What is it about?
Since structural crystallography began in 1914, the sizes of atoms and ions have played a major role in solving crystal structures and systematizing many metric aspects of crystal structures and their properties, to the extent that Pauling’s rules, first published in 1929, are still taught in many introductory Chemistry and Mineralogy courses. There is a major contradiction between the sizes of ions/atoms in crystals (1) derived from mean experimental interatomic distances (ionic radii), and (2) derived from quantum-mechanical calculations of the electron density (bonded radii) that has persisted for nearly 50 years. Users of ionic radii persist as such radii have proved very useful, whereas (some) producers of bonded radii dismiss the results of using ionic radii as nonsense.
Why is it important?
These different views of the sizes of atoms/ions in crystals represent a major hiatus between theory and experiment, and obviously need to be resolved. There are two types of use of ion radii: (1) methods which use the relative sizes (radii) of cations and anions; (2) those methods which compare the radii of different cations (or the radii of different anions). Type (1) methods do not work (See Featured Image) and should not be used. Type (2) methods can be very precise and lead to useful and accurate predictions. This behaviour can be understood by recognizing that ionic radii (derived from experimental interatomic distances) are proxy variables for mean interatomic distance and do not represent real sizes of ions in crystals.