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. The structure models, derived from charge-flipping/low-density elimination results, were refined within the tiling-decoration method but also discussed in the five-dimensional embedding approach. The basic structural building units of the closely related structures are decagonal clusters with 33 Å diameter, which are consistent with the available electron-microscopic images. The refined structure models agree very well with the experimental data.

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. Here, we report that typically brittle quasicrystals can exhibit remarkable ductility of over 50% strains and high strengths of ∼4.5 GPa at room temperature and sub-micrometer scales. In contrast to the generally accepted dominant deformation mechanism in quasicrystals—dislocation climb, our observation suggests that dislocation glide may govern plasticity under high-stress and low-temperature conditions. The ability to plastically deform quasicrystals at room temperature should lead to an improved understanding of their deformation mechanism and application in small-scale devices.

The physical space approach to quasicrystal structure refinement [1] will be presented as an alternative to the commonly used higher-dimensional approach. This method allows a purely 3D optimization of a quasicrystalline structure. Its advantages and limitations will be discussed based on three examples of structure refinement of decagonal quasicrystals: Al-Cu-Co, Al-Cu-Rh, Al-Cu-Ir. The synchrotron diffraction experiments were performed at the Swiss-Norwegian beam line at ESRF, Grenoble, France. All three decagonal phases show~4 Å periodicity (two atomic layers per period). A computer program SUPERFLIP based on the charge-flipping algorithm was used for the initial phasing of the data and obtaining the electron density maps. These maps were used for deriving Rhombic Penrose Tiling (RPT) models with a tiling edge-length of~17 Å. The atomic decoration of the unit tiles is based on the~33 Å cluster derived from the HRTEM images of the Al-Cu-Rh and proposed by Hiraga & Oshuna. The decoration of RPT with Hiraga clusters is such, that the cluster centers form the Pentagonal Penrose Tiling of an edge-length of~20 Å. The Hiraga cluster can be considered as a supercluster built of 5 clusters proposed by Deloudi et al. based on the HRTEM images of the Al-Cu-Co phase. Such a structure explains well the strong Patterson maxima of~12,~20 and~33 Å occurring for all three phases and corresponding to the typical inter-cluster distances. Our work shows the first solution of a quasicrystal as a ternary alloy (Rh and Ir phases). The final R-values are reasonable, the structure is consistent with the available HRTEM images and the chemical composition agrees well with the EDX measurements. The reconstructions of the atomic surfaces for the refined structures will also be presented and compared to the ones found in the literature for other decagonal quasicrystal refinements.

A very serious concern of scientists dealing with crystal structure refinement, including theoretical research, pertains to the characteristic bias in calculated versus 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. It is shown that the most commonly used exponential Debye-Waller factor for phasons fails in the case of quasicrystals, and a novel method of calculating the correction factor within a statistical approach is proposed. The results obtained for model quasiperiodic systems show that phasonic perturbations can be successfully described and refinement fits of high quality are achievable. The standard Debye-Waller factor for phonons works equally well for periodic and quasiperiodic crystals, and it is only in the last steps of a refinement that different correction functions need to be applied to improve the fit quality.