Showing papers on "Cluster (physics) published in 1980"
314 citations
TL;DR: In this article, the authors derived geometric shape models for spheres, cubes, and disks which gave the EXAFS average coordination number for first, second, and third coordination spheres as a function of cluster size.
276 citations
TL;DR: In this paper, a new thermodynamic analysis is given for the equilibrium between a liquid cluster and the surrounding supersaturated gas phase in an infinite constant volume, and it is shown that for constant total density and intermediate volume this equilibrium is stable, although it is unstable for very large volume.
Abstract: A new thermodynamic analysis is given for the equilibrium between a liquid cluster and the surrounding supersaturated gas phase in afinite constant volume. It is shown that for constant total density and intermediate volume this equilibrium is stable, although it is unstable for very large volume. We show that observation of the critical cluster sizel* then yields information on the surface free energy of the liquid cluster. The accuracy of previous approximate prescriptions for obtaining the free energy of physical clusters is investigated. As an application, the theory is used to analyze Monte Carlo simulations of the two-dimensional lattice gas model at low temperatures. We obtain cluster surface area, diffusivity, and free energy for clusters with 26≥l≥500. It is found that the capillarity approximation is inaccurate forl≥100, but the free energy of small clusters ishigher than the result of classical nucleation theory, in contrast to what one expects from Tolman-like corrections. We interpret these results, deriving low-temperature series expansions for very small clusters, thus showing that the capillarity approximation both underestimates the surface energy and overestimates the surface entropy of very small clusters. Finally, we use our results to give a speculative explanation of recent nucleation experiments. The dependence of the cluster diffusivity on cluster size is tentatively explained in terms of a crossover between two mechanisms yielding different power laws.
162 citations
TL;DR: In this paper, the authors employ detailed electronic structure calculations to investigate a model of grain boundary embrittlement, and show that adding sulphur to a cluster of nickel atoms causes strong bonds to be formed between the sulphur atom and the nickel atoms nearest to it, while simultaneously weakening bonds between these nickel atoms and their neighbouring nickel atoms in the cluster.
Abstract: This paper reports the first study employing detailed electronic structure calculations to investigate a model of grain boundary embrittlement. The results show that adding sulphur to a cluster of nickel atoms causes strong bonds to be formed between the sulphur atom and the nickel atoms nearest to it, while simultaneously weakening bonds between these nickel atoms and their neighbouring nickel atoms in the cluster. As a consequence one can suggest that sulphur forms very strong bonds within the plane of the boundary but weakens metal–metal bonds perpendicular to this plane. Although, for the present, the results can be considered only as suggesting one possible embrittling mechanism, they do demonstrate the insight which such calculations can provide into this very central question of grain boundary embrittlement.
139 citations
TL;DR: In this paper, a branch-neighbor-avoiding walk is proposed for percolation clusters, which gives critical exponents ν and γ and also exponents for the dependence of cluster variables on the walk's time.
130 citations
TL;DR: In this paper, a theory for describing molecule-solid surface interactions using correlated configurationinteraction (CI) wave functions for the surface region is described, starting with a delocalized self-consistent field wave function for the lattice, approximated as a cluster of atoms.
Abstract: A theory for describing molecule-solid surface interactions using correlated configuration-interaction (CI) wave functions for the surface region is described. Starting with a delocalized self-consistent-field wave function for the lattice, approximated as a cluster of atoms, a local surface region is defined by a unitary, localization transformation of the single-particle orbitals of the lattice wave function based on electron exchange maximization with the surface sites of interest. CI calculations on the resulting $N$-electron subspace plus adsorbate permit an accurate description of bonding at the surface. Ab initio computational techniques for treating the many-electron problem and large clusters of metal atoms are described.
129 citations
TL;DR: In this article, the ground state electronic structure of small nickel atom clusters (Nin, n=1-6) has been calculated using the ab initio effective core potential self-consistent field (SCF) method in a Gaussian expansion basis.
