Multilayer relaxation of the Al(210) surface

The surface structure of Al(210) has been determined by means of a systematic minimization of the discrepancy between experimental low-energy electron diffraction intensity-energy spectra and spectra calculated using multiple-scattering theory, as a function of the structural and nonstructural variables of the calculations. The experimental data base consists of intensity-energy spectra for 14 symmetry-inequivalent diffracted beams, measured at normal incidence and at 135 K in the energy range 40--340 eV. The surface structure is found to exhibit an oscillatory, multilayer relaxation. The relaxations {Δ}dᵢ and {Δ}rᵢ of the first five interlayer spacings and registries with respect to the corresponding bulk values are determined to be {Δ}d₁=-(16±{}2)%, {Δ}d₂=-(1±{}3)%, {Δ}d₃=+(9 ±{}3)%, {Δ}d₄=-(4±{}4)%, {Δ}d₅=-(1±{}5)%, and {Δ}r₁=(0±{}3)%, {Δ}r₂=-(3±{}3)%, {Δ}r₃=+(2±{}3)%, {Δ}r₄=-(2±{}4)%, {Δ}r₅=-(1±{}5)%.These results are in qualitative agreement with the results of pseudopotential calculations of the surface structure of Al(210) by Barnett, Landman, and Cleveland [Phys. Rev. Lett. 51, 1359 (1983)] in the sense that the signs of the relaxations, where + indicates an expansion and - a contraction, are the same for each of the relaxations. Furthermore, the present results are in near-quantitative agreement with the relaxations calculated by Jiang, Marcus, and Jona [Solid State Commun. 59, 275 (1986)] and F. Jona (private communication), using a simple electrostatic, point-ion--frozen-background model. The present results for Al(210) are discussed in the context of previous experimental studies of the multilayer relaxation of open metal surfaces, which are reviewed with a view to the identification of trends in the observed phenomena. In particular, the relaxation behavior of the first six surfaces of Al and Fe are discussed in the framework of the point-ion--frozen-background model. It is demonstrated that the relaxation trends can be predicted by simple considerations of the electrostatic forces on the layers of the unrelaxed surface structures, thus providing the basis for a simple, intuitive description of multilayer relaxation.