Wigner-Seitz cells face centered cubic lattice

The symmetry of the lattice will impose distinct shapes on the Brillouin zones (which by definition are the Wigner-Seitz cells of the reciprocal lattice) for each type of symmetry. Figure 8.11 shows the first Brillouin zone for a face-centered cubic structure. 

Muffin-Tin Orbital theory is in the spirit of the very early treatment of alkali metals by Wigner and Seitz (1934), who focused on a single atomic cell (those points nearer the atom being studied than any other atom) in which the potential is nearly spherically symmetric. They then replaced the cell by a sphere of equal volume, the sphere of radius /q that we introduced in the discussion of simple metal.s. This is illustrated in Fig. 20-12 for a face-centered cubic lattice. Wigner... 

Figure 2.37 Unit cell and Wigner-Seitz cell (thick lines) of the face centered cubic lattice.

The term first Brillouin zone is applied only to the k-space cell. Because the reciprocal of the body-centered cubic lattice is a face-centered cubic lattice, the first Brillouin zone of the bcc is just the fee Wigner-Seitz cell (Figure 4.8). Conversely, the first Brillouin zone of the fee lattice is just the bcc Wigner-Seitz cell. 

Figure 4.8a, iQustrates the construction of the Wigner-Seitz cells for the face-centered and the body-centered cubic crystal lattices. An atom is located at the center of each polyhedron. 

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See also in sourсe #XX -- [ ]

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