Question

How many tetrahedral holes are occupied in a diamond?
A. 25%
B. 50%
C. 75%
D. 100%

Answer 1

Hint: The hole or void enclosed by 4 spheres located at the corners of the regular tetrahedron is called a tetrahedral void. If the number of unit cells is ‘n’ then tetrahedral voids are ‘2n’. The coordination number for a tetrahedral hole is four.

Complete step by step solution:
- We have to find how many numbers of tetrahedral holes or voids are occupied in a diamond.
- Diamond is the hardest in nature.
- The structure of the diamond is similar to the structure of the ZnS (zinc sulphide).
- In the fcc, (Face centred cubic structure) of ZnS, Zinc or sulphide occupies fcc lattice points in an alternative manner.
- Means half tetrahedral holes or voids are occupied by zinc and the remaining half is occupied by sulphur.
- Like ZnS in diamond Carbon occupies half of the tetrahedral voids or holes.
- The total number of tetrahedral voids in fcc is 8.
- Out of 8 voids, carbon occupies half of it means four.
- Therefore the percentage of occupancy of the tetrahedral void by carbon in the diamond is 50%.

So, the correct option is B.

Note: Coordination number in tetrahedral voids is 4. And coordination number on octahedral void is 8. Tetrahedral voids found in fcc and octahedral voids found in HCP (Hexagonal close packing). The total number of octahedral voids is equal to the number of unit cells present in HCP.