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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Wigner-Seitz cell | 1 |
| Wigner–Seitz cell canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4721205 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Wigner–Seitz cell Context triple: [Wigner Jenő Pál, knownFor, Wigner–Seitz cell]
-
A.
Brillouin zone
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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B.
Wigner-Seitz radius r_s
The Wigner-Seitz radius r_s is a dimensionless parameter in condensed matter physics that quantifies the average spacing between electrons in an electron gas, commonly used to characterize correlation strength and phases such as the Wigner crystal.
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C.
Fermi surface
The Fermi surface is the boundary in momentum space separating occupied from unoccupied electron states at zero temperature, crucial for determining a metal’s electronic and superconducting properties.
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D.
Wigner crystal
A Wigner crystal is an ordered lattice of electrons that forms in low-density systems when their mutual Coulomb repulsion dominates over kinetic energy, leading to a crystalline arrangement of charge.
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E.
Steinmetz solid
The Steinmetz solid is a three-dimensional geometric shape formed by the intersection of two or more cylinders at right angles, often studied in calculus and solid geometry for its interesting volume and symmetry properties.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Wigner–Seitz cell Target entity description: 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.
-
A.
Brillouin zone
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.
-
B.
Wigner-Seitz radius r_s
The Wigner-Seitz radius r_s is a dimensionless parameter in condensed matter physics that quantifies the average spacing between electrons in an electron gas, commonly used to characterize correlation strength and phases such as the Wigner crystal.
-
C.
Fermi surface
The Fermi surface is the boundary in momentum space separating occupied from unoccupied electron states at zero temperature, crucial for determining a metal’s electronic and superconducting properties.
-
D.
Wigner crystal
A Wigner crystal is an ordered lattice of electrons that forms in low-density systems when their mutual Coulomb repulsion dominates over kinetic energy, leading to a crystalline arrangement of charge.
-
E.
Steinmetz solid
The Steinmetz solid is a three-dimensional geometric shape formed by the intersection of two or more cylinders at right angles, often studied in calculus and solid geometry for its interesting volume and symmetry properties.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
concept in crystallography
ⓘ
concept in solid-state physics ⓘ geometric construction ⓘ primitive cell ⓘ |
| appliesTo |
Bravais lattices
ⓘ
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
ⓘ
Frederick Seitz ⓘ |
| partOf | Bravais lattice description ⓘ |
| relatedConcept |
Brillouin zone
ⓘ
Voronoi diagram ⓘ 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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Wigner–Seitz cell Description of subject: 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.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Wigner–Seitz cell