Unit Cells

To determine the correct number of tetrahedral and octahedral voids in a hexagonal primitive unit cell, we need to understand the structure of the hexagonal close-packed (hcp) arrangement.

1. The hexagonal close-packed (hcp) structure consists of two layers: the top and a bottom layer representing hexagonal packing, with an additional layer that fits into the spaces of these two layers.
2. In an hcp arrangement, each atom is surrounded by 12 others, which creates the possibility of voids being formed.
3. There are two types of voids based on their geometrical configuration:
   • Tetrahedral Voids: Formed when an atom in one layer fits into the triangular void formed by three atoms in the adjacent layer. In a unit cell, the number of tetrahedral voids is twice the number of atoms. Since there are 6 atoms in an hcp unit cell, there are tetrahedral voids.
   • Octahedral Voids: Occur when an atom sits in the space formed by touching three top-layer atoms and three bottom-layer atoms. For an hcp unit cell, the number of octahedral voids is equal to the number of atoms. Therefore, in an hcp unit cell, there are 6 octahedral voids.
4. Considering the above points, the number of tetrahedral and octahedral voids in a hexagonal primitive unit cell is 12 and 6 respectively.

Thus, the correct option is 12,6.