Interatomic Distances of crystals of elements and compounds

Interatomic distances can be derived from the measured lattice parameters of simple structures with the same accuracy as the parameters of the unit cell. For instance, in copper the separation of the centres of adjacent atoms is simply 1/ 2 times the cell edge. Values of the interatomic distances for most metals and for some other elements deduced in this way are given in Section A7.1 of Appendix 7. They are often useful in considering ‘atomic radii’, if the crystal structure is viewed as being made up of spheres in contact. A difference is found between the values of the atomic radii deduced from different crystal structures of the same element when the element shows allotropic forms. The mineralogist Victor M. Goldschmidt showed that contractions of about 3 and 12% occur when a given element alters its structure from one of coordination 12 (e.g. c.c.p.) to one of coordination 8 and 4, respectively.

In crystals of compounds, interatomic distances can again be deduced from measured lattice parameters. They are useful in considering structures of compounds in terms of hard spheres in contact. However, there is a problem in dividing up the distance between two unlike atoms or ions so as to give each its own characteristic radius. This problem can only be solved by making a theoretical estimate of the size of at least one ion. Consequently, all values of ionic radii are part experimental, part theoretical in origin. Some values of ionic radii are also given in Section A7.1 of Appendix 7.

In crystals of compounds, the state of ionization of an atom may be quite different from that in the crystal of the element, and its size will differ accordingly. The value of the ionic radius of a metal is usually less than that of the atomic radius, defined as half the distance of closest approach of atoms in the element. This is because metals form positive ions in which the electrons are drawn inwards by the excess positive charge on the nucleus. Conversely, the ionic radius of an electronegative element is usually much greater than the atomic radius.

Reference: https://crystal-algerien1970.blogspot.com/2020/03/crystallography-and-crystal-defects.html