Question

Which of the following is correct for fcc lattice?

• A. There are equal no of octahedral and tetrahedral voids in a unit cell.
• B. The tetrahedral voids are present at the edge centers.
• C. Octahedral voids are present at the body center and edge centers.
• D. Its packing efficiency (PE) is higher than hcp lattice PE.

Hint:

In FCC, octahedral voids are at the body center and edge centers, while tetrahedral voids are along the body diagonals.

Answer 1

The Correct Option is C

In an FCC lattice, there are 4 atoms per unit cell. The number of octahedral voids equals the number of atoms (4), and the number of tetrahedral voids is twice the number of atoms (8), so they are not equal (ruling out option 1). Tetrahedral voids are located along the body diagonals, not at the edge centers, which are occupied by atoms (ruling out option 2). Octahedral voids are indeed located at the body center (1/2, 1/2, 1/2) and edge centers (e.g., 1/2, 0, 0), making option 3 correct. Finally, the packing efficiency of FCC and HCP lattices is the same (74%), so option 4 is incorrect. Thus, the correct answer is option 3.