Measurement and Factors Affecting Ionic Radii

The ionic radius of an atom is measured by calculating its spatial proportions in an ionic bond with another ion within a crystal lattice. However, it is to consistently and accurately determine the proportions of the ionic bonds. After comparing many compounds, chemist Linus Pauling assign a radius of 140 pm to O^2- and use this as a reference point to determine the sizes of other Ionic Radii (Jensen 2010).

Ionic radius is not a permanent trait of an ion, but changes depending on coordination number, spin state, and other variables (Shannon 1976). For a given ion, the ionic radius increases with increasing coordination number and is larger in a high-spin state than in a low-spin state. 

According to group theory, the idea of ionic radii as a measurement of spherical shapes only applies to ions that form highly-symmetric crystal lattices like Na⁺ and Cl ^-. The point group symmetry of a lattice determines whether or not the ionic radii in that lattice can be accurately measured (Johnson 1973). For instance, lattices with O_h and T_d symmetries are considered to have high symmetry; thus the electron densities of the component ions occupy relatively-spherical regions and ionic radii can be measured fairly accurately. However, for less symmetrical and more polar lattices such as those with C_n, C_nh, and C_nv symmetries, significant changes in the electron density can occur, causing deviations from spherical shape; these deviations make ionic radii more difficult to measure.