QUANTITATIVE-EVALUATION OF PHASONS IN OCTAGONAL QUASI-CRYSTALS BY HIGH-RESOLUTION ELECTRON-MICROSCOPY

Thanks to the presence of ordered domains, the electron diffraction sp ots in the eightfold electron diffraction pattern of the Mn80Si15Al5 o ctagonal quasicrystal can be classified into basic and superlattice re flections. Using only the basic components in the Fourier transform of a high-resolution electron microscopic image to reconstruct its inver se Fourier transform, a well defined, eightfold, aperiodic distributio n of image points results, from which an eightfold quasilattice consis ting of squares and 45 degrees rhombi can be obtained. Primary and sec ondary Ammann lines are drawn on these square and rhombus tiles and th ere are 66 jags in the primary Ammann lines and 34 jags in the seconda ry lines. These correspond to about 5% tiling mistakes, with respect t o both vertex and edge matching violations, in this octagonal aperiodi c tiling. Thus the phasons in a phason-perturbed quasicrystal can be q uantitatively evaluated from its image-processed high-resolution elect ron microscopic image.