Submonolayers of carbon on $\alpha \text{-Fe}$ facets: An ab initio study

Motivated by recent in situ studies of carbon nanotube growth from large transition-metal nanoparticles, we study various $\alpha$-iron (ferrite) facets at different carbon concentrations using ab initio methods. The studied (110), (100), and (111) facets show qualitatively different behavior when carbon concentration changes. In particular, adsorbed carbon atoms repel each other on the (110) facet, resulting in carbon dimer and graphitic material formation. Carbon on the (100) facet forms stable structures at concentrations of about 0.5 monolayer and at 1.0 monolayer this facet becomes unstable due to a frustration of the top-layer iron atoms. The stability of the (111) facet is weakly affected by the amount of adsorbed carbon and its stability increases further with respect to the (100) facet with increasing carbon concentration. The exchange of carbon atoms between the surface and subsurface regions on the (111) facet is easier than on the other facets and the formation of carbon dimers is exothermic. These findings are in accordance with a recent in situ experimental study where the existence of graphene-decorated (111) facets is related to increased carbon concentration.

Figure 1

(Color online) Computational unit cells for different $\alpha$-iron surfaces used in the simulations viewed from (a,c,e) top and from (b,d,f) side. [(a) and (b)] (110), [(c) and (d)] (100), and [(e) and (f)] (111) surfaces. Atoms in topmost (lowermost) layers are marked with brighter (darker) shades. Atoms in the unit cells used in this work are marked with blue color. For (110) and (100) the unit cells correspond to $3\times 3$ periodicity while for (111) to $2\times 2$ periodicity. (g) A portion of bulk $\alpha$-iron cut at different angles, demonstrating the relative positions of different surfaces. For (100) surface, the topmost layer is marked with black color. For (111) surface, the two topmost layers are marked with blue color.

Figure 2

(Color online) Local coordination at the bulk octahedral site in $\alpha$-iron and how it is exposed on the (110), (100), and (111) facets. The octahedral site is marked in all insets with green color. (a) The coordination of octahedral site in the bulk. Exposed bulk octahedral sites on the (b) (110), (c) (100), and (d) (111) facets.

Figure 3

(Color online) Some of the most stable geometries for C and ${\text{C}}_2$ on the Fe(110) surface. Different geometries are tagged with the same labels as in Table . Coadsorption geometries, where atoms are adsorbed into the same unit cell are tagged with the label CA. Iron atom displacements upon carbon adsorption in (C-1) have been marked with arrows. These can be related to Fig. 2. In (CA-2) one adsorbed carbon atom is pushed toward vacuum.

Figure 4

(Color online) Some of the most stable geometries for C and ${\text{C}}_2$ on the Fe(100) surface. Different geometries are tagged with the same labels as in Table . Coadsorption geometries, where atoms are adsorbed into the same unit cell are tagged with the label CA. Iron atom displacements upon carbon adsorption in (C-1) have been marked with arrows. These can be related to Fig. 2.

Figure 5

(Color online) Some of the most stable geometries for C and ${\text{C}}_2$ on the Fe(111) surface. Different geometries are tagged with the same labels as in Table . Coadsorption geometries, where atoms are adsorbed into the same unit cell are tagged with the label CA. Iron atom displacements upon carbon adsorption in (C-1) have been marked with arrows. These can be related to Fig. 2.

Figure 6

(Color online) Adsorption geometries where carbon atoms are adsorbed in the sublattice formed by the C-1 sites (see Fig. 4). $N_C$ is the number of carbon atoms and $N_{conf}$ the number of all possible coadsorption configurations when $N_C$ atoms are adsorbed on a $\left(3\times 3\right)$ C-1 sublattice. For a particular coadsorption geometry illustrated in the table, energy $E_c$ and the mean Bader electron occupations for carbon atoms $\left({\overline{Q}}_b\right)$ have been tabulated (for an isolated carbon atom ${\overline{Q}}_b=4.0$). Displacements of some iron atoms upon carbon adsorption have been highlighted by blue arrows. In the last row and column, the energy gain when forming a ${\text{C}}_2$ molecule at the 1 ML concentration is calculated.

Figure 7

(Color online) Relaxed adsorption geometries on (110) after carbon atoms have been placed in a sublattice formed by the C-1 (C3–1, C4–1,C6–2), C-3 (C3–2, C4–4, C6–1) and ${\text{C}}_2\text{−}1$ (C4–2, C4–3) configurations of Fig. 3. Number of carbon atoms per unit cell $\left(N_C\right)$ and energies $E_c$ have been tabulated.

Figure 8

(Color online) Relaxed adsorption geometries on (111) after carbon atoms have been placed in a sublattice formed by the C-1 and C-2 sites (see Fig. 5). Number of carbon atoms per unit cell $\left(N_C\right)$ and energies $E_c$ have been tabulated.

Figure 9

(Color online) Surface energy $G$ [Eq. (7)] as function of carbon coverage (atoms per ${\text{Å}}^2$) on the (110), (100), and (111) facets. Energies correspond to the fully relaxed adsorption geometries of Figs. 3, 4, 5, 6, 7, 8. Energy at zero concentration has been fixed to the surface energy of the empty facet [$140\text{meV}/{\text{Å}}^2$ for (110) and (100), $160\text{meV}/{\text{Å}}^2$ for (111)], as described by Eq. (7).

Figure 10

(Color online) (a) Diffusion on (111) into the C-1 and C-2 sites (Fig. 4) and (b) into a deeper subsurface site (N). The energy of adsorbate “C-4” (Fig. 5) has been marked in panel (b) with a dashed line.