Bcc and Fcc transition metals and alloys: A central role for the Jahn-Teller effect in explaining their ideal and distorted structures

Transition metal elements, alloys, and intermetallic compounds often adopt the body centered cubic (bcc) and face centered cubic (fcc) structures. By comparing quantitative density functional with qualitative tight-binding calculations, we analyze the electronic factors which make the bcc and fcc structures energetically favorable. To do so, we develop a tight-binding function, DeltaE(star), a function that measures the energetic effects of transferring electrons within wave vector stars. This function allows one to connect distortions in solids to the Jahn-Teller effect in molecules and to provide an orbital perspective on structure determining deformations in alloys. We illustrate its use by considering first a two-dimensional square net. We then turn to three-dimensional fcc and bcc structures, and distortions of these. Using DeltaE(star), we rationalize the differences in energy of these structures. We are able to deduce which orbitals are responsible for instabilities in seven to nine valence electron per atom (e(-)/a) bcc systems and five and six e-/a fcc structures. Finally we demonstrate that these results account for the bcc and fcc type structures found in both the elements and binary intermetallic compounds of group 4 through 9 transition metal atoms. The outline of a theory of metal structure deformations based on loss of point group operation rather than translational symmetry is presented.