Body center cubic models

Beta radiation Electron emission from unstable nuclei, 26,30,528 Binary molecular compound, 41-42,190 Binding energy Energy equivalent of the mass defect measure of nuclear stability, 522,523 Bismuth (m) sulfide, 540 Blassie, Michael, 629 Blind staggers, 574 Blister copper, 539 Blood alcohol concentrations, 43t Body-centered cubic cell (BCC) A cubic unit cell with an atom at each comer and one at the center, 246 Bohrmodd Model of the hydrogen atom... 

FIGURE 5.32 The body-centered cubic (bcc) structure. This structure is not packed as closely as the others that we have illustrated. It is less common among metals than the close-packed structures. Some ionic structures are based on this model. 

Recently, similar but not identical, lattice models of water have been proposed by Fleming and Gibbs 61) and by Bell ezK In both models molecules are restricted to occupation of the sites of a body centered cubic array. The fundamental tetra-hedrality of the water-water interaction is accounted for in that four noncontiguous nearest neighbor points of the total of eight nearest neighbor points of a... 

In order to understand and interpret the many details that can be observed, it is necessary to examine how the metal atoms can arrange themselves on a spherical surface. The best way to do this is to make a model of a body-centered cubic crystal, such as tungsten, whose surface is as close to a mathematical sphere as the size of its atoms permits. We have constructed such a model in which marbles represent tungsten atoms. The radius of curvature of the model is 25 atom (or marble) diameters. This is 40 to 100 times smaller than the metal points used in the microscope but does not change any of the essential features which we wish to bring out. 

Describe the electron-sea model of the bonding in cesium metal. Cesium has a body-centered cubic structure. 

One of the earliest applications of the method of different orbitals for different spins appears in Slater s classic study of the cohesion of monovalent metals 133>. In Slater s model of the body-centered cubic structure of the alkali metals, the lowest unperturbed, zero spin-state is taken to be one in which the valence electrons about the atoms at the cube-comers have one spin, spin , while those at the cube-centers have the opposite spin, spin (3. 

Since most of the methods and examples in this review are focused on metals, this section will be shortened. Albeit, it is important to note that multiscale modeling has been applied to basic metal alloy structures such as face center cubic aluminum alloys, hexagonal close pack magnesium alloys, and body center cubic iron and... 

The (a) simple cubic (sc), (b) body-centered cubic (bcc), and (c) face-centered cubic (fee) closest packing models. The spheres are considered as touching, but in the upper structures they are shown... 

OL-Tungsten is the only stable modification. It has a body-centered cubic lattice of space group - Im3m (No. 229). A diffraction pattern is shown in Fig. 1.7, together with a crystal structure model. 

Robinson and Dalton use Monte Carlo statistical mechanics to explore concentration and shape dependencies of the chromophores. Monte Carlo methods provide valuable information about the distribution of a collection of chromophores but are not able to provide atomistic information about the systems. The Monte Carlo simulations performed by Robinson and Dalton employ an array of point dipoles on a periodic lattice with the given parameters for the shape of the chromophores and the chromophore spacing adjustable to achieve the desired chromophore concentration. The model system consisted of 1000 chromophores on a body-centered cubic... 

In these beds, pore size is determined by the number of nearest neighbors (coordination number) n, the sphere radius r, and the type of packing geometry. Two radii characterize the pore size one for the "throat" and one for the "cavity" of the pore (18). Isotherms have been calculated similar to those of Reference (2.), for polysulfone (density 1.370 g/cm ) spheres for values of n 4,6,8,10 (tetrahedral, primitive cubical, body-centered cubical, body-centered tetragonal geometries, respectively). Nitrogen vapor at -195.6°C was assumed and the adsorbed layer thickness was calculated with Halsey s equation (15) as in the cylindrical pore model. Calculated isotherms are plotted in Figure 5. 

A few AB solids have body-centered cubic structures, with a CN of 8. An example is CsCl, which is calculated to be much more stable in the ionic model. Again ionic bonding seems to favor a high CN, since the Madelung constant increases, being 1.763 for bcc. This theory proves to be short-lived, however, when we consider bonding in the metals. By definition, the bonding here must be covalent, since identical atoms are bonded. 

Fig. 69. (a) Part of the body-centered cubic lattice ordered in the B2 structure (left part) and in the Dtp structure (right part). Left part shows assignment of four sublattices a, b, c and d, In the B2 structure (cf. also fig. 66a), the concentrations of A atoms are the same at the a and c sublatticcs, but differ from the concentrations of the b, d sublattices, while in the DOj structure the concentration of the b sublattice differs from that of the d sublatlice, but both differ from those of the a, c sublattices (which are still the same). In terms of an Ising spin model, these sublattice concentrations translate into sublattice magnetizations mu, mu, mc, m,i, which allow to define three order parameter components / = ma + mL- — mu — m,/, fa = m - mc + mu — m,j, and fa = -ma + m., + mu — nij. 

Low index surface orientations of face-centered and body-centered cubic (fee and bcc, respectively) lattices are commonly used for LEED experiments. These important surfaces are readily visualized using atomic models, and a useful atlas has been compiled by Nicholas (318). Salient structural features are obvious from such models. This can be... 

Fio. 33. Hard-sphere model of body-centered cubic emitter, [110] oriented. Number of nearest neighbor atoms around surface atom White-4 Dark Grey-5 Light Grey-6, Black-7. 

As indicated in the hard-sphere model in Fig. 33 a hemispherical emitter surface is made up of a variety of crystal planes. The closer packed of these, such as the 110, 211, and 100 in the body centered cubic lattice, have a higher work function they therefore appear as dark spots in the more brightly emitting areas corresponding to stepped regions. With the aid of a standard orthographic projection (Fig. 34). the orientation of the emitter and the identity of the planes can thus be deduced from the symmetry of the pattern. 

Krigbaum and Lin [142] studied a bcc (body-centered cubic) lattice model of PTL Their simulations demonstrated that some overall features of... 

Besides semiconductor elements (e.g., silicon, carbon), there have been considerable efforts in the last several years devoted to the tight-binding modeling of metals. Since the strong directional d-band bonding in many body-centered cubic transition metals resembles the covalent bonding in semiconductors to some extent, they may provide good opportunities for TBMD approaches. 

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