Novel lattice-searching method for modeling the optimal strain-free close-packed isomers of clusters

Small icosahedral, decahedral, and fcc structures have been studied by unbiased global optimization methods or Wulff construction and Northby lattice methods. Strain-free close-packed structures are not much discussed because the structures are very difficult to optimize and there is no common strain-free close-packed lattice. We propose a new strategy to construct such a lattice containing all possible strain-free close-packed isomers, and by searching the lattice with an efficient method the optimal close-packed structures were modeled. Testing with the Morse potential at rho0=14.0 for cluster size 10相似文献   

Clusters as crystal fragments of silicon bulk

Silicon clusters of 13 to 43 atoms were studied with the semi-empirical method SINDO1. Crystalline structures of face-centered cubic (fcc), hexagonal close packed (hcp) and diamond type and noncrystalline structures of icosahedral type were compared. Noncrystalline structures are most stable for clusters up to 13 atoms. Clusters with 19 and more atoms of the fcc structure are preferable to the less dense diamond structure. With more than 35 Si atoms, the diamond structure is favored over the hcp structure. The binding energy of fcc and hcp structures decreases and that of the diamond structure increases with increasing cluster size. A similar trend is observed for the HOMO-LUMO energy gap which is taken as a measure of the band gap.     

Global optimization study of small (10 < or = N < or = 120) Pd clusters supported on MgO(100)

Experimental evidence suggests that Pd clusters on MgO, known to be good reaction catalysts, have face centered cubic (fcc) epitaxial structures. The structure of such clusters is the result of the interplay of Pd-Pd and Pd-substrate bonds, the former inclined to favor icosahedral (Ih) and decahedral (Dh)-like structures, the latter leading to place Pd atoms on top of oxygen sites, according to an epitaxial stacking. This paper shows the results of a basin-hopping global optimization procedure applied to free and MgO-supported Pd clusters in the size range 10 < or = N < or = 120. Pd-MgO interactions are modeled by an analytical function fitted to ab initio results, while Pd-Pd interactions are modeled by a semiempirical potential. Besides the tight-binding Rosato-Guillopé-Legrand (RGL) potential, we have adopted a modified version of RGL that better reproduces the experimental surface energy of palladium, modifying the attractive part of Pd atoms potential energy. We have compared the two potential models, and as a result, the RGL potential favors clusters with epitaxial arrangements, so that cluster structures are epitaxial fcc in almost all the size ranges considered. On the contrary, the alternative potential model preserves some Ih-like characteristics typical of the free Pd clusters, and it suggests that a transition size from Ih-like to epitaxial structures can take place at about 100 atoms.     

Binding energy of large icosahedral and cuboctahedral Lennard-Jones clusters

It is widely believed that the lowest energy configurations for small rare gas clusters have icosahedral symmetry. This contrasts with the bulk crystal structures which have cuboctahedral fcc symmetry. It is of interest to understand the transition between this finite and bulk behavior. To model this transition in rare gas clusters we have undertaken optimization studies within the Lennard-Jones pair potential model. Using a combination of Monte Carlo and Partan Search optimization methods, the lowest energy relaxed structures of Lennard-Jones clusters having icosahedral and cuboctahedral symmetry were found. Studies were performed for complete shell clusters ranging in size from one shell having 13 atoms to 14 shells having 10,179 atoms. It was found that the icosahedral structures are lower in energy than the cuboctahedral structures for cluster sizes having 13 shells or fewer. Additional studies were performed using the more accurate Aziz-Chen [HFD-C] pair potential parameterized for argon. The conclusions appear to be relatively insensitive to the form of the potential.     

A new magic titanium-doped gold cluster and orientation dependent cluster-cluster interaction

The stability and structures of titanium-doped gold clusters Au(n)Ti (n=2-16) are studied by the relativistic all-electron density-functional calculations. The most stable structures for Au(n)Ti clusters with n=2-7 are found to be planar. A structural transition of Au(n)Ti clusters from two-dimensional to three-dimensional geometry occurs at n=8, while the Au(n)Ti (n=12-16) prefer a gold cage structure with Ti atom locating at the center. Binding energy and second-order energy differences indicate that the Au(14)Ti has a significantly higher stability than its neighbors. A high ionization potential, low electron affinity, and large energy gap being the typical characters of a magic cluster are found for the Au(14)Ti. For cluster-cluster interaction between magic transition-metal-doped gold clusters, calculations were performed for cluster dimers, in which the clusters have an icosahedral or nonicosahedral structure. It is concluded that both electronic shell effect and relative orientation of clusters are responsible for the cluster-cluster interaction.     

