Thermodynamic Parameters of Liquid Gold-Aluminum Alloys L. ERDI~LYI, J. TOMISKA, AND D. J. FABIAN

A. NECKEL,

G. ROSE,

E. S. RAMAKRISHNAN,

T h e r m o d y n a m i c a c t i v i t i e s and e n t h a l p i e s for Au-A1 a l l o y s have b e e n m e a s u r e d by Knuds e n - c e l l m a s s s p e c t r o m e t r y , i n d e p e n d e n t l y u s i n g c l o s e l y s i m i l a r t e c h n i q u e s in l a b o r a t o r i e s in Vienna and S t r a t h c l y d e . The r e s u l t s a r e c o n s i s t e n t and i n d i c a t e , for Au r i c h a l l o y s , gold a c t i v i t i e s with p o s i t i v e d e v i a t i o n s f r o m Raoult i d e a l i t y . T h i s is in d i s a g r e e m e n t with E M F m e a s u r e m e n t s of Au a c t i v i t y p r e v i o u s l y r e p o r t e d ; the r e s u l t s a l s o indicate e n d o t h e r m i c i t i e s (of ~38 k J / m o l at xA1 ~ 0.5) that a r e s o m e 5 to 6 k J / m o l l a r g e r than t h o s e i n d i c a t e d by the EMF measurements.

GoLD

and a l u m i n u m f o r m a s e r i e s of i n t e r e s t i n g i n t e r m e t a l l i c compounds, AuAlz, AuA1, AuzA1, AusAL~, and AuaA1 of v a r y i n g s t a b i l i t y and c o m p o s i t i o n r a n g e . AuA12 is p a r t i c u l a r l y s t r o n g l y bonded in the s o l i d , with high m e l t i n g point (1333 K, c l o s e to that of p u r e gold) and heat of f o r m a t i o n , is b r i t t l e and has a p r o n o u n c e d p u r p l e color; it has a l m o s t no s o l i d s o l u b i l i t y f o r gold o r a l u m i n u m . The gold r i c h a l l o y s a r e much l e s s s t r o n g l y bonded, with l o w e r h e a t s of f o r m a t i o n and wide r a n g e s of c o m p o s i t i o n ; Au~A1, f o r e x a m p l e , m e l t s at 818 K in a p e r i t e c t i c r e a c t i o n , while a e u t e c t i c (798 K) f o r m s a t s l i g h t l y l o w e r gold c o n c e n t r a t i o n (N77.5 a t . pct). The liquid s t a t e Au-A1 a l l o y s have been s t u d i e d t h e r m o d y n a m i c a l l y by s e v e r a l i n v e s t i g a t o r s . C h a r q u e t et al 1 conducted E M F m e a s u r e m e n t s of the a c t i v i t i e s of the two c o m p o n e n t s , and o b s e r v e d l a r g e n e g a t i v e d e v i a t i o n s f r o m Raoult i d e a l i t y o v e r the e n t i r e c o m p o s i t i o n r a n g e , with c o r r e s p o n d i n g l y l a r g e n e g a t i v e e x c e s s f r e e e n t h a l p i e s and h e a t s of mixing. The gene r a l t r e n d of t h e s e r e s u l t s was s u b s e q u e n t l y conf i r m e d in f u r t h e r E M F s t u d i e s , by P r e d e l et al 2 and Y a z a w a el al 3, who adopted a l s o a d i s t r i b u t i o n method f o r the a l u m i n u m r i c h a l l o y s , m e a s u r i n g the p a r t i t i o n of gold between a l u m i n u m and l e a d . In the i n v e s t i g a t i o n s we r e p o r t h e r e a c t i v i t i e s and e n t h a l p i e s w e r e m e a s u r e d by K n u d s e n - c e l l m a s s s p e c t r o m e t r y . The m e a s u r e m e n t s w e r e made i n d e p e n d e n t l y with a s i n g l e f o c u s i n g V A R I A N - M A T (Atlas) CH4 i n s t r u m e n t at the I n s t i t u t fiJr T e c h n i s c h e E l e k t r o c h e m i e , T e c h n i c a l U n i v e r s i t y Vienna, and with a double f o c u s i n g A E I MS702 at S t r a t h c l y d e U n i v e r s i t y , G l a s g o w . The e x p e r i m e n t a l t e c h n i q u e s w e r e c l o s e l y s i m i l a r and we r e p o r t the r e s u l t s t o g e t h e r b e c a u s e they a r e c o n s i s t e n t and i n d i c a t e , for the gold r i c h a l l o y s , a c t i v i t i e s of gold that a r e in s o m e d i s a g r e e m e n t with the e a r l i e r E M F m e a s u r e m e n t s c i t e d . EXPERIMENTAL The Knudsen c e l l and m a s s s p e c t r o m e t r i c t e c h n i q u e s adopted have b e e n d e s c r i b e d in p r e v i o u s r e p o r t s , e.g. Cuthill et al %~ and N e c k e l et al.% 7 S i m i l a r p r e c a u t i o n s L. ERDELYI and J. TOMISKA are University Assistants, Technical University of Vienna. A. NECKEL is Professor, Technical University, University of Vienna. G. ROSE is Scientific Officer, AWRE, Dorset, England. E. E. RAMAKRISHNAN is Scientist, BHEL, Vikas Nagar, India. D. J. FABIAN is Reader, University of Strathclyde, Glasgow, England. Manuscript submitted November 30, 1978. METALLURGICAL TRANSACTIONS A

