SOUND VELOCITY AND THERMODYNAMIC PROPERTIES OF EXPANDED FLUID MERCURY

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SOUND VELOCITY AND THERMODYNAMIC PROPERTIES OF EXPANDED FLUID MERCURY

K. Suzuki, M. Inutake, S. Fujiwaka, M. Yao, H. Endo

To cite this version:

K. Suzuki, M. Inutake, S. Fujiwaka, M. Yao, H. Endo. SOUND VELOCITY AND THERMODY- NAMIC PROPERTIES OF EXPANDED FLUID MERCURY. Journal de Physique Colloques, 1980, 41 (C8), pp.C8-66-C8-69. �10.1051/jphyscol:1980818�. �jpa-00220282�

JOURNAL DE PHYSIQUE CoZZoque C8, suppZ6ment au n08, Tome 41, aoct 1980, page C8-66

SOUND VELOCITY AND THERMODYNAMIC PROPERTIES OF EXPANDED FLUID MERCURY

K . Suzuki, M. Inutake

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CoZZege o f General Education, ~ n i v . o f Tokyo, Tokyo 153, Japan

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INTRODUCTION

A number o f experiments a t high t e m p e r a t u r e s and under high p r e s s u r e s have demonstrated t h a t t h e m e t a l i c l i q u i d Hg can be transformed t o a semicon-

d u c t i n g o r i n s u l a t i n g s t a t e i n t h e low d e n s i t y region1). I t i s i n t e r e s t i n g t o s t u d y t h e r e l a t i o n - s h i p between t h i s e l e c t r i c (M-NM) t r a n s i t i o n and t h e thermodynamic l i q u i d - g a s t r a n s i t i o n .

I n t h e p r e s e n t r e p o r t , we p r e s e n t t h e r e s u l t s of t h e sound v e l o c i t y measurements i n Hg up t o 1600°C and 2000 b a r . The measurements have been made by means of an u l t r a s o n i c transmission/echo t e c h n i q u e which has been developed f o r such h i g h t e m p e r a t u r e / p r e s s u r e condition2.y3! Combining t h e sound v e l o c i t y r e s u l t s with a v a i l a b l e PpT d a t a 4 % ) , o t h e r thermodynamic q u a n t i t i e s have been c a l c u l a t e d .

EXPERIMENTAL

A h i g h p r e s s u r e v e s s e l and an u l t r a s o n i c c e l l a r e shown i n Fig. 1. The mercury sample i s con-

THERMOCOUPLE WATER COOLING JACKET

,

ui

t a i n e d i n t h e c e l l made o f a niobium t u b e c l o s e d a t both ends by s y n t h e t i c s a p p h i r e r o d s . The sample between t h e s a p p h i r e r o d s i s connected w i t h a mercury r e s e r v o i r through a s m a l l channel i n t h e i n n e r w a l l o f t h e niobium t u b e . The s i z e o f t h e sample i s 1-2.5 mm i n a x i a l l e n g t h and 10 mm i n diameter. The temperature o f t h e sample was con- t r o l l e d by a molybdenum-heater f u r n a c e around t h e c e l l , and measured by a Pt-30%Rh:Pt-6%Rh thermo- couple. The c e l l was s e t i n t h e high p r e s s u r e v e s s e l made of beryllium-copper, and p r e s s u r i z e d w i t h argon g a s . The p r e s s u r e was measured by a Heise p r e s s u r e gauge. E i t h e r temperature and p r e s - s u r e can be c o n t r o l l e d independently by feed-back systems o f d e t e c t i n g t h e s i g n a l s from t h e thermo- couple and t h e p r e s s u r e gauge, r e s p e c t i v e l y .

The sound v e l o c i t y was measured by an u l t r a - s o n i c p u l s e tra.nsmission/echo t e c h n i q u e 2 ) . A s e t of q u a r t z t r a n s d u c e r s o f 20 MHz was bonded t o t h e c o l d ends o f t h e s a p p h i r e b u f f e r - r o d s . The time r e q u i r e d f o r an u l t r a s o n i c s i g n a l t o t r a v e r s e from one t r a n s d u c e r t o t h e o t h e r was measured a t f i r s t . Then t h e time r e q u i r e d f o r an echo t o r e t u r n from t h e rod/sample i n t e r f a c e was measured f o r each b u f f e r - r o d . The d i f f e r e n c e between t h e transmis-

'NIOBIUM-SAPPHIRE CELL s i o n time and t h e average o f t h e above two echo

MERCURY RESERVOIR

t i m e s g i v e s t h e t i m e r e q u i r e d f o r t h e s i g n a l t o t r a v e r s e t h e sample. The sound v e l o c i t y can b e

