Thermodynamic Properties of Liquid Ag-Si Alloys HIROSHI SAKAOAND JOHN F. ELLIOTT 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 s i l i c o n in liquid A g - S i a l l o y s in the r a n g e of 1100 to 1325~ have b e e n m e a s u r e d b y an e l e c t r o c h e m i c a l c e l l e m p l o y i n g s i l i c a - s a t u r a t e d l i t h i u m s i l i c a t e a s the e l e c t r o l y t e . The r a n g e of c o m p o s i t i o n s t u d i e d is 0.015 < Xsi < 0.29. F o r the change in s t a n d a r d s t a t e f r o m p u r e liquid s i l i c o n to s i l i c o n at infinite dilution with the c o m p o s i t i o n in a t o m f r a c t i o n : Si (1) = Si (inf. dil.) : AG ~ = 5,000 + 5.47 T, ( J / g - a t o m ) The r e s u l t s of the s t u d y a r e in good a g r e e m e n t with the m e a s u r e m e n t s on the p h a s e d i a gram by Hager. T H E t h e r m o d y n a m i c p r o p e r t i e s of s i l i c o n in liquid s i l v e r - s i l i c o n a l l o y s h a s b e e n a s u b j e c t of i n t e r e s t f o r d e t e r m i n i n g the a c t i v i t y of s i l i c o n in liquid i r o n b y the d i s t r i b u t i o n method. In t h i s method, 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 s i l i c o n b e t w e e n i m m i s c i b l e l a y e r s of liquid i r o n and liquid s i l v e r is m e a s u r e d . 1 The s y s t e m is a l s o of g e n e r a l i n t e r e s t b e c a u s e it shows only s l i g h t d e v i a t i o n s f r o m i d e a l b e h a v i o r , even though the two c o m p o n e n t s d i f f e r m a t e r i a l l y in c h e m i c a l and p h y s i c a l p r o p e r t i e s . T h i s b e h a v i o r was d e s c r i b e d b y H a g e r 2 who d e t e r m i n e d the liquidus l i n e s and e u t e c t i c t e m p e r a t u r e of the p h a s e d i a g r a m , and who u s e d the p h a s e d i a g r a m to c a l c u l a t e a c t i v i t i e s in the s y s t e m . M e a s u r e m e n t s of the p a r t i a l p r e s s u r e of s i l v e r b y O'Keefe, 3 by V e r m a n d ~ , A n s a r a and D e s r ~ , 4 and b y Robinson and T a r b y s p r o v i d e i n f o r m a t i o n on the whole s y s t e m . Howe v e r , t h e s e m e a s u r e m e n t s a r e not of s u f f i c i e n t p r e c i s i o n to p r o v i d e a c c u r a t e v a l u e s f o r the a c t i v i t y of s i l i c o n at dilute c o n c e n t r a t i o n s . M e a s u r e m e n t s u t i l i z ing the s o l u b i l i t y of s i l i c o n c a r b i d e ~ o r s i l i c o n n i t r i d e 8 a l s o a r e r e l a t i v e l y i m p r e c i s e b e c a u s e of the i m p r e c i s i o n in o u r knowledge of the s t a n d a r d f r e e e n e r g i e s of f o r m a t i o n of t h e s e c o m p o u n d s . A s t u d y of p o s s i b l e e x p e r i m e n t a l m e t h o d s t h a t m i g h t b e u s e d showed that an e l e c t r o c h e m i c a l m e t h o d was the m o s t p r o m i s i n g way f o r m e a s u r i n g the a c t i v i t y of s i l i c o n a t dilute c o n c e n t r a t i o n s . This p a p e r d e s c r i b e s the r e s u l t of a study u s i n g the E m f method. THE E X P E R I M E N T S The c e l l u t i l i z e d was

I Si4§ I

Mo, Si (s) (sat. (-) in liq. Ag) Li20-SiO2 Si (in liq. (+)Ag), Mo SiO2(sat.) The overall process in the cell with the passage of positive current from the left electrode to the right in the cell is the transfer of silicon from a chemical potential of pure solid silicon on the left, ~Si, o at its HIROSHI SAKAO, Member of AIME; Visiting Scientist, Mass. Instit. Technology, Cambridge, Mass. (1969) is Professor, Faculty of Engineering, Nagoya University, Nagoya-shi, Japan. JOHN F. ELLIOTT, Fellow of TMS and of ASM, is Professor of Metallurgy, Mass. Inst. Technology, Cambridge, Mass. 02139. Manuscript submitted February 7, 1974. METALLURGICAL TRANSACTIONS

c h e m i c a l p o t e n t i a l in the A g - S i solution, ~ s i , on the right. S i ( s ) ~ S i ( a l l o y ) ; AG = ~ S i -

o

~si =-4~e

[1]

