 99$ AI2O3 .brick, made by Harbison Walker. The graphite susceptor crucible and l i d were machined out of graphite stock and this was enclosed in a large fireclay crucible (see Figures 3 and k). (c) Furnace A 170/550 v, 3 phase, 12 kw output, Phillips induction furnace was used (see Figure 3) for the experiments. (d) Temperature Control Temperature control was accomplished with a chromel-alumel thermo couple attached to an IMRA recorder. The Phillips induction unit had been adapted for automatic temperature control by hooking up a type PH 1653 regulating unit to the recorder and thermocouple, (see Figure 3)« - 13 - Figure 3. Experimental Setup and Furnace Figure k. Cross-Section o f Experimental Setup - 15 - (e) Procedure The materials were weighed and added to the crucible which was• placed inside the graphite susceptor. The experimental apparatus was set up as in Figure k. The temperature was raised to approximately 1000 ° C . and the regulator was set to control the temperature at this level. The time of the runs was chosen as two hours, after which the alumina crucible was removed and quenched with a fan in order to retain the equilibrium conditions. The melts were broken out of the crucible and the three phases separated. The lead was analysed for sodium content and the cryolite for NaF-AlF^ ratio, and CaJV> where necessary. (f) Chemical. Analysis Analysis of the lead phase for sodium was carried out using a Beckman flame spectrophotometer. Standard solutions of 0 , 0 2 5 , 0.05 and 0.1 mg/ml NaCl were used for calibration. Analyses of the cryolite were kindly carried out by the Kaiser Aluminum and Chemical Corporation, Spokane, Washington and by the Aluminum Company of Canada, Kitimat, B.C. (g) Determination of Activities of Sodium A summary of the thermodynamic data for the lead-sodium system is presented in Appendix A. An extrapolation of the known data to higher temperature has been carried out and the relationship between activities of sodium in lead and the concentration of sodium in lead is shown in Figure A-7. As a result of the thermodynamic equilibrium established in the experimental procedure, the measured concentrations of sodium in lead can be converted directly to equivalent activities of sodium in aluminum using Figure A-7. - 16 - (h) Equilibration Time The reaction time of two hours was chosen as a result of previous work. Jander and Hermann"^ stated that a period of one hour was sufficient for the melt to reach equilibrium. However Feinleib and Porter^3 found that i t was necessary to react their melts for a period of two hours, and attributed this to the fact that they had lead as an additional phase in the system. They used intermittent stirring in an attempt to reach equilibrium as quickly as possible. In this work i t was hoped that susceptance by the melt would cause enough stirring action for equilibrium to be reached within two hours. As a check on the establishment of equilibrium conditions, two sets of special runs were prepared. One set was made up with an excess of NaF in the bath, and a similar amount of Na was removed from the lead phase. The second set contained an excess of AlF^ in the bath. Both sets contained exactly the same quantity of the significant materials, but the distribution between the phases of the system was changed. The two sets were subjected to the same test conditions and compared to see i f they approached the same equilibrium values as a normal run. As a further check on the equilibrium, one of the standard test runs was extended to four hours. The composition and results of the two sets of equilibration check runs are shown in Table III. The analyses are in reasonable agreement and are within experimental error. The results of the four hour run (# 6 l ) show l i t t l e deviation from comparable two hour runs. Therefore i t can be assumed that equilibrium was reached in the period of two hours. -.17 - Run NaT 41 20.25 gm 20.0 gm 19-36 gm 60.0 gm 1.17 gm 42 20.0 gm 40.0 gm 60.0 gm O.78 gm 43 20.0 gm 40.0 gm 60.0 gm 59 20.25 gm 20.0 gm 19.36 gm 60.00 gm 1.17 gm 6o 2.0.0 gm 40.0 gm 60.0 gm O.78 gm 6 l 20.0 gm 40.0 gm 60.0 gm TABLE III. Equilibrium Time Data Composition Time Wt.$ Na ^Na NaF-AlF, Ratio Al 2 hrs 2.20 .024 1.42 Pb-Na alloy (3) 1.4l .Pb (high purity foi l) Na3AlF6 (9) NaF Al 2 hrs 2.40 .027 1-44 Fb-Na (3) 1.37 Al 2 hrs 2.60 .030 1.45 Pb-Na (3) 1.43 Al 2 hrs 1.50 .018 1.25 Pb-Na alloy (3) 1.27 Al 2 hrs 1.70 .019 1.24 Pb-Na alloy (3) 1.20 NaqAiFg (16) 4 hrs 1.80 .015 1.26 Fb-Na alloy (3) 1.18   Na^AlFg (16) - 1 8 - (i) Equilibrium Temperature The experimental setup, shewn in' Figure k. was designed to provide equilibrium heating conditions. It was assumed that a constant temperature could be maintained within the graphite crucible due to the four TT geometry. However, i f the melt were to act as a susceptor as well, there would be a thermal gradient between the alumina crucible and the graphite susceptor and the recorded temperature would be slightly in error. A check on the accuracy of the recorded temperature readings was made by designing a special experimental setup to obtain an independent temperature measurement within the melt, (see Figure 5 ) . An otherwise normal equilibration run was made and potentiometer readings taken at specific intervals. The data collected are presented in Table IV. The potentiometer readings taken from the thermocouple immersed in the melt, increased slowly for- an hour and then remained stable at 4 l . 7 mv ( l 0 1 0 ° C . ) which was 0 . 4 mv ( 1 0 ° C . ) above that of the recording thermocouple. The equilibrium temp erature in. this, study has therefore been taken as 1 0 1 0 ° C . ± 5 ° C . The results of the temperature study suggest that the melt acts as a susceptor. Therefore considerable stirring action could be expected which would assist in attaining equilibrium. - 19 - Check Thermocouple Fire cloy C r u c i b l e Recording Thermocouple Graphite Crucible Alumina Crucible Figure 5. Cross-Section of Experimental Setup for Temperature Check - 20 - TABLE IV. Equilibration Temperature Data IMRA Recorder Temperature Pye Potentiometer Temperature' mv. ,°C. mv. ^C. •41.3 1010 4 l . l 994 " . " 4l.4 1002 . " " 41.6 1007 41.6 1007 41.7 1010 " 41-7 1010 " 41.7 1010 " " 41.7 1010 21 - RESULTS The molten material in an aluminum electrolytic cel l consists of two phases, aluminum metal (which acts as the cathode of the cell) and cryolite (which acts as the electrolyte). A thermodynamic equilibrium exists between the two phases, which is expressed by the simplified equation A l ( l ) .+ '(3NaF)(l) ( A 1 F 3 ) ( 1 ) + [ 3Na ] ( d l l ) . . . . (1) The free energy ^ ^ 2 8 3 f o r ^ e r e a c t i o n n a s "been calculated in Appendix B and is equivalent to 62,915 calories. log K = -62,915 = 10.72 . 4.575 (I283) K for the reaction is equal to fea]3 X (fAlFp = 1.91 X l o " 1 1 «A1 X (?NaFj3 As the solubility of sodium in molten aluminum is of. the order of .01$, the activity of aluminum metal can be considered as unity. Therefore, a deter mination of the ratio of activities of aluminum fluoride and sodium fluoride in cryolite would provide sufficient information to solve the equilibrium equation for the activity of sodium in the system. Activities of NaF have been calculated from the NaF-AlF^ phase 27 28 19 diagram. The technique used was developed by Wagner ' ' for determining activities from phase diagrams having inter-metallic compounds. Activities of AlF^ were calculated using the Gibbs-Duhem equation. The calculation methods for the determination of the activities is discussed in Appendix C and the data presented. - 22 - The e q u i l i b r i u m equation i s solved f o r p e r t i n e n t data over the range of NaF-AlF^ r a t i o s employed i n commercial aluminum p r a c t i s e . The a c t i v i t i e s of sodium are p l o t t e d as a f u n c t i o n of NaF-AlF^ r a t i o i n F i g u r e 6 . and t h i s curve w i l l be designated AB i n subsequent s e c t i o n s . 1. Displacement of T h e o r e t i c a l A c t i v i t y Line by D i l u t i o n I f both alumina and calcium f l u o r i d e are considered only as d i l u e n t s i n the melt the a c t i v i t i e s of RaF and A l F ^ c a l c u l a t e d i n Appendix C can be adjusted by a d i l u t i o n f a c t o r and the a c t i v i t i e s of sodium c a l c u l a t e d f o r melts c o n t i n i n g these i m p u r i t i e s . The d i l u t i o n f a c t o r can be estimated on 32 the b a s i s of the phase diagrams of Fenerty and Hollingshead which are presented i n Appendix D. These diagrams show the s a t u r a t i o n l i m i t s of alumina as a f u n c t i o n of content and CaJV, content. 2. A c t i v i t y of Sodium i n Contact w i t h Alumina-Saturated Pure C r y o l i t e Measured sodium a c t i v i t y values f o r alumina-saturated pure c r y o l i t e , and alumina-saturated pure c r y o l i t e plus 5$, 10$, 15$ and 20$ AIF3 are p l o t t e d i n F i g ure 7- as a f u n c t i o n of NaF-AlF^ r a t i o . The data are shown i n Table E-I. The t h e o r e t i c a l curve AB (see Figure 6 ) i s adjusted by an average d i l u t i o n f a c t o r of . 