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ANALYSIS OF THE VISCOSITY OF MOLTEN
K-KCL MIXTURE IN THE METALLIC RANGE IN
CONNECTION WITH STRUCTURE
J. Jal, J. Dupuy, G. Chaussemy, A. Kaddoun, J. Fornazero
To cite this version:
JOURNAL DE PHYSIQUE
CoZZoque C8, suppZGment au n08, Tome
41,aoCt
1980,page
C8-367
ANALYSIS OF T H E VISCOSITY O F MOLTEN K-KCL MIXTURE IN T H E METALLIC RANGE IN CONNECTION
WITH S T R U C T U R E
*
J.F. J a l , J . Dupuy, G. Chaussemy
*,
A. Kaddoun and J . Fornazero*
De'pmtement de Physique des MatGriaux,
LA 172*~aboratoire
des semiconducteurs non c r i s t a l l i n s , Universite' CZaude Bernard Lyon
I , 69622 V i2 Zeurbanne Ce'dex, France.
S t a t i s t i c a l models have been s u c c e s s f u l l y used f o r denses f l u i d s . P a r t i c u l a r l y , a hard s p h e r e mo- d e l i s a good approximation t o account f o r t r a n s - p o r t p r o p e r t i e s of v a r i o u s molten s u b s t a n c e s s u c h a s m e t a l s 11,2
1
and s a l t s 13,41 above t h e m e l t i n g p o i n t.
Amore s u i t a b l e a n a l y s i s can b e made i f t h e s t r u c t u r a l d a t a o b t a i n e d from n e u t r o n d i f f r a c t i o n experiments a r e considered. I n t h i s paper o r i g i n a l r e s u l t s concerning both v i s c o s i t y and n e u t r o n d i f - f r a c t i o n measurements a r e analyzed f o r 25 moles %
K C 1 i n K m i x t u r e ; t h e e x p e r i m e n t a l v a l u e s a r e com- pared w i t h t h o s e f o r pure K and K C 1 . A t t h i s con- c e n t r a t i b n t h e c o n d u c t i v i t y i s s t i l l m e t a l l i c ( f i g . 1).
The models used f o r v i s c o s i t y a r e t h o s e pre- v i o u s l y used by Protopapas and J . J . Van Loef i n
l i q u i d m e t a l s and molten s a l t s r e s p e c t i v e l y . Our experimental s t u d y i s based on d e n s i t y , v i s c o s i t y
F i g . 1- C o n d u c t i v i t y and phase diagram of K-KC1 and 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 measurements. We
s o l u t i o n s ' ( t h e r v e r t i c a l l i n e s g i v e t h e l i m i t s of b r i e f l y d e s c r i b e t h e b a s i s of t h e experimental pro-
Mott c r i t e r i a f o r c o n d u c t i v i t y regimes. The arrow c e d u r e f o r v i s c o s i t y d e t e r m i n a t i o n , b u t d o n ' t d i s -
g i v e s t h e c o n c e n t r a t i o n i n v e s t i g a t e d i n t h i s s t u d y ) . c u s s i n d e t a i l s t h e v a l i d i t y of &he method. The
rheology f o r each l i q u i d has been considered e l s e - where (51.
1 . VISCOSITY
thermal exchange, and e n c l o s e by a non i n d u c t i v e
EperimentaZ
e l e c t r i c a l f u r n a c e i n which t h e temperature was T h e K i n e m a t i c v i s c o s i t y was determined by a n os-
c o n t r o l l e d by two thermocouples and a P.I.D. tempe- c i l l a t i n g cup v i s c o m e t e r . The penduilum was placed
r a t u r e r e g u l a t i o n . An e r r o r of about 7 % was e s t i - i n a q u a r t z chamber f i l l e d w i t h helium under redu-
mated f o r t h e a b s o l u t e v i s c o s i t y v a l u e , however ced pressure(80 mm Hg) i n o r d e r t o a c h i e v e a good
measuring t h e temperature dependence of t h e
JOURNAL DE PHYSIQUE
C8-368
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 i s about 2 %.
The l i q u i d i s enclosed i n a c y l i n d r i c a l s e a l e d c o n t a i n e r . The problems of chemical a t t a c k of con- t a i n e r by t h e s t u d i e d l i q u i d have been c o n s i d e r e d .
ResuZts
our r e s u l t s f o r K C 1 and K-KC1 mixture a r e given i n f i g u r e 2. For K t h e v a l u e s a r e t h o s e of Hand- book of t a b l e s f o r a p p l i e d e n g i n e e r i n g s c i e n c e
(R.C. Weast) 16
1.
