Body-centered cubic unit

Three types of unit cells. In each case, there is an atom at each of the eight corners of the cube. In the body-centered cubic unit cell, there is an additional atom in the center of the cube. In the face-centered cubic unit cell, there is an atom in the center of each of the six faces. 

Vanadium crystallizes with a body-centered cubic unit cell. The volume of the unit cell is 0.0278 nm3. What is its atomic radius ... 

It follows that 3a2 = (4r)1 and therefore that a = 4r/3112. Each unit cell contains one sphere at each of the eight corners and one sphere at the center 8 X 1/8 +1=2 spheres so the total mass of a body-centered cubic unit cell is 2M/NA. Therefore,... 

A body-centered cubic unit cell contains 2 atoms in total ... 

FIGURE 10.22 Geometries of (a) primitive-cubic and (b) body-centered cubic unit cells in both a skeletal view (top) and a space-filling view (bottom). Part (c) shows how eight primitive-cubic unit cells stack together to share a common corner. 

A body-centered cubic unit cell has eight corner atoms plus an additional atom in the center of the cube (Figure 10.22b). This body-centered cubic unit cell, with two repeating offset layers and with the spheres in a given layer slightly separated, is the repeat unit found in body-centered cubic packing. 

Tungsten crystallizes in a body-centered cubic unit cell with an edge length of 317 pm. What is the length (in picometers) of a unit-cell diagonal that passes through the center atom ... 

Calculate the percent volume occupied by the spheres in a body-centered cubic unit cell. 

Sketch of body-centered cubic unit cell. 

Cesium chloride crystallizes with a structure derived from the simple cubic primitive cell. Ch ions occupy the 8 comer sites with Cs+ in the center of the cell note that this is not a body-centered cubic unit cell since the ion at the center is not the same as those at the comers. Thus there is one CsCl unit per unit cell and the coordination numbers of Cs+ and Ch are both 8. Crystals of CsBr and Csl adopt the CsCl structure, but all other alkali halides crystallize in the NaCl structure. 

In the body-centered cubic unit cell the spheres touch along the body diagonal. 

The relationship of the body diagonal (b) to the face diagonal (f) and edge (e) for the body-centered cubic unit cell. 

Titanium metal has a body-centered cubic unit cell. The density of titanium is 4.50 g/cm3. Calculate the edge length of the unit cell and a value for the atomic radius of titanium. Hint In a hodv-centered arrangement of sph eres, the spheres touch along the body diagonal.)... 

Figure 3.5. (a) Face-centered cubic unit cell in real space, (b) The corresponding body-centered cubic unit cell in reciprocal space. 

X-ray Diffraction of Pure MoFe, High Temperature Form. X-ray diffraction powder photographs of MoFe taken at 10 °C. can be indexed on the basis of a body-centered cubic unit cell with a lattice constant, a = 6.23 zb 0.01 A. The similarity of the MoFe diffraction pattern to that of molybdenum metal indicates that the molybdenum atoms in the hexafluoride, as in the metal, are located at the body center and comers of a cube. 

Body-centered cubic unit cell UsNieSU... 

Titanium crystallizes in a body-centered cubic unit ceU with an edge length of 3.306 A. The density of titanium is 4.401 g/cm Use these data to calculate Avogadro s number. 

In the extended body-centered cubic unit cell, each corner atom is shared by eight unit cells, and so each of the eight corner atoms contributes only Vs atom to the total number of atoms in one unit cell. This atom plus the center atom gives a total of two atoms per unit cell. 

In the body-centered cubic unit cell, shown in Figure 12.24B, identieal particles lie at each corner and in the center of the eube. Those at the eorners do not touch each other, but they all touch the one in the eenter. Eaeh partiele is surrounded by eight nearest neighbors, four above and four below, so the eoordination number is 8. 

B, Body-centered cubic unit cell. C, Face-centered cubic unit cell. 

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