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Chemistry · Ch 1 — The Solid State

Face-Centred Cubic Unit Cell

1.5.3

Face-Centred Cubic Unit Cell

A face-centred cubic (fcc) unit cell has atoms at all eight corners and also at the centre of each of the six faces. As Fig. 1.15 shows, an atom at a face centre is shared between two adjacent unit cells, so only 12\tfrac{1}{2} of it belongs to one cell. Fig. 1.16 shows the cell as (a) an open structure, (b) a space-filling model, and (c) the actual portions of the atoms in one cell.

Counting the contributions:

  • 8 corner atoms =8×18=1= 8 \times \dfrac{1}{8} = 1 atom …
Figure 1.15An atom at face centre of unit cell is shared between 2 unit cells

What this figure shows. Two adjacent transparent purple/pink cuboidal cells sharing a common face; a single orange/red sphere sits on that shared face, showing 1/2 of the face-centred atom belongs to each of the two cells. …

Figure 1.16A face-centred cubic unit cell (a) open structure (b) space filling structure (c) actual portions of atoms belonging to one unit cell.

What this figure shows. Three panels of an fcc cell. (a) 'open structure': black wireframe cube (dashed hidden edges) with small green spheres at the 8 corners and one at the centre of each of the 6 faces.

(b) 'space-filling': cluster of large green spheres.

(c) 'actual portions': cube showing 1/8 corner wedges and 1/2 face spheres of green atoms inside the cube. …