HAL Id: jpa-00225199
https://hal.archives-ouvertes.fr/jpa-00225199
Submitted on 1 Jan 1985
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
ON THE ORIGIN OF PHASE SEPARATION IN
LIQUID METAL-SALT MIXTURES
C. Holzhey, W. Schirmacher
To cite this version:
ON T H E O R I G I N O F PHASE S E P A R A T I O N I N L I Q U I D M E T A L - S A L T M I X T U R E S
+*
C . Holzhey and W. SchirmacherPhys. Dept. E13, Techn. Univ. Miinchen, 0-8046 Garching, F.R.G. + ~ n s t i t u t Laue-Langevin, 156 X, 38042 Grenoble Cedex, France
R6sumQ
-
Les p r o p r i 6 t g s thermodynamiques d e s s o l u t i o n s mQtaux a l c a l i n s-
s e l s fondus sont 6 t u d i 6 e s 2 l ' a i d e d ' u n modsle dans l e q u e l l ' i n t e r a c t i o n des cons- t i t u e n t s e s t d Q c r i t e par un p o t e n t i e l de Coulomb Q c r a n t 6 p a r l e s Q l e c t r o n s . Nous montrons que l a s g p a r a t i o n d e phase dans c e s systsmes e s t d i r e c t e m e n tl i Q e h l a t r a n s i t i o n m Q t a l
-
non mgtal q u i s e p r 6 s e n t e e n f o n c t i o n d e l a con- c e n t r a t i o n .A b s t r a c t
-
The thermodynamic p r o p e r t i e s of l i q u i d metal s a l t mixtures a r e s t u d i e d w i t h t h e h e l p of a model i n which t h e m e t a l l i c and h a l o g e n i c c o n s t i t u - e n t s i n t e r a c t with each o t h e r v i a an e l e c t r o n i c a l l y screened Coulomb p o t e n t i a l . It i s shown t h a t t h e phase s e p a r a t i o n of l i q u i d metal s a l t mixtures i s a d i r e c t consequence of t h e metal-nonmetal t r a n s i t i o n t h a t occurs i n t h e s esystems a s a f u n c t i o n of c o n c e n t r a t i o n . I
-
INTRODUCTIONLiquid s o l u t i o n s of a l k a l i m e t a l s and t h e i r molten h a l i d e s have t h e i n t e r e s t i n g p r o p e r t y t h a t t h e r a t i o of e l e c t r o n s t o metal i o n s v a r i e s with composition, g i v i n g a continuous t r a n s i t i o n from t h e n e a r l y - f r e e - e l e c t r o n l i q u i d a l k a l i metal t o t h e h i g h l y charge-ordered i o n i c l i q u i d . Another p o i n t of i n t e r e s t i s t h a t t h e phase diagrams of most a l k a l i m e t a l - a l k a l i h a l i d e mixtures a r e c h a r a c t e r i s e d by l i q u i d -
l i q u i d i m m i s c i b i l i t y below a c r i t i c a l temperature Tc
111.
Like i n expandedm e t a l s 12-41 and metal ammonia s o l u t i o n s /5/ t h e q u e s t i o n a r i s e s a s t o whether t h e r e e x i s t s a connection between t h e m e t a l nonmetal t r a n s i t i o n (MNM) 161 t h a t occurs a s a f u n c t i o n of s a l t c o n c e n t r a t i o n and t h e observed phase s e p a r a t i o n .
It has been pointed out by Mott 161 and Yonezawa and Ogawa 141 t h a t a change i n t h e e l e c t r o n i c s t r u c t u r e r e l a t e d t o t h e MNM t r a n s i t i o n could g i v e r i s e t o a s e p a r a t i o n i n t o a m e t a l - r i c h and a d i l u t e phase. I n t h e p r e s e n t c o n t r i b u t i o n we show by means of a simple model f o r a m e t a l s a l t s o l u t i o n t h a t t h e demixion can be explained a s t h e r e s u l t of a g r a d u a l r e d u c t i o n of t h e e l e c t r o n i c s c r e e n i n g w i t h i n c r e a s i n g s a l t c o n t e n t , which precedes t h e m e t a l - i n s u l a t o r t r a n s i t i o n . I f t h i s change of s c r e e n i n g with c o n c e n t r a t i o n i s not v e r y s t r o n g , an almost symmetric phase diagram i s p r e d i c t e d , whereas asymmeties a r i s e i f t h e c o n c e n t r a t i o n d e r i v a t i v e of Ad (where d i s an average hard c o r e diameter) becomes comparable o r l a r g e r t h a n 1 .