Continuation calculations of boron- (aluminum-, titanium-, and nickel-) doped La13 clusters

In this work, we have calculated boron-, aluminum-, titanium-, and nickel-doped La13 clusters by DMOL method based on the density-functional theory. Two doping modes are employed: surface and center doping. The boron, aluminum, and nickel atoms prefer to occupy the surface sites while the titanium atom prefers to occupy the center site. The doped La13 clusters with these four kinds of atoms have lower binding energy than pure La13 clusters. The icosahedral isomers are of lower binding energy than cubotahedral and decahedral isomers for La12B(-1), La12Al(-1), and La12Ni, while doping makes the cubotahedral La12Ti stable with a binding energy a little lower than icosahedral La12Ti. There are electronic shell effects in icosahedral La12B(-1) and La12Al(-1). The icosahedral La12B(-1) is promising to be formed during the doped process experimentally. Furthermore, we have also discussed the distorted structures of center doping by bond lengths, density of states, and charge transfers.     

Structural transformation of Au-Pd bimetallic nanoclusters on thermal heating and cooling: a dynamic analysis

Classical molecular dynamics simulation is used for structural thermodynamic and dynamic analysis of Au-Pd bimetallic clusters. It is observed that the Pd-core/Au-shell structure is the most stable, and can be formed through annealing of other structures such as Au-core/Pd-shell, eutecticlike, or solid solution. Depending on the starting temperature and initial composition, three-layer icosahedral nanorod, face-centered cubic (fcc) nanorod, and fcc cluster can be obtained on slow cooling. The three-layer icosahedral nanorod structure is not as stable as the Pd-core/Au-shell decahedron; however it is more stable than the solid-solution decahedron structure up to 400 K. Our findings provide valuable insight into catalysis using Au-Pd and other similar bimetallic clusters.     

Disordered structures of the TM-Mg-Zn 1/1 quasicrystal approximants (TM = Hf, Zr, or Ti) and chemical intergrowth

The structures of three quasicrystal approximant phases in the TM-Mg-Zn (TM = Hf, Zr, Ti) systems with the analyzed compositions Hf5Mg18Zn77, Zr5Mg18Zn77, and Ti5.5Mg17.5Zn77 have been synthesized, and their structures have been analyzed by single-crystal X-ray diffraction. The structure analyses revealed that these cubic phases with the space group Pm3 contain two different rhombic-triacontahedral clusters. These clusters are so-called Bergman-type atomic clusters and previously known approximants of face-centered icosahedral (F-type) quasicrystals are composed only of Mackay-type clusters, thus these compounds are seen as new prototype structures. Electron density maps calculated by the maximum entropy method (MEM) show that one of the atomic clusters displays characteristic structural disorder. The disorder in these phases is related to the chemical intergrowth of different Friauf polyhedra, and the prospects of new guide lines for finding quasicrystals composed of such polyhedra are discussed.     

Transition between icosahedral and cuboctahedral nanoclusters of lead

We have used ab initio methods to study the possible transition between icosahedral (ico) and cuboctahedral (fcc) structures in lead nanoclusters of sizes up to 309 atoms. Spontaneous fcc-to-ico transition in Pb(13) was observed in the ab initio molecular dynamics (MD) simulations at various temperatures. The transition path can be described predominantly by an angular variable s, which can, generally be applied to the similar transitions in clusters of larger sizes and was observed to follow the Mackay model. We have calculated the two-dimensional energy surface that describes the transition in Pb(13) and found a barrierless fcc-to-ico transition path, which is consistent with the observed spontaneous transition in the ab initio MD simulations. The atomic displacements in the transition were identified as one of the vibrational eigenmodes of these two Pb(13) clusters. For clusters of larger sizes (Pb(n), where n = 55, 147, and 309), the possible transitions following similar paths were determined not to be barrierless and the sizes of the barriers were determined by the ab initio elastic band method.     

