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long-range order in another direction; these special substances are called
liquid crystals. Solid crystals have both short-range order and long-range
order.
Solids that have short-range order but lack long-range order are called

amorphous (amorphous solid). Almost any material can be made
amorphous by rapid solidification from the melt (molten state). This
condition is unstable, and the solid will crystallize in time. If the timescale

for crystallization is years, then the amorphous state appears stable.
Glasses are an example of amorphous solids. In crystalline silicon (Si)
each atom is tetrahedrally bonded to four neighbours. In amorphous silicon
(a-Si) the same short-range order exists, but the bond directions become

changed at distances farther away from any atom. Amorphous silicon is a
type of glass. Quasicrystals are another type of solid that lack long-range
order.

Most solid materials found in nature exist in polycrystalline

(polycrystal) form rather than as a single crystal. They are actually
composed of millions of grains (small crystals) packed together to fill all
space. Each individual grain has a different orientation than its neighbours.

Although long-range order exists within one grain, at the boundary
between grains, the ordering changes direction. A typical piece of iron or
copper (Cu) is polycrystalline. Single crystals of metals are soft and

malleable, while polycrystalline metals are harder and stronger and are
more useful industrially. Most polycrystalline materials can be made into
large single crystals after extended heat treatment. In the past blacksmiths
would heat a piece of metal to make it malleable: heat makes a few grains

grow large by incorporating smaller ones. The smiths would bend the
softened metal into shape and then pound it awhile; the pounding would
make it polycrystalline again, increasing its strength.

4.2. The Unit Cell. Lattice Systems
The crystal structure of a material (the arrangement of atoms within a
given type of crystal) can be described in terms of its unit cell (fig.4.1.1)

The unit cell is a small box containing one or more atoms, a spatial
arrangement of atoms. The unit cells stacked in three-dimensional space
describe the bulk arrangement of atoms of the crystal. The crystal structure

has a three-dimensional shape. The unit cell is given by its lattice
parameters, which are the length of the cell edges and the angles between

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