Lever Rule

  • Given a binary phase diagram, the composition of an alloy, its temperature, and assuming that the alloy is at equilibrium, determine:

    • what phase(s) is (are) present,

    • the composition(s) of the phase(s), and

    • the mass fraction(s) of the phase(s)

The Lever Rule is a way in which to calculate the proportions of each phase present on a phase diagram in a two phase field at a given temperature and composition.
The lever rule is a mechanical analogy to the mass balance calculation. The tie line in the two-phase region is analogous to a lever balanced on a fulcrum. Finding the amounts of phases in a two phase region:

  1. Locate composition and temperature in diagram

  2. In two phase region draw the tie line or isotherm

  3. Fraction of a phase is determined by taking the length of the tie line to the phase boundary for the other phase, and dividing by the total length of tie line

Solved Examples

Solved Example:

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Refer the following Cu-Ag phase diagram. At 900$^\circ$C, the approximate composition of the solution at 20% Ag is:

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Correct Answer: A

Solved Example:

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Pure iron is the structure of: (UKPSC JE Mech 2013)

Correct Answer: A

Solved Example:

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The lower critical temperature for all steels, in Deg Celsius, is: (RRB JE ME CBT 2 Aug 2019)

Correct Answer: B

Solved Example:

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In grey cast iron, carbon is present in the form of:

Correct Answer: C

Solved Example:

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In nodular iron, graphite is in the form of:

Correct Answer: D

Solved Example:

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What cast iron has modular or spheroidal graphite?

Correct Answer: A

Solved Example:

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The temperature at which ferromagnetic alpha iron transforms to para-magnetic alpha iron is:

Correct Answer: A

Solved Example:

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Ferromagnetic $\alpha$-iron exists in temperature range of:

Correct Answer: A

Solved Example:

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Paramagnetic $\alpha$-iron changes to $\gamma$-iron at:

Correct Answer: B

Solved Example:

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Pearlite is a combination of: (Vizag MT Mech 2013- Re-exam)

Correct Answer: A

Solved Example:

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Austenite is a combination of:

Correct Answer: B