Lever Rule

1. Lever Rule

The Lever Rule is a mathematical tool used in phase diagrams to determine the relative proportions (weight fractions) of different phases in a two-phase region. It is widely applied in metallurgy, materials science, and thermodynamics to analyze binary phase diagrams.

2. Graphical Interpretation

• The tie line connects the compositions of phases α\alphaα and β\betaβ at a given temperature.

• The lever arm is the distance between C0C_0C0​ and the phase boundaries.

• The weight fraction of a phase is proportional to the opposite segment of the tie line (like a balance lever).

4.Applications of the Lever Rule

✅ Determining Phase Fractions – Used in binary phase diagrams 

(e.g., Fe-C, Cu-Ni, Al-Si systems).

✅ Alloy Design – Helps in estimating the proportion of solid and liquid during solidification.
✅ Heat Treatment Processes – Used to understand partial melting and phase transformation kinetics.
✅ Microstructural Analysis – Predicts the amount of eutectic, proeutectic, and other phases in metallographic studies.