Abstract
On the basis of similarity of thermal expansion of liquid metals and data on the temperature dependence of density of zirconium, hafnium, and tungsten, estimates of the critical parameters of these metals are obtained.
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Young, D.A. and Alder, B.J., Critical Point of Metals from van der Waals Model, Phys. Rev. A: At., Mol., Opt. Phys., 1971, vol. 3, no. 1, p. 364.
Tkachenko, S.I., Khishchenko, K.V., Vorob’ev, V.S., Levashov, P.R., Lomonosov, I.V., and Fortov, V.E., Metastable States of Liquid Metal under Conditions of Electric Explosion, Teplofiz. Vys. Temp., 2001, vol. 39, no. 5, p. 728 [High Temp. (Engl. Transl.), 2001, vol. 39, no. 5, p. 674].
Fortov, V.E., Dremin, A.N., and Leont’ev, A.A., Evaluation of the Parameters of the Critical Point, Teplofiz. Vys. Temp., 1975, vol. 13, no. 5, p. 1072 [High Temp. (Engl. Transl.), 1975, vol. 13, no. 5, p. 984].
Filippov, L.P., Metody rascheta i prognozirovaniya svoistv veshchestv (Methods for Calculating and Predicting the Properties of Substances), Moscow: Moscow State University, 1988.
Martynyuk, M.M., Analysis of the Temperature Dependence of the Density of Liquid Metals on the Basis of the Law of Corresponding States, Zh. Fiz. Khim., 1984, vol. 58, no. 8, p. 1896.
Apfelbaum, E.M. and Vorob’ev, V.S., Correspondence between the Critical and Zeno-Line Parameters for Classical and Quantum Liquids, J. Phys. Chem. B, 2009, vol. 113, p. 3521.
Likal’ter, A.A., Critical Parameters of Metals, Teplofiz. Vys. Temp., 1985, vol. 23, no. 3, p. 465 [High Temp. (Engl. Transl.), 1985, vol. 23, no. 3, p 371].
Korobenko, V.N. and Savvatimskii, A.I., Liquid Zirconium Properties up to 4100 K (Density, Enthalpy, Heat Capacity, Emissivity, and Resistivity), Zh. Fiz. Khim., 2003, vol. 77, no. 10, p. 1742 [Russ. J. Phys. Chem. A (Engl. Transl.), 2003, vol. 77, no. 10, p. 1564].
Korobenko, V.N. and Savvatimskii, A.I., The Density of Liquid Hafnium from the Melting Point to the Boiling Point, Teplofiz. Vys. Temp., 2007, vol. 45, no. 2, p. 187 [High Temp. (Engl. Transl.), 2007, vol. 45, no. 2, p.159 ].
Koval’, S.V., Kuskova, N.I., and Tkachenko, S.I., Investigation of the Mechanism of Electric Explosion of Conductors and of the Thermal Characteristics of Liquid Metals, Teplofiz. Vys. Temp., 1997, vol. 35, no. 6, p. 876 [High Temp. (Engl. Transl.), 1997, vol. 35, no. 6, p. 863].
Hornung, K., Adiabatic and Isothermal Compressibility in the Liquid State, in Handbook of Thermodynamic and Transport Properties of Alkali Metals (IUPAC: Chemical Data Series No. 30), Ohse, R.W., Ed., Oxford: Blackwell Scientific, 1985, p. 487.
Drotning, W.D., Thermal Expansion of Iron, Cobalt, Nickel, and Copper at Temperatures up to 600 K above Melting, High Temp.-High Pressures, 1981, vol. 13, no. 4, p. 441.
Vukalovich, M.P., Ivanov, A.I., Fokin, L.R., and Yakovlev, A.T., Teplofizicheskie svoistva rtuti (Thermal and Physical Properties of Mercury), Moscow: Izd. Standartov, 1971.
Drotning, W.D., Thermal Expansion of Molten Tin, Lead, and Aluminum to 1300 K, High Temp. Sci., 1979, vol. 11, no. 4, p. 265.
