Institute of Metals Division - The Atomic Volumes of the Metallic Elements

The allotropic volume changes of the ,metallic elements are reviezoed with the conclusion that in general atomic volume is conserved to better than 1 pct in such transformations. A table of the atomic volumes of the metallic elements is given and its use in considering the size factor in alloys is discussed. The importance of the concept of atomic-size factor, due to Hume-Rothery and coworkers,' is firmly established. Most attempts at quantitative formulations of this concept have employed the atomic radius (half some interatomic distance) as the measure of size and innumerable tables of such radii exist. This is probably, however, an unfortunate choice of parameter. Firstly, discussion in terms of interatomic distances requires a knowledge of the crystal structure. While this is known, except for a few cases, for the elemental structures, there are still many undetermined alloy structures. Secondly, except for the simpler structures, face-centered cubic (Al),* body-centered cubic (A2),* and hexagonal-close-packed (A3).* with ideal axial ratio, there is no unique in- teratomic distance, an m y decision must be made as to which distance, or which average of the distances, should be used. However, the most important point is that for metals the dominant bonding parameter can generally be expected to be atomic volume and not interatomic distance. This is perhaps most explicitly stated in the Wigner-Seitz cellular method.' In this approximation, cellular polyhedra of atomic volume v are replaced by spheres of radius Y,: 4/3 ?rs3 = v. That is, there is no reference to the interatomic distances. If atomic volume is in fact the dominant parameter, then in allotropic transformations we might expect to find atomic volume approximately conserved. For example, in the A1 ? A2 transformation we would thus have