Crystal structures — coordination number of the face-centred cubic (FCC) lattice What is the coordination number (number of nearest neighbours) for atoms in a face-centred cubic space lattice?

Introduction / Context:The coordination number is a key descriptor of atomic packing and nearest-neighbour interactions in crystal structures. It influences density, slip behaviour, and many mechanical properties such as ductility and stacking-fault energy. FCC and HCP metals typically show high ductility partly due to their high coordination.Given Data / Assumptions:

• Ideal, defect-free face-centred cubic lattice.
• Nearest-neighbour definition based on equal shortest interatomic distance.

Concept / Approach:In the FCC lattice, each atom contacts 12 nearest neighbours: 4 in its own close-packed plane, 4 in the plane above, and 4 in the plane below. This dense packing leads to a packing factor of 0.74, identical to that of hexagonal close-packed structures. The high coordination correlates with multiple slip systems (e.g., {111}<110>), underpinning the excellent formability of FCC metals such as aluminium, copper, and austenitic stainless steels.Step-by-Step Solution:

Verification / Alternative check:Geometry of close packing shows each sphere touching 12 others; the same count emerges from radial distribution functions where the first peak integrates to 12 for ideal FCC.

Why Other Options Are Wrong:

• Six or eight: correspond to simple cubic (6) or body-centred cubic (8 nearest, if defined strictly; sometimes 14 including next-nearest).
• Eighteen or twenty: exceed nearest-neighbour count for close packing.

Common Pitfalls:Confusing coordination number with the number of slip systems; mixing BCC next-nearest neighbours (total 14) with true nearest neighbours count.

Final Answer: