Question 1

What is the lever rule?

Accepted Answer

The lever rule is a method for calculating the mass fraction of each phase in a two-phase region. For overall composition x₀, liquid composition x_L, and solid composition x_α, the solid fraction is f_α=(x₀−x_L)/(x_α−x_L) and the liquid fraction is f_L=1−f_α. The name comes from an analogy to a mechanical lever, where the overall composition acts as the fulcrum.

Question 2

What is the difference between an isomorphous and a eutectic phase diagram?

Accepted Answer

An isomorphous system has complete mutual solubility across all compositions, with only a liquidus and a solidus line (e.g., Cu-Ni). A eutectic system has limited solid-state solubility, with a eutectic point (lowest melting point) at which the liquid simultaneously transforms into two solid phases (e.g., Pb-Sn, Al-Si). Eutectic systems have a eutectic temperature T_E and eutectic composition x_E.

Question 3

What is the difference between equilibrium solidification and the Scheil equation?

Accepted Answer

In equilibrium solidification, diffusion in both phases is fast enough to maintain equilibrium compositions at all times. The Scheil equation assumes zero diffusion in the solid phase, so once solidified, the solid composition does not change. Scheil equation: C_S = k·C_0·(1−f_S)^(k−1), where k is the partition coefficient. Real castings exhibit intermediate behavior.

Question 4

How can this tool be used in materials design and CAE?

Accepted Answer

This tool is useful for predicting solidification sequences in alloy design, determining the two-phase temperature range for casting and heat treatment processes, and initial estimates of segregation. In CAE, it supports microstructure prediction in weld heat-affected zones (HAZ), foundational understanding of multi-component CALPHAD calculations, and preprocessing for solidification simulations coupled with FEM thermal analysis.

Binary Phase Diagram & Lever Rule Calculator

Lever Rule & Theory