9 Three dimensional close packing from two dimensional hexagonal close packed layers

Описание: Three dimensional structures can be generated by placing two dimensional layers one above the other.
Place first layer of hexagonal close packed layer ‘A’
Then, place second layer over the first layer such that the second layer fits in the depression of the first layer
Since the spheres of the two layers are aligned differently, second layer can be named as ‘B’
All the triangular voids of first layer are not covered by spheres of second layer. This gives rise to different arrangements.

When the triangular voids of first layer are covered by second layer or vice versa, it gives rise to a tetrahedral void because a tetrahedron is formed when centers of the four nearing spheres are joined.
When triangular voids of second layer are placed on triangular voids of first layer, they do not overlap.
Apex of one triangle points upward and apex of the other points downward. Such voids are surrounded by six spheres.
So, an octahedral void is formed because, when the center of the nearing spheres is joined, it forms an octahedron.
The number of these two types of voids depends upon the number of close packed spheres.
If the number of close packed sphere = N
The number of octahedral voids generated =N
The number of tetrahedral voids generated = 2N
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