w e r e taken in the p r e s e n t m a s s s p e c t r o m e t r i c i n v e s t i g a t i o n s to a c h i e v e h o m o g e n e o u s f u r n a c e t e m p e r a t u r e for the Knudsen c e l l . The CH4 i n s t r u m e n t e m p l o y s e l e c t r o n b o m b a r d m e n t heating, with two c a t h o d e s to d i m i n i s h the t e m p e r a t u r e g r a d i e n t , while the A E I MS702 c e l l f u r n a c e is h e a t e d by two i n d e p e n d e n t l y controlled radiation elements. Temperature measurement in both i n s t r u m e n t s is made by p y r o m e t e r s i g h t e d t h r o u g h the K n u d s e n - c e l l o r i f i c e . The p y r o m e t e r is c a l i b r a t e d , for the CH4 i n s t r u m e n t , at the m e l t i n g points of c o p p e r and nickel; with the MS702 i n s t r u m e n t , t e m p e r a t u r e m o n i t o r i n g is by t h e r m o c o u p l e which is c a l i b r a t e d by the p y r o m e t e r at the m e l t i n g points of p u r e gold, a l u m i n u m and s i l v e r . T h e t e m p e r a t u r e r a n g e s c o v e r e d in t h e s e i n v e s t i g a t i o n s w e r e 1420 to 1740 K with the V i e n n a i n s t r u m e n t and 1320 to 1660 K with the S t r a t h c l y d e i n s t r u m e n t . C e l l l i n e r s for the Knudsen effusion s t u d i e s w e r e m a d e chiefly f r o m v i t r e o u s c a r b o n , but a l s o in s o m e i n s t a n c e s f r o m high g r a d e g r a p h i t e that showed no r e a c t i o n with the m o l t e n a l l o y s ; for the a l u m i n u m r i c h m e l t s a l u m i n i a l i n e r s w e r e used, which gave a c c e p t a b l e r e s u l t s with n e g l i g i b l e c o n t r i b u t i o n of A1§ i n t e n s i t y f r o m AlzO r e s u l t i n g f r o m r e a c t i o n with A1203 and f r a g m e n t a t i o n . A n e x t r a AY c o n t r i b u t i o n f r o m AlzO was o b s e r v e d to i n t e r f e r e a p p r e c i a b l y with the m e a s u r e m e n t s of A1§ o r i g i n a t i n g f r o m the gold r i c h a l l o y s . The i o n i z a t i o n e n e r g y e m p l o y e d in the V i e n n a i n s t r u m e n t was 11 eV but with the Glasgow i n s t r u m e n t was l i m i t e d to h i g h e r e l e c t r o n e n e r g i e s ~70 eV. With a l u m i n u m c o n c e n t r a t i o n s h i g h e r than 50 a t . pct the m e a s u r e m e n t s b e c a m e i n c r e a s i n g l y difficult to m a k e on account of the d e c r e a s i n g Au+ i n t e n s i t y . F o r e x a m p l e , with the V i e n n a m a s s s p e c t r o m e t e r , f o r a l u m i n u m c o n c e n t r a t i o n s f r o m 75 to 85 at. p c t the r e c o r d e d Au § i n t e n s i t y was in the r e g i o n of 10 mV c o m p a r e d with A1§ i n t e n s i t i e s a s high a s 30 V o r m o r e . F o r t h i s r e a s o n the i o n i z i n g b e a m , f o r m e a s u r e m e n t s of AI* at t h e s e a l l o y c o n c e n t r a t i o n s , was l o w e r e d f r o m 20 to 3 ~A; then for c o m p a r i s o n of i n t e n s i t i e s a r a t i o ([AI+)20~A/(IAI§ had to b e a p p l i e d . The a l l o y s a m p l e s w e r e p r e p a r e d by m e l t i n g d i r e c t l y within the Knudsen c e l l s of the m a s s s p e c t r o m e t e r s , by c h a r g i n g the c e l l - l i n e r s (or c r u c i b l e s ) with weighed a m o u n t s of the p u r e c o m p o n e n t s . O v e r a l l m a s s e s f r o m 300 mg, +f o r the A1 r i c h , to 850 mg f o r the Au r i c h a l loys w e r e p r e p a r e d , at ~1400 K. U s i n g c e l l l i n e r s of v i t r e o u s c a r b o n , o r of s u i t a b l e g r a p h i t e , no wetting of the c r u c i b l e w a l l s was o b s e r v e d up to A1 contents of

ISSN 0360-2133/79/1011-1437500.75/0 9 1979 AMERICAN SOCIETY FOR METALS AND THE METALLURGICALSOCIETY OF A1ME

VOLUME10A, OCTOBER 1979-1437

50 at. pct. With a l l o y s of A1 content f r o m 50 to 65 a t . p c t the d e g r e e of wetting i n c r e a s e s , and f i n a l l y a c r e e p i n g of the m e l t out of the c r u c i b l e , was o b s e r v e d an effect that could not be avoided by u s e of l e s s s a m p l e . Even when using c o r u n d u m l i n e r s , a l l o y s of a l u m i n u m content above ~50 at. pct showed a s t r o n g i n c r e a s i n g t e n d e n c y to wet the c r u c i b l e o r l i n e r , but in this c a s e the c r e e p i n g - o u t of the m e l t could be a v o i d e d by r e s t r i c t i n g the s a m p l e c h a r g e to 300 rag. No d i s s o l v e d c a r b o n a p p e a r e d to be p r e s e n t in the s a m p l e s following a m e a s u r e m e n t (in the c a s e of g r a p h i t e l i n e r s ) but its p r e s e n c e and a consequent l o w e r i n g of v a p o r i z a t i o n r a t e cannot be c o m p l e t e l y e x c l u d e d . Evaporation loss during a measurement, especially when the a l l o y c o m p o n e n t s have w i d e l y d i f f e r e n t p a r t i a l v a p o r p r e s s u r e s , can lead to f a l s e c o n c e n t r a t i o n s . The m a s s l o s s m i of component i d u r i n g an effusion run at c o n s t a n t t e m p e r a t u r e T is given by the r e l a t i o n : m i = PitA ~ / M i / 2 R T

