Past exam of the materials science course of the University of Cambridge / 2019 / Paper 1 / 4 / b / i / Solution

At $200{}^{\circ }\mathrm{C}$, moving from Bi-rich to Sn-rich composition gives $(\mathrm{Bi})$, $(\mathrm{Bi})+L$, $L$, $L+(\beta \mathrm{Sn})$, $(\beta \mathrm{Sn})$. Approximate liquid coexistence compositions read from the diagram are $x_{\mathrm{Sn}}\simeq 0.33$ on the left and $0.87$ on the right; the coexisting solids lie near their respective pure ends. The stable Gibbs free energy follows solid curves near the endpoints, two common-tangent constructions in the coexistence intervals, and the liquid curve between them.