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ELECTRICAL AND THERMODYNAMIC
PROPERTIES OF LIQUID Hg AND DILUTE
AMALGANS AT HIGH TEMPERATURES AND
HIGH PRESSURES
M. Yao, H. Endo
To cite this version:
JOURNAL
DE
PHYSIQUE CoZZoque C8, suppZ6ment a u n08, Tome 41, a o c t 1980, pageC8-58
ELECTRICAL AND THERMODYNAMIC PROPERTIES OF LIQUID Hg AND DILUTE AMALSANS AT HIEH
TEMPERATURES AND HIGH PRESSURES
M. Yao and H. Endo
Department o f P h y s i c s , FacuZty o f S c i e n c e , Kyoto U n i v e r s i t y , Kyoto 606, Japan.
Abstract.- The simultaneous measurements of the density and the electrical conductivity have been carried out for expanded Hg and amalgams up to
1500°~
and1700
bar. Anomalous behaviours have been found in the thermodynamic properties of Hg at nearly the same density as that where the metal- nonmetal transition occurs. The isochores on the pressure-temperature plane shift by a slight addition of other elements.INTRODUCTION-- The metallic liquid H g can be transformed to a semiconducting or in-
MO electrodes
sulating state when the density is reduced
epoxy r k l n
by raising temperature under high pres- i -
' tef IonO-rmas
stainless steel container c
--
d - 4 1 , sures. I n spite o f a large amount of exper- ? --
imental information, a conclusive descrip- Fig. 1. Cell assembly for the measurements o f d and
o.
tion has not yet obtained for the rnecha- nism of the metal-nonmetal
(M-NM)
transi- tion i n an expanded Hg. This is partially due to the lack o f accuracy i n the experi- mental data at high temperatures and high pressures. I n order to get the accurate information of the electronic properties, we have performed the simultaneous measure- ments o f the density d and the electricalconductivity d for expanded H g and dilute amalgams up to
1 5 0 0 ~ ~
and1700
bar. We dis- cuss the changes i n thermodymanic proper- ties caused by the M-NM transition.EXPERIMENTAL PROCEDURE-- The cell assembly
part sinked on heating run and floated o n cooling run when the density o f the sample was equal to that o f the sinker. The posi- tion of the sinker was detected by changes i n electrical resistances o f the upper and lower parts o f the test part. I n this way the isochore o f the sample was determined on the pressure P
-
temperatureT
plane. The experimental errors were less than ~ O C i n temperature,5
bar i n pressure and0.5%
i n density. Further experimental details will be described elsewhere [ 2 ]
.
RESULTS AND DISCUSSION-- T h e isotherm and for the simultaneous measurements of d and isochore conductivities are shown as func-
are shown in Fig. 1. The density was tions o f pressure i n Fig.
2.
Inside the measured by the Archimedean method using thin solid line is the liquid-gas coexis-sinkers
with
k n o r ~ specific gravity, which tence region. Present data are i n fairly was similar to the method adopted by Neale good agreement with those by Tsuji et al. and Cusackrl]. The sinker put i n the test[ 3 ]
and by Schdnherr et al.[4J. The pres- sure variation o f isothermal conductivityF i g . 2 . I s o t h e r m a l and i s o c h o r e c o n d u c t i v i - t i e s o f Hg a s f u n c t i o n s o f p r e s s u r e . becomes v e r y l a r g e a s t h e t e m p e r a t u r e i n - c r e a s e s t o t h e c r i t i c a l t e m p e r a t u r e (-1490 O C ) . Although t h e p r e s s u r e dependence of t h e i s o c h o r e c o n d u c t i v i t y , d e n o t e d by t h e b o l d l i n e , i s n o t s o r e m a r k a b l e a s t h a t o f t h e i s o t h e r m a l c o n d u c t i v i t y , t h e former
becomes a p p r e c i a b l e when t h e d e n s i t y be-
comes s m a l l e r .
density
(
g/cm3
)
10
8
l
o
r
-pure Hg
0
/molar
volume (cm3)
F i g .3 .
