Past exam of the materials science course of the University of Cambridge / 2016 / Paper 1 / 4 / e / Solution

At equilibrium at room temperature the phases are pure Ag and pure Cu, with mass fractions $0.80$ and $0.20$. A representative solidification structure contains primary Ag-rich grains or dendrites surrounded by a finer two-phase eutectic aggregate. Subsequent equilibrium solute rejection modifies both constituents as they cool.

The $42.1\%$ primary-$\alpha$ and $57.9\%$ eutectic-constituent fractions calculated at the eutectic arrest describe how the liquid froze. They are not the final pure-Ag and pure-Cu phase fractions. For example, just below the arrest the total copper-rich phase fraction is $(20-9)/(92-9)=11/83=0.1325$; it rises to $0.20$ as solubility is lost on further equilibrium cooling. The distinction separates a microstructural constituent from a thermodynamic phase.

Faster solidification usually refines the dendrite and eutectic spacings. If solid-state diffusion cannot keep up, composition gradients, supersaturated solids and delayed precipitation can persist. Their exact fractions then depend on the thermal history; faster cooling does not change the alloy's overall $20\%$ copper inventory. Complete long-term equilibration would restore the same equilibrium phase compositions and mass fractions.