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Sound velocity and thermodynamic properties of liquid rubidium and potassium at high temperatures and pressures
s.-1 El
,O”RNAL
OF
NON-CRYSTALLINESO
ELSEWER
Journal of Non-Crystalline
Solids 205-207
(1996)
459-461
Sound velocity and thermodynamic properties of liquid rubidium and potassium at high temperatures and pressures D.I. Arnold a’* , O.I. Girney bt E.V. Grodzinsky a, V.F. Kozhevnikov S.P. Naurzakov a ’ RRC ‘Kurchatov b Moscow Aviation
Institute’, Institute,
123182 Moscow, 125871 Moscow,
b,
Russia Russia
Abstract The sound velocity of liquid rubidium and potassium was measured by a pulsed phase-sensitive techniqueat temperatures up to 2000K and pressures up to 600bar for a frequencyof 10MHz. Tablesof smootheddataarepresented.Questionsof the theory of corresponding statesfor liquid alkali metalsarediscussed.
1. Introduction
2. Experimental results
Sound velocity (SV) is one of the important thermophysical characteristics of matter. In particular data on SV and the equation of state allow us to put together a complete picture of the bulk thermodynamic properties for liquids, as has been done for liquid cesium [1,2], for example. Refs. [3-51 give the results of systematic SV measurementsperformed for all alkali metals at temperaturesup to 1100 K at saturation. Chasanov et al. have measured SV in liquid saturatedsodium at temperaturesup to 1800 K [6]. Below we present the results of SV measurements for temperaturesup to 2000 K and pressures up to 600 bar for rubidium and potassium.
The measurementswere performed by a pulse phase-sensitive technique [7] at a frequency of 10 MHz. The technique measuresthe variation of the sound propagation time through a sample of known length (from 2 to 4 mm) with an accuracy of about 1 ns. The value of SV was calculated with respect to a reference point with a known SV. The sample was placed in a hermetically sealed molybdenum horizontal cell that consistedof a tubular cell body, two buffer rods and a spacer. The hermetic expander was manufactured from two soft stainlesssteal bellows [2,7]. The pressuredifference between the sample and the ambient argon gas did not exceed 0.1 bar. The cell with a coaxial graphite heater was placed in a high-pressure bomb with argon gas as the pressurizing medium. Two W-Re 5/20 thermocouples were mounted on the outside wall of the cell body. The error of the temperature measurements
* Corresponding 194 1994.
author.
Tel.:
0022-3093/96/$1.5.00 Copyright PII SOO22-3093(96)00260-S
+7-095
196 7294; fax:
0 1996 Elsevier
Science
+7-095
B.V. All rights reserved.
460
D.I. Arnold
Table 1 Sound velocity
et al. / Journal
of Non-Crystalline
Solids 205-207
(1996)
459-461
in rubidium
T (K) 500
750
1000
1250
1500
1750
2000
1184 1206 1228 1246
1087 1116 1145 1173
987 1026 1063 1099
858 930 976 1022
705 816 886 942
675 790 875
683 766
Saturation 200bar 400 bar 600 bar
400
Table 2 Sound velocity
in potassium
Fig. 2. Temperature sium.
500
750
1000
1250
1500
1750
1000
1200
1400
1600
1800
2000
1797 1821 1843 1866
1666 1701 1726 1752
1523 1578 1608 1638
1374 1446 1488 1526
1210 1259 1359 1411
1120 1220 1295
dependence
of sound velocity
in liquid
potas-
2000
1172
was up to 20 K at high temperature and the error of the pressure measurements was 1 bar. The reference point for both metals was 350 K and 2 bar. Taking into account the error of the data for the reference point, the error of the SV data obtained is 0.6%. The measurements were carried out mainly along isobars. The data on the saturated curve consist of points on an isobar at 2 bar and the points on the extrapolated sections of isobars at 10, 20, 30, 40 and 50 bar. We could not perform the measurements near the boiling point because of the rise of the pressure drop in the cell at boiling, which damages the cell. The maximum temperatures were attained at high pressures, and the maximum temperature near the
“1
BOO
TEMPERATURE,K
T (K) Saturation 200 bar 400 bar 600 bar
600
saturation curve was about 1700 K due to a considerable decrease in the sample sound impedance compared to the buffer rod impedance. The data for Rb and K obtained (Tables 1 and 2) agree well with the availabIe literature data [8,9]. The smoothed temperature dependencies of SV for Rb and K are presented in Fig. 1 and Fig. 2.
3. Discussion In the classical corresponding state theory [ 101 the critical points T, and pc are used as the reducing parameters. But for many applications the use of the triple point parameters is more suitable, since the triple point temperature and density are practically equal to the melting point T, and density pm. The relations T,/T, and p,/p,, for Cs, Rb, K and Na apply for most of the data [ll] within 3% for the temperatures and within 9% for the densities. On the basis of the presented SV data for Rb, K and cesium [I], it can be shown that the reduced values of SV for these metals coincide with an uncertainty within 57%. The tables of the thermodynamic properties of cesium in Refs. [1,2] can be used to calculate the respective properties of the other alkali metals, although for lithium the error can be somewhat greater.
