Page 13 - Modern physical chemistry

2 Structure in Solids

ity, coefficient of linear expansion, electrical and thermal conductivity, refractive index,
and dielectric constant may vary with direction.
The planes along which slippage and cleavage occur form parallel sets intersecting
in a regular fashion. Apparently, something is arranged in order in a crystal. Furthermore,
the isotropic states seem to arise when the basic parts shift to break down this long-
range order. Let us seek information on the bases and their arrangements in space.
A quasicrystal does not have the long-range order of a true crystal. It does, however,
possess enough short-range order to exhibit crystal-like diffraction patterns. A glass,
liquid, or gas does not possess such short-range order.

1.3 Diffraction

In everyday life, one gathers information about the external world with one's senses.
The most important of these involve sight and touch.
Some of the light scattered by neighboring objects is collected by one's eyes, then
refracted and projected to form images on the retinas. Signals from these are transmitted
to appropriate regions of the brain. The resulting mental impressions are supported by
tactile evidence. For, each visible body may be touched, felt, squeezed, and possibly moved.
Sounds can be traced to macroscopic sources. Similarity, smells and tastes can be.
These procedures tell us nothing about the minute internal structure of materials,
however. A finer probe is needed. Shorter wavelength radiation, in the X-ray region, is
suitable. But since refractors do not exist for such radiation, one has to analyze each
scattered pattern directly.
In the open where no scattering occurs, the radiation appears to propagate along def-
inite lines called rays. Where scattering does occur, the pertinent rays are bent or forked.
Only in certain directions do neighboring rays reinforce each other. We say that diffrac-
tion has occurred.
At a typical point along a given ray, the pertinent physical properties vary in concert.
Within a given medium, variations in the different components are scaled and rotated
(and/or translated) versions of each other. Away from its source, electromagnetic radia-
tion consists of a changing electric field strength E perpendicular to a corresponding
magnetic field strength H, both perpendicular to the direction of motion.
When a component varies sinusoidally, as figure 1.1 shows, we say the variation is
monochromatic, with a definite frequency and wavelength. The frequency v is given by
the number of crests passing a fixed point in unit time, while the wavelength A equals the
distance between crests. The phase velocity w is the velocity at which a given crest moves.

Distance

FIGURE 1.1 Electric field strength E in a monochromatic electromagnetic wave.