Debye model
E518983
The Debye model is a theoretical approach in solid-state physics that explains the heat capacity of crystalline solids by treating their lattice vibrations (phonons) as a spectrum of quantized modes up to a maximum cutoff frequency.
All labels observed (5)
| Label | Occurrences |
|---|---|
| Debye model canonical | 1 |
| Debye model of solids | 1 |
| Debye model of specific heat | 1 |
| Einstein model of solids | 1 |
| Einstein model of specific heat | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5420105 — 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: Debye model Context triple: [Peter Debye, knownFor, Debye 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.
-
B.
Dulong–Petit law for molar heat capacity of many solids at high temperature
The Dulong–Petit law states that many crystalline solids have an approximately constant molar heat capacity of about 3R at sufficiently high temperatures, reflecting classical equipartition of energy among atomic vibrations.
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C.
Dulong–Petit law
The Dulong–Petit law is an early empirical rule in thermodynamics stating that many solid elements have approximately the same molar heat capacity at high temperatures.
-
D.
Sackur–Tetrode equation
The Sackur–Tetrode equation is a fundamental formula in statistical mechanics that gives the absolute entropy of an ideal monatomic gas in terms of its volume, temperature, and particle number.
-
E.
Curie–Weiss law
The Curie–Weiss law is a refinement of Curie’s law in magnetism that accounts for magnetic interactions between atoms by introducing a characteristic temperature, improving the description of paramagnetic susceptibility near ferromagnetic phase transitions.
- 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: Debye model Target entity description: The Debye model is a theoretical approach in solid-state physics that explains the heat capacity of crystalline solids by treating their lattice vibrations (phonons) as a spectrum of quantized modes up to a maximum cutoff frequency.
-
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.
Dulong–Petit law for molar heat capacity of many solids at high temperature
The Dulong–Petit law states that many crystalline solids have an approximately constant molar heat capacity of about 3R at sufficiently high temperatures, reflecting classical equipartition of energy among atomic vibrations.
-
C.
Dulong–Petit law
The Dulong–Petit law is an early empirical rule in thermodynamics stating that many solid elements have approximately the same molar heat capacity at high temperatures.
-
D.
Sackur–Tetrode equation
The Sackur–Tetrode equation is a fundamental formula in statistical mechanics that gives the absolute entropy of an ideal monatomic gas in terms of its volume, temperature, and particle number.
-
E.
Curie–Weiss law
The Curie–Weiss law is a refinement of Curie’s law in magnetism that accounts for magnetic interactions between atoms by introducing a characteristic temperature, improving the description of paramagnetic susceptibility near ferromagnetic phase transitions.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
solid-state physics concept
ⓘ
theoretical model ⓘ |
| appliesTo |
crystalline solids
ⓘ
insulating solids ⓘ |
| approximates | vibrational spectrum of a crystal ⓘ |
| assumes |
3N normal modes for N atoms
ⓘ
continuous distribution of vibrational modes ⓘ isotropic elastic continuum ⓘ linear dispersion relation at low frequencies ⓘ |
| category |
lattice dynamics model
ⓘ
thermodynamic model ⓘ |
| cutoffParameter |
Debye frequency
ⓘ
Debye temperature NERFINISHED ⓘ Debye wavevector NERFINISHED ⓘ |
| describes |
heat capacity of crystalline solids
ⓘ
lattice vibrations ⓘ phonons ⓘ |
| explains |
T^3 law for heat capacity at low temperatures
ⓘ
low-temperature heat capacity of solids ⓘ |
| field |
condensed matter physics
ⓘ
solid-state physics ⓘ statistical mechanics ⓘ |
| improvesOn | Einstein model of heat capacity ⓘ |
| influenced | development of phonon theory ⓘ |
| introducedBy | Peter Debye NERFINISHED ⓘ |
| limitation |
assumes isotropic sound velocity
ⓘ
neglects optical phonon branches ⓘ |
| mathematicalForm | integral over phonon frequencies up to Debye cutoff ⓘ |
| namedAfter | Peter Debye NERFINISHED ⓘ |
| predicts |
Dulong–Petit law as high-temperature limit
ⓘ
heat capacity proportional to T^3 at low temperature ⓘ heat capacity tends to 3Nk_B at high temperature ⓘ |
| relatedTo |
Debye function
NERFINISHED
ⓘ
Einstein model NERFINISHED ⓘ phonon theory of solids ⓘ |
| temperatureRegime | low temperatures ⓘ |
| usedFor |
estimating Debye temperature from heat capacity data
ⓘ
modeling thermal properties of solids ⓘ |
| usesConcept |
Debye frequency
ⓘ
Debye temperature NERFINISHED ⓘ acoustic phonons ⓘ cutoff frequency ⓘ density of states ⓘ phonon spectrum ⓘ quantized vibrational modes ⓘ |
| usesConstant | Boltzmann constant NERFINISHED ⓘ |
| usesQuantity | Avogadro constant NERFINISHED ⓘ |
| yearProposed | 1912 ⓘ |
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: Debye model Description of subject: The Debye model is a theoretical approach in solid-state physics that explains the heat capacity of crystalline solids by treating their lattice vibrations (phonons) as a spectrum of quantized modes up to a maximum cutoff frequency.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
Dulong–Petit law for molar heat capacity of many solids at high temperature
→
relatedConcept
→
Debye model
ⓘ
this entity surface form:
Einstein model of solids
Dulong–Petit law for molar heat capacity of many solids at high temperature
→
relatedConcept
→
Debye model
ⓘ
this entity surface form:
Debye model of solids
this entity surface form:
Einstein model of specific heat
this entity surface form:
Debye model of specific heat