Heat Capacities of Vanadium and Tantalum in the Normal and Superconducting Phases

R. D. Worley; M. W. Zemansky; H. A. Boorse

doi:10.1103/PhysRev.99.447

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Heat Capacities of Vanadium and Tantalum in the Normal and Superconducting Phases

R. D. Worley^*, M. W. Zemansky^†, and H. A. Boorse^‡

Pupin Physics Laboratories, Columbia University, New York, New York

^*Now at Bell Telephone Laboratories, Inc., Whippany, New Jersey.
^†Permanent address: The City College of New York, New York, New York.
^‡Permanent address: Barnard College, Columbia University, New York. New York.

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Phys. Rev. 99, 447 – Published 15 July, 1955

DOI: https://doi.org/10.1103/PhysRev.99.447

Abstract

The heat capacities of two samples of vanadium and two of tantalum have been measured in the normal and superconducting phases in the temperature interval between 1.7° and 5°K. Below the transition temperature $T_{0}$ , the superconducting heat capacity of both metals could be represented accurately by the relation $C_{s} = A T + B T^{2}$ . In the normal phase the data obeyed the usual relation $C_{n} = γ T + (\frac{464}{θ^{3}}) T^{3}$ . From these data $H$ vs $T$ curves were calculated and values of $H_{0}$ , the threshold field at absolute zero, were obtained. For the better vanadium sample the values of the various constants were found to be $T_{0} = 4.89 °$ K, $A = - 1.97 \times 10^{- 3}$ cal/mole $\deg^{2}$ , $B = 1.69 \times 10^{- 3}$ cal/mole $\deg^{3}$ , $γ = 21.1 \times 10^{- 4}$ cal/mole $\deg^{2}$ , $Θ = 273 °$ K, and $H_{0} = 1340$ oersteds; for the better tantalum sample $T_{0} = 4.38 °$ K, $A = - 1.45 \times 10^{- 3}$ cal/mole $\deg^{2}$ , $B = 1.33 \times 10^{- 3}$ cal/mole $\deg^{3}$ , $γ = 13.0 \times 10^{- 4}$ cal/mole $\deg^{2}$ , $Θ = 231 °$ K, and $H_{0} = 860$ gauss. The measured heat capacities were compared with the predictions of the Koppe theory and the $α$ model.

References (38)

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[c1] Webber, Reynolds, and McGuire, Phys. Rev. 76, 293 (1949)

[c2] A. Wexler and W. S. Corak, Phys. Rev. 85, 85 (1952)

[c3] W. H. Keesom and M. Désirant, Physica 8, 273 (1941)

[c4] J. G. Daunt and K. Mendelssohn, Proc. Roy. Soc. (London) A160, 127 (1937)

[c5] K. Mendelssohn, Nature 148, 316 (1941)

[c6] M. Désirant, Report of the International Conference on Fundamental Particles and Low Temperatures (Physical Society, London, 1947), Vol. 2, p. 124

[c7] Brown, Zemansky, and Boorse, Phys. Rev. 92, 52 (1953)

[c8] Worley, Zemansky, and Boorse, Phys. Rev. 93, 45 (1954)

[c9] H. van Dijk and D. Shoenberg, Nature 164, 151 (1949)

[c10] R. Berman and C. A. Swenson, Phys. Rev. 95, 311 (1954)

[c11] J. Kistemaker, Physica 12, 272 (1946)

[c12] R. W. Gurney, Phys. Rev. 88, 465 (1952)

[c13] P. H. Keesom and N. Pearlman, Phys. Rev. 88, 398 (1952)

[c14] Adenstadt, Pequiquot, and Raymer, Trans. Am. Soc. Metals 44, 990 (1952)

[c15] J. Eisenstein, Revs. Modern Phys. 26, 277 (1954)

[c16] Worley, Zemansky, and Boorse, Phys. Rev. 93, 1567 (1953)

[c17] J. E. Goldman, remarks at Third International Conference on Low Temperature Physics and Chemistry (Rice Institute, Houston, 1953)

[c18] D. Shoenberg, Superconductivity (Cambridge University Press, London 1952), pp. 224-227

[c19] R. T. Webber, Phys. Rev. 72, 1241 (1947)

[c20] W. Meissner and H. Westerhoff, Z. Physik 87, 206 (1934)

[c21] L. C. Jackson, Proceedings of the International Conference on Low Temperature Physics (Oxford, 1951), p. 16

[c22] Silsbee, Scott, and Brickwedde, J. Research Natl. Bur. Standards 18, 295 (1937)

[c23] Ziegler, Brucksch, and Hickman, Phys. Rev. 62, 354 (1942)

[c24] T. S. Smith and J. G. Daunt, Phys. Rev. 88, 1172 (1952)

[c25] D. Shoenberg, Proc. Cambridge Phil. Soc. 36, 84 (1940)

[c26] W. I. Khotkevitch and V. R. Golik, J. Exptl. Theoret. Phys. (U.S.S.R.) 20, 427 (1950)

[c27] E. Maxwell and O. S. Lutes, Phys. Rev. 95, 333 (1954)

[c28] S. Beatty, J. Metals 4, Trans., 987 (1952)

[c29] B. G. Lasarew and A. A. Galkin, J. Phys. (U.S.S.R.) 8, 371 (1944)

[c30] C. Chou and D. White, Eighth Annual Calorimetry Conference, Chicago, Sept. 1953 (unpublished)

[c31] Corak, Goodman, Satterthwaite, and Wexler, Phys. Rev. 96, 1442 (1954)

[c32] C. J. Gorter and H. B. G. Casimir, Physik. Z. 35, 963 (1934)

[c33] Serin, Reynolds, and Lohman, Phys. Rev. 86, 162 (1952)

[c34] E. Maxwell, Phys. Rev. 86, 235 (1952)

[c35] P. M. Marcus and E. Maxwell, Phys. Rev. 91, 1035 (1953)

[c36] H. Koppe, Ann. Physik 1, 405 (1947)

[c37] W. Heisenberg, Z. Naturforsch. 2a, 185 (1947)

[c38] A. Sommerfeld and H. Bethe, Handbuch der Physik (Verlag Julius Springer, Berlin, 1933), Vol. 24, Part 2

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Heat Capacities of Vanadium and Tantalum in the Normal and Superconducting Phases

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