Rutile 7: an equivalent unit cell

The structure to the left shows eight unit cells marked out in a black wireframe that we are familiar with, and an equivalent unit cell in yellow. The yellow unit cell also links titanium ions but they are taken from the body-centre titaniums in the eight original unit cells. The relationship of the yellow cell to the black cell is therefore that the latter has been displaced along half of the unit cell diagonal. Looking at the yellow unit cell from the direction in which the picture loads, it follows from the square symmetry of that projection that it is equivalent to the black unit cell; it has just been rotated by 180° and displaced by half a unit cell length in the tetragonally distorted direction. It is this 180° rotation which makes the diagonal axis of the titanium oxide octahedron rotate so that it is pointing in a perpendicular direction. One can therefore conclude that all the titanium ions are in equivalent positions.

Go to page 8 to consider a polyhedral representation of rutile.

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