The c h a r g e t r a n s f e r r e a c t i o n s p e r a t o m of s i l i c o n at e a c h e l e c t r o d e with a s i l i c a t e e l e c t r o l y t e invoIved 4 e l e c t r o n s 9 (Z = 4). 9 is F a r a d a y ' s c o n s t a n t , 96,487 c o u l o m b s p e r e q u i v a l e n t . The a c t i v i t y , a~i , a c t i v i t y c o e f f i c i e n t , ~si, and e x c e s s r e l a t i v e p a r t i a l m o l a r e n t r o p y of s i l i c o n in the a l l o y s , S Xs is, a l l r e l a t i v e to p u r e s o l i d s i l i c o n a s i n d i c a t e d b y the s u p e r s c r i p t s , a r e o b t a i n e d d i r e c t l y f r o m the r e v e r s i b l e p o t e n t i a l of the c e l l , ~, a s f o l l o w s : In aSsi : - Z ~ s In yssi = - Z ~ E / R T -

[2] In Xsi

S E s = Z ~ B e ~ a T - R In x s i

Si

[3] [4]

Xsi is the a t o m f r a c t i o n of s i l i c o n in the liquid a l l o y . The d e s i g n of the c e l l is shown in F i g . 1. L i t h i u m s i l i c a t e was s e l e c t e d a s the e l e c t r o l y t e p r i m a r i l y b e c a u s e the s t a n d a r d f r e e e n e r g y of f o r m a t i o n of Li20 (per m o l e of O2) is a p p r o x i m a t e l y 120 k J m o r e n e g a tive than that of s i l i c a . Thus, the r e d u c t i o n of l i t h i u m into the e l e c t r o d e s by the r e a c t i o n b e t w e e n s i l i c o n and Li20 is e s s e n t i a l l y avoided. It is to be noted that p r e l i m i n a r y m e a s u r e m e n t s with a s o d i u m - s i l i c a t e e l e c t r o l y t e m e t with f a i l u r e b e c a u s e of the exchange r e a c tion involving s i l i c o n and s o d i u m . A s e c o n d r e a s o n f o r s e l e c t i n g l i t h i u m s i l i c a t e m e l t s f o r the e l e c t r o l y t e is that t h e r e is a e u t e c t l c at 19 wt pct Li20 and 1030~ 1~ A c c o r d i n g l y , the e l e c t r o l y t e can be a m i x t u r e of the e u t e c t i c liquid and s o l i d p a r t i c l e s of p u r e s i l i c a o v e r the t e m p e r a t u r e r a n g e of i n t e r e s t , i . e . , 1100 to 1325~ An e l e c t r o l y t e s a t u r a t e d with s i l i c a p e r m i t t e d use of s i l i c a a s the r e f r a c t o r y m a t e r i a l for the c e l l . The a v e r a g e c o m p o s i t i o n of the e l e c t r o l y t e was f r o m 10.5 to 12 wt pct LifO. The e l e c t r o l y t e was p r e p a r e d b y m i x i n g p u r e p o w d e r e d s i l i c a and ground L i 2 0 - S i O 2 of the e u t e c t i c c o m p o s i t i o n (19 wt pct Li20). The s i l i c a p o w d e r was p r e p a r e d b y igniting s i l i c i c a c i d ( M a l l i n k r o d t a n a l y t i c a l r e a g e n t g r a d e ) in a i r at 1000~ The L i 2 0 - S i O 2 e u t e c tic p o w d e r was p r e p a r e d b y m i x i n g the r e q u i r e d a m o u n t s of l i t h i u m c a r b o n a t e and s i l i c i c a c i d ( M a l l i n k r o d t a n a l y t i c a l r e a g e n t g r a d e ) and igniting t h e m in V O L U M E 5, S E P T E M B E R 1 9 7 4 - 2 0 6 3

