Carbon atom adsorption on and diffusion into Fe(110) and Fe(100) from first principles

We employ spin-polarized periodic density functional theory (DFT) to examine carbon atom adsorption on, absorption in, and diffusion into Fe(110) and Fe(100). We find that carbon atoms bind strongly with Fe surfaces and prefer high coordination sites. The carbon atom is predicted to adsorb on the long-bridge site on Fe(110) and the fourfold hollow site on Fe(100). Due to the very short distance between the carbon atom and the subsurface Fe atom of Fe(100), the carbon atom binds more strongly with Fe(100) than with Fe(110). In the subsurface region, the carbon atom prefers the octahedral site, as in bulk Fe. We find that the carbon atom is more stable in the subsurface octahedral site of Fe(110) than that of Fe(100), since the strain caused by the interstitial carbon atom is released by pushing one surface Fe atom towards vacuum by 0.5 Å in Fe(110), while the distortion in Fe(100) propagates far into the lattice. Diffusion of carbon atoms into Fe(110) and Fe(100) subsurfaces goes through transition states where the carbon atom is coordinated to four Fe atoms. The barriers to diffusion into Fe(110) and Fe(100) are 1.18 eV and 1.47 eV, respectively. The larger diffusion barrier into Fe(100) is mainly due to the stronger bonding between carbon and the Fe(100) surface. We predict that the rate-limiting step for $\mathrm{C}$ incorporation into bulk Fe is the initial diffusion to subsurface sites, while the rate-limiting step for absorbed carbon segregation to the surface is bulk diffusion, with no expected difference between rates to segregate to different surfaces. Lastly, we predict that graphite formation will be more favorable on $\mathrm{C}$-covered Fe(110) than $\mathrm{C}$-covered Fe(100).

Figure 1

High-symmetry adsorption sites on Fe surfaces. (a) Fe(110): OT denotes on top, SB denotes short bridge, LB denotes long bridge, and TF denotes threefold; (b) Fe(100): B denotes bridge, H denotes hollow. Surface $(1\times 1)$ cells for both Fe(110) and Fe(100) are also shown.

Figure 2

Most stable structures of the $\mathrm{C}$ atom on Fe surfaces at $1∕9\mathrm{ML}$: (a) Fe(110); (b) Fe(100). Fe atoms are in gray and $\mathrm{C}$ in white.

Figure 3

Side view of the structural model for $\mathrm{c}\left(2\times 2\right)\text{−}\mathrm{C}$ on Fe(100). Small circles are $\mathrm{C}$ atoms and big circles are Fe atoms. Circles of the same color are in the same plane. $d_{ij}$ is the interlayer spacing between layer $i$ and layer $j$, with the zeroth layer being the adsorbate layer. $b_i$ is the buckling magnitude in the $i$th substrate layer.

Figure 4

Most stable structures of the $\mathrm{C}$ atom in Fe subsurfaces. (a) Fe(110); (b) Fe(100). Fe atoms are in gray and $\mathrm{C}$ in white.

Figure 5

Minimum energy path of $\mathrm{C}$ diffusion into Fe(110) and the structures for the initial, transition, and final states. Fe atoms are in gray and $\mathrm{C}$ in white.

Figure 6

Minimum energy path of $\mathrm{C}$ diffusion into Fe(100) and several structures along the path. Fe atoms are in gray and $\mathrm{C}$ in white.