Brillouin function
E675970
The Brillouin function is a mathematical function in statistical mechanics that describes the magnetization of a paramagnetic material as a function of temperature and applied magnetic field.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Brillouin function canonical | 1 |
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
function in statistical mechanics
ⓘ
mathematical function ⓘ special function ⓘ |
| appliesTo |
dilute magnetic ions in crystals
ⓘ
localized spin systems ⓘ paramagnetic salts ⓘ |
| argument |
ratio of magnetic energy to thermal energy
ⓘ
x = g μ_B J B / (k_B T) ⓘ |
| assumes | non-interacting magnetic moments ⓘ |
| dependsOn |
applied magnetic field
ⓘ
temperature ⓘ total angular momentum quantum number J ⓘ |
| describes | magnetization of a paramagnetic material ⓘ |
| domain | real numbers ⓘ |
| expressedInTermsOf | hyperbolic cotangent functions ⓘ |
| field |
condensed matter physics
ⓘ
statistical mechanics ⓘ |
| hasFormula | B_J(x) = (2J+1)/(2J) coth[(2J+1)x/(2J)] - (1/(2J)) coth[x/(2J)] ⓘ |
| isMonotonic | true ⓘ |
| isOddFunction | true ⓘ |
| limitCase |
linear in x for small x
ⓘ
reduces to Langevin function for J → ∞ NERFINISHED ⓘ saturates to -1 for large negative x ⓘ saturates to 1 for large positive x ⓘ |
| namedAfter | Léon Brillouin NERFINISHED ⓘ |
| parameter |
Bohr magneton μ_B
NERFINISHED
ⓘ
Boltzmann constant k_B NERFINISHED ⓘ Landé g-factor NERFINISHED ⓘ absolute temperature T ⓘ magnetic field B ⓘ |
| range | [-1, 1] ⓘ |
| relatedConcept |
Curie law
NERFINISHED
ⓘ
Curie–Weiss law NERFINISHED ⓘ magnetic susceptibility ⓘ |
| relatedTo | Langevin function NERFINISHED ⓘ |
| usedFor |
description of Langevin paramagnetism generalization
ⓘ
magnetization curves of paramagnets ⓘ paramagnetism modeling ⓘ |
| usedIn |
Curie–Weiss law derivations
ⓘ
analysis of magnetocaloric effect ⓘ description of rare-earth paramagnets ⓘ design of paramagnetic thermometers ⓘ mean-field theory of ferromagnets ⓘ theory of localized magnetic moments ⓘ |
| usedToFit | experimental magnetization data ⓘ |
| variable | total angular momentum J = L + S ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.