Structure analysis of two-dimensional quasicrystals

Aperiodic materials, such as two-dimensional quasicrystalline structures, s how characteristic elements in transmission electron microscopy images that are closely related to structure elements in the corresponding material. A lthough the arrangement of these structure elements fundamentally influence s the properties of the two-dimensional quasicrystalline structures, it can not be determined in a satisfactory way by conventional diffraction-based m ethods. We have developed an automated procedure for analysing images obtai ned 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 analys is. It is illustrated with new tiling analyses of highly perfect decagonal Al-Co-Ni quasicrystals.