The number of tetrahedral and octahedral voids in hexagonal primitive unit cell are ____ are _____

Options

A. 8, 4
B. 2, 1
C. 12, 6
D. 6, 12

Answer

To determine the number of tetrahedral and octahedral voids in a hexagonal primitive unit cell, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Structure of the Hexagonal Primitive Unit Cell**:
- A hexagonal primitive unit cell contains a total of 6 atoms in its crystal structure.

2. **Calculate the Number of Octahedral Voids**:
- The number of octahedral voids in a crystal structure is equal to the number of atoms present in that structure.
- Therefore, for a hexagonal primitive unit cell, the number of octahedral voids = Number of atoms = 6.

3. **Calculate the Number of Tetrahedral Voids**:
- The number of tetrahedral voids is given by the formula: Number of tetrahedral voids = 2 × (Number of atoms).
- For a hexagonal primitive unit cell, this means:
- Number of tetrahedral voids = 2 × 6 = 12.

4. **Summarize the Results**:
- The number of tetrahedral voids is 12.
- The number of octahedral voids is 6.

### Final Answer:
- The number of tetrahedral voids in a hexagonal primitive unit cell is **12**.
- The number of octahedral voids in a hexagonal primitive unit cell is **6**.