Quasi-crystal lattices

Crystals are sohds. Sohds, on the other hand can be crystalhne, quasi-crystal-hne, or amorphous. Sohds differ from liquids by a shear modulus different from zero so that solids can support shearing forces. Microscopically this means that there exists some long-range orientational order in the sohd. The orientation between a pair of atoms at some point in the solid and a second (arbitrary) pair of atoms at a distant point must on average remain fixed if a shear modulus should exist. Crystals have this orientational order and in addition a translational order their atoms are arranged in regular lattices. 

For the description of die temperature and stress-related behavior of the crystal we used die method of consistent quasi-hannonic lattice dynamics (CLD), which permits die determination of the equilibrium crystal structure of minimum free energy. The techniques of lattice dynamics are well developed, and an explanation of CLD and its application to the calculation of the minimum free-energy crystal structure and properties of poly(ethylene) has already been presented. ... 

Plastic crystals The long-range orientational order is lost, the long-range positional order is preserved, i.e. a plastic quasi-crystalline lattice is still present. 

According to the formula (7) absorption spectrum for conductivity electrons in bulk metal should be a smooth curve down to co->0. Ag film in the near UV range demonstrates spectrum of such type. Appearance of a near UV absorption peak in a spectrum of M nanocrystal is caused by the surface charges that resulted from displacement of conductivity electrons under action of an external field. These charges create in a nanocrystal the internal field directed against external one [16]. For conductivity electrons this internal field plays a role of quasi-elastic bonds between valent electrons and cations in a crystal lattice. 

The materials may be in a quasi-ionic phase when 1 > p > 0.5, or in a quasi-neutral phase when 0.5 > p > 0. In the simplest theoretical approach, the value of p depends on only three parameters D) the ionization potential of D Aa, the electron affinity of A and M, the electrostatic Madelung energy of the crystal lattice. A fully ionic lattice (p = 1) is then realized when /D - Aa > M, and a fully neutral lattice (p = 0) when /D — Aa < M. This result is, however, greatly obscured by the neglect of transfer integral t and of other relevant parameters [44]. 

FIGURE 10.1 Unreconstructed (lxl) noble metal surfaces for (a) (100), (b) (111), and (c) (110) planes. Reconstructed (d) quasi-hexagonal structure (only the topmost layer is shown) and (e) (1x2) (110) plane. Black, dark-gray, and light-gray balls denote the upper (top), second, and third lower rows of the crystal lattice, respectively. 

A second mechanism for increasing disorder on melting which cannot be conveniently represented by a quasi-crystalline model for the melt involves the formation of association complexes. Quite generally, these can be defined as clusters of the units of structure (e.g., molecules or ions) in the crystal which have approximately the same distance between nearest neighbours as in the crystal lattice, but which need not have the full regularity of crystal packing. As already stated, only one particular form of cluster, the crystal nucleus can normally be extended indefinitely... 

Quasi-crystals have macroscopic symmetries which are incompatible with a crystal lattice (Section 2.4.1). The first example was discovered in 1984 when the alloy AlMn is rapidly quenched, it forms quasi-crystals of icosahedral symmetry (Section 2.5.6). It is generally accepted that the structure of quasicrystals is derived from aperiodic space filling by several types of unit cell rather than one unique cell. In two-dimensional space, the best-known example is that of Penrose tiling. It is made up of two types of rhombus and has fivefold symmetry. We assume that the icosahedral structure of AlMn is derived from a three-dimensional stacking analogous to Penrose tiling. As is the case for incommensurate crystals, quasi-crystals can be described by perfectly periodic lattices in spaces of dimension higher than three in the case of AlMn, we require six-dimensional space. 

Sid] Sidorenko, A.F., Dmitriev, E.A., Apasova, EA., Crystal Lattice Constants in Some Quasi-binary Alloys Based on FeSi (in Russian), Trudy Uralsk. Politekhn. Inst., (167), 124-127 (1968) (Crys. Structure, Experimental, 3)... 

The QC method which presents a relationship between the deformations of a continuum with that of its crystal lattice uses the classical Cau-chy-Bom rule and representative atoms. The quasi-continuum method mixes atomistic-continuum formulation and is based on a finite element discretization of a continuum mechanics variation principle. 

Crystal lattices have symmetry elements such as rotation axes, mirror planes, inversion points, and combinations of these. A crystalline lattice has translation symmetry, except for quasi-crystals or icosahedral phases, which have lattices with point symmetry elements only. Glasses are amorphous solids that do not have any symmetry element in their lattices. 

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