Abstract
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.
Highlights
The question regarding the exact atomic positions in quasicrystals has confused crystallographers for more than two decades since the discovery of the icosahedral quasicrystal in rapidly solidified Al–Mn alloys (Shechtman et al, 1984)
By analyzing the relationship of the structure- The structure determination in the present case is more factor amplitudes and phases of reflections from a series of complicated since the origins in space groups Pnma and B2mm are different. that are close to each other in reciprocal space have similar The structure-factor phase relations of the symmetry-related structure-factor amplitudes and phases for all the approx- reflections are not consistent in the two structures
The point group may be deduced from convergent-beam electron-diffraction (CBED) patterns
Summary
The question regarding the exact atomic positions in quasicrystals has confused crystallographers for more than two decades since the discovery of the icosahedral quasicrystal in rapidly solidified Al–Mn alloys (Shechtman et al, 1984). Only the Electrostatic potential maps can be obtained by combining the "6 structure ( known as 0) was solved by single-crystal X- structure-factor phases from HRTEM images with amplitudes ray diffraction (Boudard et al, 1996). By analyzing the relationship of the structure- The structure determination in the present case is more factor amplitudes and phases of reflections from a series of complicated since the origins in space groups Pnma (known quasicrystal approximants, we found that the strong reflections structure "6) and B2mm (unknown structure "16) are different. In order to obtain "6 and "16, additional annealing was applied for up to 69 h at 1323 K to approximants (see Table 1) have been successfully deduced Al75Rh25 and for 2 h at 1369 K to Al77Rh23 Samples for from their known related structures by the strong-reflections transmission electron microscopy observation were crushed and dispersed on holey carbon films on Cu grids. Factors from the structure model, calculating three-dimensional electron-density maps from crystal structure factors, determining peak positions from the electron-density maps and simulating HRTEM images and precession electron-diffraction patterns from the structure model
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