Solid-state physics Ashcroft and Mermin Problem 15.4

4. The first Brillouin zone for a crystal with an foc Bravais lattice extends furthest from the origin (1) at the point W where the square face and two hexagonal faces meet (Figure 15.4). Show that the free electron Fermi sphere for valence 3 extends beyond that point (specifically, kF/TW = (1296/12572)1/6 = 1.008), so that the first Brillouin zone is entirely filled.The Noble Metals 289 Figure 15.4 & (a) Calculated energy bands in copper. (After G. A. Bur- dick, Phys. Rev. 129, 138 (1963).) The & vs. k curves are &F shown along several lines in the interior and on the surface of the first zone. (The point I is at the center of the zone.) The d-bands occupy the darkest region of the figure, X W L r K whose width is about 3.5 eV. (a) (b) The lowest-lying free electron energies along the same lines as in (a). (The energy scales in (a) and (b) & are not the same.) WK &F X W L r K (b)