M. Kobas

Large, larger, largest ‒ a family of cluster-based tantalum copper aluminides with giant unit cells. I. Structure solution and refinement

This is the first of two parts, where we report the structure determination of a novel family of cluster-based intermetallic phases of unprecedented complexity: cF444-Al(63.6)Ta(36.4) (AT-19), a = 19.1663 (1) A, V = 7040 A3, cF(5928-x)-Al(56.6)Cu(3.9)Ta(39.5), x = 20 (ACT-45), a = 45.376 (1) A, V = 93,428 A(3) and cF(23,256-x)-Al(55.4)Cu(5.4)Ta(39.1), x = 122 (ACT-71), a = 71.490 (4) A, V = 365,372 A3. The space group is F43m in all three cases. These cluster-based structures are closely related to the class of Frank-Kasper phases. It is remarkable that all three structures show the same average structure that resembles the cubic Laves phase.

Reciprocal-space imaging of a real quasicrystal. A feasibility study with PILATUS 6M

How many of the theoretically densely distributed Bragg reflections of a quasicrystal can be observed employing an area detector and synchrotron radiation? How does the reflection density of a real quasicrystal change as a function of exposure time, and what is the minimum distance between reflections? What does the distribution of diffuse scattering look like? To answer these questions, the Bragg reflection density of a perfect icosahedral quasicrystal with composition Al64Cu23Fe13 was measured employing a novel type of single-photon-counting X-ray pixel detector, PILATUS 6M, which allows noise-free data collection with the extraordinarily large dynamic range of 20 bit. The reflection density was found to be two orders of magnitude lower than expected for a strictly quasiperiodic structure. Moreover, diffuse scattering reflects significant structural disorder, breaking six-dimensional F-lattice symmetry. These findings have some implications for the interpretation of physical properties.

5D Modelling of decagonal Al–Co–Ni based on the W-approximant

A structure model for decagonal Al–Co–Ni with 8 Å periodicity along the decagonal axis is proposed. The model agrees well with available experimental information, such as electron microscopic images and three-dimensional (3D) Patterson maps calculated from X-ray-diffraction data. The model is based on a novel columnar cluster with 20 Å diameter and symmetry 5/mm building the W-approximant, Al72.5Co20Ni7.5. The proposed cluster also allows modelling of the various types of disorder and superstructures found in decagonal Al–Co–Ni.

The Disordered 8 Å Superstructure of a Decagonal Al70Co12Ni18 Quasicrystal

Diffuse inter-layers from a decagonal quasicrystal with nominal composition Al 70 Co 12 Ni 18 were investigated at 1120 K, 1070 K and 300 K. Patterson maps calculated from the inter-layers are interpreted such that the main units for correlated displacements along a 5 are structure motifs (‘clusters’) having a diameter of about 15 Å. At 1120 K, displacements of the clusters are uncorrelated along quasiperiodic directions, while they form about 42 Å-sized super-clusters at lower temperatures. The arrangement but not the inner structure of the super-clusters differs significantly at 1070 K and 300 K. Further, a first approach to the atomic structure of the 15 Å cluster is presented.

Modelling local disorder and diffuse scattering in quasicrystals

Higher-dimensional and three-dimensional techniques are complementary approaches for modelling disorder and diffuse scattering in quasicrystals. The concept of phasonic disorder allows a higher-dimensional description of disorder and calculation of diffuse intensities without knowing the atomic structure of the quasicrystal. In three-dimensional space, disorder can be analyzed by application of Patterson techniques. Local order may be modelled quantitatively without considering medium or long-range order properties of the quasicrystal. Furthermore, a priori knowledge about the structure of clusters present in the crystal can be easily utilized with Patterson methods. Potential and limitations of the techniques are discussed and demonstrated by means of experimental data.

Modelling Disorder of Decagonal Al-Co-Ni Quasicrystals

The question whether quasicrystals exist only on global average or also on a local scale entails the question about their stabilization. A detailed model of the real structure and temperature dependent structural changes should provide insight into this problem. Simulations of disordered structures on different scales (ranging from sub-clusters to clusters with 6–20 diameter) and in different dimensions (structural disorder in 3D and phasonic diffuse scattering (PDS) in 5D) were performed for decagonal Al 70 Co 12 Ni 18 . A good reproduction of the experimental diffuse scattering has been achieved.

Phasonic disorder in decagonal Al–Co–Ni

Diffuse scattering from decagonal Al70Co12Ni18 (Edagawa phase) was investigated by means of Patterson methods. Basically two systems of diffuse intensities can be observed. The first system is found in quasiperiodic layers containing Bragg reflections. Model calculations show that underlying disorder can equally well be explained as phasonic disorder in a five dimensional approach, as well as fivefold orientational disorder of clusters in three dimensions. A second set of diffuse intensities is observed in layers halfway between the Bragg layers. Disorder associated thereto shows some correlation to phasonic/orientational disorder, but a different temperature dependency of the respective disorder phenomena suggests that these correlations are accidental.