Coordination Number - Crystallography Usage

Crystallography Usage

In materials science, the bulk coordination number of a given atom in the interior of a crystal lattice is the number of atoms touching the given atom. Iron at 20 °C has a body-centered cubic (BCC) crystal in which each interior iron atom occupies the centre of a cube formed by eight neighbouring iron atoms. The bulk coordination number for this structure is therefore 8.

The highest bulk coordination number is 12, found in both hexagonal close-packed (HCP) and cubic close-packed (CCP) (also known as face-centered cubic or FCC) structures. This value of 12 corresponds to the theoretical limit of the kissing number problem when all spheres are identical.

The two most common allotropes of carbon have different coordination numbers. In diamond, each carbon atom is at the centre of a tetrahedron formed by four other carbon atoms, so the coordination number is four, as for methane. Graphite is made of two-dimensional layers in which each carbon is covalently bonded to three other carbons. Atoms in other layers are much further away and are not nearest neighbours, so the coordination number of a carbon atom in graphite is 3 as in ethylene.

Simple ionic structures are described by two coordination numbers, one for each type of ion. Calcium fluoride (CaF₂) is an (8, 4) structure, meaning that each cation Ca2+ is surrounded by eight F− anion neighbors, and each anion F− by four Ca2+. For sodium chloride (NaCl), the numbers of cations and anions are equal, and both coordination numbers are six so that the structure is (6, 6).

For an atom at a surface of a crystal, the surface coordination number is always less than the bulk coordination number. The surface coordination number is dependent on the Miller indices of the surface. In a body-centered cubic (BCC) crystal, the bulk coordination number is 8, whereas, for the (100) surface, the surface coordination number is 4.