Solved Examples
Example 1 In close packing of identical spheres, show that: (i) there are as many
octahedral voids as there are spheres, and (ii) there are twice as many tetrahedral
voids as there are spheres.
Solution: A single close-packed layer of identical spheres contains two types of
triangular voids. Stacking of additional close-packed layers produce tetrahedral and
octahedral voids. If the triangular void has a sphere directly above it (Fig. 1.29), the
resulting void is termed as tetrahedral void. On the other hand, if a triangular void in
one layer is covered by another triangular void in the next layer (Fig. 1.30), the
resulting void is termed as octahedral void.
Fig. 1.27 A close packed layer showing B and C voids
(a)
(b)
A
A
C
B
A
B
Fig. 1.28 a Hexagonal close packing b Cubic close packing
1.5 Close Packing of Identical Atoms (Spheres)
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