Zinc sulfide crystallizes in two different forms: wurtzite and zinc blende.
The ionic radius of the zinc(II) ion is 0.74 Å and that of the sulfide ion is 1.70 Å.
The ratio of radii for the cation and anion is thus r+/r- = 0.74/1.70 = 0.44.
With a radius ratio of 0.44, one might expect the zinc(II) ions to occupy octahedral holes; however, the value of 0.44 is only slightly larger than rhole/r = 0.414 for an octahedral hole. There is also some covalent character in the Zn2+-S2- interaction, which tends to shorten the interatomic distance. Experimentally, one finds that the zinc(II) ions occupy tetrahedral holes.
If the sulfide ions originally adopt a hexagonal closest-packed structure, the ZnS crystal is wurtzite. If the sulfide ions originally adopt a cubic closest-packed structure, the ZnS crystal is zinc blende.
The virtual reality displays depict the structure of wurtzite. The yellow spheres represent the sulfide ions and the blue spheres represent the zinc(II) ions.
Examine the images and note how the sulfide ions lie in an expanded hexagonal closest-packed structure. The zinc(II) ions, which are smaller than the sulfide ions, are inserted into tetrahedral holes and push the sulfide ions apart so that no two sulfide ions are in contact with each other. The resulting structure has (4,4)-coordination. Observe that none of the octahedral holes are occupied.
The dimensions of the wurtzite unit cell are a = b = 3.82 Å and c = 6.26 Å. The lengths of the sides of the diamond forming the base of the unit cell are given by a and b. The height of the unit cell is given by c.
- How many sulfide ions lie inside the unit cell? (Portions of a sulfide ion lying outside the unit cell do not count.)
- How many zinc(II) ions like inside the unit cell? The structure as a whole is electrically neutral and thus the unit cell must be electrically neutral. Therefore Zn2+ and S2- ions must be present in a 1:1 ratio.
- What is the volume of the wurtzite unit cell (in cm3)?
- What is the density of wurtzite (in g cm-3)?
- The measured densities of natural samples of wurtzite lie in the range of 4.0 to 4.1 g cm-3. How does your calculated density compare with the experimental values?
- Compare the calculated density of wurtzite with that of zinc blende. Are they the same or different? Explain why.
|Unit Cell||Portions of Atoms lying inside the Unit Cell|
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