Primitive Unit Cells

There are very many unit cell structures if we consider all the atoms or ions in the crystal. However, if we focus on just one atom or ion, we can reduce the number to just 14 primitive cells. Three of these, the simple cubic, facecentered cubic (fcc), and body-centered cubic (bcc) unit cells, are shown in Figure 1.1. The lattice points, represented by small spheres in the drawings, correspond to the centers of the atoms, ions, or molecules occupying the lattice.

Following the procedure we used for NaCl, the number of atoms, ions, or molecules per unit cell is 1 for the simple cubic lattice, 4 for the fcc lattice, and 2 for the bcc lattice.

Figure 1.1. Three cubic unit cells.

Looking again at Figure 9-1, we see that the Cl^- ions form a fcc unit cell with the Na⁺ ions placed between each pair of Cl^- ions. Thus NaCl is a particular structure derived from the fcc primitive cell. Cesium chloride crystallizes with a structure derived from the simple cubic primitive cell. Cl^- ions occupy the 8 corner sites with Cs⁺ in the center of the cell; note that this is not a body-centered cubic unit cell since the ion at the center is not the same as those at the corners. Thus there is one CsCl unit per unit cell and the coordination numbers of Cs⁺ and Cl^- are both 8. Crystals of CsBr and CsI adopt the CsCl structure, but all other alkali halides crystallize in the NaCl structure.