An alloy designer is considering three binary combinations based on the atomic radius…
CHEMISTRY · Multi-part · AP · Chemistry · Compound Structure and Properties · Compound Structure and Properties
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 (|r1−r2|) 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).