a p l a t i n u m dish at 1000~ in a i r . Subsequently, the t e m p e r a t u r e was r a i s e d to 1230~ and the m i x t u r e was fused. The cold g l a s s y product was m i l l e d to a fine powder in an a l u m i n a b a l l m i l l . The e l e c t r o l y t e was placed in the cell as a mixed powder or in s o m e c a s e s the m i x t u r e was s i n t e r e d into a c y l i n d r i c a l block in a s i l i c a c r u c i b l e of the size used in the cell. S u b s e quently, r e c e s s e s and holes were d r i l l e d in the block so that the cell could be a s s e m b l e d with all of the e l e c t r o d e s and leads positioned e x a c t l y as r e q u i r e d and with the e l e c t r o l y t e in place. Both methods were s a t i s f a c t o r y but the second allowed a l a r g e r a m o u n t of e l e c t r o l y t e to be p l a c e d in the c e l l . The d e s i g n of the cell is shown in Fig. 1. The cell c r u c i b l e , 55 m m I.D. • 50 m m high, and the e l e c t r o d e c r u c i b l e s , 10 m m I.D. x 15 m m high, w e r e c l e a r q u a r t z g l a s s . The a s s e m b l y was wrapped in m o l y b d e n u m foil to p r o t e c t the f u r n a c e tube (porcelain) f r o m attack b y p o s s i b l e leakage of the e l e c t r o l y t e o r by LizO f u m e s . Radiation s h i e l d s s p a c e d at i n t e r v a l s of 25 m m above the cell also held the e l e c t r o d e leads in position and p r e v e n t e d s e r i o u s c o n v e c t i v e flow of g a s e s in the s y s t e m . Each cell had four e l e c t r o d e s , one or two w e r e s a t u r a t e d with s i l i c o n and s e r v e d as r e f e r e n c e e l e c t r o d e s . The other two o r t h r e e were Ag-Si cathodes, and in s o m e c e l l s t h e r e w e r e one o r two F e - S i c a t h odes in place of Ag-Si cathodes. The e l e c t r o d e s were p r e p a r e d b y m e l t i n g the a p p r o p r i a t e weights of s i l v e r (99.99 pct pure) and s i l i c o n (99.99 pc, pure). T h e s e e l e c t r o d e s w e r e solidified and then placed within the c e l l when it was a s s e m b l e d . The c o m p o s i t i o n s of a l l of the cathode e l e c t r o d e s w e r e d e t e r m i n e d b y c h e m i c a l a n a l y s i s of each b u t t o n on c o m pletion of an e x p e r i m e n t . The leads w e r e withdrawn f r o m the e l e c t r o d e s p r i o r to shutting down the cell. Seven of the twelve cathode alloys w e r e cut in half and two d e t e r m i n a t i o n s w e r e made of the c o m p o s i t i o n s . F o r alloys below 2.0 pct Si, the a g r e e m e n t was within 0.02 wt pc,, i.e., 1.79 and 1.77 wt pct. The a n a l y z e d c o m p o s i t i o n s were also within a few h u n d r e d t h s p e r c e n t of the c o m p o s i t i o n s a s weighed out, but the a v e r a g e of the c h e m i c a l d e t e r m i n a t i o n s was t a k e n as the c o m p o s i t i o n of the alloy. At the higher c o m p o s i t i o n s , the s i l icon p r e c i p i t a t e d on cooling and floated to the top of the m e t a l button. Thus, it was u n l i k e l y that duplicate d e t e r m i n a t i o n s would be in good a g r e e m e n t b e c a u s e the s i l i con might not have been u n i f o r m l y d i s t r i b u t e d and s o m e

~Tubutor

Spacer

-- Quertz Lead Tube

i

l j

J

Radiotion Shield

- - M o Wrapper - - Q u a r t z Crucible --Electrolyte --Electeode Crucible, Quortz .

