Fcc Motif Research Articles

Structural Evolution of Palladium Clusters Pd55--Pd147-: Transition to the Bulk.

We present a study of the structural evolution of palladium cluster anions in a size range from 55 to 147 atoms using a combination of trapped ion electron diffraction and density functional theory computations. We show that Pdn- clusters (n = 55, 65, 75, 85, 95, 105, and 147) change from an icosahedral motif at Pd55- to the bulk fcc motif at Pd147-. This size-dependent structure transition is probed experimentally at a temperature of 95 K and characterized by a continuously increasing fraction of fcc isomers over the considered size range showing a crossover to the fcc motif at n ≈ 90.

Contrasting motif preferences of platinum and gold nanoclusters between 55 and 309 atoms.

The atomic structure of size-selected Pt clusters in the range 10–600 atoms is investigated with aberration-corrected scanning transmission electron microscopy and reveals significantly different behaviour from the existing data for Au clusters. The Pt clusters show a dominance of the FCC motif from relatively small sizes, whereas traditionally for Au multiple motifs – the icosahedron, decahedron and FCC motifs (and related structures) compete. The new data motivates a comprehensive computational investigation to better understand similarities and differences in the structures and energetics of the two different metallic clusters. Low energy structures of Pt and Au clusters with 55, 101, 147, 228 and 309 atoms (±2%) are identified using a global optimisation algorithm, and the relative energies found by local minimisation using density functional theory. Our computational results support the experimental observations; for Au clusters all motifs are comparably stable over the whole size range, whereas for Pt, the motifs only compete at the smallest sizes, after which the FCC motif is the most stable. Structural analysis suggests the greater tendency of Au towards amorphisation enables the icosahedron and decahedron to remain competitive at larger sizes.

Reassignment of 'magic numbers' for Au clusters of decahedral and FCC structural motifs.

Calculations of low free energy structures of gold clusters with a few hundred to a few thousand atoms have been performed. For the study to be computationally feasible, a systematic scheme for generating low energy atomic structures with a given structural motif and a chosen size is used. Comparison of the relative stability of clusters with the decahedral and FCC motifs reveals periodic windows of stability for asymmetric, open-shell FCC clusters while the stability of the decahedral structural motif shows a smoother variation in stability with cluster size. As a result, the FCC structural motif is most stable for clusters with around 440, 610, 800, 1050… atoms, while the decahedral motif is more stable for atomic numbers of around 525, 705, 925, 1175… These new 'magic numbers' represent regions around which a number of asymmetric, open shell clusters of a given motif are most stable, in contrast to the discrete set of highly symmetric magic size structures that are commonly cited. As temperature is raised, the decahedral motif gains stability over the FCC motif. These results help explain reported experimental observations and can guide future laboratory preparations of shape selected clusters.

Pair distribution function analysis applied to decahedral gold nanoparticles

The five-fold symmetry of face-centered cubic (fcc) derived nanoparticles is inconsistent with the translational symmetry of a Bravais lattice and generally explained by multiple twinning of a tetrahedral subunit about a (joint) symmetry axis, with or without structural modification to the fcc motif. Unlike in bulk materials, five-fold twinning in cubic nanoparticles is common and strongly affects their structural, chemical, and electronic properties. To test and verify theoretical approaches, it is therefore pertinent that the local structural features of such materials can be fully characterized. The small size of nanoparticles severely limits the application of traditional analysis techniques, such as Bragg diffraction. A complete description of the atomic arrangement in nanoparticles therefore requires a departure from the concept of translational symmetry, and prevents fully evaluating all the structural features experimentally. We describe how recent advances in instrumentation, together with the increasing power of computing, are shaping the development of alternative analysis methods of scattering data for nanostructures. We present the application of Debye scattering and pair distribution function (PDF) analysis towards modeling of the total scattering data for the example of decahedral gold nanoparticles. PDF measurements provide a statistical description of the pair correlations of atoms within a material, allowing one to evaluate the probability of finding two atoms within a given distance. We explored the sensitivity of existing synchrotron x-ray PDF instruments for distinguishing four different simple models for our gold nanoparticles: a multiply twinned fcc decahedron with either a single gap or multiple distributed gaps, a relaxed body-centered orthorhombic (bco) decahedron, and a hybrid decahedron. The data simulations of the models were then compared with experimental data from synchrotron x-ray total scattering. We present our experimentally derived atomistic models of the gold nanoparticles, with surprising results and a perspective on remaining challenges. Our findings provide evidence for the suitability of PDF analysis in the characterization of other nanosized particles that may have commercial applications.