OAG E Ox = R T In

(l-x)Iz + CG(T )

[5]

xI1

w h e r e x = mol f r a c t i o n component 2. The t e m p e r a t u r e dependent t e r m C G ( T ) b r i n g s t o g e t h e r a l l the c o n c e n t r a t i o n independent f a c t o r s in the f o r m :

(IlyiNi201O CG(T) = R T In ~ . NlhO L~2Y2

[6]

2//2

Then, CG (T) can be obtained by i n t e g r a t i o n o v e r the whole c o n c e n t r a t i o n r a n g e : CG (T) = - R T 7 1 1 n

12(1 - x) Ilx dx

[7]

x=O

while the e x c e s s m o l a r Gibbs f r e e e n e r g y is given by:

PAl

mAu-PAu

~

u

[2]

A f t e r e a c h m e a s u r e m e n t the t o t a l weight l o s s of s a m ple (reAl + mAu) could thus be a s c e r t a i n e d , a l l o w i n g f o r a c o r r e c t e d weight l o s s of the c r u c i b l e , and then with the help of Eq. [2] the weight l o s s f o r e a c h c o m ponent could be d e t e r m i n e d . F o r c a l c u l a t i o n of the p a r t i a l p r e s s u r e s PAl and PAu a m e d i u m t e m p e r a t u r e , 1600 K, was s e l e c t e d . The p a r t i a l v a p o r p r e s s u r e s , u s i n g v a p o r p r e s s u r e d a t a for the p u r e c o m p o n e n t s f r o m N e s m e y a n o v 8 and a p p r o x i m a t e v a l u e s for the a c t i v i t i e s , w e r e c a l c u l a t e d . T o t a l e v a p o r a t i o n l o s s e s lay b e t w e e n 0.2 m g (gold r i c h a l l o y s ) and 1.7 mg (A1 r i c h a l l o y s ) . On the b a s i s of the c a l c u l a t e d weight l o s s e s the a l l o y c o n c e n t r a t i o n s w e r e amended where necessary.

The p a r t i a l p r e s s u r e Pi of component i of the cond e n s e d phase in the c e l l , is r e l a t e d to the m e a s u r e d i n t e n s i t y I~ of ion s p e c i e s of an i s o t o p e k of c o m p o n e n t i b y the e x p r e s s i o n : pi = ~iYiFN-------~l i T where g e o m e t r i c c o n s t a n t of the i n s t r u m e n t , i o n i z a t i o n c r o s s - s e c t i o n for c o m p o n e n t i, ion-electron multiplier efficiency, abundancy of i s o t o p e k of s p e c i e s i, absolute temperature.

D i r e c t d e t e r m i n a t i o n of t h e r m o d y n a m i c a c t i v i t i e s ai, using, 1438-VOLUME 10A, OCTOBER 1979

GE(x) = RTxf:O in 12(1 I,x- x) dx + Cc(T)x

[3]

[8]

By s i m i l a r r e a s o n i n g , the t e m p e r a t u r e d e p e n d e n c e of the r a t i o of the ion b e a m s y i e l d s the p a r t i a l d e r i v a t i v e of the heat of m i x i n g A H E, oAHE - R ~x

In (IJI1) ~(1/T)

+ CH

[9]

w h e r e the i n t e g r a t i o n c o n s t a n t C H given by:

CH : - R

x~jl 01n(IJI1) dx = H~ x ~o 0 ( l / T )

- H~

[10]

is e f f e c t i v e l y e q u a l to the d i f f e r e n c e of h e a t s of e v a p o r a t i o n of the two p u r e c o m p o n e n t s .11 T h e heat of m i x i n g can then be e x p r e s s e d a s :

x ~1n(I2/I1) A H E ( x ) = R 2:fo ~(1/T dx + CHX

E v a l u a t i o n of T h e r m o d y n a m i c D a t a

F = ei = Ni/~ = = T =

[4]

[1]

w h e r e Pi is the p a r t i a l v a p o r p r e s s u r e of i, t is the m e a s u r e m e n t t i m e , A is the o r i f i c e c r o s s - s e c t i o n (cell o r i f i c e d i a m w e r e t y p i c a l l y f r o m 0.7 to 0.9 m m with the V i e n n a i n s t r u m e n t and f r o m 0.75 to 1.0 m m with the S t r a t h c l y d e i n s t r u m e n t ) , M i is the a t o m i c weight of component i, R the gas constant, and T the a b s o l u t e t e m p e r a t u r e . F r o m this r e l a t i o n we obtain, for the b i n a r y a l l o y s Au-A1, an e x p r e s s i o n for the r a t i o of masses evaporating: real

ai = pi/p ~

(where pO = v a p o r p r e s s u r e of p u r e component i) f r o m m e a s u r e m e n t s of Pi and p~ in s e p a r a t e e x p e r i m e n t s , is b e s e t with d i f f i c u l t i e s a s s o c i a t e d with i n d e t e r m i n a t e c h a n g e s in the i n s t r u m e n t g e o m e t r i c c o n s t a n t F . To c o u n t e r t h i s , Belton and F r u e h a n , 9 and a l s o N e c k e l and W a g n e r , 1~ have p r o p o s e d a method involving m e a s u r e ment of the r a t i o of i n t e n s i t i e s of ions of i s o t o p e s p e c i e s of the two c o m p o n e n t s of the a l l o y . T h e m e t h od a d o p t e d by N e c k e l and W a g n e r 1~ l e a d s to a d i r e c t d e r i v a t i o n of the e x c e s s m o l a r Gibbs f r e e e n e r g i e s A G E by m e a n s of the e x p r e s s i o n :

