Quasicrystals structure

Another characteristic point is the special attention that in intermetallic science, as in several fields of chemistry, needs to be dedicated to the structural aspects and to the description of the phases. The structure of intermetallic alloys in their different states, liquid, amorphous (glassy), quasi-crystalline and fully, three-dimensionally (3D) periodic crystalline are closely related to the different properties shown by these substances. Two chapters are therefore dedicated to selected aspects of intermetallic structural chemistry. Particular attention is dedicated to the solid state, in which a very large variety of properties and structures can be found. Solid intermetallic phases, generally non-molecular by nature, are characterized by their 3D crystal (or quasicrystal) structure. A great many crystal structures (often complex or very complex) have been elucidated, and intermetallic crystallochemistry is a fundamental topic of reference. A great number of papers have been published containing results obtained by powder and single crystal X-ray diffractometry and by neutron and electron diffraction methods. A characteristic nomenclature and several symbols and representations have been developed for the description, classification and identification of these phases. 

In this chapter, general aspects and structural properties of crystalline solid phases are described, and a short introduction is given to modulated and quasicrystal structures (quasi-periodic crystals). Elements of structure systematics with the description of a number of structure types are presented in the subsequent Chapter 7. Finally, both in this chapter and in Chapter 6, dedicated to preparation techniques, characteristic features of typical metastable phases are considered with attention to amorphous and glassy alloys. 

In the same paper (Yamamoto 1996) an authoritative description is given of several interrelated topics such as super-space group determination, structure determination, indexing of diffraction patterns of quasicrystals, polygonal tiling, icosahedral tiling, structure factor calculation, description of quasicrystal structures, cluster models of quasicrystals. 

Borides Sohd-state Chemistry Carbides Transition Metal Solid-state Chemistry Electronic Structure of Sohds Quasicrystals Structure Property Maps for Inorganic Solids Superconductivity Zintl Compounds. 

A related model for quasicrystal structures has also been presented by Aslanov. ... 

This model is a member of a series of structures, all built on a simple principle of interpenetration of polyhedra of five-fold point symmetry. The simplest member of the family is shown in Fig. (2.18(a)). Higher members, formed by successive interpenetrations of icosahedra fill space (Fig. 2.18(b)) and a perfectly ordered quasicrystal structure is obtained, there is no need to use oblate or prolate polyhedra they are generated by a single structure building principle [24]. 

Quasicrystal structures have been known for a long time to occur in condensed matter and rejected as inexplicable curiosities. They may emerge naturally too in mathematical descriptions of surfaces. (The decagonal variant certainly arises, cf. [36]). It is not an entirely idle speculation to conjecture, e.g. that the principles exploited in construction of quasi-crystals may be precisely those used by nature to build protems that solve the problem... 

A very effective demonstration of enhanced plasmonic effects from laterally illuminated MWCNTs has been demonstrated by the diffraction patterns observed from a 2D Penrose tiled quasicrystal structure [29]. This stmcture has been seen... 

Comment on Quasicrystal structure of rapidly solidified Ti-Ni-based alloys . Phys. Rev. B39 (1989) 1964-1965. 

How can icosahedra, which we know cannot fill aU space, form solids with enough long-range order to diffract x-rays One of the simplest ways would be to place each icosahedron on a Bravais lattice site and fill in the space between them with other atoms. Actually, most quasicrystal structures are more complicated than this and will not be dealt with here. 

Trebin, H.-R. (ed.) (2003) Quasicrystals. Structure and Physical Properties, Wiley-VCH Verlag GmbH, Weinheim. 

Ebert, P., Yurechko, M., Kluge, F., Horn, K., and Urban, K. (2003) in Quasicrystals. Structure and Physical Properties (ed. H.-R. Trebin), Wiley-VCH Verlag GmbH, Weinheim, p. 

The many papers in this proceedings are partitioned into very abstruse theoretical analyses of structure and stability of quasicrystals on the one hand, and practical studies of surface structures, mechanical properties and potential applications. The subject shows signs of becoming as deeply divided between theorists and practical investigators, out of touch with each other, as magnetism became in the preceding century. 

During the nearly ten years which have passed since the appearance of the " Shechtman paper" a large amount of both experimental and theoretical research has been carried out on quasiperiodic structures. For more material about quasicrystals we refer to a paper in La Recherche by the French collaborator in the Sheehtman team [6], to a thesis by Dulea [7J, and to a survey paper with a large number of referenees [8]. 

In this paper we will briefly review the findings of an earlier study of the properties of quasicrystals using SHG and present further experimental data to probe their structure and nonlinear optical properties. Finally, a model describing the behavior of quasicrystals in an external electric field is developed. 

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

In concluding this section in which some properties of modulated structures and of quasicrystals have been considered, we underline that the characteristics of these two types of structures do not coincide. Incommensurately modulated structures show main and satellite diffractions, an average structure and crystallographic point symmetry. The quasicrystals have no average structure, non-crystallographic point symmetry, and give one kind of diffraction only. 

Notes on the crystallography of quasi-periodic structures. A general way to face the problems related to the interpretation of quasi-periodic structures (modulated structures, quasicrystals) is based on the introduction and application of higher-dimensional crystallography (de Wolff 1974, 1977, Janner and Janssen 1980, Yamamoto 1982, 1996, Steurer 1995). 

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