In the Pb-Sn system, take the eutectic temperature as 183 °C, the eutectic composition as 61.9 wt% Sn, and the compositions of the α and β phases at that temperature as 18.3 wt% Sn and 97.8 wt% Sn. When a 30 wt% Sn alloy is cooled under equilibrium to just below the eutectic temperature, which value is closest to the mass fraction of the microstructure that is eutectic structure?

Answer: A. About 0.27

The eutectic structure is what the liquid (61.9 wt% Sn) remaining just above the eutectic temperature turns into through the eutectic reaction. So apply the lever rule in the α + L region just above the eutectic temperature: W_eutectic = W_L = (30 − 18.3)/(61.9 − 18.3) = 11.7/43.6 ≈ 0.27. About 0.73 is the fraction of the remaining primary α, the mistake of taking the opposite distance. About 0.15 is the fraction of all β phase just below the eutectic temperature, (30 − 18.3)/(97.8 − 18.3). All the β is inside the eutectic structure, but the eutectic structure also contains α, so the two do not match. The key to this kind of problem is distinguishing microconstituents (primary and eutectic) from phases (α and β).