~ M 2 L e a d

~Iioy

Wire

Fig. 1--Cell design for Ag-Si alloys. 2064-VOLUME 5, SEPTEMBER 1974

might have been lost in cutting the button. Anode 13-1 was cut and the determinations were 3.57 and 3.69 wt pct and the average was used. Several cells were run with only Ag-Si electrodes. A check of possible contamination of the electrodes by iron and molybdenum was made by analyzing one electrode (No. 11-2) for these elements, 0.0003 pct Fe and less than 0.0001 pct Me were found. Another electrode contained 0.005 pct Me. Several of the Ag-Si cathodes were contained In ceils which also had Fe-Si cathodes, one such Ag-Si alloy (17-1) was found to contain 0.0009 pet Fe. The electrolyte In cells containing both Fe-Si and Ag-Si alloys showed between 0.04 and 0.05 pct Fe. These impurity levels were considered to indicate that there were no serious problems with exchange reactions in these cells. To prevent contamination of the electrodes with molybdenum from the lead wire, the tip of each wire was immersed briefly in a molten Ag-Si alloy. A thin silicide coating resulted which prevented solution of the wire and also depletion of silicon from the electrodes during the experiments. The analyses of the electrodes described above Indicate that the prior treatment of the leads was effective. The atmosphere in the cell was a r gon containing 3 pct hydrogen at a pressure slightly greater than atmospheric. Each gas was purified separately, the argon by passing it successively through columns of ascarite, copper at 500~ and iron at 700~ and hydrogen by passing it through a platinum catalyst, drierite and ascarite. Initially, the cold cell system was evacuated by mechanical pumping and then it was filled with the purified gases. A slight flow of gas was maintained through the cell. The t e m p e r a t u r e of the cell was d e t e r m i n e d b y a P t - P t / 1 0 pct Rh t h e r m o c o u p l e located i m m e d i a t e l y below the tube c o n t a i n i n g the cell. The r e a d i n g of this t h e r m o c o u p l e was c a l i b r a t e d by m a k i n g s i m u l t a n e o u s m e a s u r e m e n t s over the e x p e r i m e n t a l t e m p e r a t u r e r a n g e with a n o t h e r t h e r m o c o u p l e of the s a m e type placed within the cell a s s e m b l y . F o r this set of m e a s u r e m e n t s , the c e l l was a s s e m b l e d e x a c t l y a s for a n e x p e r i m e n t except that the e l e c t r o l y t e and e l e c t r o d e s were omitted. A t h e r m a l s u r v e y of the cell a s s e m b l y showed the t e m p e r a t u r e g r a d i e n t s to be l e s s than 0.7~ the v a r i a t i o n of t e m p e r a t u r e b e c a u s e of c y c l i n g of the c o n t r o l l e r to be a p p r o x i m a t e l y 0.5~ and the d r i f t over several hours was not more than I~ The thermocouples were calibrated against the gold and palladium points by the wire method. It is assumed that the total uncertainty in the temperature of a set of readings of the cell potentials was not more than 1.3~ Thermocouple potentials were measured with a Rubicon-type B potentiometer. Cell potentials were measured with a Keithley model 630 potentiometer which has an Impedance of 1014 ohms. The readings of the cell were also checked occasionally with the Rubicon potentiometer to test the quality of the measurements by passing very small positive and negative currents through the cell for short periods. For most checks of this type, the potential r e turned smoothly from either side to its original value within 20 to 40 s. When it did not, adjustment of the position of the lead usually corrected the condition. It appeared that the potential of an electrode settled down to a constant value as rapidly as thermal equiMETALLURGICAL TRANSACTIONS

J1

0.0i59 00182 X$~i

o: ~ o -

0 Series A A Series B

-

B X 104

0.0~86 "'00286

100 90

Table I. Equations o f 9 for Electrodes, e = A + B T

Electrode No.

00566 .0474

-

(11-2)

I0

/

~

/

Composition,xsi

A, volts

volts/K

18-4

0.0159

-0.1245

1.564

15-1

0.0182

-0.1130

1.457

18-2 17-1 14-1 18-1 11-2 12-1 4-4 13-1 4-3 4-2

0.0286 0.0286 0.0366 0,0474 0.0661 0,0651 0.0917 0.1264 0.1804 0.2874

-0.1216 -0.1025 -0.1229 -0.1222 -0.1176 -0.1316 -0.I 287 -0.1374 -0.1543 -0.1481

1.426 1.292 1.380 1.321 1.233 1.307 1.198

1.174 1.187 1.040

O9~

o 2874

~.

ideol

0 1050

IlOO

1150 1200 125o Tempere|ure, ~

1300

0.7

1550

I~ 0 . 6

Fig. 2--Experimental data on emf of cells: Series A, Ag-Si only; Series B, Ag-Si electrodes in ceils that also contained Fe-Si electrodes.

i_~os 5

0.5-/4i 0.4

librlum in the cell was attained. This usually required approximatelyone hour after the temperature setting on the controller was changed. The temperatures at which measurements were obtained were in an overlapping sequence alternating with an increase in temperature, followed by a decrease in temperature. The life-time of a cell was approximately 48 h because of devitrifieation of the quartz crucible and damage to the connecting leads because of attack by silicon. Coulometric determinations of the value of Z in Eq. [2] w e r e a t t e m p t e d . T h e s e e f f o r t s m e t with f a i l u r e , a p p a r e n t l y b e c a u s e the c u r r e n t r e q u i r e d to p r o d u c e the t r a n s f e r of s u f f i c i e n t m e t a l in the t i m e of an e x p e r i m e n t a l s o c a u s e d s o m e s i l i c o n to d e p o s i t on the l e a d w i r e . Hence, a q u a n t i t a t i v e r e l a t i o n s h i p of a d e q u a t e p r e c i s i o n b e t w e e n e l e c t r i c a l t r a n s p o r t and m a s s t r a n s p o r t was not p o s s i b l e .

