Packing of Atoms in Solids

In the previous chapter, as a first step in understanding the stiffness of solids, we examined the stiffnesses of the bonds holding atoms together. But bond stiffness alone does not fully explain the stiffness of solids the way in which the atoms are packed together is equally important. In this chapter we examine how atoms are arranged in some typical engineering solids. 

In order to build up a three-dimensional packing pattern, it is easier, conceptually, to begin by 

Obviously, properties like the shear modulus might well be different for close-packed planes and cube planes, because the number of bonds attaching them per unit area is different. This is one of the reasons that it is important to have a method of describing various planar packing arrangements. 

Let us now look at the c.p.h. unit cell as shown in Fig. 5.4. A view looking down the vertical axis reveals the ABA stacking of close-packed planes. We build up our c.p.h. crystal by adding hexagonal building blocks to one another hexagonal blocks also stack so that they fill space. Here, again, we can use the unit cell concept to open up views of the various types of planes. 

We could make scale drawings of the many types of planes that we see in all unit cells but the concept of a unit cell also allows us to describe any plane by a set of numbers called Miller Indices. The two examples given in Fig. 5.5 should enable you to find the 

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The reader would be familiar with the packing of atoms in crystalline solids to produce regular, repeating, three-dimensional patterns such as the simple cubic, body-centered cubic, face-centered cubic, and hexagonal close-packed structures. The packing density and coordination number of these crystal structures for a pure metal are listed in Table 6.2. 

Figure 9.4. (a) A projection of the Mo3A18 unit cell is viewed down the c axis. Mo atoms are the larger circles. (b) The arrangement of atoms in a close-packed layer of Mo3Al8. There are open circles for A1 and squares for Mo in this layer. The repeating positions are solid dots in the cell for 33 layers. 

The second model extends the surface diffusion model to include the importance of the atomic placement of atoms in the randomly packed alloy. The model considers that a continuous connected cluster of the less noble atoms must exist to maintain the selective dissolution process for more than just the few monolayers of the alloy. This percolating cluster of atoms provides a continuous active pathway for the corrosion process as well as a pathway for the electrolyte to penetrate the solid. This is expected to depend on a sharp critical composition of the less noble element, below which dealloying does not occur.54, (Corcoran)5... 

Pure silver has the cubic close-packed structure a (fig. 13.11). This phase is capable of accommodating up to 42 atomic per cent of cadmium in solid solution by the purely random replacement of silver atoms. The sites occupied are still those of the cubic face-centred structure, no change in which occurs except a progressive and approximately linear variation... 

Wo have already made the general statement that when any two metals are used to form an alloy the actual structure of the alloy depends on whether, for the medals concerned, the tendency to produce a solid solution is greater than the opposing tendency to form an intermetallic compound. Since the formation of solid solutions is mainly governed by the relative sizes of the two atoms, while compound formation involves relationships between the atoms and their extra-nuclear electrons, it is probably more convenient to discuss first the sizes of metal atoms, usually expressed in terms of atom diameters. We have recently shown that in all types of pure metal crystals there are certain directions of atom close packing, and if, as is convenient, we continue to regard atoms as spheres, it is readily seen that the shortest interatomic distances are of the same magnitude as the respective atomic diameters. We shall therefore proceed to discuss the closest distance of approach of atoms in the typical metallic lattices. 

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