Octahedral void at edge center in ccp arrangement is equally distributed amongst

Options

A. 8 unit cells
B. 6 unit cells
C. 4 unit cells
D. 2 unit cells

Answer

To determine how many units of octahedral voids are distributed at the edge center in a cubic close-packed (CCP) arrangement, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the CCP Structure**:
- In a cubic close-packed (CCP) arrangement, also known as face-centered cubic (FCC), atoms are arranged in a specific manner where each unit cell has atoms at the corners and the centers of each face.

2. **Identifying Octahedral Voids**:
- Octahedral voids are formed when six atoms are arranged in an octahedral geometry. In the CCP structure, octahedral voids are located at specific positions, including the center of the cube and at the edge centers.

3. **Locating Edge Center Voids**:
- Each edge of the cube has an octahedral void located at its center. Since a cube has 12 edges, we need to consider how many of these edge-centered voids are unique to the unit cell.

4. **Sharing of Edge Center Voids**:
- Each edge-centered octahedral void is shared between four adjacent unit cells. Therefore, when we count the total number of edge-centered voids, we must account for this sharing.

5. **Calculating the Total Number of Edge Center Voids**:
- There are 12 edges in a cube, and each edge contributes one octahedral void. However, since each void is shared by four unit cells, the effective number of unique octahedral voids contributed by the edge centers is:
\[ \text{Total edge center voids} = \frac{12 \text{ (edges)}}{4 \text{ (shared)}} = 3 \]

6. **Conclusion**:
- Therefore, the total number of octahedral voids at the edge centers in a cubic close-packed arrangement is **3**.

### Final Answer:
The number of units of octahedral voids distributed at the edge center in a CCP arrangement is **3**.