How many atoms are in a face centered cubic structure?

How many atoms are in a face centered cubic structure?

• A. Four
• B. Six
• C. Twelve
• D. Fourteen

Answer: (D)

In an FCC unit cell, you count atoms by accounting for how they’re shared with neighboring cells. There are atoms at the eight corners and at the centers of the six faces. Each corner atom is shared by eight unit cells, so it contributes 1/8 to this cell: eight times 1/8 gives 1 atom. Each face-centered atom is shared by two unit cells, so it contributes 1/2 to this cell: six times 1/2 gives 3 atoms. Adding these contributions, 1 + 3 equals 4 atoms per conventional FCC unit cell. The option that would give fourteen isn’t consistent with how atoms are shared in the lattice, so it isn’t correct for an FCC structure.

In an FCC unit cell, you count atoms by accounting for how they’re shared with neighboring cells. There are atoms at the eight corners and at the centers of the six faces. Each corner atom is shared by eight unit cells, so it contributes 1/8 to this cell: eight times 1/8 gives 1 atom. Each face-centered atom is shared by two unit cells, so it contributes 1/2 to this cell: six times 1/2 gives 3 atoms. Adding these contributions, 1 + 3 equals 4 atoms per conventional FCC unit cell. The option that would give fourteen isn’t consistent with how atoms are shared in the lattice, so it isn’t correct for an FCC structure.