Chemistry · Ch 11 — The Solid State

Primitive Cubic Unit Cell

11.5.1

Primitive Cubic Unit Cell

A primitive (simple) cubic unit cell has atoms only at its eight corners. As Fig. 1.12 shows, each corner atom is shared between eight adjacent unit cells — four in the same layer and four in the layer above (or below). Therefore only $\tfrac{1}{8}$ of each corner atom actually belongs to a given unit cell.

Fig. 1.13 depicts the same cell three ways: (a) an open structure, where each sphere marks only the centre of the particle (easiest to follow the arrangement); (b) a space-filling model showing the real size of the particles; and (c) the actual portions of the atoms that lie inside one cell. …

Figure 1.12In a simple cubic unit cell, each corner atom is shared between 8 unit cells.

What this figure shows. A cluster of eight cubes meeting at a common corner where a single sphere sits; the sphere is shared among all eight surrounding unit cells (four in the upper layer, four in the lower), showing only 1/8 of the corner atom belongs to one cell. …

Figure 1.13A primitive 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 simple cubic cell. (a) 'open structure': black wireframe cube with a small green sphere at each of the 8 corners.

(b) 'space-filling': eight large green spheres touching along cube edges.

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