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              <p>Combining first principles calculations with recently-developed statistical physics tools, we determine carbon diffusion mechanisms and the resulting diffusion coeffcients in pure-Fe and weaklyalloyed $M_3$C cementites. The predicted coefficients in Fe3C are in good agreement with experimental measurements of carburization rate in ferritic steels. In our proposed diffusion mechanisms, C migrates by jumps between interstitial sites rather than via the C Frenkel pair mechanism, as proposed by previous studies based on semi-empirical simulations. In the alloyed cementites, the C diffusion can be slowed down due to the presence of Mn solutes up to 500 K, while it is mostly unaffected by the addition of Mo or Cr solutes.</p>
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