The more r e c e n t r e s u l t s concerning K C 1 171
a r e not g i v e n i n f i g u r e 2 . However our d a t a a r e a few % s m a l l e r.
dKCl = 1.98-
0 . 5 8 . 1 0 - ~ T d = 1.11-
0 . 3 0 . 1 0 - ~ T f o r K-KC1 m i x t u r e r e g d = 1.06 - 0 . 3 0 . 1 0 - ~ T (25 moles %) exp P r e v i o u s l y Dymond 181 p o i n t e d o u t t h a t v i s c o s i t y d a t a can b e analyzed i n term of t h e molar volume V and t h e volume V of t h e hard s p h e r e f l u i d , f o rm
O N . 02
hard packing ( V =
-
,G i s t h e hard s p h e r e d i a -O 42
meter and N t h e Avogadro's number) according t o A
t h e r e l a t i o n :
The behavior of the Zi@ids considered above i s
i n good agreement with t h i s r e l a t i o n as shown i n
$/2
figure
3 where-
r\ v e r s u s V m i s p l o t t e d .
For t h e K-KC1 m i x t u r e our v a l u e s f o r TI a r e con- s i s t e n t w i t h t h e v i s c o s i t i e s of t h e two components, however a d i f f e r e n c e of about 20 % i s observed bet- ween t h e experimental v a l u e
n.
and t h o s e o b t a i n e dexp w i t h t h e e m p i r i c a l r e l a t i o n : l o g " r e g u l a r =0.25 l o g nKC1+0.75 l o g qK (13 "exp
-
" r e g,-
20 % 'exp The v i s c o s i t y f o r K-KC1 m i x t u r e i n t h e m e t a l l i c conduction r a n g e i s s m a l l e r t h a n $or a r e g u l a r so- l u t i o n :t h i s observation i s c o n s ~ s t e n t
with t h e
positive excess value observed.in these substances
by density measurzments
.
d = 0.84-
0 . 2 2 . 1 0 ~ ~ T (T i n OC) K F i g . 3 - ~ z a n s p o r t q u a n t i t i e s T"~/' f o r v a r i o u s li- q u i d s v e r s u s t h e molar volume ( t h e i n s e r t r e f e r s t o t h e measured v i s c o s i t i e s v e r s u s p o s t u l a t e d r e g u l a r molar volume ).
The V v a l u e s a r e o b t a i n e d by e x t r a p o l a t i o n . For K, t h e l i n e a r i t y i s n o t observedabove1000 K. 2. ANALYSISCoherence between v i s c o s i t y and d e n s i t y
dcrta.
T1/2
The l i n e a r r e l a t i o n s h i p between
-
and Vm i s observed o n l y i f t h e v a l u e s o f n and d a r e c o n s i s - t e n t i . e . a s t r a i g h t l i n e is o b t a i n e d by conside- r i n g e i t h e r t h e{n
reg,dregl s e t o f v a l u e s o r {nexp,dexp) ( f i g . 3 ) . But by u s i n g t h e h exp3 d r e g1
c o u p l e s , no l i n e a r i t y is observed. d i s t h e r e g d e n s i t y c a l c u l a t e d i n t h e h y p o t h e s i s of a r e g u l a r composition of molar volumes.Fig.2- V i s c o s i t i e s of molten s a l t s
(t)
.and mixtu- r e o f molten m e t a l i n molten s a l t s(a)
(25 moles %( f i g u r e 3 , i n s e t ) .
Hard sphere diameter and packing fraction
From t h e e x t r a p o l a t e d V v a l u e s , t h e packing f r a c t i o n can be c a r r i e d o u t according t o t h e f o l - lowing r e l a t i o n :
I n t a b l e I t h e v a l u e s of Vo,u, Vm a n d u a t t h e mel- t i n g p o i n t T a r e given f o r pure K and K C 1 and f o r
m
both " r e g u l a r " and "experimental" K-KC1 mixture.
*
: K : K C 1 : K-KC1*
: K-KC1 : (R) :(M)
.-__---_--.--__---.---.---
Vo(cc) : 3 2 . 7 0 : 3 0 . 0 2 : 30.37 : 32.11 dl;) : 4 . 2 5 : 4 . 1 3 : 4.14 : 4 . 2 2 Vm(cc) : : 4 7 . 6 2 : 4 8 . 9 3 : 56.24 : 56.20 a t T F : 11 : 0 . 5 0 5 : 0 . 4 5 4 : 0 . 3 9 9 : 0 . 4 2 3 0 : 4 . 6 7 : 4 . 5 3 : 4 . 5 6 : 4 . 6 3(* c o n c e n t r a t i o n : 2 5 moles
z
of KCI, (R) according t o formule 1,
(M) : experimental v a l u e s ,)For t h e K-KC2 mixture, t h e packing fraction
0.43a t t h e melting point i s
c l o s e t o t h e v a l u e p=0.47 correspondingt o t h e Lindeman
la
191
.
