Richardson–Dushman equation
E835820
The Richardson–Dushman equation is a fundamental formula in thermionic emission theory that relates the current density of electrons emitted from a heated metal surface to its temperature and material-specific constants.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Richardson–Dushman equation canonical | 1 |
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
equation
ⓘ
physical law ⓘ |
| alsoKnownAs |
Richardson equation
NERFINISHED
ⓘ
Richardson–Dushman law NERFINISHED ⓘ |
| appliesTo |
electron emission from heated cathodes
ⓘ
electron emission from heated metal surfaces ⓘ |
| assumes |
clean metal surface
ⓘ
no space-charge limitation ⓘ thermally equilibrated electron gas in metal ⓘ |
| canBeModifiedBy | Schottky correction for electric field ⓘ |
| category |
electron emission theory
ⓘ
statistical mechanics applications ⓘ |
| dependsOn |
Boltzmann constant
NERFINISHED
ⓘ
absolute temperature ⓘ material work function ⓘ |
| derivedFrom |
Fermi–Dirac statistics
NERFINISHED
ⓘ
classical emission over a potential barrier ⓘ |
| describes | thermionic emission current density ⓘ |
| domainOfValidity | high-temperature operation of metals ⓘ |
| field |
solid-state physics
ⓘ
surface physics ⓘ thermionic emission ⓘ vacuum electronics ⓘ |
| hasHistoricalSignificance | foundation of early vacuum tube theory ⓘ |
| hasMathematicalForm | J = A T^2 exp(-\phi / k_B T) ⓘ |
| hasUnitForJ | ampere per square meter ⓘ |
| ignores | Schottky effect unless modified ⓘ |
| includesParameter |
Richardson constant
NERFINISHED
ⓘ
metal work function ⓘ |
| namedAfter |
Irving Langmuir Dushman
NERFINISHED
ⓘ
Owen Willans Richardson NERFINISHED ⓘ |
| predicts |
exponential dependence of emission on work function
ⓘ
quadratic dependence of emission on temperature ⓘ |
| relatedTo |
Child–Langmuir law
NERFINISHED
ⓘ
Fowler–Nordheim equation NERFINISHED ⓘ |
| relates |
thermionic current density to absolute temperature
ⓘ
thermionic current density to work function ⓘ |
| temperatureDependence | strongly temperature dependent ⓘ |
| usedIn |
analysis of hot electron emitters
ⓘ
design of thermionic cathodes ⓘ electron gun design ⓘ vacuum tube engineering ⓘ |
| usesSymbol |
A for Richardson constant
ⓘ
J for current density ⓘ T for absolute temperature ⓘ \phi for work function ⓘ k_B for Boltzmann constant ⓘ |
| validFor | thermionic emission in vacuum ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.