The electronic properties of a large number of icosahedral-crystal systems have been studied experimentally. These systems include alloys of the simple metals and those that contain transition metals. Some of the icosahedral phases (i-phases) are thermally stable while others are metastable; and their degree of structural order varies within each of the stability classes. The importance of sample quality to the exposition of intrinsic properties is emphasized, particularly for systems with high resistivities. As a result, experiments on single-phase samples from the diversity of systems studied have shed light on the physics of quasicrystalline alloys. Comparison made with the approximant and amorphous phases have provided important insights to the understanding of quasicrystallinity, randomness, and atomic-potential effects on electronic properties. Reduction in the electronic density of states (DOS) at the Fermi level relative to the free-electronic value is observed in the stable i-phase syste...

Electronic properties of quasicrystals an experimental review

Electron microscopy observations of the newly discovered icosahedral phase in the Al‐Cu‐Fe ternary system show a domain structure as expected from a group‐subgroup formal decomposition from a primitive six-dimensional (6D) hypercubic unit cell to a face‐centred one with twice the lattice parameter, as suggested by Ebalard and Spaepen. The structure of Al65Cu20Fe15 can be seen as an ordered F superstructure of the usual primitive quasilattice with, at least, two motifs in the 6D representation. The smoothness of the observed antiphase boundaries and the relative weak intensities of the superstructure reflections suggest that the ordered motifs should share many geometrical features. A possibility could be that at least one of the orbits of a given atomic species arranges in space according to a 6D primitive skeleton and chemical ordering occurs on the remaining orbits.

Antiphase domains in icosahedral Al‐Cu‐Fe alloy

Two distinct orthorhombic phases form in the Al65Cu20Fe10Cr5 and Al63Cu17.5Co17.5Si2 alloys and represent an important class of approximant structures of the decagonal phase. Their structural units (convex pentagon, concave pentagon and rhombus) as revealed by high resolution electron microscopy (HREM) images can also be used to construct the Penrose tiling. We propose that one single orthorhombic phase may not be able to account for the transformation towards the high-temperature decagonal phase. For this transformation to be possible, the microcrystalline structure must satisfy a delicate balance among building blocks that is required to achieve a Penrose tiling. Two concepts are distinguished: the approximant phase and the approximation state. An analysis of the orientation relationships between a CsCl type of structure and orthorhombic phases suggests that such orthorhombic phases are three-dimensional superstruc-tures based on the CsCl unit cell. Furthermore, this relationship leads to the d...

The orthorhombic approximant phases of the decagonal phase

Neutron diffraction data were obtained from a single-phase icosahedral powder of the system Al74Si5Mn21 and its modification by isomorphous substitution on the Mn sites Amplitudes and phase differences of the partial structure factors (FAl, FMn) were determined From their Qperpendicular to -dependences within a strip-projection approach, phases were reconstructed Atomic densities were then calculated in the physical space and in the six-dimensional periodic lattice, resulting in the first experimentally deduced decoration of the quasi-periodic network The Mackay icosahedron no longer appears as the necessary basic structural unit In six dimensions the structure has a simple CsCl-like space-group symmetry

http://iopscience.iop.org/article/10.1088/0953-8984/1/6/001/pdf

Icosahedral crystals: neutron diffraction tells you where the atoms are

Using both powder and single crystal samples, neutron and X-ray diffraction data were obtained with quasicrystals of the AlLiCu system. Isotopic substitution on the Li and Cu atomic sites allowed amplitudes and phase shift of the partial structure factors to be determined. Using a high-dimensional crystallography approach results in the phases to be reconstructed and atomic densities were calculated. The six-dimensional periodic structure appeared as a primitive hypercubic lattice with mid-edge and vertex Al/Cu atomic surfaces plus a Li bodycentre site. The major drawbacks of the experimental approach are then bypassed by modelling details of the six-dimensional structure, still in agreement with diffraction data. The related three-dimensional quasiperiodic structure can be described in terms of connected clusters or, alternatively, families of atomic planes. Comparison with the structure of the crystalline R-phase is of interest.

https://iopscience.iop.org/article/10.1088/0953-8984/3/1/001/pdf

Atomic structure of the icosahedral Al-Li-Cu quasicrystal

X-ray diffraction results on several uniformly oriented quasicrystals of an Al-Li-Cu alloy are reported. By means of long exposed monochromatic Laue and precession photographs, we confirm the parity rules for a primitive icosahedral quasilattice. Moreover, for the first time, complex diffuse scattering related to the icosahedral symmetry has been observed. Spherical shells of diffuse scattering appear in reciprocal space : the centres of the most intense shells are located on the five-fold axes.

https://hal.archives-ouvertes.fr/jpa-00210562/document

X-ray diffraction study on uniformly oriented quasicrystals

Dodecahedral particles of Al-Fe-Cu alloy, obtained by slow solidification, have been studied by X-ray diffraction and transmission electron microscopy. Their peculiar microcrystalline structure of overall pseudo-icosahedral symmetry, previously identified by high resolution imaging and electron diffraction, is shown to be conformed by indexing of X-ray precession patterns. The crystal system is rhombohedral with cell parameters a = 32.16 A and α = 36°. The space tiling problem of mean perfect icosahedral order, using only one rhombohedral cell, is discussed on the basis of some preliminary investigations in high resolution electron microscopy.

https://hal.archives-ouvertes.fr/jpa-00212396/document

X-ray and TEM studies of Al-Fe-Cu dodecahedral particles : characterization of their microcrystalline state of pseudo-icosahedral symmetry

We report X-ray diffraction results on a 300 μ single quasi crystal of AlLiCu. The diffraction peaks are consisted with the icosahedral symmetry. Moreover, for the first time, complex localized diffuse scattering related to the quasi crystalline symmetry have been observed Analyse des cliches de diffraction. En plus des taches de diffraction, correspondant bien a une symetrie icosaedrique, des diffusions diffuses localisees complexes mais respectant la symetrie de l'etat quasi-cristallin ont ete mises en evidence

Diffraction des rayons X par un mono-quasicristal AlLiCu

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X-ray diffraction study on uniformly oriented quasicrystals

X-ray and TEM studies of Al-Fe-Cu dodecahedral particles : characterization of their microcrystalline state of pseudo-icosahedral symmetry

Diffraction des rayons X par un mono-quasicristal AlLiCu