Investigation of the thermodynamics of V-O solid solutions by distribution coefficient measurements in the V-O-Na system
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I N V E S T I G A T I O N of the t h e r m o d y n a m i c s of the t e r m i n a l V-O solid solution is m a d e difficult by the ext r e m e l y low oxygen p a r t i a l p r e s s u r e s i n v o l v e d (10 -30 to 10 -45 aim). Oxygen p r e s s u r e s in this r a n g e c a n n o t be m a i n t a i n e d and m e a s u r e d in s t a n d a r d g a s e o u s e q u i l i b r a t i o n e x p e r i m e n t s ; however, they can be m a i n t a i n e d and d e t e r m i n e d in liquid s o d i u m by c o n t r o l l i n g the oxygen c o n c e n t r a t i o n at l e v e l s below 20 ppm. T h e r e f o r e , e q u i l i b r i u m d i s t r i b u t i o n c o e f f i c i e n t m e a s u r e m e n t s of oxygen in the V - O - N a s y s t e m p r o v i d e a c o n v e n i e n t method for studying the t h e r m o d y n a m i c s of the s o l u tion of oxygen in v a n a d i u m . The d i s t r i b u t i o n coefficient, which is the e q u i l i b r i u m r a t i o of oxygen in v a n a d i u m to oxygen in s o d i u m , can be d e r i v e d f r o m b a s i c t h e r m o d y n a m i c data for the b i n a r y V-O and Na-O s y s t e m s , if the two m e t a l s a r e c o m p l e t e l y i m m i s c i b l e when in p h y s i c a l c o n t a c t and both c o n t a i n oxygen in solution. Since the p a r t i a l m o l a l free e n e r g i e s of oxygen in each m e t a l a r e equal when the s y s t e m is in e q u i l i b r i u m , the e q u i l i b r i u m d i s t r i b u tion of oxygen is o b t a i n e d by s e t t i n g the f r e e - e n e r g y ~ change equal to z e r o for the t r a n s f e r of oxygen f r o m sodium tO v a n a d i u m ONa~ O v
AF = FOv - F 0 y :
0
[1]
where ONa and O V denote oxygen in s o l u t i o n in s o d i u m and v a n a d i u m , r e s p e c t i v e l y . The equation for the e q u i l i b r i u m d i s t r i b u t i o n of oxygen in t e r m s of the a c t i v i t y has been developed p r e v i o u s l y . 1
~~ a~ aoNa
[ AF a.o
a ~ exp L ao_Na
RT
[2]
The s u p e r s c r i p t on the a ' s r e f e r to s a t u r a t e d s o l u t i o n s of oxygen in the m e t a l s . Since the a c t i v i t i e s can be e x p r e s s e d in t e r m s of the a c t i v i t y c o e f f i c i e n t s y and the atom f r a c t i o n s N i . e . , a i = y i N i , the e q u i l i b r i u m d i s t r i b u t i o n of oxygen in t e r m s of atom f r a c t i o n can be w r i t t e n as DALE L. SMITH is Associate Nuclear Engineer, Materials Science Division, Argonne National Laboratory, Argonne, Ill. Manuscript submitted June 29, 1970. METALLURGICALTRANSACTIONS
o Vqv NQv
YON a NO_Na
9v o
N~ 9v NO
TQN a
0_Na
[AFNa20 -- AFvso] exp L
RT
J
[3]
If the s o l u t i o n s of oxygen in both m e t a l s obey R a o u l t ' s * *The standardstate 7 = 1 at N = N~ is appropriatefor treatingterminalsolutionsof this type and is usedthroughoutthiscouuuunieatiou. law, Eq. [3] r e d u c e s to the f a m i l i a r N e r n s t equation for the d i s t r i b u t i o n of a solute b e t w e e n two i m m i s c i b l e phases. Nov _
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