0.2 0,1

}

0.5

054

Fig. 3--Activity of Si relative to pure solid Si and of Ag r e l a tive to liquid Ag at 1200~

0.31

0.05 I

0.1 J

-02

XSI 0.3 ~._L

0.15 0.2 J ] ~

~

~

0.4 !

0.5 J

0.6 0.70.8 ! ! ~-7

~

"% 09

o8

o,

o,

o5

o,

02

o,

o

x~g

The c e l l p o t e n t i a l s w e r e s t e a d y and r e p r o d u c i b l e and they a r e p l o t t ed in Fig. 2. S e r i e s A a r e t h o s e e l e c t r o d e s f r o m c e l l s containing only A g - S i c a t h o d e s ; s e r i e s B a r e f r o m c e l l s containing s o m e F e - S i c a t h o d e s a s well. (The r e s u l t s of the w o r k with F e - S i a l l o y s will be r e p o r t e d l a t e r . ) The data f o r each cathode a r e f i t t e d by a l e a s t - s q u a r e s equation of the f o r m :

[5]

the coefficients of which are given in Table L The potentials for electrode 11-2 appear to be high by approximately 3.5 mv, but there is no apparent reason for excluding them. The values of the activity of silicon relati~,e to pure solid silicon at 1200~ were calculated by Eq. [2] from the data in Table I. Corresponding values of aAg were METALLURGICALTRANSACTIONS

F

02 XSi

,o

THE M E A S U R E M E N T S

= A + BT,

1

01

Fig. 4--Activity coefficient of Si referred to pure liquid Si as standard state. Solid line: 1200~ circles: observed points; squares: calculated from Hager's liquidus; broken line: ll00~ obtained by i n t e g r a t i n g the G i b b s - D u h e m equation. The r e s u l t s a r e shown in F i g . 3. It is m o r e m e a n i n g f u l to c o n s i d e r the p r o p e r t i e s of s i l i c o n r e l a t i v e to p u r e liquid s i l i c o n . The t r a n s f o r m a tion of s t a n d a r d s t a t e s is a c c o m p l i s h e d u si n g data on the n o r m a l m e l t i n g point of s i l i c o n , Trn = 1687 K; the h e a t of fusion at the n o r m a l m e l t i n g point, A H r n = 50,550 J / g - a t o m ; and the h e a t c a p a c i t i e s , C/. = 25.5

J/g-atom K and C~ = 28.3 + ( T - T m) 25 • 10"-4J/gatom K, for the pure liquid and solid states, respectively,u Using these data, the equation for the conversion of pure solid silicon to pure liquid silicon (underVOLUME 5, SEPTEMBER 1974-2065

2 I

]

o

i

i

i

F-

r

p

I

F-v

0

30

-I

_o~01

-2 x.

i cq

-3 -4

t~ r-0

-5 -6

0.1

0.2

o r

-7 -8 -9 -I0

I OA

0

I 0,2

f _J_ 0,5 0.4

p 0.5

I 0.6

_c 0.7

I 0.8

0.9

1.0

•

Fig. 5--Excess relative partial molar entropy of Si in Ag. The standard state is pare liquid Si.

Table II. Partial Molar Properties o f Si and Ag at 1 2 0 0 ~ Relative to the Liquid*

Xsi

|

logT/io ojGEI-G~ o,

O.O,amm 0.105 0.05 0.115 0.I 0.160 0.15 0.214 0.2 0.235 0.3 0,255 0.4 0.225 0.5 0.180 0.6 0.130 0.7 0.080 0.8 0.035 0.9 0.010 1.0 0.000

eEl o~ ~,l u~ ~si -osi "'si--si

J/g-at.

J/g-at.K

2960 3242 4511 6033 6625 7190 6343 5075 3665 2255 986 280 0

-5.4 -4,1 -3.0 -2.1 -1.3 -0,1 +0.6 +1.0 +I .0 40.9 +0.6 +0.3 0.0

~ HAg-HAg

kJ/g-at, lOgTAg -4.99 -2.80 +0.09 +2.94 +4.71 +7.04 +7.23 6.55 5.14 3.58 1.87 0.70 0.0

0,000 -0.001 -0.004 -0.012 -0,016 -0.022 -0.005 +0.032 +0.094 +0.185 +0.314 +0.475 +0.660

aAg

kJ/g-at.

