Ionic radii

Empirical values for ionic radii are used for predicting interatomic distances and packing in crystals, even when the forces are far from being purely ionic. The ions are regarded as hard spheres, whose size is, to a first approximation, constant in all environments. To a second approximation, it has long been recognized that there is a dependence on coordination number, and, more recently, for transition-metal ions, a dependence also on spin state. Separate values are listed accordingly in the table.

The coordination number of an atom is the number of its first-nearest neighbours of opposite sign. It may sometimes be ambiguous when the neighbours are not all at exactly the same distance; judgement and experience, rather than formal rules, must then decide which of them are to be counted as first-nearest. Different decisions on this point will lead to small differences in estimates of the mean cation–anion distance within the polyhedron (the figure whose vertices are the first-nearest neighbour anions around the cation).

The spin state of a transition-metal ion refers to its spin angular momentum. Normally this depends on the ground state of the free atom, and is given by Hund's rule; this is the high-spin state. In a particular crystal structure, however, ions may be situated in strong ligand fields which reduce the spin angular momentum; this is the low-spin state².

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