S t r u c t u r a l c o r r e l a t i o n and conclusion
For simple l i q u i d s t h e t o t a l d i s t r i b u t i o n func- t i o n g i v e s t h e r e l a t i v e p r o b a b i l i t y of f i n d i n g a n atom a t t h e d i s t a n c e r . I n a multicomponent f l u i d t h e i n f o r m a t i o n i s modified by t h e c o h e r e n t s c a t t e - r i n g l e n g t h s and t h e r e l a t i v e c o n c e n t r a t i o n , s o f t h e c o n s t i t u e n t s . A mean d i s t r i b u t i o n f u n c t i o n Gm(R) has
been determined by c a r r y i n g o u t experiments on sub- s t i t u t i o n a l i s o t r o p i c c h l o r i n e i n K C 1
1
101 ( f i g u r e 4 ) . The p r i n c i p a l peaks of 4 I T R ~ G (R) a r e a t t h e m Fame p o s i t i o n s t h a t f o r t h e t o t a l r a d i a l d i s t r i b u - MEAN DISTRIBUTION1
1
I
G *(I) TOTAL DISTRIBUTIONF i g 4-Mean d i s t r i b u t i o n f u n c t i o n deduced from p a i r d i s t r i b u t i o n f u n c t i o n s and t o t a l d i s t r i b u t i o n dedu- ced from t h e s t r u c t u r e f a c t o r of KC^.
For m e t a l l i c and i o n i c Z i p i d s
(1 2(
and
13Irespecti-
v e l y ) t h e hard core s i z e
ohas been found t o be
r e l a t e d t o t h e interatomic distance by a factor o f
0.91.
I n t a b l e I t h e L?- 0.91 v a l u e s a r e considered,
t h e
distances obtained are approximatively equal t o t h e
p o s i t i o n of t h e second peak f o r KC2 and
K-KCZmix-
t u r e 1111
( f i g . 5 ) .Fig. 5-Total d i s t r i b u t i o n f u n c t i o n of t h e mixture
K-KC1 ( 2 5 moles % ) (T=800°C) compared t o t h e K
d i s t r i b u t i o n f u n c t i o n (T=130°C). t i o n f u n c t i o n GN(R) ( f i g u r e 4 ) .
JOURNAL DE PHYSIQUE Thus t h e second p e a k c o r r e s p o n d s f o r t h e m i x t u r e a s f o r K C 1 , t o t h e mean s p a c e between s t r u c t u r a l u n i t s . I n K-KC1 m i x t u r e t h e K-K d i s t a n c e i s p r e s e n t o n G ( r ) , t h u s t h i s o b s e r v a t i o n g i v e s r i s e t o t h e f o l - l o w i n g , c o n c l u s i o n a c c o r d i n g l y t o t h e v i s c o s i t y da- t a :
The
X-KC2melt i n the metalZic range can be
essentiaZZy regarded as a non regular dense liquid
having a packing f ~ a c t i o n
of
0.43a t the melting
point,
t h e mean d i s t a n c e between s t r u c t u r a l d e n s i - t i e s b e i n g s t i l l t h e m e t a l l i c K-K d i s t a n c e .T h i s c o n c l u s i o n deduced from a phenomenologi- c a l s t a t i s t i c a l p o i n t of v u e c a n b e u s e f u l 1 : ( i ) t o a n a l y s e t h e change o c c u r i n g i n s h o r t r a n g e i n t e r a c t i o n f o r c e s when K C 1 i s d i s s o l v e d i n K , i n t h e m e t a l l i c r e g i o n ( i i ) t o p r e c i s e t h e c r i t e r i a o f t h e metal-non-metal t r a n s i t i o n . REFERENCES
11
I
P. PROTOPAPAS, H . C . ANDERSON, N.A.D. PARLEE J . Chem. P h y s ; , 1973,3 ,
1 5P. PROTOPAPAS, T h e s i s S t a n d f o r d U n i v e r s i t y , Ph.D. 1975
121 N.W. ASCHROFT, J. LEKNER, Phys. Rev. 1966, 145, 83
-
131 J.J. VAN LEOF, P h y s i c a , 1974, 75, p. 115
Z. f u r N a t u r f , 1976,
31,
967141 B . J . ALDER, J . E . WAINWRIGHT, Phys. Rev. L e t t . 1967,
2,
988151 A. EL HARBY, A. KADOUN, Rapport d l a c t i v i t B D.E.A. Lyon 1980 ( i n t e r n a l r e p o r t )
16
1
R.C. WEAST, Handbook o f t a b l e s f o r a p p l i e d e n g i n e e r i n g s c i e n c e s , 5 5 t h e d i t i o n 171 W . BROCHNER, K . GRJOTHEIM, T. OHTA, H.A. @YEB e r i c h t e d e r Bunsen G e s e l l s c h a f t , 1975, 79, 4, p . 344
-
18
1
J . H . DYMOND, J a l of Chem. Phys., 1974,60,
p. 96919
1
J.J. VAN LOEF, J a 1 of Chem. Phys. , 1 9 7 4 , s , p. 16051101 J . Y . DERRIEN, ThPse D'Etat Lyon 1975
