  By means of first-principles calculations coupled with the kinetic Monte
Carlo simulations, we have systematically investigated the effects of dilute
substitutional solutes on the behaviors of carbon in $\alpha$-Fe. Our results
uncover that: ($i$) Without the Fe vacancy the interactions between most
solutes and carbon are repulsive due to the strain relief, whereas Mn has a
weak attractive interaction with its nearest-neighbor carbon due to the local
ferromagnetic coupling effect. ($ii$) The presence of the Fe vacancy results in
attractive interactions of all the solutes with carbon. In particular, the
Mn-vacancy pair shows an exceptionally large binding energy of -0.81 eV with
carbon. ($iii$) The alloying addition significantly impacts the atomic-scale
concentration distributions and chemical potential of carbon in the Fe matrix.
Among them, Mn and Cr increase the carbon chemical potential whereas Al and Si
reduce it. ($iv$) Within the dilute scale of the alloying solution, the solute
concentration and temperature dependent carbon diffusivities demonstrate that
Mn has a little impact on the carbon diffusion whereas Cr (Al or Si) remarkably
retards the carbon diffusion. Our results provide certain implication for
better understanding the experimental observations related with the carbon
solubility limit, carbon micro-segregation and carbide precipitations in the
ferritic steels.
