Skip to main content
Log in

A Thomas-Fermi model for the electric field gradient in hcp-metals and numerical calculations for zinc

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

The electronic charge distribution between the ions of hcp-metals, especially of group IIb metals, is calculated in a selfconsistent way according to quantum statistics. The electric field gradient at the nuclear site which is produced by this charge distribution has the correct sign; it explains, however, only a part of the electronic contribution which is extracted from experimental data.

An additional “electronic charge shift” which is due to thep-band admixture is derived from the condition that the total energy per unit cell must exhibit a minimum at the observedc/a ratio which is different from the ideal hcp-value.

Finally the local contribution of this additional charge shift is estimated which is caused by the asymmetric charge distribution ofp-electrons within the own ionic sphere. Numerical results are obtained for zinc. They are compared with earlier band structure calculations and with the experimental data.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Vianden, R.: Hyperfine Interact.15–16, 189 (1983)

    Google Scholar 

  2. Vianden, R.: Hyperfine Interact.15–16, 1081 (1983)

    Google Scholar 

  3. Kaufmann, E.N., Vianden, R.: Rev. Mod. Phys.51, 161 (1979)

    Google Scholar 

  4. Kaufmann, E.N.: Hyperfine Interact.9, 219 (1981)

    Google Scholar 

  5. Mahapatra, N.C., Pattnaik, P.C., Thompson, M.D., Das, T.P.: Phys. Rev. B16, 3001 (1977)

    Google Scholar 

  6. Pattnaik, P.C., Thompson, M.P., Das, T.P.: Phys. Rev. B16, 5390 (1977)

    Google Scholar 

  7. Nishiyama, K., Dimmling, F., Kornrumpf, T., Riegel, D.: Phys. Rev. Lett.57, 357 (1976)

    Google Scholar 

  8. Nishiyama, K., Riegel, D.: Hyperfine Interact.4, 490 (1978)

    Google Scholar 

  9. Piecuch, M., Janot, C.: Hyperfine Interact.5, 69 (1977); Hyperfine Interact.11, 13 (1981)

    Google Scholar 

  10. Haas, H., Menningen, M.: Hyperfine Interact.9, 277 (1981)

    Google Scholar 

  11. Jena, P., Rath, J.: Phys. Rev. B23, 3823 (1981)

    Google Scholar 

  12. Bodenstedt, E.: Hyperfine Interact.15–16, 1061 (1983)

    Google Scholar 

  13. Raghavan, R.S., Kaufmann, E.N., Raghavan, P.: Phys. Rev. Lett.34, 1280 (1975)

    Google Scholar 

  14. Bodenstedt, E., Perscheid, B.: Hyperfien Interact.5 291 (1978)

    Google Scholar 

  15. Thomas, L.H.: Proc. Camb. Philos. Soc.23, 542 (1927)

    Google Scholar 

  16. Fermi, E.: Z. Phys.48, 73 (1928);49, 550 (1928)

    Google Scholar 

  17. Dirac, P.A.M.: Proc. Camb. Philos. Soc.26, 276 (1930)

    Google Scholar 

  18. March, N.H.: Adv. Phys.6, 1 (1957)

    Google Scholar 

  19. Ewald, P.P.: Ann. Phys. (Leipzig)64, 253 (1921)

    Google Scholar 

  20. DeWette, F.W., Nijboer, B.R.A.: Physica24, 1105 (1958)

    Google Scholar 

  21. DeWette, F.W.: Physica25, 1225 (1959)

    Google Scholar 

  22. DeWette, F.W.: Phys. Rev.123, 103 (1961)

    Google Scholar 

  23. Nagel, S.: Phys. Rev. B24, 4240 (1981)

    Google Scholar 

  24. Pearson, W.B.: A handbook of lattice spacings and structures of metals and alloys. Part 2, p. 886. New York: Pergamon Press 1958

    Google Scholar 

  25. Owen, E.A., Yates, E.L.: Philos. Mag.17, 113 (1934)

    Google Scholar 

  26. Sternheimer, R.M.: Phys. Rev.159, 266 (1967)

    Google Scholar 

  27. Feiock, F.D., Johnson, W.R.: Phys. Rev.187, 39 (1969)

    Google Scholar 

  28. Clementi, E., Roetti, C.: At. Data Nucl. Data Tables14, 177 (1974)

    Google Scholar 

  29. Das, T.P. Pomerantz, M.: Phys. Rev.123, 2070 (1969)

    Google Scholar 

  30. D'Ans, Lax: Taschenbuch für Chemiker und Physiker. Lax, E., Synowietz, C. (eds.), 3. Aufl., pp. 1–105. Berlin, Heidelberg, New York: Springer Verlag 1967

    Google Scholar 

  31. American Institute of Physics Handbook. Gray, D.E. (ed.), 2. Aufl., pp. 7–14, 15. New York: McGraw-Hill Book Company, Inc. 1963

    Google Scholar 

  32. Alers, G.A., Neighbours, J.R.: J. Phys. Chem. Solids 7, 58 (1958)

    Google Scholar 

  33. Kopfermann, H.: Kernmomente. 2. Aufl., pp. 139 ff and p. 432. Frankfurt: Akademische Verlagsgesellschaft 1956

    Google Scholar 

  34. Potzel, W., Obenhuber, T., Forker, A., Kalvins, G.M.: Hyperfine Interact.12, 135 (1982)

    Google Scholar 

  35. Laulainen, N.S., McDermott, M.N. Phys. Rev.177, 1606 (1969)

    Google Scholar 

  36. Bodenstedt, E.: Hyperfine Interact.15–16, 1061 (1983)

    Google Scholar 

  37. Wichert, Th.: Hyperfine Interact.15, 335 (1983)

    Google Scholar 

  38. International Tables forX-Ray Crystallography. Henry, N.F.M., Lonsdale, K. (eds.). Birmingham: The Kynoch Press 1965

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bodenstedt, E., Perscheid, B. & Nagel, S. A Thomas-Fermi model for the electric field gradient in hcp-metals and numerical calculations for zinc. Z. Physik B - Condensed Matter 63, 9–24 (1986). https://doi.org/10.1007/BF01312573

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01312573

Keywords

Navigation