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distinct from the electric repulsion between like ions) decreases the potential energy by

about 11 percent. A really precise knowledge of nis not essential; if n10 instead of

n9, U 0 would change by only 1 percent.

Example 10.1

In an NaCl crystal, the equilibrium distance r 0 between ions is 0.281 nm. Find the cohesive

energy in NaCl.

Solution

Since 1.748 and n9, the potential energy per ion pair is

U 0   1    1  

1.27  10 ^18 J7.96 eV

Half this figure, 3.98 eV, represents the contribution per ion to the cohesive energy of the

crystal.

Now we need the electron transfer energy, which is the sum of the 5.14-eV ionization

energy of Na and the 3.61-eV electron affinity of Cl, or 1.53 eV. Each atom therefore con-

tributes 0.77 eV to the cohesive energy from this source. The total cohesive energy per atom

is thus

Ecohesive(3.980.77) eV3.21 eV

which is not far from the experimental value of 3.28 eV.

Most ionic solids are hard, owing to the strength of the bonds between their con-

stituent ions, and have high melting points. They are usually brittle as well, since the

slipping of atoms past one another that accounts for the ductility of metals is prevented

by the ordering of positive and negative ions imposed by the nature of the bonds. Polar

liquids such as water are able to dissolve many ionic crystals, but covalent liquids such

as gasoline generally cannot. Because the outer electrons of their ions are tightly bound,

ionic crystals are good electrical insulators and are transparent to visible light. How-

ever, such crystals strongly absorb infrared radiation at the frequencies at which the

ions vibrate about their equilibrium positions.

10.3 COVALENT CRYSTALS

Shared electrons lead to the strongest bonds

The cohesive forces in covalent crystals arise from the sharing of electrons by adjacent

atoms. Each atom that participates in a covalent bond contributes an electron to the

bond. Figure 10.8 shows the tetrahedral structure of a diamond crystal, each of whose

carbon atoms is linked by covalent bonds to four other carbon atoms.

Another crystalline form of carbon is graphite. Graphite consists of layers of car-

bon atoms in a hexagonal network in which each atom is joined to three others by

covalent bonds 120° apart, as in Fig. 10.9. One electron per atom participates in

1



9

(9  109 N m^2 /C^2 )(1.748)(1.60    10 ^19 C)^2



2.81    10 ^10 m

1



n

e^2



4  0 r 0

342 Chapter Ten

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