8 8 and i s shown as a dotted l i n e i n Figure 7- The d i l u t i o n f a c t o r i s obtained from Figure D-l and the a c t i v i t y c a l c u l a t i o n i s c a r r i e d out i n Table D-I. A s t r a i g h t l i n e has been drawn through the experimental p o i n t s and appears i n Figure 7* as a s o l i d l i n e CD. This l i n e i s used i n subsequent s e c t i o n s as a reference l i n e . .06 .ok .02 .01 008 006 00k I A / A 002 A' i . lo A - A / / / A s 001 , , , . I.OO ITTo O o 1T30 rn+o IT50 NaF-AlF^ R a t i o F i g u r e 6. P l o t of ^Na vs. NaF-AlF^ R a t i o - 25 - 3. A c t i v i t y of Sodium i n Contact with Commercial Reduction C e l l Electrolytes Commercial reduction c e l l electrolytes (alumina-saturated) of i n i t i a l NaF-AlF^ ratios.of 1.55 and 1-39 were used i n t h i s section of the study. Analyses are shown i n Table I. Measured sodium a c t i v i t y values for the two commercial electrolytes and f o r the commercial electrolytes ( r a t i o 1.55) plus 5$ and 10$ AlF^ are plotted i n Figure 8 as a function of NaF-AlF^ r a t i o . The data are shown i n Table E-II. The t h e o r e t i c a l curve AB (see Figure 6 ) i s adjusted by an average d i l u t i o n factor of .825 and i s shown as a dotted l i n e i n Figure 8. The d i l u t i o n factor i s obtained by a comparison of Figures D-2 and D-3, and the a c t i v i t y calculation i s carried out i n Table D-II. The reference l i n e CD from Figure 7- appears as a s o l i d l i n e i n the diagram. k. Effect of CaFg Content on the A c t i v i t y of Sodium i n Contact with Alumina- Saturated Pure Cryolite A batch of alumina-saturated pure c r y o l i t e was prepared with 10$ AlF^ and 7$ CaFg as additives for t h i s section of the study. Measured sodium a c t i v i t y values for the test runs using the above batch are plotted i n Figure 9 as a function of NaF-AlF^ r a t i o . The data are shown i n Table E - I I I . The t h e o r e t i c a l curve AB (see Figure 6 ) i s adjusted by a d i l u t i o n factor of .Qk and i s shown as a dotted l i n e i n Figure 9« The d i l u t i o n factor i s obtained from Figure D-3, and the a c t i v i t y calculation i s carried out i n Table D-III. - 26 r - 27 - Figure 9- Plot of ^Na vs. NaF-AlFg Ratio for Alumina- Saturated Pure Cryolite containing CaF? - 28 - The reference l i n e CD from Figure 7 appears as a s o l i d l i n e i n the diagram. 5. . E f f e c t of CaFp Content on the A c t i v i t y of Sodium i n Contact w i t h Commercial Reduction C e l l E l e c t r o l y t e A batch of commercial r e d u c t i o n c e l l e l e c t r o l y t e ( i n i t i a l r a t i o 1.55) was prepared w i t h the a d d i t i o n of 7$ CaF2> Measured sodium a c t i v i t y values f o r the t e s t runs u s i n g the above batch are p l o t t e d i n F i g u r e 10. as a f u n c t i o n of NaF-AlF^ r a t i o . The data are shown i n Table E - I I I . The t h e o r e t i c a l curve AB (see Figure 6) i s adjusted by a d i l u t i o n f a c t o r of .78 and i s shown as a dotted l i n e i n F i g u r e 10. The d i l u t i o n f a c t o r i s obtained from F i g u r e D-2, and the a c t i v i t y c a l c u l a t i o n i s c a r r i e d out i n Table D-IV. The reference l i n e CD from Figure 7 appears as a s o l i d l i n e i n the diagram. 6. D i s c u s s i o n of D i l u t i o n F a c t o r At t h i s p o i n t i t i s i n t e r e s t i n g t o note the e f f e c t t h a t d i l u t i o n has on the a c t i v i t y c a l c u l a t i o n . Values of a c t i v i t i e s f o r sodium which are adjusted f o r d i l u t i o n a f f e c t s are only s l i g h t l y lower than those obtained f o r pure c r y o l i t e . This i s due t o the r e l a t i o n s h i p between NaF and A l F j i n the c a l c u a t i o n . The curve r e t a i n s the same shape w i t h very l i t t l e displacement up t o a d i l u e n t content,of 22$. A comparison of the a c t i v i t y r e l a t i o n s h i p s between pure c r y o l i t e and c r y o l i t e c o n t a i n i n g 22$ d i l u e n t i s shown i n F i g u r e 11. As the experimental r e s u l t s noted i n t h i s study l i e w i t h i n t h i s range of d i l u t i o n i t i s reasonable t o consider a l l the r e s u l t s as b e i n g compatible w i t h one another. The d i f f e r e n c e s i n a c t i v i t i e s w i l l not be s i g n i f i c a n t and should l i e w i t h i n experimental e r r o r . - 29 -.2 .1 .08 .06 .ok .02 .01 008 006 004 002 1 B , A A" A'' A , " /A' A / A' - A - ' «A-~ .A' ^ A ' ' A' A - ' A Pure Cryolite A Pure Cryolite (Dilution Factor .88) A / / A / s A' A 00 1.10 1.20 1.30 1.40 1750 I76o I770 TTKo NaF-AlF^ Ratio Figure 11. Comparison of <?Na Curves for Pure Cryolite and Cryolite containing 22$ Diluent. - 31 - 7» .Comparison of Activity Results The data from Figures 7, 8, 9, and 10 is combined and presented in a single plot in Figure 12. as a function of NaF-AlF^ ratio. The theoretical curve from Figure 6 is superimposed on the plot as a dotted line AB. The reference line CD from Figure 7 appears as a solid line. This line f its a l l of the experimental data reasonably well except for the points at high ratio which contained an excess of CaFg ()> 10$). 8. Determination of Activity Data for NaF and AlFg The reference line in the preceding figures has been used to analyse the experimental data and determine thermodynamic properties of NaF arid AlF^ over the experimental range. The analysis can be carried out by solving two simultaneous equations and a differential equation, assuming that one of the values on one of the log V curves developed in N 2 Appendix C. is correct (see Figures C-2,C-3 ). The tie point E was chosen as NA-jjp = .223 which corresponds to an NaF-AlFo ratio of 1-75 and the 3 ' • ^ corresponding activity coefficient (V) was taken from the log ^ NaF NA1F, 2 curve (see Figure C-2) as the starting point for the computation. -3 The choice of the tie point E was made because of its proximity to the tie point for the compound integration of cryolite at N^-JJ, = -165, (the eutectic between NaF and NaoAlFg)." Furthermore, the log ^NaF curve should AlF^ be more accurate in this range as any error in the 3 regular solution correction would have l i t t l e effect. A computer program was written and the computation was carried out on an IBM 1620. The mathematical analysis, computer program and data appear in Appendix F. - 33 - Log o NaF and log 3 curves have been obtained from this N A1F 3 2 . %aF 2 data and are plotted in Figures 13,-lh and 15• An attempt to obtain heat of solution data from this calculation was not successful due the sensitivity of the numbers in this range. It would appear that the tie point E at %.1F3 = * 2 23 i s slightly in error, possibly due to the shape of the liquidus curve of the cryolite compound in the NaF-AlF^ phase diagram. The flattening of the compound peak (see Figure C-l) due to dissociation may introduce small errors in the compound integration technique for activity calcuations. Figure 13 compares the two experimental log curves over the range of experimental measurements. The two theoretical curves are super imposed as dotted lines on the diagram. If the tie point E were raised slightly, both experimental curves would be shifted higher and more in line with the theoretical curves. A smoothing out of the theoretical log NaF N A1F 3 2 curve in the region of the tie point would raise the tie point and this change could be substantiated i f a discrepancy occurs in the compound integration technique. Figure Ik and 15 compare each of the experimental log *6 curves with their theoretical counterparts over the fu l l range of theoretical calculation. The general shapes of the curves compare favourably. -28 •2k >o -20 •16 hi -12 r oo " -4 /A A' / / / / . A/ A " ' A - AT . A ' A~_ A - -A- -A-A' A' A ^ /• / t , A A Theoretical A Calculated A- -AA- A 1.0 N, NaF Figure lk. Activity Data for NaF -20 ^ ' ^ - Q D - O - O - o - O o ^ „ n - - Q - 0 - 0 . •16 •— ,Cr' OCT'" 0 - . -12 ro i 1 OJ 5 O Theoretical A Calculated o o 1.0 • 9- .8 N NaF • 5 Figure 15. Activity Data for AIF3 DISCUSSION 1. Comparison with Previous Work The sodium concentration data of Pearson and Waddington, Jander and Hermann (see Figure l) and Hollingshead (see Figure G-3) can be related to the activities of sodium by using the calibration curve (see Figure G-6) developed in Appendix G. The majority of these data are in reasonable agreement with the experimental line CD developed in this study, particularly at.NaF-AlF^ ratios common to commercial practise (see Figure l 6 ) . Activities determined from the experimental work of Feinleib and Porter-^ are also shown on this plot. The measured results were used to calculate activities using Figure A-7- Their, work, which was carried out at three different temperatures, shows some divergence from the results obtained here. Sodium activities determined at 9^0° and 1010°C. were somewhat higher than the experimental activity line. CD, whereas the values at 970°C. showed very good agreement 35 with the results of this study. A recent paper by Stokes and Frank outlines a method of determining activities of sodium, by a spectroscopic measurement of sodium in the vapour phase above molten cryolite. The study was carried out with pure cryolite of NaF-AlF^ ratio 1.50 over a temperature range from 700-1100°C. Their value for sodium activity at 1010°C. is plotted in Figure l 6 . along with a value from their thermodynamic calculations. The sodium activity calculated from thermodynamic data is in agreement with the results obtained here but their experimental value is significantly lower. 2. The Effect of CaFp Additions on Sodium Activity The activity of sodium in melts containing quantities of CaFg tends to.be lower than in pure cryolite, (see Figure 12). This can be noted between NaF-AlF-^ ratios of 1.35 and 1.4-5 where sodium activities have been determined for melts of pure cryolite and reduction cel l electrolyte. At lower ratios • 70 -90 1.10 1-30 1 .50 1-70 1-90 2.10 NaF-AlF^ Ratio Figure l 6 . Comparison of Activity Data - 39 - the effect is not as noticable although for melts of pure cryolite with additions of CaFg 't n e sodium activities are in the lower range of the results. A marked depression in the activities of sodium is noted at high NaF-AlF^ ratios for reduction cell electrolytes containing an excess of CaF2 (10-14$). The depression of the sodium activities at NaF-AlF^ ratios between 1.00 and 1.50 would appear to be explained by the effect of dilution. However, at higher ratios, the large depression cannot be explained by a dilution effect alone. It is possible that the large excess of fluorine ions, in the melt is tending to reverse the cryolite dissociation reaction either by a direct effect on the equilibrium or by increasing the amount of dimerized sodium fluoride. - u o - INTERPRETATION OF THE RESULTS IN TERMS OF COMMERCIAL OPERATION An interesting sidelight to this study is the relationship between the difference of the reversible deposition potentials of aluminum and sodium at one atmosphere partial pressure as a function of NaF-AlF^ ratio. The difference E^ is the extra voltage required to evolve sodium at one atmosphere pressure reversibly in conjunction with the reversible deposition potential of Al . Calculation of the extra voltage can be made by using the following expression E L = PT In nF #e where = the limiting activity and = "the equilibrium activity. This equation for the case of sodium at 1010°C. reduces, to E T = 2-55 X 1 0 " 1 log #L The limiting, activity ^L is equivalent to the sodium activity at one atmosphere partial pressure, that is = 1/PC where P ° = the vapour pressure in atmospheres of pure sodium at the temperature under consideration. This value can be calculated from 2U the expression log P/^N = -5780 -1.18 log T + 11.50 T Q P is equal to 2lU0 mm or 2.82 atmospheres at 1010 C. The limiting activity then becomes ^L = = .35^ 2.82 The equilibrium activity, *ZQ, is the activity of sodium at the cathode potential required to deposit aluminum reversibly. The differences in the reversible deposition potentials, E- ,^ have been calculated and the data appears in Table V. and in Figure 17 as a function of NaF-AlF3 ratio. - 41 - TABLE V. Difference between Reversible Deposition Potentials of Na and Al (E )^ Bath Ratio Na Activity E L 1.00 .OO85 4l3 mv 1.10 .0117 377 mv . 