Langevin function
E829089
The Langevin function is a mathematical function that describes how the magnetization of a paramagnetic material depends on an applied magnetic field and temperature in classical statistical mechanics.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical function
ⓘ
special function ⓘ |
| appearsIn |
Langevin model of paramagnetism
NERFINISHED
ⓘ
classical theory of paramagnetism ⓘ |
| appliesTo |
classical paramagnetism
ⓘ
paramagnetic materials ⓘ |
| approximationOf | Brillouin function for large spin quantum number ⓘ |
| argumentRepresents |
ratio of magnetic energy to thermal energy
ⓘ
μ B / (k_B T) ⓘ |
| category |
functions in magnetism
ⓘ
functions in statistical mechanics ⓘ |
| definition | L(x) = coth(x) − 1/x ⓘ |
| derivedFrom |
Boltzmann statistics
NERFINISHED
ⓘ
classical dipole moment distribution ⓘ |
| describes |
dependence of magnetization on applied magnetic field
ⓘ
dependence of magnetization on temperature ⓘ magnetization of a paramagnetic material ⓘ |
| domain | real numbers ⓘ |
| field |
classical physics
ⓘ
condensed matter physics ⓘ magnetism ⓘ statistical mechanics ⓘ |
| governs | classical paramagnetic magnetization curve saturation ⓘ |
| hasSeriesExpansion | L(x) = x/3 − x^3/45 + 2x^5/945 − … ⓘ |
| introducedIn | early 20th century ⓘ |
| inverseFunction | inverse Langevin function ⓘ |
| inverseUsedIn |
polymer chain elasticity models
ⓘ
rubber elasticity theory ⓘ |
| limitBehavior |
L(x) → 1 as x → ∞
ⓘ
L(x) → −1 as x → −∞ ⓘ L(x) ≈ x/3 for small x ⓘ |
| namedAfter | Paul Langevin NERFINISHED ⓘ |
| property |
monotonic increasing function
ⓘ
odd function ⓘ |
| range | (−1, 1) ⓘ |
| relatedConcept | Langevin equation NERFINISHED ⓘ |
| relatedTo |
Brillouin function
NERFINISHED
ⓘ
Curie law NERFINISHED ⓘ Curie–Weiss law NERFINISHED ⓘ hyperbolic cotangent function ⓘ |
| symbol | L(x) ⓘ |
| usedFor |
determining magnetic moment from M–H data
ⓘ
magnetization curve fitting ⓘ |
| usedIn |
magnetic nanoparticle characterization
ⓘ
magnetic susceptibility calculations ⓘ superparamagnetism modeling ⓘ theory of paramagnetism ⓘ |
| variable | x ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.