The phonons of the Al surfaces: comparison between semi-empirical and ab-initio calculations

We report inelastic He-atom surface scattering data for the low-index surfaces of aluminum. The experimental data are analyzed by using a semi-empirical Born-von Karman model in which both two-body and three-body interactions are taken into account and by using an ab initio pseudopotential approach. Our analysis shows that the semi-empirical model containing long-range forces agrees with great accuracy with the pseudopotential calculations for what concerns both the range of the interactions and the dispersion of the surface vibrational modes. The calculations of the reflection coefficients allow us to study the nature of the weak resonances observed in the time-of-flight spectra. These structures are related to a picking up of modes with polarization vector normal to the surface due to the modification introduced by the surface on the entire force field. Our analysis of Al proves that for simple metals an accurate semi-empirical model can reproduce with great accuracy both the surface lattice dynamics, without introducing new free parameters in the surface interatomic potential, as well as an ab initio pseudopotential calculation.