Past exam of the materials science course of the University of Cambridge / 2015 / Paper 1 / 7 / a

At two-phase equilibrium, the endpoints of a common tangent to the two molar free-energy curves give the coexisting compositions. They are not the separate curve minima. Reading the graph gives approximately $x_{B,\alpha }\simeq 0.02$ and $x_{B,m}\simeq 0.64$, with a few atomic-percent graphical uncertainty.

Let $f_{\alpha }$ be the fraction of atoms in the precipitate thermodynamic phase. Conservation of the overall B fraction givesand henceAbout85percent remains in the B-richer matrix. Smooth readings of the original curves put the result near14–15percent; the graph does not justify many significant figures. The result is an atomic or molar thermodynamic phase fraction. Its identification with a volume fraction in the next estimate requires comparable atomic volumes of the two thermodynamic phases.