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

Abstract

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}, {101̅ 0}, and {101̅ 1} 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.

A computational study of the properties of low- and high-index Pd, Cu and Zn surfaces

“…4. The morphology predicted for all three species is in good agreement with other computational work by Tran et al 10 and Lin et al 56 The surface coverage of each facet type, presented in Table 8, shows that the (111) facet is most prevalent for Pd (48.83%), followed by the (100) facet (18.80%). The high index (332) and (210) facets cover 18.30% and 6.96%, respectively.…”

A Computational Study of the Properties of Pd, Cu and Zn Surfaces

“…In order to ensure accuracy for the Wulff construction process, additional high index (332), The structures predicted by the Wulff construction for a 5,000 atoms nanoparticle of Pd, Cu and Zn are given in Figure 6. The morphology predicted for all three species is in good agreement with other computational work by Tran et al 11 and Lin et al 57 . The surface coverage of each facet type, presented in Table 9, shows that the (111) facet is most prevalent for Pd (48.83 %), followed by the (100) facet (18.80 %).…”

“…PBEDa silva et al2 Patra et al15 Tran et al11 Singh-Miller et al49 Lin et al57 studies. The addition of the Tkatchenko-Scheffler vdW correction to PBE (PBE+TS) increases the surface energies for the (111), (100) and (100) facets by 0.16, 0.1 and 0.14 J/m 2 Direct comparison for each Pd surface facet with experiment is not straightforward, as experimental surface energies are averaged over the various crystal facets (1.63 J/m 2 at 0 K, and 1.74 J/m 2 at the 1828 K 3,58 ); however, broad comparison of each DF with experiment can be made.Comparing our average results for each DF with experiment leads to the conclusions, firstly, that PBE and mBEEF underestimate the surface energies of Pd by a small amount (averages of 1.50 and 1.46 J/m 2 , respectively); secondly, that PBE+TS and PBE+MBD-NL compare well with experiment (averages of 1.63 and 1.72 J/m 2 , respectively); and finally, that all other DFs overestimate the surface energy of Pd.…”

A computational study of the properties of low- and high-index Pd, Cu and Zn surfaces

“…For Pd, the order of stability of all facets is (111) > ( 100 The structures predicted by the Wulff construction for a 5,000 atoms nanoparticle of Pd, Cu and Zn are given in Figure 6. The morphology predicted for all three species is in good agreement with other computational work by Tran et al 11 and Lin et al 57 . The surface coverage of each facet type, presented in Table 9, shows that the (111) facet is most prevalent for Pd (48.83 %), followed by the (100) facet (18.80 %).…”

“…2 Patra et al15 Tran et al11 Singh-Miller et al49 Lin et al57 Janthon et al58 * The value were calculated using linear regression for a set of slabs with different thicknesses.…”