▎ 摘　　要

Three key positions of graphene on a catalyst surface can be identified based on precise computations, namely as sunk (S), step-attached (SA), and on-terrace (OT). Surprisingly, the preferred modes are not all alike but vary from metal to metal, depending on the energies of graphene-edge "wetting" by the catalyst: on a catalyst surface of soft metal like Au(111), Cu(111) or Pd(111), the graphene tends to grow in step-attached or embedded mode, while on a rigid catalyst surface such as Pt(111), Ni(111), Rh(111), Ir(111), or Ru(0001), graphene prefers growing as step-attached or on-terrace. Accordingly, as further energy analysis shows, the graphene formed via the S and SA modes should have orientations fixed relative to the metal crystal lattice, thus prescribing epitaxial growth of graphene on Au(111), Cu(111) and Pd(111). This conclusion indeed correlates well with numerous experimental data, also solving some puzzles observed, and suggesting better ways for growing larger-area single-crystalline graphene by making proper catalyst selections.