Compensation between Surface Energy and hcp/fcc Phase Energy of Late Transition Metals from First-Principles Calculations

Crystal structures and surface energies of transition metals are of fundamental importance to the activity, selectivity, and stability in heterogeneous catalysis, but the interplay between crystal structures and surface energies as well as its dependence on composition remains elusive. In the present work, we performed comprehensive density functional theory calculations of Co, Ni, Ru, Rh, Pd, Os, and Ir in both hexagonal close-packed (hcp) and face-centered cubic (fcc) phases and considered numerous surfaces to derive the equilibrium morphology and the surface energy. Irrespective of the transition metals considered, the fcc phase exposes mainly {111} and {100} facets, whereas the hcp phase exposes mainly {0001}, {10 (1) over bar0}, and {10 (1) over bar1} facets. For Co, Ru, and Os preferring the hcp bulk at ambient conditions, the corresponding surface energies are found higher to be than those in the fcc bulk, whereas for Ni, Rh, Pd, and Ir preferring the fcc bulk phase at ambient conditions, the opposite trend is found. A negative linear relationship of the surface energy difference between the fcc and hcp phases with respect to the corresponding bulk energy difference is established; a phase with a higher bulk energy has a lower surface energy as compensation. The compensation effect on the surface energy and the bulk energy provides a driving force for the size-induced phase transition of the nanoparticles. The results are used to rationalize the available experiments, and the insights revealed might be used to design better catalysts.