Question

In FCC, 50% of tetrahedral voids are filled. Find the effective number of atoms in a unit cell if it consists of the same atoms in the lattice and voids.

• A. 6
• B. 8
• C. 4
• D. 5

Answer 1

The correct option is B

8

Explanation for the correct option:

The correct option is (B)

1. FCC has a total of 4 body diagonals.
2. The number of atoms in the FCC is 4.
3. In FCC, there are two tetrahedral voids on every diagonal of the unit cell.
4. Thus, a total of 8 tetrahedral voids are present in the unit cell.
5. Now as per the question only 50% of tetrahedral voids are filled. So, total tetrahedral voids are 4.
6. The effective number of atoms in the new unit cell = Number of atoms in FCC + Number of atoms in tetrahedral voids.
7. $Z_{eff}=4+4$
8. $Z_{eff}=8$

Hence, the correct answer is option B.