Distinguishing quasiperiodic from random order in high-resolution TEM images

We investigate the question of whether an experimental tiling that was constructed by superimposition onto a high-resolution transmission electron microscopy (HRTEM) image belongs to the ideal quasiperiodic or to the random tiling class. To answer this question, statistical arguments and our method are applied to different decagonal Al-Co-Ni phases. This method allows us to distinguish between both classes even if tiling errors and poor statistics are involved. A possible stabilization mechanism is discussed for a high-temperature phase that is ideally quasiperiodic.