HIGH PRESSURE Ar GAS

a I ' O r ' e a s i l y c a l c u l a t e d from t h e sample t h i c k n e s s and t h e

t r a v e r s e t i m e . I t should b e n o t e d h e r e t h a t o n l y Fig.1. High p r e s s u r e v e s s e l and u l t r a s o n i c c e l l

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980818

t h e d i f f e r e n c e between t h e t r a n s i t t i m e and t h e echo times i s concerned w i t h t h e d e t e r m i n a t i o n of sound v e l o c i t y . Therefore t h e e f f e c t of t h e change of t h e sound v e l o c i t y i n t h e b u f f e r - r o d s i s essen- t i a l l y e l i m i n a t e d .

ESULTS

I n Fig. 2 , t h e isotherms o f t h e sound v e l o c i t y a r e given a s a f u n c t i o n of p r e s s u r e . The experimen- t a l e r r o r s i n t h e sound v e l o c i t y and t h e tempera- t u r e a r e w i t h i n +2% and f15OC, r e s p e c t i v e l y . The sound v e l o c i t y o b t a i n e d by S p e t z l e r e t a 1 7 ) a r e a l s o p l o t t e d i n Fig. 2 f o r c?mparison. I t i s c l e a r l y s e e n t h a t where t h e t e m p e r a t u r e and p r e s s u r e domains o v e r l a p o u r r e s u l t s a r e i n good agreement w i t h t h o s e of S p e t z l e r ' s group. A comparison of t h e p r e s e n t r e s u l t s with our e a r l i e r d a t a 3 ) g i v e s s a t i s - f y i n g agreement. The p r e s e n t d a t a , however, shows a s l i g h t l y g e n t l e r s l o p e t h a n t h e e a r l i e r r e s u l t s i n d i c a t e d . When t h e p r e s s u r e i s decreased a t a c o n s t a n t t e m p e r a t u r e below t h e c r i t i c a l t e m p e r a t u r e (-1480°C), t h e sound v e l o c i t y changes d i s c o n t i n u o u s - l y from a l a r g e v a l u e i n t h e l i q u i d phase t o a s m a l l e r one i n t h e gaseous phase a c r o s s t h e l i q u i d - g a s c o e x i s t e n c e l i n e . No such d i s c o n t i n u o u s jump a p p e a r s above T I n t h e v i c i n i t y of t h e c r i t i c a l

c'

p o i n t , t h e u l t r a s o n i c s i g n a l was h i g h l y a t t e n u a t e d owing t o t h e l a r g e d e n s i t y f l u c t u a t i o n s .

DERIVED RESULTS AND DISCUSSION

The sound v e l o c i t y i s r e l a t e d t o o t h e r thermo- dynamic q u a n t i t i e s by t h e following e q u a t i o n s :

c 2 = - 1 _{( 1 )}

s MTa ²

C = ^P t ^{2 )}

P ( B T - B s )

Fig. 2. Sound v e l o c i t y isotherms i n Hg a s a f u n c t i o n of p r e s s u r e .

p r e s e n t experiment

" \

---- S p e t z l e r e t a l . ' '

= -BT = 2 ( 3 )

f3 s Cv

where Bs i s t h e a d i a b a t i c c o m p r e s s i b i l i t y , BT i s t h e i s o t h e r m a l c o m p r e s s i b i l i t y , cu, i s t h e i s o b a r i c

P

expansion c o e f f i c i e n t , C i s t h e s p e c i f i c h e a t a t P

c o n s t a n t p r e s s u r e , C i s t h e s p e c i f i c h e a t a t v

c o n s t a n t volume, and y i s t h e s p e c i f i c h e a t r a t i o . S i n c e t h e sound v e l o c i t y can b e o b t a i n e d wi'th a high degree of a c c u r a c y it may b e very h e l p q u l t o d e r i v e from it o t h e r thermodynamic q u a n t i t i e s which a r e n o t o r p a r t l y a v a i l a b l e .

The a d i a b a t i c c o m p r e s s i b i l i t y c a l c u l a t e d from t h e eq. 1 is p l o t t e d i n Fig. 3. The d e n s i t y v a l u e s n a v e been c a l c u l a t e d from i s o c h o r e e q u a t i o n s g i v e n

by ~ c h s n h e r r e t a l e 5 ). The u n c e r t a i n t i e s on t h e d e n s i t y and t h e sound v e l o c i t y g i v e a p o s s i b l e e r r o r which i s s m a l l e r t h a n 55%. The g r a p h y c a l s u r v a y of t h e s e d a t a i n Fig. 3 shows t h e s h a r p i n c r e a s e i n a d i a b a t i c c o m p r e s s i b i l i t y when t h e

JOURNAL DE PHYSIQUE

P( bar)

Fig. 3. Adiabatic compressibility isotherms in liquid Hg as a function of pressure.

