Calculate the linear density of ions along the [111] direction UO2, which has the CaF2 structure (Figure 1).

Figure 1:

Fluorite (CaF2) unit cell showing (a) ion positions and (b) full-size ions. [Part (b) courtesy of Accelrys, Inc.]

O Ca+ F Fions located at corners of a cube (at one-quarter of the distance along the body diagonal) (b) (a) Structure: fluorite (CaF) type Bravais lattice: fcc Ions/unit cell: 4Ca++8F- Typical ceramics: UO, ThO, and TeO