Which of the following statements are true regarding tatrahedral voids in fcc lattice ?

Options

A. Tetrahedral voids formed by one corner spheres and three face spheres.
B. Two tetrahedral volds can exist on one diagonal body line in fcc cubic
C. Tetrahedral voids are equal to number of spheres involved in body
D. Volume of tetrahedral voids are half of the octahedral voids.

Answer

To determine which statements are true regarding tetrahedral voids in an FCC (Face-Centered Cubic) lattice, we will analyze the characteristics of the FCC structure and the voids present within it.

### Step-by-Step Solution:

1. **Understanding FCC Lattice Structure**:
- An FCC lattice consists of atoms located at each corner of the cube and at the centers of each face.
- This arrangement leads to a specific number of tetrahedral and octahedral voids.

2. **Identifying Tetrahedral Voids**:
- In an FCC lattice, tetrahedral voids are formed by one atom at a corner and three atoms at the face centers.
- Each corner atom contributes to multiple tetrahedral voids due to the shared nature of the lattice.

3. **Counting Tetrahedral Voids**:
- There are a total of 4 main diagonals in the FCC lattice.
- Each diagonal contains 2 tetrahedral voids.
- Therefore, the total number of tetrahedral voids in an FCC lattice is calculated as:
\[ \text{Total Tetrahedral Voids} = 4 \text{ (diagonals)} \times 2 \text{ (voids per diagonal)} = 8 \]

4. **Evaluating the Statements**:
- **Statement A**: "Tetrahedral voids are formed by one corner sphere and three face-centered spheres."
- This statement is **True** as it accurately describes how tetrahedral voids are formed.

- **Statement B**: "Two tetrahedral voids can exist on one diagonal line in FCC cubic."
- This statement is **True** as we have established that each diagonal contains two tetrahedral voids.

- **Statement C**: "Tetrahedral voids are equal to the number of spheres involved in the body."
- This statement is **False**. In an FCC lattice, there are 4 atoms (spheres) per unit cell, but there are 8 tetrahedral voids, which is not equal.

- **Statement D**: "Volume of the tetrahedral voids is half of that of the octahedral voids."
- This statement is **False**. In an FCC lattice, there are 4 octahedral voids and 8 tetrahedral voids, meaning the volume of tetrahedral voids is not half but rather larger than that of octahedral voids.

5. **Conclusion**:
- The true statements regarding tetrahedral voids in an FCC lattice are **A and B**.

### Summary of True Statements:
- **A**: True
- **B**: True
- **C**: False
- **D**: False