--” -
400
600
800
1000
1200
1400
1600
1800
\
2000
2200
4. Conclusions
TEMPERATURE,K Fig. 1. Temperature ium.
dependence
of sound velocity
in liquid
rubid-
The SV in liquid rubidium and potassium have been measured at temperatures up to 2000 K and
D.I. Arnold
et al./ Journal
of Non-Crystalline
pressures up to 600 bar. It is shown that liquid alkali metals obey the principle of corresponding states when the melting point parameters are used as the reducing parameters. References 111 V.F. Kozhevnikov, Zh. Eksp. Teor. Fiz. 97 (1990) 541 (Sov. Phys. JETF 70 (1990) 298). [2] V.F. Kozhevnikov, S.P. Naurzakov and A.P. Senchenkov, J. Moscow Phys. Sot. I (1991) 171. [3] 1.1. Novikov, V.V. Roshchupkin, Y.S. Trelin, T.A. Tsyganova and A.G. Mozgovoi, in: Review on Thermophysical Properties of Substances, No. 6(32) (High Temperature Institute of USSR Academia of Science, Moscow, 1981) (in Russian).
Solids 20.5-207
(1996)
459-461
461
[4] 1.1. Novikov, Y.S. Trelin, T.A. Tsyganova, Teplofiz. Vys. Temp. 7 (1969) 1220 (in Russian). [5] 1.1. Novikov, Y.S. Trelin, T.A. Tsyganova, Teplofiz. Vys. Temp. 8 (1970) 450 (in Russian). 161 M.G. Chasanov, L. Leibowitz, D.F. Fisher and R.A. Blomquist, J. Appl. Phys. 43 (1972) 748. [7] D.I. Arnold, A.M. Gordeenko, P.N. Exnilov, V.F. Kozhevnikov and S.P. Naurzakov, Prib. Tekh. Exsp. 5(1985) 143 [Instrum. Exp. Tech. 28 (1985) 11731. [8] Y.S. Trelin, I.N. Vasil’ev, V.B. Proskurin and T.A. Tsyganova, Teplofiz. Vys. Temp. 4 (1966) 363 (in Russian). [9] 1.1. Novikov, Y.S. Trelin and T.A. Tsyganova, Teplofiz. Vys. Temp. 10 (1972) 1114 (in Russian). [lo] L.D. Landau and E.M. Lifshitz, Statistical Physics, Part I (Nauka, Moscow, 1976). [II] R.W. Ohse, ed., Handbook of Thermodynamic and Transport Properties of Alkali Metals (IUPAC, 1985).
,O”RNAL
OF
NON-CRYSTALLINESO
ELSEWER
Journal of Non-Crystalline
Solids 205-207
(1996)
459-461
Sound velocity and thermodynamic properties of liquid rubidium and potassium at high temperatures and pressures D.I. Arnold a’* , O.I. Girney bt E.V. Grodzinsky a, V.F. Kozhevnikov S.P. Naurzakov a ’ RRC ‘Kurchatov b Moscow Aviation
Institute’, Institute,
123182 Moscow, 125871 Moscow,
b,
Russia Russia
Abstract The sound velocity of liquid rubidium and potassium was measured by a pulsed phase-sensitive techniqueat temperatures up to 2000K and pressures up to 600bar for a frequencyof 10MHz. Tablesof smootheddataarepresented.Questionsof the theory of corresponding statesfor liquid alkali metalsarediscussed.
1. Introduction
2. Experimental results
Sound velocity (SV) is one of the important thermophysical characteristics of matter. In particular data on SV and the equation of state allow us to put together a complete picture of the bulk thermodynamic properties for liquids, as has been done for liquid cesium [1,2], for example. Refs. [3-51 give the results of systematic SV measurementsperformed for all alkali metals at temperaturesup to 1100 K at saturation. Chasanov et al. have measured SV in liquid saturatedsodium at temperaturesup to 1800 K [6]. Below we present the results of SV measurements for temperaturesup to 2000 K and pressures up to 600 bar for rubidium and potassium.
The measurementswere performed by a pulse phase-sensitive technique [7] at a frequency of 10 MHz. The technique measuresthe variation of the sound propagation time through a sample of known length (from 2 to 4 mm) with an accuracy of about 1 ns. The value of SV was calculated with respect to a reference point with a known SV. The sample was placed in a hermetically sealed molybdenum horizontal cell that consistedof a tubular cell body, two buffer rods and a spacer. The hermetic expander was manufactured from two soft stainlesssteal bellows [2,7]. The pressuredifference between the sample and the ambient argon gas did not exceed 0.1 bar. The cell with a coaxial graphite heater was placed in a high-pressure bomb with argon gas as the pressurizing medium. Two W-Re 5/20 thermocouples were mounted on the outside wall of the cell body. The error of the temperature measurements
* Corresponding 194 1994.
author.
Tel.:
0022-3093/96/$1.5.00 Copyright PII SOO22-3093(96)00260-S
+7-095
196 7294; fax:
0 1996 Elsevier
Science
+7-095
B.V. All rights reserved.
