
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. 
Back to
Knowhere 

Page
24  Structure matters  CP packing 