1.20 .0160 3U3 mv 1.30 . .0220 308 mv 1.40 .0305 272 mv 1.50 .0420 236 mv 1.60 . •• . • .O575 202 mv 1.70 .O78O 168 mv 100 1.00 1.10 1.20 1.30 l.kO 1.50 1.60 TTfO NaF-AlFo Ratio Figure 17. Difference Between Reversible Deposition Voltages of Na and Al as a function of NaF-AlF^ Ratio - 3^ - Commercial reduction cells, however, do not operate reversibly. The deposition o f aluminum in an electrolytic cel l is carried out as an irreversible electrode process. The cell is open to the air and the process operates under a pressure o f one atmosphere. Cathodic overvoltages are set up due to kinetics o f the reaction. If these overvoltages build up to the point where the limiting activity of sodium is exceeded, gaseous sodium could be produced in the melt. Providing there is no hindrance to the transport of the gaseous sodium i t wil l be liberated to the atmosphere, thereby decreasing the efficiency of the ce l l . The actual overvoltage required for the release of sodium at the cathode and its eventual liberation to the air may be somewhat more than the difference in the reversible deposition potentials. Not only may the sodium have its own overvoltage (probably very small in comparsion to that of aluminum) but sodium may exist in a gaseous form in a metastable condition in the melt due to pressure from the melt and transport phenomena. Therefore the data calculated here can only be considered as an indication of the order of overvoltage required for the simultaneous deposition and release of sodium. From the data in Figure 17 i t would appear that overvoltages of the order of .2-.k volts would cause sodium to be deposited at the aluminum cathode of the ce l l . As sodium is often observed in industrial cells i t seems probable that cathodic overvoltages in the cel l are high enough to exceed the necessary voltage difference for co-deposition of the two metals 10 and for the release of sodium gas. Piontelli and Montanelli indicate that at normal cathode current densities commercial reduction cells are operating at a cathode overvoltage of .k-.5 volts. However in a more 33 recent paper, - Piontelli indicates that these values are a maximum and that overvoltages of the order of .20 volts are more probable. - kk „ A well known characteristic of commercial reduction cells is the variation of current efficiency with NaF-AlF^ ratio. As the ratio increases, •current efficiency decreases. This trend can he related to the results obtained here. At high bath ratios an overvoltage of . 1 - . 2 volts may cause the deposition and release of"sodium, whereas at lower ratios a higher overvoltage is required. Even at low ratios, however, sodium deposition may be a factor in the current inefficiency of an aluminum reduction ce l l . During the daily operation of a ce l l , changes, in current densities and electrolyte composition may cause localized overvoltages on the aluminum cathode which exceed the cr i t ical value for sodium deposition and release. Furthermore throughout the l i fe of an aluminum reduction cel l variations occur in the current distribution to the metal cathode. These variations may effect current densities such that overvoltages in certain areas of. the cel l may exceed the cr i t ica l value. - ^ - CONCLUSIONS Activities of sodium in aluminum-cryolite melts have been measured ,by the equilibration of the three phase system alumina-saturated cryolite, aluminum and lead. An approximate linear increase in the activity of sodium was noted on a log plot of activity as a function of NaF-AlF-^ weight ratio over the range pertinent to commercial reduction cel l operation. Additions of CaFg to cryolite melts appeared to depress the activity of sodium slightly. Activities of sodium in aluminum-cryolite melts have been estimated by a' thermodynamic analysis of the NaF-AlF^ phase diagram, employin Wagner's technique of compound integration for the determination of activitie of NaF and the Gibbs-Duhem equation for the determination of activities of AlF^. Substitution of the activities of NaF and AlF^ in the K equilibrium equation for the reaction between-cryolite and aluminum metal gives the sodium activities. These theoretically determined activities show a fair agreement with the experimental values except at NaF-AlF^ ratios above 1.50. The experimental results are in fair agreement with previous work carried out by Pearson and Waddington, Jander and Hermann, Feinleib and Porter, and Hollingshead. The experimental data has been used to compute activity data for NaF and AlF^ which shows a fair agreement with the theoretical calculations. The difference between the reversible deposition potential of aluminum and that of sodium at one atmosphere partial pressure varies from .15-.H-0 volts over a range of NaF-AlF^ ratio of 1 . 7 0 to 1.00; increasing with decreasing ratio. Indications are that the cathodic overvoltages in - 46- commercial reduction, cells are high enough to cause the simultaneous deposition of sodium and aluminum and that this mechanism contributes to the current inefficiency of the ce l l . The relationship between the . differences in deposition potentials as a function of NaF-AlF^ ratio developed here- corresponds to observations made in commercial practise, that i s , current efficiency decreases as the NaF-AlFo ratio increases. - 4 7 - RECOMMENDATION FOR FURTHER WORK It could be of Interest to determine activities of sodium over a range of NaF-AlF-^ wt. ratios.of 1.00-2.00 using one basic material, alumina- saturated pure cryolite to determine i f their is any break in the experimental relationship of low activity sodium as a function of NaF-AlF^ ratio above ratios of I .50. The depressive effect of CaF^ additions on the activities of sodium indicated here may well be another field worthy of investigation. The effect on sodium activity of additions of materials such as MgFg, LiF, BeFg, NaCl, BaClg and KG1 could also be of interest as these materials have a l l been suggested for use in the electrolytic melts. Finally, a study of the pure system cryolite-aluminum would be of interest in order to resolve, the assumptions which i t is necessary to make when using saturated alumina melts. This study wi l l depend upon the develop ment of an inert container material. - k8 - APPENDIX A Analysis of Fb-Na Binary System - 49,- APPENDIX A Analysis of Pb-Na Binary System The lead-sodium binary has been investigated thoroughly and the 17 best representation of the data is given by Hansen . The significant section involved in this work lies in the range 60-100$ FD (see Figure A- l ) , 330 j- 60 70 80 90 100 Mole Per Cent Pb Figure A - l . Significant Section of Pb-Na Binary which includes the compound NaFb .^ The presence of the compound explains some of the deviations from regularity which are found in the following analysis. - 50 - Very l i t t l e published data is available on the activity of sodium l 8 in lead at high temperatures. Hauffe and Vierke measured the activity at M-25°C. and 4 7 5 ° C by an emf technique between pure sodium and various lh sodium lead alloys and Feinleib and Porter carried out a similar invest igation up to 820 ° C . The activity of sodium in the alloy was obtained by the Nernst equation E = RT In ^ a ^ ) = 1-984 X lO - ^ T log ^ N a ^ j *-Wd,(pure) Hauffe and Vierke noted wide departures from ideal solution behaviour in their study. The temperature coefficient of the emf of a cel l is directly related to the change in entropy in the cel l reaction. This is expressed by the> equation dE •= 4J3 dT nF If the cel l is that of a regular solution or a semi-regular solution nF dE - - D R In N dx where D is a constant. The value of D is unity for a regular solution and lies between the limits of 0.95 and 1.5 for those solutions 19 wich-appear to be semi-regular . An analysis of Feinleib and Porter's data, on the basis of the temperature.coefficient of the emf, is presented in -Table A-I and plotted in Figure A-2. This shows a wide divergence from regular or semi-regular solution behaviour over the significant range of composition. The presence of the compound NaPb^  is probably the cause of the inconsistency in this region. - 51 - TABLE A-I Temperature, EMF Data for Pb-Na Alloys Na .. l n % a A E AT(°C. ) dE/dT .151 -I.89 .011 317 35 X 10" 6 .212 -1.55 .015 325 46 x 10 .223 -1.50 .017 336 51 X 10" 6 •293 -1.23 .019 297 64 x 10" 6 .358 -1.03 .029 355 82 x i o ~ 6 .361 -1.02 .047 312 151 X 10" 6 .401 -0,91 .039 250 156 X 10 - 52 - Figure A - 2 . Temperature Coefficient of EMF from Hauffe and Vierke's'Data - 53 - Feinleib and Porter extrapolated their data to 1010 C. to obtain sodium activity values which could be used in a study of the aluminum- cryolite system. They checked