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3D atomic packing |
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Additional layers of spheres (atoms) can be stacked on top of each other to
build a |
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crystal structure in three dimensions. This can be done in two
characteristic ways - |
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either directly on top so that the spheres are lined up vertically, or
staggered so that |
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the
spheres of one layer nestle into the depressions formed between the spheres
of |
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adjacent layers. |
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If this is done for the spheres packed together in the square pattern shown
before, |
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two
different 3D packing arrangements result. |
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click
image to enlarge |
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 |
 |
 |
overhead view |
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Figure 32 - Simple cubic (CP) packing of spheres |
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Simple cubic packed (CP) |
The vertical packing arrangement shown in Figure 32 is called simple cubic
or |
cubic primitive (CP), because
joining the adjacent sphere centers (nuclei) by lines |
forms the outline of a cube.
The overhead view shows that the spheres of one layer |
"eclipse" the spheres of
other layers thereby hiding them from view. By convention |
spheres (atoms)
that are lined up vertically like this in different layers are all |
identified by the same alphabet
letter, in this case the letter "A". The numbers |
indicate the vertical layer that the spheres are located in. |
Notice that each horizontal and vertical layer of spheres is parallel to the
(100) |
cubic planes. Each sphere in the CP packing is adjacent to six other
spheres - the |
four surrounding spheres in the same layer and one on top of and below it in
the |
adjacent layers. Therefore each sphere is said to have a coordination
number of six. |
As shown in the above image the CP packing can be modeled topologically as a |
space filling of cubes. Such a model is called a polyhedral framework
model of the |
packing because it is constructed as a stack of discrete polyhedra. |
Back to
Knowhere |
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24 - Structure matters - CP packing |
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