Showing papers on "Cluster (physics) published in 1983"

Formation of fractal clusters and networks by irreversible diffusion-limited aggregation

Abstract: A model for diffusion-controlled aggregation in which growing clusters as well as individual particles are mobile has been investigated. Two versions of the model in which the cluster diffusion coefficient is either size independent or inversely proportional to number of particles (mass) give very similar results. In the limit of low concentration and large system size both models lead to structures with a fractal (Hausdorff) dimensionality of about 1.45-1.5 in two-dimensional lattice-based simulations.

Electronic structure of supported small metal clusters

Abstract: Photoemission, Auger, and x-ray absorption spectroscopy have been used in a systematic study of small metal clusters on a variety of supports. The degree of cluster-support interaction for clusters of group-VIII and noble metals can be divided into two categories: supports with localized $p$ or $d$ orbitals with binding energies overlapping those of the cluster $d$ orbitals and supports without such orbitals. The first type is considered strongly interacting, whereas the latter type is only weakly interacting. For weakly interacting substrates such as carbon, the energy shifts in photoemission, Auger, and x-ray absorption edges, as well as changes in x-ray edge intensities, photoemission valence-orbital intensities and splittings, and photoemission and Auger linewidths all show that initial-state properties are much more sensitive to cluster size than are the final-state properties. The photoemission spectra of small clusters and those of alloys and intermetallic compounds are quantitatively compared. For weakly interacting substrates and host metals, the photoemission spectra of clusters and alloys are virtually identical, depending only on the average coordination number $\overline{n}$. In these systems the net interatomic charge transfer to the substrate or host atoms is very small. However, there is a significant intra-atomic charge transfer, which increases the $d$-electron count with increasing cluster size or alloy concentration. For strongly interacting supports, the cluster binding energy is usually shifted to lower binding energy. This shift can be understood from simple molecular-orbital arguments. The experimental conclusions are supported by calculations with the use of the thermodynamic model of Johansson and M\aa{}rtensson. Their model accurately predicts the observed binding-energy shifts and shows that initial-state effects dominate for weakly interacting systems and that final-state processes are relatively more important for the reactive substrates.

Noncrystalline structure of argon clusters. I. Polyicosahedral structure of ArN clusters, 20<N<50

Abstract: Small argon clusters are produced in a free jet expansion and studied by electron diffraction. Due to their very low proportion in the beam sample in comparison to the monomers, the smallest detectable clusters contain about 20 atoms. When they grow up to some 50 atoms, they present the same noncrystalline structure. This structure is identical to that of solid models constructed during a molecular dynamics calculation by cooling a liquid drop of atoms interacting through a Lennard‐Jones potential. Because it is composed of icosahedra of 13 atoms, either joined one to the other either interpenetrating each other, this structure may be called polyicosahedral. The comparison between theoretical and experimental diffraction functions leads to an estimate of the cluster temperature 27±3 K and of the proportion of monomers in the beam. We discuss the similarity in the radial distribution functions of both PIC models and bulk amorphous materials, and give arguments for the stability of the clusters.

A cluster approach to the structure of imperfect materials and their relaxation spectroscopy

Abstract: A new theory is proposed for the explanation of observed relaxation phenomena, which differs significantly from theories suggested by the authors before. The theory is based on a model of structural organization of macroscopically sized samples of imperfectly structured materials, both solids and liquids, and is intermediate in character. In terms of the model, a microscopic structure is maintained over a cluster containing a number of microscopic units, with an array of clusters described by a steady-state distribution completing the macroscopic picture. The structural regularity of each level of morphological organization is precisely defined by a coarse-grained index, which is given a thermodynamic interpretation in terms of binding energies and configurational entropy. The limiting cases of an ideal liquid and a perfect crystal are recovered as asymptotic extremes in terms of this definition. The consequences of this model for the relaxation dynamics of the structure are examined and it is shown that prepared fluctuations decay in a time-power law manner as coupled zero-point motions evolve either within clusters or between clusters, with a power determined by the relevant regularity index. As a result, the origin of power law noise in materials is explained in terms of configurational entropy, and its relation with gaussian and white noise, which appear as asymptotic limits, outlined. The shape of the steady-state distribution of the array of clusters is also determined without any a priori assumptions, and it is shown to range from an unbounded form to a δ function as the regularity of the array superstructure increases. Experimental examples of dielectric relaxation spectroscopy have been used to illustrate these structural concepts and outline the way in which this technique can be used to deduce the structural organization of the sample. Finally, a short description is given of some commonly observed forms of response and their structural interpretation.