I1
-
MODEL We c o n s i d e r a b i n a r y l i q u i d m e t a l halogen mixture M X t h a t i n t e r a c t s v i a t h e I -c c following i n t e r a t o m i c p a i r p o t e n t i a l s : 2 $ . . ( r ) =$!?(r) + Q . Q . e exp{-hr] / r 1 3 11 1 3( j g ) ( r ) i s a hard c o r e r e p u l s i o n which we f o r s i m p l i c i t y r e p l a c e by a hard sphere p o t e n t i a l with a common hard sphere diameter d.
*permanent a d d r e s s : Phys. Dept. E13, Techn. Univ. Miinchen, D-8046 Garching, F.R.G.
C8-374
JOURNAL DE PHYSIQUE
The second term r e p r e s e n t s a n e l e c t r o n i c a l l y s c r e e n e d Coulomb i n t e r a c t i o n w i t h e f f e c t i v e c h a r g e s Q 1 > 0 , Q2 < 0 and s c r e e n i n g p a r a m e t e r A . With t h e h e l p of s u c h a model t h e thermodynamic and s t r u c t u r a l p r o p e r t i e s of s t r o n g l y i n t e r a c t i n g l i q u i d b i n a r y a l l o y s h a v e been s t u d i e d s u c c e s s f u l l y / 7 - l o / . The p a r t i a l r a d i a l d i s t r i b u t i o n f u n c t i o n s g i j ( r ) c o r r e s p o n d i n g t o ( 1 ) c a n b e c a l c u l a t e d a n a l y t i c a l l y / 1 1 / i n t h e mean s p h e r i c a l a p p r o x i m a t i o n (MSA) i f one imposes t h e l o c a l c h a r g e n e u t r a l i t y c o n d i t i o n
With (1) and ( 2 ) t h e s t r u c t u r e d e p e n d e n t p a r t of t h e i n t e r n a l e n e r g y of t h e system t a k e s t h e form / 9 / A== where @ i s t h e " o r d e r i n g p o t e n t i a l " C C and g ( r ) i s t h e c o r r e l a t i o n f u n c t i o n of c o n c e n t r a t i o n f l u c t u a t i o n s /12/ which d e s c r % e s t h e l o c a l c h e m i c a l s h o r t - r a n g e o r d e r .
D e t a i l e d MSA c a l c u l a t i o n s / 1 3 , 1 4 / f o r p o t e n t i a l s of t h e form (1) have shown t h a t a s long a s t h e e f f e c t i v e c h a r g e s a r e of t h e o r d e r of 1 and t h e s c r e e n i n g p a r a m e t e r
i s n o t much l a r g e r t h a n d-I one h a s always s t r o n g h e t e r o c o o r d i n a t i o n i n d i c a t e d by a s h a r p n e g a t i v e peak i n g e c ( r ) l o c a t e d n e a r r = d. The peak h e i g h t d o e s n o t v a r y s t r o n g l y w i t h A .
I n s t e a d o f c a l c u l a t i 1 1 ~ E w i t h t h e h e l p of t h e MSA, which w i l l b e done i n a f u t u r e p u b l i c a t i o n (*) we t h e r e f o r e u s e t h e f o l l o w i n g ~ a r a m a t r i z a t i o n of gcc :
where A > 0 i s a s h o r t - r a n g e o r d e r p a r a m e t e r of t h e o r d e r of 1 which we assume n o t t o depend on c o n c e n t r a t i o n and t e m p e r a t u r e . These s i m p l i c a t i o n s which c a n b e e a s i l y r e l a x e d d o n o t change t h e q u a l i t a t i v e r e s u l t s of o u r t h e o r y . P u t t i n g e q s . ( I ) , ( 3 ) , ( 4 ) and ( 5 ) t o g e t h e r we a r r i v e a t t h e f o l l o w i n g e x p r e s s i o n f o r E :
~ 2 2
