Brillouin and Langevin functions

<p>The Brillouin and Langevin functions are a pair of <a href="/facts/Special_functions/JETSeucA">special functions</a> that appear when studying an idealized <a href="/facts/Paramagnetic/vj1SMbbp">paramagnetic</a> material in <a href="/facts/Statistical_mechanics/6zMsNYYG">statistical mechanics</a>. These functions are named after French physicists <a href="/facts/Paul_Langevin/Tjfjw4uT">Paul Langevin</a> and <a href="/facts/L%C3%A9on_Brillouin/8AAtqyeH">Léon Brillouin</a> who contributed to the microscopic understanding of magnetic properties of matter.
</p><p>The Langevin function is derived using statistical mechanics, and describes how magnetic dipoles are alignment by an applied field. The Brillouin function was developed later to give an explanation that considers quantum physics. The Langevin function could then be a seen as a special case of the more general Brillouin function if the quantum number 
  
    
      
        J
      
    
    {\displaystyle J}
  
 would be infinite (
  
    
      
        J
        →
        ∞
      
    
    {\displaystyle J\rightarrow \infty }
  
).
</p>

Brillouin and Langevin functions open-in-new

Brillouin and Langevin functions