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

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.