2 E = - A - - (1 - C ) e e x p [ - ~ ( ~ ) d j / d (6) The e l e c t r o n i c s c r e e n i n g p a r a m e t e r A c a n b e c a l c u l a t e d a s a f u n c t i o n of m e t a l c o n c e n t r a t i o n u s i n g modern t h e o r i e s of t h e i n t e r a c t i n g e l e c t r o n g a s / 1 7 / . F o r t h e p r e s e n t p u r p o s e , however, i t i s e n t i r e l y s u f f i c i e n t t o n o t e t h a t h is a m o n o t o n i c a l l y d e c r e a s i n g f u n c t i o n of t h e h a l o g e n c o n c e n t r a t i o n c . A s a f i n a l s t e p we perform a t r a n s f o r m a t i o n from t h e h a l o g e n c o n c e n t r a t i o n c t o t h e e x c e s s m e t a l molar f r a c t i o n c o r r e s p o n d i n g t o t h e f o r m u l a %(MX)l, v i a 116/ T h i s y i e l d s 2 2 E X = - 1 - A e exp [ - h ( x ) d j / dl i n e a r v a r i a t i o n of
X
( x ) by expanding around a n i n t e r m e d i a t e c o n c e n t r a t i o n x o and k e e p i n g o n l y t h e l i n e a r term : > 0 . From t h i s we o b t a i n f o r t h e e n t h a l p y of mixing x 0 2 w i t h E = A e exp[
h ' xo-
hod] /d For t h e e x c e s s e n t r o p y we u s e f o r s i m p l i c i t y t h e n o n - i n t e r a c t i n g e n t r o p y of t h e p s e u d o b i n a r y s y s t e m :T h i s seems t o be c o n s i s t e n t w i t h o u r a p p r o x i m a t i o n (5) f o r g c c ( r ) which means t h a t t h e r e s h o u l d be a l w a y s a s many m e t a l atoms around a h a l o g e n a s p o s s i b l e .
I n t r o d u c i n g t h e d i m e n s i o n l e s s q u a n t i t i e s s = S / k g and t = kgT/Eo we o b t a i n f o r t h e e x c e s s f r e e e n e r g y f = AF / E :
f = (1 - x ) (1 - exp {--h'xJ - t s ( x ) (12) From eq. (8) o r t h e more e x p l i c i t o n e (12) i t i s s e e n i m m e d i a t e l y t h a t w i t h i n o u r model demixing ( i . e . a 2 f / a x 2 4 0 ) o c c u r s i f and o n l y i f h i s a f u n c t i o n of concen- t r a t i o n . T h i s i s q u i t e d i f f e r e n t from t h e u s u a l c a s e o f a n A-B a l l o y where t h e i n t e r a t o m i c p o t e n t i a l s d o n o t depend on c o n c e n t r a t i o n and where t h e d e n i x i ~ g i s a r e s u l t of p r e f e r r e d A-A and B-B p a i r i n g .
I11 - RESULTS AND DISCUSSION
F i g . 1
-
F r e e e n e r g y i s o t h e r m s f o r a ) A ' = 0 . 2 , t = 0 . 0 6 ,...
0.1 and b) h ' = 2 t = 0 . 5 ,...
0 . 9 .03-376 JOURNAL
DE
PHYSIQUEI f o n l y q u a d r a t i c terms i n x a r e k e p t we o b t a i n a AH c o r r e s p o n d i n g t o t h e symmetric "conformal s o l u t i o n " model / 1 8 , 1 9 / of a m e t a l - s a l t m i x t u r e w i t h i n t e r a c t i o n para- meter w = EoA1 i n d i c a t i n g a demixing tendency. L e t u s emphasize a g a i n t h a t i t s m i c r o s c o p i c o r i g i n i n t h e c a s e of o u r model d i f f e r s f u n d a m e n t a l l y from t h e demixing of a b i n a r y m i x t u r e w i t h c o n c e n t r a t i o n independent i n t e r a t o m i c p o t e n t i a l s . F i g . 2 - P h a s e diagrams c o r r e s p o n d i n g t o f i g . 1 . I n f i g . 2 t h e phase diagrams c o r r e s p o n d i n g t o t h e i s o t h e r m s of f i g . 1 a r e g i v e n . The s p i n o d a l s a r e g i v e n by t h e e x p r e s s i o n The o b s e r v e d d i f f e r e n c e s i n t h e s h a p e s of p h a s e dia.grams e . g . f o r t h e K-KX s e r i e s
11,