their extrapolated activity data using a double alloy cel l at high temperatures. For this case the Nernst equation becomes , E = 1.984 X 10" 4 T log #± M a(Fb) * 2 N a ( F b ) They obtained a fair agreement between the data obtained from the double alloy cells and their extrapolated data and therefore assumed the extra polation to be correct. As a check on their data, a plot of log a vs. l /T was determined. A plot of this data should- give a straight line with a slope equivalent to the heat of solution. It can be seen from Figure A-3« that the data is thermodynamically inconsistent. In order to adjust the activities to f i t thermodynamic theory and extrapolate this data to higher temperatures, the two sets of data of Hauffe and Vierke and Feinleib and Porter (see Table A-Il) were used to establish a rigid thermodynamic analysis. At low temperatures both sets of data were consistent and a plot of log $ ^ a vs. ( l - N ^ ) 2 was determined at K^^C. (see Figure A - k ) . Making use of Feinleib and Porter's activity data, (see Table A-IIl) a series of log l /T plots were drawn and the best possible straight lines were determined. The heats of solution (L) were calculated from these lines. A plot of the heats of solution, as a function of concentration, was then developed by obtaining the best f i t with this data and that of the double alloy cells (see Figure A-5). The log )(vs•.. l /T plot was redrawn (see Figure A-6) using ^ values at k-T^C. - 5^ - obtained from Figure A-k as the base point and extrapolating to 1010 C. by the heats of solution obtained from Figure A-5. The composite data from the plots is tabulated in Table A-IV. The )f values were converted to activities and a calibration plot established (see Figure A - 7 ) . - 55 - Figure A-3. Plot of Log vs. l /T from Feinleib. and Porter's Pb-Na Activity Data - 56 - TA3LE A-II 1 8 Pb-Na Activity Data at 4 7 5 ° C . (from Hauffe and Vierke and Feinleib and Porter ) 2 logfaa N W o ' ?Na *Na log $ Na 1-N„ (l-% a) ( l ^ J 2 Data from Hauffe and Vierke • 9 3 5 . 9 2 5 . 9 8 9 - . 0 0 4 8 0 4 . 0 6 5 . 0 0 4 2 2 5 - 1 . 1 4 .815 . 7 1 0 . 8 7 1 - . 0 5 9 9 8 2 . 1 8 5 . 0 3 4 2 2 5 - 1 . 7 5 • 757 . 3 6 3 • 4 7 9 - . 3 1 9 6 6 4 . 2 4 3 . 0 5 9 0 4 9 - 5 . 4 i . 6 7 8 . 2 1 5 . 3 1 7 - . 4 9 8 9 4 1 . 3 2 2 . 1 0 3 6 8 4 - 4 . 8 1 . 5 6 7 . 0 9 0 . 1 5 8 - . 8 0 1 3 4 3 . 4 3 3 . 1 8 7 4 8 9 - . 4 . 2 7 . 4 7 0 . 0 3 8 . 0 8 1 - I . O 9 1 5 1 5 • 5 3 0 . 2 8 0 9 0 0 - 3 . 8 9 . 3 9 2 . o i l ' . 0 2 9 - I . 5 3 7 6 0 2 . 6 0 8 . 3 6 9 6 6 4 - 4 . 1 6 . 8 7 3 . 8 4 0 . 9 6 3 - . 0 . 1 6 3 7 4 . 1 2 7 . 0 1 6 1 2 1 - 1 . 0 2 . 7 9 ^ . 5 1 5 .649 - . 1 8 7 7 5 5 . 2 0 6 . 0 4 2 4 3 6 - 4 . 4 2 . 7 0 5 . 2 4 6 . 3 4 9 - . 4 5 7 1 7 5 . 2 9 5 . 0 8 7 0 2 5 - 5 . 2 5 . 6 2 5 . 1 3 5 . 2 1 6 - . 6 6 5 5 4 6 • 3 7 5 . 1 4 0 6 2 5 - 4 . 7 3 . 5 6 2 . 0 7 4 . 1 3 1 - . 8 8 2 7 2 9 . 4 3 8 . 1 9 1 8 4 4 - 4 . 6 0 .444 . 0 2 0 . 0 4 6 - 1 . 3 3 7 2 4 2 . 5 5 6 . 3 0 9 1 3 6 - 4 . 3 3 . 3 3 6 . 0 0 7 . 0 1 9 - 1 . 7 2 1 2 4 6 .664 . 4 4 0 8 9 6 - 3 . 9 0 Data from Feinleifc ) and Porter . 1 5 1 .00124 . 0 0 8 2 1 - 2 . 0 8 5 6 5 7 .849 . 7 2 0 8 0 1 - 2 . 8 9 . 2 1 2 . 0 0 2 0 . 0 0 9 4 3 - 2 . 0 2 5 4 8 8 . 7 8 8 . 6 2 0 9 4 4 - 3 - 2 6 . 2 2 3 . 0 0 2 8 . 0 1 2 6 - 1 . 8 9 9 6 2 9 • 7 7 7 . 6 0 3 7 2 9 - 3 . 1 5 • 2 9 3 . O O 6 5 . 0 2 2 2 - 1 . 6 5 3 6 4 7 . 7 0 7 . 4 9 9 8 4 9 - 3 . 3 1 . 3 5 8 . 0 1 0 . 0 2 7 9 - 1 . 5 5 U 3 9 6 .642 . 4 1 2 1 6 4 -3-77 . 3 6 1 . 0 0 7 6 . 0 2 1 1 - 1 . 6 7 5 7 1 8 . 6 3 9 . 4 0 8 3 2 1 - 4 . 1 0 . 4 o i . 0 1 4 . 0 3 4 9 - 1 . 4 5 7 1 7 5 • 5 9 9 . 3 5 8 8 0 1 - 4 . 0 6 - 5 8 - TABLE A-III Pb-Na Activity Data ^ (from Feinleib and Porter ) N Ci X L T(°K.) l /T (X 1 0 " J ) 0 . 1 5 1 . 0 0 1 4 2 . 0 0 9 4 . 0 0 2 1 5 •0142 . 0 0 2 9 5 . 0 1 9 5 . o o 4 o o . 0 2 6 5 .OO585 . 0 3 8 7 . 0 0 7 2 0 . 0 4 7 7 .OO875 .0580 . 0 1 0 9 0 . 0 7 2 2 0 . 2 1 2 . 0 0 2 3 6 . 0 1 1 1 . 0 0 3 1 7 . 0 1 5 0 . 0 0 4 9 8 . 0 2 3 5 .OO638 . 0 3 0 1 . 0 0 7 7 8 .O367 . 0 0 9 7 7 . 0 4 6 1 . 0 1 1 6 . 0 5 4 7 . 0 1 4 2 . 0 6 7 0 . 0 1 6 5 . 0 7 7 8 0 . 2 2 3 . 0 0 3 0 0 . 0 1 3 5 . 0 0 4 1 5 . 0 1 8 6 . 0 0 5 9 0 . 0 2 6 5 . . 0 0 8 2 5 . . 0 3 7 0 . 0 1 0 7 . 0 4 8 0 . 0 1 3 9 . 0 6 2 3 . 0 1 7 0 . 0 7 6 2 . 0 2 1 5 . 0 9 6 4 0 . 2 9 3 . 0 0 8 8 . 0 3 0 0 . 0 1 0 5 . 0 3 5 8 . 0 1 3 7 . 0 4 6 8 . 0 1 8 1 . 0 6 . 1 8 - . 0 2 3 1 . 0 7 8 8 . 0 2 9 2 . 0 9 9 7 . 0 3 8 5 . 1 3 1 0 . 3 5 8 . 0 0 9 5 . 0 2 6 5 . 0 1 5 0 . 0 4 1 9 . 0 2 0 5 . 0 5 7 3 . 0 2 8 5 . 0 7 9 6 . 0 3 6 2 . 1 0 1 . 0 4 2 5 . 1 1 9 . 0 5 0 0 . 1 4 0 . 0 5 8 0 . 1 6 2 1 0 , 3 9 8 7 6 8 1 . 3 0 2 8 2 6 1 . 2 1 1 8 7 3 1 . 1 4 5 9 2 5 1 . 0 8 1 9 8 9 1 . 0 1 1 1 0 2 0 . 9 8 0 1 0 5 1 . 9 5 2 1 0 8 5 . 9 2 2 1 0 , 3 9 8 7 7 5 1 . 2 9 0 8 2 5 1 . 2 1 2 8 9 5 1 . 1 1 7 9 3 7 1 . 0 6 7 9 6 8 1 . 0 3 3 1 0 0 3 - 9 9 7 1 0 3 1 - 9 7 0 1 0 7 1 - 9 3 4 - 1 1 0 0 . 9 0 9 9 , 3 9 4 - 7 5 8 . 1 . 3 1 9 8 0 4 1 . 2 4 4 8 6 8 1 . 1 5 2 9 2 3 . 1 . 0 8 3 9 6 1 1.041 1 0 2 2 . 9 7 9 1 0 6 3 . 9 4 1 1 0 9 5 . 9 1 3 8 , 7 1 4 8 0 3 1 . 2 4 5 8 3 8 1 . 1 9 3 - 8 9 1 1 . 1 2 2 948 1 . 0 5 5 . 1 0 0 0 1 . 0 0 0 1 0 4 8 . 9 5 1 * - 1 1 0 0 . 9 0 9 8 , 2 8 8 7 4 - 5 1 - 3 4 - 2 8 1 2 1 . 2 3 2 8 6 6 1 . 1 5 5 9 3 1 1 . 0 7 4 - 9 8 2 1 . 0 1 8 1 0 2 1 . 9 7 9 1 0 6 1 . 9 4 3 1 0 9 9 . 9 1 0 continued. - 59 - Table A-III Continued 0.3.61 .0088 .0244 .0125 .0346 .OI85 .0513 .0215 .0596 .0290 . 0803 .0370 .103 .ok6o .127 .0570 .158 • 0175 .0436 .0230 ..0574 .0310 .0773 .0410 .102 .0500 .125 .0655 . .163 .0715 .178 L . T(°K) l /T , (x IQ-3)- 9,839 773 1-29J4- 834 1.214 895 1.117 933 1-072 973 1.028 1010 .990 1051 .952 IO85 .922 8,748 783 I.277 833 1.200 885 1.130 936 ,1.068 978 1.022 1013 .987 1033 .968 - 09 -TABLE A-IV Composite Fb-Na Activity Data NNa log V i a ( l - % a > y ^ - v 2 log ^Na ^Na 475 L l/T X 10" 3 d i f f . ^ 1010 ^1010 .151 -2.95 .849 .720801 -2.1264 f"~?" .00748 .00113 -10.400 .400 .138 .0208 .171 -3.O2 .849 .687241 -2.0755 .00840 .00143 -10,200 .449 .149 .0254 .212 -3-11 .788 .620944 -I.9622 .0109 .00231 - 9,900 .462 .173 .0367 .222 -3.20 • 778 .605284 -I.9369 .0116 .00258 - 9,800 .467 .181 .0402 .223 -3-20 • 777 .603729 -1.9319 .0117- .00261 - 9,800 .467 .181 • 04o4 •293 -3-48 .707 .499849 -1-7395 .0182 •00533 - 9,200 .497 .241 .0706 .301 -3.50 .699 .488601 -1.7101 .0195 .00587 - 9,100 • 503 .250 .0753 • 358 -3.90 .642 .412164 -1.607440 .0247 .00884 - 9,4oo .487 • 34-8 .125 .361 -3-92 .639 .408321 -1.6006l8 .0251 .00906 , 9,450 .484 .360 .130 • 371 -4.00 .629 .394-5641 -I.582564 .0261 .00968 - 9,550 .479 .380 .141 .401 -4.14 •599 .358801 -1.4854 .0327 .0131 - 9,000 .508 .4io .164 - 6k - APPENDIX B Calculation of K Equilibrium - 6 5 - APPENDIX B Calculation of K Equilibrium at 1 0 1 0 ° C . ( l 2 8 3 ° K ) from Free Energy Data 2 5 ' 3 \ ( A l ) ( l ) + (3NaF) ( l ) — ( A 1 F 3 ) ( 1 ) + [SNa] ( d i l ) 3Na ( l ) + 3 / 2 F 2 ( g ) 3NaP ( l ) Al(l ) + 3 / 2 F 2 ( g ) A 1 F 3 ( 1 ) A F.J, reaction = AF^ - AF± RT In K K = fea]3 ( ^AlFQ f A l (^NaF)3 1. Calculation of. AF^ 3 N A F ( B ) 2 9 8 3 N a ( s ) 2 9 8 3 N a F ( D l 2 8 3 3 / 2 F p , x 3 / 2 F ? , » 2 ( g ) 2 9 8 ~ 2 ( s ) i 2 8 3 , ( 1 ) A P 1 •(2) A F 2 . (3)AF 3 •(5)AF 5 A F n A F 3 A F^ A F c 1 2 8 3 (a) A F 3 = AH298 + / CpdT ' + A Hp - T A H 2 9 8 = - 1 3 6 , 0 0 0 cal/mole 3 4 A s 2 9 8 = 1 3 - 1 e - u - A % = 8 0 3 0 cal/mole 2 5 P S ? A S F = 6 . 3 5 e.u. J i 3 4 1 2 8 3 A s 2 9 8 y ^ 1 ^ ^ / 1 2 8 3 ^ 2 . - 1 25 / CpdT'. = 1 0 . 1 * 0 T + I . 9 U X 10'3 T + 0 . 3 3 X 10' T - 3 3 8 4 y 2 9 8 2 9 8 1 2 8 3 2 9 8 T _Q c 2 5 Cp dT = 10.40 In T + 3 . 8 8 X 10 T + 0.165 X 10^  - 6 0 . 6 1 - 4 9 1 , 2 9 2 calories - 6 6 - 3 7 1 / 1 2 8 3 (b) A F k = AH 8 + / CpdT + A H t r a n s + / CpdT y J 2 9 8 . / 3 7 1 T A s. ' 2 9 8 2 9 8 A H trans A S trans" + ^ ^trans + 1 2 8 3 " C£dT 3 7 1 371 A S 2 9 8 + / CpdT '298 4 E U Q = 0 3 4 1 2 . 3 1 e.u." 6 2 2 cal/mole 2 5 1.68 e.u. 2 5 371 CpdT 298 4.02 T + 4.52 X 10" 3 T 2 - 1599 2 5 / /* 1283 CpdT = 6.83 T - 1.08 X 10 5 T _ 1 - 224325 371 3 7 1 298 CpdT = 4.02 In T + 9.04 X 10~ 3 T - 25.59 2 5 3 ? 1 1 2 8 3 CpdT T = 6 . 8 3 In T - .54 X 105 T" 2 - 40.0225 = - 7 1 , 0 8 5 calories . / l 2 8 3 (c) = A H ^ g +y^CpdT - T AH' fl = 0 298 1 2 8 3 A S 2 9 8 + / C£ dT 2 9 8 A S 2 9Q = 48.58 e .u. 3 i + Z1283 -3 2 5 1 2 / CpdT = 8.26 T + 0.30 X 10 T + 0.84 X lO"5 T - ± - 2771 €/ 298 / 1283 / CpdT = 8.26 In T + 0.60 X 10" 3 T + 0.42 X 10 5 T~ 2 - 47.7I </ OQAT A F^ = - 1 0 4 , 4 1 2 calories F^ = -491,292 + 71,085' + 104,412 = -315,795 Calories - 67 - 2. Calculation of A Fo A 1 F 3 ( s ) 2 9 8 ~ * A 1 F 3 ( l ) i 2 8 3 A 1 ( s ) 2 9 8 —> A 1 ( D i 2 8 3  3 / 2 F 2 ( g ) 2 9 8 . 3 / 2 F 2 ( g ) 2 9 8 AF2 = LF6 - A F ? - A F 5 / 7 2 7 /1283 (a) A F 6 = A H 2 9 Q + / 2 9 f T + ^ H t r a n s + * % />727 1283 A S 2 9 8 + / C £ d T + A S t r a n s + / C £ dT +ASj 2 9 S <^727 T • A H 2 9 8 = -323,000 cal/mole3^ A S29Q- = 23.8 e .u . 3 A H t r a n s = 1 5 0 cal/mole25 A S, = .21 e.u. ^ trans AHp = 6200 cal/mole (see Appendix C) A^jp = k e.u. (see Appendix C) P 727 CpdT •=.