Surface Phonon Calculations in Metals and Comparison with Experimental Techniques
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.
KeywordsForce Constant Phonon Frequency Dynamical Matrix Surface Phonon Repulsive Part
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