Question

Calcium sulfide adopts the sodium chloride crystal structure (Figure). How many${\mathbf{S}}^{\mathbf{2}\mathbf{-}}$ions are in the CaS unit cell?

Short answer

Four${\mathbf{S}}^{\mathbf{2}\mathbf{-}}$ ions are present in the CaS unit cell

Step-by-step solution

Sodium chloride structure

Sodium chloride structure is an anion-occupied face-centered array with cations occupying interpenetrating FCC lattice.

Ions in the unit cell

The face-centered cubic unit cell consists of 8 anions in the corner, thus one anion contributing$\frac{\mathbf{1}}{\mathbf{8}}$ to the unit cell. Along with that, anions are present in the center of the six respective faces of the cell. Hereby, each anion contributing$\frac{\mathbf{1}}{\mathbf{2}}$ to the unit cell.

Thus, each unit cell consists of $\mathbf{8}\mathbf{\times }\left(\frac{1}{8}\right)\mathbf{+}\mathbf{6}\mathbf{\times }\left(\frac{1}{2}\right)\mathbf{=}\mathbf{4}$, i.e., four anions in the unit cell.

Similarly, for cations, the ions are arranged in an FCC array, thus four cations in the unit cell.