Macroscopic lattice structure

Figure 1. Macroscopic lattice structures. (a) Rock lattice generated by convective currents in the soil of Spitsbergen.

It will certainly take an integrated examination of chemical structure, microscopic and macroscopic lattice structure to provide the key to unravelling the mysteries of ICP. Our approach in understanding ICPs as mesoscopic metals (cf [68]) might provide a useful basis for further scientific and technological progress. 

The macroscopic appearance of crystals, with their polygonal facets and the underlying lattice structure, is the consequence of quantum mechanical... 

Fig. 7.55. At a microscopic scale, roughness is associated with lattice steps, vacancies, and so only which are determined by the lattice structure of the smface. At a macroscopic level, crystallographic character may be revealed in the topographic features, for example, hillocks formed on the (100) surface. It has been found that the etched surface in 25% KOH has well-defined terraces and step features, whereas it has a nodule type of appearance in 50% KOH solution. Table 7.5 provides a summary of the characteristics of the surface etched features in KOH with respect to the crystal orientation of the surfaces.

The crystal structures of metals are relatively simple. Those of some minerals can be complex, but minerals usually have simpler structures that can be recognized within the more complex structure. The unit cell is a structural component that, when repeated in all directions, results in a macroscopic crystal. Structures of the 14 possible crystal structures (Bravais lattices) are shown in Figure 7.1. Several different unit cells are possible for some structures the one used may be chosen for convenience, depending on the particular application. The atoms (or ions) on the corners, edges, or faces of the unit cell are shared with other unit cells as follows ... 

Many crystals have crystal lattice structure themselves, so they are natural optical anisotropic media. However, in some amorphous material, under the action of certain external field (such as electromagnetic fields, mechanical forces, etc.), their atoms or molecules will be orientated in certain rules, thus the material will change from isotropic into anisotropic macroscopically, which is called as the artificial optical anisotropy. In... 

The authors also note that in case of a layered structure, one would anticipate lower than cubic symmetry for the lattice. It is possible that the lattice is composed of a mixture of tetragonal or orthorhombic microdomains, while macroscopically, the system appears to be cubic for XRD. This behavior is not unknown for perovskites. It has been shown by theoretical calculations for Fe-doped YBa2Cu307 that a macroscopically tetragonal structure (as seen by XRD) can originate from a randomly oriented ensemble of orthorhombic microdomains [20]. 

Other parameters, including the lattice sound speed Cs and weight factor fj, are lattice structure dependent. For example, for a typical D2Q9 (two dimensions and nine lattice velocities see Fig. 1) lattice structure, we have tQ = 4/9, ii 4 = 1/9, f5 8 = 1/36, and = A /3Afi, where Ax is the spatial distance between two nearest lattice nodes. Through the Chapman-Enskog expansion, one can recover the macroscopic continuity and momentum (Navier-Stokes) equations from the above-defined LBM dynamics ... 

The way in which water softens the stratum corneum appears to be performed at a rather macroscopic level, i.e. by its filling inter- and intracellular spaces of the dead corneocj es, and to some extent perhaps at the molecular level by binding to cell protein macromolecules, both keratinous and non-keratinous. The aggregate result, however, is to provide an aqueous lubricating system for the cellular lattice structure of the stratum corneum, a lubrication that accounts for unusual pliability of the stratum corneum. 

Very recently, people who engage in computer simulation of crystals that contain dislocations have begun attempts to bridge the continuum/atomistic divide, now that extremely powerful computers have become available. It is now possible to model a variety of aspects of dislocation mechanics in terms of the atomic structure of the lattice around dislocations, instead of simply treating them as lines with macroscopic properties (Schiotz et al. 1998, Gumbsch 1998). What this amounts to is linking computational methods across different length scales (Bulatov et al. 1996). We will return to this briefly in Chapter 12. 

This review is structured as follows. In the next section we present the theory for adsorbates that remain in quasi-equilibrium throughout the desorption process, in which case a few macroscopic variables, namely the partial coverages 0, and their rate equations are needed. We introduce the lattice gas model and discuss results ranging from non-interacting adsorbates to systems with multiple interactions, treated essentially exactly with the transfer matrix method, in Sec. II. Examples of the accuracy possible in the modehng of experimental data using this theory, from our own work, are presented for such diverse systems as multilayers of alkali metals on metals, competitive desorption of tellurium from tungsten, and dissociative... 

Heterogeneities associated with a metal have been classified in Table 1.1 as atomic see Fig. 1.1), microscopic (visible under an optical microscope), and macroscopic, and their effects are considered in various sections of the present work. It is relevant to observe, however, that the detailed mechanism of all aspects of corrosion, e.g. the passage of a metallic cation from the lattice to the solution, specific effects of ions and species in solution in accelerating or inhibiting corrosion or causing stress-corrosion cracking, etc. must involve a consideration of the detailed atomic structure of the metal or alloy. 

These conditions show us immediately that in the case of the four-neighbor HPP lattice (V = 4) f is noni.sotropic, and the macroscopic equations therefore cannot yield a Navier-Stokes equation. For the hexagonal FHP lattice, on the other hand, we have V = 6 and P[. is isotropic through order Wolfram [wolf86c] predicts what models are conducive to f lavier-Stokes-like dynamics by using group theory to analyze the symmetry of tensor structures for polygons and polyhedra in d-dimensions. 

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