Fig. 4. Thick curves denote reduced sound velocity(c/c ) and reduced

tP

.

adiabatic compressibility(6 /B

s s ⁾

tP.

versus re6uced density(p/ptp. )

.

Thin lines represent the same for

~ r 8 )

.

critical point is approached.

It is interesting to see the behaviour of the sound velocity and the compressibility in the M-NM transition region. A change in the nature of the interatomic force may cause a change in the com- pressibility and hence in the sound velocity. The sound velocity and the adiabatic compressibility along the saturated vapour-pressure curve are plotted in Fig. 4 as a function of density. The sound velocity, the adiabatic compressibility, and the density are normalized by the respective values at the triple point. The normalization is

performed for convinuence sake when the results are compared with those of liquid argon as an example of nonmetalic liquid. At densities larger than 9 g/cm3, the sound velocity decreases approxi- mately linearly with d~creasing density. B i

densities smaller than 9 g/cm3, it deviates from the straight line. At this density, the density dependence of the adiabatic compressibility changes slightly. It should be noted that the onset of the M-NM transition is the same density, 9-10 g/cm 3

.

The anomalies found in the density dependences of the sound velocity and the adiabatic compres- sibility may be associated with the M-NM transition.

Such anomalies cannot be seen in the nonmetalic liquid argon.

Fig. 5(a) and 5 ( b ) show the specific heat ratio, the specific heat at constant pressure and the specific heat at constant volume derived from the eqs. ( 3 ) by using the following values:

the density, BT and a _P data by Neale et al. 4) ,

those by Yao and ~ n d o ~ ) , and the sound velocity interporated from our experiment. Fig. 5(a) shows a sharp increase in the specific heat ratio when the critical temperature is approached. A similar increase is found in Fig 5(b) for the specific heat

a t c o n s t a n t p r e s s u r e . No evidence of t h e i n c r e a s e

Fig. 5 ( a ) . S p e c i f i c h e a t r a t i o a s a f u n c t i o n of t e m p e r a t u r e .

-+

Fig. 5 ( b ) . S p e c i f i c h e a t a t c o n s t a n t p r e s s u r e and s p e c i f i c h e a t a t con- s t a n t volume a s a f u n c t i o n o f tem- p e r a t u r e .

o f t h e s p e c i f i c h e a t a t c o n s t a n t volume can be found i n Fig. 5 ( b ) . This does not mean t h a t t h e s p e c i f i c h e a t a t c o n s t a n t volume does n o t d i v e r g e a t t h e c r i t i c a l p o i n t b u t t h e change of t h e s p e c i f i c h e a t a t c o n s t a n t volume i n t h e P and T r a n g e under i n v e s t i g a t i o n seems n o t t o b e a p p r e c i a b l y l a r g e r t h a n t h e u n c e r t a i n t y i n t h e p r e s e n t e v a l u a t i o n .

ACKNOWLEDGEMENTS

The a u t h o 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 s . M . Watabe, H. Hoshino and D r . K. T s u j i f o r many d i s c u s s i o n s . They g r a t e f u l l y acknowledge t h e

encouragement o f P r o f s . K. Takayama, H. Ikegami, and H. Isoda.

REFERENCES

1. F. Hensel: I n s t . Phys. Conf. S e r .

30

ow,, J I L .

2 . K. Suzuki, M. I n u t a k e and S. Fujiwaka: Proc.

6-th I n t . Conf. I n t e r n a l F r i c t i o n and U l t r a - Sonic A t t e n u a t i o n i n S o l i d s (Univ. Tokyo P r e s s , 1977) 319. , -

3. M . I n u t a k e , K. Suzuki and S. Fujiwaka: Proc.

14-th I n t . Conf. Phenomena i n I o n i z e d Gases (J. de Phys. C7, 1979) 685.

4. F. Neale, N . Cusack and R. Johnson: J. Phys. F Metal Phys. 9 (1979) 113.

5. G. Sch6nherr; R. Schmutzler and F. Hensel: P h i l .

Mag. (1979) 411.

6. M. Yao and H. Endo: J. Phys. Soc. Jpn ( t o b e p u b l i s h e d )

7. H. S p e t z l e r , M. Meyer and Tin Chan: High Tern.- Hieh P r e s s . 7 (1975) 481.

-

8. J. Thoen, ~ . - ~ a n ~ e e l and W. Van Dael: Physica 45 (1969) 339.

-

-$- due t o Neale e t a l . ⁴

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