Brillouin zone
E48477
The Brillouin zone is the fundamental region of reciprocal space in a crystal lattice, defining the allowed wavevectors for electrons and underpinning the structure of electronic band diagrams.
Aliases (2)
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
concept in solid-state physics
→
region of reciprocal space → |
| appliesTo |
crystalline solids
→
periodic potentials → |
| boundaryDefinedBy |
Bragg reflection conditions
→
planes perpendicular to reciprocal lattice vectors → |
| characterizes |
allowed wavevectors in a crystal
→
|
| definedIn |
reciprocal lattice
→
|
| dependsOn |
crystal lattice symmetry
→
|
| describes |
fundamental region of reciprocal space
→
|
| dimensionEquals |
dimension of the crystal lattice
→
|
| field |
condensed matter physics
→
crystallography → solid-state physics → |
| firstDefinedBy |
Léon Brillouin
→
|
| hasGeneralization |
extended zone scheme
→
reduced zone scheme → repeated zone scheme → |
| hasOrder |
first Brillouin zone
→
higher-order Brillouin zones → second Brillouin zone → |
| hasPart |
high-symmetry lines
→
high-symmetry planes → high-symmetry points → |
| hasProperty |
bounded by Bragg planes
→
contains all inequivalent k-vectors → periodic under reciprocal lattice translations → |
| is |
Wigner–Seitz cell in reciprocal space
→
|
| mathematicallyConstructedAs |
set of points closer to origin than to any other reciprocal lattice point
→
|
| namedAfter |
Léon Brillouin
→
|
| relatedTo |
Bloch's theorem
→
Fermi surface → band gap → dispersion relation → electron dispersion → phonon dispersion → reciprocal lattice vector → |
| shapeDependsOn |
Bravais lattice type
→
|
| usedFor |
Bloch wavevector labeling
→
analysis of electron states in crystals → classification of phonon modes → construction of electronic band structures → |
| usedIn |
X-ray scattering analysis
→
angle-resolved photoemission spectroscopy analysis → band structure diagrams → electron diffraction analysis → neutron scattering analysis → |
| usedToExplain |
Umklapp scattering
→
band folding → energy band gaps at zone boundaries → |
Referenced by (3)
| Subject (surface form when different) | Predicate |
|---|---|
|
Fermi surface
("Brillouin zone boundaries")
→
|
interactsWith |
|
Brillouin zone
("Wigner–Seitz cell in reciprocal space")
→
|
is |
|
Fermi surface
→
|
relatedTo |