IMPURITY DIFFUSION IN LIQUID ALUMINUM AND COPPER

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IMPURITY DIFFUSION IN LIQUID ALUMINUM

AND COPPER

T. Ejima, T. Yamamura

To cite this version:

JOURNAL DE

PHYSIQUE

CoZZoque C8, suppZhent

au

n o

8,

Tome

41,

aoiit

1980,

page

C8-345

I M P U R I T Y D I F F U S I O N IN L I Q U I D A L U M I N U M A N D COPPER

T. Ejima and T. Yamamura

Department of MetaZZurgy, Tohoku University, Sendai, Japan.

1. Introduction

Theoretical analysis of chemical diffusion can hardiy be nade because numerous factors are con- prised in the process. The studies of inpurity diffusion, that is, the diffusion of solute into pure solvent from the solvent liquid containing an extremely small amount of solute, would enable to evaluate the effects of various factors on liffu- sion and pernit sone insight into chenical diffu- sion. In order to obtain valuable information on the mechanism of chemical diffusion and the rela- tive importance of such factors as valence, mass and size, the experinents on impurity diffusion have been carried out by using a modified capillary reservoir metsod. As the solvent metai monovalenr copper and trivalent aluminum were chosen. Solute eleaents were systematicaily chosen on the basis of periodic table.

2. Experimental

For the measurements of diffusion coefficients of liquid metals, nany nethods, such as, capillary reservoir method, long capillary method and shear cell nethod have been proposed and nolified. In the present study, the capillary reservoir method o r i g ~ inally proposed by Anderson and ~ a d d i n g G h was used because the source of errors had been well eluci- dated. The details of the experimental procedure were described in the papers previously published by o6Z)of the authors. Capillaries of 1 7 m long and 1 . h dianeter were used for the experinents. The coinpositions of the tracers- in the reservoir liquid were nostly not more than atqmic Tercent. The precision of the diffusion coefficients determined were about 6.5% or less.

3. Xesults and Discussion 3.1 Effect Arising from Difference in valence

In order to evaluate the effects of the valence of solke elenents on diffusion, fourth period elements 5 9 ~ e , 60~o, Xi, 6 4 ~ u and I 2 ~ a which are of nearly the same size and mass with one another, were chosen as solutes. A linear relation was found between the logarithmic value of diffusion coefficient and the reciprocal value of temperature

in K within the limits ofexperinental error.

Assuqing the ,following equation (I),

D =

Doexp(-E/?.T) (1)

the pre-exponential tern Do and the apparent acti- vation energy E were calculated by neans of the least square method. Although an atom in solid state diffuses by several well defined mechanisms, mechanism for the diffusion in liquid state has not been well founded. Thus, it is still remained uncertain r.fhat the apparent activation energy means. For example, as the temperaturk increases not only kinetic energy of the system increases but also the structure of the liquid changes. In such a case the apparent activation energy would change continuous- ly with increasing temperature. As mentioned above, however, the plots of Arrhenius type show a linear relation in the tenperature range of melt- ing point. of aluminum to 200 C above it wherein the measurements were carried out. Since there is a clear correlation between the apparent activation energy and the position of a solute in the periodic table, the ay?arent activation energy seems to be

a

significant parameter for clarifing the relative importance of the factors which mizht control the diffusivity of impurity in liquid metal in limited range of temperature.

The nost-significant difference found among the elements belonging to the fourth period is

Relative Valence ,

A Z

6 0 - I

Fig. 1 Relation between apparent activation energy for diffusion and relat~vc valmca. 55

Solvent

1

- -O- Cu (Ejima et al.) -

JOURNAL DE PHYSIQUE

C8-346

t h a t of t h e v a l e n c e . The r e l a t i o n between t h e ap- p a r e n t a c t i v a t i o n energy f o r d i f f u s i o n of i m p u r i t y and. v a l e n c e of t h e s o l u t e element r e l a t i v e t o t h e s o l v e n t i s shown i n F i g . 1 . Here, t h e r e l a t i v e v a l - e n c e o f Fe, Co, N i , Cu, Ga and As were defined. a s -5 -4, -3, -2, 0 , a n d 1. As shown i n Fig.1, t h e appar- e n t a c t i v a t i o n e n e r g y i n c r e a s e s l i n e a r l y w i t h i n - c r e a s i n g r e l a t i v e v a l e n c e . As a l s o shown i n Fig.:, t h e same t r e n d can be found f o r tfie i n p u r i t y d i f f u - s i o n i n l i q u i d cop422 a n d

sil44.k.

