Theoretical Study of the Vibrational Properties of a (117)F.C.C. Surface
The phonon dispersion relations for the (117) face of a F.C.C. crystal have been calculated by the method of generating coefficients for Green functions. The model takes account only of central forces between nearest neighbour atoms.
The unit cell contains four atoms, two are located on the terrace, the other ones being located respectively on the top and the bottom of the step. The waves propagating in the direction normal to the step are decoupled into transverse and sagital vibrations. Each vibrational mode gives a surface phonon branch and two very well defined resonant branches. The different polarization amplitudes for each atom of the surface cell are determined.
These results can be qualitatively accounted for by three times folding the dispersion realtion for the (100) face of F.C.C. crystal which is the crystallographic configuration of the (117) terrace.