Lattice relaxation at an aluminum surface: Self-consistent linear-electronic-response approach

Abstract

We present a calculation of multilayer relaxation at the (110) surface of aluminum based on the numerical minimization of the total energy of a metal slab. The total energy is evaluated with use of pseudopotential perturbation theory. The electron-ion interaction gives rise to two contributions of electronic origin to the total energy. These are related to spatial variations of the electron density, and to the screening of the ions by the mobile sp electrons. Both electronic energies are evaluated self-consistently within the perturbation-theoretic framework. The electron-density profile at the surface (the Lang-Kohn profile), and the linear-density-response function of the conduction electrons, are evaluated in the local-density approximation of density-functional theory. We discuss the physics of the forces driving the relaxation, with emphasis on the range of these forces. Electronic screening is shown to play a fundamental role in the multilayer relaxation process, both quantitatively and qualitatively (it gives rise to long-range-effects). Numerical results for the interplanar spacings in the relaxed crystal are given for a 19-layer film. Agreement with the experimental values of the first few interplanar spacings is fair. It is suggested that the experimental analysis be carried out letting a large enough number of lattice planes participate on an equal footing in the search for the relaxed structure. Comparison is made with the theoretical work of Barnett, Landman, and Cleveland and of Ho and Bohnen.