Supersonic copper clusters

Abstract: Copper clusters ranging in size from 1 to 29 atoms have been prepared in a supersonic beam by laser vaporization of a rotating copper target rod within the throat of a pulsed supersonic nozzle using helium for the carrier gas. The clusters were cooled extensively in the supersonic expansion [T(translational) 1 to 4 K, T(rotational)=4 K, T(vibrational)=20 to 70 K]. These clusters were detected in the supersonic beam by laser photoionization with time‐of‐flight mass analysis. Using a number of fixed frequency outputs of an exciplex laser, the threshold behavior of the photoionization cross section was monitored as a function of cluster size. The 7.9 eV photon energy of the F2 excimer laser was found to be above the ionization potential of all clusters, and the photoion mass spectrum thus produced showed the copper cluster concentration in the beam to follow a monotonically decreasing function of cluster size. The 6.4 eV ArF exciplex laser photon energy was found to be above the photoionization threshold of clusters with three or more atoms in the case of odd‐numbered clusters, but only for clusters with eight or more atoms for even‐numbered clusters. Extending out to clusters as large as 29 atoms, laser photoionization at 6.4 eV produced a time‐of‐flight mass distribution with a pronounced even/odd alternation in cluster photoion intensity. This alternation in ionization threshold behavior was attributed to an even/odd alternation in the electronic structure of the copper clusters with the highest occupied molecular orbital (HOMO) of the even clusters being considerably more strongly bonding than it is in the clusters with an odd number of copper atoms. The 4.98 eV photon energy of the KrF exciplex laser was found to lie below the ionization threshold of all clusters in the 1 to 29 atom range. An extensive survey of the ultraviolet absorption spectrum of the copper dimer was also performed with this supersonic beam source. Resonance two‐photon ionization (R2PI) with mass selective detection allowed the detection of five new electronic band systems in the region between 2690 and 3200 A, for each of the three naturally occurring isotopic forms of Cu2. In the process of scanning the R2PI spectrum of these new electronic states, the ionization potential of the copper dimer was determined to be 7.894±0.015 eV.

Molybdenum Chalcogenides: Clusters, Chains, and Extended Solids. The Approach to Bonding in Three Dimensions

Abstract: A combined molecular orbital and crystal orbital analysis of systems containing Mo/sub 3n/X/sub 3n + 2/ (n = 2,3,4,infinity; X=S,Se,Te) units is presented. The modes of packing Mo/sub 6/X/sub 8/, Mo/sub 9/X/sub 11/, and Mo/sub 12/X/sub 14/ clusters into crystals are explained in terms of the cluster frontier orbitals. Intercluster Mo-X bonds are seen to result from an interaction between chalcogen donor orbitals and the cluster LUMO's that are localized on Mo atoms residing in the ''square faces'' of the clusters. Closed-shell electron counts for the clusters are elucidated. The relationship between the cluster frontier orbitals and surface states is discussed. Finally, relationships between the band structure of (Mo/sub 3/X/sub 3//sup -/)/sub infinity/ chains and the finite cluster molecular orbit also are explained.

