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

Abstract

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.

Statistical Approach to Diffraction of Periodic and Non-Periodic Crystals—Review

“…Such concept, with potential application to structure refinement of complex systems, was proposed in [25] with all details given. As a confirmation of utility of the statistical method applied to arbitrary decorated structure numerous decagonal quasicrystals modeled by the (rhombic) Penrose tiling were successfully refined in [33][34][35]. In addition, for an icosahedral quasicrystal modeled by the Ammann tiling the structure factor for arbitrary decoration and the so-called simple decoration scheme was derived and discussed in [23,36].…”

“…The general formula for Debye-Waller factor is exp[−k 2 σ 2 ], where k is the scattering vector and σ is a variance of the distribution of atomic arrangement (both in physical or perpendicular space). Small peaks, which usually have large perpendicular-space component of the scattering vector in superspace description (see e.g., [35] and supplemental materials), are biased in the modern refinement results. We attributed the latter to the improper corrective factor for phasons, which is standard (exponential) Debye-Waller factor, commonly used in structure refinements of quasicrystals, and proposed a novel method of analysis of phononic and even more phasonic effects within statistical method.…”

Phononic and Phasonic Debye-Waller Factors for 1D Quasicrystals

“…The latter method was already applied to the Fibonacci chain in our previous paper [21]. It appears that the number of parameters required is not high, several (6)(7)(8)(9) parameters are fully enough to restore the shape of the average unit cell satisfactorily well.…”

“…Including weak reflections in a refinement procedure frequently makes the refinement results worse which can be seen in many refinements (see e.g. [7][8][9]). We show how to improve the use of D-W factor for phasons and phonons in quasicrystals.…”

Structure Model for Icosahedral Quasicrystal Based on Ammann Tiling

“…It was also shown that the shape of the AUC is directly related to the shape of the atomic surface in the higher-dimensional description [9]. The statistical approach has already been successfully applied to decagonal AlNiCo and AlCuTM (TM = Co, Ir, Rh) phases [10,11]. The starting structural model for i-QCs within the statistical approach is the 3D Ammann tiling (AT), also called Ammann KramerNeri tiling, which is just the generalization of the rhombic Penrose tiling to 3D [12].…”