Temperature d e r i v a t i v e ( a l n o / ~ T ) o f o a t c o n s t a n t volume a s a f u n c t i o n o fv
m o l a r volume. The open c i r c l e s r e p r e s e n t t h e p r e s e n t d a t a and t h e clmsed c i r c l e s t h e d a t a by Neale and C u s a c k [ l ] . F i g u r e3
shows t h e t e m p e r a t u r e d e r i v a - t i v e ( a l n o / a ~ ) ~ o f c o n d u c t i v i t y a t con- s t a n t volume a s a f u n c t i o n o f m o l a r v o l ~ m e . The r a p i d i n c r e a s e o f t h e d e r i v a t i v e a t d e n s i t i e s below 10 g/cm3 o r s o i n d i - c a t e s t h e o n s e t of t h e M-NM t r a n s i t i o n . F i g u r e4
shows t h e i s o c h o r e s o f 10.45, 1 0 . 0 , 9.6, 9.0 and 8 . 2 g/crn3 f o r p u r e Hg on t h e P-T p l a n e t o g e t h e r w i t h t h e s a t u - r a t e d v a p o u r p r e s s u r e c u r v e d e t e r m i n e d by t h e jump i n t h e r e s i s t a n c e . The i s o c h o r e s show n e g l i g i b l e d e p a r t u r e from l i n e a r i t y . The e x p e r i m e n t a l e q u a t i o n - o f - s t a t e d a t a a r e d e s c r i b e d i n t h e form o f t h e i s o c h o r e e q u a t i o n : P=)/
V~-
P 0 F i g u r e s 5 ( a ) and ( b ) r e s p e c t i v e l y show f V and Po a s f u n c t i o n s o f m o l a r volume.The volume dependences o f b o t h f V and P 0 change a t n e a r l y t h e same d e n s i t y a s t h a t
where t h e M-NM t r a n s i t i o n o c c u r s ( s e e F i g .
3 ) .
They a r e l a r g e a t s m a l l e r vol-wnes and become s m a l l w i t h i n c r e a s i n g volume. Theo b s e r v e d change i n t h e volume dependences
o f
)/y
and Po may b e a s s o c i a t e d w i t h t h e change i n t h e n a t u r e o f t h e i n t e r a t o m i cf o r c e c o r r e s p o n d i n g t o t h e M-NM t r a n s i -
t i o n . Such a n anomalous change was ob-
JOURNAL DE PHYSlQUE molar volume (cm3
1
density (g/cm3) 11 10 8 molar volume (cm31
F i g s .5
( a ) and ( b ).
Volume v a r i a t i o n s offv
and P.
The open and c l o s e d c i r c l e s denote tRe same a s t h o s e i n F i g .3.
b:0.2 a t . % B i amalgam, + : 0 . 3 a t . % Cd amalgam.served i n t h e volume dependence o f t h e
sound velocity[5]. R e c e n t l y Ogawa e t a l .
s t u d y t h e o r e t i c a l l y t h e r e l a t i o n between
anomalies i n thermodynamic p r o p e r t i e s and
a weak d i s c o n t i n u i t y i n t h e volume depen-
dence o f t h e t o t a l energy o f t h e e l e c t r o n system a t a M-NM t r a n s i t i o n p o i n t 161. From t h e PVT d a t a , t h e i s o t h e r m a l com- p r e s s b i l i t y
PT
and t h e l o n g wavelengthl i m i t
o f t h e s t r u c t u r e f a c t o r , S ( O )(
= PkBTPT) ,
a r e e s t i m a t e d . These a r e p l o t t e d i n F i g . 6 a s f u n c t i o n s o f molar volume a t 1600 b a r . Rapid i n c r e a s e i n b o t hP
T and ~ ( 0 ) a r e observed a t d e n s i t i e s below 10.0 g/:/cm3 o r so. The d e n s i t y f l u c t u a t i o n s a r e l a r g e n e a r t h e M-NM t r a n s i t i o n r e g i o n , though t h eM-NM
t r a n s i t i o n o c c u r s a t much h i g h e r d e n s i t y t h a n t h e c r i t i c a l d e n s i t y . I n F i g s .7
