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What is the total number of atoms per unit cell in a face-centred cubic (fcc) structure?


A face-centred cubic (fcc) unit cell contains atoms at all the corners and at the centre of all the faces of the cube. It can be seen that each atom located at the face-centre is shared between two adjacent
unit cells and only 1/2 of each atom belongs to a unit cell.

Thus, in a face-centred cubic
(fcc) unit cell:
(i) 8 corners atoms × 1/8 atom per unit cell=8×1/8
  = 1 atom
(ii) 6 face-centred atoms ×
1/2 atom per unit cell = 6 ×1/2 = 3 atoms
∴ Total number of atoms per unit cell = 4 atoms

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