The hydrodynamics of particle clusters and sediment entrapment in coarse alluvial channels

Abstract: Particles projecting from the bed of an alluvial channel distort the fluid stream to produce a distinctive pressure field. This has considerable significance for both the entrapment and entrainment of other particles and is a primary cause of the widespread occurrence of pebble clusters and boulder shadows. Lift and drag forces are determined on clustered hemispherical particles of varying size. In the wake of an obstructing particle both forces are shown to vary directly with particle separation in a linear fashion. On the stoss side of the cluster, drag is uniform regardless of the separation of the component particles, but lift is shown to increase when particle separation is small, so affecting stability. This mutual interference of neighbouring clustered bed particles is a vital consideration of incipient motion and is shown by field evidence to cause a wide range in transport stage for particles of similar size and shape. On average, 46% of clustered particles are entrained by flood flow compared to 87% of particles in open plane-beds. The influence of clusters is a major determinant of sedimentary sorting.

Surface Enhanced Raman Scattering by Metal Spheres. I. Cluster Effect

Abstract: An electromagnetic theory for the light absorption by a cluster of metal spheres and the Raman scattering by a molecule adsorbed on it is presented, which takes into account the retardation effect exactly and is applicable to an arbitrary cluster size. The theory is applied to a two-sphere cluster of Ag and Au. It is shown that the absorption spectrum is doubly peaked and the maximum enhancement factor of the Raman intensity amounts to 10 7 ∼10 8 when the distance between spheres is decreased. Absorption spectra of three- and four-sphere clusters are also calculated, which indicate that the essential features of the experimental observations are explained by the two-sphere cluster.

Structure of solid water clusters formed in a free jet expansion

Abstract: Clusters are produced in a free jet expansion of water vapor. Keeping constant the nozzle diameter (d=0.4 mm) and temperature (T=430 K), an increase in inlet vapor pressure from 1 to 5 bar produces an increase in mean cluster size from several tens to several thousands of molecules per cluster. An electron diffraction analysis provides information about the cluster structure and dynamics. A direct observation of diffraction patterns shows that the largest clusters exhibit mainly a crystalline structure, namely, diamond cubic which is the metastable phase of bulk solid water, whereas the smallest ones are amorphous. In order to elucidate the local order in the latter, a comparison is made between the experimental curves and the diffraction functions calculated for various noncrystalline models. The best agreement is obtained with a model which presents distorted rings of three to six H2O molecules, constructed by cooling a liquid water droplet through a molecular dynamics calculation. In particular, this m...

Two-dimensional spectrophotometry of the cores of X-ray luminous clusters

Abstract: The results of a two-dimensional spectrophotometric survey of the core regions of 11 rich clusters of galaxies are presented. A number of these clusters have spectacular optical emission line systems in their cores. Both morphologically and kinematically, the emission line regions divide into extended, 20-100 kpc systems of long linear filaments associated with the cluster core and more compact, homogeneous elongated regions associated with the dominant central cluster galaxy. It is suggested that the present results can be expected, as hot X-ray emitting gas cools in the cluster center. Luminosities almost entirely agree with expected values. The morphology of the systems can be understood if the filaments form initially in the cooling flow and, in some cases, are subsequently accreted by the central galaxy.

Mean-Field Theory for Diffusion-Limited Cluster Formation

Abstract: A mean-field theory for the diffusion-controlled cluster formation is presented by considering the competition among the different portions of a growing cluster for the incoming diffusive particles. This competition is shown to introduce a screening length which depends inversely on the density of the cluster. The Hausdorff dimensionality $D$ of these clusters is shown to be $\frac{({d}^{2}+1)}{(d+1)}$ where $d$ is the Euclidean dimensionality. This result is in excellent agreement with that of the computer simulations of Witten and Sander and of Meakin.

