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Liu et al. J. Mater. Inf. 2025, 5, 27 I http://dx.doi.org/10.20517/jmi.2024.105 Page 13 of 18

Figure 6. Results of variable-composition calculations on the -Fe 2C(111) surface. (A) A schematic representation of the variable-
composition search, where “-3C” indicates three fewer carbon atoms compared to the unreconstructed structure; (B) Side and top views
of unreconstructed and reconstructed structures of the most stable configuration at the lower Δ C limit; (C) Plot of the relative surface
energies of the most stable reconstructions with different total carbon numbers against Δ C .

built according to the previous work of Liu et al. [24] . Previous studies [25] have demonstrated the important
role of [Fe 4C] squares (or A-P5 sites) in facilitating both CO dissociation and C-C coupling reactions. We
obtained a reconstructed structure containing a row of inclined [Fe 4C] squares as shown in Figure 5A, which
implies that the reconstructed edge sites on -Fe 5C 2(510) surfaces could serve as active sites for iron-based
Fischer-Tropsch reactions.

-Fe 5C 2(021)and -Fe 3C(010)werealsoconsideredaspotentialactivesurfacesiniron-basedFTS [17,25] . Among
them, the -Fe 5C 2(021) surface exhibits greater structural complexity compared to the other three surfaces,
consisting of both [Fe 4C] squares and [Fe 5C] pentagons [Supplementary Figure 4]. Despite this complexity,
our workflow successfully performed global optimizations and identified the reconstructed surfaces with edge
sites. The most stable reconstructed structure is illustrated in Figure 5C, where newly formed [Fe 4C] squares
arealsoobserved(alsoseeSupplementaryFigure6foradditionalstructures). Therelativesurfaceenergies(Δ )
against Δ C are plotted in Figure 5D. Although all of them are less stable than the clean -Fe 5C 2(021) surface,
with relatively small energy differences, they may still play certain roles in the FTS at a high temperature.

The clean -Fe 3C(010) surface exhibits a highly ordered structure. The most stable reconstructed structure of
-Fe 3C(010) surface with edge sites is presented in Figure 5E. This behavior resembles the phenomenon of “is-
land decay” in surface science [76] , where a rough surface evolves toward a smoother surface to achieve higher
stability (also see Supplementary Figure 7 for two additional reconstructions). Similar to the -Fe 5C 2(021)
surface, newly formed [Fe 4C] are observed in these reconstructed -Fe 3C(010) surfaces, while the original
surface morphology is still preserved. The relative surface energies (Δ ) as a function of Δ C are also plotted
in Figure 5F. Notably, none of the reconstructed -Fe 3C(010) surfaces are found to be more stable than the
cleansurface. Moreover, theenergydifferencesaresignificantlylargerthanthoseon -Fe 5C 2(021)surfaces, in-
dicating that the formation of edge sites on -Fe 3C(010) is much less favorable under a typical Fischer-Tropsch
reaction condition.

Compared to other surfaces, the -Fe 2C(111) surface exhibits a relatively simple structure and all surface Fe-
4fold square sites are fully occupied by carbon atoms [Supplementary Figure 4]. Here, we demonstrated
variable-composition global optimization calculations involving different numbers of carbon atoms. When
performing fixed-composition calculations, two edges of each surface were optimized using GA separately.
While performing variable-composition calculations, the number of atoms at each edge can be changed and
these searches will be repeated several times under different total numbers of atoms [Figure 6A]. One example
of a reconstructed surface is shown in Figure 6B, where carbon atoms migrate from one edge to the other,
forming C-C dimers to fully bond with neighboring atoms. The relative surface energies (Δ ) of the recon-
structed surfaces against Δ C are plotted in Figure 6C. Structures with varying carbon numbers are detailed in