IMPURITY DIFFUSION IN LIQUID METALS

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IMPURITY DIFFUSION IN LIQUID METALS

A. Bruson, M. Gerl

To cite this version:

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JOURNAL DE PHYSIQUE Co ZZoque C8, suppZ6ment au n08, Tome 41, aofit 1980, page

C8-349

IMPURITY DIFFUSION

I N

LIQUID METALS

A . Bruson and M. Gerl

Universitd de Nancy L.A. 155.

1

-

I n t r o d u c t i o n

I, Laboratoire de Physique du SoZide, CO N0140

-

54037 _{NANCY Cedex, France.}

number of i m p u r i t i e s h a s been undertaken i n l i q u i . ?

Cu and i n l i q u i d Sn

,

i n t h e temperature range (Tm

-

1850

K)

u s i n g a s h e a r c e l l d e v i c e whic!l prs-

Molecular dynamics (M.D.) c a l c u l a t i o n s i n l i q u i d s

v i d e s a c c u r a t e r e s u l t s , and which,has been d e s c r i b e d (1-4) show t h a t t h e t r u e d i f f u s i o n c o e f f i c i e n t D

E

d i f f e r s markedly from t h e d i f f u s i o n c o e f f i c i e n t D elsewhere ( 7 - 9 ) .

c a l c u l a t e d u s i n g Enskog's t h e o r y . D e t a i l e d M . D . The comparison of t h e d i f f u s i o n c o e f f i c i e n t s of

s i m u l a t i o n s on H.S. systems ( 5 - 6 ) show t h a t two r e - 6 4 ~ u , llOmAg

,

' 9 5 ~g i v e s a n experimental d e t e r - ~

gimes of v e l o c i t y c o r r e l a t i o n can be d e f i n e d : ( i ) mination of t h e mass e f f e c t and measurements on

a t l a r g e d e n s i t y , t h e b a c k s c a t t e r i n g of a given t e s t very d i l u t e d a l l o y s o f Cu o r Sn w i t h l l o m ~ g , " ' ~ n , p a r t i c l e on i t s f i r s t neighbour s h e l l l e a d s t o " 3 ~ n andX2'sb p r o v i d e an e s t i m a t i o n of t h e s i z e e f - E D/D < 1 and t h e v e l o c i t y a u t o c o r r e l a t i o n f u n c t i o n f e c t . Z ( t ) t a k e s l a r g e n e g a t i v e v a l u e s y ( i i ) a t i n t e r - _{2 . t .}

_-

_{S e l f d i f f u s i o n}_:_{d e n s i t y e f f e c t}

...

mediate d e n s i t y , Z ( t ) e x h i b i t s a l o n g time t a i l ,

d e c r e a s i n g a s t-3'2, which can be t r a c e d t o c o l l e c - The dynamical c o r r e l a t i o n s , which depend on t h e

t i v e motions i n f l u i d ; l o n g wavelength modes a r e d e n s i t y o f t h e f l u i d , a r e expressed a s t h e r a t i o

E

D/D of t h e experimental d i f f u s i o n c o e f f i c i e n t

D

e x c i t e d by t h e i n i t i a l motion o f a given atom and

m

E

g i v e r i s e t o an i n c r e a s e o f D with r e s p e c t t o D

.

t o t h e d i f f u s i o n c o e f f i c i e n t DL c a l c u l a t e d uying

These dynamical c o r r e l a t i o n s depend on t h e reduced EnSkog's according

mass M

=

mi/m and on t h e reduced s i z e

1 =

Ui/ Us

of t h e s o l u t e with r e s p e c t t o t h e s o l v e n t : ( i ) a s

M i n c r e a s e s , b a c k s c a t t e r i n g e f f e c t d e c r e a s e s and

hydrodynamic modes a r e more e q s i l y e x c i t e d ; t h e r e -

-

a

is t h e e q u i v a l e n t hard sphere diameter i n t h e

E

fore D/D increases ; ( i i ) as

1

increases, backscat- p r e s c r i p t i o n of PROTOPAPAS ( 1 0 ) according t o t e r i n g i n c r e a s e s and D / D ~ d e c r e a s e s when b a c k s c a t t e -

r i n g regime i s predominentbut, -- a t i n t e r m e d i a t ~ den-

s i t y , hydrodynamic modes a r e more e a s i l y e x c i t e d by where cr i s c a l c u l a t e d , from t h e d e n s i t y and t h e a l a r g e p a r t i c l e t h a n by a s m a l l one, and D/D= i n - packicg f r a c t i o n y , a t t h e m e l t i n g t e n p e r a t u r e T

.

m

c r e a s e s i n t h e p e r s i s t e n c e regime.