• 17.27 T + 5.48 X 10" 3 T 2 + 2.30 X 10 5 T _ 1 - 6408' 298 1283 Cp 727 25 P 1 2 8 3 -5 25 / dT = 20.93 T +I.50 X 10" 3 T 2 - 16,009 J 121 727 C£ dT = 17.27 In T + IO.96 X 10" 3 T + 1.15 X 10 5 T" 2 - 102.97 2 5 T 298 1283 C£ dT = 20.93 In T + 3.00 X 10~ 3 T - l40.13 2 5 T 727 A F6 = -372,715 calories - 68 - (b) A.F. 7 932 /1283 932 fl 1283 A s298 + / 2£ cLT + A S p + / Cp_ dT / 932 T 932 CpdT 298 1283 CpdT 932 .1283 Cp_ dT T 932 4 H. •298 0 3k 4 S 2 9 s = 6.77 e.u A H F = 2570 cal/mole2^ A s. F = 2.76 e.u 25 4.94 T + 1.48 X 10" 3 T 2 - l6o4 25 = 7-00 6524 25 932 Cjo dT = 4.94 In T + 2.96 X 10" J T - 29.03 T 298 25 nc 7-00 In T - 47.86 A-Frj = • - 15,423 calories AF = - 372,715 + 15,423 + 104,412 = -252,880 Calories A Reaction = -252,880 + 372,715 -• 62,915 calories A F = - RT In K log K = -62,915 = -10.72 4.575 (1283) K = 1.91 X 10" 1 1 - 69 - APPENDIX C Analysis of NaF-AlF? Binary System APPENDIX C Analysis of NaF-AlF,, Binary System 1. Determination of the Activity.of NaF from the NaF-AlF^ Phase Diagram Sodium fluoride activities were determined by the method developed by 27 2 8 19 Wagner ' J . This method has been employed recently for the investigation 29 of binary chlorides by Chu and Egan . The phase diagram of Grjotheim (see Figure C-l) has been used for the thermodynamic calculations. The activity of NaF can be calculated by successive integrations of the compounds in the system using the expression RT log #NaF = A % T M ( I - N 2 ) A T + (i-Xp). / J \ b i au N 2 - Xg / (N 2-X 2) where A % = heat of fusion of the compound T^ = melting point of the compound A T = T - T T = liquidus temperature N-j_, N g = mole fractions of AlF^ and NaF X-^ , X 2 = mole fractions of AlF^ and NaF corresponding to the compound. Estimation of the heat of fusion of the intermediate compounds is a major uncertainty in this method. In previous work involving this technique the substances have been considered as ideal mixtures and in this case the heat of fusion can be determined by calculating an entropy term which is corrected for the heat of mixing. However, in the case of fused salts, which dissociate on melting, measured calorimetric heats of fusion include heats of dissociation. The contribution of this heat term to the observed value is 29 often difficult.to determine. In the study by Chu and Egan on molten binary mixtures, the heat of fusion was calculated on an' empirical basis. They assumed the entropy of fusion to be equivalent to the sum of the entropies of the pure components. The entropy of fusion of the intermediate compounds in the NaF-AlF^systef" - 71 - 1050 0 NaF (731°) A i * / 1300 1250 1200 o 1150 - 3 •+-» 1100 2L e 1050 1000 10 20 Mole 30 AO percent AIF3 50 60 2 Figure C - l . NaF-AlF^ Phase Diagram (Diagram from Grjotheim ) - 72 - is chosen on an empirical basis and substantiated by the following analysis. It is suggested that a melt of Na^AlFg will contain preponderately Na+ and AlFg 3 ions as. statistically independent constituents. As a broad assumption one can consider each particle as dissociating into four particles. Therefore, i t is reasonable to expect that the entropy of fusion could be about the same as that 30 of two particles of NaF which also breaks up into four particles 3 The recent summary of the cryolite situation by Foster assumes the extensive dissociation of the compound into simpler ions. The possibility that- dissociation is not complete or that secondary dissociation of the A1F ion 6 is dissociated further to A1F^~ and F ions should not affect the entropy approximation greatly as these two possibilities would tend to compensate for' one another. However, i t can be seen that these complications make i t very difficult to estimate the entropies with any degree of certainty. The heat of fusion of pure NaF was determined from the most recent 25 data of Kelley and the entropy of fusion calculated to be 6.35 e.u.'s. There fore the entropy of fusion for the intermediate compounds in the NaF-AlF^ system are assumed to be 12.70 entropy units. Relative values of log ^NaF have been calculated over the composition range 86.5 mole per cent to 60 mole per cent NaF as shown in Column 16 of Table C-I. These values are relative to the compound cryolite and are not absolute values. In order to obtain the correct values i t is necessary to obtain a tie point with the activity of pure NaF. This is accomplished by calculating the ^NaF at the eutectic point 86.5 mole per cent NaF. As in general, thermo dynamic calculations of this nature are carried out using )f and log X the correction is applied in Column 19 of Table C-I. - 73 - TABLE C-I Determination of #NaF by Integration of Compound Na3AlFg in NaF-AlF, Phase Diagram 1 2 , . 3 4 5 6 7 T°K. : . X2 x i N2NaF N1A1F 3 A T N 2-x 2 1007 •75 •25 .600 .400 274.6 -.150 1198 •75 . • 25 .649 •351 83.6 -.101 1221.5 •75 .25 .663 • 337 60.1 -.087 12k3-7 •75 .25 .679 • 321 37.9 -.071 1267.2 •75 • 25 • .704 .296 14.4 . -.046 1277.5 •75 . .25 .724 .276 4.1 -.026 1281 .;o •75 .25 .738 .262 0.6 -.012 1281.3 •75 .25 • 7^ 5 .255 0.3 -.005 1281.6 •75 • 25 • 750 .250 0 0 1281.3 •75 .25 • 75^ .246 0.3 .004 1280.4 •75 • 25 • • 759 .241 1.2 .009 1277.2 •75 • 25 . .768 .232 4.4 .018 1272.6 •75 . • 25 • 777 .223 9.0 .027 1264.1 •75 .25 .789 .211 17-5 .039 1249.5 • 75 • 25 .806 .194 32.1 .056 1227.2 •75 .25 .827 •173 54.4 .077 1214.3 • 75 .25 • 837 .163 67.3 .087 1207.2 •75. •25 .842 .158 74.4 .092 1180.8 • 75 .25 .856 .144 100.8 .106 1161.0 •75. .25 . .865 • 135 120.6 .165 1161.0 1.0 0 .865 • 135 106.5 -.135 1180.5 1.0 0 .883 • 117 87.O -.117 1196.9 1.0 0 • 899 .101 70.6 -.101 1206.8 1.0 0 .907 • 093 60.7 -•093 1223.3 1.0 0 .926 .074 44.2 -.074 1240.0 . 1.0 0 .949 .051 27-5 -.051 1225.7 1.0 0 • 976 .024 12.5 -.024 1261.8 : 1.0 0 .987 .013 5-7 -.013 1262.0 1.0 0 .988 .012 5-5 -.012 1267.5 1.0 0 l 0 0 0 - 7k - TABLE C-I Continued 8 9 - 10 11 12 13 14 % A T x A T (N 2 -X ? ) 2 X 1 A T / X-^T dN 8 + 1 2 x 12.70 N 2 -X 2 _L d. d. (N 2"X 2) 2 J / ( N 2 - X 2 f x 2 -732.27 68.65 .0225 3051. -311-90 -1044.17 -13,261.0 -29O.53 20.90 .0102 2049 . -186.95 - 477-48 - 6,064.0 -232.8O' 15.03 •00757 1986 -158.74 - 391.54 - 4,972.6 -171.35 9.48 .00504 1881 -127.78 - 299.13 - %799-0 - 92.66 3-60 .00212 .1698 - 82.78 - 175.44 - 2,228.1 - 43.52 1.03 .OOO676 .1524 - 50.28' - 93-80 - 1,191.3 - 13.10 • 15 . .000144 1042 - 31.38 - 44.48 - 564.9 - 15.30 • 075 .000025 3000 - 17.38 - - 32.68 415.0 0 0 0 0 0 0 0 18.45 • 075 .00016 4688 17.10 35-55 451.5 32.13- • 30 .000081 3704 36.85 68.98 876.1 56.71 1.10 .000324 3395 68.62 125-33 1591.7 74.33 2.25 .000729 3086 97.87 172.20 2186.9 94.68 4.38 .00152 2882 133.57 228.25 2898.8 111.20 8.03 .00314 2557 179.47 290.67 3691.5 122.22 13.60 ' .00593. 2293 230.08 352.30 4474.2 126.09 16.83 .00757 2223 252.58 378.67 4809•l 127.77 18.60 .00846 2199 . 263.63 391-40 4970.8 136.94 .25.20 .0112 . 2250 .294,78 431.72 5482.8 141.57 30.15 . 0132 2284 315.17 456.74 5800.6 x 6.35 -106.5 - - - -106.5 -676 - 87.0 - - . - - - 87.O -553 - 70.6 - - - - - 70-6 -448 - 60.7 - ' -• • - - - 60.7 -385 - 44.2 - - - - - 44.2 -281 - 27.5 ' - - - - 27-5 -175 - 12.5 - .- .. - - - 12-5 - 79-^ - 5-7 - - - - - 5.7 - 36.2 - 5.5 - - - - - 5-5 - 34.9 0 — — . — — 0 0 - 75 - TABLE C-I Continued 15 16 17 18 19 20 RT log %aF log y NaF log ^NaF log ^Na] @ T',s „ add -1.219 @ 1283 4607 -2.878 -.222 -2.656 -3.875 -3.042 5481 -1.106 -.188 - .918 -2.137 -1.996 5588 - .890 -.178 - .712 -1-931 -1-839 5690 - .668 -.168 - .500 -1.719 -I.669 5797 - .384 • -.152 - .232 -1.451 -1.434 5845 - .204 -.140 - .064 -I.283 -I.278 5861 - .096 -.132 .036 -I.183 -1.182 5862 - .071 -.128 • 057 -1.162 -1.161 5863 0 -.125 • 125 -1.094 -1.093 5862 .077 -.123 .200 -1.019 -1.018 5858 .150 -.120 .270 - .949 - .947 5843 .272 -.115 .387 - .832 . - .827 5822 .376 -.110 .486 - -733 -..726 5783 .501 -.103 .604 - .615 - .606 5717 .646 -.094 • 740 - .479 - .467 5614 • 797 -.082 .879 - .340 - .325 5555 .866 -.077 .943 - .276 - .261 5523 .900 -.075 • 975 - .244 - -23P 5402 1.015 -.067 1.082 - -137 - .126 5312 1.092 - .O63 1.155 - .064 - .058 5312 - .127 -.063 - .064 _ - .058 5401 - .102 -.054 - .048 - - .044 5476 - .0818 . -.0462 - .0356 - - -033 5521 - .0697 -.0424 - .0273 - - .026 5597 - .0502 -.0333 - .0169 - - .016 5673 - .0309 -.0227 - .0082 - - .008 5745 - .0138 -.0105 - .0033 - - .003 5773 - .00627 -.00568 - .00059 - - .001 5774 - .00604 -.00524 - .00080 - - .001 5799 0 0 0 - 0 - 76 - The two other c a l c u l a t i o n s are c a r r i e d out over the p e r i t e c t i c compound Na^Al (see Table C - l l ) and the compound NaAlF^ (see Table C - I I l ) to extend the data across the diagram. These are t i e d i n r e s p e c t i v e l y to the cor rected values over the c r y o l i t e compound range, and the e u t e c t i c at 56 mole per cent NaF. A l l the values are cor rected to 1283°K assuming regu lar s o l u t i o n behaviour . Th is assmumption can be made as the s i g n i f i c a n t data f o r t h i s work near the c r y o l i t e peak i s f a i r l y c lose to the experimental temperature. 2. Determination of the A c t i v i t y of A lF^ Once the thermodynamic data f o r one of the const i tuents of a b inary diagram i s known, i t i s poss ib le to obta in the data f o r the other by apply ing the Gibbs-Duhem e q u a t i o n 2 ^ ' T h e express ion used f o r t h i s case i s N NaF = 1 l o g ^ A 1 F 3 = - N N a F X N M F l o g ^NaF + / l o g N a p d % (N, " j 2 ^ / U A 1 F / ' A1F„ w 3. -3 % a F = A 6 3 The f i r s t term i s c a l c u l a t e d f o r the N,T „ values obtained from Tables NaF C - I , C - I I , and C- I I I . The data i s shown i n d e t a i l . i n Table C-IV. The second term i s evaluated by p l o t t i n g the l o g .0* NaF term as a func t ion of NaF concentrat ion and performing a g r a p h i c a l i n t e g r a t i o n . The logJfjTaF vs;. p lo t i s shown (NA1F ^  i n F igure C - 2 . The sum of the two terms gives a r e l a t i v e l o g o' ^^'3 v a ^- u e > 1 ° u ^ a c o r r e c t i o n must be app l ied at the t i e point of 46 . 3 mole per cent NaF. The t i e point i s e s t a b l i s h e d by obta in ing a cons is tent set of data i n respect to. the metastable standard state of pure -molten • A l F . Assuming that A lF^ has a mel t ing point of approximately 1550°K. which i s s l i g h t l y above the a c t u a l subl imat ion p o i n t , and us ing an entropy of f u s i o n of k entropy u n i t s , a value f o r the heat of f u s i o n of 6200 c a l o r i e s i s obtained. Using t h i s data l o g % A l F - s TABLE C-II Determination of %aF "by Integration of Compound Na^Al^F^ in NaF-AlF^ Phase Diagram 1 2 : 3 4 5 6 7 ..- 8 9.. T°K x 2 x i . N2NaF N1A1F 3 A T N 2 - x 2 NL A T (N 2 - X 2 ) ( N 2 - X 2 ) 2 1013 ..625 • 375 .625 -375 0 . 0 0 0 1010.5 .625 • 375 .6125 .3875.. 2-5 -.0125 -77-50 .OOOI56 1007 .625 • 375 .600 .400 6 -.025 -96.00 .000625 963 .625 • 375 .56O .440 50 -.065 -338.46 .00423 10 11 12 13 14 15 16.' 18 X - L A T (N 2- X 2 ) 2 c p\1 A T 8 + 11 x 12.70 RT log ^NaF l 0 * NNaF y log %NaF log 0 NaF @ T's add -3-425 0 0 0 0 4635 0 .-.204 -.204 0 6010 -87.56 -165.56 -2102.61 4623 --455 -.213 -.242, 0 3600 -147.62 -243.62 -3093-97 4607 -.672 -.222 -.450 -3.875 4433 -308.26 -646.72 -8213.34 4406 -1.864 -.252 -1.612 -5.037 TABLE C-III Determination of ^NaF by Integration of Compound NaAlF^ in NaF-AlF^ Phase Diagram 1;;,. 