[11]

F o r e v a l u a t i o n of the e x p e r i m e n t a l r e s u l t s an a n a l y t i c a l technique, s u i t a b l e f o r c o m p u t e r c a l c u l a t i o n s , was e m p l o y e d . The t e m p e r a t u r e d e p e n d e n c e of the r a t i o s of i n t e n s i t i e s of the ion b e a m s , for one p a r t i c u l a r conc e n t r a t i o n , was obtained t h r o u g h a l i n e a r r e g r e s s i o n in a c c o r d a n c e with the e x p r e s s i o n :

1 1n i 12(x) l ~ - = k(x) ~ + d(x)

[12]

F u r t h e r e v a l u a t i o n s followed the technique d e s c r i b e d by T o m i s k a et al, 12 which u s e s a R e d l i c h and K i s t e r e x p a n s i o n 13 f o r a t h e r m o d y n a m i c e x c e s s function of mixing, Z, N Z = ( x - x 2) ~ B Z ( 2 x - 1) n-1 [13] METALLURGICAL TRANSACTIONS A

(where Z = A G E ; &H E , AS E, and N is the total n u m b e r of R e d l i c h - K i s t e r p a r a m e t e r s ) . Use of the R e d l i c h K i s t e r e x p a n s i o n for Z = AG E in Eq. [5] leads to the re lat ion:

R T In (1 - x)I2 XII

_

BI(AGE) (1 -- 2X) + N B n (AGE) ( 2 x -

1) n - 2

n:2

• [ ( 2 n + 2 ) ( x - x ~) - 1 ] -

Cc(T)

[141

The technique is then to a d j u s t the R e d l i c h - K i s t e r parameters B n ( A G E ) and the c o n s t a n t CG(T) , by m e a n s of a l e a s t s q u a r e method, to fit as c l o s e l y as p o s s i b l e the experimental values of RT In (I X)I2/~clt. In an entirely analogous manner the Redlich-Kister parameters Bn (AHE) and the constant CH for the heat of mixing are determined from Eq. [9]. The RedlichKister parameters for AGE, AHE, and ASE are connected by the relation: -

Bn (AGE) = Bn (AHE) - T Bn tASE)

[15]

f r o m which, in a g r e e m e n t with Eq. [12], the p a r a m e t e r s a n d Bn(ASE) e m e r g e a s t e m p e r a t u r e indep e n d e n t . F o r our p r e s e n t alloy r e s u l t s a s a t i s f a c t o r y b e s t - f i t was achieved u s i n g a 3 - p a r a m e t e r e x p a n s i o n (N = 3) for AG E and &H E.

Bn (AHE)

RESULTS AND DISCUSSION For each alloy concentration the ratios of the intensities of the ion beams were determined at about 15 different temperatures. Regression of the experimental data according to Eq. [12] yields the values for the slopes and intercepts, summarized in Table I. In Fig. I we show the experimental values obtained for RT In 12(I - x)/I1x as well as the 'best-fit' curve for these measurements at T = 1540 K. The lefthand ordinate applies to the Vienna measurements and the righthand ordinate to the Strathclyde measurements. A similar correspondence of the data was obtained at 1660 K. B e c a u s e of the higher e l e c t r o n e n e r g y applied in the Glasgow i n s t r u m e n t , the i o n i z a t i o n c r o s s - s e c t i o n s a i a r e l a r g e r and the v a l u e s of the c o n s t a n t CG(T) a r e t h e r e f o r e d i f f e r e n t f r o m those for m e a s u r e m e n t s with the V i e n n a i n s t r u m e n t . However, the r e s u l t s f r o m both l a b o r a t o r i e s follow p r a c t i c a l l y the s a m e c u r v e of conc e n t r a t i o n d e p e n d e n c e . The d e v i a t i o n s o b s e r v e d for the A1 r i c h alloys (XA1 > 0.8) a r e the r e s u l t of the e x t r a polation n e c e s s a r y on a c c o u n t of the l i m i t e d c o n c e n t r a tion range of the e x p e r i m e n t a l data. In F i g . 2 we c o m p a r e , for T = 1540 K, our p r e s e n t r e s u l t s with those r e p o r t e d by other i n v e s t i g a t o r s ; for

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70~ f~ in to O

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Fig. 1 - R T In [(1 - XA1)IAIIXAt[Au ] as a f u n c t i o n o f the m o l e fraction o f a l u m i n u m XAi at 1540 K. o, - - : Vienna; (1, - . - : S t r a t h c l y d e . METALLURGICAL TRANSACTIONS A

00

l

I

l

I

0.2

0.4

0.6

0.8

XA[

1.0

Fig. 2 - M o l a r excess Gibbs energies AG E o f liquid Au-A1 a l l o y s at 1540 K. - - : this w o r k , Vienna; - . - : this w o r k , S t r a t h c l y d e ; .... : C h a r q u e t et alt (recalculated from 1338 K); - - - : Predel et al = (recalculated from 1300 K); - . . : Y a z a w a et al3 (recalculated from 1373 K). V O L U M E IOA, OCTOBER 1979

