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Chemistry · Ch 11 — The Solid State

Body-Centred Cubic Unit Cell

11.5.2

Body-Centred Cubic Unit Cell

A body-centred cubic (bcc) unit cell has an atom at each of the eight corners and, in addition, one atom right at the body centre. Fig. 1.14 shows it as (a) an open structure, (b) a space-filling model, and (c) the actual portions of atoms belonging to the cell.

The atom at the body centre lies entirely inside the cell, so it belongs wholly to it, while each corner atom contributes only 18\tfrac{1}{8}:

  • 8 corner atoms =8×18=1= 8 \times \dfrac{1}{8} = 1 atom …
Figure 1.14A body-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 a bcc cell. (a) 'open structure': black wireframe cube with small green spheres at the 8 corners plus one green sphere at the body centre, with body diagonals drawn.

(b) 'space-filling': large green corner spheres with a central sphere touching them along the body diagonal.

(c) 'actual portions': cube showing 1/8 corner wedges of green spheres plus the whole central sphere. …