12.90P - Chemistry: Molecular Nature Of Matter And Change

Question

Zinc oxide adopts the zinc blende crystal structure (Figure). How many ${\mathbf{Zn}}^{\mathbf{2}\mathbf{+}}$ ions are in the ZnO unit cell?

Step-by-Step Solution

Answer

Four ${\mathbf{Zn}}^{\mathbf{2}\mathbf{+}}$ ions are present in the ZnO unit cell

Step 1: Zinc blende structure

Zinc blende is a cubic closed packed structure with the anions occupying the face-centered lattice and the cations are packed in half of the tetrahedral voids.

Step 2: 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 $\mathbf{8}\mathbf{\times }\frac{\mathbf{1}}{\mathbf{8}}\mathbf{+}\mathbf{6}\mathbf{\times }\frac{\mathbf{1}}{\mathbf{2}}\mathbf{=}\mathbf{4}$, i.e., four anions in the unit cell.

The cations occupy half of the tetrahedral sites. Here in this unit cell, the number of tetrahedral sites is 8. Thus, in this zinc blende structure, the number of sites occupied by data-custom-editor="chemistry" ${\mathbf{Zn}}^{\mathbf{2}\mathbf{+}}$ cations is four in number.