Chemistry - A Molecular Science

Chapter 8 Solid Materials

energy difference between the top of the valence band and the bottom of the conduction band is called the

band gap

. Conduction can occur only if there are unfilled orbitals into

which electrons can move, but there are no unf

illed orbitals available in a filled valence

band, so electrons must be excited from the valence band into the conduction band if the substance is to conduct. Thus, a material with the band structure in Figure 8.10 is an insulator

if the band gap is much greater than

thermal energy and no electrons occupy the

conduction band. However, if the band gap is not much greater than thermal energy, some electrons do populate the conduction band and the material becomes a conductor. Increasing the temperature (thermal energy) of a material with a small to moderate band gap increases its conductivity by increasing

the population of the conduction band. A

substance whose conductivity increases with temperature is called a

semiconductor

.*

Silicon and germanium have moderate band ga

ps (100 and 67 kJ/mol, respectively) and

are semiconductors, while diamond, which has a mu

ch larger band gap (502 kJ/mol), is an

insulator.

Energy

conduction band valence band

Fermi level

Band gap

Figure 8.10 Conductivity and the band gap The band diagram is that of a semi

conductor if the band gap is small

or that of an insulator if

the band gap is large.

Energy

FermiLevel

(a)

(b)

Some metals, such as zinc, that have f

illed valence shells can still be metallic

conductors if there is overlap between the high

est energy filled band and the lowest energy

unoccupied band. In zinc, the band formed from the filled 4s orbitals and the band formed from the empty 4p orbitals overlap. High energy

electrons in the filled band move into

crystal orbitals at lower energy in the unoccupied band to produce two partially filled bands as shown in Figure 8.11. The presence of

two partially filled bands makes zinc a

metallic conductor even th

ough all of its valence orbitals are full.

* The conductivities of metallic conductors decrease slightly at elevated

temperatures due to the increas

ed thermal motion of the atoms.

8.7

IONIC SOLIDS AND IONIC RADII

To this point, we have focused on crystals in

which all of the particles are identical, but

ionic substances are composed of two or more

different ions, so their structures consist of

at least two different types of particles. The

ions in an ionic crystal can be treated as

charged spheres that pack to maximize cati

on-anion interactions. In a sodium chloride

crystal, each sodium ion is surrounded by six chloride ions and each chloride ion by six sodium ions. The result is an extended solid of alternating sodium and chloride ions with no unique NaCl molecules. Breaking or melting an ionic crystal requires breaking a large number of strong interactions (ionic bonds).

Consequently, ionic substances are generally

hard and have high melting points (600-2000

oC). The strength of the interaction depends

upon the magnitude of the charges on the ions and the separation between them. Thus,

Figure 8.11 Metallic conductor produced by the overlap of a filled and an empty band (a) High-energy electrons in a filled band seek lower energy

orbitals in the empty band.

(b) At equilibrium, both bands are par

tially filled, so the substance

is a metallic conductor.

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