Wigner–Seitz cell
E463100
The Wigner–Seitz cell is a primitive region of space in a crystal lattice that contains all points closer to a given lattice point than to any other, serving as a fundamental building block in solid-state physics and crystallography.
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
concept in crystallography
ⓘ
concept in solid-state physics ⓘ geometric construction ⓘ primitive cell ⓘ |
| appliesTo |
Bravais lattices
NERFINISHED
ⓘ
three-dimensional lattices ⓘ two-dimensional lattices ⓘ |
| belongsToDomain |
condensed matter physics
ⓘ
theoretical crystallography ⓘ |
| constructionMethod |
Voronoi decomposition of a Bravais lattice
ⓘ
draw lines to all neighboring lattice points and construct perpendicular bisecting planes or lines ⓘ |
| definedAs | region of space closer to a given lattice point than to any other lattice point ⓘ |
| equivalentTo | Voronoi cell of a lattice point ⓘ |
| forLatticeType |
body-centered cubic lattice
ⓘ
face-centered cubic lattice ⓘ hexagonal close-packed lattice ⓘ simple cubic lattice ⓘ |
| hasDimensionality | same as the dimensionality of the lattice ⓘ |
| hasProperty |
contains exactly one lattice point per cell on average
ⓘ
convex polygon in two dimensions ⓘ convex polyhedron in three dimensions ⓘ fills space without gaps or overlaps when translated by all lattice vectors ⓘ unique for a given lattice point and metric ⓘ volume equals primitive cell volume ⓘ |
| hasShapeForLatticeType |
body-centered cubic lattice: truncated octahedron
ⓘ
face-centered cubic lattice: rhombic dodecahedron ⓘ hexagonal close-packed lattice: hexagonal prism with additional facets ⓘ simple cubic lattice: cube centered on a lattice point ⓘ |
| mathematicalNature | Dirichlet domain of a lattice point ⓘ |
| namedAfter |
Eugene Wigner
NERFINISHED
ⓘ
Frederick Seitz NERFINISHED ⓘ |
| partOf | Bravais lattice description ⓘ |
| relatedConcept |
Brillouin zone
NERFINISHED
ⓘ
Voronoi diagram NERFINISHED ⓘ primitive cell ⓘ reciprocal lattice ⓘ |
| shapeDependsOn |
lattice parameters
ⓘ
lattice symmetry ⓘ |
| tilingProperty | forms a space-filling tessellation when repeated over all lattice points ⓘ |
| usedFor |
analyzing electronic band structure
ⓘ
defining basis of atoms in a crystal ⓘ defining first Brillouin zone in reciprocal space ⓘ describing local environment of lattice sites ⓘ simplifying integrals over the crystal volume ⓘ |
| usedIn |
crystallography
ⓘ
materials science ⓘ solid-state physics ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.