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.