Basic Metal Cluster Reactions

Abstract: Publisher Summary This chapter discusses basic metal cluster reactions Addition or removal of electrons, the simplest type of chemical reaction, is much more common for transition metal than for main group element compounds Among the metal complexes, the clusters are predestined for this process Possible unidentate reagents are atomic cations and other simple electrophiles as well as atomic anions and other simple nucleophiles All cluster syntheses involve growth or fragmentation of metal atom aggregates But until very recently, the buildup of clusters or the use of clusters as fragment sources involved empirical approaches with little predictability The 18-electron rule generally governs the bonding in clusters with up to five metal atoms Clusters with five, six, and sometimes seven metal atoms can often be treated in terms of skeletal electron counting, describing the frameworks by the nido, closo, and capping formalisms A systematization of basic cluster reactions has been attempted based on the present status of knowledge The number of reactions reported is still relatively small for certain reaction types

Experimental investigation of small helium clusters: magic numbers and the onset of condensation

Abstract: Clusters of He atoms formed in a supersonic free jet expansion have been studied by electron-bombardment ionization and mass spectrometry. Distinct magic-number enhancements of ion intensity are observed for clusters of 7, 10, 14, and 30 atoms for both helium isotopes, and for 23 atoms of $^{4}\mathrm{He}$. Dramatic differences in the onset of cluster formation between the two isotopes may be related to the stability of $^{4}\mathrm{He}$ dimers.

Iron-sulfur stoichiometry and structure of iron-sulfur clusters in three-iron proteins: Evidence for [3Fe-4S] clusters

Abstract: Beef heart aconitase contains 3Fe clusters in its inactive and 4Fe clusters in its active form. The fully active form can be restored from the inactive one by insertion of Fe2+, whereas S2- is not required. Chemical analyses for iron and labile sulfide yield Fe/S2- ratios of 0.66-0.74 for the inactive and 0.90-1.03 for the active form. Sulfane sulfur (S0) was not detected. We propose on the basis of these data that the inactive form may arise from the active one by loss of one iron only per cluster with the sulfur remaining as S2- in a [3Fe-4S] structure. Measurements by extended x-ray absorption fine structure (EXAFS) spectroscopy on the 3Fe form of aconitase yield a Fe··S distance of 2.24 A and a Fe··Fe distance of 2.71 A. This Fe··Fe distance is in agreement with that obtained by EXAFS on ferredoxin II of Desulfovibrio gigas, another 3Fe protein, but disagrees with Fe··Fe distances observed for the 3Fe cluster of Azotobacter vinelandii ferredoxin I by x-ray diffraction—namely, 4.1 A. We suggest that this difference may be due to the presence of a [3Fe-3S] structure in the Azotobacter ferredoxin I crystals vs. a [3Fe-4S] structure in liquid or frozen solutions of aconitase. The [3Fe-3S] cluster has been shown to have a relatively flat twist-boat structure, whereas a [3Fe-4S] cluster could be expected to essentially maintain the compact structure of the [4Fe-4S] cluster. This would explain the differences in Fe··Fe distances. Two possible structural models for a [3Fe-4S] cluster are discussed.

Laser Studies of Metal Cluster Beams

Abstract: Recent developments in laser and molecular beam technology have now made it possible to produce supersonic beams of virtually any element in the periodic table. Using laser vaporization of the appropriate target, the beam source conditions may be adjusted to produce either the cold free atoms alone, or clusters of these atoms with each other—or with another element. Since the vaporization laser heats only a small spot on the target, extremely high local temperatures can be obtained without heating any other part of the apparatus; and beams of even the highest boiling element (tungsten) are readily obtained both in atomic and cluster form. The physics and chemistry of these exotic cluster species is almost completely unknown on the fundamental level. Even for clusters containing 100 atoms, most of these atoms lie on the surface, and the chemical and physical properties will be predominately surface phenomena. Initial studies of these clusters have entailed the use of one- and two- photon laser ionization with time-of-flight mass selective detection. Using a variety of fixed frequency lasers, the work function of copper clusters has been examined as a function of cluster size in the range from 2 to 29 atoms per cluster. Considerable detailed information has also been obtained for the electronic structure and bond lengths of a number of transition metal dimers and trimers (including Cu2, Cr2, V2, Mo2, and Cu3) through the use of high resolution laser spectroscopy with mass-selective photoionization detection.

