What is the coordination number of a face-centered cubic (FCC) lattice?

• A. 6
• B. 8
• C. 12
• D. 14

Answer: (C)

Coordination number is how many nearest-neighbor atoms surround a given atom. In a face-centered cubic arrangement, atoms are packed so that each atom makes contact with twelve others. This comes from the geometry around a lattice point: the closest contacts occur along the face diagonals of the cube, placing twelve neighboring atoms at the touching distance in a cuboctahedral arrangement. That close-packed, highly connected shell yields 12 nearest neighbors. This is larger than in simpler packings like simple cubic or body-centered cubic, where there are fewer touching neighbors. So the coordination number for FCC is twelve.