Page 46 - Materials Chemistry, Second Edition

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2.3. The Crystalline State

pack: either simple cubic or close-packed. For example, think about dropping marbles
into a large beaker partially filled with water. As the marbles settle to the bottom of the
container, they will seek their most stable resting position. These positions will be
mostly within the voids formed between three spheres (close-packed), rather than on
top of the crests of individual spheres (simple cubic packing). Whereas the coordina-
tion number (i.e., number of nearest neighbors) of individual species for simple cubic
packing is six, the coordination number for close-packing is 12.
Since a simple cubic arrangement would have a significant amount of excess
void-space, this presents a much less efficient manner to pack individual spheres.
This larger volume of empty space in simple packing would result in a lower density
for the solid relative to its close-packing analog. It should also be noted that
the sliding of one layer over another would be more preferred for simple cubic
relative to close-packing. This corresponds to a greater degree of crystal defects that
are possible for these solids.
Although marble migration is only mentioned as an example, this process is not
far removed from the crystallization process. In the formation of single crystals,
individual ions/atoms/molecules slowly come into contact with one another, and
nucleate from thermodynamically favored positions. Sometimes metastable phases
may be obtained if one does not allow such preferential migration to occur, through
rapid cooling events, for instance.
Figure 2.12 serves to aid in the visualization of sphere packing sequences in three-
dimensions. After a few spheres (in A sites) are arranged in a close-packed

Figure 2.12. Representations of hexagonal close-packing (hcp) and face-centered cubic (fcc) packing.
Reproduced with permission from Silberberg, M. S. Chemistry: The Molecular Nature of Matter, 2nd ed.,
McGraw-Hill: New York, 2000.