The interplay of the atomic structure and phonon spectra in a variety of two dimensional phases forming during submonolayer Pb adsorption on a Cu(001) surface has been investigated using embedded atom method interatomic interaction potentials. Complementary calculations of the equilibrium atomic structure of these phases were performed using density functional theory. It has been shown that the dynamic stability of the Pb/Cu(001) structures increases with increasing the coverage from 0.375 ML to ultimately 0.6 ML, when a dense Pb layer is formed. The increase of the coverage also results in progressive shift of the Rayleigh mode of the copper surface to higher energy and the appearance of new mixed adsorbate-substrate vibration modes.
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