Thermodynamics of the liquid binary iron-tin by mass spectrometry
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T H E s y s t e m F e - S n h a s a b r o a d m i s c i b i l i t y gap in the liquid a b o v e a m o n o t e c t i c t e m p e r a t u r e of 1130~ The p r e s e n t s t u d y w a s u n d e r t a k e n to i n v e s t i g a t e the t h e r m o d y n a m i c e x c e s s functions of the s y s t e m by the m a s s s p e c t r o m e t r i c i n t e n s i t y r a t i o m e t h o d . ~'z The e f f e c t s of c o m p o s i t i o n on the functions of i n t e r e s t a r e d e l i n e a t e d in F i g . 1. The ion c u r r e n t i n t e n s i t i e s , Ii, a r e p r o p o r t i o n a l to the t h e r m o d y n a m i c a c t i v i t i e s , ai; CG is a c o n s t a n t .
F i g . 3 r e f e r s to the e q u a l - a r e a m e t h o d by N e c k e l and W a g n e r 2 which i n v o l v e s the e x p l i c i t c a l c u l a t i o n of the c o n s t a n t CG in Eq. [2]. GE i s l i n e a r a c r o s s the t w o p h a s e r e g i o n , thus aGE/ax2 and the i n t e g r a t i o n f u n c tion, Eq. [2] r e m a i n c o n s t a n t . The c o r r e s p o n d i n g v a l u e of the o r d i n a t e i s given by ~7 in Fig. 3. ~? i s d e r i v e d f r o m the e q u a l i t y of the individual a c t i v i t i e s for the c o e x i s t e n t p h a s e s .
[1]
In ~- = In a___~2+ CG al 11
I
I
F o r the c a l c u l a t i o n of e x c e s s Gibbs e n e r g i e s , GE, and of a c t i v i t y c o e f f i c i e n t s , vi, the s o - c a l l e d i n t e g r a t i o n function i s given b y
I2xl _
In Ilx2
1 aGE =In 72 + C G R T ax2 71
In x~
~-x gap
x2
miscibility gap
-
I
[2]
The i n t e n s i t y r a t i o , 12//11, i s c o n s t a n t a c r o s s a t w o p h a s e r e g i o n . Although vi i s not defined in t h i s r e g i o n , a f o r m a l i n t e g r a t i o n function, In /~-~]gap
L. V
L I z Xl n it x - ' ~
I I I I
\k
/
\
can be e m p l o y e d in a continuous i n t e g r a t i o n a c r o s s the complete binary system. The G i b b s - D u h e m i n t e g r a t i o n of Belton and F r u e han 1 i s d e m o n s t r a t e d in F i g . 2. LnT~, i.e., lnT~ at xl = 0, is c o m p u t e d by adding
k
\ d
\ \ Xl In-~-2 +d
1) in 7~(l), f r o m the i n t e g r a t i o n b e t w e e n xl = 1 and xl(/); 2) In 7~(r) - l n T ~ ( l ) = In [x~(l)/xx(r)]; and 3) In 7~ - l n T x ( r ) f r o m the i n t e g r a t i o n b e t w e e n xl(r) and x~ = 0.
\
\,j
A l t e r n a t e l y one m a y c a r r y out a s i n g l e i n t e g r a t i o n f r o m xx = 1 to xl = 0 by taking Eq. [3] into a c c o u n t : Xl (r) - x,(/) f
x2dIn
X~=ln xz
~x,(l) = In ~l(r) - In 7~(l)
I I
[4]
SIGURD WAGNER, formerly Postdoctoral Fellow, Department of Metallurgical Engineering, Ohio State University, Columbus, Ohio, is now with Bell Telephone Laboratories, Murray Hill, N. J. 07974. GEORGE R. St.PIERRE is Armco Professor of Metallurgy, Department of Metallurgical Engineering, Ohio State University, Columbus,
Ohio. Manuscript submitted April 3, 1972. METALLURGICAL TRANSACTIONS
x2(r ) I
X2(t)
I
X2
Fig. 1--Ln (Iz/I1) and In phase region.
(12xl/ltx2)
f
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