The structure and stability of seventeen facets of the Hagg carbide phase (x-Fe5C2) under the consideration of K2O 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 K2O promoter, the morphology of the x-Fe5C2 phase under the variation of K2O content has been predicated. At the surface Fe/K atomic ratio of 30, the morphology of the x-Fe5C2 phase can be modified apparently. Among the most exposed (1 1 1), (1 0 0), (1 1 (1) over bar), (5 1 0) and ((4) over bar 1 1) facets, the (1 1 (1) over bar), (5 1 0) and ((4) over bar 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. (C) 2015 Published by Elsevier B.V.