Approximants Of Icosahedral Quasicrystals Research Articles

Features of the Mackay Clusters with and without a Center Atom in Al Based Approximants of Icosahedral Quasicrystals

The Packing Features of Mackay and Pseudo Mackay Clusters in Al Based Approximants to Icosahedral Phases Are Surveyed. The Cubic Approximants of α-AlMnSi, AlReSi, and α-(Al,Si)CuFe Indicate Typical Mackay Clusters Composed by the Dense Icosahedral Shell Packing. On the other Hand, the Cubic Approximants of α-Alcuru and α-(Al,Si)CuFe and the Non-Cubic Approximants of Ir9Al28, χ-AlPdRe, and R-AlPdCo Shows so-Called Pseudo Mackay Clusters in which the Icosahedral Packing Feature Is Disappeared at their First Shells. The Distorted First Shells Represent a Variation of Pseudo Mackay Clusters, which Could Be Classified into Three Subgroups Based on the Symmetry.

Influence of the Chemical Composition of Alloys on the Ideal Local Order in Approximants of the Icosahedral Quasicrystals

Correlations between atomic displacements from ideal structural positions in the physical space and the atomic coordinates in the perpendicular space are revealed for approximants of icosahedral quasic� rystals. On average, the displacement magnitude increases with an increase in the distance from the center of projection on the perpendicular space; this indicates that disordering in quasicrystals is concentrated at the periphery of atomic surfaces. It is found that the chemical composition of an alloy significantly affects the specific features of distortion of the ideal structure of quasicrystals and their approximants.

Distortions of the atomic structure of 2/1 approximants of icosahedral quasicrystals

Ideal structures of several 2/1 approximants of icosahedral quasicrystals with the sp. gr. Pm $$\overline 3 $$ and Pa $$\overline 3 $$ have been constructed. It is shown that most atoms have dodecadhedral local coordination. The structural features of the crystals studied have been analyzed. It is found that displacements of atoms from ideal positions in real crystals tend to increase with an increase in the distance to the center of the approximant projection on the perpendicular space. Large displacements are generally related to the presence of very close neighbors in the ideal structure of the approximant. The importance of the investigation of approximants as a source of information about the structure of polyatomic nanoclusters is indicated.

Approximants of icosahedral quasicrystals: Atomic structure, inherent defects, and superstructural ordering

The structural features of approximants of icosahedral and decagonal quasicrystals and new unusual approximants (rhombohedral AlPd and cubic Al68Pd20Ru12) are considered. It is shown that most approximants can be described in terms of universal local ordering of atoms, in which the nearest neighbors of each atom occupy the vertices of an almost ideal dodecahedron: the so-called dodecahedral local ordering. A set of general atomic motifs in the approximants of different orders is found for quasicrystals of different types. It is shown that the dodecahedral local ordering can be easily described by the project method, in which the basis vectors directed along icosahedral threefold axes are used. Different types of defects inherent in dodecahedral local ordering are analyzed.

Search for possible structures of cubic approximants of icosahedral quasicrystals

Admissible structures of the approximants are obtained within the model of the dodecahedral local order (DLO) with due regard for the constraints imposed by the space symmetry. It is shown that the number of cubic approximants of icosahedral quasicrystals having a certain order and dodecahedral local order is finite and that the number of positions that can be occupied by the atoms from the unit cells of an approximant of each order is also finite. The corresponding estimates from above are made. In particular, it is shown that there exists only one structure for the 1/−1 approximant. It is also shown that it is possible to determine all the structures for any approximant of any order. The corresponding algorithm of the exhaustive search for these structures is suggested. The implementation of this algorithm provided the determination of all the structures of the 0/1 approximants and also some possible structures of the 0/1 and 1/1 approximants. The tables of possible approximant structures can be useful in the studies of new phases having approximant structures.

Gorsky-Bragg-Williams theory of phase transitions in the approximants of icosahedral quasicrystals

The Gorsky-Bragg-Williams (GBW) theory has been modified to describe phase transitions caused by the ordering of two kinds of atoms in the even and the odd sublattices of the structures of icosahedral quasicrystals with the dodecahedral local order (DLO) and their approximants. The modified method is exemplified by numerical calculations of such phase transitions in the structures of several simplest approximants.

ChemInform Abstract: Investigations in the Ag—Mg and Ag—Al—Mg Systems. Part 1. Models for Cubic Approximants of Icosahedral Quasicrystals in the Ag—Al—Mg System.

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Investigations in the AgMg and AgAlMg systems I. Models for cubic approximants of icosahedral quasicrystals in the AgAlMg system

In this paper models of cubic approximants in the AgAlMg system are developed and their structure chemistry is described. The analysis of two complex binary AgMg phases by means of the 13-cluster concept showed that a third component is necessary to construct quasicrystals or large approximants. The four unit cells of the quasiperiodic tiling by Levine, Steinhardt and Socolar, the rhombohedron, the rhombic dodecahedron, the rhombic icosahedron, and the rhombic triacontahedron, are used to build periodic structures. Together with an atomic decoration of the zonohedra the complete structures of a FK-type 1 1 -approximant, a MI-type 1 1 -approximant, a 2 1 -approximant, and a 3 2 -approximant are generated. The structures of the models are described. The FK-type 1 1 -approximant is isostructural to the Bergman phase Mg 32(Al,Zn) 49. The MI-type 1 1 -approximant is an almost bcc packing of Mackay icosahedra and therefore one variant of the cubic 1 1 -approximants within the I3-family. The two higher approximants contain regions which are typical of I3-phases and regions of Frank-Kasper type. The 3 2 -approximant has a large unit cell with a lattice parameter of 37.96 Å and 2828 atoms in the unit cell. But there are only six different coordination polyhedra in it. Calculated single crystal precession photographs along the twofold, threefold, and fivefold directions as well as powder diffraction patterns are shown and compared with experimental data of other authors.