Cubic cell body-centered

Body-centered cubic cell (BCC). This is a cube with atoms at each comer and one in the center of the cube. Here again, comer atoms do not touch each other. Instead, contact occurs along the body diagonal the atom at the center of the cube touches atoms at opposite comers. 

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... 

C) The body-centered cubic cell looks like this ... 

The formula that relates the atomic radius (r) to the length of one edge of the cube (5) for a body-centered cubic cell is 4r = sjz. 

If the body-centered cubic cell is elongated along what becomes the c axis, the structure becomes fee (or ccp) when c/a /2. In Section... 

Using the structure-factor equation (5) show that for a body-centered cubic cell all reflections will be absent for which the sum of the indices is odd. 

In calculating the value of R for a particular diffraction line, various factors should be kept in mind. The unit cell volume v is calculated from the measured lattice parameters, which are a function of carbon and alloy content. When the martensite doublets are unresolved, the structure factor and multiplicity of the martensite are calculated on the basis of a body-centered cubic cell this procedure, in effect, adds together the integrated intensities of the two lines of the doublet, which is exactly what is done experimentally when the integrated intensity of an unresolved doublet is measured. For greatest accuracy in the calculation of F, the atomic scattering factor f should be corrected for anomalous scattering by an amount A/ (see Sec. 13-4), particularly when Co Ka radiation is used. The value of the temperature factor can be taken from the curve of Fig. 4-20. 

The other types of cubic cells are the body-centered cubic cell (bcc) and the face-centered cubic cell (fee) (Figure 11.17). A body-centered cubic arrangement differs from a simple cube in that the second layer of spheres fits into the depressions of the first layer and the third layer into the depressions of the second layer (Figure 11.18). The coordination number of each sphere in this stmetnre is 8 (each sphere is in contact with four spheres in the layer above and four spheres in the layer below). In the face-centered cubic cell there are spheres at the center of each of the six faces of the cube, in addition to the eight comer spheres. 

Clearly there is more empty space in the simple cubic and body-centered cubic cells than in the face-centered cubic cell. Closest packing, the most efficient arrangement of spheres, starts with the structure shown in Figure 11.20(a), which we call layer A. Focusing on the only enclosed sphere we see that it has six immediate neighbors in that layer. In the second layer (which we call layer B), spheres are packed into the depressions between the spheres in the first layer so that all the spheres are as close together as possible [Figure 11.20(b)]. 

FIGURE 11.22 The relationship between the edge length (a) and radius (rj of atoms in the simple cubic cell, body-centered cubic cell, and face-centered cubic cell. 

Figure 11.22 summarizes the relationship between the atomic radius r and the edge length a of a simple cubic cell, a body-centered cubic cell, and a face-centered cubic cell. This relationship can be used to determine the atomic radius of a sphere if the density of the crystal is known, as the following example shows. 

The crystal consists of atoms, ions, or molecules any face of a crystal consists of a layer of atoms, ions, or molecules. The method of describing faces of a crystal can be used to describe the planes of atoms in the crystal. Consider the body-centered cubic cell in Fig. 27.23(a) the intercepts of the shaded planes of atoms are oo, 1, 1, so the indices are Oil. In Fig. 27.23(b), the shaded plane has intercepts oo, 2, 1, so the reciprocals are 0, 1 ... 

In a simple cubic cell there are eight comer spheres. One-eighth of each belongs to the individual cell giving a total of one whole sphere per cell. In a body-centered cubic cell, there are eight comer spheres and one body-center sphere giving a total of two spheres per unit cell (one from the comers and one from the body-center). In a face-center sphere, there are eight comer spheres and six face-centered spheres (six faces). The total number of spheres would be four one from the comers and three from the faces. 

In a body-centered cubic cell, there is one sphere at the cubic center and one at each of the eight comers. Each comer sphere is shared among eight adjacent unit cells. We have ... 

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