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Grüneisen Functions for Some Type-I Superconductors

R. W. Munn*

  • Department of Theoretical Chemistry, University of Bristol, England

  • *Present address: Division of Pure Chemistry, National Research Council, Ottawa, Canada.

Phys. Rev. 178, 677 – Published 10 February, 1969

DOI: https://doi.org/10.1103/PhysRev.178.677

Abstract

The thermal expansion of some type-I superconductors (indium, lead, tantalum, and tin) is discussed thermodynamically in terms of Grüneisen functions, which describe the volume dependence of the entropy. The Grüneisen functions for the normal and superconducting states can be taken to differ only in their electronic components, γen and γes. Values of γen obtained from thermal-expansion measurements in the normal state are shown to be more reliable than values obtained from critical-field measurements on superconductors, because the magnetic data are not accurate enough in the limiting low-temperature region determining γen. The values of γes for the four metals all appear to be negative, unlike γen. Theoretical values of γes calculated using the BCS theory for weak coupling and the similarity principle are consistent with experiment for all the metals except lead. The disagreement for lead is probably due to its particularly strong electron-phonon coupling. According to the theory, the values of γes depend through dlnTcdlnV on the volume dependence of the electron-phonon interaction, as well as on properties of the normal state. The experimental evidence for significant changes in lattice properties is discussed; such a change appears to be established for indium but not for lead.

References (39)

  1. T. H. K. Barron and R. W. Munn, Phil. Mag. 15, 101 (1967)
  2. G. A. Alers and D. L. Waldorf, Phys. Rev. Letters 6, 677 (1961)
  3. D. Schoenberg, Superconductivity (Cambridge University Press, London, 1960), p. 74 A. B. Pippard, Classical Thermodynamics (Cambridge University Press, London, 1966), p. 135
  4. K. Andres, Phys. Rev. 168, 708 (1968)
  5. K. Andres, Phys. Kondensierten Materie 2, 294 (1964)
  6. J. G. Collins and G. K. White, Progress in Low Temperature Physics, IV (North-Holland Publishing Co., Amsterdam, 1964), p. 450
  7. C. H. Hinrichs and C. A. Swenson, Phys. Rev. 123, 1106 (1961)
  8. J. L. Olsen and H. Rohrer, Helv. Phys. Acta 33, 872 (1960)
  9. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957)
  10. J. E. Schirber and C. A. Swenson, Phys. Rev. 123, 1115 (1961)
  11. D. K. Finnemore and D. E. Mapother, Phys. Rev. 140, A510 (1965)
  12. I. V. Berman, N. B. Brandt, and N. I. Ginzburg, Zh. Eksperim. i Teor. Fiz. 53, 124 (1967) [English transl.: Soviet Phys.—JETP 26, 86 (1968)]
  13. J. G. Collins, J. A. Cowan, and G. K. White, Cryogenics 7, 219 (1967)
  14. G. K. White, Phil. Mag. 7, 271 (1962)
  15. K. Andres, Cryogenics 2, 93 (1961)
  16. G. K. White, Cryogenics 2, 292 (1962)
  17. G. K. White, Phys. Letters 8, 294 (1964)
  18. J. E. Schirber and C. A. Swenson, Phys. Rev. 127, 72 (1962)
  19. H. R. O'Neal and N. E. Phillips, Phys. Rev. 137, A748 (1965)
  20. B. S. Chandrasekhar and J. A. Rayne, Phys. Rev. 124, 1011 (1961)
  21. P. H. Keesom and B. J. C. van der Hoeven, Phys. Letters 3, 360 (1963) Phys. Rev. 137, A103 (1965)
  22. G. A. Alers and D. L. Waldorf, J. Appl. Phys. 33, 2283 (1962) [2]
  23. [3]
  24. D. L. Decker, D. E. Mapother, and R. W. Shaw, Phys. Rev. 112, 1888 (1958)
  25. M. Garfinkel and D. E. Mapother, Phys. Rev. 122, 459 (1961)
  26. R. Hultgren, R. L. Orr, P. D. Anderson, and K. Kelley, Selected Values of Thermodynamic Properties of Metals and Alloys (John Wiley & Sons, Inc., New York, 1963)
  27. F. H. Featherston and J. R. Neighbours, Phys. Rev. 130, 1324 (1963)
  28. C. A. Bryant and P. H. Keesom, Phys. Rev. Letters 4, 460 (1960) Phys. Rev. 123, 491 (1961)
  29. J. A. Rayne and B. S. Chandrasekhar, Phys. Rev. 120, 1658 (1960)
  30. D. P. Seraphim and P. M. Marcus, IBM J. Res. Develop. 6, 94 (1962)
  31. R. O. Davies, Phil. Mag. 43, 472 (1952)
  32. N. B. Brandt and N. I. Ginzburg, Usp. Fiz. Nauk 85, 485 (1965) [English transl.: Soviet Phys.—Usp. 8, 202 (1965)]
  33. B. Mühlschlegel, Z. Physik 155, 313 (1959)
  34. G. Rickayzen, Theory of Superconductivity (Interscience Publishers, Inc., New York, 1966)
  35. L. D. Jennings and C. A. Swenson, Phys. Rev. 112, 31 (1958)
  36. T. F. Smith and C. W. Chu, Phys. Rev. 159, 353 (1967)
  37. M. Blackman, Handbuch der Physik VII/1, 374 (1955)
  38. J. L. Olsen, K. Andres, and T. H. Geballe, Phys. Letters 26A, 239 (1968) W. L. McMillan, Phys. Rev. 167, 331 (1968) P. E. Seiden, 168, 403 (1968)
  39. N. E. Phillips, M. H. Lambert, and W. R. Gardner, Rev. Mod. Phys. 36, 131 (1964)

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