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THERMODYNAMIC AND ELECTRIC TRANSPORT PROPERTIES OF FLUID CESIUM AND RUBIDIUM
IN THE M-NM TRANSITION REGION
G. Franz, W. Freyland, F. Hensel
To cite this version:
G. Franz, W. Freyland, F. Hensel. THERMODYNAMIC AND ELECTRIC TRANSPORT PROP- ERTIES OF FLUID CESIUM AND RUBIDIUM IN THE M-NM TRANSITION REGION. Journal de Physique Colloques, 1980, 41 (C8), pp.C8-70-C8-73. �10.1051/jphyscol:1980819�. �jpa-00220293�
JOURNAL DE PHYSIQLE CoZZoque C8, suppZ6ment au n08, Tome 41, ao2t 1980, page (28-70
THERMODYNAMIC AND ELECTRIC T R A N S P O R T PROPERTIES O F F L U I D CESIUPl A N D RUBIDIUP: I N T H E M-NM TRANSITION REGION
G. Franz, W. Freyland and F. Hensel
Fachbereich PhysikaZische Chemie, PhiZipps-Univers-Ctat, Hans-Meerwein-Strasse, 0-3550 Marburg, R.F.A.
Abstract.- The paper reports new experimental results of the electrical conductivity, a, and the PVT-data of fluid cesium and rubidium which have been measured simultaneously at sub- and super- critical conditions. In the presentation of these data special emphasis is given to the observed corresponding state behaviour. In the M-NM transition region, i.e. in the density range
p < p < 2p - p being the critical density - a striking similarity is found in the conductivity
cfiange betwEen cgsium and rubidium. Next to the critical point, defined by the steep divergence of the thermodynamic derivatives obtained from the PVT-data, such as compressibility and thermal expansivity, the observed conductivity for both cesium and rubidium is 250 2 I50 ~-'cm-l.
I INTRODUCTION The main objective of the present brief pa- In recent years an increased theoretical per is to discuss partly these questions on and technological interest has stimulated the basis of new experimental results of extensive research on fluid metals at sub- conductivity and equation of state data ob- and supercritical conditions - for reviews tained for fluid cesium and rubidium at see e.g. (1),(2),(3) -. Especially the occu- sub- and supercritical pressures and tempe- rence of a M-NM transition in these one ratures.
component fluids has attracted attention.
Here the basic qaestions of theoretical in- 11 EXPERIMENTAL RESULTS AND DISCUSSION terest are: Where in the phase diagram does The experimental technique used forthe PIT- the transition occur? What is the dominant measurements is based on a dilatometric me- mechanism and what are the characteristic thod. The fluid metal sample at high tempe- changes of the electronic structure? As far ratures was contained in a thin walled cell as the behaviour of the thermophysical pro- machined from refractory metal which allows perties is concerned, one of the central a simultaneous measurement of the PVT-data questions is: Does a corresponding state and the electrical conductivity. For a de- behaviour exist for fluid metals, in gene- tailed description of the experimental set- ral, or is it restricted to various single up, the high temperature-high pressure ap- classes of metals depending on the mecha- paratus, and the measuring procedure, refe- nism which controls the EI-NII transition? rence is given to a previous publication (4).
This last aspect is a central point of many Concerning the experimental uncertainty of calculations and predictions of thermodyna- the results presented below, the following mic properties the knowledge of which is numbers are representative:
necessary for possible technological appli- 1. error estimate of the electrical conduc- cations of fluid metals at high temperatu- tivity, o: 53% for a > - 10 Q -Icm-'; '6% for res. o - > 1 0 ~ ~ - l c m - ~ ; 260% for a Q, 1 0 ~ ~ - ~ c m - ~ and
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980819
t e m p e r a t u r e s s l i g h t l y above t h e c r i t i c a l
t e m p e r a t u r e Tc.
c
2 . e r r o r e s t i m a t e o f t h e mass d e n s i t y , p : I oL
' 1 . 2 % f o r P / p c ', 3 ; f 3 % f o r ~ / p , % 2 and 2 4 . 5 % f o r p/pC Q 1 , p, = c r i t i c a l d e n s i t y . I t s h o u l d be p o i n t e d o u t t h a t t h e s e num- 9
b e r s r e f e r t o a n e s t i m a t e o f t h e maximum a b s o l u t e e r r o r . The r e p r o d u c i b i l i t y o f t h e r e -
s u l t s f o r d i f f e r e n t r u n s i s much b e t t e r and - -
?-.
t h e r e l a t i v e e r r o r ; which i s o f i n t e r e s t F l O 2 f o r t h e d e t e r m i n a t i o n o f t h e t e m p e r a t u r e - (2
-
and p r e s s u r e d e r i v a t i v e s , i s much s m a l l e r . b
x t h i s work a Ref. ( 5 ) I t i s a l s o n o t e w o r t h y , t h a t t h e a g r e e m e n t 0 R e f . ( 6 ) 1
between t h e p r e s e n t r e s u l t s and t h o s e of o t h e r a u t h o r s i s p a r t l y b e t t e r t h a n t h e above g i v e n u n c e r t a i n t i e s .
