Structure and energetics of model metal clusters

Abstract

A Finnis–Sinclair-type many-body potential and a combined Lennard-Jones (two-body) plus Axilrod–Teller (three-body) potential are employed to study the structural properties of model clusters in the size range 13 to 309 atoms. For the first potential, parameter values for the fcc transition metals as proposed by Sutton and Chen are used, while for the latter potential a least-squares fitting routine is employed to fit the parameters to bulk data. For suitable parameter ranges, the relative energies of optimized decahedral, icosahedral, and face-centered-cubic (fcc) cuboctahedral clusters are compared in the light of experimental observations for these metals. Variation of the parameters in the Finnis–Sinclair potential, which govern the range of the repulsive two-body term and the attractive many-body term, influences the size at which the icosahedra and fcc cuboctahedra cross over in energy. Similarly, an increase in the three-body contribution in the LJ+AT clusters leads to a decrease in the crossover size from several thousand to a few hundred atoms. For appropriate parameter ranges, a convex curvature of the facets as well as a contraction of the clusters is observed for both potentials. These effects are compared with experimental observations for the fcc transition metals copper, silver, gold, nickel, palladium, and platinum.

Surface chemistry of catalysis by gold

“…(197) Of particular interest is the transition between fcc structures which predominant for very large clusters, and decahedral or icosahedral particles, whose formation is predicted to be favored for very small particles. Whereas Cleveland et al predicted that gold should transition from fcc structures to decahedral particles for sizes below 200 atoms and to icosahedral particles at sizes below 100 atoms (210), Uppenbrink and Wales found that the transition from fcc structures to icosahedral particles should occur at 550 atoms for gold (209). As we will discuss in the following section, the details of the structure may have strong implications for its reactivity.…”

“…To date, there is some debate over the lowest energy arrangements of such clusters, as proposals for disordered structures (204,205) and various types of faceted particles (176,(206)(207)(208)(209)(210) have both been put forward. As pointed out by Marks (201), the determination of the correct equilibrium structures of small particles is complicated by changes that can occur during observation due to the influence of the HREM (212) and due to the influence of the underlying support.…”

Reversible Size Control of Silver Nanoclusters via Ligand-Exchange

“…On the other hand, the surface energy increases with decreasing R, which tends to increase the cluster size towards a lower surface-to-volume ratio. [41][42][43] An equilibrium is reached when the two effects balance each other for some cluster radius. Interestingly, this equilibrium happens only when all clusters are identical and thereby have the same chemical potential for their constituent atoms.…”

“…35 The ligand-free surface energy of metallic clusters is always positive (γ>0) and depends on cluster size such that smaller clusters have a higher γ. [41][42][43] Page 17 of 31…”

Nanocatalysis: hypothesis on the action mechanism of gold

“…6) Changes in some properties of Au clusters are thought to vary as the function of their sizes; which are assumed to be important in the nanocatalysis problem: a) the structural phase transition from FCC (bulk material) to the dodecahedral cluster (at R=25Å) and icosahedral cluster (at R=16Å) [38] is discussed; there are data that the latter transition is observed at a much larger size (not at 100 atoms, but at 550 atoms in the cluster) [39]. Note that the transition to the icosahedron was experimentally observed in Y-zeolites at R=10Å [41] and in 50-atomic Pt clusters on carbon [40]; b) there was a decrease in the bond lengths of Cr, Fe, Cu, Ag, Pd, Au, Pt metals at the size R<30Å [42][43][44][45][46][47][48][49][50][51][52][53]; so, at R=30Å the length of Au-Au bond is d=2.84Å, and at R=8Å it is d=2.72Å, whereas the bulk material has d=2.88Å [48,49,51].…”