The t r e n d o b s e r v e d can b e e x p l a i n e d by c o n s i d e r i n g t h e e l e c t r o s t a t i c i n t e r a c t i o n between s o l u t e and s o l v e n t atoms. I n o r d e r t o i n d u c e t h e d i f f u s i v e motion of i m p u r i t y atoms i n l i q u i E , i t i s r e q u i r e d t h a t a k i n d of cav- i t y o r a low d e n s i t y r e g i o n i s f o r n e d i n t h e v i c i n - i t y of t h e i n p u r i t y atom by t h e d e n s i t y f l u c t u a t i o n i n t h e s o l v e n t . By t h e e l e c t r o s t a t i c f i e l d of t h e i m p u r i t y atom, a n a d d i t i o n a l r e p u l s i v e ( a t t r a c t i v e ) f o r c e i s a c t e d on tile i m p u r i t y a t o n w i t h p o s i t i v e ( n e g a t i v e ) e x c e s s c h a r g e . T h e r e f o r e , t h e e n e r g y which i s n e c e s s a r y f o r t h e f o r m a t i o n of low d e n s i t y r e g i o n a d j a c e n t t o t h e i n p u r i t y a t o n w i t h p o s i t i v e r e l a t i v e v a l e n c e would b e s n a l l e r t h a n t h a t of t h e i ~ ? u r i t y atom w i t h n e g a t i v e v a l e n c e : T h i s a g r e e d w e l l w i t h t h e observed r e s u l t s mentioned above.

On t h e o t h e r hand, i n t h e c a s e s of f i f t h and s i x t h p e r i o l s o l u t e s , t h i s c o r r e l a t i o n c o u l d n o t b e found. T h i s s u g g e s t s t h a t n o t o n l y v a l e n c e b u t a l s o t h e o t h e r f a c t o r s a r e i m p o r t a n t f o r t h e l i f f u - s i o n of f i f t h an< s i x t h p e r i o d s o l u t e s . 3.2 C o r r e l a t i o n between T!~ermodynamic P r o p e r t i e s and D i f f u s i v i t y As mentioned i n t h e p r e v i o u s s e c t i o n , l o c a l bonding between s o l u t e and s o l v e n t atoms i s i n ? o r - t a n t f o r t h e d i f f u s i o n o f s o l u t e . It i s , however, d i f f i c u l t t o e v a l u a t e t h e l o c a l bonding a c c u r a t e l y . T h e r e f o r e , t h e r n o d y n a m i c a l p r o p e r t i e s which r e f l e c t t h e c h e m i c a l bonding between s o l u t e and s o l v e n t were compared w i t h t h e d i f f u s i o n c o e f f i c i e n t s meas- ured. i n t h e p r e s e n t s t u d y . I n F i g . 2 , i m p u r i t y d i f f u s i o n c o e f f i c i e n t s a r e p l o t t e d a g a i n s t t h e ex- c e s s n o l a r f r e e energy o f n i x i n g between s o l u t e and s o l v e n t a t i n f i n i t e d i l u t i o n of s o l u t e . A s shown i n F i g . 2 , t h e i m p u r i t y d i f f u s i o n c o e f f i c i e n t i n - c r e a s e s w i t h i n c r e a s i n g e x c e s s f r e e energy of mix- i n g . Tine t r e n d o b s e r v e d may w e l l b e u n d e r s t o o d i f t h e f o l l o w i n g c o n c e p t i s a c c e p t e d : The d i f f u s i v e d i s p l a c e m e n t t a k e s p l a c e i f t h e r e i s some k i n d of a v i t y o r d e n s i t y f l u c t u a t i o n a t t h e n e a r e s t neigh- b o u r s of t h e i m p u r i t y atom, t h a t i s , d i f f u s i o n

Fig. 2 Relation between diffusion coefficient and molar free energy of mixing.

( Solvent: aluminum

I .

