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In chemistry and crystallography, the coordination number of a central atom in a molecule or crystal is the number of its nearest neighbours. This number is determined somewhat differently for molecules than for crystals.
In chemistry, the emphasis is on bonding structure in molecules or ions and the coordination number of an atom is determined by simply counting the other atoms to which it is bonded (by either single or multiple bonds). For example, [Cr(NH3)2Cl2Br2]1- has Cr3+ as its central cation, which has a coordination number of 6.
However the solid-state structures of crystals 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 that it touches. For an atom in the interior of a crystal lattice, the number of atoms touching the given atom is the bulk coordination number; for an atom at a surface of a crystal, this is the surface coordination number. http://en.wikipedia.org/wiki/Coordination_number