Discussion
In Fe-Fe3C phase diagram, the eutectoid composition is 0.8 weight % of carbon at 725 ºC. The maximum solubility of carbon in α-ferrite phase is 0.025 weight % of carbon. A steel sample, having no other alloying element except 0.5 weight % of carbon, is slowly cooled from 1000 ºC to room temperature. The fraction of pro-eutectoid α-ferrite in the above steel sample at room temperature is
Answer: A
The fraction of pro-eutectoid ferrite is 0.387.
A 0.5% carbon steel is hypoeutectoid. On slow cooling, ferrite forms first; just above the eutectoid temperature the alloy is ferrite of 0.025% C and austenite of eutectoid composition, 0.8% C, which then turns to pearlite. The lever rule at that temperature gives
\[ \begin{aligned} f_{\alpha} &= \frac{0.8 - 0.5}{0.8 - 0.025} \\ &= \frac{0.3}{0.775} \approx 0.387 \end{aligned} \]
The rest, 0.613, becomes pearlite. 0.775 is the denominator alone, and 0.864 and 0.475 do not follow from the lever rule with these compositions.
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