Past exam of the materials science course of the University of Cambridge / 2018 / Paper 1 / 3 / b / Solution

Sample A is the Cu–Au alloy. At the indicated copper-rich composition, the supplied Cu–Au diagram permits one copper-rich solid-solution phase. The Cu–Ag diagram instead gives two equilibrium solid phases at room temperature. A single consistent set of FCC peaks therefore identifies A under the stated equilibrium assumptions; similar pure-metal lattice parameters alone would not distinguish gold from silver.

Use Vegard's law as an approximate atomic-fraction interpolation:With the higher-angle estimate from part(a),This is about $5.1$ atomic percent, not weight percent. Using rounded molar masses $M_{\mathrm{Au}}\simeq 197$ and $M_{\mathrm{Cu}}\simeq 63.55\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$,Using the first peak alone instead gives roughly $12.6wt\%$. The justified conclusion is therefore about $13$–$14wt\%$ gold, with uncertainty from angle rounding, calibration and the approximate linear lattice-composition relation.