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

Sample B should show two FCC peak families, one from a copper-rich phase and one from a silver-rich phase. Their lattice parameters are set by the compositions of the coexisting phases, not by one lattice parameter at the overall alloy composition.

For corresponding Miller indices the silver-rich phase has a larger lattice parameter and hence a larger interplanar spacing, so its reflection occurs at smaller $2\theta$. Some reflections may overlap or be weak. Relative intensities depend on phase fractions, atomic scattering factors, absorption and texture; a raw peak-height ratio is not directly a mass fraction.

At room temperature the mutual solubilities in the supplied Cu–Ag diagram are small, so the two families would be near the elemental copper and silver positions. Slow cooling is important: a metastable supersaturated single phase would be a different interpretation. Quantitative phase or composition analysis would require calibrated diffraction and an appropriate refinement, not merely counting the visible peaks.