Work Function of Electrons of Metal and Ionization Potential of the Metal Cluster Containing Vacancies

V. V. Pogosov, V. I. Reva

Zaporizhzhya National Technical University, 64 Zhukovskogo Str., 69063 Zaporizhzhya, Ukraine

Received: 05.11.2016. Download: PDF

A method combining two approaches is proposed. The first one is based on the density-functional theory solution within the stabilized jelly model for a metal monovacancy ignoring an external surface. The second one uses a solution for a defect-free metal in the presence of an external flat surface, but with lowered atomic density. This lowered density of atoms appears due to the existence of superlattice of vacancies with a relative concentration $c_{\textrm{v}}$ within the defect metal. Using $c_{\textrm{v}}$ as a small parameter, all metal characteristics are expanded into $c_{\textrm{v}}$-series. The zero terms of the expansion correspond to defect-free metal, and linear-$c_{\textrm{v}}$ corrections are expressed through its characteristics. The consecutive procedure for the calculation of a size dependence of ionization potential and electron affinity for a large spherical metal cluster of radius $R_{N\textrm{,v}}$ containing $N$ atoms and $N_{\textrm{v}}$ vacancies is presented. Within the scope of the effective-medium approach, the perturbation theory over the small parameters $R_{\textrm{v}}/R_{N\textrm{,v}}$ and $L_{\textrm{v}}/R_{\textrm{v}}$ is proposed for electrons’ ground-state energy ($R_{\textrm{v}}$ is the average distance between the vacancies and $L_{\textrm{v}}$ is the electron–vacancy scattering length). The profile of effective potential, phase shifts of the scattered wave functions, and electron scattering length previously have been calculated by means of the Kohn–Sham method for a macroscopic metal sample within the stabilized jelly model. Obtained analytical dependences can be useful for both the analysis of results of photoionization experiments and the determination of the size dependences of the vacancy concentration including the vicinity of the melting point.

Key words: metal, atomic cluster, vacancy, density functional theory, model of stable jelly, perturbation theory, work function, ionization potential.



PACS: 32.10.Hq, 36.40.Vz,, 71.15.Mb, 73.22.Dj, 73.30.+y, 73.61.At

Citation: V. V. Pogosov and V. I. Reva, Work Function of Electrons of Metal and Ionization Potential of the Metal Cluster Containing Vacancies, Metallofiz. Noveishie Tekhnol., 39, No. 3: 285—308 (2017) (in Ukrainian)

