  The energetics of transition and noble metal (Rh, Pd, Cu) vicinal surfaces,
i.e., surface energy, step energy, kink energy and electronic interactions
between steps, is studied at 0K from electronic structure calculations in the
tight-binding approximation using a {\it s, p} and {\it d} valence orbital
basis set. Then, the surface phonon spectra of copper are investigated in the
harmonic approximation with the help of a semi-empirical inter-atomic
potential. This allows to derive the contribution of phonons at finite
temperatures to the step free energy and to the interactions between steps. The
last part is devoted to the stability of vicinal surfaces relative to faceting
with special attention to the domain of orientations (100)-(111).
Semi-empirical potentials are shown to be not realistic enough to give a
reliable answer to this problem. The results derived from electronic structure
calculations predict a variety of behaviors and, in particular, a possible
faceting into two other vicinal orientations. Finally, temperature effects are
discussed. Comparisons are made with other theoretical works and available
experiments.
