What is common in HCP and FCC unit cell ?

Options

A. octahedral voids are completely inside the unit cell
B. tetrahedral voids are completely inside the unit cell
C. Number of layers constituting the unit cell are same
D. None of these

Answer

To determine what is common in HCP (Hexagonal Close Packing) and FCC (Face-Centered Cubic) unit cells, we can analyze their structures and characteristics step by step.

### Step-by-Step Solution:

1. **Understanding HCP Structure**:
- HCP consists of layers of atoms arranged in a specific pattern. The arrangement is ABAB, meaning the first layer (A) is followed by a second layer (B) and then the first layer (A) is repeated.
- In HCP, the spheres in the third layer cover the tetrahedral holes of the first layer.

2. **Understanding FCC Structure**:
- FCC has a different arrangement known as ABC. The first layer (A) is followed by a second layer (B), and then a third layer (C) is placed in such a way that it is different from the first two layers.
- In FCC, the third layer is stacked in the depressions of the second layer.

3. **Common Features**:
- Both HCP and FCC are types of close-packed structures, which means they maximize the packing efficiency of spheres.
- Both structures contain octahedral and tetrahedral voids.
- In FCC, there are 4 octahedral voids and 8 tetrahedral voids.
- In HCP, there are 6 octahedral voids and 12 tetrahedral voids.

4. **Packing Efficiency**:
- Both HCP and FCC have a packing efficiency of approximately 74%, which is the highest possible for spheres.

5. **Coordination Number**:
- Both structures have a coordination number of 12, meaning each atom is in contact with 12 other atoms.

6. **Conclusion**:
- The common features between HCP and FCC unit cells include:
- Both are close-packed structures.
- Both have a packing efficiency of 74%.
- Both have a coordination number of 12.
- Both contain octahedral and tetrahedral voids.

### Final Answer:
The common features in HCP and FCC unit cells are that both are close-packed structures with a packing efficiency of approximately 74%, a coordination number of 12, and both contain octahedral and tetrahedral voids.

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