Past exam of the materials science course of the University of Cambridge / 2015 / Paper 1 / 3 / b

In tempered martensite, the metastable carbon-supersaturated martensitic matrix can evolve toward a lower-carbon ferritic matrix containing fine carbides. Carbon segregation and precipitation reduce supersaturation and tetragonal lattice distortion; recovery can reduce internal strain while the original plate or lath pattern remains recognizable. This is tempering, rather than a fresh austenite-to-pearlite transformation.^[ref]

A generic sketch consequently replaces a uniform highly strained plate interior by a lower-carbon matrix with dispersed carbide particles, as in the third panel above. This provides a qualitative materials explanation for a changed fracture response. It does not specify a manufacturing optimization, and tempering is not a guarantee of monotonic toughness improvement in every steel: carbide morphology, impurities and retained austenite matter. The source reports the observed outcome, so the explanation must not be turned into a universal process recommendation.

Use the supplied Arrhenius law as a diffusion-scale calculation. The stated temperature and duration become $T=573.15\mathrm{K}$ and $t=10800\mathrm{s}$. With $R=8.31446\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$,With the standard diffusion-distance convention, the characteristic scale isThe one-dimensional rms displacement $\sqrt{2Dt}$ is about30micrometres, and the three-dimensional rms displacement $\sqrt{6Dt}$ about53micrometres. These different prefactors follow from the diffusion-distance convention; the diffusion coefficient is unchanged.

The scale is much larger than atomic spacing and can permit local carbon redistribution and carbide formation over microstructural distances. It is not evidence that the entire macroscopic specimen becomes compositionally homogeneous. Trapping, concentration gradients, evolving carbides and the use of a ferrite diffusivity for an initially defect-rich transformation product limit a literal tracer-distance interpretation.