A complicated quasicrystal approximant ∊(16) predicted by the strong-reflections approach

The structure of a complicated quasicrystal approximant ∊(16) was predicted from a known and related quasicrystal approximant ∊(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 ∊(16) were deduced from those of the known ∊(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 ∊(16). An electron-density map of ∊(16) was calculated by inverse Fourier transformation of the structure factors of the 256 strongest reflections. Similar to that of ∊(6), the predicted structure of ∊(16) contains eight layers in each unit cell, stacked along the b axis. Along the b axis, ∊(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. ∊(16) with 153 unique atoms in the unit cell is the most complicated approximant structure ever solved or predicted.