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# Crystal Structure of Rutile

Titanium dioxide occurs naturally as the mineral rutile.

The ionic radius of the titanium(IV) ion is 0.745 Å and that of the oxide ion is 1.26 Å. The ratio of radii for the cation and anion is thus r+/r- = 0.745/1.26 = 0.591.

With a radius ratio of 0.591, the cubic holes are too large (rhole/r = 0.732) to be suitable. The titanium(IV) ions will prefer to occupy octahedral holes in a closest-packed structure. Nature chooses to pack the oxide ions in rutile in a hexagonal closest-packed structure.

The images below depict the structure of rutile. The red spheres represent the oxide ions and the blue spheres represent the titanium(IV) ions.

Examine the images and note how the oxide ions lie in an expanded hexagonal closest-packed structure. The titanium(IV) ions, which are smaller than the oxide ions, are inserted into octahedral holes and push the oxide ions apart so that no two oxide ions are in contact with each other. The unit cell for rutile, however, is based upon the titanium(IV) ions, not the oxide ions. Tip the unit cell on its edge to more clearly observe the packing of the oxide ions. The unit cell contains two layers of oxide ions, with three ions in each layer. The rutile structure has (6,3)-coordination. Observe that none of the tetrahedral holes are occupied. The titanium(IV) ions lie in octahedral holes. What is the geometry of ions surrounding the oxide ions?

The dimensions of the rutile unit cell are a = b = 4.5937 Å and c = 2.9587 Å.

1. How many oxide ions lie inside the unit cell? (Portions of an oxide ion lying outside the unit cell do not count.)
2. How many titanium(IV) ions like inside the unit cell? The structure as a whole is electrically neutral and thus the unit cell must be electrically neutral. Therefore Ti4+ and O2- ions must be present in a 1:2 ratio.
3. What is the volume of the rutile unit cell (in cm3)?
4. What is the density of rutile (in g cm-3)?
5. The measured density of naturally occuring rutile is 4.23 g cm-3. How does your calculated density compare with the experimental values?
Unit Cell Portions of Atoms lying inside the Unit Cell

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Ionic Solids