Prediction of activities of oxygen in dilute quaternary solutions using binary data
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It follows that
e E AliA(A+B+C) = I, ~ NB Al'tA(A+B)
A E P'A(A+C) NA
+ ~
-
(1
[4]
--NA)2[AGfB+Cl]N~/Nc
iii) The t h i r d a l t e r n a t e e x p r e s s i o n 3 in t e r m s of b i n a r y v a l u e s of AG E along c o m p o s i t i o n paths with c o n s t a n t NA/NB, NB/N C and NA/Nc, shown in Fig. 2, is:
E AG(A+B+C) = (1 - .z[AG(A+B) Rr - ~ c ~ ~ R~
AG~A+B+C) = AH(A+B+C) = NANB~AB + NANC~AC + NBNC[3BC
+ (1-
- .2/Ac~+cl NA~ ~, R T
NA/N~,
)NB/Nc
+ (1-- NB)2(AG~R~+C) )NA//NC
where
[3AB=-ZN'IEAt3-(EAA
; EBB)landsoforth[1 ]
[5]
The p a r t i a l m o l a r p r o p e r t i e s a r e given by e x p r e s s i o n s of the type
and
A
A#~(A+B+C) = AHA(A+B+C) = #Aa~VB(WB + NC) + #ACNC(NB + NC)
[2]
- NSNC~BC
~ N ~BE/ NI AC : cor~l:.
ii) The v a l u e of hG~A+B+C) m a y a l s o be e x p r e s s e d in t e r m s of b i n a r y v a l u e s of AG E along c o m p o s i t i o n p a t h s w h e r e NA a n d NB/N C a r e c o n s t a n t , 3 a s shown in F i g . 1.
AG~A+B+C) _ RT
NB AG(A+B) + NA) RT
(1 -
•
NC Yg)
(1 -
~C?A+C)] . (1 N A ) 2 RT .JNA
•
,
L
RT
[a]
.]NB/N C
K. T. JACOB and C. B. ALCOCKare Postdoctoral Fellow, and Professor and Chairman, respectively, Department of Metallurgy and Materials Science, University of Toronto, Toronto, Canada. Manuscript submitted July 28, 1971. METALLURGICALTRANSACTIONS
E
+C) ' /~G(A+C)
~ B
~I ~st.
c)
c
Fig. 1--Location of binary data points used in Eqs. [3] and [4]. VOLUME 3, JULY 1972-1913
E
E A ItB (A+B+C) = [(1 -- Nc)AP.B(A+B)
+ NC(1 -- Nc)AG~A+B ) ]NA/N B + [(1 - NA)ApEB(B+C)
* NA(1 -- N A ) A G ~ + c ) ] N B / N c (1 -
-
N
z
E
B) [C(A+C]NA/NC
[6]
Olson and Toop a have shown that the e x c e s s f r e e e n ergy of n o n r e g u l a r liquid s o l u t i o n s f o r m e d by t h r e e m e t a l l i c c o n s t i t u e n t s m a y be obtained in an e m p i r i c a l m a n n e r f r o m the data on the t h r e e b i n a r i e s involved, even though the b i n a r i e s do not c o n f o r m to a s i m p l e r e g u l a r b e h a v i o r . The second and t h i r d t r e a t m e n t s shown above a r e m o r e useful for the e m p i r i c a l c a l c u lation of b i n a r y e x c e s s f r e e e n e r g i e s for n o n r ~ g u l a r s y s t e m s , b e c a u s e the e x p e r i m e n t a l b i n a r y AG v a l u e s m a y be used d i r e c t l y in t h e s e e x p r e s s i o n s r a t h e r than a v e r a g e d v a l u e s for the c o n s t a n t s ~ A B , and so forth, in Eqs. [1] and [2]. However, the second method of r e p r e s e n t a t i o n has b e e n shown a to give different r e s u l t s for the e x c e s s t e r n a r y f r e e e n e r g y s u r f a c e of a n o n r e g u l a r solution, depending on the choice of component s u b s c r i p t s . Eqs. [5] and [6] a r e t h e r e f o r e most s u i t a b l e for c a l c u l a t i n g AG~+B+C) and the a c t i v i t y coeffic i e n t s of A, B, and C in a t e r n a r y solution, f o r m e d by three metallic constituents. B a s e d on a r e g u l a r solution model, the p a r
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