Skip to main content
Log in

On the localization of positrons in metal vacancies

  • Metals
  • Published:
Physics of the Solid State Aims and scope Submit manuscript

Abstract

The probability of localization of positrons in single vacancies of Al, Cu, and Zn as a function of temperature has been calculated. Vacancy has been simulated by a cavity with a radius of the Wigner–Seitz cell in the stabilized jellium model. A formula for the rate of trapping of a positron by a vacancy as a function of the positron energy has been obtained using the “golden” rule for transitions under the assumption that the positron energy is spent on excitation of electron–hole pairs. The temperature dependence of the localization rate has been calculated for thermalized positrons. It has been found that, in the vicinity of the triple point, the localization rate is close in order of magnitude to the annihilation rate. Based on the results reported in our previous publications devoted to the evaluation of the influence of vacancies on the work function of free positrons, it has been assumed that, near the surface of the metal, there are vacancies charged by positrons. In the approximation of a two-dimensional superlattice, the near-surface vacancy barrier has been estimated. The experimentally revealed shift of the energy distribution of re-emitted positrons has been assumed to be caused by the reflection of low-energy positrons from the vacancy barrier back into the bulk of the metal where they annihilate.

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. M. J. Puska and R. M. Nieminen, Rev. Mod. Phys. 66, 841 (1994).

    Article  ADS  Google Scholar 

  2. F. Tuomisto and I. Makkonen, Rev. Mod. Phys. 85, 1583 (2013).

    Article  ADS  Google Scholar 

  3. S. Mukherjee, M. P. Nadesalingam, P. Guagliardo, A. D. Sergeant, B. Barbiellini, J. F. Williams, N. G. Fazleev, and A. H. Weiss, Phys. Rev. Lett. 104, 247403 (2010).

    Article  ADS  Google Scholar 

  4. Z. Wang, S. Su, F. C.-C. Ling, W. Anwand, and A. Wagner, J. Appl. Phys. 116, 033508 (2014).

    Article  ADS  Google Scholar 

  5. S. Hagiwara, C. Hu, and K. Watanabe, Phys. Rev. B: Condens. Matter 91, 115409 (2015).

    Article  ADS  Google Scholar 

  6. F. A. Selim, D. Solodovnikov, V. Y. Weber, and K. G. Lynn, Appl. Phys. Lett. 91, 104105 (2007).

    Article  ADS  Google Scholar 

  7. S. W. H. Eijt, A. van Veen, H. Schut, P. E. Mijnarends, A. B. Denison, B. Barbiellini, and A. Bansil, Nat. Mater. 5, 23 (2006).

    Article  ADS  Google Scholar 

  8. J. R. Danielson, D. Sh. E. Dubin, R. G. Greaves, and C. M. Surko, Rev. Mod. Phys. 87, 247 (2015).

    Article  ADS  Google Scholar 

  9. B. Nielsen, K. G. Lynn, and Y.-C. Chen, Phys. Rev. Lett. 57, 1789 (1986).

    Article  ADS  Google Scholar 

  10. M. Jibaly, A. Weiss, A. R. Koymen, D. Mehl, L. Stiborek, and C. Lei, Phys. Rev. B: Condens. Matter 44, 12166 (1991).

    Article  ADS  Google Scholar 

  11. K. G. Lynn, T. McKay, and B. Nielsen, Phys. Rev. B: Condens. Matter 36, 7107 (1987).

    Article  ADS  Google Scholar 

  12. T. McMullen and M. J. Stott, Phys. Rev. B: Condens. Matter 34, 8985 (1986).

    Article  ADS  Google Scholar 

  13. M. J. Puska and M. P. Manninen, J. Phys. F: Met. Phys. 17, 2235 (1987).

    Article  ADS  Google Scholar 

  14. K. O. Jensen and A. B. Walker, J. Phys.: Condens. Matter 2, 9757 (1990).

    ADS  Google Scholar 

  15. I. Makkonen and M. J. Puska, Phys. Rev. B: Condens. Matter 76, 054119 (2007).

    Article  ADS  Google Scholar 

  16. A. V. Babich, P. V. Vakula, and V. V. Pogosov, Phys. Solid State 56 (5), 873 (2014).

    Article  ADS  Google Scholar 

  17. A. V. Babich, P. V. Vakula, and V. V. Pogosov, Phys. Solid State 56 (9), 1726 (2014).

    Article  ADS  Google Scholar 

  18. A. V. Babich, V. V. Pogosov, and V. I. Reva, Tec Sh. Phys. Lett. (in press).

  19. J. D. Levine and E. P. Gyftopoulos, Surf. Sci. 1, 225 (1964).

    Article  ADS  Google Scholar 

  20. Z. Fu, G. W. Lemire, G. A. Bishea, and M. D. Morse, J. Chem. Phys. 93, 8420 (1990).

    Article  ADS  Google Scholar 

  21. J. P. Perdew, Y. Wang, and E. Engel, Phys. Rev. Lett. 66, 508 (1991).

    Article  ADS  Google Scholar 

  22. A. Pimpinelli and J. Villain, Physica A (Amsterdam) 204, 521 (1994).

    Article  ADS  Google Scholar 

  23. E. Gramsch, K. G. Lynn, J. Throwe, and I. Kanazawa, Phys. Rev. B: Condens. Matter 59, 14282 (1999).

    Article  ADS  Google Scholar 

  24. V. V. Pogosov, A. V. Babich, P. V. Vakula, and A. G. Kravtsova, Tec Sh. Phys. 56 (11), 1689 (2011).

    Article  Google Scholar 

  25. I. T. Iakubov, A. G. Khrapak, V. V. Pogosov, and S. A. Trigger, Phys. Status Solidi B 145, 455 (1988).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. V. Pogosov.

Additional information

Original Russian Text © A.V. Babich, V.V. Pogosov, V.I. Reva, 2015, published in Fizika Tverdogo Tela, 2015, Vol. 57, No. 11, pp. 2081–2089.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Babich, A.V., Pogosov, V.V. & Reva, V.I. On the localization of positrons in metal vacancies. Phys. Solid State 57, 2135–2144 (2015). https://doi.org/10.1134/S1063783415110050

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063783415110050

Keywords

Navigation