Mackay,Anti-Mackay,Double-Mackay,Pseudo-Mackay,and Related Icosahedral Shell Clusters

Mackay introduced two important crystallographic concepts in a short paper published 40 years ago. One is the icosahedral shell structure (iss) consisting of concentric icosahedra displaying fivefold rotational symmetry. The number of atoms contained within these icosahedral shells and subshells agrees well with the magic numbers in rare gas clusters, (C₆₀) _N molecules, and some metal clusters determined by mass spectroscopy or simulated on energy considerations. The cluster of 55 atoms within the second icosahedral shell occurs frequently and has been called Mackay icosahedron, or simply MI, which occurs not only in various clusters, but also in intermetallic compounds and quasicrystals. The second concept is the hierarchic icosahedral structures caused by the presence of a stacking fault in the fcc packing of the successive triangular faces in the iss. For instance, a fault occurs after the ABC layers resulting an ABCB packing. This is, in fact, a hierarchic icosahedral structure of a core icosahedron connected to 12 outer icosahedra by vertex sharing, or an icosahedron of icosahedra (double MI. Contrary to Mackay's iss, a faulted hierarchic icosahedral shell is, in fact, a twinlike face capping of the underlying triangles; it is, therefore, called an anti-Mackay cluster. The hierarchic icosahedral structure in an Al-Mn-Pd icosahedral quasicrystal has a core of body-centered cube rather than an icosahedron and, therefore, is called a pseudo-Mackay cluster. The hierarchic icosahedral structures have been studied separately in the past in the fields of clusters, nanoparticles, intermetallic compounds, and quasicrystals, but the underlying geometry should be the same. In the following a unified geometrical analysis is presented.     

Coexistence of ferroelectricity and ferromagnetism in tantalum clusters

The atomic and electronic structures of Ta(N) (N=2-23) clusters have been determined in the framework of pseudopotential density-functional calculations, based upon an unbiased global search with guided simulated annealing to an empirical potential. It is found that the ground-state structures of Ta(N) are very similar to those of Nb(N), showing no preference for the icosahedral growth. Also, a size- and structure-dependent ferroelectricity is found in these tantalum clusters. More importantly, it is found that the ferroelectricity and ferromagnetism can coexist in the homogeneous transition-metal cluster, offering a possibility to obtain a new type of "multiferroic" materials composed of the clusters. Finally, the far-infrared spectroscopy is suggested to be an efficient tool to distinguish the ferroelectric clusters.     

Evolution of size and shape in the colloidal crystallization of gold nanoparticles

The addition of dodecanethiol to a solution of oleylamine-stabilized gold nanoparticles in chloroform leads to aggregation of nanoparticles and formation of colloidal crystals. Based on results from dynamic light scattering and scanning electron microscopy we identify three different growth mechanisms: direct nanoparticle aggregation, cluster aggregation, and heterogeneous aggregation. These mechanisms produce amorphous, single-crystalline, polycrystalline, and core-shell type clusters. In the latter, gold nanoparticles encapsulate an impurity nucleus. All crystalline structures exhibit fcc or icosahedral packing and are terminated by (100) and (111) planes, which leads to truncated tetrahedral, octahedral, and icosahedral shapes. Importantly, most clusters in this system grow by aggregation of 60-80 nm structurally nonrigid clusters that form in the first 60 s of the experiment. The aggregation mechanism is discussed in terms of classical and other nucleation theories.     

Structural stability of boron clusters with octahedral and tetrahedral symmetries

The structural stability of cagelike boron clusters with octahedral and tetrahedral symmetries has been investigated by means of first-principles calculations. Twenty-eight cluster models, ranging from B(10) to B(66), were systematically constructed using regular and semiregular polyhedra as prototypes. The binding energies per atom were, on the whole, slightly lower than those of icosahedral clusters B(80) and B(100), which are supposed to be the most stable in the icosahedral group. The larger clusters did not always have higher binding energies. Isothermal molecular dynamics simulations were performed to determine the deformation temperatures at which clusters began to break or change their structures. We found eight clusters that had nonzero deformation temperatures, indicating that they are in metastable states. The octahedral cluster B(18) had the highest deformation temperature among these, similar to that of icosahedral B(80) and B(100). The analysis of the electronic structure of B(18) showed that it attained this high stability owing to Jahn-Teller distortion.     

Structural transition from icosahedra to decahedra of large Lennard-Jones clusters

The lowest icosahedral and decahedral energies of LJ1001-1610 clusters are obtained using a greedy search method (GSM) based on lattice construction. By comparing the lowest energies of icosahedral and decahedral clusters with the same atoms, the structural transition of LJ clusters is studied. Results show that the critical size from icosahedra to decahedra is located at N = 1034. When the cluster size is larger than 1034, the optimal structures are decahedra except the LJ1367-1422 clusters near the magic number, 1402, of icosahedra. However, the energies of icosahedra near the next magic number, 2044, are higher than that of decahedra, which implies that decahedra will be the optimal structure when the cluster size is larger than 1422, even for those clusters near the magic numbers of icosahedra.     

