Vibrations in submonolayer structures of Na on Cu(111)

We present the results of a comparative study of the equilibrium crystal structure and vibrational properties of the Na∕Cu(111) system at coverages up to monolayer saturation. The calculations are performed with interaction potentials from the embedded-atom method. The following ordered structures are considered: p(3×3), p(2×2), (√3×√3)30^∘, and (3∕2×3∕2). The surface relaxation, phonon dispersion, and polarization of vibrational modes for the adsorbate and substrate atoms as well as the local density of states are discussed. It is found that the bond length between an adsorbate and the nearest-neighbor substrate atom slightly increases with increasing coverage. Adsorption of sodium also results in a small rumpling in two upper substrate layers. The mode associated with adatom-substrate stretch vibrations was obtained in our calculation at about 220.3em0exmeV for all the structures considered. The strength of this mode decreases with increasing coverage in accordance with the experiment. On the other hand, we find that the frustrated translation mode frequency of sodium on Cu(111) is strongly coverage dependent.