Question:
In the iron-carbon equilibrium phase diagram, the eutectoid reaction occurs at 723°C with the eutectoid composition of 0.83 weight % carbon. Ferrite and cementite phases are considered to contain 0.022 weight % carbon and 6.67 weight % carbon, respectively. If a steel specimen with 0.7 weight % carbon is cooled from 950°C to below 723°C, the fraction of eutectoid ferrite is .............
In the iron-carbon equilibrium phase diagram, the eutectoid reaction occurs at 723°C with the eutectoid composition of 0.83 weight % carbon. Ferrite and cementite phases are considered to contain 0.022 weight % carbon and 6.67 weight % carbon, respectively. If a steel specimen with 0.7 weight % carbon is cooled from 950°C to below 723°C, the fraction of eutectoid ferrite is .............
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The lever rule is a useful method for calculating the phase fractions in a two-phase region. The fraction of each phase is inversely proportional to the distance from the phase boundary.
Updated On: Mar 12, 2026
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Correct Answer: 0.72
Solution and Explanation
To determine the fraction of eutectoid ferrite, we can use the lever rule from phase diagrams. The lever rule states that the fraction of a phase in a two-phase region is given by:
\[
f_{\alpha} = \frac{C_{\beta} - C_0}{C_{\beta} - C_{\alpha}},
\]
where:
- \( f_{\alpha} \) is the fraction of eutectoid ferrite,
- \( C_0 \) is the composition of the specimen, which is 0.7 weight % carbon,
- \( C_{\alpha} \) is the composition of ferrite, which is 0.022 weight % carbon,
- \( C_{\beta} \) is the composition of cementite, which is 6.67 weight % carbon.
Now, substituting the values into the equation: \[ f_{\alpha} = \frac{6.67 - 0.7}{6.67 - 0.022} = 0.74. \] Thus, the fraction of eutectoid ferrite lies between 0.72 and 0.76. This is the portion of the steel that is in the eutectoid ferrite phase after cooling below the eutectoid temperature.
Now, substituting the values into the equation: \[ f_{\alpha} = \frac{6.67 - 0.7}{6.67 - 0.022} = 0.74. \] Thus, the fraction of eutectoid ferrite lies between 0.72 and 0.76. This is the portion of the steel that is in the eutectoid ferrite phase after cooling below the eutectoid temperature.
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