Steinberg, D.J., Simple Relationship between the Temperature Dependence of the Density of Liquid Metals and Their Boiling Temperatures, Metall. Trans., 1974, vol. 5, p. 1341.
Magalinskii, V.B., Sidorenko, S.N., and Filippov, L.P., On the Characteristic Lines on the Temperature-Density Plane, in Statisticheskaya i kvantovaya fizika i ee prilozheniya (Statistical and Quantum Physics and Its Applications), Moscow: P. Lumumba Peoples’ Friendship University, 1986, p. 11.
Apfelbaum, E.M., Vorob’ev, V.S., and Martynov, G.A., Triangle of Liquid-Gas States, J. Phys. Chem. B, 2006, vol. 110, no. 16, p. 8474.
CRC Handbook of Chemistry and Physics, Linde, D.R. and Frederikse, H.P.R., Eds., Boca Raton: CRC Press, 1993.
Paradis, P.-F. and Rhim, W.-K., Thermophysical Properties of Zirconium at High Temperatures, J. Mater. Res., 1999, vol. 14, no. 9, p. 3713.
Paradis, P.-F., Ishikawa, T., and Yoda, S., Non-Contact Measurements of the Thermophysical Properties of Hafnium-3 Mass% Zirconium at High Temperature, Int. J. Thermophys., 2003, vol. 24, no. 1, p. 239.
Paradis, P.-F., Ishikawa, T., Fujii, R., and Yoda, S., Physical Properties of Liquid and Undercooled Tungsten by Levitation Techniques, Appl. Phys. Lett., 2005, vol. 86, no. 4, p. 041 901.
Ohse, R.W., Babelot, R.-F., Magill, J., and Tetenbaum, M., An Assessment of the Melting, Boiling, and Critical Point Data of the Alkali Metals, in Handbook of Thermodynamic and Transport Properties of Alkali Metals (IUPAC: Chemical Data Series No. 30) Ohse, R.W., Ed., Oxford: Blackwell Scientific, 1985, p. 329.
Jüngst, S., Knuth, B., and Hensel, F., Observation of Singular Diameters in the Coexistence Curves of Metals, Phys. Rev. Lett., 1985, vol. 55, no. 20, p. 2160.
Hensel, F., Hohl, G.F., Schaumlöffel, D., Pilgrim, W.C., and Franck, E.U., Empirical Regularities in the Behaviour of the Critical Constants of Fluid Alkali Metals, Z. Phys. Chem., 2000, vol. 214, no. 6, p. 823.
Ohse, R.W. and Tippelskirch, H., The Critical Constants of the Elements and of Some Refractory Materials with High Critical Temperatures, High Temp.-High Pressures, 1977, vol. 9, no. 4, p. 367.
Fucke, W. and Seydel, U., Improved Experimental Determination of Critical-Point Data for Tungsten, High Temp.-High Pressures, 1980, vol. 12, no. 4, p. 419.
Filippov, L.P., Svoistva zhidkikh metallov (Properties of Liquid Metals), Moscow: Moscow State University, 1988.
Hess, H., Kloss, A., Rakhel, A., and Shneidenbach, H., Determination of Thermophysical Properties of Fluid Metals by Wire-Explosion Experiments, Int. J. Thermophys., 1999, vol. 20, no. 4, p. 1279.
Rakhel, A.D., Kloss, A., and Hess, H., On the Critical Point of Tungsten, Int. J. Thermophys., 2002, vol. 23, no. 5, p. 1369.
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Original Russian Text © S.V. Onufriev, 2011, published in Teplofizika Vysokikh Temperatur, 2011, Vol. 49, No. 2, pp. 213–220.
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Onufriev, S.V. Estimation of zirconium, hafnium, and tungsten critical parameters. High Temp 49, 205–212 (2011). https://doi.org/10.1134/S0018151X1102012X
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DOI: https://doi.org/10.1134/S0018151X1102012X