Quasicrystal structures studied by high-resolution transmission electron microscopy

Structural investigations, using a transmission electron microscope (TEM), have been highly beneficial for the analysis of icosahedral and decagonal quasicrystals. Many structural properties of quasicrystals can be recognized and quantified by electron diffraction patterns alone. Nevertheless, a much more complete understanding of the real structure of quasicrystals can be achieved by the analysis of high-resolution transmission electron microscopy (HRTEM) images. Compared to diffraction- based techniques, HRTEM offers several advantages, however, special points which must be considered in the interpretation of HRTEM images will be discussed. For the case of 2-dimensional quasicrystals, e.g. the decagonal phases, HRTEM images can directly reveal the (projected) atomic structure as well as the long-range translational order. This is possible because 2-dimensional quasicrystals are periodic along one direction and the atoms thus form periodic atom columns as in crystalline materials. Therefore, the imaging theory established for crystals can similarly be applied to electron micrographs of 2-dimensional quasicrystals taken with the electron beam parallel to the unique periodic axis. It is evident, that possible limitations due to projection effects along the electron beam direction have to be considered in the interpretation of the images. HRTEM images of decagonal quasicrystals have frequently been employed to differentiate between disorder and order, i.e., to infer the difference between a random and perfect quasiperiodic tiling, respectively.