3D atomic packing .
     Additional layers of spheres (atoms) can be stacked on top of each other to build a .
crystal structure in three dimensions.  This can be done in two characteristic ways - .
either directly on top so that the spheres are lined up vertically, or staggered so that .
the spheres of one layer nestle into the depressions formed between the spheres of .
adjacent layers. .
     If this is done for the spheres packed together in the square pattern shown before, .
two different 3D packing arrangements result. .

click image to enlarge




overhead view



Figure 32 - Simple cubic (CP) packing of spheres

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.

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Page  24 -  Structure matters - CP packing

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