Electronic band structures of the alkali metals and of the noble metals and their α-phase alloys

In the monovalent metals the electronic band structure is strongly affected by the size of the band gap E_s-E_p at the Brillouin zone faces, a large gap implying a large distortion of the Fermi surface. Here E_s and E_p are the energies of the purely s-like and p-like states on the zone faces. We have made crude estimates of E_s-E_p for the alkali and noble metals, in terms of the s-p excitation energy Δ_sp of the free atoms. These suggest a single model which correlates most of the experimental information about the band structures of these metals. In particular the Fermi surface of lithium appears to make considerable contact with the zone faces. In the α-phase alloys of the noble metals, the solute always has a larger value of Δ_sp than the solvent, which raises the energy E_p relative to E_s. The Fermi surface becomes more nearly spherical in copper alloys than in copper, since E_p<E_s, whereas it distorts further in the gold alloys (E_p>E_s). This accounts for many Knight shift, electronic specific heat, magnetic susceptibility and other data on these alloys. Furthermore it provides the extension of Jones' explanation of the Hume-Rothery rule demanded by the non-spherical Fermi surface in pure copper and gold.