Abstract: The ground state electronic structure of small nickel atom clusters (Nin, n=1–6) has been calculated using the ab initio effective core potential self‐consistent field (SCF) method in a Gaussian expansion basis. The electronic configuration of the nickel atoms in the clusters is found to be very close to 3d94s1. The ground state electronic configurations for Nin generally have n unpaired 3d electrons in molecular orbitals (MO’s) spanning the same irreducible representations as the 4s atomic orbitals while the n 4s electrons fill their MO’s in accord with a simple three‐dimensional Huckel model with overlap. Exceptions to this description are found in the cases of linear systems where the 3d holes prefer δ over σ symmetry and in octahedral Ni6 where a different preferred set of 3d holes is obtained. The SCF ground state wave functions correspond roughly to a model in which the 3d electrons can be viewed as weakly interacting localized 3d9 units. The clusters are bound together primarily by the 4s electrons with the 4p orbital contribution increasing in importance with cluster size and dimensionality. The binding energy per nickel atom generally increases as the size of the cluster increases, although at six atoms this quantity has not yet converged with cluster size. The density of states diagram for the occupied one electron energy levels in Ni6 is found to be very different from the corresponding types of diagrams obtained in the muffin tin (MT)–Xα method for small nickel atom clusters. This difference is examined in detail, with consideration given to the effects of relaxation energy and to the different orbital level filling criteria used in the two methods.
126 citations
TL;DR: It is shown that the problem of determining a partition into a given number of clusters with minimum diameter or with maximum split can be solved by the classical single-link clustering algorithm and by a graph-theoretic algorithm involving the optimal coloration of a sequence of partial graphs.
Abstract: Cluster analysis is concerned with the problem of partitioning a given set of entities into homogeneous and well-separated subsets called clusters. The concepts of homogeneity and of separation can be made precise when a measure of dissimilarity between the entities is given. Let us define the diameter of a partition of the given set of entities into clusters as the maximum dissimilarity between any pair of entities in the same cluster and the split of a partition as the minimum dissimilarity between entities in different clusters. The problems of determining a partition into a given number of clusters with minimum diameter (i.e., a partition of maximum homogeneity) or with maximum split (i.e., a partition of maximum separation) are first considered. It is shown that the latter problem can be solved by the classical single-link clustering algorithm, while the former can be solved by a graph-theoretic algorithm involving the optimal coloration of a sequence of partial graphs, described in more detail in a previous paper. A partition into a given number of clusters will be called efficient if and only if there exists no partition into at most the same number of clusters with smaller diameter and not smaller split or with larger split and not larger diameter. Two efficient partitions are called equivalent if and only if they have the same values for the split and for the diameter.
117 citations
TL;DR: The results show that the three sites of the three-iron cluster have intrinsic hyperfine interactions similar to those of ferric rubredoxin; the differences in the observed interactions reflect the geometrical features of spin coupling.
Abstract: Recent Mossbauer and EPR studies of two ferredoxins and of aconitase have given evidence for a three-iron cluster, probably of a [3Fe-3S] type. The studies of the oxidized EPR-active centers have shown that the three iron sites are characterized by significantly different magnetic hyperfine coupling constants. For the ferredoxin from Azotobacter vinelandii, for instance, we have observed A1 = -41 MHz, A2 = +18 MHz, and [A3] = 5 MHz. We demonstrate here that the magnetic properties of the clusters can be explained with a simple model of three high-spin ferric ions (S = 5/2) exchange-coupled to a system spin S = 1/2. The model assumes isotropic exchange and different couplings between the iron sites. The results show that the three sites have intrinsic hyperfine interactions similar to those of ferric rubredoxin; the differences in the observed interactions reflect the geometrical features of spin coupling. Furthermore, the three exchange coupling constants are equal within a factor of 2. This implies that the three-iron cluster is a single covalently linked structure and should not be considered as a [2Fe-2S] cluster weakly coupled to a third iron atom.
105 citations
104 citations
TL;DR: In this paper, the authors discuss mixed-metal clusters, methods of characterization, reactivity, and dynamic nuclear magnetic resonance (NMR) studies, and methods of finding the key intermediates that condense to give the cluster products.
