Resources written by Chas McCaw for sixth form chemistry teaching and beyond.
General interest:
Graphite Buckminsterfullerene Ice White phosphorus Benzene Cyclohexane AdamantaneCubic:
Sodium Caesium chloride Polonium Copper Halite Fluorite Antifluorite Zinc blende DiamondNon-cubic:
Hexagonal:
Magnesium WurtziteTetragonal:
RutileTrigonal:
α-quartzTriclinic:
Copper(II) sulfateOrthorhombic:
α-SulfurMonoclinic:
β-SulfurOther compounds that adopt this structure: GeO2, cassiterite (SnO2), plattnerite (PbO2), pyrolusite (MnO2), TaO2, MgF2, MnF2, FeF2, CoF2, NiF2 and ZnF2.
The unit cell of rutile is shown to the left. The black wireframe just marks out the repeating unit of space in the structure - the lines are not supposed to depict any kind of chemical bond. The oxide ions are shown in red and the titanium ions in silver. The unit cell is tetragonal, which is like a cube except one of the dimensions is a different length to the other two, making it a square prism. This modification away from the cubic structure is known as a tetragonal distortion. The titanium ions occupy the corners and the body-centre of the unit cell. There are six oxide ions in the unit cell, of which two are fully inside. From these two it is apparent that the oxide ions are coordinated to (ie in contact with) three neighbouring titanium ions. These three ions lie in a trigonal planar arrangement around each oxide ion. So altogether there are 15 ions involved with the unit cell, but the cell occupancy is less than this since many of the ions are only partially inside the cell.
Cell occupancy:
The cell occupancy of titanium ions = (8 x 1/8) + 1 = 2.
The cell occupancy of oxide ions = (4 x 1/2) + 2 = 4.
The cell occupancy reflects the 1:2 stoichiometry of titanium and oxygen in the formula of titanium oxide.
Coordination numbers:
The coordination number of oxide is 3, ie it has three nearest neighbours. The coordination number of titanium is 6. This is clearly seen with the titanium in the centre in the unit cell. Note that the nearest neighbours of an ion are the counter ions of opposite change. This is how the structure maximises the attractive ionic forces between ions of opposite charge.
Go to page 4 to consider the stacking of unit cells.
Other compounds with a tetragonal unit cell:
PCl5, CI4, N(CH3)4I, PdS, XeF2, CuAu, adamantane (C10H16), calomel (HgCl), litharge (PbO), minium (Pb3O4), anatase (TiO2), zircon (ZrSiO4), hausmanite (Mn3O4) and xenotime (YPO4).