What is the coordination number for atoms in a face-centered cubic lattice?

• A. 12
• B. 8
• C. 6
• D. 4

Answer: (A)

Coordination number is the number of nearest-neighbor atoms that each atom touches. In a face-centered cubic lattice, atoms sit at the corners and at the centers of the faces. The closest contacts occur along the face diagonals, giving twelve distinct nearest neighbors. You can think of it as four neighbors in the same layer, four in the layer above, and four in the layer below, all at the distance a/√2. This dense packing leads to twelve contacts per atom. For comparison, simpler packings have fewer: six for simple cubic, eight for body-centered cubic, and four for diamond-type structures.