Comparison of semiempirical and ab-initio pseudopotential calculations of the lattice-dynamics of aluminium surfaces with He-scattering time-of-flight spectra

We report a detailed comparison of two theoretical methods for the study of the surface lattice dynamics of sp-bonded aluminum and compare the results with He-atom time-of-flight spectra for the (001), (110), and (111) surfaces of this metal. One of the theoretical methods is a semiempirical Born-von Karman scheme in which the interatomic force constants are related to central pairwise forces and also to ''angle-dependent'' interactions between triplets of atoms. The other method is an ab initio scheme in which the interatomic force constants are calculated from the electron-density response function and second-order pseudopotential perturbation theory. Both schemes require the inclusion of long-range central forces (up to ten nearest neighbors) in order to obtain converged results. In addition, the semiempirical approach must include three-body forces up to second-nearest neighbors to allow for the breakdown of the Cauchy relation, which in the ab initio method arises as a direct consequence of the volume dependence of the effective pair potential. The semiempirical approach reproduces accurately the surface phonon-dispersion curves calculated with the ab initio scheme. The leading surface force constants obtained in both methods have similar values, which provides justification for the physical significance of the semiempirical force constants. Both methods reproduce, with great accuracy, the experimental dispersion relations for the Rayleigh surface phonons, except for the case of the (110) surface. Assuming that the He atom couples only to the ion cores, the reflection coefficients calculated in both methods reproduce well the intensities of the weak resonances observed in the He time-of-flight spectra below the longitudinal edge. These structures can be explained in terms of Fano resonances.