A three-dimensional structure model of eight-fold quasicrystals obtained by high-resolution electron microscopy

Abstract

A structure model of octagonal quasicrystals has been obtained using electron microscopy and crystallographic image processing. Octagonal quasicrystals in a rapidly solidified Mn-Si-Al alloy were studied by high-resolution electron microscopy (HREM). HREM images taken along the main symmetry directions, that is the eightfold and the two twofold axes were combined into a density map. The symmetry of the model is 8₄/mmc. Within each unit-cell repeat of 0.63 nm along the eightfold direction there are four layers. Alternating layers have eightfold and fourfold symmetry. Projections of the model match the HREM images. The shortest interatomic distances, 0.24 nm, and the density of 6.9 g cm⁻³ for the model are in good agreement with expected values.