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

Convert atomic fractions to mass fractions before using the diagram's weight-percent scale:With $M_{\mathrm{Sn}}=118.71$ and $M_{\mathrm{Bi}}=208.98\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$, the overall $x=0.30$ is $19.58wt\%$ Sn. At $150{}^{\circ }\mathrm{C}$, the diagram gives approximately $x_B=0.028$ and $x_L=0.555$. These are about $1.61$ and $41.47wt\%$ Sn. The lever rule givesThe microstructure has primary Bi-rich crystals surrounded by remaining liquid. The phase compositions and fractions are approximate readings of a printed phase diagram, not exact thermodynamic values. Faster cooling generally gives finer crystals, solute segregation and departure from these equilibrium compositions.

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.