Electronic Structure ofIB−IIBBeta-Phase Alloys

Previous research on the theoretical electronic structure of ordered beta brass (${\beta }^{\prime }$ CuZn) has been systematically extended to other ordered beta-phase alloys belonging to groups $\mathrm{I}B$ and $\mathrm{II}B$ of the periodic table, and also to disordered beta brass ($\beta$ CuZn). In the case of the ordered alloys, the band structures and Fermi surfaces of ${\beta }^{\prime }$ AgZn and ${\beta }^{\prime }$ AgCd have been computed by the Kohn-Rostoker (K-R) technique and compared with results similarly obtained for ${\beta }^{\prime }$ CuZn. The bands are qualitatively alike, differing principally in the locations of the $d$ bands relative to the conduction bands. The sensitivity of these locations is given special attention in the material ${\beta }^{\prime }$ CuZn. The problem is partially resolved by resorting to a semiempirical "adjustment" of the $d$ bands. The Fermi surfaces, which are close to the one-orthogonalized-plane-wave prototype, are relatively insensitive to the exact nature of the potential. The bands of ${\beta }^{\prime }$ AuZn and ${\beta }^{\prime }$ AuCd have not been calculated explicitly, although it is reasonable to assume that their electronic structures are basically similar to those of the Cu and Ag alloys. The optical properties of the ${\beta }^{\prime }$ alloys, including their variations with temperature and composition, are discussed on the basis of the computed bands. The bands and Fermi surface of disordered beta brass have been determined to first order of approximation by combining the K-R method with the "virtual-crystal" model. The electronic structure of $\beta$ CuZn differs from that of ${\beta }^{\prime }$ CuZn in the following respects: The energy gap across the zone boundary is absent, corresponding to an absence of both the discontinuity in the Fermi surface across that boundary and the "holes" in the corners of the cube. The gap across each face of the dodecahedral zone boundary is reduced from 3.5 to 1.5 eV. Both these effects imply a somewhat more free-electron behavior for the disordered alloy. Finally, the bands are used to discuss the relative importance of electronic contributions and order to the stability of the beta-phase alloys.