1439

tins c o m p a m s o n the r e s u t t s obtained in other laborat o r i e s a r e extrapolated at 1540 K. The m e a s u r e m e n t s at the Strathclyde and Vienna l a b o r a t o r i e s a g r e e well, and for A G E yield m i n i m u m v a l u e s of r e s p e c t i v e l y - 2 3 . 8 k J / m o l (XA1 = 0.54) a n d - 24.2 k J / m o l (xA1 = 0.55). The r e s u l t s r e p o r t e d by Yazawa e t al 3 a l s o a g r e e s a t i s f a c t o r i l y with those of the p r e s e n t i n v e s t i gations, although with the m i n i m u m d i s p l a c e d to higher gold c o n c e n t r a t i o n s (XA1 = 0.43); h o w e v e r , the m e a s u r e m e n t s r e p o r t e d by Charquet e t al ~ and, above all, P r e d e l e t al e yield e s s e n t i a l l y m o r e negative A G E v a l u e s . F o r T = 1660 K the A G E v a l u e s obtained in the Strathclyde and,Vienna l a b o r a t o r i e s a l s o a g r e e d c l o s e ly (as in F i g . 2 for 1540 K) a c r o s s the whole c o m p o s i tion range. The a G E values can be e x p r e s s e d by the RedlichK i s t e r p a r a m e t e r s given in Table II; and a r e a l s o s u m m a r i z e d for T = 1540 K in Table III and for T = 1660 K in Table IV. The t h e r m o d y n a m i c a c t i v i t i e s a r e s u m m a r i z e d in Table V and F i g 3. In contrast to the findings r e p o r t e d by the other i n v e s t i g a t o r s cited, we o b s e r v e gold a c t i v i t i e s of the Au r i c h a l l o y s that show s m a l l p o s i t i v e deviations f r o m Raoult ideality. F i g u r e 4 s h o w s the heats of mixing for the p r e s e n t

Table I. Slopes k (x) and intercepts d (x) of the Regression Lines In [ l A l ( X ) / I A u (x)] = k ( x } / T + d ( x ) for the Experimental Data at Various Mole Fractions of Aluminum XA1

Part A Laboratory Vienna XA1

k (x)

0.0501 0.0752 0.1029 0.1596 0.1870 0.2302 0,2952 0.3647 0.3743 0.4738 0.5044 0.5597 0,6005 0.6628 0.7282 0.7891 0.8274 0.8477

-10899.0 -10909.0 -8899.1 -9314.0 -8058.4 -7674.5 -5988.9 -3885.6 -2379.7 1690.9 2745.5 6005.5 6232,8 10180.6 12160.5 15310.9 14411.4 17944.0

d (x) 3.5115 3.6343 2.9228 3_5477 3.0188 2.9474 2.2862 2.2632 1.8262 1.3537 0.9779 0.1171 1.3015 -0.1022 0.4081 -0.1870 1.1832 -0.7296

Part B Laboratory Strathclyde XA1

k (x)

d(x)

0.1000 0.1000 0.1500 0.2000 0.2000 0.2000 0.3000 0.3000 0.3000 0.4000 0.4000 0.4000 0.4000 0.5000 0.5000 0.5000 0.5000 0.6000 0.6000

-61.0 -2599.3 -4005.8 -2129.9 -3042.6 -8183.6 436.6 107.2 9159.0 -11494.0 786.6 1592.3 -3627.6 15394.7 -10559.0 -9309.7 17437.3 -4157.0 16330.3

-3.8617 -2.1625 - ! .0829 -1.9635 -1.3710 1.9259 -2.3513 -2.2604 -7.4560 7. 5072 -0.7801 -1.9090 2.3331 -8.1871 7.9529 7.6773 -9.1985 6.8161 -6.7514

1440-VOLUME

10A, OCTOBER 1979

Table II. Redlich-Kister Parameters and Constants of Integration (C G ( T ) = C H - TC$) of the Liquid System Au-AI

Parameter

Vienna

Strathclyde

BI anE [J/mol]

-154,607

-146,420

92 AHE [J/mol]

-12,333

-41,810

B3 AHE [J/mol]

27,945

24,012

CH [J/mol] B1ase [J/mol-K]

-27,235 -39.3459

-33.45

B2ASE [J/mol" KI

7.1150

-9.35

B3ASE [J/mol "K]

1.2607

1.77

Cs [J/mol- K]

12.8356

w o r k at 1600 K and c o m p a r e s t h e s e with those r e p o r t ed by Y a z a w a e t al a (for 1373 K) and by P r e d e l e t al "~ (for 1300 K). While the heats of mixing f r o m the Vienna m e a s u r e m e n t s w e r e obtained through evaluation of E q s . [9] to [11], those f r o m the 8trathclyde laboratory w e r e d e t e r mined as f o l l o w s . F i r s t the e x c e s s e n t r o p i e s of mixing w e r e calculated f r o m the AG E values at 1540 and 1660 K; then, using t h e s e A S E v a l u e s , the e x c e s s heats of mixing A H E w e r e d e t e r m i n e d f r o m A G E (1600 K). The Vienna m e a s u r e m e n t s for A H E lead to a m a x i m u m e x o t h e r m i c value o f - 3 8 . 7 k J / m o l (at XA1 = 0.52) while the Strathclyde m e a s u r e m e n t s yield an e x o t h e r m i c m a x i m u m o f - 3 7 . 2 k J / m o l (at xA1 = 0.56). The heats of m i x i n g obtained by the other i n v e s t i g a t o r s indicate l e s s e x o t h e r m i c i t y ; h o w e v e r , in contrast to the

Table III, Integral and Partial Excess Gibbs Energies of Liquid Au-AI alloys at 1540 K in kJ/mol.

