Quasicrystals electronic structure

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

Alloys Borates Solid-state Chemistry Carbides Transition Metal Solid-state Chemistry Chalcogenides Solid-state Chemistry Diffraction Methods in Inorganic Chemistry Electronic Structure of Solids Fluorides Solid-state Chemistry Halides Solid-state Chemistry Intercalation Chemistry Ionic Conductors Magnetic Oxides Magnetism of Extended Arrays in Inorganic Solids Nitrides Transition Metal Solid-state Chemistry Noncrystalline Solids Oxide Catalysts in Solid-state Chemistry Oxides Solid-state Chemistry Quasicrystals Semiconductor Interfaces Solids Characterization by Powder Diffraction Solids Computer Modeling Superconductivity Surfaces. 

First, in quantum physics, problems of an electron in complex potentials have been formulated to explain properties of the naturally existing crystals, disordered solids and quasicrystals. Similar structures in optics were mainly man-made for the purpose of optical engineering. 

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. 

We have reconstructed the 3D structure of a complex quasicrystal approximant v-AlCrFe (P6 m, a = 40.687 and c = 12.546 A) (Zou et al, 2004). Due to the huge unit cell, it was necessary to combine crystallographic data from 13 projections to resolve the atoms. Electron microscopy images containing both amplitude and phase information were combined with amplitudes from electron diffraction patterns. 124 of the 129 unique atoms (1176 in the unit cell) were found in the remarkably clean calculated potential maps. This investigation demonstrates that inorganic crystals of any complexity can be solved by electron crystallography. 

Abstract. We compute the velocity correlation function of electronic states close to the Fermi energy, in approximants of quasicrystals. As we show the long time value of this correlation function is small. This means a small Fermi velocity, in agreement with previous band structure studies. Furthermore the correlation function is negative on a large time interval which means a phenomenon of backscattering. As shown in previous studies the backscattering can explain unusual conduction properties, observed in these alloys, such as for example the increase of conductivity with disorder. 

Molecular quantum potential and non-local interaction depend on molecular size and the nature of intramolecular cohesion. Macromolecular assemblies such as polymers, biopolymers, liquids, glasses, crystals and quasicrystals are different forms of condensed matter with characteristic quanmm potentials. The one property they have in common is non-local long-range interaction, albeit of different intensity. Without enquiring into the mechanism of their formation, various forms of condensed matter are considered to have well-defined electronic potential energies that depend on the nuclear framework. A regular array of nuclei in a structure such as diamond maximizes cohesive interaction between nuclei and electrons, precisely balanced by the quantum potential, almost as in an atom. 

In this section we discuss some disordered magnetic systems that do not fit well under any of the subject headings of the other sections in this review. am-DyAg (sect. 8.3.1) is the only amorphous f-moment material studied with [iSR to date, as the pyrochlores (sect. 8.3.2) are the only perfectly fhistrated f-magnets studied with p,SR. Quasicrystals (sect. 8.3.3) must stand somewhat separately because they have atomic structure that is neither amorphous nor merely disordered-crystalline. For a discussion of spin-glass-like behavior in Ce, Yb, and U strongly correlated electron materials, see sect. 9. 

It was reported recently, that polymeric can also form quasicrystals. Hayashida et al. [50] demonstrated that certain blends of polyisoprene, polystyrene, and poly(2-vinylpyridine) form starshaped copolymers that assemble into quaskrystals. By probing the samples with transmission electron microscopy and X-ray diffraction methods, they conclude that the films are composed of periodic patterns of triangles and squares that exhibit 12-fold symmetry. These are signs of quasicrystalline ordering. Such ordering differ from conventional crystals lack of periodic structures yet are well-ordered, as indicated by the sharp diffraction patterns they generate. Quasi-crystals also differ from ordinary crystals in another fundamental way. They exhibit rotational symmetries (often five or tenfold). There are still some basic questions about their stracture. 

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