The phonon spectra and vibrational thermodynamical properties of Cu vicinal surfaces

We present a many-body empirical potential giving the total energy in Cu crystals, the transferability of which is proven by comparing with experiments the phonon band structure for the bulk and the three low index surfaces. After the determination of the multilayer relaxation of a set of vicinal surfaces, we investigate their vibrational spectra by means of their projected phonon band structure and the local spectral densities of states corresponding to a given value of k(//) which are discussed in relation with recent experiments. Finally, the root mean square displacement of specific atoms for low and high index surfaces are compared with the bulk one and the contribution of the vibrations to the free energy of steps is calculated as a function of temperature and of the terrace width for the p(100) x (111) and p(111) x (100) surfaces (2 less than or equal to p less than or equal to 7). It is found that for these vicinal surfaces the step-step interactions mediated by phonons are attractive and may have the same order of magnitude as the other interactions. (C) 2002 Elsevier Science B.V. All rights reserved.