rutile structure

The white pigment in most paint, sunscreen and toothpaste is titanium dioxide, and its most common crystal form is named rutile after the mineral. Rutile is the standard structure for a great many MX2 compounds in which the cation is too small to take the eight-fold coordination of fluorite, and so settles for six. It is a tetragonal structure — a stretched box rather than a perfect cube — which makes it a useful contrast to all the cubic structures.

Picture each titanium ion sitting at the centre of an octahedron of six oxide ions (coordination 6), and each oxide ion shared between three titaniums, sitting in a flat trigonal-planar arrangement (coordination 3). So rutile is 6:3 coordinate, and the 6-to-3 ratio is exactly the 1-to-2 stoichiometry of TiO2. The TiO6 octahedra link by sharing edges to form chains running through the crystal, and the chains link by sharing corners. In terms of holes, you can view it as a roughly hexagonal-close-packed array of oxide ions with the titanium ions filling half of the octahedral holes. The unit cell is tetragonal with two TiO2 units (Z = 2).

Rutile is adopted by many dioxides and difluorides where the cation is moderately small: TiO2 itself, plus SnO2, MnO2, the difluorides MgF2, ZnF2, FeF2, and others. The structure choice tracks the radius ratio: when the cation is too large to be six-coordinate among oxides it takes the fluorite (eight-coordinate) structure instead, which is why ZrO2 (larger Zr4+) is fluorite while TiO2 (smaller Ti4+) is rutile. Rutile thus completes the trio of common MX2 structures (fluorite for big cations, rutile for medium, and layer structures for the most covalent), a neat illustration of how size sorts compounds into structural families.