Discommensurate microstructures in phason-strained octagonal quasicrystal phases of Mo-Cr-Ni

Phason-strained octagonal quasicrystal phases of Mo-Cr-Ni have been studied by electron diffraction and dark-field imaging. The shifting of some of the diffraction spots lowers the symmetry from eightfold to fourfold. Diffraction patterns of the orthogonal twofold axes show that the shifted spots are split along the fourfold axis. Discommensurations (DC’s) observed in dark-field images of split reflections are aligned perpendicular to the fourfold axis. We have found that the density of the DC’s in widely separated and adjacent regions may vary by more than 1 order of magnitude. The density of the DC’s is directly related to the separation of the splitting. The large difference in the density of DC’s in adjacent regions supports the interpretation that the DC’s in the Mo-Cr-Ni phases are due to the ordering of atomic species in the quasilattice. Our observations are consistent with some of the results of the two-dimensional octagonal random tiling model of Li, Park, and Widom.