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VISCOSITY AND LOCAL ORDER IN PbxSe(1-x)
MELTS
G. Chaussemy, J. Fornazero, A. Laugier
To cite this version:
JOURNAL DE PHYSIQUE
ColZoque
C8,suppze'ment
au
n08, Tome 41, ao$t 1980, page
C8-371
VISCOSITY
AND LOCAL
ORDER IN Pb,Se(l-,) MELTSG. Chaussemy, J. F o r n a z e r o and A. L a u g i e r
*
Laboratoire des Semiconducteurs non cristaZZins, Universit6
C .Bernard, Lyon
I , 69622ViZleurbanne Ce'dex, France
* l n s t i t u t Nationaz des Sciences Applique'es, Laboratoire de Physique de Za Mati&re,
20, avenue
A.Einstein,
69622ViZZewbanne Cddex, France.
A b s t r a c t . - E x p e r i m e n t a l r e s u l t s c o n c e r n i n g t h e k i n e m a t i c v i s c o s i t y o f Pb Se,-x m e l t s a r e a n a l y s e d
X
i n t e r m o f a h a r d s p h e r e model and t h e a s s o c i a t e d s o l u t i o n s thermodynamics.
S o l i d l e a d s e l e n i d e h a s a X a C 1 s t r u c t u r e w i t h cova- l o g
v
v e r s u s%
i s p l o t t e d . The e x p e r i m e n t a l va- l e n t - i o n i c bonds. I n t h e l i q u i d s t a t e t h e l o c a l o r - l u e s ofv
a r e i n g o o d agreement w i t h t h e A r r h e n i u s ' d e r of t h e s o l i d i s p r o b a b l y c o n s e r v e d , a t l e a s t law :v
= A exp(-), T.l e x c e p t f o r t h e m o n o t e c t i c com-kT
t h e l i q u i d p r e s e n t s a m o l e c u l a r s t r u c t u r e r a t h e r p o s i 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 i e s T? have t h a n a c h a i n s t r u c t u r e
1
11 121 .
been c a l c u l a t e d by a l e a s t s q u a r e method. An e r r o r Thermodynamics d a t a i n d i c a t e t h a t in Pbx Se(1-x) of a b o u t 1 0 X i s e s t i m a t e d f o r t h e a b s o l u t e v a l u e of m e l t s t h e a s s o c i a t i o n i s s t r o n g 12
1
131
.
L o c a l o r -v
however, measuring t h e t e m p e r a t u r e dependence of d e r is governed by t h r e e s o r t s of c h e m i c a l bonds : t h e v i s c o s i t y t h e r e l a t i v e p r e c i s i o n is e s t i m a t e d t o Pb-
Se Se --.SeY*and Pb-
Pb. I n a r e c e n t p a p e r b e 4% i n t h e whole t e m p e r a t u r e r a n g e .141
,
a c c o r d i n g t o v i s c o s i t y measurements and neu- The d e n s i t y of Pbx Se(l-x) m e l t s i s n o t known e x c e p t t r o n d i f f r a c t i o n e x p e r i m e n t s we s u g g e s t e d t h a t ( i ) f o r p u r e Pb, and s t o e c h i o m e t r i c Pb S e : we h a v e sup- Pb-
Pb bonds a r e a b s e n t ( a t l e a s t in t h e Se r i c h posed t h a t t h e non s t o e c h i o m e t r i c c o m p o s i t i o n s a r e p a r t of t h e phase d i a g r a m-
f i g u r e 1) ( i i ) The Pb-
r e g u l a r s o l u t i o n s of Pb and Pb Se ( x > 0.5) o r Pb S e S e bonds a r e s t r o n g e r t h a n S e-
S e o n e s . T r a f i s p o r t and S e (X <O.9). T.!e h a v e observed f o r m o l t e n s a l t s p r o p e r t i e s , and p a r t i c u l a r l y v i s c o s i t y , of d e n s e s t h a t non r e g u l a r compositicin of t h e molar volumes l i q u i d s depend s c h e m a t i c a l l y of two p a r a m e t e r s : d o n ' t g i v e r i s e t o s i g n i f i c a n t d i f f e r e n c e s of t h e( i ) . The geometry of s t r u c t u r a l u n i t s ( i i ) t h e in- e x p e r i m e n t a l k i n e m a t i c v i s c o s i t y 191. t e r a c t i o n e n e r g i e s between s t r u c t u r a l u n i t s o r d i f - f e r e n t atoms of t h e m e l t . 1100 I n t h i s p a p e r o r i g i n a l r e s u l t s c o n c e r n i n g v i s c o s i t y of Pbx Se a l l o y s f o r x
>
0.24 ( e x c l u d i n g t h e 1000 ( 1-x) demixion zone) a r e a n a l y z e d .The a n a l y s e i s based on two s i m p l e models : 900
-
A h a r d s p h e r e model i n v o l v i n g t h e f r e e volume for-malism and t h e Macedo-Litovitz e q u a t i o n 15
1
.
