nearly-free electron model
E645945
The nearly-free electron model is a quantum mechanical approximation in solid-state physics that describes how electrons move in a weak periodic potential within a crystal lattice, leading to the formation of electronic band structures.
All labels observed (2)
| Label | Occurrences |
|---|---|
| nearly-free electron model canonical | 1 |
| quantum free-electron model | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7145281 — 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: nearly-free electron model Context triple: [Bloch waves, usedFor, nearly-free electron model]
-
A.
Drude model
The Drude model is a classical theory that describes the electrical and thermal properties of metals by treating conduction electrons as a gas of free, non-interacting particles undergoing random collisions.
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B.
Eliashberg theory
Eliashberg theory is an extension of BCS superconductivity that incorporates strong-coupling and frequency-dependent effects to more accurately describe real superconducting materials.
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C.
Peierls–Nabarro model
The Peierls–Nabarro model is a theoretical framework in solid-state physics that describes the behavior and motion of dislocations in crystal lattices by accounting for the periodic atomic potential.
-
D.
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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E.
Mott minimum metallic conductivity
Mott minimum metallic conductivity is a theoretical lower bound on the electrical conductivity of a metal, proposed by Sir Nevill F. Mott, below which a material can no longer sustain metallic (delocalized) electronic transport.
- 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: nearly-free electron model Target entity description: The nearly-free electron model is a quantum mechanical approximation in solid-state physics that describes how electrons move in a weak periodic potential within a crystal lattice, leading to the formation of electronic band structures.
-
A.
Drude model
The Drude model is a classical theory that describes the electrical and thermal properties of metals by treating conduction electrons as a gas of free, non-interacting particles undergoing random collisions.
-
B.
Eliashberg theory
Eliashberg theory is an extension of BCS superconductivity that incorporates strong-coupling and frequency-dependent effects to more accurately describe real superconducting materials.
-
C.
Peierls–Nabarro model
The Peierls–Nabarro model is a theoretical framework in solid-state physics that describes the behavior and motion of dislocations in crystal lattices by accounting for the periodic atomic potential.
-
D.
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.
-
E.
Mott minimum metallic conductivity
Mott minimum metallic conductivity is a theoretical lower bound on the electrical conductivity of a metal, proposed by Sir Nevill F. Mott, below which a material can no longer sustain metallic (delocalized) electronic transport.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
quantum mechanical approximation
ⓘ
theoretical model in solid-state physics ⓘ |
| appliesTo |
electrons in crystalline solids
ⓘ
metals ⓘ semiconductors ⓘ |
| approximationType |
perturbative treatment of lattice potential
ⓘ
weak-potential approximation ⓘ |
| assumes |
electrons move almost freely in a crystal lattice
ⓘ
independent electrons neglecting electron–electron interactions ⓘ weak electron–lattice interaction ⓘ weak periodic potential from ions ⓘ |
| basedOn |
Bloch theorem
ⓘ
Schrödinger equation in a periodic potential ⓘ |
| category |
electronic structure model
ⓘ
model of electrons in periodic potentials ⓘ |
| comparesWith |
free electron gas model
ⓘ
nearly localized electron picture ⓘ |
| contrastsWith | strongly bound electron models ⓘ |
| describes |
electronic band structure in crystals
ⓘ
electrons in a weak periodic potential ⓘ |
| explains |
deviation from free-electron parabolic dispersion near zone boundaries
ⓘ
formation of band gaps at Brillouin zone boundaries ⓘ formation of energy bands ⓘ |
| field |
condensed matter physics
ⓘ
solid-state physics ⓘ |
| goal |
calculate electronic band structure
ⓘ
understand conduction properties of solids ⓘ |
| historicalContext | developed in early quantum theory of solids ⓘ |
| leadsTo |
energy level splitting at degeneracy points
ⓘ
zone-folding of free-electron dispersion ⓘ |
| mathematicalFormulation | Schrödinger equation with periodic potential V(r) ⓘ |
| predicts |
effective mass of electrons in bands
ⓘ
energy dispersion relations E(k) ⓘ opening of band gaps at zone boundaries ⓘ |
| relatedTo |
band theory of solids
ⓘ
free electron model ⓘ tight-binding model ⓘ |
| requires |
periodic crystal lattice
ⓘ
translational symmetry ⓘ |
| usedFor |
qualitative understanding of band formation
ⓘ
simple analytic band-structure calculations ⓘ |
| usedIn | introductory solid-state physics courses ⓘ |
| usesConcept |
Brillouin zone
ⓘ
Fourier expansion of periodic potentials ⓘ perturbation theory ⓘ plane-wave basis ⓘ reciprocal lattice ⓘ |
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: nearly-free electron model Description of subject: The nearly-free electron model is a quantum mechanical approximation in solid-state physics that describes how electrons move in a weak periodic potential within a crystal lattice, leading to the formation of electronic band structures.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: nearly-free electron model