= Solution
Use the supplied Arrhenius law as a diffusion-scale calculation. The stated temperature and duration become $T=573.15\ {\rm K}$ and $t=10800\ {\rm s}$. With $R=8.31446\ {\rm J\,mol^{-1}\,K^{-1}}$,
$$
D=2\times10^{-6}
\exp\left[-\frac{84138}{(8.31446)(573.15)}\right]
\simeq4.30\times10^{-14}\ {\rm m^2\,s^{-1}}.
$$
With the standard <diffusion-distance convention>, the characteristic scale is
$$
\boxed{\ell_D=\sqrt{Dt}\simeq2.15\times10^{-5}\ {\rm m}
\simeq22\ {\rm \mu m}.}
$$
The 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.
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