Quantitative Adsorbate Structure Determination for Quasicrystals Using X-Ray Standing Waves

The quantitative structure determination of adsorbed species on quasicrystal surfaces has so far appeared to present insurmountable problems. The normal incidence standing x-ray wave field technique offers a simple solution, without extensive data sets or large computations. Its application to quasicrystals raises several conceptual difficulties that are related to the phase problem in x-ray diffraction. We demonstrate their solution for the case of Si atoms adsorbed on the decagonal Co-rich modification of the Al-Co-Ni quasicrystal to determine the local structure, comprising 6-atom clusters in particular hollow sites.

Figure 1

Comparison of experimental (00004) NIXSW absorption profiles from the substrate and from the adsorbed Si atoms with best-fit calculated spectra.

Figure 2

(Left) Argand diagram showing the two groups of structure factors for the $\{0\overline{1}\overline{1}01\}$ reflections, each corresponding to five different azimuthal directions. (Right) Comparison of the experimental NIXSW substrate adsorption profiles with theoretical simulations for each of these two groups of azimuths with different structure factors.

Figure 3

(a) Plan view of the outermost layer of the clean surface with two different types of local 5f sites circled. The two red (rightmost) and two blue (leftmost) circles show sites RSU and USD (see text) sites, respectively. Al and transition metal atoms are shown as yellow (open) and green (filled), respectively, and two adsorbed Si atoms are shown as red (filled) at the centers of two of the circles. (b) Simulated NIXSW profiles in each azimuthal group for absorber atoms at RSU and USD central sites. (c) Simulated NIXSW profiles in azimuthal group $B$ for absorbing atoms at 3 different RSU sites. (d) Similar simulated NIXSW profiles at different lateral displacement from the RSU site.

Figure 4

Schematic diagram of the two Si pentagonal cluster models, together with a comparison of the experimental $\{0\overline{1}\overline{1}01\}$ Si NIXSW absorption profile with simulations based on these models and a mixture of them.