Derive the lever rule for the amount in weight percent of each phase in two-phase regions of a binary phase diagram. Use a phase diagram in which two elements are completely soluble in each other.
Obtain the weight percentages of the liquid and solid phases in any two phase region of binary equilibrium phase diagram by the help of lever rule.
Explanation of Solution
Let the phase diagram of two elements
The lever equations can be obtained by the help of weight balances. The first equation of lever rule is derived by taking the sum of the weight fraction of liquid and solid phase as 1.
Write the sum of the phases as,
Here, weight fraction of liquid and solid phase is
Derive the second equation of the lever rule by a using a weight balance of
Write the weight balance by considering
Substitute
Rewrite Equation (II) to get weight fraction of solid phase.
Substitute
Equations (III) and (IV) are called as lever rule equations for solid and liquid phase respectively.
Hence, the lever rule equations are
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Chapter 8 Solutions
Foundations of Materials Science and Engineering
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