Energy bands and Fermi surfaces for ${\beta }^{\prime }-\mathrm{M}\mathrm{g}\mathrm{H}\mathrm{g}$ and ${\beta }^{\prime }-\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{l}$

The energy bands of ordered ${\beta }^{\prime }-\mathrm{M}\mathrm{g}\mathrm{H}\mathrm{g}$ and ${\beta }^{\prime }-\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{l}$ have been calculated by the relativistic linear-muffintin-orbital method. We show how the gross features of the energy bands may be estimated from Wigner-Seitz rules. The densities of states are calculated and the heat capacities derived. The Fermi surfaces are found to be $\mathrm{sp}$-like but there are narrow $5d$ bands far below—and wide $3d$ and $6d$ bands far above—the Fermi levels. For ${\beta }^{\prime }-\mathrm{M}\mathrm{g}\mathrm{H}\mathrm{g}$ the calculated angular variation of extremal cross sections of the Fermi surface agrees very well with de Haas-van Alphen data and thereby provide an interpretation of these measurements. The average mass enhancement is found to be 1.6.