Electronic Structure of Ordered Beta Brass

Abstract

The electronic band structure of ordered beta brass (${\ensuremath{\beta}}^{\ensuremath{'}}$ CuZn) has been calculated from first principles by the Green's-function technique. Two slightly different crystal potentials of the muffin-tin type have been tested, both based on free-atom Hartree-Fock wave functions. Each potential has yielded essentially identical results as far as the conduction bands near the Fermi energy are concerned. The difference between the potentials is reflected principally in the location of the $d$ bands relative to the conduction bands. Cross sections of the Fermi surface have been constructed and suggest the presence of a surface which can be generated by small modifications of the one-orthogonalized-plane-wave prototype. The first (cubic) Brillouin zone is full except for holes in the corners, and the second (dodecahedral) zone is somewhat more than half full with measurable contact of the Fermi surface with the {110} faces of this zone. These observations agree quantitatively with the interpretation of presently available de Haas-van Alphen data. Optical transitions responsible for the color of the alloy have been tentatively identified as occurring over an energy range of 2.5 to 3.5 eV, from the Fermi surface to higher unoccupied levels. The band structure is also compared with the results of electronic-specific-heat, Hall-effect, and elastic-modulus experiments. A band calculation of the cellular type has been carried out separately and compared with the Green's-function bands. The stability of the beta phase is discussed in terms of the Fermi surface, and is related to the present understanding of Cu and of other alloy phases of the CuZn system.