Cubic body-centered arrangement

The unit of structure corresponding to the cubic body-centered arrangement. There are two atoms in the unit, with coordinates 0, 0, 0 and f. h... 

The /3-alloys are different in nature from the 7-alloys and the a-manganese and /3-manganese structures discussed above, in that they are not complex structures, but are simple, being based upon the body-centered arrangement. /3-Brass, for example, has either a disordered structure, above 480°K, the copper and zinc atoms in essentially equal number being distributed largely at random over the points of a body-centered cubic lattice, or an ordered structure, below 300°K, with copper and zinc at the positions 000 and, respectively, of the cubic unit. Moreover, the physical properties of /3-brass are not those that indicate a filled zone structure. 

All of these hexafluorides are dimorphic, with a high-temperature, cubic form and an orthorhombic form, stable below the transition temperature (92). The cubic form corresponds to a body-centered arrangement of the spherical units, with very high thermal disorder of the molecules in the lattice, leading to a better approximation to a sphere. Recently, the structures of the cubic forms of molybdenum (93) and tungsten (94) hexafluorides have been studied using neutron powder data, with the profile-refinement method and Kubic Harmonic analysis. In both compounds the fluorine density is nonuniformly distributed in a spherical shell of radius equal to the M—F distance. Thus, rotation is not completely free, and there is some preferential orientation of fluorine atoms along the axial directions. The M—F distances are the same as in the gas phase and in the orthorhombic form. 

L. Pauling, Icosahedral quasicrystals of intermetallic compounds are icosahedral twins of cubic crystals of three kinds, consisting of large (about 5000 atoms) icosahedral complexes in either a cubic body-centered or a cubic face-centered arrangement or smaller (about 1350 atoms) icosahedral complexes in the /2-tungsten arrangement. Proc. Natl. Acad. Sci. (USA) 86, 8595-8599 (1989). 

In the fluorite structure, also shown in Fig. 3.5, the situation is reversed with the anions filling all the tetrahedral interstices of the close-packed cation sublattice. The resulting compound is MX2. The oxides of large quadrivalent cations (Zr, Hf, Th) and the fluorides of large divalent cations (Ca, Sr. Ba. Cd, Hg, Pb) both crystallize in that structure. Another way to view this structure is to focus on the anions, which are in a simple cubic arrangement (see Fig. 3.5) with alternate cubic body centers occupied by cations. If viewed from this perspective, the eightfold coordination of the cations becomes... 

X-ray diffraction patterns of Linde B zeolites are shown in Figure 2 and Table II. The similarity of the main diffraction peaks is obvious. The synthetic phases produced by various workers have been arranged in Table III to show their relationship to each other. Zeolite Bx is correlated with the cubic body-centered phases of Barrer (2) (Na-Pl) and Taylor and Roy s Na-Pc (13). The Linde B2, B3, Br and B6 phases are similar to the tetragonal body-centered phases of Barrer (2) (Na-P2) and... 

Titanium metai has a body-centered cubic unit ceii. The density of titanium is 4.50 g/cm. Caicuiate the edge iength of the unit ceii and a vaiue for the atomic radius of titanium. Hint in a body-centered arrangement of spheres, the spheres touch across the body diagonai.)... 

Section 11.7 In a crystalline soUd, particles are arranged in a regularly repeating pattern. An amorphous solid is one whose particles show no such order. The essential structural features of a crystalline solid can be represented by its unit cell, toe smallest part of toe crystal that can, by simple displacement, reproduce the three-dimensional structure. The three-dimensional structures of a crystal can also be represented by its crystal lattice. The points in a crystal lattice represent positions in toe structure where there are identical environments. The simplest unit cells are cubic. There are three kinds of cubic unit cells primitive cubic, body-centered cubic, and face-centered cubic. 

Solids can be crystalline or amorphous. A crystalline solid has an ordered arrangement of structural units placed at crystal lattice points. We may think of a crystal as constructed from unit celb. Cubic unit cells are of three kinds simple cubic, body-centered cubic, and face-centered cubic. One of the most important ways of determining the structure of a crystalline solid is by x-ray diffraction. 

A similar effect occurs in highly chiral nematic Hquid crystals. In a narrow temperature range (seldom wider than 1°C) between the chiral nematic phase and the isotropic Hquid phase, up to three phases are stable in which a cubic lattice of defects (where the director is not defined) exist in a compHcated, orientationaHy ordered twisted stmcture (11). Again, the introduction of these defects allows the bulk of the Hquid crystal to adopt a chiral stmcture which is energetically more favorable than both the chiral nematic and isotropic phases. The distance between defects is hundreds of nanometers, so these phases reflect light just as crystals reflect x-rays. They are called the blue phases because the first phases of this type observed reflected light in the blue part of the spectmm. The arrangement of defects possesses body-centered cubic symmetry for one blue phase, simple cubic symmetry for another blue phase, and seems to be amorphous for a third blue phase. 

Using data from rotation and Laue photographs, it is shown that the unit of structure of sodalite, containing < NaiAlzSiiOi2Gl, has a0 = 8.87 A. The lattice is the simple cubic one, Fc the structure closely approximates one based on a body centered lattice, however. The atomic arrangement has... 

Disordered alloys may form when two metals are mixed if both have body-centered cubic structures and if their atomic radii do not differ by much (e.g. K and Rb). The formation of ordered alloys, however, is usually favored at higher temperatures the tendency towards disordered structures increases. Such an arrangement can even be adopted if metals are combined which do not crystallize with body-centered cubic packings themselves, on condition of the appropriate composition. /J-Brass (CuZn) is an example below 300 °C it has a CsCl structure, but between 300 °C and 500 °C a A type transformation takes place resulting in a disordered alloy with a body-centered cubic structure. 

The CsCl type offers the simplest way to combine atoms of two different elements in the same arrangement as in body-centered cubic packing the atom in the center of the unit cell is surrounded by eight atoms of the other element in the vertices of the unit cell. In this way each atom only has adjacent atoms of the other element. This is a condition that cannot be fulfilled in a closest-packing of spheres (cf. preceding section). 

For simple monovalent metals, the pseudopotential interaction between ion cores and electrons is weak, leading to a uniform density for the conduction electrons in the interior, as would obtain if there were no point ions, but rather a uniform positive background. The arrangement of ions is determined by the ion-electron and interionic forces, but the former have no effect if the electrons are uniformly distributed. As the interionic forces are mainly coulombic, it is not surprising that the alkali metals crystallize in a body-centered cubic lattice, which is the lattice with the smallest Madelung energy for a given density.46 Diffraction measurements... 

An A-B diblock copolymer is a polymer consisting of a sequence of A-type monomers chemically joined to a sequence of B-type monomers. Even a small amount of incompatibility (difference in interactions) between monomers A and monomers B can induce phase transitions. However, A-homopolymer and B-homopolymer are chemically joined in a diblock therefore a system of diblocks cannot undergo a macroscopic phase separation. Instead a number of order-disorder phase transitions take place in the system between the isotropic phase and spatially ordered phases in which A-rich and B-rich domains, of the size of a diblock copolymer, are periodically arranged in lamellar, hexagonal, body-centered cubic (bcc), and the double gyroid structures. The covalent bond joining the blocks rests at the interface between A-rich and B-rich domains. 

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