Cluster studies of CO adsorption. III. CO on small Cu clusters

Abstract: Chemisorption of CO on (100) and (111) Cu surfaces has been investigated by calculations on a series of small clusters. The dependency of the results on both the adsorption site (top or hollow) and the size of the cluster has been analyzed using a decomposition of the adsorption energy in various terms (steric repulsion, σ bonding, π backbonding). Some properties, i.e., M–CO distance, M–CO vibration, C–O distance, can be obtained from small cluster calculations as they are determined by ‘‘local’’ bonding aspects, whereas, e.g., the adsorption energy is not reliable due to delocalized features of the bonding being not well represented by small clusters. The deficiency of small clusters in modeling the polarizability of a metal substrate is stressed.

Dynamical constraints on star formation efficiency.

Abstract: Dynamical constraints are placed on the local star formation efficiency during the formation of star clusters. Virial models are used to examine the expected changes in cluster velocity dispersion, density and radius during the period when the gas not converted into stars is removed from the system. Comparison of observed initial and final states of open clusters indicate local efficiencies of about 30% if the gas dispersal is slow relative to the dynamical crossing time and 55% if the gas loss is rapid. Efficiencies are somewhat dependent on support mechanisms of molecular clouds, but it is argued that observations of young clusters are in accord with the assumptions of the models used here.

Ring Laser Gyro Data Analysis With Cluster Sampling Technique

Abstract: Cluster Sampling Technique (CST) is a powerful method for measuring the output stability of the ring laser gyro or any other oscillator in the time domain. The relationship between the cluster variance and the power spectral density of noise contained in the data is derived. The former, being a directly measurable quantity, can provide information on the types and magnitudes of various noise terms. Analytical expressions for the cluster variance are derived for a number of prominent noise terms that are known to affect the gyro performance. The technique is applied to a long-term drift run of a Honeywell gyro and various noise terms are determined.

The dynamics of rich clusters of galaxies. II - The Perseus cluster

Abstract: The dynamics of the Perseus cluster are analyzed using self-consistent equilibrium analytical models. Using existing data in the literature plus new radial velocities reported here, composite surface density and velocity dispersion profiles are derived. These profiles have been compared with dynamical models described by Kent and Gunn (1982). The best fit suggest the presence of a significant degree of anisotropy in the velocity distribution: galaxy orbits are constrained to pass within a radius of seven cluster radii, or 1.3 deg of the cluster center. For Hubble constant = 50, a core radius of 340 kpc 11 arcmin and a mass to visual light ratio M/L = 300 are found. Using these results, X-ray observations of the intracluster medium in Perseus are reanalyzed. A previously noted discrepancy between the observed temperature of the hot gas and the cluster velocity dispersion is reduced but not eliminated. A cooling accretion flow previously deduced to exist in this cluster is shown to extend to only about one-third of the cluster radius.

A theory of the anomalous thermodynamic properties of liquid water

Abstract: A theory of the anomalous thermodynamic properties of liquid water is presented. The theory is based on a simple model intermolecular potential that contains short‐ranged repulsions, hydrogen‐bonding attractions, and longer ranged interactions. Cluster theory approximations derived in the previous paper [J. Chem. Phys. 77,1962 (1982)] are used to calculate the thermodynamic energy and free energy for the model fluid as a function of temperature and density. The model fluid is found to have many of the anomalous properties of real water, such as a density maximum at low pressure, a compressibility minimum, and high heat capacity. The model is not a quantitatively accurate one for real water, nor does it have the anomalous properties observed for supercooled water. The reasons for the anomalies of the model fluid are discussed in order to shed some light on the physical basis for these anomalies in real water.