Goldschmidt radii

The coordination number of an atom describes the number of nearest neighbors. Close-packed atoms have a coordination number of 12:

6 surrounding, 3 above, 3 below

Structures which are not close-packed can have different coordination numbers. For example, the body-centered cubic structure has a coordination number of eight:

An informal definition of atomic radius in a metal is half of the difference between the centers of two adjacent atoms. But this distance generally increases with the co-ordination number of the solid. After an extensive study of different elements and alloys, Victor Goldschmidt found the following relationship between average atomic radii and coordination numbers:

Victor Goldschmidt (1888 - 1947)