Body-centered cubic array

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... 

Lyotropic liquid crystals form in solutions of polar molecules such as soap in water. One end of the molecule is hydrophilic and the other end is hydrophobic. The molecules are aligned such that the hydrophilic end is exposed to water and the hydrophobic end is shielded from the water. There are several forms. The molecules may be arranged in lamellae or spherical units (Figure 16.7). The spherical units tend to be arranged in body-centered cubic arrays. The lamellae may be flat or rolled up to form columns that are arranged in hexagonal patterns. 

The initially formed ammoniates Ln(NH3)6 (Eq. la) can be isolated by evaporation of NH3 as gold metallic solids and low temperature X-ray studies at 200 K reveal a body-centered cubic array of octahedral molecules [38a]. Eu(NH3)6 can easily be converted to pure Eu(NH2)2 by catalytical (Fe203) [40a] and thermal (50 °C) treatment [40b] (Eq. lb,c). In the case of ytterbium... 

Pyrolusite is a mineral containing manganese ions and oxide ions. Its structure can best be described as a body-centered cubic array of manganese ions with two oxide ions inside the unit cell and two oxide ions each on two faces of the cubic unit cell. What is the charge on the manganese ions in pyrolusite ... 

For most applications Equation (8.24) may be adequate since the advantages of more complex models have not been extensively verified. The porosities for body-center cubic array (BCC) and face-center cubic array (FCC) are in the range of 0.3-0.25 and 0.2, respectively (Figure 8.5). 

For both a face-centered cubic and a body-centered cubic array, the coefficient of c / in Eq. (26) changes only slightly—to 1.79 (Hasimoto, 1959). 

The calculation of M for a three-dimensional array is much more complicated, and depends on the structure of the array. For the particular case of the face-centered-cubic NaCl crystal structure, its value is M = 1.747, whereas, for the body-centered-cubic CsCl structure, it is M = 1.763. 

Cesium, chloride (CsCl) structure (Fig. 4-H)- The CsCl structure can be described as interpenetrating simple cubic arrays of Cs+ and CP. Again, the Cs+ and CP positions are fully interchangeable. The structure is sometimes wrongly called body-centered cubic (bcc). The terminology is appropriate only when the shaded and unshaded atoms of Fig. 4.11 are identical, as in Fig. 4.8. In any case, the coordination number is eight for any atom. The unit cell of CsCl contains one net CsCl unit. 

The cuprite structure consists of a body-centered cubic (bcc) array of oxygen atoms, and the copper atoms occupy centers of four of the eight cubes into which the bbc cell may be divided. In this partially covalent structure, copper has a linear coordination and oxygen a tetrahedral coordination. 

Calculations have thus far been performed for the three standard cubic arrays, namely simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fee). As a result of this geometric symmetry, the couple N and particle stress dyadic A are given by the configuration-specific relations... 

In what array (simple cubic, body-centered cubic, and face-centered cubic) do atoms pack most efficiently (greatest percent of space occupied by spheres) Support your answer mathematically. 

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... 

Properties of solids differ from those of fluids because in solids the motions of molecules are highly restricted. The molecules may be confined to periodic arrays, producing crystalline structures such as the face-centered cubic (fee) and body-centered cubic (bcc), or they may be periodic only in certain directions, producing layered or amorphous structures such as graphite. Besides equilibrium structures, many solids can exist for prolonged periods in metastable structures examples include glasses. 

Several ordered states distinguished by their symmetries have been identified the preferred one depends primarily on the polymer composition [29,38,39]. Some common patterns are lamellar sheets, ordered bicontinuous double diamond (OBDD), hexagonally packed cylindrical arrays, and body-centered-cubic spherical microstructures. If the volume fractions of the two halves of the polymer chain are similar, the interface between the two regions will be flat and the lamellar phase will form. However, if one block is much smaller than the other, then for packing reasons, the interface will curve toward the smaller half (see Fig. 19b), giving, in order of increasing curvature, the OBDD, cylindrical, and spherical microstructure. 

What is the coordination number of each sphere in (a) a three-dimensional, close-packed array of equal-sized spheres (b) a primitive cubic structure (c) a body-centered cubic lattice ... 

MetaUic barium has a body-centered cubic structure (all atoms at the lattice points) and a density of 3.51 g/cm. Assume barium atoms to be spheres. The spheres in a body-centered array occupy 68.0% of the total space. Find the atomic radius of barium. (See Problem 11.87.)... 

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