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The structure and stability of seventeen facets of the Hägg carbide phase (χ-Fe 5 C 2) under the consideration of K 2 O promotion have been analyzed utilizing density functional theory approach and ab initio atomistic thermodynamics. On the basis of different interaction strengths of these facets with K 2 O promoter, the morphology of the χ-Fe 5 C 2 phase under the variation of K 2 O content has been predicated. At the surface Fe/K atomic ratio of 30, the morphology of the χ-Fe 5 C 2 phase can be modified apparently. Among the most exposed (1 1 1),(1 0 0),(1 1 1¯),(5 1 0) and (4¯ 1 1) facets, the (1 1 1¯),(5 1 0) and (4¯ 1 1) facets have more open surface structures as well as provide more surface Fe atoms and less carbon atoms. However, all these mostly exposed facets do not favor CO direct dissociation at low CO coverage.