Calculation of surface phonon dispersion on Ni(100) and Ni(100)+c(2×2) along the (010) direction by means of the matching procedure. II

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Abstract
For pt.I see ibid., vol.20, p.4725 (1987). A detailed application of the matching procedure is presented in order to calculate the surface phonon dispersion on Ni(100) and Ni(100)+c(2*2)-O in the (010) direction. The phonons even and odd with respect to the (010) plane are analysed with special regard to the effect of adsorbate-induced Brillouin zone (BZ) folding. Studying each phonon symmetry separately enables one to identify the respective contributions from the BZ centre and edge in the electron energy-loss spectra. The equations of motion for Ni(100)+c(2*2)-O are worked out from those for the Ni(100) case. Information on the dispersion of bulk phonons projected onto the (100) surface and the associated Van Hove singularities is obtained by solving a secular equation. The surface phonon and resonance dispersion curves are found by matching the solutions of the secular equation to the surface conditions, which amounts to studying the scattering of incoming bulk waves by the surface. The eigenvectors obtained on the (100) surface permit one to perform a perturbation treatment of the adsorbate-substrate coupling. Finally, a comparative discussion with Green-function-based techniques is given.