Anisotropy effect of multi-center Lennard-Jones molecular clusters

Models of randomly packed hard molecules of Multi-Center Lennard-Jones (MCLJ) clusters exhibit some features of anisotropy effects. To investigate the anisotropy effect on the structures of molecular clusters, four highly symmetrical molecules are modeled: 4-atom tetrahedron (TLJ), 6-atom octahedron (OLJ), 8-atom cube (CLJ), and 12-atom icosahedron (ILJ). The intermolecular interactions are described using the MCLJ model. Using the funnel hopping algorithm, we located the putative global minimum structures of these four MCLJ molecular clusters up to cluster size N=80. The structural patterns of these MCLJ clusters are much different to that of Lennard-Jones clusters, and some new rules and structures are found. The structures of TLJ clusters are most irregular due to the highest anisotropy effect of the tetrahedral molecule. For OLJ clusters, a new structural pattern, rhombic dodecahedron, is viewed. The structures of CLJ clusters are also interesting, which look like oblique face-centered cubic (fcc) structures. For ILJ clusters, icosahedral motifs are favored at cluster size N⩽19, and fcc motifs are favored more at N>19.

Effect of MgO(100) support on structure and properties of Pd and Pt nanoparticles with 49-155 atoms

Presently, density functional computational studies of nanostructures in heterogeneous catalysts consider either sufficiently big ("scalable with size") unsupported metal nanoparticles (NPs) or small supported metal clusters. Both models may not be sufficiently representative of a few nm in size supported transition metal NPs dealt with in experiment. As a first step in closing the gap between theoretical models and prepared systems, we investigate the effect of a rather chemically inert oxide support, MgO(100), on relative energies and various properties of Pd and Pt NPs that consist of 49-155 atoms (1.2-1.6 nm in size) and exhibit bulk-like fcc structural arrangements. Shapes and interface configurations of metal NPs on MgO were obtained as a result of thorough optimization within the fcc motif using interatomic potentials. Then the stability and properties of the NPs were studied with a density functional method. We comprehensively characterize interaction between the NPs and MgO(100) support, their interface and effect of the support on NP properties. While the effect of MgO on relative stabilities of NPs with different shapes is found to be significant, other properties of the NPs such as electronic structure and interatomic distances within NP do not notably change upon deposition. This work paves the way to large-scale first-principles computational studies of more realistic models of oxide-supported metal catalysts.

Geometrical structures of gold clusters on Gupta and Sutton-Chen potentials

The putative stable structures of Au clusters are investigated up to 200 atoms. The interaction of Au atoms is described by Gupta potential and Sutton-Chen potential with experimental-fitted parameters and Sutton-Chen potential with density-functional-theory (DFT)-fitted parameters. The stable structures of Au clusters are optimized by dynamic lattice searching (DLS) and DLS with constructed cores (DLSc) methods. The topological geometries, growth patterns, and energies of Au3–38 clusters for both potentials are studied, and their difference could be found from the second finite difference of the energy. Furthermore, for both potentials of Au100–200 clusters, the dominant motif is decahedron, except for face-centered-cubic (fcc) structures at Au150 and Au160 and stacking fault (SF) fcc motif at Au130 and Au140 of Sutton-Chen potential.

New Cluster–Polyoxometalate Hybrids Derived from the Incorporation of {Mo3S4} and {Mo3CuS4} Units into {EW15} Cores (E = AsIII, SbIII, TeIV)

AbstractA new family of hybrid chalcogenide cluster‐incorporated polyoxometalates (POMs) have been prepared in which the POM standard building block {W3O4}10+ is replaced by topologically similar chalcogenide cluster fragments {Mo3S4}4+, {Mo3S2O2}4+, and {Mo3CuS4}5+ with M–M bonds. The family includes [EW15Mo3S4(H2O)3O53]9– (E = As, Sb), [TeW15Mo3S4(H2O)3O53]8–, and [AsW15Mo3O2S2(H2O)3O53]9–. The built‐in sulfide ligands represent a new center of coordination for “soft” metal ions: [AsW15Mo3S4(H2O)3O53]9– reacted with Cu+ to form a new heterometal derivative [AsW15Mo3(CuCl)S4(H2O)3O53]9–. Crystal structures of Cs6.5K(NH4)1.5[{Mo3S4(H2O)3}AsW15O53]·14H2O (1), Cs5.85Na3.15[{Mo3S4(H2O)3}SbW15O53]·14.85H2O (2), Cs6Na2[{Mo3S4(H2O)3}TeW15O53]·11.7H2O (3), Cs7.15Na1.85[{Mo3S4(H2O)2Cl}TeW15O53]·11.2H2O (4), Cs6(H3O)3[{Mo3O2S2(H2O)3}AsW15O53]·9.85H2O (5), and Cs5.25K1.75(NH4)2[{Mo3S4(H2O)3CuCl}AsW15O53]·12.07H2O (6) were determined. The highly charged isolated anions in 1–6 are arranged in one of the two well‐known topological types – fcc motif. The cations and hydrate water molecules are severely disordered over thevoids between the anions. The anions in 1–4 are involved in specific nonvalent S···S interactions with S–S distances of 2.95–3.68 Å.