  1. R. S. Berry and B. M. Smirnov, J. Exp. Theor. Phys., 98, Iss. 2: 366 (2004). Crossref
  2. R. S. Berry and B. M. Smirnov, Phys. Rep., 527, No. 4: 205 (2013). Crossref
  3. A. V. Babich, V. V. Pogosov and V. I. Reva, Fiz. Tverd. Tela, 57, No. 11: 2081 (2015) (in Russian).
  4. C. Hock, C. Bartels, S. Straßburg, M. Schmidt, H. Haberland, B. von Issendorff, and A. Aguado, Phys. Rev. Lett., 102: 043401 (2009). Crossref
  5. C. C. Yang and S. Li, Phys. Rev. B, 75: 165413 (2007). Crossref
  6. G. Guisbiers, Nanoscale Res. Lett., 5: 1132 (2010). Crossref
  7. G. A. Breaux, C. M. Neal, B. Cao, and M. F. Jarrold, Phys. Rev. Lett., 94, No. 17: 173401 (2005). Crossref
  8. A. K. Starace, B. Cao, O. H. Judd, I. Bhattacharyya, and M. F. Jarrold, J. Chem. Phys., 132: 034302 (2010). Crossref
  9. C. Bréchignac, Ph. Cahuzac, J. Leygnier, and J. Weiner, J. Chem. Phys., 90: 1492 (1989). Crossref
  10. U. Ray, M. F. Jarrold, J. E. Bower, and J. S. Kraus, J. Chem. Phys., 91, No. 5: 2912 (1989). Crossref
  11. C. Bréchignac, H. Busch, Ph. Cahuzac, and J. Leygnier, J. Chern. Phys., 101, No. 8: 6992 (1994). Crossref
  12. A. Halder and V. V. Kresin., J. Chem. Phys., 143, No. 16: 164313 (2015). Crossref
  13. M. Seidl, J. P. Perdew, M. Brajczewska, and C. Fiolhais, J. Chem. Phys., 108, No. 19: 8182 (1998). Crossref
  14. V. V. Pogosov, Vvedenie v Fiziku Zaryadovykh i Razmernykh Effektov: Poverkhnost, Klastery, Nizkorazmernye Sistemy [Introduction to Physics of Charged and Size Effects: Surface, Clusters, Low-Dimensional Systems] (Moscow: Fizmatlit: 2006) (in Russian).
  15. A. V. Babich, P. V. Vakula, and V. V. Pogosov, Fiz. Tverd. Tela, 56: No. 5: 841 (2014) (in Russian).
  16. I. T. Iakubov and V. V. Pogosov, Physica A, 214, No. 2: 287 (1995). Crossref
  17. A. Kiejna and V. V. Pogosov, J. Phys.: Condens. Matter, 8, No. 23: 4245 (1996). Crossref
  18. J. P. Perdew, H. Q. Tran, and E. D. Smith, Phys. Rev. B, 42, No. 18: 11627 (1990). Crossref
  19. V. V. Pogosov, Solid State Commun., 89, No. 12: 1017 (1994). Crossref
  20. C. Freysoldt, B. Grabowski, T. Hickel, J. Neugebauer, G. Kresse, A. Janotti, and C. G. Van de Walle, Rev. Mod. Phys., 86, No. 1: 253 (2014). Crossref
  21. M. A. Shtremel, Prochnost Splavov. Defekty Reshetki [Strength of Alloys. Lattice Defects] (Moscow: Metallurgiya: 1982) (in Russian).
  22. E. M. Gullikson and A. P. Mills, Jr., Phys. Rev. B, 35, No. 16: 8759 (1987). Crossref
  23. V. V. Pogosov, W. V. Pogosov, and D. P. Kotlyarov, J. Exp. Theor. Phys., 90, Iss. 5: 908 (2000). Crossref
  24. V. V. Pogosov, Fiz. Tverd. Tela, 35, No. 4: 1010 (1993) (in Russian).
  25. B. E. Springett, M. H. Cohen, and J. Jortner, Phys. Rev., 159, No. 1: 183 (1967). Crossref
  26. I. T. Iakubov and V. V. Pogosov, J. Chem. Phys., 106, No. 6: 2306 (1997). Crossref
  27. J. Bardeen, J. Chem. Phys., 6, No. 7: 367 (1938). Crossref
  28. M. H. Cohen and F. S. Ham, J. Phys. Chem. Sol., 16, Nos. 3–4: 177 (1960). Crossref
  29. M. J. Stott and P. Kubica, Phys. Rev. B, 11, No. 1: 1 (1975). Crossref
  30. T. P. Martin, Phys. Rep., 273, No. 4: 199 (1996). Crossref
  31. W. A. de Heer, Rev. Mod. Phys., 65, No. 3: 611 (1993). Crossref
  32. M. Brack, Rev. Mod. Phys., 65, No. 3: 677 (1993). Crossref
  33. M. A. Hoffmann, G. Wrigge, and B. von Issendorff, Phys. Rev. B, 66, No. 4: 041404 (2002). Crossref
  34. P. Ziesche, J. P. Perdew, and C. Fiolhais, Phys. Rev. B, 49, No. 12: 7916 (1994). Crossref
  35. J. A. Alonso and N. H. March, Surf. Sci., 160, No. 2: 509 (1985). Crossref