Chemistry
Chemistry
Problem
An alloy designer is considering three binary combinations based on the atomic radius data below. All three candidate alloys would adopt the face-centred cubic lattice of copper. Element Atomic radius / pm Cu 128 Zn 134 Sn 140 For each binary pair (Cu–Zn, Cu–Sn, and Zn–Sn), the designer must decide whether the alloying mechanism would be predominantly substitutional or interstitial in the fcc lattice and assess its viability. (a) Rank the three radius differences (||) from smallest to largest. Show the numerical values you obtain. (b) Using your ranking, classify the expected alloying mechanism (substitutional or interstitial) for each binary pair. Provide brief reasoning for each classification that explicitly refers to the size data. (c) For the binary pair with the largest radius difference, discuss two crystallographic or energetic factors that might limit the solid-solubility range, even if the alloy forms by the mechanism you identified in part (b).Intuitive explanation
The key to predicting alloying mechanism is the Hume-Rothery rule: when atomic radii differ by more than 15%, the solute atom is too large or small to fit into substitutional lattice sites without severe distortion, forcing it into interstitial positions instead. Calculate the percentage size mismatch for each pair, then compare to this threshold—substitutional alloys are generally more stable and useful than interstitial ones. This tells you which combinations are most viable for practical alloy design.
Intuitive explanation
The key to predicting alloying mechanism is the Hume-Rothery rule: when atomic radii differ by more than 15%, the solute atom is too large or small to fit into substitutional lattice sites without severe distortion, forcing it into interstitial positions instead. Calculate the percentage size mismatch for each pair, then compare to this threshold—substitutional alloys are generally more stable and useful than interstitial ones. This tells you which combinations are most viable for practical alloy design.