Skip to main content
SpringerLink
Log in

Statistical Properties of Conduction Electrons in an Isolated Metal Nanosphere

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We explore differences between canonical and grand canonical ensembles of 500–2000 free electrons confined in a spherical well with a radius from 1.2 to 2 nm. The averaged occupation numbers of the electronic energy levels and their variances are calculated. For isolated Ag and Au particles, the sum of the variances of all occupation numbers differs from the corresponding bulk-metal value by a factor of 0.005 to 2.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

References

  1. Abrikosov, A.A.: Fundamentals of the Theory of Metals. Elsevier, Amsterdam (1988)

    Google Scholar 

  2. Ashcroft, N.W., Mermin, N.D.: Solid State Physics. Holt, Rinehart & Winston, New York (1979)

    Google Scholar 

  3. Bjørnholm, S., Borggreen, J., Echt, O., Hansen, K., Pedersen, J., Rasmussen, H.D.: Mean-field quantization of several hundred electrons in sodium metal clusters. Phys. Rev. Lett. 65, 1627–1630 (1990)

    Article  ADS  Google Scholar 

  4. Blanter, Y., Büttiker, M.: Shot noise in mesoscopic conductors. Phys. Rep. 336, 1–166 (2000)

    Article  ADS  Google Scholar 

  5. Brack, M.: The physics of simple metal clusters: self-consistent jellium model and semiclassical approaches. Rev. Mod. Phys. 65, 677–732 (1993)

    Article  ADS  Google Scholar 

  6. Chen, M., Cai, Y., Yan, Z., Goodman, D.W.: On the origin of the unique properties of supported Au nanoparticles. J. Am. Chem. Soc. 128, 6341–6346 (2006)

    Article  Google Scholar 

  7. Denton, R., Mühlschlegel, B., Scalapino, D.J.: Electronic heat capacity and susceptibility of small metal particles. Phys. Rev. Lett. 26, 707–711 (1971)

    Article  ADS  Google Scholar 

  8. Flambaum, V.V., Izrailev, F.M.: Distribution of occupation numbers in finite Fermi systems and role of interaction in chaos and thermalization. Phys. Rev. E 55, R13–R16 (1997)

    Article  ADS  Google Scholar 

  9. Flambaum, V.V., Izrailev, F.M.: Statistical theory of finite Fermi systems based on the structure of chaotic eigenstates. Phys. Rev. E 56, 5144–5159 (1997)

    Article  ADS  Google Scholar 

  10. Genzken, O., Brack, M.: Temperature dependence of supershells in large sodium clusters. Phys. Rev. Lett. 67, 3286–3289 (1991)

    Article  ADS  Google Scholar 

  11. Goeppert Mayer, M.: Nuclear configurations in the spin-orbit coupling model. I. Empirical evidence. Phys. Rev. 78, 16–21 (1950)

    Article  ADS  MATH  Google Scholar 

  12. Goeppert Mayer, M.: Nobel Lectures in Physics (1963–1970), pp. 20–37. World Scientific, Singapore (1998)

    Google Scholar 

  13. Göhlich, H., Lange, T., Bergmann, T., Martin, T.P.: Electronic shell structure in large metallic clusters. Phys. Rev. Lett. 65, 748–751 (1990)

    Article  ADS  Google Scholar 

  14. de Heer, W.A.: The physics of simple metal clusters: experimental aspects and simple models. Rev. Mod. Phys. 65, 611–676 (1993)

    Article  ADS  Google Scholar 

  15. Kaplan, T.A.: The chemical potential. J. Stat. Phys. 122, 1237–1260 (2006)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Koskinen, M., Manninen, M.: Photoionization of metal clusters. Phys. Rev. B 54, 796–806 (1996)

    Article  Google Scholar 

  17. Kreibig, U., Vollmer, M.: Optical Properties of Metal Clusters. Springer, Berlin (1995)

    Book  Google Scholar 

  18. Landsberg, P.T., Harshman, P.: Canonical versus grand canonical occupation numbers for simple systems. J. Stat. Phys. 53, 475–482 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  19. Lebowitz, J.L., Percus, J.K., Verlet, L.: Ensemble dependence of fluctuations with application to machine computations. Phys. Rev. 153, 250–254 (1967)

    Article  ADS  Google Scholar 

  20. Liboff, R.L.: Geometrical properties of the Fermi energy. Found. Phys. 15, 339–352 (1985)

    Article  ADS  Google Scholar 

  21. Liboff, R.L.: Density of states and other quantum properties of a spherical cavity. Phys. Rev. A 43, 5765–5769 (1991)

    Article  ADS  Google Scholar 

  22. Martin, T., Bergmann, T., Göhlich, H., Lange, T.: Observation of electronic shells and shells of atoms in large Na clusters. Chem. Phys. Lett. 172, 209–213 (1990)

    Article  ADS  Google Scholar 

  23. Pedersen, J., Bjørnholm, S., Borggreen, J., Hansen, K., Martin, T.P., Rasmussen, H.D.: Observation of quantum supershells in clusters of sodium atoms. Nature 353, 733–735 (1991)

    Article  ADS  Google Scholar 

  24. Persson, J.L., Whetten, R.L., Cheng, H.P., Berry, R.: Evidence for quantized electronic level structure for 100–1300 electrons in metal-atomic clusters. Chem. Phys. Lett. 186, 215–222 (1991)

    Article  ADS  Google Scholar 

  25. Ralph, D.C., Black, C.T., Tinkham, M.: Spectroscopic measurements of discrete electronic states in single metal particles. Phys. Rev. Lett. 74, 3241–3244 (1995)

    Article  ADS  Google Scholar 

  26. Roldughin, V.I.: Quantum-size colloid metal systems. Russ. Chem. Rev. 69, 821–843 (2000)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Taras Shevchenko National University of Kyiv, 01601, Kyiv, Ukraine

    Vitaly V. Datsyuk & Iryna V. Ivanytska

Authors
  1. Vitaly V. Datsyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Iryna V. Ivanytska
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vitaly V. Datsyuk.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Datsyuk, V.V., Ivanytska, I.V. Statistical Properties of Conduction Electrons in an Isolated Metal Nanosphere. J Stat Phys 152, 969–978 (2013). https://doi.org/10.1007/s10955-013-0798-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-013-0798-5

Keywords

Search

Navigation