Page 447 - Schaum's Outline of Theory and Problems of Applied Physics

432 THE SOLID STATE [CHAP. 35

C
Cl −
C
Na +
Fig. 35-1 Fig. 35-2

the locations of these parts are always changing. Van der Waals forces are quite weak, and substances composed
of whole molecules, such as water, usually have low melting and boiling points and little mechanical strength in
the solid state. Table 35.1 shows the four types of crystalline solids.

SOLVED PROBLEM 35.1

Are all solids crystalline?
No. The atoms, ions, or molecules of which a crystalline solid is composed fall into regular, repeated patterns.
The presence of such long-range order is the defining property of crystals. Other solids lack long-range order in their
structures and may be regarded as supercooled liquids whose stiffness is due to exceptionally high viscosity. Glass,
pitch, and many plastics are examples of such amorphous (“without form”) solids.

SOLVED PROBLEM 35.2
How are the crystal structures of solids usually determined?

The structure of a crystal is usually determined by the interference patterns produced when an X-ray beam
passes through it. A crystal consists of a regular array of atoms, each of which is able to scatter an electromagnetic
wave that happens to strike it. A beam of X-rays, all with the same wavelength, that falls upon a crystal will be
scattered in all directions within it; but, owing to the regular arrangement of the atoms, in certain directions the
scattered waves will constructively interfere with one another while in others they will destructively interfere. The
phenomenon is known as X-ray diffraction. The resulting pattern of high and low X-ray intensities can be analyzed
to yield the arrangement in space of the scattering centers, which are the atoms of the crystal.

ENERGY BANDS
The atoms in almost all crystalline solids, whether metals or not, are so close together that their outer electrons
constitute a single system of electrons common to the entire crystal. In place of each precisely defined character-
istic energy level of an individual atom, the entire crystal possesses an allowed energy band which spans a range
of possible energies. This is a consequence of the excludion principle mentioned in Chapter 34. The allowed
energy bands in a solid thus correspond to the energy levels in an atom, and an electron in a solid can have only
those energies that fall within these energy bands. If adjacent allowed energy bands do not overlap, the intervals
between them represent energies which their electrons cannot have. Such intervals are called forbidden bands.
The electrical behavior of a crystalline solid is determined both by its energy-band structure and by how these
bands are normally filled with electrons. The highest energy band that normally may contain electrons is known
as the upper energy band.