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The Solid State 337

(a) (b)

(c) (d)

Figure 10.2Point defects in a crystal. (a) Vacancy. (b) Interstitial. (c) Substitutional impurity.

(d) Interstitial impurity.

The analogy between an amorphous solid and a liquid helps in understanding both

states of matter. The density of a given liquid is usually close to that of the corre-

sponding solid, for instance, which suggests that the degree of packing is similar. This

inference is supported by the compressibilities of these states. Furthermore, x-ray dif-

fraction indicates that many liquids have definite short-range structures at any instant,

quite similar to those of amorphous solids except that the groupings of liquid mole-

cules are continually shifting. A conspicuous example of short-range order in a liquid

occurs in water just above the melting point, where the result is a lower density than

at higher temperatures because H 2 O molecules are less tightly packed when linked in

crystals than when free to move.

The bonds in an amorphous solid vary in strength because of the lack of long-range

order. When an amorphous solid is heated, the weakest bonds break at lower tem-

peratures than the others, and the solid softens gradually. In a crystalline solid the

bonds break simultaneously, and melting has a sudden onset. Metallic “glasses” have

been made from mixtures of metals whose atoms differ greatly in size, which prevents

them from forming the ordered structures of crystals when cooled from a molten state.

One such metallic glass has half the density of steel but twice its strength, and is hard

but can be deformed without breaking. Its gradual softening when heated make the

material exceptionally easy to shape.

Crystal Defects

In a perfect crystal each atom has a definite equilibrium location in a regular array.

Actual crystals are never perfect. Defects such as missing atoms, atoms out of place,

irregularities in the spacing of rows of atoms and the presence of impurities have a

considerable bearing on the physical properties of a crystal. Thus the behavior of a

solid under stress is largely determined by the nature and concentration of defects in

its structure, as is the electrical behavior of a semiconductor.

The simplest category of crystal imperfection is the point defect.Figure 10.2 shows

the basic kinds of point defect. Both vacancies and interstitials, which require about 1 to

2 eV to be created, occur in all crystals as a result of thermal excitation, and their num-

ber accordingly increases rapidly with temperature. Of much importance is the produc-

tion of such defects by particle radiation. In a nuclear reactor, for instance, energetic

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