Is quasicrystal structure analysis a never-end- ing story? Why is still not a single quasicrystal structure known with the same precision and reliability as structures of regular periodic crystals? What is the state-of-the-art of structure analysis of axial quasicrystals? The present com- prehensive review summarizes the results of almost twenty years of structure analysis of axial quasicrystals and tries to answer these questions as far as possible. More than 2000 references have been screened for the most reliable structural models of pentagonal, octagonal, decagonal and dodecagonal quasicrystals. These models, mainly based on diffraction data and/or on bulk and surface microscopic images are critically discussed together with the limits and potentialities of the respective methods employed.

https://www.degruyter.com/downloadpdf/j/zkri.2004.219.issue-7/zkri.219.7.391.35643/zkri.219.7.391.35643.xml

Twenty years of structure research on quasicrystals. Part I. Pentagonal, octagonal, decagonal and dodecagonal quasicrystals

Perfect single grains of the AlPdMn icosahedral phase have been used for structure determination by X-ray and neutron diffraction. Owing to the large difference between X-ray and neutron scattering factors, information is gained on the atomic positions of the three elements. A model is proposed as deduced from a six-dimensional (6D) Patterson analysis. Six different atomic hypersurfaces are located on node and body-centre sites of the 6D lattice. The superstructure that leads to a face-centred lattice is mainly due to a strong chemical ordering, all the palladium being on the even node and odd body centre of the 6D cube. The resulting 3D structure contains icosahedral clusters similar to the external shell of the Mackay icosahedron, with two kinds of chemical decoration. The structure may also be described via a quasi-periodic stacking of fivefold planes. Each set of planes is characterized by an average chemical composition and local order. This kind of description helps in the understanding of quasi-crystal growth, formation of dislocations and dynamic properties.

http://iopscience.iop.org/article/10.1088/0953-8984/4/50/007/pdf

Neutron and X-ray single-crystal study of the AlPdMn icosahedral phase

Quasicrystalline low-friction coatings

Clusters of argon, krypton, and xenon are grown in a free jet and ionized by electron impact. The size of these clusters, (Rg)+n, extends up to n≂1000. Individual cluster sizes are mass resolved up to n≂570 in the case of Ar+n. The well known, but puzzling differences in the size distributions of Kr and Xe clusters disappear beyond n≂130, while those between Ar and Xe disappear beyond n≂220. The most pronounced ‘‘magic numbers’’ in the distributions of large cluster ions occur at n=147 (148 for Ar), 309, and 561, in striking agreement with the number of atoms required to build icosahedral clusters with 3, 4, and 5 complete coordination shells, respectively. Closure of the 6th icosahedral coordination shell is indicated by another strong intensity drop at n≂923 in the unresolved part of the spectra. Several additional intensity extrema are observed between major shell closures. A simple structural model, assuming an icosahedral core decorated by the additional atoms, accounts for these anomalies reasonably well up to n=561.

Mass spectrometric evidence for icosahedral structure in large rare gas clusters: Ar, Kr, Xe

An overview is given of the crystallography of aperiodic crystals, in particular of incommensurately modulated structures and incommensurate intergrowth compounds. The symmetry, the description of the structure and diffraction are described. An extensive discussion is given of crystallographic methods for determination of incommensurate crystal structures. A series of specific compounds is discussed in detail, covering the various ways of incommensurateness. Special attention is given to the commensurate approximation and to the superspace description of superstructures. An historical introduction and a section on the relation between physical properties and incommensurate structure are included.

Incommensurate crystal structures

A single grain of the icosahedral Al—Pd—Mn phase has been extracted from an ingot, slowly cooled from the melt by the Bridgman technique It has an approximate size of 1·5 cm × 0·5 cm × 0·5 cm and has been fully characterized by various techniques to be of perfect icosahedral symmetry

Centimetre-size single grain of the perfect Al-Pd-Mn icosahedral phase

Preliminary diffraction study of icosahedral quasi-crystals using isomorphous substitution

Neutron-diffraction data were obtained from single-phase icosahedral powder of the system ${\mathrm{Al}}_{74}$${\mathrm{Si}}_{5}$${\mathrm{Mn}}_{21}$ and its modification by isomorphous substitution on the Mn sites. Amplitudes and phase differences of the partial structure factors (${F}_{\mathrm{Al}}, {F}_{\mathrm{Mn}}$) were determined. From their ${Q}_{\ensuremath{\perp}}$ dependences, and within a strip-projection approach, phases were reconstructed. Atomic densities calculated in the physical 3D space show that Mackay icosahedra, the structural units usually invoked for quasicrystal models, do not emerge as the basic ingredients of the atomic arrangements.

Chr. Janot

Papers

Centimetre-size single grain of the perfect Al-Pd-Mn icosahedral phase

Preliminary diffraction study of icosahedral quasi-crystals using isomorphous substitution

Neutron-diffraction approach to the atomic decoration of the Al-Mn icosahedral quasicrystal.

Isomorphism in quasiperiodic structures

Diffraction approach to the structure of decagonal quasi-crystals