Pushing the limits of crystallography.

A very serious concern of scientists dealing with crystal structure refinement, including theoretical research, pertains to the characteristic bias in calculated measured diffraction intensities, observed particularly in the weak reflection regime. This bias is here attributed to corrective factors for phonons and, even more distinctly, phasons, and credible proof supporting this assumption is given. The lack of a consistent theory of phasons in quasicrystals significantly contributes to this characteristic bias.

Superior room-temperature ductility of typically brittle quasicrystals at small sizes.

The discovery of quasicrystals three decades ago unveiled a class of matter that exhibits long-range order but lacks translational periodicity. Owing to their unique structures, quasicrystals possess many unusual properties. However, a well-known bottleneck that impedes their widespread application is their intrinsic brittleness: plastic deformation has been found to only be possible at high temperatures or under hydrostatic pressures, and their deformation mechanism at low temperatures is still unclear.

Generalized Penrose tiling as a quasilattice for decagonal quasicrystal structure analysis.

The generalized Penrose tiling is, in fact, an infinite set of decagonal tilings. It is constructed with the same rhombs (thick and thin) as the conventional Penrose tiling, but its long-range order depends on the so-called shift parameter (s ∈ 〈0; 1)). The structure factor is derived for the arbitrarily decorated generalized Penrose tiling within the average unit cell approach.

High-temperature structural study of decagonal Al-Cu-Rh.

The structure of decagonal Al-Cu-Rh has been studied as a function of temperature by in-situ single-crystal X-ray diffraction in order to contribute to the discussion on energy or entropy stabilization of quasicrystals. The experiments were performed at 293, 1223, 1153, 1083 and 1013 K. A common subset of 1460 unique reflections was used for the comparative structure refinements at each temperature.

What periodicities can be found in diffraction patterns of quasicrystals?

The structure of quasicrystals is aperiodic. Their diffraction patterns, however, can be considered periodic. They are composed solely of series of peaks which exhibit a fully periodic arrangement in reciprocal space.

Comparative structural study of decagonal quasicrystals in the systems Al-Cu-Me (Me = Co, Rh, Ir).

A comparative single-crystal X-ray diffraction structure analysis of the family of Al-Cu-Me (Me = Co, Rh and Ir) decagonal quasicrystals is presented. In contrast to decagonal Al-Cu-Co, the other two decagonal phases do not show any structured disorder diffuse scattering indicating a higher degree of order. Furthermore, the atomic sites of Rh and Ir can be clearly identified, while Cu and Co cannot be distinguished because of their too similar atomic scattering factors.