We investigate the atomic structure of the fivefold surface of an icosahedral AlCu-Fe alloy, using scanning tunneling microscopy (STM) imaging and a special dynamical low energy-electron diffraction (LEED) method. STM indicates that the step heights adopt (primarily) two values in the ratio of tau, but the spatial distribution of these two values does not follow a Fibonacci sequence, thus breaking the ideal bulk-like quasicrystalline layer stacking order perpendicular to the surface. The appearance of screw dislocations in the STM images is another indication of imperfect quasicrystallinity. On the other hand, the LEED analysis, which was successfully applied to Al-Pd-Mn in a previous study, is equally successful for Al-Cu-Fe. Similar structural features are found for both materials, in particular for interlayer relaxations and surface terminations. Although there is no structural periodicity, there are clear atomic planes in the bulk of the quasicrystal, some of which can be grouped in recurring patterns. The surface tends to form between these grouped layers in both alloys. For Al-Cu-Fe, the step heights measured by STM are consistent with the thicknesses of the grouped layers favored in LEED. These results suggest that the fivefold Al-Cu-Fe surface exhibits a quasicrystalline layering structure, but with stacking defects.

Low-energy electron diffraction intensity vs voltage ͑LEED I-V͒ measurements and analysis are used to determine the multilayer surface relaxation of W͑110͒. Measurements and analysis are presented for both flat and vicinal surfaces, demonstrating that surface roughness leads to only small errors in LEED structure determinations. Flat, clean W͑110͒ exhibits first-(d 12) and second-(d 23) layer relaxations of Ϫ3.0Ϯ1.3% and ϩ0.2Ϯ1.3%, respectively, relative to the bulk lattice spacing d 0 ϭ2.237 Å. This experimentally determined surface relaxation of W͑110͒ is compatible with a recent combined density-functional theory calculation and LEED study ͓M.