The Al-Si system has a eutectic point at 577 °C and 12.6 wt% Si; at that temperature the Si solubility of the α (Al) phase is 1.65 wt%, and the Si phase can be taken as essentially pure Si (100 wt%). When an 18 wt% Si hypereutectic alloy is cooled under equilibrium to just above the eutectic temperature, which value is closest to the mass fraction of primary Si?

Answer: C. About 6.2%

Just above the eutectic temperature, primary Si coexists with liquid of the eutectic composition (12.6 wt% Si). From the lever rule, W_primary Si = (18 − 12.6)/(100 − 12.6) = 5.4/87.4 ≈ 0.062, or about 6.2%. About 5.4% takes the composition difference 18 − 12.6 directly as a percentage without dividing by the length of the tie line. About 16.6% is the fraction of all Si phase just below the eutectic temperature, (18 − 1.65)/(100 − 1.65), which includes the Si inside the eutectic structure. Hypereutectic Al-Si alloys are used for pistons and similar parts because the hard primary Si provides wear resistance, and treatments are applied to refine the primary Si.