Tetrahedral and Octahedral Voids in Hexagonal Primitive Unit Cell

In a crystal lattice, voids or holes are the spaces present between the constituent particles. These voids can be classified into tetrahedral and octahedral voids based on their geometrical arrangement.

Tetrahedral Voids:
Tetrahedral voids are formed when four spheres are arranged in a tetrahedral shape. These voids are situated at the center of each edge of a regular tetrahedron formed by the constituent particles.

Octahedral Voids:
Octahedral voids are formed when six spheres are arranged in an octahedral shape. These voids are located at the center of each face of a regular octahedron formed by the constituent particles.

Hexagonal Primitive Unit Cell:
A hexagonal primitive unit cell is a type of crystal lattice structure where the constituent particles are arranged in a hexagonal pattern. This unit cell has one lattice point at each of its corners and three additional lattice points at the centers of the three faces.

Number of Tetrahedral Voids:
To determine the number of tetrahedral voids in a hexagonal primitive unit cell, we can consider the arrangement of constituent particles. The number of tetrahedral voids is equal to the number of particles present in the unit cell. In a hexagonal primitive unit cell, there are 6 particles at the corner positions.

Therefore, the number of tetrahedral voids in a hexagonal primitive unit cell is 6.

Number of Octahedral Voids:
To determine the number of octahedral voids in a hexagonal primitive unit cell, we again consider the arrangement of constituent particles. The number of octahedral voids is equal to twice the number of particles present in the unit cell.

In a hexagonal primitive unit cell, there are 6 particles at the corner positions. Since each particle contributes to one octahedral void, the number of octahedral voids is 6 x 2 = 12.

Therefore, the number of octahedral voids in a hexagonal primitive unit cell is 12.

Hence, the correct option for the number of tetrahedral and octahedral voids in a hexagonal primitive unit cell is b) 12, 6.