Surface Phonon Calculations in Metals and Comparison with Experimental Techniques

  • V. Bortolani
  • A. Franchini
  • G. Santoro


There has been considerable recent progresses in the experimental techniques to detect surface phonons over the entire Brillouin zone for noble and transition metals with the high resolution electron energy loss spectroscopy and with the inelastic atomic scattering. However the cross sections are in general not strictly proportional to the density of states so that in the interpretation of the experimental spectra it is necessary a knowledge of the scattering mechanisms.

In these lectures we will present the theory of atomic scattering focusing in particular on the atom surface potential. This potential is separated in an attractive part of the Van der Waals type and in a repulsive part related to the surface charge which is approximate as a superposition of atomic charges. The lateral Fourier trasform of this potential, which enters in the cross sections, has a gaussian form which is essential in order to explain the falling off of the Rayleigh peaks at the zone boundary.

The bulk phonons are evaluated within a microscopic approach based on a force constants parametrization. We include central and angular forces in order to simulate the anisotropy of the electron gas produced by the presence of d levels. The surface phonons are evaluated, with these force constants, for a sufficiently thick slab in order to avoid interference effects between the modes of the two surfaces.

We also show that is necessary to modify the surface force constants in order to explain the atom scattering data. We will outline in a perturbative pseudopotential approach that the effect of the surface on the electron gas can reduce the surface force constants.


Force Constant Phonon Frequency Dynamical Matrix Surface Phonon Repulsive Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    V. Bortolani, F. Nizzoli and G. Santoro, Phys.Rev.Lett. 41, 39 (1978).CrossRefGoogle Scholar
  2. 2.
    V. Bortolani, F. Nizzoli, G. Santoro, A. Marvin and J.R. Sandercock, Phys.Rev.Lett. 43, 224 (1979).CrossRefGoogle Scholar
  3. 3.
    N. Cabrera, V. Celli and R. Manson, Phys.Rev.Lett 22, 346 (1969);CrossRefGoogle Scholar
  4. 4.
    M. G. Brusdeylins, R.B. Doak and J.P. Toennies, Phys.Rev.Lett. 16, 937 (1981); and to be publishedGoogle Scholar
  5. 5.
    R.B. Doak, U. Harten and J.P. Toennies, Phys. Rev. Lett. 51, 578 (1983).CrossRefGoogle Scholar
  6. 6.
    S. Lehwald, J.M. Szeftel, H. Ibach, T.S. Rahman and D.L. Mills, Phys.Rev.Lett. 5, 518 (1983).CrossRefGoogle Scholar
  7. 7.
    B.N. Brockhouse, “Phonons and neutron scattering” in Phonons and Phonon Interactions, Edited by T.A. Bak, W.A.Benjamin, Inc. New York, pag. 221 (1964);Google Scholar
  8. 8.
    L. Van Hove, Phys. Rev. 95, 249 (1954).CrossRefGoogle Scholar
  9. 9.
    R.J. Glauber, Phys. Rev. 98, 1092 (1955).CrossRefGoogle Scholar
  10. 10.
    M. Born and K. Huang, Dynamical Theory of Crystal Lattices, Oxford Univ. Press (1954).Google Scholar
  11. 11.
    D. Castiel, L. Dobrzynski and D. Spanjaard, Surf. Sci. 59, 252 (1976).CrossRefGoogle Scholar
  12. 12.
    D.H. Dutton, B.N. Brockhouse and A.P. Miller, Canad.J.Phys., 50, 2915 (1972).CrossRefGoogle Scholar
  13. 13.
    S.K. Sinha, Phys. Rev. 143, 422 (1966).CrossRefGoogle Scholar
  14. 14.
    W.A. Kamitakahra and B.N. Brockhouse, Phys.Lett., 29A, 639 (1969).CrossRefGoogle Scholar
  15. 15.
    J.W. Lynn, H.G. Smith and R.N.Nicklow, Phys. Rev. B8, 3493 (1973).CrossRefGoogle Scholar
  16. 16.
    R.J. Birgenau, J. Cordes, G. Dolling and A.D.B. Woods, Phys. Rev. 136, A1359 (1964).CrossRefGoogle Scholar
  17. 17.
    J.F. Cornwell, Group Theory and Electronic Energy Bands in Solids, North-Holland Publ.Comp. Amsterdam (1969).Google Scholar
  18. 18.
    W.R. Lambert, P.L. Trevol, R.B. Doak and M.J. Cardillo, J.Vac.Sci.Technol. A2, 1066 (1984).CrossRefGoogle Scholar
  19. 19.
    R. Manson and V. Celli, Surf. Sci. 26, 695 (1971)Google Scholar
  20. 20.
    V. Bortolani, A. Franchini, N. Garcia, F. Nizzoli and G. Santoro, Phys. Rev. B28, 7358 (1983).CrossRefGoogle Scholar
  21. 21.
    V. Celli, in Dynamics of Gas-Surface Interaction, ed. G.Benedek and U.Valbusa ( Springer, Berlin, 1982 ) p. 1Google Scholar
  22. 22.
    E. Zaremba and W. Kohn, Phys. Rev. B15, 1769 (1977)CrossRefGoogle Scholar
  23. 23.
    V. Bortolani, A. Franchini, F. Nizzoli and G. Santoro, in Dynamics of Gas-Surface Interaction, ed. G.Benedek and U.Valbusa ( Springer, Berlin, 1982 ) p. 196CrossRefGoogle Scholar
  24. 24.
    N. Esbjerg and J.K. Norskov, Phys. Rev. Lett. 45, 807 (1980)CrossRefGoogle Scholar
  25. 25.
    P.Norlander and J.Harris, J. Phys. C: Solid St. Phys. 17, 1141 (1984)CrossRefGoogle Scholar
  26. 26.
    V. Bortolani, A. Franchini, F. Nizzoli, G. Santoro, Phys. Rev. Lett. 52, 429 (1984)CrossRefGoogle Scholar
  27. 27.
    G.W. Farnell, in “Physical Acoustics”, vol. VI, ed. W.P.Mason and R.N. Thurston ( Academic Press, New York, 1970 ) p. 109.Google Scholar
  28. 28.
    D.E. Beck, V. Celli,G. Lo Vecchio and A. Magnaterra, Nuovo Cim. B17, 230 (1970)CrossRefGoogle Scholar
  29. 29.
    A. Moriarty, Phys. Rev. B6, 1239 (1972).Google Scholar
  30. 30.
    J.P.Toennies and coworkers, data presented at the Modena Meeting of the Surface Group of GNSM, December 1983, unpublished and to be publishedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • V. Bortolani
    • 1
  • A. Franchini
    • 1
  • G. Santoro
    • 1
  1. 1.Dipartimento di FisicaUniversita’ di Modena and Gruppo Nazionale Struttura della MateriaModenaItaly

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