2 3 . 4 5 .6 7 ; : ,8 9 •' T°K . x 2 x l N 2NaF N1A1F3 .. A T  : . N 2 - X 2 \ A T ( N 2 - X 2 ) (N 2- X 2 ) 2 977 • .494 .506 •463 • -537 . 27 -.031 -467.71 .000961 993 ...494 '•- .506 .479 •521 11 -.015 -382.07 .000225 1004 .494 • 506 .494 .. .506 0 0 0 0 988 .494 .506 • 530 .470 . 16 .036 208.89 .00130 963. .494 .506 .560 .44o 14 .066 273.33 .00436 1 0 11 12 13 14 15 16 17 18 X X A T ( N 2 - *2)2J X 2 (N 2 - X 2 ) 2 8 + 1 1 x 12.70 R T log ^NaF l o g NNaF log^ NaF log & NaF @ T ' s add -8.158 14,216 -682.70 -1150.41 -14,610.2 4470 -3.269 -.334 -2.935 -11,093 24,738 -371.07 - 753-14 - 9,564.9 4543 -2.105 -.320 -1.785 - 9.943 0 0 0 0 0 0 -•307 .307 - 7.851 6,228 557.39 766.28 - 9,731.8 452.0 +2.153 -.276 2.429 - 5.729 4,758 722.18 995.51 12,642.3 4406 2.869 -.252 3.121 - 5-037 - 79 - TABLE C-IV a Determination of '-AlF- by Gibbs-Duhem Integration 1 2 3 4 5 6 N2NaF N 2 1 N-L X N 2 log K NaF 1283 % X N 2  N l 2 log^NaF log 8 NaF N 2 .463 .288 .865 -8.447 7.307 -29-33 A79 .271 •923 -ft 695 7 . I 6 3 -28.40 .414 .256 •977 -6.143 6.002 -24.00 • 530 .221 1.127 -4.4io 4.970 -19-95 .560 .194 1.1268 -3.782 4.796 -19.49 .600 .160 1.500 -3-042 4.563 -19.01 ' .649 • 123 1.854 -1.996 3-701 -16.23 .663 .114 1.956 -1.839 3-597 -16.13 .679 .103 2.117 -1.665 3.525 -16.17 • 704 .O876 2.374 -1.434 3-404 -16-37 • 724 •.O762 2.625 -1.279 • 3-357 -I6.78 .738 .0686 2.813 -I.181 3-322 -17-22 • 745 .0650 2.923 -1.160 3-391 -17-85 • 750 .0625 3.008 -1.093 3.288 -17-49 • 754 .0605 3-074 -1.018 3-129 -I6.83 • 759 .0581 - 3-150 - .947 2.983 -16.30 .768 .0538 3.309 - .827 2.737 -15-37 • 777 .0497 ' 3-481 - .726 2.527 -14-61 .789 .0445 3-753 - .606 2.274 -13-62 .806 .0376 4.149 - Mft. 1.938 -12.42 .827 .0299 4.783 - .325- 1.555 -10.86 • 837 .0266 5-113 - .261 1.335 - 9.81 .842 .0250 5.320 - .-30 1.224 - 9.20 .856 .0207 5.942 • - .126 .749 - 6.09 .865 .0182 6.429 - .058 -373 - 3.19 .886 .0137 7.518 - -044 .331 - 3.21 .899 .0102 8.902 - -033 .294 - 3.24 •907 .OO865 9-757 - -026 .254 - 3.01 • .926 .00548 ' 12.500 - -016 .200 - 2.92 •9^9 .00260 18.615 - .00(8 .149 - 3-08 .987 .00017 75.294 - .001 • 075 - 5.88 1 0 0 0 0 0 - 80 - TABLE C-IV Continued 10 11 5 + 8 log V AlFo 1283 * add -7.644 log ^AlFo 0 0 7.307 - -337 - 1.58 -.432 -.432 6.642 -1.002 - 4.38 -.365 -•797 5-205 -2.439 -10.00 -.791 -1.588 3-382 -4.262 -15.17 -.592 -2.180 2.616 -5.028 -16.01 -.770 -2.950 1.613 -6.031 -16.75 -.863 -3.813 - .112 -7-756 -18.42 -.227 -4.o4o - .443 -8.087 -18.38 -.258 -4.298 - -773 -8.417 -18.26 -. 407 -4.705 -I.301 -8.945 -18.03 -.331 -5.036 -1.679 -9.323 -17.79 -.238 -5.274 -1-952 -9.596 -17.61 -.123 -5.397 -2.006 -9.650 -17.39 -.088 -5.485 -2.197 -9.841 -17-48 -.069 -5.554 -2.425 -IO.069 -17.70 -.083 -5.637 -2.654 -IO.298 -17.88 -.143 -5.780 -3-043 -IO.687 -18.11 -.135 -5.915 -3'. 388 -11.032 -18.26 -..169 -6.084 -3.817 - l l . 4 6 l -18.40 -.220 -6.304 -4.387 -12.031 -18.51 -.240 -6.544 -5.028 -12.672 -18.53 -.100 -6.644 -5-355 -12.999 -18.54 -.046 -6.690 -5-530 -13.17^ -18.58 -.098 -6.788 -6.146 -13.790 -18.81 -.031 -6.819 -6.613 -14.257 -19.06 -.033 -6.852 -6.656 -14.300 -18.33 -•033 -6.885 -6.680 -14.324 -17.73 -.017 -6.902 -6.736 -14.380 -17.47 -.038 -6-940 - -6.802 -14.446 -16.84 -.050 -6.990 -6.878 -14.522 -16.12 -.155 • -7-145 -7.070 -14.714 •15.11 -.076 -7-221 -7.221 -14.865 14.87 log yNaF N 2 A1F 3 2 NaF 14 <w4«-l- Figure C-2. Plot of log ^NaF vs. Ni N A1F 3 2 'NaF - 82 - at 46.3 mole per cent ALF^ has a value of - . 1 9 1 which when adjusted "by the r e g u l a r s o l u t i o n c o r r e c t i o n becomes - . 3 3 7 ' The l o g ^ A l F ^ values i n Column 1 0 of Table C-IV can then be c o r r e c t e d by adding -7.644 . A p l o t of l o g ^ A l F ^ vs.. N N a F 2 J^NaF i s shown i n ^ Figure C--3. The shape and l o c a t i o n of t h i s curve i s c o n s i s t e n t w i t h the previous assumptions. 3 . Determination of A c t i v i t y of Sodium i n Aluminum Numerical values f o r l o g ^ N a F and l o g o' A l F ^ are now a v a i l a b l e from Tables C-I, C - I I , C - I I I and C-IV. A c t i v i t y data f o r sodium i n molten aluminum i s c a l c u l a t e d f o r a range of NaF-AlF^ r a t i o s i n Tables C-V and C-VT, u s i n g the e q u i l i b r i u m equation. The curve i s p l o t t e d i n Figure 6 . This curve represents the a c t i v i t y of sodium metal d i s s o l v e d i n pure aluminum, i n e q u i l i b r i u m w i t h pure fused c r y o l i t e e l e c t r o l y t e of a given r a t i o at 1 0 1 0 ° C . 20. 16 12 log^Am1-, N 2 NaF 8 O ^ O ' ' A ' ^ 0 " - 0 - ° ^ Q ^ - o - - o - ' - o - o - G ^ \ \ \ \ \ \ \ ox \ \ \ \ \ \ o\ \ \ \ 1 1 4 1 1 1 1.0 .8 N. • 7 NaF Figure 0-3. Plot of logQ^AIF, vs. N, %aF 2 NaF TABLE C-V A c t i v i t y Data f o r NaF and A l F from Phase Diagram NaF ^ 3 Bath Rat io log^NaF #NaF ^NaF log tfALF3 &A1F €a1F3 697 •321 1.06 -I.665 2.16 X l O " 2 1.47 X 10' •2 -8.417 3.83 X 10" •9 1.23 x 10" •9 7 Oh .296 1.19 -1.434 3.68 X l O " 2 2-59 x 10" •2 -8.945 1.1k X 10" •9 3-37 x 10" •10 724 .276 1.31 -1.279 5.26 X l O " 2 3". 81 x 10" •2 ; -9.323 4.75 x 10' •10 1.31 X 10" •10 738 .262 1.41 -1.181 6.59 x l O " 2 4.86 X 10" .0 -9.596 2.54 X 10" -10 6.65 X 10" 11 7^ 5 .255 1.46 -I.160 6.92 X l O " 2 5.16 X 10" •2 -9.650 2.24 X 10' •10 5.71 X 10" •11 750 .250 1.50 - I . O 9 3 8.07 X l O " 2 6.05 x 10' -2 -9.841 1.44 X 10" •10 3.60 X 10" -11 75 k .246 1-53 -1.018 9.59 x l O " 2 7-23 X 10' •2 -10.069 8.53 x 10" •11 2: 10 X 10" •11 759 .241 1-57 - .947 1.13 x l O ' 1 8.58 X 10" •2 -10.298 5.04 X 10_ •11 1.22 X 10" •11 768 .232 1.66 - .827 1.49 X 10" 1 1.14 x 10" •1 -10.687 2.06 X 10" •11 4.78 X 10" •12 777 .223 1-75 - .726 1.88 x l O " 1 1.46 x 10" -1 -11.032 9.29 X 10" •12 2.07 X 10" 12 TABLE C-VT A c t i v i t i e s of Sodium from Phase Diagram Bath R a t i o ^AIF 3 ^NaF ( ^ f a F ) 3 K ( €NaF)3 1.91 X 10" 1 1 K (^TaF)3 £ A I F 3 ~ ^Na 1-75 2.07 X 10" -2 1.46 X 10" -1 3.11 X 10" •3 5.94 X l O " 1 ^ 2.87 x 10" -2 .306 1.66 4.78 x 10' .0 1.1k X 10" -1 1.48 x 10" •3 2.83 X IO"1^ 5.92 X 10' -3 .181 1.57 1.22 X 10' •11 8.58 X 10" -2 6.32.x 10" •4 1.21 X 10" l l + 9.92 X 10" -4 .0997 1-53 2.10 X 10" -11 7.23 X 10" •2 3.78 X 10" •4 7.22 x 10" 1 5 3.44 X 10" -4 .0701 1.50 3.60 X 10" -11 6.05 X 10" -2 2.21 X 10" •4 4.22 X 1 0 - 1 5 1.17 X 10" -4 .0489 1.U6 5.71 x 10" -11 5.16 X 10' -2 1.37 X 10" •4 2.62 X i o _ 1 5 4.59 X 10" •5 .0358 l . 4 i 6.65 X 10' -11 4.86 X 10' -2 1.15 X 10" •4 2.20 X 10" 1 5 3.31 x 10' -5 .0321 1.31 1.31 X 10' -10 3.81 X 10' •2 5-53 x 10-•5 1.06 X 10~ 1 5 8.09 x 10" -6 .0201 1.19 3-37 x 10' •10 2.59 x 10" •2 1.74 x 10" •5 3.32 x 10" 1 6 9.85 X 10" •7 .00995 1.06 1.23 x 10" •9 1.47 X 10" -2 3.18 x 10" •6 6.07 x 10" 1 7 4.94 X 10" -8 .00367 - 86 - APPENDIX D Dilution. Calculations 0 5 wt % AlOj CO 15 Figure D-2. Liquidus Diagrams for Cryolite-Alumina with 5> 10., 15 and 20$ Calcium Fluoride K)S0 Figure D-3» Liquidus Diagrams for Cryolite-Alumina-10$ Aluminum Fluoride with 5, 10 and 20$ Calcium Fluroide (Diagrams from Fenerty and Hollingshead ) TABLE D-I Sodium . Activities for Cryolite (Dilution Factor . 8 8 ) Bath ' ^ 3 ^ A 1 F 3 *NaF («NaF)3 K. (*?NaF)3 K . ^ a F ) 3 Ratio 1 0 0 $ 1 0 0 $ 8 8 $ 8 8 $ / ? M F 1 - 7 5 2 . 0 7 X 1 0 " • 1 2 1 . 4 5 X 1 0 " - 1 1 . 8 2 X 1 0 " - 1 2 1 . 2 8 X 1 0 " • 1 2 . 1 0 X 1 0 " • 3 4 . 1 0 x 1 0 " • 1 4 2 . 2 0 X 1 0 " • 2 . 2 8 0 1 . 6 6 4 . 7 8 X 1 0 " • 1 2 1.14 X 1 0 " - 1 4 . 2 0 X 1 0 ' • 1 2 1 . 0 0 X 1 0 " • 1 1 . 0 0 X 1 0 " • 3 i . 9 1 X 1 0 " • 1 4 4 . 5 5 x 1 0 " • 3 . 1 6 6 1 - 5 7 1 . 2 2 X 1 0 " • 1 1 8 . 5 8 X 1 0 " - 2 1 . 0 7 X 1 0 " • 1 1 7 . 5 5 x 1 0 " • 2 4 . 3 0 X 1 0 " • 4 8 . 2 1 X 1 0 " - 1 5 7 . 6 8 X 1 0 " • 4 . 0 9 1 6 1 . 5 3 2 . 1 0 X 1 0 " • 1 1 7 - 2 3 X 1 0 " .0 I I . 8 5 X 1 0 ' - 1 1 6 . 3 6 x 1 0 " • 2 2 . 5 8 X 1 0 " • 4 4 . 9 3 x 1 0 " - 1 5 2 . 6 6 x 1 0 " • 4 . 0 6 4 4 . 1 . 5 0 3 . 6 0 X 1 0 " • 1 1 6 . 0 5 X 1 0 ' - 2 3 - I T X 1 0 " • 1 1 5 . 3 2 x 1 0 . " - 2 1 . 5 1 X 1 0 " • 4 2 . 8 8 X 1 0 " • 1 5 9 . 0 9 x 1 0 " • 5 . 0 4 5 0 1.46 5 , 7 1 X 1 0 " • 1 1 5.14 X 1 0 ' - 2 5 - 0 3 X 1 0 " • 1 1 4 . 5 2 x 1 0 " • 2 ' 9.24 X 1 0 " • 5 1 - 7 7 x 1 0 " • 1 5 3 . 5 2 x 1 0 " • 5 . 0 3 2 8 i . 4 i 6 . 6 5 X 1 0 " • 1 1 4 . 8 6 X 1 0 " - 2 5 . 8 5 X 1 0 " • 1 1 4 . 2 8 X 1 0 " - 2 7.84 ..x 1 0 _ • 5 1 . 5 0 x 1 0 " • 1 5 2 . 5 6 X 1 0 ^ . 0 2 9 5 1 . 3 1 1 . 3 1 X 1 0 " - 1 0 3 . 8 2 X 1 0 " • 2 1 . 1 5 X 1 0 ' • 1 0 3 - 3 6 x 1 0 - 2 3 - 7 9 x 1 0 " • 5 7 . 2 4 x 1 0 " - 1 6 . 6 . 2 9 X 1 0 " - 6 . 0 1 8 4 1 . 1 9 3 - 3 7 X 1 0 " • 1 0 2 . 5 9 X 1 0 ' • 2 2 . 9 6 X 1 0 ' • 1 0 2 . 2 8 x 1 0 " • 2 1 . 1 9 x 1 0 " • 5 2 . 2 7 X 1 0 " • 1 6 7 . 6 6 X 1 0 " • 7 . 0 0 9 1 5 1 . 0 6 1 . 2 3 X 1 0 " • 9 1.46 X 1 0 " .0 1 . 0 8 X 1 0 " • 9 1 . 2 9 X 1 0 " • 2 2 . 1 5 x 1 0 " • 6 4 . 1 1 x 1 0 " • 1 7 3 . 8 0 X 1 0 " • 8 • 0 0 3 3 6 TABLE D-II Sodium Activities for Cryolite (Dilution Factor -825) Bath ^AlF «NaF ^AlF #Na1\ (<%aF)3 K . ( « N a F ) 3 K.(<gfraF)3 Ratio 100^ 0 100$ 82 .5 $ 8 2 ' 5 ^ ° LQ I Y T O " 1 1 ^ M F 3 N a 1.75 2.07 x 10" •12 1.45 x 10" -1 1.71 x 10" •12 1.20 X 10" 1 1.73 x 10" •3 -14 3.30 x 10 1.93 x 10" •2 .268 1.66 4.78 x 10" •12 1.1k x 10' -1 4.06 x 10" •12 9.41 x i o ~ 2 8.33 x 10' •4 1.59 x IO"1^  3.91 x 10" •3 .158 1-57 1.22 X 10" •11 8.58 x 10" -2 1.01 x 10" •11 7.08 x i o r 2 3.55 x 10" •4 6.7:8 x 10" 1 5 6.71 x 10" •4 .0875 1-53 2.10 X 10" •11 7.23 x 10" -2 1.73 x 10" •11 5.97 x i o r 2 2.13 x 10" •4 4.07 x i o ~ 1 5 2.35 x 10" •4 .0616 1.50 3.60 X 10" •11 6.05 x 10" -2 2.97 x 10" •U 4.99 x 10" 2 1.24 x 10" •4 2.37 x io° 1 5 7.98 x 10" •5 .0430 1.46 5.71 X 10' •11 5.14 x 10" -2 4.71 x 10" •11 4.24 x i o p 2 7.62 x 10" •5 1.46 x 10" 1 5 3.10 x 10" •5 .0314 l . 4 l 6.65 x 10" -11 4.86 X 10" -2 5.49 x 10" •11 4.01 x i o e 2 6.45 x 10' •5 1.23 x i o ~ 1 5 2.24 X 10" •5 .0282 1-31 1.31 x 10" •10 3.82 x 10" -2 1.08 x 10" •10 3.15 x 10" 2 3.13 x 10' •5 5.98 x 10" 1 6 5.54 x 10" •6 • 0177 CO VO TABLE D-III Sodium Activities for Cryolite (Dilution Factor .84) B^th «A1F 3 0feF ( ^NaF)^ M ^ N a F p K.