Unit cell packing

Figure 3.35. Position of the holes in closest packing. Unit cell projections are shown for the cubic and hexagonal sphere closest packing. Coordinates of the spheres and of the tetrahedral and octahedral holes are given. The values indicated inside the drawing correspond to the third coordinate (along the vertical axis) when two values are given, these correspond to two positions along the same vertical line.

Seeded crystals grow in the orthorhombic space group C222j and diffract to a resolution of up to 6 A (Fig. 8). They have relatively small, densely packed unit cells of 215 300 590 A, in contrast to the open structure and the large unit cells of the... 

Figure 1.11 Hexagonal close-packed unit cell...

Atoms are assumed to touch in closest packed structures, yet every closest packed unit cell contains a significant amount of empty space. Why ... 

The zinc blende lattice Is named after its parent compound, ZnS. Zinc sulfide also exists in a different structure known as the wurtzite lattice. Molecules that can exist in more than one type of crystalline form exhibit polymorphism. The wurtzite lattice is comprised of one type of ion forming a hexagonal closest-packed unit cell, with the other type of ion occupying half of the tetrahedral holes. The following molecules can assume the wurtzite lattice ZnO, ZnS, ZnSe, ZnTe, BeO, Agl, CdS, MnS, SiC, AIN, and NH4F. Both types of lattices consist of corner-shared tetrahedrons, but the tetrahedrons in wurtzite are canted in alternating layers. 

As illustrated in Figure 4, this model is based on close-packed unit cells with side lengths L and height d, each bearing one polymer chain. The volume V occupied by a single chain can be calculated from... 

Figure 4. Two-dimensional model consisting of close-packed unit cells for the calculation of the surface grafting density and/or themolecular weight of...

One of the first structures to be determined was the natural polysaccharide cellulose. In this case the repeat unit is cellobiose, composed of two glucoside rings. In the 1980s, NMR experiments established that native cellulose is actually a composite of a triclinic parallel-packed unit cell called cellulose / , and a monoclinic parallel-packed unit cell called cellulose I. Experimentally, the structures are only difficultly distinguishable via X-ray analysis (7a, 7b). Figure 6.1 (3) illustrates the general form of the cellulose unit cell. 

Explain why the element carbon does not have a face-centered cubic or hexagonal close-packed unit cell even though we typically designate the element carbon with the monatomic formula C. 

Three views of the hexagonal close-packed unit cell, (a) The ABABAB layering scheme, b) The coordination number of a given sphere (center of shaded hexagon) is 12. (c) The number of spheres per unit cell is six. 

Figure 28.3 Closest Packing of Spheres, (a) Layers of spheres, (b) The hexagonal close-packed unit cell. This figure shows that the third layer has each sphere directly over a sphere of the first layer, (c) The face-centered cubic close-packed unit cell. This unit cell is oriented so that the layers of atoms in Figure 28.3a are parallel to a plane that passes through the lattice point at the top rear of the cell, the lower left of the cell, and the lower right of the cell.

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