Packing geometry coordination number and

1 Coordination number and packing geometry. On the basis of the previous definition of the coordination number (as the number of first neighbours), and of the corresponding coordination geometries (as listed in Table 3.4) some additional remarks may be useful for the particular case of packing of hard sphere atoms. 

If we have N hard spheres (of radius rs) forming a close-packed polyhedron, another sphere (of smaller radius rc) can fit neatly into the central hole of the polyhedron if the radius ratio has a well-defined value (see also 3.8.1.1). The ideal radius ratio (rc/rs) for a perfect fit is 0.225.. (in a regular tetrahedron, CN 4), 0.414.. (regular octahedron CN 6), 0.528.. (Archimedean trigonal prism CN 6), 0.645... (Archimedean square antiprism CN 8), 0.732.. (cube CN 8), 0.902... (regular icosahedron CN 12), 1 (cuboctahedron and twinned cuboctahedron CN 12). 

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See also in sourсe #XX -- [ ]

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