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In hexagonal close packing (HCP) of spheres in three dimensions, which statement correctly describes the octahedral and tetrahedral voids in one unit cell?

1. There are 12 octahedral voids, all completely inside the hexagonal unit cell.
2. There are 6 octahedral voids, all completely inside the hexagonal unit cell.
3. There are 6 octahedral voids: 3 completely inside and 3 formed from partial contributions at the unit cell boundary.
4. There are 6 tetrahedral voids completely inside the hexagonal unit cell.

Correct answer: There are 6 octahedral voids: 3 completely inside and 3 formed from partial contributions at the unit cell boundary.

Solution

In HCP, the unit cell contains 6 atoms. The number of octahedral voids = 6 (one per atom). Of these 6 octahedral voids, 3 are located entirely within the unit cell and 3 are partially inside (shared at the boundaries). Thus option C is correct.

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