Icosahedral quasicrystals

Ch. Dilger, R. Mikulla, J. Roth, H.-R. Trebin. Simulation of shear stress in icosahedral quasicrystals. Phil Mag A 75 425, 1997. 

Giant Aluminum Clusters with Shell Structures Consisting of Nested Polyhedra Pieces of Icosahedral Quasicrystals... 

Icosahedral quasicrystals. Many icosahedral phases (both stable and metastable) have been identified in several systems, mainly Al-based but also Mg-based, Ti-based, etc. 

According to Steurer (1996) two main groups of icosahedral quasicrystals can be considered. 

Figure 11. Icosahedral quasicrystals in a quenched Al/Mn sample. Sample by Agnes Csanady (Budapest) and scanning electron micrograph by Hans-Ude Nissen (Zurich). Reproduced by permission.

At present, a number of quasi-crystalline alloys with icosahedral, decagonal, and octagonal symmetry are synthesized by different methods. The quasicrystalline form of the solids turned out to be widespread in a great extent. The absence of the translation symmetry and the presence of numerous interstitial sites of the different types in the structure of icosahedral quasicrystals makes some of them interesting objects for hydride chemistry. We cannot wait for any sensational discoveries here, as the general laws of M-H interaction do not depend on matrix structure. However, encouraging results were obtained for icosahedral Ti45Zr38Nii7... 

Figure 9-64. Quasicrystals (a-b) Flower-like icosahedral quasicrystal in a quenched Al/Mn sample (from Csanady et al.) [152] (c) Pentagonal dodecahedron in quasicrystalline Al/Cu/Ru obtained by slow cooling from melt (courtesy of H.-U. Nissen, Zurich) [153],...

L. Pauling, Icosahedral quasicrystals are twins of cubic crystals containing large icosa-hedral clusters of atoms The 1012-atom primitive cubic structure of Al6CuLi3, the C-phase of Al37Cu3Li2iMg3, and GaMg2Zn3. Proc. Natl. Acad. Sd. (USA) 85, 3666-3669 (1988). 

L. Pauling, Icosahedral quasicrystals of intermetallic compounds are icosahedral twins of cubic crystals of three kinds, consisting of large (about 5000 atoms) icosahedral complexes in either a cubic body-centered or a cubic face-centered arrangement or smaller (about 1350 atoms) icosahedral complexes in the /2-tungsten arrangement. Proc. Natl. Acad. Sci. (USA) 86, 8595-8599 (1989). 

It turns out that icosahedral coordination (Z = 12), and other coordination polytetrahedra with coordination numbers Z= 14, 15, and 16, are a major component of some liquid stmctures, more stable than a close-packed one, as was demonstrated by F. C. Frank and J. Kasper. When these liquid stmctures are rapidly solidified, the resultant stmcture has icoshedra threaded by a network of wedge discUnations, having resisted reconstmction into crystaUine units with three-dimensional translational periodicity (Mackay, 1985 TumbuU, 2000). Stable ternary intermetaUic icosahedral quasicrystals... 

For an isotropic medium (e.g. cubic crystal or icosahedral quasicrystal), D is... 

Quasicrystals are solid materials exhibiting diffraction patterns with apparently sharp spots containing symmetry axes such as fivefold or eightfold axes, which are incompatible with the three-dimensional periodicity associated with crystal lattices. Many such materials are aluminum alloys, which exhibit diffraction patterns with fivefold symmetry axes such materials are called icosahedral quasicrystals. " Such quasicrystals " may be defined to have delta functions in their Fourier transforms, but their local point symmetries are incompatible with the periodic order of traditional crystallography. Structures with fivefold symmetry exhibit quasiperiodicity in two dimensions and periodicity in the third. Quasicrystals are thus seen to exhibit a lower order than in true crystals but a higher order than truly amorphous materials. 

There are several classes of icosahedral quasicrystals with diverse compositions. The following classes are the most important ... 

Note that the low-temperature structure is neither a quasicrystal nor an icosahedral glass. Given the molecular symmetry, one might have predicted the latter, whereas icosahedral quasicrystals require two distinct structural units to satisfy space filling. While the precise energetic requirements for crystal versus icosahedral glass formation are not understood, it seems likely that the structural order at low T is driven both by a preference for close packing and,by local orientational order. 

We studied the structure of the bulk terminations according to a model M ) of icosahedral quasicrystals of an F-phase (see Refs. [3-5]). The model in a physical space is based on an icosahedral tiling [6] projected from the Dg,... 

The model is a superposition of three icosahedral quasilattices, q, a and b, of atomic positions in the physical space E, as explained in A model of icosahedral quasicrystals based on the tiling 7 (2r) , These are defined in the Table 12-1. 

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