Multiple-beam x-ray-diffraction studies of decagonal quasicrystals

The problem under investigation is the structure of decagonal quasicrystals: the issue of centrosymmetry, and the effect of stoichiometry and composition. Phase information on structure factors is an important ingredient for structural investigations and the method used in this work is based on multiple Bragg scattering, a situation in which two or more Bragg reflections are simultaneously excited in the crystal. Three different but similar decagonal quasicrystals are investigated in this work: Al-Cu-Co, Al-Ni-Fe, and Al-Ni-Co. The lattice constants of all three quasicrystals are surprisingly identical. There an, however, differences in their structures. These differences are manifested in the phases of the Bragg reflections involved. What is measured, in a three-beam experiment, is the triplet invariant delta = phi H + phi(P-H) - phi(p), a linear combination of phases. The main reflection is called P, the simultaneous reflection is H, and P-H is the coupling reflection. The structural differences between these seemingly isomorphous quasicrystals are evidenced by the different values of the triplet invariants for the same main and simultaneous reflections. In all cases we obtain delta values far from 0 degrees and 180 degrees, the only values compatible with centrosymmetric structures. We conclude that the decagonal quasicrystals investigated in this work are not centrosymmetric.