In fig. 34 the dispersion relationship for an fcc crystal is shown. It is just plotted fromΓ(centre) to L
(111-direction) and to X (100-direction). The energies here are switched around because the nearest
neighbors are in the 111-direction and there is the lowest energy. The facts about the overlap and the
effective mass are also true for fcc. Out of the dispersion relationship it is possible to calculatekx, ky
Figure 34: Dispersion relationship for an fcc crystal.andkzfor a constant energy. The solutions are surfaces with constant energy, this is what is shown
in fig. 35. The surface with the energy equal to the Fermi energy is with a good approximation (tight
binding) the fermisurface.
Figure 35: Surfaces of constant energy for a fcc crystal calculated with the Tight Binding
approximation.
Now the same for bcc crystals. Here the nearest neighbors are in the 111 direction, and so is the lower
energy. You can see that in fig. 36 the brillouin zone is a rhombic dodecahedron. There are corners
with three lines to it and corners with four lines to it. One corner is the N point (closest point) of the
lowest energy. Here the fermi surface shows unexpected behavior, see fig. 37. At a certain energy it is
shaped like a cube. Then it breaks up and the states are getting fewer at higher energies.