Lever rule

In chemistry, the lever rule is a formula used to determine the mole fraction (x_i) or the mass fraction (w_i) of each phase of a binary equilibrium phase diagram. It can be used to determine the fraction of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line.

In an alloy or a mixture with two phases, α and β, which themselves contain two elements, A and B, the lever rule states that the mass fraction of the α phase is

${\displaystyle w^{\alpha }={\frac {w_{\rm {B}}-w_{\rm {B}}^{\beta }}{w_{\rm {B}}^{\alpha }-w_{\rm {B}}^{\beta }}}}$

where

• ${\displaystyle w_{\rm {B}}^{\alpha }}$ is the mass fraction of element B in the α phase
• ${\displaystyle w_{\rm {B}}^{\beta }}$ is the mass fraction of element B in the β phase
• ${\displaystyle w_{\rm {B}}}$ is the mass fraction of element B in the entire alloy or mixture

all at some fixed temperature or pressure.