460
D.I. Arnold
Table 1 Sound velocity
et al. / Journal
of Non-Crystalline
Solids 205-207
(1996)
459-461
in rubidium
T (K) 500
750
1000
1250
1500
1750
2000
1184 1206 1228 1246
1087 1116 1145 1173
987 1026 1063 1099
858 930 976 1022
705 816 886 942
675 790 875
683 766
Saturation 200bar 400 bar 600 bar
400
Table 2 Sound velocity
in potassium
Fig. 2. Temperature sium.
500
750
1000
1250
1500
1750
1000
1200
1400
1600
1800
2000
1797 1821 1843 1866
1666 1701 1726 1752
1523 1578 1608 1638
1374 1446 1488 1526
1210 1259 1359 1411
1120 1220 1295
dependence
of sound velocity
in liquid
potas-
2000
1172
was up to 20 K at high temperature and the error of the pressure measurements was 1 bar. The reference point for both metals was 350 K and 2 bar. Taking into account the error of the data for the reference point, the error of the SV data obtained is 0.6%. The measurements were carried out mainly along isobars. The data on the saturated curve consist of points on an isobar at 2 bar and the points on the extrapolated sections of isobars at 10, 20, 30, 40 and 50 bar. We could not perform the measurements near the boiling point because of the rise of the pressure drop in the cell at boiling, which damages the cell. The maximum temperatures were attained at high pressures, and the maximum temperature near the
“1
BOO
TEMPERATURE,K
T (K) Saturation 200 bar 400 bar 600 bar
600
saturation curve was about 1700 K due to a considerable decrease in the sample sound impedance compared to the buffer rod impedance. The data for Rb and K obtained (Tables 1 and 2) agree well with the availabIe literature data [8,9]. The smoothed temperature dependencies of SV for Rb and K are presented in Fig. 1 and Fig. 2.
3. Discussion In the classical corresponding state theory [ 101 the critical points T, and pc are used as the reducing parameters. But for many applications the use of the triple point parameters is more suitable, since the triple point temperature and density are practically equal to the melting point T, and density pm. The relations T,/T, and p,/p,, for Cs, Rb, K and Na apply for most of the data [ll] within 3% for the temperatures and within 9% for the densities. On the basis of the presented SV data for Rb, K and cesium [I], it can be shown that the reduced values of SV for these metals coincide with an uncertainty within 57%. The tables of the thermodynamic properties of cesium in Refs. [1,2] can be used to calculate the respective properties of the other alkali metals, although for lithium the error can be somewhat greater.
--” -
400
600
800
1000
1200
1400
1600
1800
\
2000
2200
4. Conclusions
TEMPERATURE,K Fig. 1. Temperature ium.
dependence
of sound velocity
in liquid
rubid-
The SV in liquid rubidium and potassium have been measured at temperatures up to 2000 K and
D.I. Arnold
et al./ Journal
of Non-Crystalline
pressures up to 600 bar. It is shown that liquid alkali metals obey the principle of corresponding states when the melting point parameters are used as the reducing parameters. References 111 V.F. Kozhevnikov, Zh. Eksp. Teor. Fiz. 97 (1990) 541 (Sov. Phys. JETF 70 (1990) 298). [2] V.F. Kozhevnikov, S.P. Naurzakov and A.P. Senchenkov, J. Moscow Phys. Sot. I (1991) 171. [3] 1.1. Novikov, V.V. Roshchupkin, Y.S. Trelin, T.A. Tsyganova and A.G. Mozgovoi, in: Review on Thermophysical Properties of Substances, No. 6(32) (High Temperature Institute of USSR Academia of Science, Moscow, 1981) (in Russian).
Solids 20.5-207
(1996)
459-461
461
[4] 1.1. Novikov, Y.S. Trelin, T.A. Tsyganova, Teplofiz. Vys. Temp. 7 (1969) 1220 (in Russian). [5] 1.1. Novikov, Y.S. Trelin, T.A. Tsyganova, Teplofiz. Vys. Temp. 8 (1970) 450 (in Russian). 161 M.G. Chasanov, L. Leibowitz, D.F. Fisher and R.A. Blomquist, J. Appl. Phys. 43 (1972) 748. [7] D.I. Arnold, A.M. Gordeenko, P.N. Exnilov, V.F. Kozhevnikov and S.P. Naurzakov, Prib. Tekh. Exsp. 5(1985) 143 [Instrum. Exp. Tech. 28 (1985) 11731. [8] Y.S. Trelin, I.N. Vasil’ev, V.B. Proskurin and T.A. Tsyganova, Teplofiz. Vys. Temp. 4 (1966) 363 (in Russian). [9] 1.1. Novikov, Y.S. Trelin and T.A. Tsyganova, Teplofiz. Vys. Temp. 10 (1972) 1114 (in Russian). [lo] L.D. Landau and E.M. Lifshitz, Statistical Physics, Part I (Nauka, Moscow, 1976). [II] R.W. Ohse, ed., Handbook of Thermodynamic and Transport Properties of Alkali Metals (IUPAC, 1985).