Unit cells, atomic coordinates and nomenclature

Irrespective of the complexity of a crystal structure, it can be constructed by the packing together of imit cells. This means that the positions of all of the atoms in the crystal do not need to be given, only those in a unit cell. The minimum amount of information needed to specify a crystal structure is thus the unit cell type, the cell parameters and the positions of the atoms in the unit cell. For example, the unit cell of the rutile form of titanium dioxide has a tetragonal unit cell, with cell parameters, ao = bo = 0.459 nm, cq = 0.296 nm.  

The unit cell dimensions are often specified in terms of the Angstrom unit. A, where 10 A = 1 nm. 

The (x,y,z) coordinates of the atoms in each unit cell are expressed as fractions of ao, bo and cq, the cell sides. Thus, an atom at the centre of a unit cell would have a position specified as (, j), irrespec- 

A unit cell reflects the symmetry of the crystal structure. Thus, an atom at a position (x, y, z) in a unit cell may require the presence of atoms at other positions in order to satisfy the symmetry of the structure. For example, a unit cell with a centre of symmetry will, of necessity, require that an atom at (x,y,z) be paired with an atom at (—x, —y, —z). To avoid long repetitive lists of atom positions in complex structures, crystallographic descriptions usually list only the minimum number of atomic positions which, when combined with the symmetry of the structure, given as the space group, generate all the atom positions in the unit cell. Additionally, the Bravais lattice type and the motif are often specified as well as the number of formula units in the unit cell, written as Z. Thus, in the unit cell of rutile, given above, Z = 2. This means that there are 

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