(a) and ( b ) r e s p e c t i v e l y , t h e r e s u l t s o f o f o r 0 . 5 a t . % B i and 2 a t . % Bi amalgams a r e shown a s f u n c t i o n s o f p r e s -s u r e . The hatched a r e a s d e n o t e t h e two-
phase r e g i o n s . A t h i g h t e m p e r a t u r e s t h e i s o t h e r m a l c o n d u c t i v i t i e s i n c r e a s e remark-
density
(9/cm3)
3
12
10
8
I
o
,kAU-
I20
25
10
molar volume(cm3)
F i g . 6. Volume v a r i a t i o n s ofPT
and ~ ( 0 ) . The dashed l i n e d e n o t e s S ( O ) f o r Hg. o:PT f o r Hg,Q:P
f o r 0.2 a t . $ B i amalgam, f o r 0 . 3 a t . 3 Cd amalgam,.:
PT
f o r Hg : ~ ~ ~ N e a l e and CusacL[l]. a b l y w i t h B i c o n c e n t r a t i o n b e i n g compared a t c o n s t a n t p r e s s u r e s l 7 7 . The i s o c h o r e c o n d u c t i v i t y a t 10.0 g/cm3 denoted by t h e bold l i n e a l s o i n c r e a s e s w i t h B i concen- t r a t i o n . The r e s u l t s o f t h e i s o c h o r e s o f 10.0 g/cm3 f o r v a r i o u s d i l u t e amalgams a r e com- p i l e d i n F i g . 8. The i s o c h o r e s a t c o n s t a n t p r e s s u r e s s h i f t towards h i g h e r tempera- t u r e s by a d d i t i o n o f a s m a l l amount o f B i ,Pb, Cd and I n , and towards lower tempera-
F i g . 8. I s o c h o r e s o f 1 0 . 0 g/cm3 f o r amal- gams
.
s l o p e s o f t h e i s o c h o r e s f o r 2 a t . % Cd, B i and Pb amalgams a r e s m a l l e r t h a n t h e s l o p e o f t h e i s o c h o r e f o r p u r e Hg. I n F i g . 9 , t h e i s o c h o r e s o f 9.6 and 9.0 g/cm3 f o r d i l u t e Cd and B i amalgams a r e shown. The s h i f t s o f t h e i s o c h o r e s f o r Bi amalgams a r e c o n s i d e r a b l y l a r g e compared w i t h t h o s e f o r Cd amalgams. The p a r a m e t e r s 6 and Po i n t h e i s o c h o r e e q u a t i o n a r e p l o t t e d i n F i g s .5
( a ) and ( b ) f o r 0 . 3 a t . $ Cd and 0 . 2 a t . $ B i amal-gams. The volume dependences o f
yv
and P 0 f o r 0 . 2 a t . $ Bi amalgam remain l a r g e a t 9 . 0 g/cm3. The v a l u e s o fP
f o r 0 . 3 a t . % T Cd and 0 . 2 a t . $ B i amalgams a r e p l o t t e d i n F i g . 6. The a d d i t i o n o f B i r e d u c e sPT.
These e v i d e n c e s s u g g e s t t h a t a s l i g h t ad- d i t i o n o f Bi s t a b i l i z e s t h e m e t a l l i c s t a t e even a t low d e n s i t i e s . It i s n o t i c e d t h a t t h e a d d i t i o n o f Cd d o e s n o t a f f e c tf,,
,
Po andPT
SO s i g n i f i c a n t l y a s t h a t o f Bi. -- pure Hg ---P Hg-02%B1-
Hg-0.5% Cd Hg-0.3'1. Cd tor Hg F i g .9 .
I s o c h o r e s o f 9 . 6 and 9.0 g/cm3 f o r Cd and B i amalgams. ACKNOWLEDGEMENTS-- A p a r t o f t h i s work was c a r r i e d o u t u n d e r t h e c o l l a b o r a t i n g r e s e a r c h program a t I n s t i t u t e o f Plasma P h y s i c s , Nagoya U n i v e r s i t y . The A u t h e r s wish t o e x p r e s s t h e i r t h a n k s t o P r o f e s s o r s K . Suzuki and M. I n u t a k e f o r h e l p f u l d i s - c u s s i o n s . REFERENCES1 . Neale,F.E., Cusack,N.E. and Johnson,
R.D., J . Phys. F. $3, 1 1 3 ( 1 9 7 9 ) . 2 . Yao,M. and Endo,H., i n p r e p a r a t i o n .