T h i s 800 model, p a r t i c u l a r l y c o n v e n i e n t f o r l i q u i d l e a d ' 161 c a n be u s e d i n Pb S e m e l t 141 : It p e r m i t s t o 700 (1-x) c a r r y o u t q u a l i t a t i v e i n f o r m a t i o n s a b o u t m o l e c u l a r packing and i n t e r a t o m i c b i n d i n g e n e r g i e s .-
The a s s o c i a t e d s o l u t i o n model o r i g i n a l l y i n t r o d u - ced by J o r d a n 171,
i s a p p l i e d i n connexion w i t h thermodynamics d a t a t o a c c o u n t f o r t h e i s o t h e r m s o f v i s c o s i t y , a s p r e v i o u s l y done f o r Ge x S e (I-x) m e l t s 181.
I EXPERIMEVTAL ANn RESULTS
The k i n e m a t i c v i s c o s i t y
v
h a s been measured by a n o s c i l l a t i n g cup v i s c o m e t e r . The e x p e r i m e n t a l proce- d u r e is d e s c r i b e d i n d e t a i l s i n r e f 11,41.f i g 1
-
P h a s e diagram of Pb-
S e system I1 ANALYSTS ANr? r)ISCUSSION :a ) h a r d s p h e r e model :
According t o t h e f r e e volume f o r m a l i s m ,
I
1 0 , l l l and*
i n c l u d i n g a n a c t i v a t i o n e n e r g i e E t o a c c o u n t f o r t h e i n t e r a c t i n g f o r c e s between s t r u c t u r a l u n i t s , t h e k i n e m a t i c v i s c o s i t y i s t h e same t h a t f o r
@'one
Cam-ponebt
ha.rd s p h e r e f l u i d16
[
: The r e s u l t s a r e summarized f i g u r e (2a-
2b) whereJOURNAL DE PHYSIQUE
C8-372
1100 1000 900 BOO 700.-
1
T ("CI - ~ [ C S ~ I C--- (0.07 e ~ ) Pb .f i g 2.a
-
Kinematic v i s c o s i t i e s v e r s u s-
1000 (x > 0 . 3 f i g 2.b-
Yinematic v i s c o s i t i e s v e r s u s-
T lo? ( x < 0.5)
.09 .OB
The w e l l h o r n Stokes- E i n s t e i n r e l a t i o n s h i p b e t - ween s e l f d i f f u s i o n and v i s c o s i t y c o e f f i c i e n t s :
Dn = kT/?va i s used i n t h e model
.
H i s t h e mo- l a r mass, d t h e d e n s i t y , T t h e a b s o l u t e t e m p e r a t u r e ,<
t h e packing f r a c t i o n r e l a t e d t o t h e hard c o r e si-3
ze
a
by : 5 = N v d a /6M.
C0 = 0.74 (hard packing).A t a given t e m p e r a t u r e t h e measured v a l u e of v c a n be f i t t e d with t h e a i d of bq. (1) t a k i n g a s u i t a b l e couple <,sY a c t i n g a s a d j u s t a b l e parameters. E cor- responds roughly t o t h e i n t e r a c t i o n energy between s t r u c t u r a l u n i t s and is n o t temperature dependent.
T h s OpDdrent acttrotton rnerqorr
w orr paren ( 1 0 a v ) accordmp to
.
3
z A exp (+IThe v a r i a t i o n of v w i t h T a r e explained by a tempe-
.07 '
1.0 .7 " 1000, T 1 K.'I ;9 1.0
r a t u r e dependent hard c o r e s i z e
a
,
a s suggested by Protopapas]
121
and considered i n a precedent work141 .The interdependence of 5 and E a t t h e melting p o i n t is v i s u a l i z e d f i g ( 3 ) .
b) V i s c o s i t y and a s s o c i a t e d s o l u t i o n s :
For Pb Se compounds t h e a s s o c i a t i o n i s gover-
x (1-x)
ned by t h e chemical e q u a t i o n : A
+
B % AB (A f o r Pb and B f o r Se)The l i q u i d i s considered a s a r e g u l a r t e r n a r y solu- t i o n w i t h t h e molar f r a c t i o n s xA
,
xB and x AB'XA = X
-
(1-x) XAB ; XB = (I-x)-
x XABI n t h i s model Schneider 121 h a s i n t r o d u c e d t h e p a r a meter p = (1-x )
/
( 1+
x ~ ) .f3
d e n o t e s t h e p va-AB
l u e f o r x = 0.5. The e q u i l i b r i u m c o n s t a n t of asso- c i a t i o n
Y
(T) and t h e a c t i v i t i e s yi can b e expres- sed i n term of 8. We have t h e f o l l o w i n g r e l a t i o n between K (T) and t h e yi :x~ X3
YA YB
K (T) =
---
-
X
AS 'AS
For
6
= 0 , t h e a s s o c i a t i o n is complete andB
= 1 corresponds t o complete d i s s o c i a t i o n . Thef3
v a l u e s have heen measured by Schneider 121 .
