Connecting the Chemical and Physical Viewpoints of What Determines Structure: From 1-D Chains to γ-Brasses

Mott and Jones (MJ) have developed a model arguing that it is favorable for a compound to adopt a structure for which the Fermi surface cuts the boundaries of the first Brillouin zone or higher zones. This perturbation-theory-based approach sees stabilization in allowing free-electron plane-wave states near the Fermi energy to mix, pushing the energies of filled states down and those of unfilled states up. A feature shared by the MJ model and the related dielectric function-based rationale for Hume-Rothery's electron-counting rules is that the arguments are made in reciprocal space. Since the MJ arguments rationalize the stability of electron phases, it should be possible to cast them in terms of real-space electronic states. Given the near-coincidence of band structures generated using models based on linear combinations of atomic orbitals (LCAO). The model can produce a band structure in either the normal or inverted region, depending on the element and the interatomic spacing.