Geometry optimization and structural distribution of silver clusters from Ag 170 to Ag 310

Silver clusters in the size range of 170–310 were optimized with a modified dynamic lattice search (DLS) method. Considering the computational complexity, only 21 clusters of several tens and magic numbers of atoms were investigated. The interaction of silver atoms is modeled by the Gupta potential. Results show that, between the 21 clusters, nine fcc and twelve m-Dh structures are obtained. Compared with the structures adopted by Ag 13 to Ag 160, the main motif is still m-Dh in the range of Ag 170–Ag 310, but the ratio of fcc structures obviously increases. It can, therefore, be deduced that the fcc motif is more stable for larger size silver clusters.

Structural motifs, mixing, and segregation effects in 38-atom binary clusters

Thirty eight-atom binary clusters composed of elements from groups 10 and 11 of the Periodic Table mixing a second-row with a third-row transition metal (TM) (i.e., clusters composed of the four pairs: Pd-Pt, Ag-Au, Pd-Au, and Ag-Pt) are studied through a combined empirical-potential (EP)/density functional (DF) method. A "system comparison" approach is adopted in order to analyze a wide diversity of structural motifs, and the energy competition among different structural motifs is studied at the DF level for these systems, mainly focusing on the composition 24-14 (the first number refers to the second-row TM atom) but also considering selected motifs with compositions 19-19 (of interest for investigating surface segregation effects) and 32-6 (also 14-24 and 6-32 for the Pd-Au pair). The results confirm the EP predictions about the stability of crystalline structures at this size for the Au-Pd pair but with decahedral or mixed fivefold-symmetric/closed-packed structures in close competition with fcc motifs for the Ag-Au or Ag-Pt and Pd-Pt pairs, respectively. Overall, the EP description is found to be reasonably accurate for the Pd-Pt and Au-Pd pairs, whereas it is less reliable for the Ag-Au and Ag-Pt pairs due to electronic structure (charge transfer or directionality) effects. The driving force to core-shell chemical ordering is put on a quantitative basis, and surface segregation of the most cohesive element into the core is confirmed, with the exception of the Ag-Au pair for which charge transfer effects favor the segregation of Au to the surface of the clusters.

Structure of Ag Clusters Grown on Fs‐Defect Sites of an MgO(1 0 0) Surface

The structure of AgN clusters (N=1-4, 6, 8, 10), both in the gas phase and grown on the MgO(1 0 0) surface containing Fs-defects, has been investigated by a density functional basin-hopping (DF-BH) approach. In analogy with what observed in the case of gold clusters, it is found that the presence of the defect implies a double frustration and a cylindrical invariance of the metal-surface interaction, causing small Ag clusters growing around the Fs defect to be highly fluxional. Nevertheless, two different structural crossovers are found to be induced by the metal-defect interaction for the adsorbed clusters such that: 1) planar structures prevail for N<or=4 (as in the gas phase); 2) noncrystalline (fivefold symmetric) structures, which are the lowest energy ones in the gas phase for medium sized AgN clusters (N>or=7), prevail for N=6 and N=8; 3) distorted face-centered cubic (fcc) structures grown pseudomorphically on the defected surface prevail for N=10. The transition from fivefold to fcc motifs is rationalized in terms of the double-frustration effect, which increases the bond strain of the noncrystalline structures. Detrapping energies from the defect were also calculated; the lowest energy pathway corresponds to the detachment of a dimer.

Structural Variation of Silver Clusters from Ag13 to Ag160

The structures of silver clusters from Ag(121) to Ag(160) were optimized with a modified dynamic lattice searching (DLS) method, named as DLS with constructed core (DLSc). The interaction among silver atoms is modeled by the Gupta potential. Structural characteristic of silver clusters with the growth of cluster size is investigated with the newly optimized structures and our previous results from Ag(13) to Ag(120). A set of amorphous structures was obtained in the size range of 13-48, together with several ordered structures. The putative stable motif is an icosahedron from Ag(49) to Ag(61) and then changes to a decahedron in the size range of 62-160. Some of the results are consistent with experiments. Furthermore, it was also found that, for clusters with decahedral motif, the stable structure is a result of the competition among the different Marks decahedral motifs. On the other hand, different from the Lennard-Jones cluster, there are some silver clusters with the face-centered cubic (fcc) motif in the size range of 13-160. But the fcc motif can only be obtained for some specific sizes.

The minimum-energy structure of nanometer-scale gold clusters

We report results of experiments in which gold clusters with controlled diameters ranging from 1nm to 20nm are grown in a gas aggregation reactor and are subsequently melted and slowly cooled in the gas phase. These clusters are soft landed on thin carbon films and their structure determined by means of HRTEM. All of the clusters down to the smallest whose lattice fringes could be resolved (N≈405) are single fcc crystals. MD calculations using an EAM potential for gold predict that the fcc motif seen in these experiments may indeed be the minimum-energy structure for gold clusters containing more than a few hundred atoms.