?Te have calcu- l a t e d t h e molar f r a c t i o n s a t 1273, 1323, 1373 and 1423 K and f o r v a r i o u s x.For v i s c o s i t i e s , i t is convenient t o u s e t h e e m p i r i - c a l r e l a t i o n of a d d i t i v i t y 11
I
:(2) Log I1 = XA l o g 'lA+
3
l o g'1B+
XAB l o g 'lABThe 11. denote t h e dynamic v i s c o s i t i e s : = Vd. The isotherms of a r e given i n f i g u r e (4) : t h e model a g r e e s w e l l w i t h experimental d a t a i n t h e
~ 4 0 . 5 r e g i o n . (The dashed l i n e s r e p r e s e n t t h e c a l - c u l a t e d isotherms)
.
The v i s c o s i t y of Selenium a c t s a s an a d j u s t a b l e pa- r a m e t e r , no experimental v a l u e being a v a i l a b l e abo- v e 1000°C.
For x ) 0.5 no f i t is p o s s i b l e , except n e a r pure l e a d .
c) Discussion
Near t h e m e l t i n g p o i n t Tm
,
t h e l i q u i d can be d i v i - ded i n t o t h r e e c l a s s e s according t o r e l a t i o n (1) and f i g u r e (3) :1) Pb-like : 2.e. m e t a l l i c behaviour i s c h a r a c t e r i -
*
F i g (?) I n t e r d e p e n d e n c e of t h e two a d j u s t a b l e para- F i g (4) E x p e r i m e n t a l and t h e o r e t i c a l (dashed l i n e s ) m e t e r s a t t h e m e l t i n g p o i n t a c c o r d i n g t o t h e model. i s o t h e r m s o f v i s c o s i t y . The p r e c e d e n t c o n s i d e r a t i o n s on r a d i a l d i s t r i b u t i o n suppose t h a t m e t a l l i c b e h a v i o u r i s c o n t i n u e d v e r y f u n c t i o n would i n d i c a t e t h a t
cm
= 0.34 and E = 0.35 c l o s e t o l e a d s e l e n i d e . 141
( f o r t h e s t o e c h i o m e t r i c c o m p o s i t i o n ) .Cm
i s r e - I n c o n c l u s i o n : Pbx Se m e l t s a r e s t r o n g l y a s s o - ( 1 - 4l a t i v e l y s m a l l . It must b e p o i n t e d o u t t h a t t h e ex- c i a t e d l i q u i d s , p a r t i c u l a r l y f o r x q 0 . 5 . The S e
-
Sep e r i m e n t a l v a l u e s of v f o r Pb Se a r e t h o s e of a t e r - and Pb
-
Se i n t e r a c t i o n s a r e s t r o n g c o m p a r a t i v e l y t o n a r y l i q u i z , t h e a s s o c i a t i o n b e i n g n o t complete. t h e Pb-
Pb o n e s . The h i g h e r packing f r a c t i o n i n mo- F r e e l e a d and S e have a l o w e r i n g e f f e c t on v i s c o s i t y . n o t e c t i c l i q u i d t h a n i n s t o e c h i o m e t r i c Pb Se can b e The a s s o c i a t e d s o l u t i o n model g i v e s a t h e o r e t i c a l v a r e g a r d e d a s an i n d i c a t i o n of a change i n l o c a l o r d e r l u e of ri f o r c o m p l e t e l y a s s o c i a t e d Pb Se : 1.9 cP a t when x is iowered from 0.5 t o 0.24. F o r x > 0.5 d i - 1323 K,
1.73 cP a t 1373 K and 1.55 cP a t 1423 K . HO sagreement w i t h t h e a s s o c i a t e d sol.l>+'nn n ~ d e l sUggeSW wever, t h e e f f e c t of d i s s o c i a t i o n i s s m a l l on t h e t h a t t h e m e t a l l i c c h a r a c t e r i s c o n t i n u e d on a l a r g e h a r d s p h e r e a n a l y s i s a s shown i n f i g u r e (3) where a r a n g e of x v a l u e s : a n analogy w i t h m e t a l - s a l t s o h - t h e o r e t i c a l c u r v e i s r e p r e s e n t e d . For p u r e S e , t h e t i o n s i s p o s s i b l e . I n t h e s e l i q u i d s 191 t h e m e t a l - model g i v e s a l s o a t h i g h t e m p e r a t u r e (0.7 cP a t m e t a l c h a r a c t e r i s t i c d i s t a n c e i s p r e s e n t in t h e ra- 1423 K ) t h i s v a l u e i s r o u g h l y c o m p a t i b l e w i t h an ex- d i a l d i s t r i b u t i o n f u n c t i o n and t h e c o n d u c t i v i t y ex- t r a p o l a t i o n of t h e e x p e r i m e n t a l c u r v e of reference181 h i b i t a metal-non m e t a l t r a n s i t i o n .The form of t h e i s o t h e r m s on t h e Pb s i d e of t h e pha- For a more p e r t i n e n t a n a l y s i s we need t b
consider
s e diagram i s more d i f f i c u l t t o e x p l a i n e x c e p t
Ff
we e l e c t r i c a l c o n d u c t i v i t y d a t a and n e u t r o n d i f f L a c t i o n r e s u l t s .R e f e r e n c e s
( 1
1
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,
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,
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