1.0130 0.948 0.892 0.827 0,770 0.666 0.593 0.538 0.496 0.459 0.412 0.300 0.000

0.0 0.0 -0.3 -0.7 -1.1 -1,9 -1.9 -1.3 +0.2 +3.6 +8.0 +15.0 +25.0

Si(s) = Si(/); aG(J/g-atom)

0.6

0.7

0.8

0.9

1.0

Fig. 6--Activity coefficient of Si at 1420~ Solid line: present data extrapolated; dotted line: Hager's data assuming regular solution. Squares calculated from Hager's points using our entropy. A Chipman and Baschwitz, 1 V Turkdogan and Grieveson, 8 9 Smith and Taylor. ? and 5. As an a p p r o x i m a t i o n , it is a s s u m e d that SsEi and Hsi a r e independent of t e m p e r a t u r e . At infinite dilution log 7/Si is 0.105 at 1473 K and SEN/ = - 5.4. F r o m t h e s e data the f r e e e n e r g y for the change in s t a n d a r d state is Si (l) = Si (indif. dil.); aG~sli ( J / g - a t o m ) = - 5 0 0 0 + 5.4 T

[7]

[8]

DISCUSSION

[6]

and the a c t i v i t y of s i l i c o n r e l a t i v e to the pure liquid state is given by s _ 2 6 7 0 / T + 1.585 [7] log a~i = log tTSi The v a l u e s of log Vzsi c a l c u l a t e d f r o m the equations given in T a b l e I b y Eqs. [3] and [7] a r e shown in Fig. 4. Below x s i = 0.05 the v a l u e s of log 7/si at 1200~ a r e a p p r o x i m a t e l y c o n s t a n t at 0.1, and the line is d r a w n to c o n n e c t this v a l u e s m o o t h l y with the c u r v e through the r e s u l t s at h i g h e r c o n c e n t r a t i o n s . The points above xsi = 0.3 were c a l c u l a t e d f r o m H a g e r ' s liquidus points 2 u s i n g the data on e n t r o p y that a r e developed in the next p a r a g r a p h . Values of log ~si at l l 0 0 ~ a r e s l i g h t l y b e low the 1200~ line below Xsi = 0.1, and above the line a t the higher c o n c e n t r a t i o n s . The e x c e s s p a r t i a l m o l a r e n t r o p y of Si c a l c u l a t e d f r o m v a l u e s of B i n Table I a r e shown in Fig. 5. The data a r e not c o m p l e t e l y c o n s i s t e n t , but at low c o n c e n t r a t i o n s they a p p e a r t r u s t w o r t h y within + 1 J / g - a t o m K o r +0.25 e.u. At higher c o n c e n t r a t i o n s , t h e r e a r e no data and the line is extended on the a s s u m p t i o n that the solution b e c o m e s m o r e n e a r l y r e g u l a r as Xsi i n c r e a s e s . The effects of t e m p e r a t u r e on the e x c e s s f r e e e n e r g y and the a c t i v i t y coefficient were c a l c u l a t e d f r o m this l i n e . The p a r t i a l m o l a r p r o p e r t i e s of both c o m p o n e n t s at 1200~ a r e given in T a b l e 11. These data a r e obtained by use of the c u r v e s in F i g s . 3, 4, 2 0 6 6 - V O L U M E 5, S E P T E M B E R 1974

0.5 Xsi

o = - 2 6 1 3 / T + 0.282 log 7Si

is:

= 51,130 - 30.34 T

0.4

and

*Under-cooled liquid silicon.

