Lever Rule: Liquid Fraction on a Binary Diagram
Fixed T and overall C₀ on an isomorphous A–B diagram. Read the tie-line ends and recover the liquid fraction f_L.
Goal
Determine f_L = (C₀ − C_α) / (C_L − C_α) by reading C_α (solidus) and C_L (liquidus) at the given T.
Equipment
- Isomorphous A–B T–x diagram
- Known T and C₀
- Composition cursors
Experiment
Theory
In the two-phase field a horizontal tie line joins solid composition C_α to liquid composition C_L. Mass balance gives f_L = (C₀ − C_α)/(C_L − C_α) and f_α + f_L = 1. The bench hides the printed fractions and the labelled end compositions. T and C₀ are known. You read the axis.
Procedure
- Temperature T and overall composition C₀ are fixed and known. You only move two composition cursors on the isotherm.
- Park one cursor on the solidus intersection (C_α, richer in B) and the other on the liquidus intersection (C_L, richer in A). The bench does not print those compositions or f_L.
- Record. The notebook computes f_L. Repeat the reading at least 6 times (re-park the cursors).
- Take the mean of the f_L column and compare with the reference.
Conclusion
The mean liquid fraction agrees with the lever rule at this T and C₀. Main uncertainties: reading the axis and parking the cursors on the intersections.