Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Effects of alloying in the dilute limit on the quantum states of electrons in magnesium

  • 18 Accesses

  • 7 Citations

Abstract

The electron quantum interference phenomenon was used to determine the effects of substitutional alloying upon the quantum-state lifetime τ and band gapsE g at the Fermi energy in single crystals of pure Mg. Vapor-grown alloys containing either Zn or Cd in concentrationsC∼0.3–15 ppm were studied. The magnetic field dependence of the interference oscillation amplitudes for these samples indicates reductions in τ and significant increases inE g relative to pure Mg (impurity concentration ∼10−8). Within experimental accuracy the observed quantum-state lifetime satisfies the relation τ−1C, with α∼2.7×1010 sec−1 per ppm of Cd and α∼2×1011 sec−1 per ppm of Zn. The band gap corresponding to Bragg reflection from the (0001) plane of the hcp structure (which in pure Mg arises solely from spin-orbit coupling) was found to increase by more than a factor of two upon the addition of only ∼10 ppm Cd to Mg. These results are discussed within the framework of the pseudopotential theory of alloying. It is shown that there are discrepancies of more than three orders of magnitude between the experimental and theoretical values forE g and of about one order of magnitude for τ in these dilute-limit alloys.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    W. Hume-Rothery,J. Inst. Metals 35, 295 (1926); H. Jones,Proc. Roy. Phys. Soc. 49, 250 (1937).

  2. 2.

    J. P. G. Shepherd and W. L. Gordon,Phys. Rev. 169, 541 (1968).

  3. 3.

    J. H. Tripp, P. M. Everett, and W. L. Gordon,Phys. Rev. B 2, 1556 (1970).

  4. 4.

    R. J. Higgins and J. A. Marcus,Phys. Rev. 141, 553 (1965).

  5. 5.

    L.-F. Chollet and I. M. Templeton,Phys. Rev. 170, 656 (1968).

  6. 6.

    P. T. Coleridge and I. M. Templeton,Can. J. Phys. 49, 2449 (1971).

  7. 7.

    I. M. Templeton, inLow Temperature Physics LT-13 (Proc. XIIIth Intern. Conf. Low Temp. Phys., Boulder, Colorado, 1972) (Plenum, New York, 1973).

  8. 8.

    R. J. Higgins and J. A. Marcus,Phys. Rev. 161, 589 (1967).

  9. 9.

    P. T. Coleridge, inLow Temperature Physics LT-13 (Proc. XIIIth Intern. Conf. Low Temp. Phys., Boulder Colorado, 1972) (Plenum, New York, 1973).

  10. 10.

    M. Springford,Adv. Phys. 20, 493 (1971).

  11. 11.

    A. V. Gold, inElectrons in Metals, Simon Fraser Summer School Lectures, Solid State Physics, 1967, J. F. Cochran and R. R. Haering, eds. (Gordon and Breach, New York, 1968), Vol. I.

  12. 12.

    D. H. Lowndes, K. Miller, and M. Springford,Phys. Rev. Letters 25, 1111 (1970).

  13. 13.

    R. W. Stark and C. B. Friedberg,Phys. Rev. Letters 26, 556 (1971).

  14. 14.

    C. B. Friedberg and R. W. Stark, inLow Temperature Physics LT-13 (Proc. XIIIth Intern. Conf. Low Temp. Phys., Boulder, Colorado, 1972) (Plenum, New York, 1973).

  15. 15.

    R. W. Stark and C. B. Friedberg, preceding paper in this issue.

  16. 16.

    R. W. Stark and C. B. Friedberg, following paper in this issue.

  17. 17.

    J. B. Ketterson and R. W. Stark,Phys. Rev. 156, 748 (1967).

  18. 18.

    R. W. Stark,Phys. Rev. 162, 589 (1967).

  19. 19.

    J. C. Kimball, R. W. Stark, and F. M. Mueller,Phys. Rev. 162, 600 (1967).

  20. 20.

    C. B. Friedberg and R. W. Stark,Phys. Rev. B 5, 2844 (1972).

  21. 21.

    R. W. Stark and L. M. Falicov,Phys. Rev. Letters 19, 795 (1965).

  22. 22.

    R. W. Stark and S. Auluck, unpublished.

  23. 23.

    V. Heine and D. Weaire,Solid State Phys. 24, 249 (1970).

  24. 24.

    R. W. Stark, unpublished.

  25. 25.

    R. D. Craig, G. A. Errock, and J. D. Waldron,Advan. Mass Spectrometry 1, 136 (1959).

  26. 26.

    R. W. Brown, R. D. Craig, and R. M. Elliott,Advan. Mass Spectrometry 2, 141 (1962).

  27. 27.

    R. W. Stark and L. M. Falicov, inProgress in Low Temperature Physics, C. J. Gorter, ed. (North-Holland, Amsterdam, 1967), Vol. V.

  28. 28.

    R. W. Stark and L. R. Windmiller,Cryogenics 8, 272 (1968).

  29. 29.

    W. Hume-Rothery and G. V. Raynor,Proc. Roy. Soc. (London)A174, 471 (1940); G. V. Raynor,Proc. Roy. Soc. (London) A174, 457 (1940).

  30. 30.

    J. M. Ziman,Principles of the Theory of Solids (Cambridge University Press, 1964), Ch. 7.

  31. 31.

    M. H. Cohen and L. M. Falicov,Phys. Rev. Letters 7, 231 (1961); L. M. Falicov and M. H. Cohen,Phys. Rev. 130, 92 (1963).

Download references

Author information

Additional information

Work supported by the National Science Foundation.

Submitted to the Department of Physics, the University of Chicago in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

Fannie and John Hertz Foundation Fellow.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Friedberg, C.B. Effects of alloying in the dilute limit on the quantum states of electrons in magnesium. J Low Temp Phys 14, 147–174 (1974). https://doi.org/10.1007/BF00654815

Download citation

Keywords

  • Magnetic Field
  • Magnesium
  • Magnetic Material
  • Quantum State
  • Electron Quantum