Mass spectrometric determination of activities for alloys with complex vapor species: Bi-Pb and Bi-Tl
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FRUEHAN
F o r s o l u t i o n s f r o m which c o m p l e x s p e c i e s v a p o r i z e (Bi2, Si2, A120, Sb4, and so forth) new m e t h o d s of d e t e r m i n i n g the t h e r m o d y n a m i c p r o p e r t i e s f r o m m a s s s p e c t r o m e t r i c data a r e d e m o n s t r a t e d . In o r d e r to t e s t the f e a s i b i l i t y of t h e s e new t e c h n i q u e s , e x p e r i m e n t s have b e e n c a r r i e d out on the liquid B i - P b and Bi-T1 s y s t e m s for which adequate t h e r m o d y n a m i c data a r e a v a i l a b l e . In e v a l u a t i n g the t h e r m o d y n a m i c p r o p e r t i e s , the ion c u r r e n t r a t i o s l~b/1~3i2 and IT1/IBi + + 2 w e r e e m p l o y e d , e.g.
log%~---
NBi=NBiNp b f iZgpba NBi=l
Ipb N13i
log
+ IBi2 Npb
M e a s u r i n g t h e s e p a r t i c u l a r ion c u r r e n t r a t i o s e l i m i n a t e s e r r o r s r e s u l t i n g from the f r a g m e n t a t i o n of the c o m p l e x v a p o r s p e c i e s in e v a l u a t i n g the t h e r m o d y n a m i c p r o p e r t i e s . A d i m e r - m o n o m e r t e c h n i q u e , which c o r r e c t s for f r a g m e n t a t i o n , w a s a l s o d e m o n s t r a t e d . The r e s u l t s u s i n g t h e s e two independent a p p r o a c h e s a r e in good a g r e e m e n t with each o t h e r as w e l l a s with p r e v i o u s i n v e s t i g a t i o n s . The a c t i v i t y c o e f f i c i e n t s in both s y s t e m s a d h e r e to the q u a d r a t i c f o r m a l i s m o v e r l a r g e c o m p o s i t i o n r a n g e s , e.g. log ~'~b = -0"255NBi
NBi < 0.8
log ~*rl = -0"8052~Bi
NBi < 0.7
A few y e a r s ago Belton and F r u e h a n 1'~ d e r i v e d exp r e s s i o n s r e l a t i n g the t h e r m o d y n a m i c p r o p e r t i e s of a solution to the ratio of the ion c u r r e n t s of the v a p o r i z ing c o m p o n e n t s as m e a s u r e d by a m a s s s p e c t r o m e t e r . F o r e x a m p l e , the a c t i v i t y coefficient (YA) of c o m p o n e n t A in a b i n a r y m i x t u r e A - B is given by
log
YA
=_
NA=NA NAf=1 NB
The s i m p l e s t a p p l i c a t i o n of this e x p r e s s i o n is when one c o m p o n e n t has a d i m e r (A2) and the o t h e r only a m o n o m e r (/3), so that Eq. [2] s i m p ! i f i e s to log
TA = _
NA=dl
N.
d log ~
NA
d
+ NB
~
I~4---2NB
in]
!
)
d , log ~I~IVB
[1]
w h e r e I + and Ni a r e the ion c u r r e n t s and m o l e f r a c t i o n s r e s p e c t i v e l y . S i m i l a r e x p r e s s i o n s w e r e given for the heats of solution as well a s for m u l t i c o m p o n e n t s y s t e m s . In the d e r i v a t i o n of t h e s e e x p r e s s i o n s it was a s s u m e d that the ion c u r r e n t of a s p e c i e s is p r o p o r tional to its v a p o r p r e s s u r e and t h e r e f o r e to its a c t i v ity in solution. However, in m a n y m e t a l l i c and salt s o l u t i o n s , c o m plex vapor s p e c i e s m a y v a p o r i z e , e. g. Si2, BG, Ag2C 12, SiO, and so fort
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