Grey tin 2026-10-20
The diamond-cubic form of tin favoured below about at ambient pressure. Its lower density than white tin contributes to the damage associated with tin pest.
Past exam of the materials science course of the University of Cambridge 2018 Paper 1 1 c Solution 2026-10-20
The metallic conventional cell has four tin atoms, whereas the conventional diamond cubic structure cell has eight. Therefore the volume per atom isThe fractional change for metallic to nonmetallic tin isThe atom count is unchanged, so this is also the unconstrained bulk volume change for complete transformation under the model. If it were macroscopically isotropic, the corresponding free linear expansion would be .
Such a large transformation strain creates stresses where transformed and untransformed regions constrain one another. Cracking, loss of mechanical integrity and disintegration can follow: the phenomenon is tin pest. The calculation establishes the volume mismatch, not the transformation rate; temperature, nucleation and impurities affect when a real specimen changes.
Past exam of the materials science course of the University of Cambridge 2019 Paper 1 4 a Solution 2026-10-20
(Bi) and are Bi-rich and Sn-rich terminal solid solutions, not intermetallic compounds. At the eutectic composition, cooling through givesThe two solids grow together as a fine eutectic microstructure, commonly lamellar or rod-like. Below about , the tin-rich component has an equilibrium tendency to transform from metallic tetragonal white tin to diamond-cubic grey tin, with a substantial volume increase. This is tin pest, which can disrupt the microstructure mechanically. The dashed transition does not transform the Bi-rich phase into tin. Actual transformation can be slow and depend strongly on impurities and nucleation; crossing the line does not guarantee immediate disintegration.