Unit cell centered rectangular

In two dimensions, five different lattices exist, see Fig. 5.6. One recognizes the hexagonal Bravais lattice as the unit cell of the cubic (111) and hep (001) surfaces, the centered rectangular cell as the unit cell of the bcc and fee (110) surfaces, and... 

Figure 11.3. The five distinct plane (2D) lattices (a) oblique, (b) primitive rectangular, (c) square, (d) and (e) are both centered rectangular but show alternative choices of unit cell, (/) hexagonal.

Figure 20.9 (a) Unit cell of the Ml (orthorhombic) phase along the c axis with the regions considered to be the active centers in propane ammoxidation shown in rectangular boxes, (b) Enlarged view of the proposed active center in Ml phase (Mo7 5Vi.5NbTe039) in [001] projection with indication (numbers) of the different atoms summarized below in the scheme of the active site, (c) Elaborated from [6a, 45]. 

We adopted a microcanonical ensemble MD method. The Lennard-Jones potential was used for the molecular interaction in the argon, OPLS potentials for methanol and water. We make a liquid slab with thickness of about 10 molecules at the center of the rectangular unit cell with periodic boundary conditions for all three dimentions. Figure 1 is a snapshot of a typical molecular configuration. Both sides of the slab are free liquid surfaces, on which molecules can evaporate and condense. The cell size along the surface normal is typically 100 A. and the surface area is -50 A x.50 A. The number of molecules is 1200 for argon, 864 for methanol, and 1024 for water. Other technical details are described elsewhere. ... 

FIGURE 4.1. (a) Symmetry in a repeating pattern. One possible unit cell, indicated by broken lines contains one object per unit cell and is described as primitive. Another possible unit cell, indicated by solid lines, contains two objects per unit cell and is said to be centered (and therefore nonprimitive ). Thus, while the simplest unit cell is not rectangular, a larger unit cell with higher symmetry, which in this case is rectangular, can readily be picked out from the arrangement of objects. 

Figure 2 A schematic representation of a protein crystal in which the motif (protein molecule) is shown as a spiral in cyan. The smallest unit cell (OPQR) is shown in black it is a rhombus lozenge-shaped with all sides equal. A larger rectangular unit cell (OPCD) is shown in red. This cell leaves one lattice point in the middle and is known as centered.

Fig. 2 The replacement of a square planar center (open circle) hy a tetrahedral (solid circle) one the open square denotes an octahedral center. (Left top) Flat network in the Hofmann-type. (Right top) Twisted network in the Hofmann-Td-type. (Left middle) A rectangular box cavity in the Hofmann-type. (Right middle) A twisted biprismatic cavity in the Hofmann-Td-type. (Bottom) A couple of Hofmann-type unit cells (left) makes a unit cell (right) of the Hofmann-Td-type.

For the bcc ciystal structure, the (110) crystal plane is the most densely packed plane. The bcc(llO) surface can be pictured as a distorted hexagonal stracture. It is often convenient to describe this surface using the centered rectangular unit cell highlighted in Fig. 5a rather than the primitive unit cell the primitive unit cell can be transformed into the centered rectangular cell by multiplying the primitive lattice vectors by the matrix ... 

When the centered rectangular unit cell is used, the clean, umeconstmcted surface forms a c(lxl) structure. In the summary of experimental results in Table 8, the centered rectangular unit cell is used except where noted. 

Table 8. Summary of experimental results obtained for halogen adsorption on the (110) surfaces of bcc transition metals. Except where noted, the adsorbate structures are based on a non-primitive centered rectangular substrate unit cell. The column headings are the same as defined for Table 1.

Fig. 2a - d. Models illustrating compression phases observed for halogen adsorption on the (111) surfaces of fee transition metals. The partially transparent circles represent the adsorbed atoms and the black quadrilaterals highlight the adsorbate unit cells both the primitive and centered rectangular unit cells are shown, (a) The (VSxVS) R30° or... 

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