What is the Lever Rule?

The Lever Rule is a fundamental tool used in materials science and chemistry to determine the relative weight percentages (mass fractions) of two phases in a binary equilibrium phase diagram. When a material exists in a two-phase region (such as a mixture of liquid and solid), the lever rule uses the horizontal tie-line (isotherm) to calculate how much of each phase is present based on the overall chemical composition.

How to Use the Lever Rule Calculator

To use this calculator, you need three values from your phase diagram:

1. Overall Composition (C₀): The total alloy or mixture concentration at the point of interest.
2. Composition of Phase α (Cα): The concentration where the tie-line intersects the left boundary (usually the solidus or solvus line).
3. Composition of Phase β (Cβ): The concentration where the tie-line intersects the right boundary (usually the liquidus or solvus line).

The calculator applies the inverse relationship: the fraction of a phase is proportional to the length of the segment on the opposite side of the overall composition point.

The Lever Rule Formula

The formulas used for calculation are:

• Mass Fraction of Alpha (Wα): (Cβ - C₀) / (Cβ - Cα)
• Mass Fraction of Beta (Wβ): (C₀ - Cα) / (Cβ - Cα)

Frequently Asked Questions

Why is it called the "Lever Rule"?

It is named after the mechanical lever principle. In physics, for a lever to balance, the weight on one side multiplied by its distance from the fulcrum must equal the weight on the other side. Similarly, in a phase diagram, the amounts of the two phases "balance" at the overall composition point (the fulcrum).

Does it work for volume fractions?

Standard lever rule calculations provide weight (mass) fractions. To find volume fractions, you would need to incorporate the densities of the individual phases.