Theoretical Study on the Electronic Structures of Small TinNm （n ＋ m = 5, 6） Clusters

45 isomers of TinNm （n ＋ m = 5, 6） clusters, including linear, some planar and some stero configurations, have been predicted by density functional theory method. For five-atom clusters Ti3N2 and Ti2N3, the most stable structures are trigonal bipyramid in D3h symmetry, and for TiaN cluster, the isomer with one nitrogen atom occupying the center of quasi-tetrahedron is the most stable. In the isomers of Ti4N2 and Ti3N3, the planar networks are more stable, but for Ti2N4, the six-membered ring configuration is the most favorable. Most linear structures can form weak-strong bonds alternately with higher energy. As regards to planar structures, the more Ti-N bonds are formed, the more stable they will be; for stero closed polyhedral isomers, their energies are lower.     

On the shell structure and geometry of monovalent metal clusters

The Hückel model is used to study the electronic structure of monovalent metal clusters. In an fcc cluster the Hückel model gives an estimate to the electronic structure of a free electron cluster. It is shown that the surface faceting of the fcc cluster can destroy the electronic shell structure already when the cluster has about 100 electrons. In the Hückel model the icosahedral structure has smaller total energy than the fcc structures, from which the Wulff construction has the smallest energy already when the cluster has 600 atoms.     

A density-functional study of the structures, binding energies and total spins of Ni-Fe clusters using nonlocal norm-conserving pseudopotentials and the generalized gradient approximation

We report ab initio calculations of the structures, binding energies, and total spins of the clusters Ni(13), Ni(19), Ni(23), Ni(26), Ni(12)Fe, Ni(11)Fe(2), Ni(18)Fe, Ni(17)Fe(2), Ni(22)Fe, Ni(20)Fe(3), and Ni(25)Fe using a density-functional method that employs linear combination of atomic orbitals as basis sets, nonlocal norm-conserving pseudopotentials, and the generalized gradient approximation for exchange and correlation. Our results show that the Fe-doped Ni clusters, which have icosahedral or polyicosahedral ground-state structures similar to those of the corresponding pure Ni clusters, are most stable with the Fe atoms occupying internal positions, as has also been inferred from experimental results on the adsorption of molecular nitrogen on the cluster surfaces. We also rule out the possibility that the experimentally observed difference between the (nonpolyicosahedral) configurations of N(2)-saturated Ni(26) and N(2)-saturated Ni(25)Fe be due to the influence of the Fe atom on the energy of the underlying metal cluster.     

Polymorph selection in the crystallization of hard-core Yukawa system

Colloid-colloid interactions in charge-stabilized dispersions can to some extent be represented by the hard-core Yukawa model. The crystallization process and polymorph selection of hard-core Yukawa model are studied by means of smart Monte Carlo simulations in the region of face-centered-cubic (fcc) phase. The contact value of hard-core Yukawa potential and the volume fraction of the colloids are fixed, while the Debye screening length can be varied. In the early stage of the crystallization, the precursors with relatively ordered liquid structure have been observed. Although the crystal structure of thermodynamically stable phase is fcc, the system crystallizes into a mixture of fcc and hexagonal close-packed (hcp) structures under small Debye screening length since the colloidal particles act as effective hard spheres. In the intermediate range of Debye screening length, the system crystallizes into a mixture of fcc, hcp, and body-centered-cubic (bcc). The existence of metastable hcp and bcc structures can be interpreted as a manifestation of the Ostwald’s step rule. Until the Debye screening length is large enough, the crystal structure obtained is almost a complete fcc suggesting the system eventually reaches to a thermodynamically stable state.     

Structural evolution of subnano platinum clusters

We present a theoretical study of the structural evolution of small minimum energy platinum clusters, using density functional theory (DFT). Three growth pathways were identified. At the subnanoscale, clusters with triangular packing are energetically most favorable. At a cluster size of approximately n = 19, a structural transition from triangular clusters to icosahedral clusters occurs. A less energetically favorable transition from triangular clusters to fcc‐like clusters takes place at around n = 38. Ionization potentials, electron affinities, and magnetic moments of the triangular clusters were also calculated. Understanding the structures and properties will facilitate studies of the chemical reactivity of Pt nanoclusters toward small molecules. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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 Nor=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.