Surface vibrational modes

Dynamic models for ionic lattices recognize explicitly the force constants between ions and their polarization. In shell models, the ions are represented as a shell and a core, coupled by a spring (see Refs. 57-59), and parameters are evaluated by matching bulk elastic and dielectric properties. Application of these models to the surface region has allowed calculation of surface vibrational modes [60] and LEED patterns [61-63] (see Section VIII-2). 

On single crystal surfaces vibrational modes are In principle wavellke excitations with the wave vector parallel to the surface ... 

Some surfaces geometries (rough surfaces) concentrate the electric fields of Raman scattering cross section so that it is surface-sensitive. This gives information on surface vibrational modes, and some information on geometry via selection rules. 

The effects of relaxation on the calculated surface phonon dispersion in Rbl have apparently been verified, particularly by the observation of a surface optical mode which lies above the bulk phonon optical bands. Except for the mysterious acoustic band mode in Rbl, the Shell model calculations have generally been quite accurate in predicting surface vibrational mode energies in both high-symmetry directions of the alkali halide (001) surfaces. 

In addition to the expansion of time resolution, the expansion of spectral range to far IR is also desirable, since metal-adsorbate vibrations and surface vibrational modes occur in this range. The available spectral range is now limited by the prism (>900 cm" for Si and >700 cm" for Ge), the low intensity of the light source, and the low sensitivity of detectors. Since the absorption coefficient of Si fortunately decreases in the far-IR region, ATR-SEIRAS in the far-IR wiU be possible with the use of a synchrotron far-IR facility and a helium-cooled bolometer [142]. 

For solid systems, the vibrational modes can have wavelengths greater than the extent of the unit cell and the calculation of the phonon spectra of solids has been carried out for a number of bulk structures, but only recently have calculations of surface vibrational modes become available for oxide systems (377). Calculation Methods. 

Lavalley, J. and Benaissa, M. (1984). IR spectroscopic evidence for surface vibrational modes upon dehydroxylation of alumina, J. Chem. Soc. Chem. Commun., 14, pp. 908-909. 

This dependence of p p (ro) on ro results because there are no surface vibrational modes with frequencies above the Debye frequency, (Dq... 

High-resolution electron energy loss (HREELS = high-resolution electron energy loss spectroscopy) experiments and inelastic scattering of helium atoms allow a determination of the surface vibration modes and of the phonon dispersion curves. The same cannot be achieved by inelastic neutron scattering, due to the high penetration depth of the neutrons... 

Due to the surface bonding characteristics which deviate from those of the bulk, surface vibrational modes are different from those of the bulk. Phonon density of states measurements have been obtained for the (100) surface of MgO [13]. 

Here is the number of vibrational degrees of freedom of a single adsorbate, which has a value of three for atomic adsorbates, but includes additional internal vibrations for adsorbed molecules. If the surface vibrational modes are insensitive to the presence of adsorbates, the surface terms cancel and the expression simplifies to ... 

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