Diffraction pattern simulations of quasiperiodic structures

Abstract

The recent experimental and theoretical interest in quasiperiodic structures has been inspired by Shechtman et al.'s discovery1 of precipitates in rapidly cooled Al–Mn, Al–Fe and Al–Cr alloys which exhibit m35 icosahedral point symmetry. Subsequent work has shown how diffraction patterns with the same symmetries as those observed experimentally can be generated from model frameworks of linked icosahedra2,3 and of three-dimensional Penrose tilings (3DPT)4,5, in which space is filled aperiodically by prolate and oblate rhombohedra with equal sides and angles of ±cos−1 (1/√5) (ref. 6). Here we demonstrate that the computed intensities of the diffracted beams of kinematical electron and X-ray diffraction patterns of quasicrystals are sensitive to the choice of atomic decoration of the underlying 3DPT. Significantly, we have been unable to find a unique atomic decoration of the prolate and oblate rhombohedra which can account fully for the experimental diffraction data. We discuss the implications of this in the light of experimental data on the lack of chemical homogeneity of the icosadredral phases.