OPTICAL REFLECTIVITY MEASUREMENTS ON
FLUID MERCURY
W. Hefner, R. Schmutzler, F. Hensel
To cite this version:
W. Hefner, R. Schmutzler, F. Hensel. OPTICAL REFLECTIVITY MEASUREMENTS
ON FLUID MERCURY. Journal de Physique Colloques, 1980, 41 (C8), pp.C8-62-C8-65.
<10.1051/jphyscol:1980817>. <jpa-00220271>
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Submitted on 1 Jan 1980
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CoZZoque C8, suppZ6ment au n o 8, Tome 4 2 , aotit 1980, page Cg-62
JOURNAL DE PHYSIQUE
OPTICAL REFLECTIVITY MEASUREMENTS ON F L U I D MERCURY
W. Hefner, R.W. Schmutzler and F. Hensel
Fachhereich PhysikaZische Chemie, PhiZipps-Universitat, Hans-Meemein-StraBe, 0-3550 Marburg, R.F.A.
I.
INTRODUCTION
l i s h e d upper and lower s u r f a c e s which l e d
Mercury vapour above t h e c r i t i c a l tempera-
o u t of t h e h o t p a r t of t h e c e l l i n t o a c o l d
t u r e i s one of t h e c l a s s i c examples i n
h i g h p r e s s u r e c l o s u r e . For measurements of
which a g r a d u a l i n s u l a t o r t o metal t r a n s i -
t h e r e f l e c t i v i t y of mercury vapour a t tempe-
t i o n o c c u r s a s t h e atoms approach eachother
r a t u r e s s m a l l e r t h a n 1 3 0 0 ~t h~e s a p p h i r e win-
w i t h i n c r e a s i n g d e n s i t y ( 1 ) , ( 2 ) . For mass
dow was r e p l a c e d by a q u a r t z window of h i g h
densities
p >
9 g/cm3 both o p t i c a l and
u l t r a v i o l e t t r a n s p a r e n c y . The mercury sam-
electrical properties are typical for a
p l e s were h e a t e d by a c y l i n d r i c a l f u r n a c e
f l u i d m e t a l . For 9 g/cm3 >
c o n c e n t r i c w i t h t h e c e l l s . The t e m p e r a t u r e
p >
5 the trans-
p o r t d a t a i n d i c a t e a f l u i d semiconductor,
was measured by two thermocouples i n con-
although the o p t i c a l absorption d a t a exhi-
t a c t w i t h t h e o u t s i d e molybdenum w a l l c l o s e
b i t an o p t i c a l band gap f o r
only
(31, ( 4 )
P
3
< 5 g/cm
-
t o t h e Hg-sample.
The t e m p e r a t u r e of t h e
sample was c a l i b r a t e d by employing t h e most
The purpose of t h e p r e s e n t b r i e f paper i s
a c c u r a t e a v a i l a b l e vapour p r e s s u r e d a t a (6).
t o p r e s e n t new measurements of t h e r e f l e c -
A t a g i v e n p r e s s u r e , t h e v a p o r i z a t i o n tempe-
t i v i t y o f l i q u i d mercury from 0.5 t o 4 and
r a t u r e c o u l d e a s i l y be found a s an a b r u p t
p a r t l y t o 5.5 eV i n t h e d e n s i t y range from
change i n t h e r e f l e c t i v i t y when t h e Hg-sam-
0 t o 13 g/cm3.
p l e i s v a p o u r i z e d . The c e l l , t o g e t h e r w i t h
The measurements a r e i n t e n -
ded t o o v e r l a p and supplement t h o s e by Ike-
t h e s u r r o u n d i n g f u r n a c e was mounted i n s i d e
z i e t a l . ( 4 ) who s t u d i e s t h e r e f l e c t i v i t y
a high pressure s t a i n l e s s s t e e l autoclave.
from 0 . 5 t o 3 eV a t d e n s i t i e s between 4
The o p t i c a l system employed t o measure t h e
and 13.6 g/cm 3
.
r e f l e c t i v i t y was t h e r e c o r d i n g s p e c t r o p h o tometer Cary 17H w i t h a u s e f u l photoenergy
II
EXPERIMENTAL
r a n g e from 0.5 t o 6 eV. The d a t a were taken
The r e f l e c t i v i t y d a t a d e s c r i b e d i n t h i s pa-
f o r t h e i n c i d e n t l i g h t n e a r l y normal t o t h e
p e r were o b t a i n e d by u s e of an experimental
s u r f a c e between mercury and t h e window.
arrangement t h e d e t a i l s of which a r e d e s cribed i n ref.(5).