Abstract: Publisher Summary This chapter discusses mixed-metal clusters, methods of characterization, reactivity, and dynamic nuclear magnetic resonance (NMR) studies. Transition-metal cluster compounds are currently under intensive scrutiny because of their potential catalytic applications, both as models for understanding catalytic metal surfaces and as catalysts in their own right. Noticeably, few metal clusters have been prepared by designed or rational synthetic procedures. Pyrolysis reactions generally involve heating together two or more stable compounds of different metals, presumably to give fragments that then combine to yield the mixed-metal clusters. Relatively few clusters have been prepared by the pyrolysis of two monomeric compounds, and only two examples are given. Metal–carbonyl dimers have proved to be useful reagents for the synthesis of mixed-metal clusters. The pyrolysis of clusters in the presence of monomers, dimers, or other clusters usually requires much more severe reaction conditions. These coordinatively unsaturated species are apparently the key intermediates that condense to give the cluster products. The reaction of carbonylmetalates with monomeric and dimeric carbonyls has yielded many mixed-metal clusters. The reaction of carbonylmetalates with trinuclear clusters provides, in many cases, a convenient synthesis of tetranuclear clusters. Carbonylmetalates displace a halide from a metal–halide complex to yield a metal–metal bonded species.
TL;DR: The detailed conformations of benzene clusters containing 2, 3, 5, 7, 9, 11, 13 and 15 molecules were calculated by the Newton-Raphson method with exp-6-1 potential functions as discussed by the authors.
Abstract: The detailed conformations of benzene clusters containing 2, 3, 5, 7, 9, 11, 13 and 15 molecules were calculated. The nonbonded potential energy of the clusters was minimized by the Newton-Raphson method with exp-6-1 potential functions. All of the clusters exhibited a predominating edge-to-side or herringbone pattern of packing. The concept of intershell coordination, as contrasted to ligand coordination, was introduced and illustrated with the undecamer and larger clusters. The pentadecamer clearly showed the beginning of a second coordination shell. The tridecamer conformation was related to a 13-molecule fragment from crystalline orthorhombic benzene. This crystal fragment has a higher energy than the tridecamer. The fragment can convert to the tridecamer conformation by a process of plane slippage with cooperative molecular motion. Two examples, an isoheptamer and an isotridecamer conformation, are given of clusters with lower total cluster energy but with a higher energy for the reference molecule. In neither case do the conformations follow a smooth trend with increasing cluster size. The isotridecamer has approximate threefold symmetry and has a conformation quite different from the crystal fragment.
TL;DR: X-ray crystallographic study of the ferredoxin-like protein (iron-sulfur protein III) from Azotobacter vinelandii has been extended to 2.5-A resolution and shows two distinctly different Fe-S clusters.
TL;DR: In this article, the properties of the Li4 and Na 4 clusters were determined using ab initio CI methods and the rhombic and bent square geometries of these alkalai metal clusters were predicted to be the most stable arrangements for the singlet and triplet states respectively.
Abstract: The properties of the Li4 and Na 4 clusters are determined utilizing ab initio CI methods. The rhombic and bent square geometries of these alkalai metal clusters are predicted to be the most stable arrangements for the singlet and triplet states respectively. More symmetrical planar square and tetrahedron Li4 and Na4 clusters exhibit pronounced biradical features and are therefore highly unstable. The conjecture is made that the biradical character of some cluster arrangements might be connected with the catalytic activity of geometric irregularities in the surface of catalysator.
TL;DR: In this article, the structure and phase behavior of 13, 19, 55 and 55 Lennard-Jones clusters were investigated using a Monte Carlo method, which allowed the canonical ensemble to be correctly simulated and all thermodynamic variables to be properly defined.
Abstract: Using a Monte Carlo method, the structure and phase behaviour of Lennard-Jones clusters composed of 13, 19 and 55 particles have been investigated. In contrast to most previous work, the clusters were placed in a hard constraining sphere of varying diameter, which allowed the canonical ensemble to be correctly simulated and all thermodynamic variables to be properly defined. In all the clusters the liquid-solid transition could be readily detected by observing the changes in radial density distribution functions and in thermodynamic quantities. For the 55 atom cluster, a two phase region was observed, characterized by a drastic increase in heat capacity of the system. In this case the cluster was composed of a solid core of 13 atoms, surrounded by a fluid-like shell. At high pressures and low temperatures the 19 and 55 atom clusters underwent a solid-solid transition.
01 Jun 1980
TL;DR: In this paper, a relationship was developed which correlates the gas phase enthalpies for successive clustering reactions, with the single-ion heats of solvation, and the success of the correlation enables the prediction of the heat-of-solvation of a given ion in a solvent such as water or ammonia from the gas-phase determination for the attachment of only five ligands to a single ion.
