Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V. Bortolani, F. Nizzoli and G. Santoro, Phys.Rev.Lett. 41, 39 (1978).
V. Bortolani, F. Nizzoli, G. Santoro, A. Marvin and J.R. Sandercock, Phys.Rev.Lett. 43, 224 (1979).
N. Cabrera, V. Celli and R. Manson, Phys.Rev.Lett 22, 346 (1969);
M. G. Brusdeylins, R.B. Doak and J.P. Toennies, Phys.Rev.Lett. 16, 937 (1981); and to be published
R.B. Doak, U. Harten and J.P. Toennies, Phys. Rev. Lett. 51, 578 (1983).
S. Lehwald, J.M. Szeftel, H. Ibach, T.S. Rahman and D.L. Mills, Phys.Rev.Lett. 5, 518 (1983).
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);
L. Van Hove, Phys. Rev. 95, 249 (1954).
R.J. Glauber, Phys. Rev. 98, 1092 (1955).
M. Born and K. Huang, Dynamical Theory of Crystal Lattices, Oxford Univ. Press (1954).
D. Castiel, L. Dobrzynski and D. Spanjaard, Surf. Sci. 59, 252 (1976).
D.H. Dutton, B.N. Brockhouse and A.P. Miller, Canad.J.Phys., 50, 2915 (1972).
S.K. Sinha, Phys. Rev. 143, 422 (1966).
W.A. Kamitakahra and B.N. Brockhouse, Phys.Lett., 29A, 639 (1969).
J.W. Lynn, H.G. Smith and R.N.Nicklow, Phys. Rev. B8, 3493 (1973).
R.J. Birgenau, J. Cordes, G. Dolling and A.D.B. Woods, Phys. Rev. 136, A1359 (1964).
J.F. Cornwell, Group Theory and Electronic Energy Bands in Solids, North-Holland Publ.Comp. Amsterdam (1969).
W.R. Lambert, P.L. Trevol, R.B. Doak and M.J. Cardillo, J.Vac.Sci.Technol. A2, 1066 (1984).
R. Manson and V. Celli, Surf. Sci. 26, 695 (1971)
V. Bortolani, A. Franchini, N. Garcia, F. Nizzoli and G. Santoro, Phys. Rev. B28, 7358 (1983).
V. Celli, in Dynamics of Gas-Surface Interaction, ed. G.Benedek and U.Valbusa ( Springer, Berlin, 1982 ) p. 1
E. Zaremba and W. Kohn, Phys. Rev. B15, 1769 (1977)
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. 196
N. Esbjerg and J.K. Norskov, Phys. Rev. Lett. 45, 807 (1980)
P.Norlander and J.Harris, J. Phys. C: Solid St. Phys. 17, 1141 (1984)
V. Bortolani, A. Franchini, F. Nizzoli, G. Santoro, Phys. Rev. Lett. 52, 429 (1984)
G.W. Farnell, in “Physical Acoustics”, vol. VI, ed. W.P.Mason and R.N. Thurston ( Academic Press, New York, 1970 ) p. 109.
D.E. Beck, V. Celli,G. Lo Vecchio and A. Magnaterra, Nuovo Cim. B17, 230 (1970)
A. Moriarty, Phys. Rev. B6, 1239 (1972).
J.P.Toennies and coworkers, data presented at the Modena Meeting of the Surface Group of GNSM, December 1983, unpublished and to be published
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer Science+Business Media New York
About this chapter
Cite this chapter
Bortolani, V., Franchini, A., Santoro, G. (1985). Surface Phonon Calculations in Metals and Comparison with Experimental Techniques. In: Devreese, J.T., Van Camp, P. (eds) Electronic Structure, Dynamics, and Quantum Structural Properties of Condensed Matter. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0899-8_9
Download citation
DOI: https://doi.org/10.1007/978-1-4757-0899-8_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-0901-8
Online ISBN: 978-1-4757-0899-8
eBook Packages: Springer Book Archive