Structures Formed by the Close Packing of Spheres

In molecular chemistry, octahedral and tetrahedral molecules can link together to form clusters. One way in which we can visualize solid structures is as semi-infinite lattices built up from unlimited numbers of tetrahedral and octahedral units (atoms or ions). We can consider poly-hedra packing in various ways by sharing edges or vertices to form dense structures. This procedure is covered in many texts,and will not be described in detail here. 

Another way in which many solids can be described is by thinking of atoms as hard spheres which can pack together as tightly as geometry will allow. This close-packing procedure creates holes which can be then filled by other atoms, and this principle can be used to explain many simple structures. 

If identical hard spheres such as ball bearings are placed in a flat box to form a single layer, each sphere is soon surrounded by six others. This arrangement provides the most efficient packing model. In general, in structural chemistry the number of nearest neighbours around an atom is 

The cubic part of the cubic close-packed structure is more difficult to see, but can be visualized by considering the alternating layers of six 

Q Use the atom/hole sharing principle to calculate the ratio of octahedral hole/tetrahedral hole/atoms in a cubic close-packed structure 

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