Abstract: The energetics of ion clustering for the full range of conditions extending from the isolated ion-single molecule cluster in the gas phase, to the bulk condensed state, is examined. Employing concepts taken from the Thomson equation a relationship is developed which correlates the gas phase enthalpies for successive clustering reactions, with the single-ion heats of solvation. The success of the correlation enables the prediction of the heat of solvation of a given ion in a solvent such as water or ammonia from the gas phase determination of the enthalpies for the attachment of only five ligands to a single ion. Employing this new relationship, the contribution of cluster bonding to the energy barrier to nucleation can thereby be readily evaluated for any size cluster.
CERN1
TL;DR: In this article, the energy loss of charged particles in a gas has been estimated by a computer simulation technique with a view of studying primary cluster counting as a mean of the particle identification.
TL;DR: In this paper, the authors observed that the helium clusters of either isotope, or neon clusters of some 104 atoms, are observed to be excited by the impact of electrons of 30 to 100 eV energy.
Abstract: Metastable electronic states of helium clusters of 106 to 108 atoms of either isotope, or of neon clusters of some 104 atoms, are observed to be excited by the impact of electrons of 30 to 100 eV energy. Being detected through the release of electrons which results from the impact of the excited neutral or ionized clusters onto the first dynode of an electron multiplier, these metastable excitations allow the time‐of‐flight spectrometry of speeds and sizes of large clusters. The energy dependence of the excitation probability of the helium clusters indicates the initial excitation of the metastable atomic triplet state while the observed flight times of about 10−3 s point to the metastable triplet molecular state as the final helium cluster excitation.
TL;DR: In this article, the MINDO/3 quantum chemistry procedure is used to calculate the structure of clusters having 9-15 silicon atoms, representing the first four layers and 1-2 surface pairs of the Si(100) surface.
TL;DR: In this article, the Helmholz free energy of several stable NaCl clusters was calculated and it was shown that the relative stability of clusters of the same size can change with temperature.
Abstract: The Helmholz free energy of several stable NaCl clusters was calculated. It is shown that the relative stability of clusters of the same size can change with temperature. For (NaCl)4, the cubic configuration is preferred below 500 K, the eight‐ring configuration above. The energy surface was examined in order to determine the energy barrier separating stable configurations and thereby the time needed to establish thermodynamic equilibrium. In one case, (CaF2)5, the barrier is so low as to permit tunneling from one configuration to the other. The relative stability of clusters having the composition NanCl+n‐1 was calculated and the results are compared with a recent SIMS investigation. Na5Cl4+ is found to be a particularly stable charged cluster.
TL;DR: In this paper, the experimental realization of trapped silver atoms in various matrix supports, with emphasis placed on optical absorption, emission and e.r.s. spectroscopic properties.
Abstract: This paper starts with the experimental realization of trapped silver atoms in various matrix supports, with emphasis placed on optical absorption, emission and e.s.r. spectroscopic properties. Special attention is devoted to ground- and excited-state silver atom interactions with the surrounding matrix cage of atoms, particularly with respect to the recently discovered phenomenon of light-induced diffusion and aggregation of silver atoms to small, precisely defined silver clusters. Various aspects and applications of photodiffusion methods are highlighted and some pertinent comparisons are made with metal concentration and bulk annealing approaches as alternatives to controlled metal nucleation. This will lead to the embryonic clusters Ag2 and Ag3 for which there now exists considerable spectroscopic, photochemical and theoretical information. Silver-containing bimetallic clusters, generated either by metal concentration deposition or photoaggregation methods, will be a natural extension to the Ag2,3 presentation; their relevance to bimetallic cluster catalysts will be briefly contemplated. The concept of generating anionic silver clusters by Na/Ag photoionization methods will be briefly described, with reference to the parent Ag– anion. In considering the higher silver clusters, one is now in a position to evaluate experimentally the genesis of silver nucleation from the stage of an isolated silver atom, through to a six-atom array and to higher, less well defined aggregates. With these data one can attempt to track the evolving optical and e.s.r. properties by reference to the build-up of cluster electronic states calculated by way of SCF-Xα-SW molecular-orbital procedures for assumed cluster geometries. The observation of rudimentary interband transitions of silver clusters in the range 6-13 atoms, that absorb in a similar energy region to the collective electronic excitations associated with plasmon absorption of silver microcrystallites, simultaneously with the evolution of conduction electron spin resonance absorption, whose observed linewidths and g-shifts conform to the theoretical predictions of Kubo and Kawabata, can in principle provide a valuable criterion on which to judge the atomic composition at which optical–electronic characteristics of silver aggregates transform from those of the molecular to the bulk state. Future directions in diatomic-metal and metal-cluster chemistry are briefly contemplated in the light of recent break-throughs with ambient-temperature metal-vapour–liquid-polymer techniques and the discovery of polymer-supported, very low nuclearity metal cluster, generated and stable at, or very close to, room temperature.
