Chemistry Reference
In-Depth Information
Fig. 10.9 Cubic face-centered cube as the elementary unit of the ABCA-packing
There are two kinds of close-packing of spheres (see Fig.
10.7
): the cubic close-
packing of spheres and the hexagonal close-packing of spheres. It derives its name
from the special hexagonal elementary unit of 7 + 3 + 7
17 spheres (see 1a and
1b in Fig.
10.7
). The hexagonal packing cannot be described with another elemen-
tary unit of a higher symmetry.
A third metal structure exists with the coordination number 8 that does
not describe a close packing of spheres: it is the cubic body-centered structure.
The model for this structure is the cubic body-centered packing of spheres.
The elementary unit of this packing is a cube, which consists of nine spheres: the
cube center is occupied by one sphere that touches the eight spheres on the corners,
these spheres do not touch (see Fig.
10.10
).
The elementary units that show the symmetry of these sphere packings, were
found in search of the smallest segment of each packing of spheres: Fig.
10.10
displays these three elementary units. Another special segment, which forms the
whole structure by shifting it in all three directions in space, is called the unit cell. It
is obtained by vertical and horizontal cuts through the centers of the spheres in the
elementary units. The number of full spheres in each unit cell can be received by
adding together all parts of the unit cell (see Fig.
10.10
).
The unit cells of the cubic structures make it easy to understand that the overall
structure can be built by putting together many unit cells in all three dimensions in
space. It should also be pointed out that there are other unit cells for other structures.
This issue can be compared to patterned wallpapers: there are also different
possibilities to find a segment that builds the whole pattern of the wallpaper by a
shift in two directions in plane.
It has to be pointed out that the pictured unit cell of the hexagonal close packing
(see Fig.
10.10
) cannot be shifted into all directions in space to build the lattice
without gaps. Only one third of the displayed cell is used to build the whole lattice
(see dashed lines in Fig.
10.10
). This one third is the true unit cell: it contains one
third of six spheres (see Fig.
10.10
), namely two full spheres when all parts are
added together.
Metal crystals can have different structures at different temperatures. It has been
known for thousands of years that iron can be deformed if it is heated to glowing red
and hardens when it cools down. Today we can explain that iron crystals undergo a
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