Ionic radius
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.
An "anomalous" ionic radius in a crystal is often a sign of significant covalent character in the bonding.
This is illustrated by the unit cell parameters for sodium and silver halides in the table.
[1] 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.
Landé[2] estimated ionic radii by considering crystals in which the anion and cation have a large difference in size, such as LiI.
Pauling used effective nuclear charge to proportion the distance between ions into anionic and a cationic radii.
A major review of crystallographic data led to the publication of revised ionic radii by Shannon.
Shannon states that "it is felt that crystal radii correspond more closely to the physical size of ions in a solid.
One approach to improving the calculated accuracy is to model ions as "soft spheres" that overlap in the crystal.
For example, for crystals of group 1 halides with the sodium chloride structure, a value of 1.6667 gives good agreement with experiment.
Inter-ionic separations calculated with these radii give remarkably good agreement with experimental values.
The concept of ionic radii is based on the assumption of a spherical ion shape.
However, from a group-theoretical point of view the assumption is only justified for ions that reside on high-symmetry crystal lattice sites like Na and Cl in halite or Zn and S in sphalerite.
For ions on lower-symmetry sites significant deviations of their electron density from a spherical shape may occur.
This holds in particular for ions on lattice sites of polar symmetry, which are the crystallographic point groups C1, C1h, Cn or Cnv, n = 2, 3, 4 or 6.
[14] A thorough analysis of the bonding geometry was recently carried out for pyrite-type compounds, where monovalent chalcogen ions reside on C3 lattice sites.
It was found that chalcogen ions have to be modeled by ellipsoidal charge distributions with different radii along the symmetry axis and perpendicular to it.