2

-

Experimental r e s u l t s

-

g ( a ) i s e s t i m a t e d u s i n g CARNP3l.W-STARLING'S equa- t i o n of s t a t e ( 1 1 )

The experimental r e s u l t s i n Sn and.Cu a r e recop- I n o r d e r t o i n v e s t i g a t e t h e s e e f f e c t s , s y s t e m a t i c

ded i n f i g u r e 1 a s a f u n c t i o n of V/Vo and compared measurements of t h e d i f f i ~ s i o n c o e f f i c i e n t of a _with_M.D. _{s i m u l a t i o n s . F i g u r e}_{1 shows t h a t t h e ex-}

(3)

c8-350

JOURNAL DE PHYSIQUE E p e r i m e n t a l v a r i a t i o n o f C (V/V )

=

D/D

,

is c o r - 1 0 and

_{g , =}

_{( 1 - y )}- 2

_c

_{l + ~ + - ( a a - 0}3 y ~

_{) I}

r e c t l y p r e d i c t e d by M.D. c a l c u l a t i o n s ; t h e two c o r -

2a8

6

r e l a t i o n r e g i m e s a r e , e x p e r i m e n t a l y p e r f e c t l y e x h i - _The

measured d i f f u s i o n coefficient D . can be

1

b i t e d . It i s p o s s i b l e t o c a l c u l a t e , a t e a c h d e n s i t y , t h e v a l u e u ' ( T ) o f t h e h a r d s p h e r e d i a m e t e r which,

( 6 ) when used i n f o r m u l a ( 1 )

,

would l e a d t o t h e v a l u e

of D I D L p r e d i c t e d by A l d e r . Using c h i s p r o c e d u r e , we g e t f o r Sn i n s t e a d o f g i v e n by PROTOPAPAS. F i g . 1

-

E x p e r i m e n t a l v a l u e s o f t h e r a t i o D/DE i n Sn

( m

)

,

i n Cu ( 0 ). 2.2.

-

I m p u r i t y d i f f u s i o n : mass and s i z e e f f e c t s

...

I n t h e c a s e o f i m p u r i t y d i f f u s i o n , we u s e t h e same p r o c e d u r e : t h e c a l c u l a t e d Enskog d i f f u s i o n c o e f f i c i e n t i s g i v e n by

where

ais

=

( a i

+

u s ) / 2

,

i and s s t a n d f o r impu- r i t y and s o l v e n t r e s p e c t i v e l y ,

u

i s t h e r e d u c e d mass : gis i s c a l c u l a t e d u s i n g MANSOORI1 s

r u l e (11)

gis

= C

ai

gss ( a s ) +

as

gii ( a i ) ] / 2

ais

(4)

-

Mass-effect.

In liquids, the correlations are dominated

by the backscattering effect. The larger the mass

of the diffusing species, the smaller the backscat-

tering.

In figure

3,

the experimental dependence of C

2 On

M is given at a reduced volume V

/

Vo

=

1.6 and 1.75.

The results are compared with those calculated by

Alder (or extrapolated from Alder's data) at V/Vo

=

1.6 .

In Cu, the experimental results are in good

agreement with M.D. calculations.Xn Sn, a discre-

pancy of about 20

%

between the absolute values of

C is observed.

2

to settle this point.

3 -

Conclusion

We have measured the diffusion coefficients of

64~U,"%~g, "'In,

Il3sn,

'24~b

and 195.4~

in liquid

Sn and Cu using a shear cell assembly which prbvides

data with a precision of about

5 %.

From a comparison

with Enskog's theory we have seen that the dynamical

correlations depend strongly on the density

of

the

solvent and on the relative size and mass of the

solute with respect to the solvent.

It would be interesting (i) to calculate the

binary collision diffusion coefficient of Sn and

Cu using realistic potentials (ii) to calculate

the diffusion coefficient of impurities in Sn

and Cu using interatomic potentials deduced from

liquid alloy theory.

-

Mass dependence of

C

(M,C

)

2 (1) Ag and Au in Sn.

(2) Cu, Ag and Au in Cu.

In liquid one would expect that C2 decrea-

ses as the size of the impurity increases.

Our experimental results, shown in figure 2, seem

to indicate the opposite trend when one goes from

Ag to In, Sn and Sb in Cu, and from Sn to Sb in Sn.

This can be interpreted as the effect of the valence

of the impurity on its diffusion coefficient. Because

of the,(screened) electrostatic potential aroundthe

impurity, the effective H S diameter used in the

Enskog

theory should

be

different from its value

in the pure solvent. Some calculation are in progress

(1) L.SJOGREN, A. SJOLANDER

Ann. Phys. 110

122, (1978)

( 2 )

B.J. ALDER, T.E. WAINWRIGHT Phys. Rev. Lett.

18, 988 (1967)

-

(3) A. RAHMAN, M.J. MANDELL

J. Chem. Phys.

P.C

.

MC

TAGUE

64, 1564 (1976)

7

(4) K. TOUKUBO, K.NAKANISHI

J. Chem. Phys.

N. WATANAGE

_-

67, 4162 (1977)

( 5 )

B.J. ALDER, W.E. ALLEY

J. Chem. Phys.

J.H. DYMOND

6_1,

1415 (1974)

( 6 )

B.J. ALDER, M.D. GP.SS

J.

Chem. Phys.

T.E. WAINWRIGHT

-

53, 3813 (1970)

(7) A. BRUSON, M. GERL

Phys. Rev. 19

6123 (197g

(8) A. BRUSON, M. GERL

Phys. Rev.

(to be publis-

hed)(1980)

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