I n F i g . l a and l b t h e measured e l e c t r i c a l c o n d u c t i v i t y , a , o f f l u i d cesium and r u b i - dium, r e s p e c t i v e l y , i s p l o t t e d v e r s u s p r e s -
s u r e f o r d i f f e r e n t s u b - and s u p e r c r i t i c a l t e m p e r a t u r e s . From t h e s e r e s u l t s t o g e t h e r w i t h t h e s i m u l t a n e o u s l y measured PVT-data t h e t e m p e r a t u r e dependence o f o a t c o n s t a n t d e n s i t y and t h e d e n s i t y d e p e n d e n c e o f o a t c o n s t a n t t e m p e r a t u r e were o b t a i n e d s e p a r a - t e l y - f o r a d e t a i l e d d e s c r i p t i o n and d i s - c u s s i o n s e e ( 7 ) -. Because o f t h e l i m i t e d number o f p a g e s a v a i l a b l e f o r t h i s p a p e r , o n l y t h e main f e a t u r e s o f t h e s e p l o t s w i l l
I % t h i s work
o R e f . ( 4 )
c h a n g e s s i g n a t a b o u t 2 p c f o r b o t h c e s i u m
and r u b i d i u m , g o i n g from n e g a t i v e v a l u e s t o Fig.1 Experimental r e s u l t s of t h e e l e c t r i c a l con- c l e a r l y p o s i t i v e v a l u e s f o r a n e x p a n s i o n b e - ductivity, o, a s a function of pressure, p,
l o w - 2 p c . and temperature T (OC) f o r a) f l u i d c e s i m
2 . A t a b o u t 2 p c , t h e e l e c t r o n mean f r e e and b) f l u i d rubidium; f o r comparison some p a t h L , c a l c u l a t e d from t h e m e a s u r e d conduc- l i t e r a t u r e data a r e included i n t h i s p l o t . t i v i t y a - assuming m e t a l l i c n e a r l y f r e e
c8-72 JOURNAL DE PHYSIQUE
electron behaviour - gets equal to the mean interatomic distance n -'I3 - n being the number density -.
3. For densities smaller than 2pc the den- sity dependence of a is within experimental errors the same for cesium and rubidium.
This is demonstrated in Fig.2, where a is plotted versus reduced densities, p/pc, for a constant supercritical temperature T/Tc =
1.05. As for the high density part of this plot, it must be critically remarked, that the temperature coefficient of a for the corresponding densities was extrapolated to the high supercritical temperature. Thus, for p/pc > 2 this figure should only give the right qualitative trend in the diffe- rent behaviour between cesium and rubidium.
On the other hand it is apparent from this drawing, that a clear distinction exists in the electrical transport behaviour bet- ween fluid alkali metals and mercury in corresponding regions of the phase diagram.
4. Near the critical point, the observed conductivity of cesium and rubidium is
250'150 n-lcm-'. The location of this con- ductivity value was fixed by the correspon- ding divergence of the isothermal compres- sibility and expansion coefficient as de- termined from the PVT-data.
In Fig.3 the measured PVT-data are summa- rized in a plot of reduced densities versus reduced pressure for different reduced tem- peratures. The most striking observation is that over the whole liquid range a corres- ponding state law holds within experimental errors. This close similarity between ce- sium and rubidium in their respective ther- modynamic properties is also reflected in
the volume dependence of the corresponding derivatives, such as isothermal compressi- bility, thermal expansivity and pressure coefficient - see (7) -. From the steep
Fig.2 Electrical conductivity, G , versus reduced density, p/pc, for a constant supercritical temperature T/Tc = 1.05 (the data of fluid Hg have been taken from (8)).
d PIP, 1 2 3 I
____f)
Fig.3 Corresponding state plot of fluid cesiun and rubidium: reduced density, p/pC, pressure, p/pc , and temperature T/Tc , respectively.
singularities of these coefficients obser- ved near the critical point, the following critical data have been determined in this work :
ACKNOWLEDGEMENT
Thanks are due to the Fonds der chemischen Industrie for financial support of this work. One of us (G.F.) wishes to express his appreciation to the Deutsche Studien- stiftung for a doctor scholarship.
REFERENCES
1 N.E.Cusack, in "M-NM Transition in Dis- ordered Systems" ed. L.R.Friedman and D.P.Tunstal1, 1978 (NASI, St .Andrew~, Scotland) .
2 F.Hense1, in "Liquid Metals", ed.R.
Evans,D.A.Greenwood, 1977 (Inst.Phys.
Conf. Ser. 30, Bristol)
3 see the articles in "Seventh Symposium on Thermophysical Properties", ed. A.
Cezairliyan, 1977 (ASME, New York) 4 H.P.Pfeifer, W.Freyland, F.Hense1, Ber.
Bunsenges.Phys.Chem. E, 204 (1979) 5 H.Renkert, F.Hense1, E.U.Franck, Ber.
Bunsenges.Phys.Chem. 75, 507 (1971) 6 W.Freyland, H.P.Pfeifer, F.Hense1, in
"Amorphous and Liquid Semiconductors", ed. J. Stuke, W. Brenig, 1974 (Taylor and Francis, London)
7 G.Franz, Doctoral Thesis, Universitat Marburg, 1980 and to be published 8 G.Schonherr, R.W.Schmutzler, F.Hense1,
Phi1.blag.B 40, 411 (1979).
