high quality analyzer. Further high resolution is only possible when the energies of the incident electrons are not far bigger than the energy losses. For HREELS the energy of the incident electrons is therefore mostly significantly smaller than 102 eV. Considering that 102 eV electrons have a mean free path of around 1 nm (corresponds to a few monolayers), which decreases with lower energies, this automatically implies that HREELS is a surface sensitive technique. This is the reason why HREELS must be measured in reflection mode and must be implemented in ultra high vacuum (UHV). This is in contrast to Core Level EELS which operates at very high energies and can therefore also be found in transmission electron microscopes (TEM). Instrumental developments have also enabled vibrational spectroscopy to be performed in TEM. In HREELS not only the electron energy loss can be measured, often the angular distribution of electrons of a certain energy loss in reference to the specular direction gives interesting insight to the structures on a surface. Physics of HREELS As mentioned above HREELS involves an inelastic scattering process on a surface. For those processes the conservation of energy as well as the conservation of momentum's projection parallel to the surface hold: E are energies, k and q are wave vectors and G denotes a reciprocal lattice vector. One should mention at this point that for non perfect surfaces G is not in any case a well defined quantum number, what has to be considered when using the second relation. Variables subscripted with i denote values of incident electrons those subscripted with s values of scattered electrons. “||” denotes parallel to the surface. For the description of the inelastic scattering processes due to the excitation of vibrational modes of adsorbates different approaches exist. The simplest approach distinguishes between regimes of small and large scattering angles: Dipole scattering The so-called dipole scattering can be applied when the scattered beam is very near to the specular direction. In this case a macroscopic theory can be applied to explain the results. It can be approached using the so-called dielectrical theory introduced by Lucas and Šunjić of which a quantum mechanical treatment was first presented by E. Evans and D.L. Mills in the early 1970s. Alternatively there is a more unfamiliar model which only holds exactly for perfect conductors: A unit cell at the surface does not have a homogeneous surrounding, hence