BeginnerTopic 16 of 100Materials & Chemical
Lever rule
Calculates fractions of phases in a two-phase region.
In depth
In a two-phase region the tie line gives compositions of phases at ends; the fraction of phase α is W_α=(C_β-C₀)/(C_β-C_α), i.e. opposite arm over total tie-line length. Also gives mass fractions of microconstituents such as proeutectoid ferrite and pearlite.
Key points
- Opposite lever arm
- Weight vs volume fraction
- Non-equilibrium cooling differs
ExampleA Cu-Ni alloy at a given T has fractions of liquid and solid computed with the lever rule.
The lever rule gives the proportions of two phases in an alloy, which is needed to predict hardness, strength and corrosion behaviour.
What is Lever rule?
Calculates fractions of phases in a two-phase region.
Why is it important to understand lever rule?
The lever rule gives the proportions of two phases in an alloy, which is needed to predict hardness, strength and corrosion behaviour.
How do I use the lever rule?
Draw a horizontal tie line across the two-phase region, and the fraction of each phase is the length of the opposite arm divided by the total tie line length.
Does the lever rule apply in a single-phase region?
No. It applies only where two phases coexist in equilibrium, so single-phase regions have a composition equal to the alloy.
How is Lever rule used in practice?
Typical applications include finding the fraction of liquid and solid during solidification of a solder, estimating how much pearlite and ferrite exist in a steel at a given temperature and predicting the mixture of two phases in a casting for hardness calculations.
What should I learn before Lever rule?
Study "Phase diagrams" first (topic 15 of 100 in Materials & Chemical). It covers the groundwork this topic builds on.
What are the key points of Lever rule?
Opposite lever arm. Weight vs volume fraction. Non-equilibrium cooling differs.
Can you give an example of Lever rule?
A Cu-Ni alloy at a given T has fractions of liquid and solid computed with the lever rule.
What comes after Lever rule?
The next topic is "Iron-carbon diagram", which builds directly on this one.
How difficult is Lever rule?
It is classed as Beginner in Materials & Chemical (topic 16 of 100). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.