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Measurement of the volume dependence of the absolute thermoelectric power of liquid mercury
Volume
27A. number
PHYSICS
9
MEASUREMENT
OF
THE
VOLUME
THERMOELECTRIC
OF
LIQUID
OF
THE
1968
ABSOLUTE
MERCURY
and F. HENSEL
Chemie und Elektrochemie Received
23 September
DEPENDENCE
POWER R. SCHMUTZLER
Institut ftir Physikalische
LETTERS
der Universitiit
Karlsruhe,
Germany
16 July 1968
Results of the measurement of the absolute thermoelectric power of liquid mercury to pressures of 1000 bars in the temperature range from 20 to 120°C are reported. The derivatives of the thermoelectric power @S/aT))p. (aS/aT)v, @S&J),. (9 Ins/a lnV)T are given.
Mercury has a large negative thermoelectric power with a pronounced temperature dependence at normal pressure. It is very different from the other liquid metals in this respect. As an explanation it has recently been suggested by Mott [l] that liquid mercury has a low density of states at the Fermi level and that for such metals Ziman’s theory [2] for liquid metals should break down. Consequently the discrepancy between the experimental and theoretical value for the thermoelectric power of mercury as calculated from Ziman’s theory must decrease with decreasing volume. In order to test this anticipation, the e.m.f. of a thermocouple of liquid mercury at elevated pressure and a copper wire was measured. The thermoelectric power of the Cu-Hg couple was obtained from the slope of the curve of the thermal e.m.f. plotted against temperature. From this value, the absolute thermoelectric power SH was obtained by subtracting the value for cofper at 1 bar SCu given by Cusack [3]. A correction for the pressure dependence of SCu, which could affect markedly the accuracy of the results [4], was not necessary because the Cu-wires in this experiment were always kept at 1 bar. In fig. 1 SHg obtained as described above is plotted against temperature at constant pressure and at constant densities. At normal pressure (3S/9T)# is an order of magnitude higher than for other liquid metals. Eq. (1) gives the values as a function of pressure within the range covered. (6S/U)#
=
With the present measurements it is possible to discuss the derivatives of S separately:
The isothermal compressibility pT and the isobaric thermal expansion o!p are known from the work of Postill et al. [5] and Davis [6 . To evaluate @S/6 T) F, a high accuracy in (3s/’ 3p)T is necessary. Therefore (W/ap), was directly measured by a thermocouple consisting of two samples of liquid mercury, kept at different
(1)
= (-20.8 x 10-3 + 0.97 x lo-6p i 2 x 10-4 J& (fi in bar) .
Fig. 1. Absolute thermoelectric power of mercury plotted against temperature. (The full lines are labelled with pressures in bars, the dotted lines with densities in g/cm3).
587
Volume
27A. number
9
PHYSICS
LETTERS
pressures. Thus the entire effect measured is the effect sought, and not only a small variation of a relatively large effect. Equation (3) gives (aS/ap)T as a function of temperature measured in this way: @S&)T
=
1968
should be possible to calculate values for S as a function of volume as was done by Animalu [2]. However, for this purpose it is necessary to know the volume dependence of the pseudopotential and of the interference function. These are not known with accuracy, but the thermoelectric power is very sensitive to both. Thus, we believe it not possible at this state to compare the experimental values with the calculated values of Animalu. This latter point and further technical details of the experiments will be discussed elsewhere.
(2)
= (1.81x10-4+0.97x10-6t) f ItY5 (t in OC) .
23 September
” deg bar
Table 1 presents the calculated (SS/SZJV at dif ferent densities Table 1
(dcm3)
13.50
13.44
13.38
- 10.5 f 1
10.0 * 1
9.6 * 1
References 103 x (ss/aT),
I-rv 1 7’ de _I
1. 2. 3. 4.
N.F.Mott, Advanc. in Phys. 16 (1967) 49. A.O.E.Animalu, Advanc. in Phys. 16 (1967) 605. N.E. Cusack, Rep. Prog. Phys. 26 (1963) 361. P. W.Bridgman, Proc. Am. Acad. Arts. Sci. 53 (1918) 269-386. R. Postill, R.G.Ross and N.E . Cusack, Phil. Mag., to be published. 6. L.A.Bavis, J. Chem. Phys. 46 (1967) 2650.
= we For (a ln S/a In 10.5 * 1. Using the basic formula of NFE-theory it *****
SELF-CONSISTENT
LIGHT
PROPAGATION
IN A RESONANT
MEDIUM
*
F. T. ARECCHI, V. DEGIORGIO C. I. S. E. Laboratories, Milano, Italy and C. G. SOMEDA Universit& Received
We study the undistorted motion of light pulses duced transparency (an-pulse).
di Bologna.
12 August 1968
in a resonant
The propagation of a light pulse in a resonant lossless medium in its ground state has been treated analytically only in particular cases [1,2] or by computer techniques [3]. On the other hand the propagation in an amplifying lossy medium has received a thorough analytical treatment [4,5]. * Work partially supported nal Research Council).
