Past exam of the materials science course of the University of Cambridge / 2019 / Paper 1 / 4 / c / ii / Solution

At $125{}^{\circ }\mathrm{C}$, primary Bi-rich crystals are surrounded by a transformed two-phase eutectic microstructure. Reading approximately $x_B=0.026$ and $x_S=0.94$ gives phase compositions $1.49$ and $89.90wt\%$ Sn. Consequently,These are total phase mass fractions, including both primary and eutectic material. They differ from the microconstituent fractions: just before the eutectic reaction, roughly $39\%$ by mass is liquid and subsequently becomes the eutectic constituent, with roughly $61\%$ primary Bi-rich material. Further slow cooling changes the phase compositions and allows secondary precipitation. Faster cooling usually refines the primary crystals and eutectic spacing and increases retained segregation; the equilibrium diagram does not specify the resulting nonequilibrium fractions uniquely.