Atomic packing

The ways in which atoms pack together (the atom packing), since this determines how many little springs there are per unit area, and the angle at which they are pulled (Fig. 4.2). 

In compound materials - in the ceramic sodium chloride, for instance - there are two (sometimes more) species of atoms, packed together. The crystal structures of such compounds can still be simple. Figure 5.8(a) shows that the ceramics NaCl, KCl and MgO, for example, also form a cubic structure. Naturally, when two species of atoms are not in the ratio 1 1, as in compounds like the nuclear fuel UO2 (a ceramic too) the structure is more complicated (it is shown in Fig. 5.8(b)), although this, too, has a cubic unit cell. 

Fig. 5.11. (a) Atom packing in amorphous (glassy) silica, (b) How the addition of soda breaks up the bonding in amorphous, silica, giving soda glass. 

In Chapter 5 we said that many important engineering materials (e.g. metals) were normally made up of crystals, and explained that a perfect crystal was an assembly of atoms packed together in a regularly repeating pattern. 

Demonstrations (a) Give four injection-moulded close-packed planes to each student to allow personal building of f.c.c. and c.p.h. (b) Atomix atomic model on overhead projector to show atom packing (Emotion Productions Inc., 4825 Sainte Catherine O, Montreal 215PQ, Canada) or ball bearings on overhead projector. 

We begin by looking at the smallest scale of controllable structural feature - the way in which the atoms in the metals are packed together to give either a crystalline or a glassy (amorphous) structure. Table 2.2 lists the crystal structures of the pure metals at room temperature. In nearly every case the metal atoms pack into the simple crystal structures of face-centred cubic (f.c.c.), body-centred cubic (b.c.c.) or close-packed hexagonal (c.p.h.). 

Metal atoms tend to behave like miniature ball-bearings and tend to pack together as tightly as possible. F.c.c. and c.p.h. give the highest possible packing density, with 74% of the volume of the metal taken up by the atomic spheres. However, in some metals, like iron or chromium, the metallic bond has some directionality and this makes the atoms pack into the more open b.c.c. structure with a packing density of 68%. 

Magnesia, MgO, is an example (Fig. 16.1b). It is an engineering ceramic, used as a refractory in furnaces, and its structure is exactly the same as that of rocksalt the atoms pack to maximise the density, with the constraint that like ions are not nearest neighbours. 

The size of the group attached to the main chain carbon atom can influence the glass transition point. For example, in polytetrafluoroethylene, which differs from polyethylene in having fluorine instead of hydrogen atoms attached to the backbone, the size of the fluorine atoms requires the molecule to take up a twisted zigzag configuration with the fluorine atoms packed tightly around the chain. In this case steric factors affect the inherent flexibility of the chain. 

The inclusion of both covalent and intermetallic crystals in Chapter 6 is predicated on the close relation between the covalent and metallic bonds, as discussed in Chapter 3. SP 54 and SP 55 are beautiful examples of the complexity of the atomic packing and bonding arrangements in alloy structures, which fascinated Pauling. 

Fig. 9.1 Atomic packing in the intermetallic phases Li5Ga4 (a) and Li2Ga7 (b).

Fig. 9.4 Atomic packing in hexagonal Li5AISi2 (a) and tetragonal Li9AISl3 (b).

A solid that contains cations and anions in balanced whole-number ratios is called an ionic compound. Sodium chloride, commonly known as table salt, is a simple example. Sodium chloride can form through the vigorous chemical reaction of elemental sodium and elemental chlorine. The appearance and composition of these substances are very different, as Figure 2-24 shows. Sodium is a soft, silver-colored metal that is an array of Na atoms packed closely together. Chlorine is a faintly yellow-green toxic gas made up of diatomic, neutral CI2 molecules. When these two elements react, they form colorless ciystals of NaCl that contain Na and Cl" ions in a 1 1 ratio. 

The structures can be considered as packings of metal atoms which have incorporated the nonmetal atoms in their interstices. Usually, the metal atom packings are not the same as those of the corresponding pure metals. The following structure types have been observed ... 

Here it is assumed that upon fracture of a grain boundary, half of the segregant is left on each free surface, and that the segregant atoms pack at the same density as they would in the pure elemental state. 

The prototype hard metals are the compounds of six of the transition metals Ti, Zr, and Hf, as well as V, Nb, and Ta. Their carbides all have the NaCl crystal structure, as do their nitrides except for Ta. The NaCi structure consists of close-packed planes of metal atoms stacked in the fee pattern with the metalloids (C, N) located in the octahedral holes. The borides have the A1B2 structure in which close-packed planes of metal atoms are stacked in the simple hexagonal pattern with all of the trigonal prismatic holes occupied by boron atoms. Thus the structures are based on the highest possible atomic packing densities consistent with the atomic sizes. 

X-ray diffraction studies have revealed that alkane chains with an even number of carbon atoms pack more closely in the crystalline state => attractive forces between individual chains are greater and melting points are higher. 

Table 4.29 Packing volume fractions for various types of atomic packing...

IV. Number of Atoms Packed in First Coordination Sphere AROUND Metal Ion... 

Our description of atomic packing leads naturally into crystal structures. While some of the simpler structures are used by metals, these structures can be employed by heteronuclear structures, as well. We have already discussed FCC and HCP, but there are 12 other types of crystal structures, for a total of 14 space lattices or Bravais lattices. These 14 space lattices belong to more general classifications called crystal systems, of which there are seven. 

Beside dislocation density, dislocation orientation is the primary factor in determining the critical shear stress required for plastic deformation. Dislocations do not move with the same degree of ease in all crystallographic directions or in all crystallographic planes. There is usually a preferred direction for slip dislocation movement. The combination of slip direction and slip plane is called the slip system, and it depends on the crystal structure of the metal. The slip plane is usually that plane having the most dense atomic packing (cf. Section 1.1.1.2). In face-centered cubic structures, this plane is the (111) plane, and the slip direction is the [110] direction. Each slip plane may contain more than one possible slip direction, so several slip systems may exist for a particular crystal structure. Eor FCC, there are a total of 12 possible slip systems four different (111) planes and three independent [110] directions for each plane. The... 

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