Part A Laboratory Vienna (Redlich-Kister parameters: B~ c E = 94.014, B2a

XA1 0.0 0.1 0.2 0.3 0,4 0.5 0.6 0.7 0.8 0.9

1.0

GE

GE

= 23.291, B~3

= 26.004;

Constant o f Integration CG (1540) = -47.004) AGE AGEAu 0 -5.29 -11.31 -16.91 -21.20 -23,50 -23.43 -20.83 -15.78 -8.64

0

0 0.58 0.66 -1.69 -7.66 -17.68 -31.44 -47.86 -65.15 -80.73 -91.30

aG~ -44.72 -58.09 -59.18 -52.43 -41.50 -29.33 -18.10 "-9.24 -3.44 -6.3

0

Part B Laboratory Sttathclyde (Reddich-Kisterparameters: AGE ^tz_E B~ cE = 94.894, B2 = 27.405, B~ v = 21.276; Constant of Integration Ca (1540) = -34.691) XAI

AcA

A~u

AGEAI

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0 -5.34 -11.33 -16.91 -21.25 -23.72 -23.89 -21.51 -16.59 --9.29 0

0 0.51 0.56 -1.65 -7.27 -16.87 -30.39 -47.15" -65.87 -84.67 -101.02

-46.21 -58.03 -58.86 -52.52 --42.23 -30.57 -19.55 -10.53 -4.27 0.91 0

METALLURGICAL TRANSACTIONS A

1.0 Table IV. Integral and Partial Excess Gibbs Energies of Liquid Au-AI Alloys at 1660 K in kJ/tool

Part A Laboratory Vienna (Redlich-Kister parameters:

0.8

BAIGE= -89.293, B~ GE= -24.145, B~G E-- 25.853; XAl

Constant of Integration Ca (1660) = -48.542) AGE a~Au

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0 -4.81 -10.48 -15.85 -20.02 -22.32 -22.34 -19.91 -15.12 -8.29 0

0 0.65 0.91 -1.15 -6.73 -16.29 -29.54 -45.44 -62.22 -77.36 -87.58

AGEA1 -39.30 -53.89 -56.04 -50.17 -39.97 -28.36 -17.54 -8.97 -3.34 0.61 0

._ 0.6

to

9

0.4

0.2

Part B Laboratory Strathclyde (Redlich-Kister parameters: B~ GE = -90.880, B~ c e = -26.283, Ba3ae = -21.062; Constant of Integration C a (1660) = -33.592) XAi

AG e

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0

AGeAu

0 -5.07 -10.80 -16.17 -20.35 -22.72 -22.87 -20.58 -15.85 -8.86 0

AGEA!

0 0.52 0.60 -1.49 --6.90 -16.15 -29.16 -45.26 -63.14 -80.93 -96.10

-43.53 -55.38 -56.42 -50.41 -40.52 -29.29 -18.68 -10.01 -4.03 0.85 0

s t r o n g d i f f e r e n c e s in A G E v a l u e s o b s e r v e d a m o n g t h e s e v a r i o u s i n v e s t i g a t i o n s , the m a x i m a of the A H E v a l u e s obtained lie within a r a n g e of ~7 k J / m o l (Fig. 4). The i n t e g r a t i o n c o n s t a n t C H i s , in a c c o r d a n c e with Eq. [10], e f f e c t i v e l y the d i f f e r e n c e of the h e a t s of e v a p o r a t i o n of the pure c o m p o n e n t s , AH~ - AH~ at the t e m p e r a t u r e of m e a s u r e m e n t . Since the v a l u e s given in the l i t e r a t u r e for h e a t s of v a p o r i z a t i o n of gold and a l u m i n u m v a r y c o n s i d e r a b l y , the d i f f e r e n c e in AHv~ for the two m e t a l s is s u b j e c t to e r r o r . A c c o r d i n g to the d a t a given in C o d a t a ~4 the d i f f e r e n c e a m o u n t s to 36.4 k J / m o l , for 1600 K; while the d a t a of Stull and Sinke ~5 give a d i f f e r e n c e of 30.7 k J / m o l for t h i s t e m p e r a t u r e . The value of C H obtained in the p r e s e n t inv e s t i g a t i o n s l i e s s o m e w h a t o u t s i d e of this r a n g e (see T a b l e II). H o w e v e r , it should be noted that even s m a l l

XAI

aAu

aAu

0.8

0.6

1.0

d e v i a t i o n s f r o m the R a l n ( I j I 1 ) / a ( 1 / T ) v s c o n c e n t r a t i o n c u r v e l e a d to l a r g e v a r i a t i o n s in C H . J u s t a s f o r A G ~ , we note l a r g e d i s c r e p a n c i e s in the v a l u e s of A S E obtained in the v a r i o u s i n v e s t i g a t i o n s ( F i g . 5). The A S E v a l u e s found in the p r e s e n t work, at 1600 K, w e r e c o n s i s t e n t l y negative with o b s e r v e d m i n i m a o f - 9 . 9 J / m o l . K (XA1 = 0.47; V i e n n a l a b o r a t o r y ) a n d - 8.5 J / m o l . K (XA1 = 0.55; S t r a t h c l y d e l a b o r a t o r y ) . T h e r e s u l t s r e p o r t e d by Y a z a w a e t al 3 a r e t h o s e in the b e s t a g r e e m e n t with o u r s . C h a r q u e t e t al ~ find a l m o s t i d e a l e n t r o p y of mixing, while the m e a s u r e m e n t s of P r e d e l e t al2 i n d i c a t e a p o s i t i v e excess entropy. The p r e s e n t r e s u l t s for A S E (taken t o g e t h e r with t h o s e of Y a z a w a e t al ~) a r e p r o b a b l y the m o r e r e l i a b l e . If it a r i s e s s o l e l y f r o m a v o l u m e change, the v a l u e of A S E for the 50-50 at. pct a l l o y ( ~ - 10 J / m o l . K, which c o r r e s p o n d s to ~ - 1 . 2 /eB/atom) would r e p r e s e n t an u n u s u a l l y l a r g e s h r i n k a g e on m i x i n g (~ 15 pct; Y o u n g 1 6 ) ; but t h i s is e n t i r e l y c o m p a t i b l e with the l a r g e a b s o l u t e v a l u e of the heat of m i x i n g A H E ~--40 k J / m o l ( c o r r e -

