Ionic radius

The ionic radius, r_ion, is a measure of the size of an ion in a crystal lattice. It is measured in either picometres (pm) or Angstrom (Å), with 1 Å = 100 pm. Typical values range from 30 pm (0.3 Å) to over 200 pm (2 Å).

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The concept of ionic radius was developed independently by Goldschmidt and Pauling in the 1920s to summarize the data being generated by the (then) new technique of X-ray crystallography: it is Pauling's approach which proved to be the more influential. X-ray crystallography can readily give the length of the side of the unit cell of a crystal, but it is much more difficult (in most cases impossible, even with more modern techniques) to distinguish a boundary between two ions. For example, it can be readily determined that each side of the unit cell of sodium chloride is 564.02 pm in length, and that this length is twice the distance between the centre of a sodium ion and the centre of a chloride ion:

2[r_ion(Na⁺) + r_ion(Cl⁻)] = 564.02 pm

However, it is not apparent what proportion of this distance is due to the size of the sodium ion and what proportion is due to the size of the chloride ion. By comparing many different compounds, and with a certain amount of chemical intuition, Pauling decided to assign a radius of 140 pm to the oxide ion O²⁻, at which point he was able to calculate the radii of the other ions by subtraction.^[1]

A major review of crystallographic data led to the publication of a revised set of ionic radii in 1976,^[2] and these are preferred to Pauling's original values. Some sources have retained Pauling's reference of r_ion(O²⁻) = 140 pm, while other sources prefer to list "effective" ionic radii based on r_ion(O²⁻) = 126 pm. The latter values are thought to be a more accurate approximation to the "true" relative sizes of anions and cations in ionic crystals.

The ionic radius is not a fixed property of a given ion, but varies with coordination number, spin state and other parameters. Nevertheless, ionic radius values are sufficiently transferable to allow periodic trends to be recognized. As with other types of atomic radius, ionic radii increase on descending a group. Ionic size (for the same ion) also increases with increasing coordination number, and an ion in a high-spin state will be larger than the same ion in a low-spin state. Anions (negatively charged) are almost invariable larger than cations (positively charged), although the fluorides of some alkali metals are rare exceptions. In general, ionic radius decreases with increasing positive charge and increases with increasing negative charge.

An "anomalous" ionic radius in a crystal is often a sign of significant covalent character in the bonding. No bond is completely ionic, and some supposedly "ionic" compounds, especially of the transition metals, are particularly covalent in character. This is illustrated by the unit cell parameters for sodium and silver halides in the table. On the basis of the fluorides, one would say that Ag⁺ is larger than Na⁺, but on the basis of the chlorides and bromides the opposite appears to be true.^[3] This is because the greater covalent character of the bonds in AgCl and AgBr reduces the bond length and hence the apparent ionic radius of Ag⁺, an effect which is not present in the halides of the more electropositive sodium, nor in silver fluoride in which the fluoride ion is relatively unpolarizable.

See also

• Atomic radii of the elements

References

1. ^ Pauling, L. (1960). The Nature of the Chemical Bond (3rd Edn.). Ithaca, NY: Cornell University Press.
2. ^ ^{a b} Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides Shannon R.D. Acta Cryst. A32 751-767 (1976) doi:10.1107/S0567739476001551
3. ^ On the basis of conventional ionic radii, Ag⁺ (129 pm) is indeed larger than Na⁺ (116 pm)