Chemistry Reference
In-Depth Information
Coordination
number
Crystal structure
Structural model
Examples
Magnesium, zinc
Mg type
hexagonal
12
hexagonal closest
packing of spheres
cubic
face-centred
cubic closest
packing of spheres
Copper, silver,
gold, Cu type
12
cubic
body-centred
body- centred
packing of spheres
Alkaline metals,
tungsten W type
8
Fig. 10.5 Main crystal structure types of metals
Fig. 10.6 Coordination polyhedrons for both close-packed arrangements of spheres: on top for
hexagonal closest packing, below for cubic closest packing
possibilities to stack three spheres on a layer of seven spheres: either the interstices
1, 3, and 5 or the interstices 2, 4, and 6 are filled. The result is two different sphere
packings, which can be characterized with sequences ABAB
...
and ABCABC
...
.
Only the layers with triangular patterns are to be counted with ABA or ABCA.
While Fig.
10.6
shows both polyhedra with the coordination number 12,
Fig.
10.7
highlights the packings that are based upon a triangular pattern and
have the shape of triangular pyramids (see 1 and 2 in Fig.
10.7
). Both elementary
units of the pyramids are shown: on one hand packing of spheres (see 1a and 2a), on
the other hand crystal lattices (see 1b and 2b). Additionally one can see that the
ABCA packing has a square pattern of spheres, when one line of spheres is taken off
the edge of the triangular pyramid (see 3 in Fig.
10.7
).
If spheres are being stacked starting from a square pattern, the result is a square
pyramid, which also has the coordination number 12 (see 1 and 2 in Fig.
10.8
). The
faces of the square pyramid have the triangular pattern, which can be continued by
