Quasicrystals compositions

A little later (Bendersky 1985, Chattopadhyay et al. 1985) decagonal (tenfold) symmetry was discovered in other Al-transition metal compounds quasiperiodic layers are stacked periodically in the third dimension. Since then, one or other of these forms of quasicrystal have been identified in many different compositions. A detailed review of the decagonal type is by Ranganathan et al. (1997). 

Photoinduced, spontaneous aggregation processes have been shown to occur when indolinobenzopyrans are irradiated in aliphatic solvents. The aggregates which are globular in appearance, consist of submicron cores of crystalline materials with an amorphous exterior and are termed "quasicrystals" (L-3). Spectroscopic studies by Krongauz and coworkers (1) indicate that the composition of the cores are AnB (n=2,3) and the amorphous exteriors AB. The most stable quasicrystals have been derived from 1-(/ -metha-crolyloxyethyl)-3,3 dimethyl-61-nitrospiro- (indoline-2,2 —[2H-1 ] benzopyran (SP-A) and its associated merocyanine form (SP-B). 

By using slightly different words, approximants are translationally normal crystal compounds generally with large unit cells that contain condensed, highly symmetric building blocks such as dodecahedra and icosahedra and have compositions close to those of related quasicrystals. 

QuasicrystaUine phases form at compositions close to the related crystalline phases. When solidified, the resultant strucmre has icosahedra threaded by a network of wedge disclinations, having resisted reconstruction into crystalline units with three-dimensional translational periodicity. The most well-known examples of quasicrystals are inorganic phases from the ternary intermetallic systems Al-Li-Cu, Al-Pd-Mn, Zn-Mg-Ln, Al-Ni-Co, Al-Cu-Co, and Al-Mn-Pd. In 2007, certain blends of polyisoprene, polystyrene, and poly(2-vinylpyridine) were found to form star-shaped copolymers that assemble into the first known organic quasicrystals (Hayashida et al., 2007). 

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

The symmetry treatment of incommensurate structures is beyond the scope of this chapter. From Equation (33) it is readily seen that for indexing, whatever the reflection of the diffraction pattern of an incommensurately modulated structure, we need to specify 3 + d integers (h, k, I, m, m2... m fl. It can be demonstrated that the observed 3D structure can be considered as a projection of a periodic structure m3 + d dimensions over the real 3D space, which is a hyper-plane not cutting the points of the 3 + d lattice except the origin. The superspace approach of de Wolff, Janssen and Janner is now well established and has become the routine way of treating the symmetry of the displacive incommensurate structures. The same approach has been extended to study general quasiperiodic structures (composite structures and quasicrystals). 

An icosahedral dominant phase was reported by H. Li et al. (1988) to exist in rapidly quenched CogoEr2o alloys, made by melt firming in He. The quasicrystals are strongly magnetic, with sperimagnetic characteristic similar to those observed in amorphous films of fire same composition. The quasicrystal crystal transition occurs at 660-900 K. 

Quasicrystals may thus be regarded as a special type of incommensurate system, which may be described by space groups of dimension larger than three in a similar way to modulated crystal phases and incommensurate composite structures. In the case of icosahedral quasicrystals the above model based on the icosahedral quaternion group //, fits well into the idea of 6D space groups. Each of the three standard coordinates, namely x, y, and z, corresponds to two coordinates in 6D space, namely a rational and an irrational coordinate corresponding to the rational and irrational portions of variables, of the form a -H o V5, where a and d are integers. Projection of the lattice points of this 6D space of icosahedral symmetry into conventional 3D space leads to the icosahedral quasicrystal lattice. 

Anderson BC, Bloom PD, Baikerikar KG, Sheares W, Mallapragada SK. Al-Cu-Fe quasicrystal/ultra-high molecular weight polyethylene composites as biomaterials for acetabular cup prosthetics. Biomaterials 2002 April 23(8) 1761-8. 

Al-Cr-Fe alloys are of interest as new lightweight alloys for structural apphcations, in particular, for the production of protective coatings formed by alumina scales from alloys of compositions that he in the Al-rich comer of the system. Al-Cr-Fe quasicrystal approximants are also potential candidates for new applications because of their specific properties. Alternatively, the addition of chromium to Fc3Al- and FeAl-based alloys produces excellent candidates for moderate and high temperature apphcations. [2005Pal] showed that... 

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