XAI

aA1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1.000 0.942 0.849 0.629 0.349 0.139 0.040 0.009 0.002 0.000

0.000 0.001 0.003 0.006 0.019 01057 0.157 0.353 0.620 0.859

1.000 0.935 0.835 0.622 0.352 0.145 0.043 0.009 0.002 0.000

0.000 0.001 0.003 0.006 0.018 0.053 0.143 0.323 0.586 0.842

1.0

0.000

1.000

0.000

1.000

METALLURGICAL TRANSACTIONS A

0.4

Table VI. Integral Heats of Mixing A H E and Integral Excess Entropies of Mixing ASEof Liquid Au-AI Alloys at 1600 K

Strathclyde

aA1

0.2

XAI. Fig. 3 - T h e r m o d y n a m i c activities a i of liquid Au-A1 alloys. : this w o r k , V i e n n a ( 1 6 0 0 K); - . - : this w o r k , S t r a t h c l y d e ( 1 6 0 0 K); . . . . . : C h a r q u e t et al I ( 1 3 3 8 K); : Predel et al 2 ( 1 3 0 0 K); . . . . : Y a z a w a et al 3 ( 1373 K).

Table V. Activities ai of Liquid Au-AI Alloys at 1600 K

Vienna

0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

AH/r [kJ/mol]

ASE [J/mol 9 K]

Vie,]na

Strathclyde

Vienna

Strathclyde

0 -11.42 -21.94 -30.49 -36.24 -38.65 -37.43 -32.56 -24.31 -13.19

0 -8.78 -18.03 -26.43 -32.90 -36.60 -36.92 -33.45 -26.06 -14.80

0.00 -3.98 --6.91 -8.82 -9.77 -9.84 -9.09 -7.62 -5.54 -2.96

0.00 -2.24 -4.35 -6.18 -7.56 -8.36 -8.46 -7.75 -6.15 -3.58

0

0.00

0.00

0

V O L U M E 10A, OCTOBER 1 9 7 9 - 1 4 4 1

-401

'

~

'

'

I

10

,

,

,

/

,

f

\

X

/ / /

-3(

f J

3-5 E

/,t/'

i

,\\, ,\ \

i' - )9

S-

'&

Is

/ //

%

/

\ \

/

5

'5

j

E

-3

I"

~~ .~

~

0 ~

-

~ ""

"'" ........

/

""

,\ '\ -21

wu3

"\,

~

LLI 1-

\

\

i,

<:l

-10

\' I

00

\

I

I

0.4

I

0.6

I

0.8

1.0

XAL Fig. 4 - M o l a r h e a t s o f m i x i n g A H E of l i q u i d Au-AI alloys. - - : this w o r k , Vienna ( 1 6 0 0 K); - . - : this work, S t r a t h c l y d e ( 1 6 0 0 K); . . . . . : C h a r q u e t et al 1( 1 3 3 8 K); - - - : Predel e t al 2 ( 1300 K); .... : Y a z a w a et al 3 (1373 K).

sponding to ~ - 4 e V / a t o m ) at t h i s c o m p o s i t i o n . L i k e w i s e we r e g a r d the h i t h e r t o u n r e p o r t e d p o s i t i v e d e v i a tion of aAu f r o m Raoult i d e a l i t y , f o r the Au r i c h a l l o y s , a s r e a l . The e u t e c t i c f o r the Au r i c h a l l o y s l i e s b e tween the low m e l t i n g i n t e r m e t a l l i c s Au4A1 and Au~A12, which e a c h m e l t p e r i t e c t i c l y , and it is in t h i s r e g i o n of c o m p o s i t i o n that the p o s i t i v e d e v i a t i o n of aAu is observed. T h e s e a s p e c t s of the p h a s e e q u i l i b r i u m d i a g r a m f o r the a l l o y s y s t e m , a s a l s o the s t r o n g bonding in the i n t e r m e t a l l i c compound AuAlz, a r e p r o b a b l y the r e s u l t of the l a r g e d i f f e r e n c e in e l e c t r o n e g a t i v i t y b e t w e e n the Au and A1 a t o m s . It is known for s o l i d Au-A1 a l l o y s (see for e x a m p l e F u g g l e et a117) that s i g n i f i c a n t s - and d - e l e c t r o n t r a n s f e r o c c u r s b e t w e e n the c o m p o n e n t a t o m s . L i k e w i s e a v e r y s t r o n g bond is known to e x i s t in the g a s e o u s m o l e c u l e AuA1 (Cuthill et alS). It would t h e r e I o r e not be unexpected, when a s m a l l p r o p o r t i o n of A1 a t o m s a r e i n t r o d u c e d to a m e l t of A u a t o m s , if s t r o n g l o c a l g r o u p i n g s o r c l u s t e r s w e r e to f o r m in the liquid Au r i c h a l l o y with s h o r t r a n g e o r d e r c o n s i s t e n t with the s t r o n g l y bonded i n t e r m e t a l l i c AuA12. T h i s would i n c r e a s e the a c t i v i t y of the a t o m s of gold in the liquid p r e s e n t in e x c e s s to the l o c a l g r o u p i n g s , c a u s i n g t h e i r i n c r e a s e d p a r t i a l v a p o r p r e s s u r e and the ob1442

