However the solid-state structures of crystallography often have less clearly defined bonds, so a simpler model is used in which the atoms are represented by touching spheres. In this model the coordination number of an atom is the number of other atoms which it touches.
In inorganic chemistry also, only the first or sigma bond between each ligand and the central atom counts, but not any pi bonds to the same ligands. In tungsten hexacarbonyl, W(CO)6, the coordination number of tungsten (W) is counted as six although pi as well as sigma bonding is important in such metal carbonyls.
Examples of high coordination number complexes are the ions formed by uranium and thorium with bidentate nitrate ion ligands, U(NO3)62− and Th(NO3)62−. Here each nitrate ligand is bound to the metal by two oxygen atoms, so that the total coordination number of the U or Th atom is 12.
When the surrounding ligands get smaller even higher coordination numbers may be possible. One in silico computational chemistry study predicted a particularly stable PbHe152+ ion composed of a central lead ion coordinated with no less than 15 helium atoms..
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 which Miller index the surface uses. In a body-centered cubic (BCC) crystal, the bulk coordination number is 8, whereas for the (100) surface, the surface coordination number is 4.