A complicated quasicrystal approximant epsilon16 predicted by the strong-reflections approach.

The structure of a complicated quasicrystal approximant epsilon(16) was predicted from a known and related quasicrystal approximant epsilon(6) by the strong-reflections approach. Electron-diffraction studies show that in reciprocal space, the positions of the strongest reflections and their intensity distributions are similar for both approximants. By applying the strong-reflections approach, the structure factors of epsilon(16) were deduced from those of the known epsilon(6) structure. Owing to the different space groups of the two structures, a shift of the phase origin had to be applied in order to obtain the phases of epsilon(16). An electron-density map of epsilon(16) was calculated by inverse Fourier transformation of the structure factors of the 256 strongest reflections. Similar to that of epsilon(6), the predicted structure of epsilon(16) contains eight layers in each unit cell, stacked along the b axis. Along the b axis, epsilon(16) is built by banana-shaped tiles and pentagonal tiles; this structure is confirmed by high-resolution transmission electron microscopy (HRTEM). The simulated precession electron-diffraction (PED) patterns from the structure model are in good agreement with the experimental ones. Epsilon(16) with 153 unique atoms in the unit cell is the most complicated approximant structure ever solved or predicted.