V O L U M E 10A, OCTOBER 1979

0.6

0.8

1.0

Fig. 5 - M o l a r excess e n t r o p i e s AS E o f liquid Au-A1 a l l o y s . - - : this work, Vienna ( 1 6 0 0 K); - 9 : this work, S t r a t h c l y d e ( 1 6 0 0 K); . . . . . : C h a r q u e t et al 1 ( 1 3 3 8 K); - - - : Predel et al 2 ( 1 3 0 0 K); .... : Y a z a w a e t a 1 3 ( 1 3 7 3 K).

\, \

0.2

0.4 XAL

\',l \,

0

0.2

s e r v e d d e v i a t i o n of gold a c t i v i t y f r o m Raoult i d e a l i t y at high gold c o n c e n t r a t i o n s . Any such t e n d e n c y for f o r m a t i o n of l o c a l c l u s t e r s of s h o r t r a n g e o r d e r would a l s o l o w e r the diffusion c o e f f i c i e n t in the liquid a l l o y , f o r t h e s e Au r i c h c o m p o s i t i o n s , which could c o r r e l a t e with the p o s i t i v e d e v i a t i o n f r o m Raoult i d e a l i t y (Shimoj ila).

ACKNOWLEDGMENTS The V i e n n a Group w i s h e s to thank P r o f e s s o r H. Nowotny f o r his i n t e r e s t in this w o r k and the F o n d s z u r F 6 r d e r u n g d e r w i s s e n s c h a f t l i c h e n F o r s c h u n g for f i n a n c i a l s u p p o r t in c o n n e c t i o n with the m a s s s p e c t r o m e t r y e q u i p m e n t . L a s z l o E r d ~ l y i thanks the B r i t i s h Council and the M i n i s t r y of Science and R e s e a r c h of the F e d e r a l R e p u b l i c A u s t r i a f o r f i n a n c i a l s u p p o r t which e n a b l e d him to u n d e r t a k e p a r t of this r e s e a r c h at the D e p a r t m e n t of M e t a l l u r g y , S t r a t h c l y d e . The S t r a t h c l y d e G r o u p thanks the Science R e s e a r c h C o u n c i l for f i n a n c i a l s u p p o r t , and P r o f e s s o r W. H. Young f o r helpful d i s c u s s i o n .

REFERENCES 1. D. Charquet, P. Desr6, and E. Bonnier: C. R. Acad. ScL [Paris), 1967, vol. 264, pp. 1637-40. 2. B. Predel and U. Schallner: Mater. ScL Eng., 1969/70, vol. 5, pp. 210-19. 3. A. Yazawa and Y. K. Lee: Trans. Jpn. Inst. Met., 1970, vol. ! 1, pp. 411-18. 4. A. M. Cuthill, P. B. Brown, and D. J. Fabian: Proceedings International School o f Mass Spectrometry, J. Marsel, ed., pp. 243-258, J. Stefan Inst., Ljubljana, 1971. METALLURGICAL TRANSACTIONSA

5. A. M. Cuthill, D. J. Fabian, and S. Shu-Shou-Shen:J. Phys. Chem., 1973, vol. 77, pp. 2008-11. 6. G. Sodeck, P. Entner, and A. Neckel: High Temp. ScL, 1970, vol. 2, pp. 311-21. 7. A. Neckel, L. Erdelyi, E. Buschmann, and H. Nowotny: Mh. Chem., 1975, vol. 106, pp. 355-67. 8. A. N. Nesmeyanov: VaporPressure of the ChemicalElements, ElsevierPubl. Comp., Amsterdam-London,New York, 1963. 9. G. R. Belton and R. J. Fruehan: J. Phys. Chem., 1967, vol. 71, pp. 1403-9. 10. A. Neckel and S. Wagner: Bet. Bunsenges. Phys. Chem. i969, vol. 73, pp. 210-17. 11. S. Wagner, G. Sodeck, and A. Neckel: High Temp. Sci., 1971, vol. 3, pp.

METALLURGICAL TRANSACTIONS A

481-90. 12. J. Tomiska, H. Nowotny, L. Erdelyi, and A. Neckel: Z. Metallkde., 1977. vol. 68, pp. 350-65. 13. O. Redlich and A. T. Kister: Ind. Eng. Chem., 1948, vol. 40, pp. 345-48. 14. Codata, NBSIR 75-968, 1975. 15. D. R. Stull and G. C. Sinke: Thermodynamic Properties of the Elements, Nat. Bureau of Standards, Washington,D.C. 1963. 16. W. H. Young: Liquid Metals, R. Evans and D. A. Greenwood, eds., Inst. Phys. Conf. Series. pl, 1976. 17. J. C. Fuggle, E. K~illne, L. M. Watson, and D. J. Fabian: Phys. Rev. B, 1977, vol. 16, pp. 750-61. 18. M. Shimoji: LiquidMetals, Chapter 6, Academic Press, 1977.

VOLUME 10A, OCTOBER 1979-1443