Wigner-Seitz cells body centered cubic lattice

Figure 2.36 Unit cell and Wigner-Seitz cell (thick lines) of the body 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 4.8 The Wigner-Seitz cells (a) and the first Brillouin zones (b) for the ce-centered cubic (fee) and body-centered cubic (bcc) crystal lattices.

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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