TL;DR: The structure and electronic properties of copper clusters Cun(n= 2-5, 8 and 13) have been studied through ab initio LCAO-MO-SCF calculations with a Gaussian basis set (12, 7, 5) contracted to [5, 3, 2] as mentioned in this paper.
Abstract: The structure and electronic properties of copper clusters Cun(n= 2-5, 8 and 13) have been studied through ab initio LCAO–MO–SCF calculations with a Gaussian basis set (12, 7, 5) contracted to [5, 3, 2]. The linear structure is more stable than the two- and three-dimensional structures for n= 3 and 4, but becomes less stable for n 5. Since for Cu8 the band of 3d levels and the 4s levels are well separated and for Cu13 the two bands just begin to overlap, the distribution of energy levels in these clusters appears to be rather different from that in the bulk metal. This is also a consequence of the fact that most of the atoms in the cluster Cu13 are surface atoms. The binding energy increases quasi-linearly with the number of atoms in the cluster up to n= 8.
TL;DR: In this article, extended Huckel MO calculations have been applied to a large number of compact close-packed bare clusters of rhodium in order to establish their bonding abilities.
TL;DR: In this paper, it is proposed that the highest-energy cosmic rays are produced in galaxies in the central regions of clusters and the particles diffuse outwards under the influence of randomly directed intergalactic magnetic fields.
Abstract: It is proposed that the highest-energy cosmic rays are produced in galaxies in the central regions of clusters. The particles diffuse outwards under the influence of randomly directed intergalactic magnetic fields. Many of the particles detected at the Earth come from the Virgo cluster but if the diffusion coefficient is high enough other, more distant clusters, will also contribute significantly. The model gives a natural explanation of the measured spectral shape and anisotropy above about 1018 eV; its requirements for cosmic-ray energy in cluster sources are not excessive if, as seems likely, the production spectrum is comparatively flat (j(E) varies as tildeE- gamma with gamma in the region of 2.1 to 2.2).
TL;DR: The behavior of individual atoms on solids has long been of interest for understanding the physical and chemical properties of surfaces as mentioned in this paper, and through the use of the field ion microscope, it is possible to directly image single atoms on metal surfaces and to examine their properties quantitatively.
Abstract: The behavior of individual atoms on solids has long been of interest for understanding the physical and chemical properties of surfaces. Now, through the use of the field ion microscope, it is possible to directly image single atoms on metal surfaces and to examine their properties quantitatively. Such studies are reviewed, with special emphasis on: (1) surface structure and its effect on diffusion; (2) the details of the jump process; (3) interactions between atoms leading to cluster formation; and (4) the properties of clusters.
TL;DR: In this article, the development of topological rules for hydrido-metal cluster compounds, similar to those proposed by Lipscomb for boron hydrides, is shown to be a direct consequence of the multicentre bonding in bridged hydride-metal bonds.
Abstract: ABSTR,6CT. The development of topological rules for hydrido-metal cluster compounds, similar to those proposed by Lipscomb for boron hydrides, is shown to be a direct consequence of the multicentre bonding in bridged hydrido-metal bonds. Evidence for this localised view of the bonding has been obtained from U.V. photoelectron spectral studies of the hydridocarbonyl cluster compounds Re3(CO)12H3, Os4(CO)12H4 and
TL;DR: In this paper, the authors used a supersonic molecular beam as a sampling system for a photoionization quadrupole mass spectrometer, which was used as the ionizing source.
TL;DR: In this paper, a self-consistent Hartree-Fock-Slater molecular cluster calculations for the chemisorption of carbon monoxide on Ni, Pd, Pt and Ir surfaces are presented.