B r i e f l y , t h e f l u i d mer-
I11
RESULTS AND DISCUSSION
c u r y samples were c o n t a i n e d i n c y l i n d r i c a l
I n f i g . 1 we show some s e l e c t e d r e s u l t s o f
molybdenum c e l l s c l o s e d a t one end by a 12
t h e r e f l e c t i v i t y of l i q u i d mercury i n t h e
cm l o n g s y n t h e t i c s a p p h i r e window w i t h po-
energy range between 0 . 5 eV and 4 . 0 eV mea-
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980817
'
0
°
0
Because of t h e l i m i t a t i o n s of t h e r e f l e c t i v i t y measurements t o a r e l a t i v e l y s m a l l frequency range due t o t h e c u t o f f of t h e s a p -
x-
f
-
12.80 ( 1 )
phire-window t h e u s u a l Kramers-Kronig gna-
11.80 ( 2 )
11 .oo ( 3 )
10.10 ( 4 )
l y s i s i s n o t a p p l i c a b l e t o a n a l y z e t h e data.
I n p l a c e o f t h a t we used a c l a s s i c a l o s c i l -
-
5
K
0.0
1.O
2.0
Energy [eVl
Fig.1
9.m (5)
l a t o r f i t method (9) t o e x t r a c t t h e r e a l
8.00 ( 6 )
part
3.0
and t h e imaginary p a r t
E~
of t h e
d i e l e c t r i c c o n s t a n t . T h i s method i s based
L.0
5.0
on t h e u s e of a simple a n a l y t i c a l form f o r
Reflectivity as a function of photon energy
t h e d i e l e c t r i c f u n c t i o n which c o n s i s t s of a
a t different densities.
sum of c o n t r i b u t i o n s from damped o s c i l l a t o r s
and a D r u d e - l i k e p a r t . The f i t t i n g procedu-
sured over t h e s u b c r i t i c a l temperature
r e i n v o l v e s an o p t i m i z a t i o n p r o c e s s where
range 4 0 0 ' ~ t o 1 4 7 0 ~ ~The
. corresponding
3
d e n s i t i e s between 12.8 g/cm3 and 8 g/cm (7)
t h e d i f f e r e n t p a r a m e t e r s a r e chosen, t h e
a t p r e s s u r e s s l i g h t l y h i g h e r t h a n t h e vapour
w i t h t h e e x p e r i m e n t a l r e s u l t s . T h i s proce-
p r e s s u r e s a r e l a b e l l e d a t each c u r v e i n fig.
d u r e i s r e p e a t e d t o y i e l d good agreement
1 . A d i r e c i t comparison of t h e p r e s e n t r e -
between t h e e x p e r i m e n t a l and t h e c a l c u l a t e d
s u l t s with the recent data of Ikezi e t a l .
r e s u l t s . The d i f f e r e n c e s between t h e c a l c u -
(4) i n t h e energy range between 0.5 eV and
l a t e d and measured R-values were minimized
3 eV g i v e s e x c e l l e n t agreement w i t h i n t h e
using a standard curve-fitting-procedure
a c c u r a c y of t h e measurements. The shape of
( 1 0 ) . The good agreement between t h e o a l c u -
the r e f l e c t i v i t y curves (especially, t h e
l a t e d and t h e measured r e f l e c t i v i t y d a t a
enhanced R i n t h e low energy range) f o r den-
o b t a i n e d a t t h e end of t h e f i t t i n g procedu-
s i t i e s of 12.8 g/cm3 and 11 . 0 g/cm3 i s v e r y
r e i s demonstrated by f i g . 1 .
s i m i l a r t o t h a t observed f o r normal m e t a l l i c
F i g s . 2 and 3 show t h e r e a l p a r t of t h e d i -
l i q u i d mercury a t room t e m p e r a t u r e ( 8 ) . A t
e l e c t r i c constant
s m a l l e r d e n s i t i e s R d e c r e a s e s and a t t h e
t i v i t y a(w)
same time t h e low energy enhancement i s r e -
a t d i f f e r e n t d e n s i t i e s a s a f u n c t i o n of t h e
duced. F i n a l l y , f o r d e n s i t i e s s m a l l e r t h a n
photon energy. The d . c . c o n d u c t i v i t y a ( 0 ) (7)
9 g/cm5 t h e energy-dependence of R resembles
i s q u i t e c l o s e t o t h e v a l u e o b t a i n e d by t h e
t h a t of l i q u i d semiconductors, i . e . R f a l l s
e x t r a p o l a t i o n of u(w). The behaviour o f
o f f i f t h e photon energy approaches z e r o .
b o t h q u a n t i t i e s , u(w) and e l (a) , p r o v i d e a
This is consistent with the conductivity
new i l l u s t r a t i o n of t h e g r a d u a l d i s a p p e a -
and thermopower which assume v a l u e s t y p i c a l
r a n c e of t h e m e t a l l i c p r o p e r t i e s i n expan-
o f l i q u i d semiconductors i n t h i s d e n s i t y
ded Hg which i s c o n s i s t e n t w i t h t h e p r e -
range.
v i o u s r e s u l t s of t h e d.c . c o n d u c t i v i t y (7.)
r e f l e c t i v i t y i s c a l c u l a t e d and compared
=
w
E,
(LO)and t h e a . c .conduc-
~ ~ ( w ) / 4ofa l i q u i d mercury
,
JOURNAL DE PHYSIQUE
C8-64
ponds to the metallic strong scattering
range ( 7 ) , a change in the behaviour of
is exhibited.
