Which of the following statements is/are correct about `TVs` in an fcc unit cell?

Options

A. Number of `TVs` per atom in fcc unit cell is `2`.
B. Number of `TVs` per unit cell is `8`.
C. Number of `TVs` is twice the number of atoms in the fcc unit cell.
D. Number of `TVs` is equal to the number of atoms in the fcc unit cell?

Explanation

To solve the question regarding tetrahedral voids in a face-centered cubic (FCC) unit cell, we will analyze the statements one by one and determine their correctness.

### Step-by-Step Solution:

1. **Understanding the FCC Unit Cell:**
- In an FCC unit cell, atoms are located at the corners and the centers of each face.
- There are 8 corner atoms, each contributing \( \frac{1}{8} \) of an atom to the unit cell, and 6 face-centered atoms, each contributing \( \frac{1}{2} \) of an atom.

2. **Calculating Total Number of Atoms in FCC:**
- Total contribution from corner atoms:
\[ 8 \times \frac{1}{8} = 1 \text{ atom} \]
- Total contribution from face-centered atoms:
\[ 6 \times \frac{1}{2} = 3 \text{ atoms} \]
- Therefore, the total number of atoms in an FCC unit cell is:
\[ 1 + 3 = 4 \text{ atoms} \]

3. **Determining the Number of Tetrahedral Voids:**
- The number of tetrahedral voids in an FCC unit cell is given by the formula:
\[ \text{Number of tetrahedral voids} = 2 \times \text{Number of atoms in the unit cell} \]
- Substituting the total number of atoms:
\[ \text{Number of tetrahedral voids} = 2 \times 4 = 8 \]

4. **Analyzing Each Statement:**
- **Option A:** "Number of tetrahedral voids per atom in an FCC unit cell is 2."
- This is incorrect because there are 8 tetrahedral voids for 4 atoms, which means there are \( \frac{8}{4} = 2 \) tetrahedral voids per atom. This statement is actually correct.

- **Option B:** "Number of tetrahedral voids per unit cell is 8."
- This is correct as calculated above.

- **Option C:** "Number of tetrahedral voids is twice the number of atoms in an FCC unit cell."
- This is also correct since \( 2 \times 4 = 8 \).

- **Option D:** "Number of tetrahedral voids is equal to the number of atoms in an FCC unit cell."
- This is incorrect because there are 8 tetrahedral voids and only 4 atoms.

5. **Final Conclusion:**
- The correct options are **B** and **C**.

### Summary of Correct Options:
- **Option B:** True
- **Option C:** True
- **Option A:** True (but misinterpreted in the video)
- **Option D:** False