Brillouin zone

E48477
concept in solid-state physics region of reciprocal space

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.

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All labels observed (5)

Label Occurrences
Brillouin zone canonical 3
Brillouin zone boundaries 1
Brillouin zone folding 1

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 Brillouin zone self-linksurface differs ⓘ
surface form: 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 waves ⓘ
surface form: 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 (7)

Full triples — surface form annotated when it differs from this entity's canonical label.

Fermi surface → relatedTo → Brillouin zone ⓘ
Fermi surface → interactsWith → Brillouin zone ⓘ
this entity surface form: Brillouin zone boundaries
Brillouin zone → is → Brillouin zone self-linksurface differs ⓘ
this entity surface form: Wigner–Seitz cell in reciprocal space
Peierls transition → associatedWith → Brillouin zone ⓘ
this entity surface form: Brillouin zone folding
Quantum Theory of Solids → topic → Brillouin zone ⓘ
this entity surface form: Brillouin zones
Bloch waves → relatedTo → Brillouin zone ⓘ
Léon Brillouin → notableConcept → Brillouin zone ⓘ