Lever rule

The lever rule is a tool used to determine weight percentages of each phase of a binary equilibrium phase diagram. It is used to determine the percent weight of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line.

In an alloy with two phases, α and β, which themselves contain two elements, A and B, the lever rule states that the weight percentage of the α phase is

where

all at some fixed temperature.

Suppose an alloy at an equilibrium temperature T consists of c wt% (weight percentage) of element B. Suppose also that at temperature T the alloy consists of two phases, α and β, for which the α consists of a wt% B, and β consists of b wt% B. Let the weight of the α phase in the alloy be ${\displaystyle W_{\alpha }}$ so that the weight of the β phase is ${\displaystyle W_{\beta }=W_{TOT}-W_{\alpha }}$, where ${\displaystyle W_{TOT}}$ is the total weight of the alloy.

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