In an FCC lattice, what is the contribution from corner atoms and face-centered atoms?

• A. 1/8 at corners and 1/4 at face centers
• B. 1/2 at corners and 1/8 at faces
• C. 1/8 at corners and 1/2 at faces
• D. 1/4 at corners and 1/4 at faces

Answer: (C)

The key idea is how atoms are shared between unit cells in a crystalline lattice. In an FCC lattice, atoms at corners are shared by eight unit cells, so each corner atom contributes 1/8 to a given unit cell. Atoms on the faces are shared by two unit cells, so each face-centered atom contributes 1/2 to a given unit cell. There are eight corners, giving 8×1/8 = 1, and six face centers, giving 6×1/2 = 3, for a total of 4 atoms per unit cell. So the contributions are 1/8 from each corner position and 1/2 from each face-centered position.