588
by the C . N. R. (Italian Natio-
Italy
medium and give the conditions
for self-in-
In this letter we give a general analytical treatment of the former problem, showing that, for a homogeneously broadened transition, the 2npulse is the only one which propagates with a constant shape at a constant envelope velocity 2) < c (c = phase velocity in the host medium). We also show under what condition the same result holds for an inhomogeneous line. The atoms-field interaction in a rotating-wave
27A. number
PHYSICS
9
MEASUREMENT
OF
THE
VOLUME
THERMOELECTRIC
OF
LIQUID
OF
THE
1968
ABSOLUTE
MERCURY
and F. HENSEL
Chemie und Elektrochemie Received
23 September
DEPENDENCE
POWER R. SCHMUTZLER
Institut ftir Physikalische
LETTERS
der Universitiit
Karlsruhe,
Germany
16 July 1968
Results of the measurement of the absolute thermoelectric power of liquid mercury to pressures of 1000 bars in the temperature range from 20 to 120°C are reported. The derivatives of the thermoelectric power @S/aT))p. (aS/aT)v, @S&J),. (9 Ins/a lnV)T are given.
Mercury has a large negative thermoelectric power with a pronounced temperature dependence at normal pressure. It is very different from the other liquid metals in this respect. As an explanation it has recently been suggested by Mott [l] that liquid mercury has a low density of states at the Fermi level and that for such metals Ziman’s theory [2] for liquid metals should break down. Consequently the discrepancy between the experimental and theoretical value for the thermoelectric power of mercury as calculated from Ziman’s theory must decrease with decreasing volume. In order to test this anticipation, the e.m.f. of a thermocouple of liquid mercury at elevated pressure and a copper wire was measured. The thermoelectric power of the Cu-Hg couple was obtained from the slope of the curve of the thermal e.m.f. plotted against temperature. From this value, the absolute thermoelectric power SH was obtained by subtracting the value for cofper at 1 bar SCu given by Cusack [3]. A correction for the pressure dependence of SCu, which could affect markedly the accuracy of the results [4], was not necessary because the Cu-wires in this experiment were always kept at 1 bar. In fig. 1 SHg obtained as described above is plotted against temperature at constant pressure and at constant densities. At normal pressure (3S/9T)# is an order of magnitude higher than for other liquid metals. Eq. (1) gives the values as a function of pressure within the range covered. (6S/U)#
=
With the present measurements it is possible to discuss the derivatives of S separately:
The isothermal compressibility pT and the isobaric thermal expansion o!p are known from the work of Postill et al. [5] and Davis [6 . To evaluate @S/6 T) F, a high accuracy in (3s/’ 3p)T is necessary. Therefore (W/ap), was directly measured by a thermocouple consisting of two samples of liquid mercury, kept at different
(1)
= (-20.8 x 10-3 + 0.97 x lo-6p i 2 x 10-4 J& (fi in bar) .
Fig. 1. Absolute thermoelectric power of mercury plotted against temperature. (The full lines are labelled with pressures in bars, the dotted lines with densities in g/cm3).
587
Volume
27A. number
9
PHYSICS
LETTERS
pressures. Thus the entire effect measured is the effect sought, and not only a small variation of a relatively large effect. Equation (3) gives (aS/ap)T as a function of temperature measured in this way: @S&)T
=
1968
should be possible to calculate values for S as a function of volume as was done by Animalu [2]. However, for this purpose it is necessary to know the volume dependence of the pseudopotential and of the interference function. These are not known with accuracy, but the thermoelectric power is very sensitive to both. Thus, we believe it not possible at this state to compare the experimental values with the calculated values of Animalu. This latter point and further technical details of the experiments will be discussed elsewhere.
(2)
= (1.81x10-4+0.97x10-6t) f ItY5 (t in OC) .
23 September
” deg bar
Table 1 presents the calculated (SS/SZJV at dif ferent densities Table 1
(dcm3)
13.50
13.44
13.38
- 10.5 f 1
10.0 * 1
9.6 * 1
References 103 x (ss/aT),
I-rv 1 7’ de _I
1. 2. 3. 4.
N.F.Mott, Advanc. in Phys. 16 (1967) 49. A.O.E.Animalu, Advanc. in Phys. 16 (1967) 605. N.E. Cusack, Rep. Prog. Phys. 26 (1963) 361. P. W.Bridgman, Proc. Am. Acad. Arts. Sci. 53 (1918) 269-386. R. Postill, R.G.Ross and N.E . Cusack, Phil. Mag., to be published. 6. L.A.Bavis, J. Chem. Phys. 46 (1967) 2650.
= we For (a ln S/a In 10.5 * 1. Using the basic formula of NFE-theory it *****
SELF-CONSISTENT
LIGHT
PROPAGATION
IN A RESONANT
MEDIUM
*
F. T. ARECCHI, V. DEGIORGIO C. I. S. E. Laboratories, Milano, Italy and C. G. SOMEDA Universit& Received
We study the undistorted motion of light pulses duced transparency (an-pulse).
di Bologna.
12 August 1968
in a resonant
The propagation of a light pulse in a resonant lossless medium in its ground state has been treated analytically only in particular cases [1,2] or by computer techniques [3]. On the other hand the propagation in an amplifying lossy medium has received a thorough analytical treatment [4,5]. * Work partially supported nal Research Council).
588
by the C . N. R. (Italian Natio-
Italy
medium and give the conditions
for self-in-
In this letter we give a general analytical treatment of the former problem, showing that, for a homogeneously broadened transition, the 2npulse is the only one which propagates with a constant shape at a constant envelope velocity 2) < c (c = phase velocity in the host medium). We also show under what condition the same result holds for an inhomogeneous line. The atoms-field interaction in a rotating-wave