Physical Chemistry , 1st ed.

Equation 21.13 is defined to give positive values for the lattice energy. It

should be understood that when oppositely charged ions come together, total

energy is always decreased.Therefore, the rxnHvalues of these processes are

always negative, indicating an exothermic process.

21.9 Crystal Defects and Semiconductors

So far in this chapter, we have been working under the assumption that crys-

talline solids are perfect crystals. Every atom, ion, or molecule is assumed to be

in exactly the right place in every unit cell throughout the entire solid crystal.

In reality, this is not the case. Most real crystals are full of imperfections. Even

crystals that are considered very well ordered have an occasional lapse in crys-

tal structure at the atomic and molecular level. These lapses are called defects.

There are several different kinds of defects in crystals. Depending on the

type and number of defects in any volume of crystal (that is, the type and den-

sity of defects), the physical and chemical properties of the crystal may be al-

tered from the properties of the perfect crystalline form. Defects can be sepa-

rated on the basis of whether they affect a single point, a line of points, or a

plane of points. For simplicity’s sake, we will assume that we are considering

an atomic crystal, but all crystals—atomic, ionic, molecular—exhibit most of

the defects discussed here.

The simplest point defect is when an atom is simply missing from its ex-

pected position. This type of defect is called a lattice vacancy(sometimes also

called a Schottky defect). In another kind of defect, an additional atom is pres-

ent. If the additional atom is crowded in with the rest of the atoms in the unit

cell, then it must squeeze itself in between the normally occupied positions. This

type of defect is called an interstitial defect.If, on the other hand, the additional

atom is a chemically different atom that is taking the place of an atom of the

normal unit cell, then it is considered a substitutional defect.Figure 21.30 shows

a two-dimensional example of these three types of point defects in crystals.

Line and plane defects are more complicated to illustrate. One type of line

defect is found when a line of atoms or unit cells starts suddenly inside a crys-

tal. Figure 21.31 shows a two-dimensional representation of this kind of line

defect. Plane defects are usually seen at the surfaces of crystals or at interfaces

between two smaller crystals in a larger piece of solid material, as seen in

Figure 21.32. Plane defects can also exist between two different Bravais lattices

of the same compound.

21.9 Crystal Defects and Semiconductors 759

Lattice vacancy

Interstitial defect

Substitutional defect

Lattice vacancy

New line

of atoms

Figure 21.30 Examples of the common types
of defects in crystals. Even crystals that look very
well ordered macroscopically may have a high
density of such defects.

Figure 21.31 A line defect in a (two-dimensional)

crystal.

Figure 21.32 The surface that separates the

two individual crystals can be considered a type

of plane defect. In a perfect crystal, such an in-

terface wouldn’t exist.

© Mark A. Scheidner/Photo Researchers, Inc.