Face-Centred Cubic (FCC) Unit Cell — Atom Location Description Which statement correctly describes the atom locations in a face-centred cubic (FCC) space lattice?

Introduction / Context:
Describing atom positions in common crystal structures such as FCC is fundamental to computing packing factors, coordination numbers, and density. Correctly identifying lattice-atom locations prevents confusion when deriving material properties from structure.

Given Data / Assumptions:

• Ideal hard-sphere model for atoms.
• Conventional cubic unit cell representation.
• Sharing of corner and face atoms among adjacent cells.

Concept / Approach:
In the FCC lattice, atoms are located at all eight cube corners and at the centres of all six faces. Although fourteen lattice points are described geometrically, the effective number of whole atoms contained per unit cell is 4 (8 corners * 1/8 + 6 faces * 1/2 = 1 + 3 = 4). The option asks for the correct description of locations, not the effective count, so the statement with eight corners and six face-centred atoms is correct.

Step-by-Step Solution:
Recall FCC geometry: corner atoms + face-centred atoms.Confirm there are six faces → 6 face-centre atoms.Select the option that lists “8 corners + 6 faces” → correct description.Note: effective contained atoms = 4 due to sharing.

Verification / Alternative check:
APF for FCC computed with 4 atoms per cell returns ~0.74, matching standard results.

Why Other Options Are Wrong:
Option (a) mixes BCC features; FCC has face-centre atoms.Option (c) describes an HCP-type hexagonal prism, not FCC.

Common Pitfalls:
Confusing geometric description (14 positions) with effective atom count (4).

Final Answer:
fourteen atoms with eight at cube corners and six at the centres of the six faces