I

I

I

I

8.0 9.0 10.0

1-' I 104K-1

Fig. 3 Relation between diffusion coefficient and temperature for homo-valent solutes in Liquid aluminum .((a) Calculated value from the principle of corresponding states )

S t o k e s - - E i n s t e i n e q u a t i o n ( 2 )

,

I) = k T / a n n r (2)

where

n

i s t h e v i s c o s i t y o f s o l v e n t and a i s a con- s t a n t . The r a d i i of t h e s e e l e q e n t s i n l i q u i d aluminum i s n o t lznown, b u t t h e i o n i c and t h e a t o m i c r a d i i i n s o l i d s t a t e a r e i n t h e o r d e r _{r (r {}

G a I n r ~ l '

The observed r e s u l t s mentioned above a g r e e d w e l l w i t h t h e p r e d i c t i o n of t h e S t o k e s - E i n s t e i n e q u a t i o n . The same r e s u l t h a s been o b t a i n e d f o r t h e case of i n p u r i t y d i f f u s i o n i n l i q u i d copper. These f a c t s i n d i c a t e t h a t s i z e i s a n i m p o r t a n t f a c t o r which c o n t r o l s t h e i m p u r i t y d i f f u s i o n i n l i q u i d m e t a l s and s h o u l d b e t a k e n i n t o c o n s i d e r a t i o n i n t h e p r e d i c t i o n of t h e i m p u r i t y d i f f u s i o n c o e f f i c i e n t . Although o n l y t h e r e p u l s i v e f o r c e among t h e p a r t i c l e s comprising a f l u i c i i s t a k e n i n t o c o n s i d e r - a t i o n i n t h e h a r d s p h e r e t h e o r y , i t h a s been suc- c e s s f u l l y a p p l i e d t o t h e p r e d i c t i o n of t h e t r a n s p o r t p r o p e r t i e s of n o b l e g a s l i q u i d s , l i q u i d n e t a l s and molten s a l t s . From t h e r e s u l t s o b t a i n e d by t h e n o l e c u l a r &ynamics f o r t h e h a r d s p h e r e s y s t e m s , ~yrn62h p r o p o s e d tha; t h e s e l f - d i f f u s i o n c o e f f i c i e n t i n a l i q u i d c a n be r e p r e s e n t e d i n t e r n s of n o l a r volume Vn by t h e f o l l o w i n g e q u a t i o n ( 3 ) , D = c

vO3"

( T f i i m ) l / Z ( ~ m

-

bVo) ( 3 ) where c and b a r e c o n s t a n t s , Wm i s t h e n o l a r w e i g h t , a n d Vo i s t h e molar v o l u n e a t c l o s e paclcing. Eq.(3) c a n be a p p l i e d t o i m p u r i t y d i f f u s i o n by s u b s t i t u t i n g Vm f o r t h e reduced n a s s of s o l u t e and s o l v e n t . I n F i g s . 4 and 5, t h e v a l u e s of D/ (T/pi)'/' and T ~ / ~ / T I a r e p l o t t e d a g a i n s t m o l a r volume of aluminum f o r f o u r t h and f i f t h p e r i o d s o l u t e s , r e s p e c t i v e l y , where q i s t h e v i s c o s i t y of aluminum, and p i i s t h e reduced mass of s o l u t e and aluminum. As shown i n F i g s . 4 and 5, t h e v a l u e s o f D/ ( ~ / u ~ ) l / ~ a n d i n c r e a s e p r o p o r t i o n a l l y w i t h i n c r e a s i n g molar volume of s o l v e n t f o r most o f f o u r t h and f i f t h p e r i o d s o l u t e s i n l i q u i d alumtnum. I n a d d i t i o n ,

t h e l i n e s showing t h e c o r r e l a t i o n s between

~ ~ / ~ / n

o r D / ( T / ~ ~ ) ' / ~ and m o l a r volume o f , s o l v e n t i n t e r -

s e c t t h e a x i s of molar volume a t t h e p o i n t s e x t r e m e l y c l o s e w i t h one a n o t h e r . The same p l o t was done f o r s i x t h p e r i o d s o l u t e s i n l i q u i d aluminum and shown

i n

F i g . 6 . The b e h a v i o u r of i r i d i u m i s t h e same a s t h a t of f o u r t h and f i f t h p e r i p d s o l u t e s . The v a l u e s of D/ ( ~ / p ~ ) ' / * f o r t h a l l i u m , l e a d and bismuth d e v i a t e from t h e l i n e a r r e l a t i o n w i t h i n c r e a s i n g m o l a r volume o r temper- a t u r e , and f u r t h e r m o r e , t h e c o o r d i n a t e s a t which t h e l i n e s i n t e r s e c t t h e a x i s of molar volume of

Molar Volume .V l104dmor vs molar volume v of liquid atum~num. where MI and M. are atomic weights of ~mpur~ty and solvent doms.

Molar Volum .V l l@m3rnoF' Fig. 5 Plots of m.0.~ vs. molar volume V of

l~quid alummum. where M, and M. are atomic weights of lmpurily and solvenl atoms.

JOURNAL DE PHYSIQUE 75 0 .VI &

%

50.0 -; t 2513 0

Molar Vo1ume.V 111S~m'moT'

vs molar volume V of lrqu~d alum~num

.

where M, and M. are atomic we~ghts of ~mpur~ty and soivent atoms.

Table 1 The parameter Vo f o r aluminm and copper solvents.

S o l u t e

I

~~/10-6m3mo1.-~

~ o l v e n t : A l u m i n u m [ ~ o l v e n t : Copper

c o n t r i b u t e t o t h e d i f f u s , i v e movemenf of s o l u t e atom

i s d i s t r i b u t e d t o e a c h atom

a t

c l o s e packing when t h e m e t a l i s f u s e d . However, s o l u t e atom s h a r e s i n t h e amount.of t h e f r e e volume which is. c o r r e -

t h e p a r t i c u l a r s o l u t e . T h e r e f o r e , t h e p l o t s o f D ( T / u ) - ~ / ~ and molar volume might b e r e d u c e d t o a d e f i n i t e l i n e i f t h e i n t e r a c t i o n between s o l u t e and o l v e n t atoms were t a k e n i n t o c o n s i d e r a t i o n .

4. Summary

I m p u r i t y d i f f u s i o n c o e f f i c i e n t s i n l i q u i d aluminum and copper f o r t h e s o l u t e e l e m e n t s system- a t i c a l l y chosen were measured by u s i n g a m o d i f i e d c a p i l l a r y r e s e r v o i r methods. The r e s u l t s o b t a i n e d a r e summarized a s f o l l o w s : ( 1 ) Temperature dependence of d i f f u s i o n c o e f f i c i e n t s c a n b e r e p r e s e n t e d by a n A r r h e n i u s t y p e e q u a t i o n . The a p p a r e n t a c t i v a t i o n e n e r g y f o r d i f f u s i o n ob- t a i n e d d e c r e a s e s w i t h i n c r e a s i n g t h e v a l e n c e o f of t h e s o l u t e f o r f o u r t h p e r i o d s o l u t e b o t h i n l i q u i d aluminum and copper. T h i s r e s u l t s i n d i c a t e t h a t t h e e l e c t r o s t a t i c i n t e r a c t i o n caused by t h e e x c e s s c h a r g e l o c a t e d a t s o l u t e atom i s i m p o r t a n t f o r i m p u r i t y d i f f u s i o n .

( 2 ) C o r r e l a t i o n s between thermodynamic p r o p e r t i e s and d i f f u s i v i t y were found. The i m p u r i t y d i f f u s i o n c o e f f i c i e n t i n c r e a s e s w i t h d e c r e a s i n g t h e e x c e s s f r e e e n e r g y of mixing between s o l u t e and s o l v e n t .

( 3 ) The d i f f u s i o n c o e f f i c i e n t i n c r e a s e s w i t h i n c r e a s i n g s i z e of d i f f u s i n g p a r t i a l e f o r homo- v a l e n t s o l u t e s b o t h i n l i q u i d aluminun and copper. There was a l i n e a r r e l a t i o n between D / ( T / u ) ' / ~ and molar volume of t h e s o l v e n t ,

where.^

i s t h e reduced mass of s o l u t e and s o l v e n t atoms.

R e f e l e n c e s

( 1 ) J. S. Anderson and K; Saddington: J. Chem. Soc., S2(1949), 381. (2) ,T. Ejima, N. I n a g a k i and M. ~ a m z a : T r a n s . JIPI,

7 (19661, 133. (3) T. Ejima, T. Yamamura, S. ~ a k a n o a n d T. Honda:

J. J a p a n I n s t . l l e t a l s , g ( 1 9 7 8 ) , 453.

(4) Y. P. Gupta: Adv. Phys., g ( 1 9 6 7 ) , 333. (5) J. H. Dymond: J . Chem. Phys., g ( 1 9 7 4 ) , 60.

sponding t o t h e s t r e n g t h of interaction between s o l u t e and s o l v e n t atoms. T h i s i s t h e r e a s o n