The band structure of aluminium I. Determination from experimental data

The band structure and particularly the shape of the Fermi surface are deduced mainly from the available experimental data on the de Haas-van Alphen and anomalous skin effects, and from the low-temperature specific heat. Since these data are rather incomplete, it is found necessary to use in conjunction with them a theoretical band-structure calculation, which, however, unavoidably contains rough approximations. Except near the surface of the Brillouin zone, E(k) is found to be very close to the free-electron energy. The first zone is found to contain 3$\cdot $6 $\times $ 10$^{-3}$ holes per atom around the zone corners. There is overflow of electrons into the second zone across all the zone faces, and these regions of the Fermi distribution are joined together near the centres of the zone edges; the third zone contains a very small number of electrons.