Phason-flips refinement of and multiple-scattering correction for the d-AlCuRh quasicrystal

The origin of the characteristic bias observed in a logarithmic plot of the calculated and measured intensities of diffraction peaks for quasicrystals has not yet been established. Structure refinement requires the inclusion of weak reflections; however, no structural model can properly describe their intensities. For this reason, detailed information about the atomic structure is not available. In this article, a possible cause for the characteristic bias, namely the lattice phason flip, is investigated. The derivation of the structure factor for a tiling with inherent phason flips is given and is tested for the AlCuRh decagonal quasicrystal. Although an improvement of the model is reported, the bias remains. A simple correction term involving a redistribution of the intensities of the peaks was tested, and successfully removed the bias from the diffraction data. This new correction is purely empirical and only mimics the effect of multiple scattering. A comprehensive study of multiple scattering requires detailed knowledge of the diffraction experiment geometry.