Centered cell

As current is passed through the cells shown in Figure 14-2, the oxygen produced in the first cell is collected and its volume is compared with the volume of chlorine produced in the center cell (the volumes being compared at identical temperatures and pressures). The volume of chlorine is found to be exactly double that of oxygen. Applying Avogadro s Hypothesis, explain how this result shows that electricity can count atoms. 

A unit cell having the smallest possible volume is called a primitive cell. For reasons of symmetry according to rule 1 and contrary to rule 3, a primitive cell is not always chosen, but instead a centered cell, which is double, triple or fourfold primitive, i.e. its volume is larger by a corresponding factor. The centered cells to be considered are shown in Fig. 2.6. 

The unit cell considered here is a primitive (P) unit cell that is, each unit cell has one lattice point. Nonprimitive cells contain two or more lattice points per unit cell. If the unit cell is centered in the (010) planes, this cell becomes a B unit cell for the (100) planes, an A cell for the (001) planes a C cell. Body-centered unit cells are designated I, and face-centered cells are called F. Regular packing of molecules into a crystal lattice often leads to symmetry relationships between the molecules. Common symmetry operations are two- or three-fold screw (rotation) axes, mirror planes, inversion centers (centers of symmetry), and rotation followed by inversion. There are 230 different ways to combine allowed symmetry operations in a crystal leading to 230 space groups.12 Not all of these are allowed for protein crystals because of amino acid asymmetry (only L-amino acids are found in proteins). Only those space groups without symmetry (triclinic) or with rotation or screw axes are allowed. However, mirror lines and inversion centers may occur in protein structures along an axis. 

Raman, C. S., Li, H., Martasek, P., Kral, V., Masters, B. S., Poulos, T. L., Crystal structure of constitutive endothelial nitric oxide synthase a paradigm for pterin function involving a novel metal center, Cell 95 (1998),... 

The unit cell considered here is a primitive (P) unit cell that is, each unit cell has one lattice point. Nonprimitive cells contain two or more lattice points per unit cell. If the unit cell is centered in the (010) planes, this cell becomes a B unit cell for the (100) planes, an A cell for the (001) planes, a C cell. Body-centered unit cells are designated I, and face-centered cells are called F. Regular packing of molecules into a crystal lattice often leads to symmetry... 

MM = multiple myeloma ATL = adult T-cell leukemia ALL = acute lymphoblastic leukemia CLL = chronic lymphocytic leukemia FCC = follicular center cell lymphoma DLC = diffuse large cell lymphoma TRB = T-cell rich B-cell lymphoma ALCL = anaplastic large cell lymphoma MALT = mucosa-associated lymphoid tissue-type lymphoma LC = lung cancer CMM = cutaneous malignant melanoma TCC = transitional cell carcinoma CSCC = cutaneous squamous cell carcinoma. 

Another idea to be clear about is that a centered cell or centered lattice need not necessarily be used. An equivalent primitive lattice can always be chosen, as illustrated by the relationship between parts (d) and (e) in Figure 11.3. 

Figure 11.13. Alternate ways of choosing a unit cell for the centered monoclinic lattice, a, fi, c, define the body-centered (/) cell a, b c define the A-centered cell a, fi, c define the F-centered cell.

Berek, C., Berger, A., Apel, M. (1991). Maturation of the immune response in germinal centers. Cell 67, 1121-1129. 

FIGURE 6.7. Immunostained PCNA in the hyperplastic human palatine tonsil, using mouse monoclonal antibody PC10 (diluted 1 10). (A) No heat pretreatment nuclei of the germinal center cells are weakly stained. (B) In contrast, the cells in the same area are strongly stained after simple heating in a hot water bath for 2 hr at 90°C. Reproduced, with permission, from Kawai et al. (1994). Copyright 1994 Blackwell Science Asia. 

A crystal lattice is an array of points arranged according to the symmetry of the crystal system. Connecting the points produces the lattice that can be divided into identical parallelepipeds. This parallelepiped is the unit cell. The space lattice can be reproduced by repeating the unit cells in three dimensions. The seven basic primitive space lattices (P) correspond to the seven systems. There are variations of the primitive cells produced by lattice points in the center of cells (body-centered cells, I) or in the center of faces (face-centered cells, F). Base-centered orthorhombic and monoclinic lattices are designated by C. Primitive cells contain one lattice point (8 x 1/8). Body-centered cells... 

We have noted that Pu has six allotropic forms including ccp (8-Pu), body-centered tetragonal (S -Pu) and bcc (e-Pu) structures. The tetragonal body-centered cell of 8 -Pu becomes the bcc cell of s-Pu when the axial ratio is unity. There are many metals having ccp and bcc structures, but Pu is the only one of these metals that also has the intermediate body-centered tetragonal structure. 

Figure 7.3. A projection of the tetragonal body-centered cell of B4CI4.

Figure 7.4. A projection along c0 of the atoms in the tetragonal cell of B5H9. Boron atoms are the smaller circles. The centers of the four B atoms in the square base of the pyramidal molecules are at 0 (and 100) and 50 giving a body-centered cell.

XeF4 is square planar as expected for a molecule with four electron bonding pairs and two unshared electron pairs on Xe. Crystals of XeF4 are monoclinic (P2i/n) with two molecules per cells (a = 5.05, b = 5.92, c = 5.77 A, and (3 = 99.6°). It is a body-centered cell and the notation is 3 2PTOT(t). 

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