E,
at the lowest energies
reached in the present experiment changes
its sign from negative at the high densities to positive at the low densities (fig.
2).
At the same time in the same low energy
range a qualitative change of the slope of
the o(w)-curve
is observed. Finally, for
densities smaller than 9 g/cm3 the shapes
of the
1.0
20
Energy CeVI
3.0
1.0
I
E,
(w) - and o(w)-curves
resemble those
of liquid semiconductors exhibiting that
5.0
the dielectric constant is essentially determined by contributions which originate
Fig.2 Calculated real part of the dielectric confrom interband transitions. Pbre physical
stant as a function of the photon energy.
insight about the transformation to a nonThe labelled n~rmbersrefer to the densities
given in fig.I
metallic state in expanded mercury can be
.
obtained from an analysis of the density
dependence of E, at densities lower than 8
g/cm 3 . It is an experimental fact that in
the limit of very low densities (e.g.p smaller than about 3 g/cm 3) even at high tempe~ d.c.conducratures of more than 1 5 0 0 ~the
tivity a (0) assumes very low values (1 3)
.
Thus according to the Kramers-Kronig dis0.0
1.0
20
Energy lev1
3.0
persion relations it is obvious that
LO
5.0
E~
at
6.0
Fig.3 Calculated conductivity as a function of
low frequencies is always positive. Furthermore, it has been demonstrated by measure-
photon energy. The labelled numbers refer
ments of the density-dependence the optical
to the densities given in fig.1.
absorption edge (3), (4) that an energy gap
exists in expanded mercury for densities
thermopower (1 1) and the Hall-effect (1 2).
smaller than 5 g/cm3 which increases with
The decrease of the Drude-like low frequen-
decreasing density. Consequently in the
cy conductivity observed for liquid Hg at
3
room temperature (p = 13.6 g/cn ) (8),(4) is
low density range
clearly evident in fig.3. In the density
ty.
range between 1 1 and 9 g/cm5, for which the
Fig.4 shows c, at a photon energy of 0.6
conductivity values show that it corres-
eV of fluid mercury as a function of the
E,
at low frequencies is
expected to decrease with decreasing densi-
analysis of reflectivity, absorption and d.
c.conductivity data it can be shown(l4) that
the a.c.conductivity has a strong maximum
.
at low frequencies ( w < 0.5 eV) We attempted
successfully to explain the positive rise
in cl (5) and the maximum in the experimentally observed frequency dependence of o(w)
(14) with the increasing importance of clusters in the dense, weakly ionized mercury
plasma. The results of this attempt will
be published elsewhere.
REFERENCES
1 Hensel,F.,1976,Liquid Metals,ed.R.Evans and D.A.
Greenwood (London: Institute of Physics) p.372
2 Cusack,N.E. ,1978,lletal Non-bletal Transitions in
Fig.4 Density dependence of
Disordered Systems,ed.L.R.Friedman and D.P.Tun-
at a constant
stall. Scottish Universities Summer School in
energy in the low density range
Physics, Edinburgh
density at the constant supercritical tem-
3 Uchtmann,H.and Hensel,F.,1975,Phys.Lett.53A,239
-
. comparison we show
perature of 1 5 3 0 ~ ~For
4 Ikezi,H.,Schwarzenegger,K.,Simons,A.L.,Passner,
also in fig.4 a graph (lower line) of the
calculated with the Clau-
behaviour of
A.L. ,McCall,S.L., 1978,Phys.Rev.B
18,2494
5 Hefner,lbl.,1980,Thesis University of Marburg
sius-E4osotti relation for w = 0 using the
6 Schmutzler,R.W., private communication
polarizability of the isolated Hg-atom. A
7 Schonherr,G.,Schmutzler,R.W.and Hensel,F.,1979,
Phi1.Wag.B 40, 411
striking upward deviation from ClausiusMosotti behaviour is observed in the densi3
ty range between 2.2 g/cm3 and 2.8 g/cm
8 Choyke,W.J.,Vosko,S.H.and
The results exhibit a rise in
9 Verleur,H.W.,1968, J.Opt.Soc.Am.
.
to nearly
10 at 2.8 g/cm3 before abruptly a smooth
decrease sets in with increasing density in
the direction to negative values characteristic of the behaviour for metals (e.g.
p =
10 g/cm3 in fig. 2).
decrease in
E,
The onset of the
is accompanied by the ap-
pearance of strongly density- and temperature dependent absorption-tails for photon
energies smaller than 1 eV. From a careful
OTKeefe,T.W.,1971,
Sol.State Corn. 9, 361
2, 1366
10 Nelder,J.A.and Mead,R.,1965,Comput.J. 7, 308
11 Schmutzler,R.W.and Hensel,F.,1972, Ber.Bunsen-
ges.phys.Chem.
76,
531
-
12 Even,U.and Jortner,J.,1972,Phys.Rev.Lett.28,31
13 Schmutzler,R.W.,Hensel,F.and,Franck,E.U.,1968,
Ber.Bunsenges.phys.Chem.
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Mag., in press.
72,1194
Overhof,H.,1980,Phil.