20, 211 c a n be e x p l a i n e d i n t e r m s of o u r t h e o r y . They a r e a l l asymmetric w i t h xc < 0.5. The s t r o n g e s t asymmetry i s observed f o r K-KF (xc % 0 . 2 ) where one h a s t h e l a r g e s t d i f f e r e n c e i n e l e c t r o n e g a t i v i t y , which can be expected t o l e a d t o a much more e f f i c i e n t r e d u c t i o n of t h e e l e c t r o n i c s c r e e n i n g t h a n i n t h e o t h e r system, where t h e e l e ~ t r o n e ~ a t i v i t y d i f f e r e n c e i s s m a l l e r and t h e p h a s e diagrams a r e more symmetric. We would l i k e t o mention a l s o t h a t t h e p a r a m e t r i z a t i o n used by Yokokawa e t a l . 122, 231 t o £ . i t t h e AH(x) d a t a c o r r e s p o n d s t o our e q u a t i o n (13) i f one i n c l u d e s t h e 3 r d o r d e r term.V
-
CONCLUSIONUsing a model of a m i x t u r e o f m e t a l and h a l o g e n atoms i n t e r a c t i n g v i a e l e c t r o - n i c a l l y s c r e e n e d Coulomb p o t e n t i a l s p l u s a h a r d c o r e r e p u l s i o n we have convinced o u r s e l v e s t h a t t h e demixing t e n d e n c i e s observed i n m e t a l m o l t e n s a l t s o l u t i o n s a r e t h e r e s u l t o f t h e c o n c e n t r a t i o n dependence of t h e e l e c t r o n i c s c r e e n i n g which a p p e a r s a s a p r e c u r s o r of t h e m e t a l nonmetal t r a n s i t i o n s i n t h e s e systems. I f t h e concen- t r a t i o n dependence i n t h e m e t a l l i c regime i s weak we p r e d i c t symmetric phase diagrams whereas asymmetries a r i s e i f t h e c o n c e n t r a t i o n v a r i a t i o n of A i s s t r o n g .
ACKNOWLEDGEMENTS
T h i s i s s u p p o r t e d by p a r t by Deutsche Forschungsgemeinschaft.
We a r e g r a t e f u l t o G. C h a b r i e r , P. Chieux, B.U. F e l d e r h o f , J.R. F r a n z , J.P. Hansen, R.B. J o n e s , M.L. Saboungi and A. Schirmer f o r h e l p f u l d i s c u s s i o n s .
REFERENCES
/ l / B r e d i g , M.A., Molten S a l t Chemistry, Ed. B l a n d e r , M. (Wiley I n t e r s c i e n c e , New York) 1964.
/2/ SchBnherr, G., Schmutzler, R.W. and Hensel, F . , P h i l , Mag. B g (1979) 411.
131
Cusak, N.E., P r o g r . Theor. Phys.2,
Suppl. (1982) p. 81.P h i l . Mag.
B50
(1984) 161.S c h i r m a c h e r , W . , J . Non C r y s t . S o l i d s
2-2
(1980) 1301.C o p e s t a k e , A.P., E v a n s , R., R u p p e r s b e r g , H. and S c h i r m a c h e r , W., J . P h y s . F E , (1984) 1993.
H a f n e r , J . , P a s t u r e l , A., and H i c t e r , P . , J . Phys. F. 1 4 (1984) 1137 and 2279. R u p p e r s b e r g , H. a n d S c h i r m a c h e r , W . , J . Phys.
F14
( 1 9 8 q 2787.Waisman, E . , J. Chem. Phys. 59 (1973) 495.
B h a t i a , A.B., and T h o r n t o n
KE.,
Phys. Rev. (1970) 3004.C o p e s t a k e , A.B. and Evans, R., J. Phys. (1982) 4961 and i n " I o n i c l i q u i d s , m o l t e n s a l t s and p o l y e l e c t r o l y t e s " L e c t u r e n o t e s i n P h y s i c s Vol. 172, S p r i n g e r B e r l i n (1982) p. 8 6 .
Holzhey, Ch., F r a n z , J . and B r o u e r s , F . , J . Phys. F14 (1964) 2475. C h a b r i e r , G . , and Hansen, J . P . , J . Phys. F. t o a p p e a r
C h a b r i e r , G. and Hansen, J . P . , Mol. Phys.
50
(1983) 901. I c h i m a r u , S . , Rev. Mod. Phys.54
(1982) 1017.Longuet-Higgins, H . C . , P r o c . Roy. Soc. - A205 (1951) 247.
B h a t i a , A.B. i n " L i q u i d M e t a l s 1976" Eds. R. Evans and D.A. Greenwood, I n t . Phys. Conf. S e r . E (1977) p. 21.
J a l , J . F . , Chieux, P . , Dupuy, J . and Dupin, J . P . , J. Phys. ( P a r i s )
5
(1980) 657.J a l , J . F . , Dupuy, J . and Chieux, P . , J . Phys.
