In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space...

primitive cell of the reciprocal lattice in momentum space is called the Brillouin zone. The concept of Voronoi decomposition was investigated by Peter Gustav...

outside the first Brillouin zone. If a material is periodic, it has a Brillouin zone, and any point outside the first Brillouin zone can also be expressed...

{\displaystyle \mathbf {k} } far outside the first Brillouin zone are still reflected back into the first Brillouin zone. See the external links section for sites...

necessary." Brillouin function Brillouin limit Brillouin scattering Brillouin zone Brillouin theorem Brillouin doublet Brillouin flow Brillouin–Wigner formula...

than the size of the first Brillouin zone, which results in a portion of the Fermi surface lying in the second (or higher) zones. As with the band structure...

Wavevectors outside the Brillouin zone simply correspond to states that are physically identical to those states within the Brillouin zone. Special high symmetry...

integration over the whole domain of the Brillouin zone can be reduced to a 48-th part of the whole Brillouin zone. As a crystal structure periodic table...

such wavevectors defines the first Brillouin zone. Additional Brillouin zones may be defined as copies of the first zone, shifted by some reciprocal lattice...

this process, one can infer the atomic arrangement of a crystal. The Brillouin zone is a Wigner–Seitz cell of the reciprocal lattice. Reciprocal space (also...

the bulk electronic wave functions, which are integrated in over the Brillouin zone, in a similar way that the genus is calculated in geometric topology...

Zones, a virtualization feature of the Solaris operating system Zone (convex polytope), in geometry/algorithmic, a kind of convex polytope Brillouin zone...

Brillouin zone. Therefore, if we restrict k to the first Brillouin zone, then every Bloch state has a unique k. Therefore, the first Brillouin zone is...

each characterized by a certain crystal momentum (k-vector) in the Brillouin zone. If the k-vectors are different, the material has an "indirect gap"...

cells in the crystal; The sum on k includes all the values of k in the Brillouin zone (or any other primitive cell of the reciprocal lattice) that are consistent...

atoms arranged on a square lattice. Energy splitting occurs at the Brillouin zone edge for one-dimensional situations because of a weak periodic potential...

are six locations in momentum space, the vertices of its hexagonal Brillouin zone, divided into two non-equivalent sets of three points. The two sets...

{1}{2}}{\frac {\mathrm {d} \phi _{k}}{\mathrm {d} k}},} integrated over the Brillouin zone k ∈ { − π , π } {\displaystyle k\in \{-\pi ,\pi \}} , produces different...

a function whose Fourier transform is the indicator function of the Brillouin zone of that lattice. For example, the sinc function for the hexagonal lattice...

{\displaystyle \mathbf {k} } is a wavevector in the reciprocal-space (Brillouin zone), and u n k ( r ) {\displaystyle u_{n\mathbf {k} }(\mathbf {r} )} is...

conduction band is vacant. The two bands touch at the zone corners (the K point in the Brillouin zone), where there is a zero density of states but no band...

has shown that nesting occurs at four points in the antiferromagnetic Brillouin zone where spin waves exist and that the superconducting energy gap is larger...

lattice and the Brillouin zone often belong to a different space group than the crystal of the solid. High-symmetry points in the Brillouin zone belong to different...

chemical element argon, currently Ar The center of a hexagonal face of the Brillouin zone of a hexagonal lattice, in physics "A", a poem by twentieth century...

gap in each direction becomes wider and the second one is to make the Brillouin zone more similar to sphere. However, the former is limited by the available...

in the Bloch momentum vector k → {\displaystyle {\vec {k}}} in the Brillouin zone; then the symmetry constraints must hold for all k → {\displaystyle...

located at the non-equivalent K points (K+ and K−) of the 2D hexagonal Brillouin zone. The interband transitions in the vicinity of the K+ (or K−) point are...

photon energy, corresponding to the band gaps at critical points of the Brillouin zone. The electroreflectance effect can be used to get a clearer picture...

which defines the energies of electron orbitals for each point in the Brillouin zone. Ab initio and semi-empirical calculations yield orbital energies, therefore...

singularities occur are often referred to as critical points of the Brillouin zone. For three-dimensional crystals, they take the form of kinks (where...