Coordination-dependent bond energies derived from DFT surface-energy data for use in computations of surface segregation phenomena in nanoclusters

Abstract

Theoretical computations of alloy surface phenomena, such as elemental segregation, within atomic pair-interaction models, necessitate the use of reliable bond energies as input. This work introduces the idea to extract the coordination dependence of bond energies from density-functional theory (DFT) computed surface energy anisotropy. Polynomial functions are fitted to DFT data reported recently for surface energies of pure Pt, Rh and Pd. Compared to other approaches, the proposed method is highly transparent, and is expected to yield better insight into the origin of alloy segregation phenomena at surfaces of bulk and nanoclusters.

Effects of Surface–Subsurface Bond-Energy Variations on Equilibrium Compositional Structures Evaluated for Pt–Ir Nanoparticles

“…The coordination dependence of surface bond-energy variations, introduced by the CBEV method, 9,24 is extracted from DFT derived pure metal surface-energy anisotropies. 11 It is based on the following expression for the surface energy 25…”

“…The self-consistency and transferability of the CBEV method were reflected in reasonably low crossvalidation scores (∼2%) obtained for the surface energies. 24 Since all subsurface sites in a CO NP are fully coordinated (ΔZ m = 0), the reduced coordination of surface sites alone affects both intrasurface and surface−subsurface bond energy and compositional variations (a two-layer model). The bondenergy variations derived for both Pt and Ir exhibit the expected general tendency to increase for lower coordinations (Figure 1).…”

“…The coordination dependence of surface bond-energy variations, introduced by the CBEV method, , is extracted from DFT derived pure metal surface-energy anisotropies . It is based on the following expression for the surface energy E normals = prefix∑ m γ m = prefix∑ m 1 2 false( prefix∑ n ( n ≠ m ) δ w m n − normalΔ Z m w normalb false) which includes contributions of the simple “bond-breaking model”, Δ Z m w b , and of strengthening of the remaining bonds, δ w mn (γ m denotes the m -site contribution to E s , and Δ Z m denotes the number of broken bonds around it).…”

Comparative modelling of chemical ordering in palladium-iridium nanoalloys

“…For surface and subsurface sites coordination-dependent bond energy variations (CBEV, δw pq ) were extracted from DFT computed surface energies via 21,22…”

“…The energetics required by FCEM can be provided by the extraction of coordination dependent bond energy variations (CBEV) from DFT computed surface energies. 21,22 The extension of FCEM/CBEV from central-symmetric to more complex chemical orderings has recently been reported for the study of Pt-Ir clusters. 23 The model was able to characterise "quasi-Janus" behaviour in the system, as has recently been investigated by Bochicchio and Ferrando.…”