cooled) in the v i c i n i t y of 1473 K (1200~

O3

A plot of log 7si at 1420~ that was obtained by extrapolating the results of this study is shown in Fig. 6. Values of log ~Si calculated by Hager from points on his phase diagram~ and the assumption of regularity are also shown. Hager's individual data points calculated to 1420~ by means of the values of the entropy from Fig. 5 are shown by squares. Above xsi = 0.2 they a g r e e well with our line. The only d i v e r g e n c e is at c o n c e n t r a t i o n s j u s t above the eutectic where the l i q u i dus c u r v e is e x c e e d i n g l y steep and the data m a y be s t r o n g l y influenced by slight e r r o r s in d e t e r m i n i n g the c o m p o s i t i o n . However, f u r t h e r c o n f i r m a t i o n of H a g e r ' s r e s u l t s is found in the following points. H a g e r ' s s o l u b i l i t y of Xsi = 0.334 at 1200~ fits the a c t i v i t y data of Fig. 3. Our line for the emf of the cell xsi = 0.2874 in Fig. 2 shows a b r e a k at 1152~ which is within 5~ of H a g e r ' s liquidus t e m p e r a t u r e for this alloy, 1157~ Fig. 6 p e r m i t s c o m p a r i s o n of the r e s u l t s of p r e v i ous work with that of the p r e s e n t study. C h i p m a n and Baschwitz I pointed out that the e n t r o p y of m i x i n g in the Ag-Si s y s t e m p r o b a b l y is not ideal and they s u g gested an a r b i t r a r y c o r r e c t i o n of +0.10 in H a g e r ' s value of log 7si at low c o n c e n t r a t i o n s . T h e i r value is shown at Xsi = 0. The s a m e c o r r e c t i o n was applied by D ' E n t r e m o n t and Chipman 6 to d e r i v e the f r e e e n e r g y of /%SIC f r o m its m e a s u r e d s o l u b i l i t y in liquid s i l v e r . Smith and T a y l o r 7 c o n f i r m e d D ' E n t r e m o n t ' s v a l u e for the s o l u b i l i t y of SiC in Ag and used this with t h e i r value for the f r e e e n e r g y of f o r m a t i o n of the c a r b i d e to obtain the a c t i v i t y coefficient. T h e i r value of log 7Si at xsi = 0.02 is a l s o shown in Fig. 6. With the aid of the new m e a s u r e m e n t s , it might be p r o f i t a b l e to r e v e r s e this c a l c u l a t i o n to obtain the f r e e e n e r g y of f o r m a t i o n of SiC. T u r k d o g a n and G r i e v e s o n s m e a s u r e d the s o l u b i l i t y of Sign4 in liquid s i l v e r , and f r o m t h e i r data and the f r e e e n e r g y of f o r m a t i o n of the compound they concluded that 7si = 1.76 at 1400~ within the METALLURGICAL TRANSACTIONS

]--

I

I

i

I

i

~

!

I

and T a r b y ' s s r e s u l t s a r e s o m e w h a t m o r e n e g a t i v e than are ours. F r o m the a c t i v i t y c o e f f i c i e n t s ( F i g s . 6 and 7) and the r e l a t i v e p a r t i a l m o l a r e n t r o p y of Si (Fig. 5), the r e l a t i v e p a r t i a l m o l a r e n t h a l p y of e a c h c o m p o n e n t was c a l c u l a t e d and is shown in Fig. 8.

0.4

0,5 a,O, 2

o~o.r Lx

SUMMARY

0

-0.1 __ I __ I 1,0 0.9 0.8

I

0.7

I

0.6

I

0.5 XAg

I __l

0.4

I

0.5

0.2

I

(3.1

0.0

Fig. 7--Activity coefficient of Ag at 1420~ Lines (this study): V Vermande e t . a l , 4 A - Robinson and Tarby. 5

/

Ag

0.1

0.2

0.3

0.4

0.5 Xsl

0.6

0~7

0.8

09

I0

F i g . 8 - - R e l a t i v e p a r t i a l m o l a r e n t h a l p y o f Si a n d o f Ag. T h e standard states are the pure liquids.

r a n g e 0.005 < xsi < 0.038. The c o r r e c t i o n to 1420~ 0 i s i n s i g n i f i c a n t and t h e i r v a l u e s is shown a s l o g 7si 0 = 0.245. Our v a l u e f o r log 7si is given in Eq. [8], f r o m which its v a l u e at s e v e r a l e x p e r i m e n t a l t e m p e r a t u r e s i s a s f o l l o w s : 0.105 at 1200~ 0.128 at 1420~ and 0.137 a t 1530~ T u p k a r y 12 m e a s u r e d the e m f of the c e l l A g - S i (l)/ CaO-B203-SiO2 (SiO2 s a t . ) / P t / O 2 (g) at 1150~ and f r o m the r e s u l t s c a l c u l a t e d the a c t i v i t y of Si in the a l l o y . The c a l c u l a t i o n d e p e n d s upon the v a l u e a d o p t e d for the f r e e e n e r g y of f o r m a t i o n of SiO2 and in view of u n c e r t a i n t i e s in t h i s d a t u m , the r e s u l t s a r e of o n l y r e l a t i v e s i g n i f i c a n c e . T h e y a r e not f a r f r o m o u r r e s u l t s at 1200~ and d i s p l a y a m i n i m u m at a c o n c e n t r a t i o n l e s s than Xsi = 0.1, i m p l y i n g a m i n i m u m in the c u r v e for

