Quantitative evaluation of phasons in octagonal quasicrystals by high-resolution electron microscopy

Abstract

Thanks to the presence of ordered domains, the electron diffraction spots in the eightfold electron diffraction pattern of the Mn 80Si 15Al 5 octagonal quasicrystal can be classified into basic and superlattice reflections. Using only the basic components in the Fourier transform of a high-resolution electron microscopic image to reconstruct its inverse Fourier transform, a well defined, eightfold, aperiodic distribution of image points results, from which an eightfold quasilattice consisting of squares and 45° rhombi can be obtained. Primary and secondary Ammann lines are drawn on these square and rhombus tiles and there are 66 jags in the primary Ammann lines and 34 jags in the secondary lines. These correspond to about 5% tiling mistakes, with respect to both vertex and edge matching violations, in this octagonal aperiodic tiling. Thus the phasons in a phason-perturbed quasicrystal can be quantitatively evaluated from its image-processed high-resolution electron microscopic image.