( gNaF)^ Ratio 1 0 0 ^ 1 0 0 ^ ^ 1 > 9 1 x 1 0 - H <?A1F5 1.75 2.07 X 10' -12 1.45 X 10' -1 1.74 X 10' -12 1.22 X 10" -1 1.82 X io-5 3.48 X 10' -14 2.00 X 10' -2 ,272 1.66 4.78 X 10' -12 1.14 X 10' -1 4.01 x 10' -12 9.58 X 10" -2 7-79 X 1 0-4 1.68 X 10" -14 4.1 9 X 10' -3 .161 1.57 1.22 X 10' -11 8.58 X 10" -2 1.03 X 10" -11 7.21 X 10" -2 3-75 X 10-^ 7.16 X 10" -15 6.95 X 10" -4 .0885 1.55 2.10 X 10" -11 7.23 X 10" _2 1.77 x 10" -11 6.07 X 10" -2 2.24 X 10"* 4.28 X 10" -15 2.42 X 10' -4 .0623 1.50 3.60 X 10" -11 6.05 X 10" -2 3.02 X 10" -11 5.08 X 10" -2 1.31 X 10-* 2.50 X 10" -15 8.27 X 10" -5 .CA35 1.46 5.71 X 10" -11 5.14 X 10" _2 4.80 X 10" -11 4.32 X 10" -2 8.06 X io-5 1.54 X 10" -15 3.28 X 10" -5 .0318 1.4l 6.65 X io--11 4.86 X 10" -2 5.58 x 10' -11 4.08 X 10" -2 6.79' X 10-5 1.30 X 10" -15 2.33 X 10" -5 .0286 1.31 1.31 X 10' -10 3.82 X 10" -2 1.10 X 10' -10 3.21 X 10" -2 3.31 X io-5 6.32 X 10" -16 5.75 X 10" -6 .0179 1.19 3-37 X 10" -10 2.59 X 10" -2 2.83 X 10' -10 2.18 X 10" -2 1.0k X io-5 1.99 X 10" -16 7.04 X 10" -7 .0089 1.06 1.23 X 10" -9 1.46 X 10" -2 1.93 x 10' -9 1.23 X 10" -2 1.86 X 10" 6 3-55 X 10" -17 3.45 X 10" -8 .00326 VO o TABLE D-IV Sodium Activities for Cryolite (Dilution Factor .78) Bath <?A1F3 £ N a F fAlFj < ^ N a F , (<&aF)5 K, ( ^NaF)^ K.( <?NaF)^  Ratio • 100$ 1 0 0^ 0 78$ 78$ 1.91 X l O " 1 1 <?A1F3 «Na 1.75 2.07 X 10" -12 1.45 X 10" -1 1.62 X 10" -12 1.13 x 10" -1 1.44 x lO" -3 2.75 X 10--14 1.70 x 10" -2 .257 1.66 4.78 X lO-" -12 1.1k X 10' -1 3.72 X 10"' -12 8.89 x 10" -2 7.03 X 10' -4 1.34 X 10' -14 3.60 X 10' -3 .153 1-57 1.22 X 10" -11 8.58 X 10' -2 9.52 x 10" -12 6.69 X 10' -2 2.99 X 10' -4 5.71 X 10' -15 6.00 x 10' -4 .0844 1.53 2.10 X 10' -11 7.23 x 10' -2 1.64 x 10' -11 5.64 x 10' -2 1.79 x 10' -4 3.42 X 10' -15 2.08 X 10' -4 . 0592 1.50 3.60 X 10' -11 6.05 X 10' -2 2.81. x 10' -11 4.72 X 10' -2 1.05 X 1.0' -4 2.01 X 10' -15 7.16 X 19' -5 .0415 1.46 5.71 x 10' -11 5.14 X 10' -2 4.45 X 10' -11 4.oi x 10" -2 6.45 X 10' -5 1.23 X 10" -15 2.76 X 10' -5 .0302 1.4l 6.65 X 10' -11 4.86 X 10' -2 5.19 x 10" -11 3.79 x 10' -2 5.44 X 10" -5 1.04 X 10" 2.00 X 10' -5 . 0271 1.31 1.31 x 10" -10 3.82 X 10" -2 1.02 X 10" -10 2.98 X 10" -2 2.65 X 10' -5 5.06 X 10' -16 4.96 X 10' -6 .0170 1.19 3.37 x 10' -10 2.59 x 10" -2 2.63 x 10' -10 2.10 X 10' -2 9.30 X 10' -6 I.78 X 10' -16 6.76 x 10" -7 .00875 1.06 1.23 x 10" -9 1.46 X 10' -2 9.60 X 10' -10 i . i 4 x 10' -2 1.48 x 10' -6 2.83 X 10' -17 2.95 x 10' -8 .00308 I VO H - 92 - APPENDIX E Experimental Results - 9 3 - TABLE E-I Sodium Activities (Alumina-Saturated Pure Cryolite) Run Init ial Bath Wt. $ . Mole $ ^Na No. Composition Ratio Na • Na 44 Pure 1.44 2 . 9 0 21.2 . 0 3 5 1 . 4 1 4 5 Pure 1 . 4 3 3 . 1 0 22.4 . 0 3 8 5 7 Pure 1 . 4 3 2 . 8 0 20.6 . 0 3 3 1 .37 47 5 $ AlFj I . 3 6 2.20 1 6 . 8 .024 "3 1 . 3 4 5 8 5 $ AlF 1 . 3 4 2.40 1 8 . 1 . 0 2 7 . ^ 1 . 3 2 5 0 10$ A1F_ 1 . 2 5 1 . 8 0 14.2 . 0 1 9 ^ 1 . 1 8 5 1 "' 1 0 $ AlF, 1 .24 I . 9 0 14.8 .020 1 . 2 4 5 9 1 0 $ AlF 1 . 2 5 1 . 5 0 1 2 . 1 . 0 1 6 5 1 . 2 7 6 0 1 0 $ AlF* 1 . 2 4 1 . 7 0 1 3 . 5 . 0 1 8 1 . 2 0 6 1 1 0 $ AlF^ 1 . 2 6 1 . 8 0 14.. 2 . 0 1 9 1 . 1 8 48 1 5 $ AlF 1 . 1 7 1.40 11 .3 . 0 1 5 5 1 . 1 3 4 9 1 5 $ AlF. 1 . 1 9 1 . 4 0 11 .3 . 0 1 5 1.12 5 2 20$ AIF3 1 . 1 8 1.00 8 . 3 .012 1 . 0 9 5 3 20$ AlF, 1 . 1 4 0 . 9 0 7 . 6 .011 O . 9 9 5 4 20$ A1F 5 1 . 0 8 1.00 8 . 3 .012 - 9k - TABLE E-II Sodium Activities (Alumina-Saturated.. Reduction Cell Electrolyte) Run Init ial Bath wt. $ Mole $ <?Na No. Composition Ratio Na Na 13- 1.55 1.68 4.78 31.2 .082 14 1.55 1.68 4.56 30.2 .076 15 1.55 1.68 4.58 30.2 .076 16 . 1.55 1.70 4.38 29.2 . O69 17 1.55 1.66 4.28 28.6 .066 18 1.55 I.67 4.90 31.6 .085 19 1.55 1.66 4.88 31.6 .085 20 1.55 1.68 5.20 33.0 .096 21 1.39 1.60 4.18 28.2 .064 22 1.39 I.63 4.00 27.2 .058 23 1.39 I.67 4.30 28.8 .067 24 1.39 1.65 4.20 28.2 .064 31 1.55 +5$ AlF I.70 4.40 29.25 .070 32 1.55 + 5$ ALFI 1.70. 4.70 30.8 .079 33 1.55 + 5$ AlFj 1.70 4.50 29.8 .073 34 1.55 + 5$ A1F 5 1.70 4.60 30.3 .076 35 1.55 +5$ AlF, 1.70 4.80 • 31.2 .082 36 1.55 + 10$'AlF, 1.67 4.90 31.6 .085- 37 1.55 + 10$ AlF^ I.67 4.30 28.8 .067 38 1.55 + 10$ AlF? 1.68 4.20 28.2 .064 39 1.55 + 10$ AlF, I.63 . 4.80 31.2 .082 4o 1.55 + 10$ AlFj I.51 3.10 22.4 .039 4 i 1.55 + 10$ AlF, 1.42 2.20 16.8 .024 J 1.4l 42 1.55 + 10$ AlF, 1.44 2.40 18.1 .027 J 1.37/ 43 1.55 + 10$ AlF, 1.45 2.60 19.4 •; .030 1.43 - 95 - TABLE E-III Sodium Activities.(Pure Cryolite and Reduction Cell Electrolyte with 7$ CaFp Addition) Run Init ial NaF-AlF, . wt.. $ Mole $ . «Na No. Composition Ratio^ Na Na , 26 1,55 + 7$ CaF2 1.76 4.10 27.8 . 062 27 1-55 + 7$ CaF 2 1.86 3.58 25.O .048 28 1-55 + 7$ CaF2 2.02 4.13 28.0 .062 29 1-55 + 7$ CaF 2 1.86 3-84 26.4 .054 30 . 1-55 + . 7$ CaF2 I.78 .4.30 28.8 .067 55 Pure + 10%. A 1 F 5 1.. 26 1.60 12.8 .017 + 7$ CaFg/ 1.13 56 Pure + 10$ A 1 F , 1.25 ; l.4o • 11,5 '• .015 + 7$ CaF2 1.20 - 96 - APPENDIX F Mathematical Analysis and Computer Data - 97 - APPENDIX F Mathematical Analysis and Computer Data Symbols (I) ~ X 1 1 ^ 1 2 8 3 YC = log ^NaF Y,^ N = In ^ NaF . = In ^A1F 3 1 2 8 3 1 2 8 3 AC '•• , = log . ^ A l F , 3 1 2 8 3 ANA = ^ N a 1 2 8 q N(I) = NA1F 3. . K = 1.91 X 1 0 {equilibrium constant) X(I) = log ^NaFT T°K R = gas constant ( 4 . 5 7 5 ) EL^j^ = heat of solution - 98 - 1. Chemical equilibrium equation ANA e 3 Y 3Y-A 3Y-A 3 /N ~A~ N (MA In 1-N/ . . . N /ANA C \1-N (1) 2. . . Gibbs-Duhem..equation A/ • s = - f l - N l Y ^) : • ~ N ~ for 1 = 1 , N = .223 1 N=N Y^ dN + B IT . N=.223 Y = -1.672. (2) f o r i . * 1, Substitute .2 into 1 3Y .+ Y (l-N) + N .N=N Y dN N N=.223 B . = • Z >N=N Y (2 + l ) - - / Y dN + B + Z N N N=.223 Differentiating with (2 + l) Y' - , Y N respect to N N -Y + Z' Y' N N Z \ i N N N 2N + 1 Z 1 dN + constant 2 N +• 1 .223 - 9 9 - where;, the constant equals the value of Y YC = Y/2.3026 AC = A/2.3026: EL •=• .(YC-X) R  . 1 - 1 1283 T -1.672 -1.672 + PRINTED ON J U L . 11 /1962 FORTRAN IA COMPILE FOR P . E . AYLEN 8300 C W. DETTWILER FOR P . AYLEN 8 30 0 C 830C READ 2 t N , C , R 834 8 2 FORMAT ( 1 3 , 3X , E 1 2 . 2 1 F 12 .0 ) 839U PRINT 3 8418 3 F O R M A T < 7 X l H Z l l X l H Y l l X l H A l l X T H L / > 8584 DO 4 1 - 1 , N 8596 READ 51 ENt ANA, X i T 8656 5 F 0 R M A T ( F 1 2 . C , F 1 2 . C , F 1 2 . C t F 1 2 . C ) 8694 Z - L O G ( ( E N / C ) » ( A N A / ( 1 . C - E N ) ) « * 3 ) 8814 YN - Z » l . C / ( ( 2 . C » E N + 1 . C ) » » 2 ) 8922 IF ( I- 1) 6 1 7 , 6 8990 7 Y - - 1 . 6 7 2 9026 60 TO 8 , 9034 6 Y - Y • ( E N P - E N ) « ( Y N + Y O ) / 2 . C + E N » Z / ( 2 . C»EN+1 . 0 ) - E N P * S/ ( 2 . C » E N P + 1 . ) ,_, 9370 8 YO - YN R 9394 S - Z 9418 ENP - EN 9442 A • 3 . 0 * Y - Z 9U9C AC - A / 2 . 3 0 2 6 9526 YC - Y / 2 . 3 0 2 6 9562 EL - ( (YC - X ) »R ) / ( 1 . 0 / 1 2 8 3 . 0 - l . C / T ) 9718 U PRINT 1 C , Z , Y C , A C , E L 9814 10 F 0 R M A T l F 1 2 . 5 , F 1 2 . 5 , F 1 2 . 5 t F 1 2 . 5 ) 9852 SKIP TO 1 9864 END Figure F - l . Computer Program TABLE F-r : Activity Data for NaF and AlF Computer, Data Computer Results Calculated Thermodynamic Values N ANA X - T z ; YC AC YC; AC ' N A1F 3 2 N 2 NaF .223 .094 . - -733 1272.6 16.84431 -.72613 -9.49375 14, 61 15.72 .232 .070 - .832 1277-2 16.03443 - .781.1.3 -9.30703 14.52 15.78 .-24l • 053 - -949 1280.4 15.27324 -.83422 -9.13570 14.35 15.86 .246 .0465 -1.019 1281.3 14.92108 T.-.85926 -9.05789 . 14.20 . 15.92 .250 .. 042 -1.094 1281.6 14,64782 -.87893 -8.99824 . 14.06 15.98 .255 • 037 -1.162 1281.3 14.30744 -.90374 -8.92482 13.91 L6.08 .262 .032 -1.183 1281.0 13.92729 -.93187 -8.84413 13-59 16.23 .276 .023 -1.283 1277.5 13.04608 -.99882 -8.66228 13.11 :16.53 .296 .0158 -1.451 1267.2 12.07363 -1^07569 -8.47057 12.28 17.08 • 321 .012 -1.719 1243.7 11.43787 -1.12841 -8.35263 10-95 18.12 - 102 - APPENDIX.G Analysis of Na-Al Binary System - 103 - APPENDIX G Analysis of Na-Al Binary System 20 A review of the literature shows very l i t t l e published data, on the Na-Al system. Originally i t was thought that there was no. mutual solubility in the liquid state. However, re-investigation of the Al-rich 21 22 alloys by Fink,: Willey and Stumpf and Ransley and Neufeld established the existence of a true monotectic. Fink et a l . established the hypo-mono4- tectic . liquidus by both direct and differential thermal analysis and set the monotectic point at .18 weight per cent sodium and at a temperature 1.2°K. below the melting point of pure aluminum. They also found that the solubility of liquid sodium decreased with increasing temperature. Ransley and Neufeld accepted Fink et al. 's thermal data for the hypo-monotectic liquidus and concentrated their interest on the solid solubility limits and the liquid miscibility boundary. They established the monotectic at 0.1.4 weight per cent sodium and observed a more orthodox increase of solubility with increasing temperature. The solid solubility of sodium in aluminum was reported by both teams of researchers to be ^.003 weight per cent at the monotectic temperature. A composite of the two phase diagrams appears as Figure G- l . An attempt was made to calculate thermodynamic data from the composite' phase diagrams. Several inconsistencies became apparent during this treatment. Ransley and Neufeld's data (see Table G-I) on the solubility of liquid sodium was plotted to obtain a graph of log N. .Vs. l /T (see Figure G-2). This plot established the monotectic point at .0017 mole per cent sodium (.1^5 weight per cent). The slope of the line gives a value for the partial heat of solution of 9230 calories. - 1 0 4 - Figure G - l . Na-Al Phase Diagrams from Data of Fink et a l . and Ransley and Neufeld. - 105 - TABLE G-I Partial Heat of Solution Data for Na-Al Binary Na Content wt. i • % a T°K l/T 0.l4 .001643 938 1.066 X 10" 5 0.15 .001761 943 1.060 x 10"5 0.15 . .001761 943 1.060.x 10-3 .0.18 .002112 973 1.028 x 10"5 •' 0.22 .002582 998 1.002 X l O - 5 0.20 .002347 998 1.002 X 10"5 0.23 .002699 1023 .9775 x 10"5. 