Elastic Moduli of Tin at the Superconducting Transition

Joseph K. Landauer

doi:10.1103/PhysRev.96.296

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Elastic Moduli of Tin at the Superconducting Transition

Joseph K. Landauer^*,†

Physics Department, The University of Chicago, Chicago 37, Illinois

^*Now at Snow, Ice, and Permafrost Research Establishment, Wilmette, Illinois.
^†The work described in this paper, which has been presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy, was carried out in the Institute for the Study of Metals of the University of Chicago.

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Phys. Rev. 96, 296 – Published 15 October, 1954

DOI: https://doi.org/10.1103/PhysRev.96.296

Abstract

A composite oscillator technique was used to measure the elastic moduli of tin in the normal and superconducting states. The experiments were performed on single crystals at about 50 kc/sec. A difference in moduli was observed, indicating that the velocity of sound is less in the superconducting than in the normal state. At 3.7°K the relative change at the superconducting transition is about 4 parts in $10^{6}$ for the longitudinal modulus $S_{11}$ and about 6 parts in $10^{6}$ for the torsional modulus, $2 (S_{44} + S_{66})$ . These relative changes increase with decreasing temperature. At room temperature, the adiabatic modulus $S_{11}$ was found to be 1.55× $10^{- 12}$ ${cm}^{2}$ /dyne, and $2 (S_{44} + S_{66})$ was 9.4× $10^{- 12}$ ${cm}^{2}$ /dyne.

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[c1] W. J. de Haas and M. Kinoshita, Leiden Comm. No. 187b (1927)

[c2] McLennan, Allen, and Wilhelm, Trans. Roy. Soc. Can. III 25, 13 (1931)

[c3] H. Bommel and J. L. Olsen, Phys. Rev. 91, 1017 (1953)

[c4] D. Shoenberg, Superconductivity (Cambridge University Press, Cambridge, 1952), p. 76

[c5] S. Quimby, Phys. Rev. 25, 558 (1925)

[c6] W. G. Cady, Piezoelectricity (McGraw-Hill Book Company, Inc., New York, 1946), p. 491

[c7] A. W. Lawson, Phys. Rev. 60, 330 (1941)

[c8] D. Shoenberg and H. van Dijk, Nature 164, 151 (1949)

[c9] R. Wyckoff, Crystal Structures (Interscience Publishers, Inc., New York, 1948), Vol. 1, p. 13

[c10] W. A. Wooster, A Textbook on Crystal Physics (Cambridge University Press, Cambridge, 1938), p. 243

[c11] [10], Chapter III

[c12] W. Voigt, Lehrbuch Der Kristallphysik (B. G. Teubner, Leipzig, 1928)

[c13] P. W. Bridgman, Proc. Nat. Acad. Sci. U. S. 10, 411 (1924)

[c14] L. Balmuth, Phys. Rev. 45, 715 (1937), p. 716

[c15] [4], p. 73

[c16] F. Seitz, The Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1940), p. 152

[c17] F. London, Superfluids (John Wiley and Sons Inc., New York, 1950), Vol. 1, p. 24

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[c23] G. J. Sizoo and H. Kamerlingh Onnes, Leiden Comm. No. 180b (1925)

[c24] H. Frohlich, Phys. Rev. 79, 845 (1950)

[c25] J. Bardeen, Phys. Rev. 80, 567 (1950)

[c26] G. Wentzel, Phys. Rev. 83, 168 (1951)

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Elastic Moduli of Tin at the Superconducting Transition

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