log YSi" The a c t i v i t y c o e f f i c i e n t of s i l v e r at 1420~ a s found b y G i b b s - D u h e m i n t e g r a t i o n , is shown in F i g . 7. Shown f o r c o m p a r i s o n a r e the d i r e c t o b s e r v a t i o n s of V e r mand~, A n s a r a , and D e s r 6 , 4 i n t e r p o l a t e d to 1420~ The f o r m e r show a s l i g h t r i s e a b o v e the i d e a l at XAg = 0.9, a d i f f e r e n c e which is q u a l i t a t i v e l y in a g r e e m e n t with the m i n i m u m log 7Si shown b y T u p k a r y . Robinson

METALLURGICAL TRANSACTIONS

A r e v e r s i b l e e l e c t r o c h e m i c a l c e l l h a s been d e v i s e d u s i n g a s i l i c a - s a t u r a t e d l i t h i u m s i l i c a t e e l e c t r o l y t e in which r e p r o d u c i b l e emf d a t a at t e m p e r a t u r e s of 1050 to 1325~ have b e e n o b t a i n e d f o r liquid A g - S i a l l o y s r e l a t i v e to p u r e s o l i d Si. The t h e r m o d y n a m i c p r o p e r t i e s have b e e n d e r i v e d f o r the t e m p e r a t u r e s of 1100 and 1200~ and f o r c o n c e n t r a t i o n s up to s a t u r a t i o n (xsi = 0.334 at 1200~ Deviations from ideality are s l i g h t , the a c t i v i t y c o e f f i c i e n t of Si r e l a t i v e to the p u r e liquid b e i n g l a r g e r than unity at a l l c o n c e n t r a t i o n s . D e r i v e d v a l u e s f o r e n t r o p y and e n t h a l p y p e r m i t c a l c u l a t i o n of e x c e s s f r e e e n e r g y and of log Ysi f r o m the p h a s e d i a g r a m . The r e s u l t s of t h i s c a l c u l a t i o n , t o g e t h e r with our data, f o r m a continuous line a c r o s s the whole c o m p o s i t i o n r a n g e 0 < xsi < 1.0. The d a t a a r e c o r r e c t e d to 1420~ f o r c o m p a r i s o n with p u b l i s h e d v a l u e s of log Ysi and log Yag" ACKNOWLEDGMENTS The a u t h o r s thank John Chipman f o r a s s i s t a n c e in t h e c a l c u l a t i o n s . This study was s p o n s o r e d b y Nagoya Univ e r s i t y , b y the A r m y R e s e a r c h Office, D u r h a m , and b y the A m e r i c a n Iron and Steel Institute.

REFERENCES 1. J. Chipman and R. Baschwitz: Trans. TMS-AIME, 1963, vol. 227, p. 473. 2. J. P. Hager: Trans. TMS-AIME, 1963, vol. 227, p. 1000. 3. T. J. O'Keefe: Thesis, Univ. of Missouri, 1965 (cited by Ref. 5). 4. A. Vermand~, J. Ansara and P. Desrd;Rev. Int. Hautes Temper et Refract., 1970, vol. 7,p. 39. 5. V. S. Robinson and S. K. Tarby:Met. Trans. 1971, vol. 2, p. 1347. 6. J. S. D'Entremont and J. Chipman: J. Phys. Chert, 1963, vol. 67, p. 499. 7. G. Smith and J. Taylor: J. Iron Steellnst., 1964, vol. 202, p. 577. 8. E. T. Turkdogan and P. Grieveson: Trans. TMS-AIME, 1963, vol. 227, p. 1143. 9. K. Schwerdtfeger and H. J. Engell;Arch. Eisenhuettenw., 1964, vol. 35, pp. 535-40. 10. E. M. Levin, H. F. McMurdie and F. P. Hall: Phase Diagrams for Ceramists, American Ceramic Soc., Columbus University, 1956. 11. R. Hultgren, R. L. Orr, P.D. Anderson and K. K. Kelley: Selected Falues of Thermodynamic Properties o/Metals and Alloys, 1963, John Wiley & Sons, Inc., and subsequent additions. 12. R. H. Tupkary: Ind. Jnl. of Technology, 1967, vol. 5, pp. 14-16.

VOLUME 5, S E P T E M B E R 1 9 7 4 - 2 0 6 7