0.22 .992582 1023 .9775 x 10"5 0.25 .002934 1048 .9542 x 10"5 0.15 .001761 958 i.o44 x io-5 0.19. .002230 988 1.012 x 10-5 1.1 Figure G-2. Plot of Log N vs. l /T for Ransley and Neufeld's Data - 107 - Examination of the hypo-monotectic liquidus established by Fink et a l . showed further discrepancies. . Therefore, i t was necessary to reconstruct a phase diagram which was consistent with thermodynamics but 23 compatible with the limited experimental data. Data supplied by Hollingshead v (see Table G-II) on the concentration of sodium in aluminum at different NaF-AlF^ bath ratios was used to obtain ^Na values in the low concentration region. A plot of the data is shown in Figure G-3. The )$Na values were obtained by uti l izing the plot developed from Appendix C (see Figure 9« ) adjusted for CaF2 and A120^ content. Using this data, i t was possible to establish a hypo-monotectic liquidus for the Na-Al binary (see Figure G-4). It was necessary to alter the temperature differential between the melting point of aluminum and the monotectic temperature to .8°K from 1.2°K. to provide thermodynamic consistency. This change should be well within the expected experimental error of the original researchers. 2k The activities of aluminum are calculated from the relationship log <?TA1 = (T 0 - T N ) A H f + log N< where T Q = 933.0°K. T,T = m.p. at N. (from phase diagram, Figure G-rk) Al A x . H f •= 2570 calories 2^ N* = solid solubility of Na in Al . = <\003$ As the solid solubility of sodium in aluminum is negligible, i t can be disregarded in this calculation. The relationship then reduced to log « T M - = - ( T Q - T H A I ) A S F *-575 T "Al where A S f = 2^70 = 2.7575 e.u. 933-0 - 108 - TABLE G-II Sodium Content of Aluminum from Reduction Cells as a-Function of NaF/AlF, Ratio (from Hollingshead2^) NaF/AlF . Na CaF Temperature by wt.-5 ppm i °C. 1.16 18 1.22 30 1.23 33 1.25 • 40 1.27 42 1.28 30 1.30 40 1.30 40 1.32 53 1.33 50 1.37 85 1.38 70 1.38 75 1.39 70 1.39 70 l . U 80 1.43 105 1.44 90 1.47 160 8.9 939 8.7 964 9-0 944 8.5 946 8.8 957 - 978 - 969 - 975 9-1 960 - 957 8.1 970 - 960 8.0 982 8.3 960 8.3 972 8.4 947 9-0 982 8.4 967 8.2 971 660.2 66o.o o o (U u •p cd u <u a EH 659.8 659.6 _ 659.4 L_ 659.2 659.0 Figure G-4. Revised Na-Al Binary - I l l - The activities of sodium can then be calculated using the Gibbs- Duhem integration technique 2^^ (' s e e Table G-III). The tie point in the integration is the monotectic point where the activity of sodium is unity, since the alloy is in equilibrium with pure sodium gas at this point. The value of O7Na at the monotectic is 588 and Column 13 of Table G-III has to be corrected by a constant factor. The values of ^ Na can then be determined at 1283°K. assuming that the solution is non-ideal using the relationship1-^ d In = d InV = L d T d T RT'2 this reduces to 1 1 — rp _ rn In 2 = " L 2 1 where )$2' ^1 = activity coefficients.at Tg and T^ L = heat of solution (9230 calories) R =• the gas constant. The ratio of l s 3-79 f ° r the above case. The activities of sodium calculated by this method (Table G-III) are plotted against concentration in Figure G-p, and as a function of weight per cent sodium in Figure G-6. TABLE G-III Determination of Sodium Activity from Revised-Na-Al Binary 3 4 5 6 7 8 N. Na N Al *A1 > A 1 log 8A1 N Na -vA1 •%a2 -%a NAI Na log 9 3 3 . 0 0 9 3 2 . 9 8 8 9 3 2 . 9 7 6 9 3 2 . 9 6 3 9 3 2 . 9 5 1 9 3 2 . 9 3 9 9 3 2 . 9 2 7 9 3 2 . 9 1 5 9 3 2 . 9 0 3 9 3 2 . 8 6 9 3 2 . 7 8 932.64 9 3 2 . 5 0 9 3 2 . 3 5 932.24 9 3 2 . 2 0 0 . 0 0 0 0 2 0 . o o o o 4 o . 0 0 0 0 6 0 . 0 0 0 0 8 0 . 0 0 0 1 0 0 . 0 0 0 1 2 0 , o o o i 4 o . 0 0 0 1 6 0 . 0 0 0 2 3 5 . 0 0 0 3 5 3 . 0 0 0 5 8 7 . 0 0 0 8 2 3 . 0 0 1 1 7 4 . 0 0 1 5 5 0 . 0 0 1 7 0 0 . 0 0 2 0 0 0 1 . 9 9 9 9 8 0 . 9 9 9 9 6 0 . 9 9 9 9 4 0 . 9 9 9 9 2 0 . 9 9 9 9 0 0 . 9 9 9 8 8 0 . 9 9 9 8 6 0 . 9 9 9 8 4 0 . 9 9 9 7 6 5 • 9 9 9 6 4 7 . 9 9 9 4 1 3 . 9 9 9 1 7 7 . 9 9 8 4 5 0 . 9 9 8 3 0 0 . 9 9 8 0 0 0 . 9 9 9 9 8 0 • 9 9 9 9 6 3 .999947 . 9 9 9 9 2 3 . 9 9 9 9 0 7 . 9 9 9 8 9 1 . 9 9 9 8 7 1 . 9 9 9 8 5 5 . 9 9 9 7 9 1 . 9 9 9 6 7 1 .999466 . 9 9 9 2 5 5 . 9 9 9 0 3 4 . 9 9 8 8 6 7 . 9 9 8 8 0 7 . 9 9 8 8 0 7 1 . 0 0 0 0 0 0 0 1 . 0 0 0 0 0 3 1 . 0 0 0 0 0 7 1 . 0 0 0 0 0 3 1 . 0 0 0 0 0 7 1 . 0 0 0 0 1 1 1 . 0 0 0 0 1 1 l . 0 0 0 0 1 5 , 0 0 0 0 2 6 . 0 0 0 0 2 4 , 0 0 0 0 5 3 . 0 0 0 0 7 8 . 0 0 0 2 0 8 . i . o o o 4 i 8 1 . 0 0 0 5 0 8 1 . 0 0 0 8 0 9 1. 1. 1. 1. 1. 0 0 . 0 0 0 0 0 1 3 . 0 0 0 0 0 3 0 . 0 0 0 0 0 1 3 . 0 0 0 0 0 3 0 .ooooo48 . 0 0 0 0 0 4 8 . 0 0 0 0 0 6 5 . 0 0 0 0 1 1 3 . 0 0 0 0 1 0 4 . 0 0 0 0 2 3 0 . 0 0 0 0 3 3 9 . 0 0 0 0 9 0 3 . 0 0 0 1 8 1 4 . 0 0 0 2 2 0 5 . 0 0 0 3 5 1 1 x 1 0 - 1 0 6 X I0'_l 6 X 1 0 y 4 x i o - 9 _ x 1 0 - 8 1 . 4 4 X 1 0 " ° 9 6 x i o _ y , 5 6 X 1 0 - 8 - 8 5 . 5 2 3 X 1 0 1.246 X 1 0 3.446 X 1 0 " ' 6 . 7 7 3 x io-7 1 . 3 7 8 X 1 0 " ° 2 . 4 0 2 5 x 1 0 " 6 2 . 8 9 x 1 0 - 6 4 x i o - 6 4 . 9 9 9 9 x 1 0 ^ 2 . 4 9 9 9 x- io4- , 1 . 6 6 6 5 6 7 X 1 0 1 . 2 4 9 9 X l p 4 9 . 9 9 9 x i o 5 8 . 3 3 2 3 3 3 x ICK 7 . 1 4 1 8 5 7 x i o 5 6 . 2 4 9 x i o 3 4 . 2 5 3 9 x 1 0 5 2 . 8 3 2 0 7 x i o 5 1 . 7 0 2 4 2 X 1CK 1.21412 X IO? 8 . 5 0 9 5 9 x 1 0 2 6 . 4 4 1 6 1 2 X 1 0 ^ 5 . 8 7 2 3 5 x 1 0 2 4 . 9 9 X 1 0 2 - . 0 3 2 4 9 9 - . 0 4 9 8 9 7 - . 0 1 6 2 4 9 - . 0 2 9 9 9 7 - . 0 3 9 9 9 5 - . 0 3 4 2 8 1 - . 0 4 0 6 1 9 - . 0 4 8 0 6 9 - . 0 2 9 4 5 4 - . 0 3 9 1 5 6 - . 0 4 1 5 9 - . 0 7 6 8 4 2 - . 1 1 6 8 5 1 - - . 1 2 9 4 8 5 - . 1 7 5 1 9 9 -TABLE G-III Continued 10 11 12 13 14 15 - 16 17 18 log YAI / log ^Al cm 9 + N 2 / N 2 - A X  iNNa^. / Na , 11 812.5 .: .197149 .164650 3.039047 -1094 .00004 289 .0116 .0034 833.3 .180691 .130694 3.OO5091 1012 .00006 268 .0161 .0051 203.1 .170327 .154078 3.028475 1068 •.00008 282 .0226 •'.-. .0068 300.0 .165296 .135299 3.009696 1023 .00010'. ••' 270 .0270 .0085 333.3 .158963 .118968 2.993365 985 .00012 260 .0306 .:• .0102 244.9 .153181 .118900 2.993297 985 .00014 260 .0364 ..0119 253.9 .148193 .107574 2.981971 959 .00016 253 .o4o8 .0136 204.6 .130999 .082930 . 2.957327 906 .000235 239 .0562 .02 83.5 . i i 4 o o i .084547 2.958944 910 .000353 240 .0847 • 03 66.7 .096428 .057272 2.931669 835 .OOO587 220 .129 • 05 50.1 .082646 .041487 2.915884 824 .000823 218 .179 .07 65.5 .062358 -.014484 2.859913 724 .001174 191 .224 .10 75-5 .035850 '• - .081001 2.793396 622 .OOI55O 164 .254 .14 76.3 .024465 -.105020 2.769377 588 .001700 155 .264 .17 logjfNa *Na " N ^ ^ a ^ <?Na _ + Na add 2,874397 -:• L = 9230 - 115 - Figure G-6. Activity of Sodium as a Function of . Weight Per Cent Na in Al Metal. - 116 - BIBLIOGRAPHY 1. Pearson, T. G. , "The Chemical Background of the Aluminum Industry", Royal Institute Chemical Lectures, Monographs and Reports, No. 3 (1955). 2. Grjotheim, K. , "Contribution to the Theory of Aluminum Electrolysis", Norke Videnskabers Selskabs Skrifter, No. 5 (1956). 3. Foster, L. M., Annals of the N. Y. Academy of Sciences, Vol. 79, . Art. 11, p. 919. 4. Bonnier, E . , Bul l . Soc. Chim., France 1950, D 131. 5. Drossbach, P., "Electrochemistry of Fused Salts", p. 119-128, Springer, Berlin (1938). 6. FreJacques, M. M. , Bull . Soc. Franc. Elec. % 684 (19^ 9). 7. Gadeau, R., ibid, jk, 5+0 (1947). 8. Grunert, E . , Z. Elektrochem, 48, 393 (1942). 9. Grjotheim, K. , Alluminio, 22, 6 679 (1953)- 10. Piontelli , . R.., and Montanelli, G. ibid 22, 6 672 (1953)- 11. Jander, ¥ . , and Hermann, H. , Z.-fur anorg. allgem. Chem. 239J 65 (1938). 12. Pearson, T. G. , and Waddington, J . , Discussions of the Faraday Society 1, 307 (19+7). 13. Feinleib, M.and Porter, B . , J . Electrochem. Soc. 103 No. 4, 232 (1956). 14. Feinleib, M. and Porter, B . , ibid, No. 5, 300 (1956). 15. Frank, W. B. and Foster, L. M. , "Constitution of Cryolite and NaF-AlFj Melts", Intern. Symp. on the Physical Chem. Process Metallurgy", Pittsburgh, Pa. 1959• 16. Foster, L. M. , and Frank, W. B . , J . Electrochem. Soc. Vol. 107, No. 12 997 (i960). .17. Hansen, M. , "Constitution of Binary Alloys", McGraw-Hill, 997 (1958). 18. Hauffe, K. , and Vierke, A. L . , Z. Elektrochem, 5_3, 151 (l9^9)- 19. Chipman, J . , Discussions of the Faraday Society 4, 23, (1948). 20. Hansen, M., "Constitution of Binary Alloys", McGraw-Hill, 117 (I958) - 117 - Bibliography Continued 21. 22. 23- 2k.- 25. 26. 27- 28. 39- 30. 31. 32. 33- 34. 35- Fink, W. L . , Willey, L. A . , and Stumpf, H. C , Trans', of A. I .M.E. , , 175, 364-7l . ( l 9 48). Ransley, C. E . , and Neufeld, H . , J . Inst. Metals j8, 25-48 (I95O-5I) Hollingshead, E. A.., personal communication. Kubaschewski. 0. and Evans., E. L. "Metallurgical Thermochemistry" (1958). Kelley, K. K. , Contribution to the Data on Theoretical Metallurgy, Bulletin 584, Bureau of Mines, (i960). Darken,' L. and Gurry, R., "Physical Chemistry of Metals",. McGraw-Hill, Chpt. 10 (1953). Wagner, C. "Thermodynamics of Alloys", Addison-Wesley Press, Cambridge Mass. (1952). Wagner, C. "Acta Metallurgica, 6, 309-19, May (1958). Chu, B. and Egan, J.,-Annals of NV Y. Academy of Sciences, Vol. 79, Art. 11, 908 (i960). . Wagner, C , private communication. Grube,.G,, and Hantelmann, B . , "The Reactions of Al and Na with Melts Physikalische Chemie der Metalle am Kaiser Wilhelm - Institut fur Metallforschung, February 1945• Fenerty, A . , and.Hollingshead, E. A . , J . of Electrochem. Soc. Vol. 107, No.' 12, 993- Piontelli , R., "Atti simposia elettrolisi sali fusi produzione metalli speciali in Italia", Milano, 5-7 Maggio i960. Glassner, Alvin,"The Thermochemical Properties of the Oxides, Fluorides, and Chlorides to 2500°K., U. S , Atomic Energy Commission Publication, ANL - 5750. Stokes, J . J , Jr . and Frank, W. B. , "Spectrosocpic Investigation of the Occurrence of Sodium in the Fumes Above Molten Cryolite", A.I.M.E. International Aluminum Symposium, N. Y. February, 1962. 

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
United States 10 3
China 6 1
France 3 0
Germany 1 18
Turkey 1 0
Russia 1 0
City Views Downloads
Unknown 6 17
Shenzhen 4 1
Wilmington 3 0
San Mateo 1 0
Beijing 1 0
Hangzhou 1 0
Istanbul 1 0
Ashburn 1 0
Kansas City 1 0
Wuppertal 1 1
Starkville 1 0
Sunnyvale 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}
Download Stats

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0105803/manifest

Comment

Related Items