Structure analysis of two-dimensional quasicrystals

Aperiodic materials, such as two-dimensional quasicrystalline structures, show characteristic elements in transmission electron microscopy images that are closely related to structure elements in the corresponding material. Although the arrangement of these structure elements fundamentally influences the properties of the two-dimensional quasicrystalline structures, it cannot be determined in a satisfactory way by conventional diffraction-based methods. We have developed an automated procedure for analysing images obtained by high-resolution transmission electron microscopy. The method, which is based on image processing, determines the two-dimensional arrangement of the characteristic features and enables subsequent statistical data analysis. It is illustrated with new tiling analyses of highly perfect decagonal Al-Co-Ni quasicrystals.