The Closest Packing of Spheres

State the Jagondzinski and the Zhdanov symbols for the closest-packings of spheres with the following stacking sequences ... 

As an example of the prevalence of high-symmetry structures we can take the closest packings of spheres only in the cubic and the hexagonal closest-packing of spheres are all atoms symmetry equivalent in other stacking variants of closest-packings several nonequivalent atomic positions are present, and these packings only seldom occur. 

These two packing schemes form the basis for the most common stmctnres derived from the closest packing of spheres. Many other arrangements that are a mixture of the two seqnences are possible and are seen in nature, such as... 

Cubic closest packed (cep) structure a solid modeled by the closest packing of spheres with an abcabc arrangement of layers the unit cell is face-centered cubic. (16.4)... 

Clearly, every lattice point has the same environment. A further property is that if along any line in the lattice there are lattice points distance x apart then there must be points at this separation (and no other lattice points) along this line when produced indefinitely in either direction. (We refer to this property of a lattice when we describe the closest packing of spheres in Chapter 4.) Note that the lattice has no physical reality it does not form part of the pattern. 

Addition of a third layer to the closest-packing of spheres in the first two layers, (a) If the third (blue) layer occupies the downward-pointing indentations of the second (red) layer in Figure 11.16, then the first (black) and third layers will become coincident, forming an ABABAB repeat pattern, (b) If the third layer occupies the upward-facing indentations, then an ABCABC repeating lattice will result. 

Figure 2.4 Lattice model for the closest packing of spheres. The bottom view in (a) can be compared with the packing shown in Figure 2.3. Part (b) shows that this packing leads to the ABCAB. . . stacking.

We can describe the structures of metals as the closest packing of spheres, first discussed in Section 11.11. Elemental metals generally crystallize in one of the basic types of crystal lattices, including face-centered cubic, body-centered cubic, and hexagonal closest packed. The crystal structure of a metal may change, however, as a function of temperature and pressure. Table 23.2 lists the crystal structures for the 3d transition metals at attnospheric pressure. 

Explain why there are two arrangements for the closest packing of spheres rather than a single one. 

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