Showing papers on "Cluster (physics) published in 1984"

Cluster analysis

Abstract: SYSTAT provides a variety of cluster analysis methods on rectangular or symmetric data matrices. Cluster analysis is a multivariate procedure for detecting natural groupings in data. It resembles discriminant analysis in one respect—the researcher seeks to classify a set of objects into subgroups although neither the number nor members of the subgroups are known. CLUSTER provides three procedures for clustering: Hierarchical Clustering, K-Clustering, and Additive Trees. The Hierarchical Clustering procedure comprises hierarchical linkage methods. The K-Clustering procedure splits a set of objects into a selected number of groups by maximizing between-cluster variation and minimizing within-cluster variation. The Additive Trees Clustering procedure produces a Sattath-Tversky additive tree clustering. Hierarchical Clustering clusters cases, variables, or both cases and variables simultaneously; K-Clustering clusters cases only; and Additive Trees clusters a similarity or dissimilarity matrix. Several distance metrics are available with Hierarchical Clustering and K-Clustering including metrics for binary, quantitative and frequency count data. Hierarchical Clustering has ten methods for linking clusters and displays the results as a tree (dendrogram) or a polar dendrogram. When the MATRIX option is used to cluster cases and variables, SYSTAT uses a gray-scale or color spectrum to represent the values. SYSTAT further provides five indices, viz., statistical criteria by which an appropriate number of clusters can be chosen from the Hierarchical Tree. Options for cutting (or pruning) and coloring the hierarchical tree are also provided. In the K-Clustering procedure SYSTAT offers two algorithms, KMEANS and KMEDIANS, for partitioning. Further, SYSTAT provides nine methods for selecting initial seeds for both KMEANS and KMEDIANS. Cluster analysis is a multivariate procedure for detecting groupings in data. The objects in these groups may be: Cases (observations or rows of a rectangular data file). For example, suppose health indicators (numbers of doctors, nurses, hospital beds, life expectancy, etc.) are recorded for countries (cases), then developed nations may form a subgroup or cluster separate from developing countries. Variables (characteristics or columns of the data). For example, suppose causes of death (cancer, cardiovascular, lung disease, diabetes, accidents, etc.) are recorded for each U.S. state (case); the results show that accidents are relatively independent of the illnesses. Cases and variables (individual entries in the data matrix). For example, certain wines are associated with good years of production. Other wines have other years that are better. Clusters may be of two sorts: overlapping or exclusive. Overlapping clusters allow the same object to appear in more than one …

Electronic Shell Structure and Abundances of Sodium Clusters

Abstract: Mass spectra are presented for sodium clusters of $N$ atoms per cluster ($N=4\ensuremath{-}100$) produced in a supersonic expansion with argon carrier gas. The spectra show large peaks or steps at $N=8, 20, 40, 58, \mathrm{and} 92$. These can be understood in terms of a one-electron shell model in which independent delocalized atomic $3s$ electrons are bound in a spherically symmetric potential well.

Production and characterization of supersonic carbon cluster beams

Abstract: Laser vaporization of a substrate within the throat of a pulsed nozzle is used to generate a supersonic beam of carbon clusters. The neutral cluster beam is probed downstream by UV laser photoionization with time‐of‐flight mass analysis of the resulting photoions. Using graphite as the substrate, carbon clusters Cn for n=1–190 have been produced having a distinctly bimodal cluster size distribution: (i) Both even and odd clusters for Cn, 1≤n≤30; and (ii) only even clusters C2n, 20≤n≤90. The nature of the bimodal distribution, and the intensity alterations in the observed C+n signals are interpreted on the basis of cluster formation and stability arguments. Ionizing laser power dependences taken at several different photon energies are used to roughly bracket the carbon cluster ionization potentials, and, at high laser intensity, to observe the onset of multiphoton fragmentation. By treating the graphite rod with KOH, a greatly altered carbon cluster distribution with mixed carbon/potassium clusters of for...

The structure of clusters of galaxies observed with Einstein

Abstract: Imaging observations from the Einstein Observatory are used to determine properties of galactic clusters and the intracluster gas. The hydrostatic-isothermal gas model is applied to obtain the cluster core radius, the limiting slope of the X-ray surface brightness distribution, and the presence and magnitude of a central luminosity excess above that predicted from the model when fit to the outer regions of the cluster. It is concluded that clusters can be divided into two basic families, one with small core radii and X-ray emission centered on a central dominant galaxy, and one with larger core radii and generally no central, stationary bright galaxy. The former type probably begins to form in the early stages of a cluster's dynamical evolution. The intracluster gas has a larger scale height than that of the galaxies based on the fit of the hydrostatic-isothermal model to the X-ray surface brightness profiles.

Oxygen‐related thermal donors in silicon: A new structural and kinetic model

Abstract: A structural model for the oxygen‐related thermal donors produced at moderate temperatures (<500 °C) is presented, where electrical activity commences with clusters containing five or more oxygen atoms and arises from a silicon atom at the center of the cluster. The donor activity of a cluster is terminated upon the ejection of this central silicon atom in order to bring about stress relaxation. A large number of electrically active donor species are predicted, differing only in the number of oxygen atoms each species contains. This structural model satisfies the stringent symmetry requirements of electron paramagnetic resonance (EPR), explains the lack of hyperfine interaction with Si29 or O17 nuclei and the large multiplicity in the number of donor species observed by infrared spectroscopy and EPR. The proposed clusters are shown to be embryonic forms of the much larger rodlike defects examined in detail by electron microscopy. Chemical reaction theory is used to deduce the kinetic consequences of the s...

Photoionization spectra and electronic structure of small iron clusters

Abstract: Laser photoionization spectra over the range 4.5–6.5 eV have been taken for iron clusters of from 2 to 25 atoms. From the observed ionization thresholds, the cluster ionization potentials are determined and trends in I.P. vs cluster size are examined. In the case of the iron dimer, a sharp, vertical threshold is seen which places the I.P. of Fe2 at 6.30±0.01 eV. Finally, SCF Xα scattered wave molecular orbital calculations have been carried out on the iron dimer and iron trimer. These results show the importance of ferromagnetic spin polarization in the electronic structure of Fe2 and Fe3.

Hierarchical model for chemically limited cluster―cluster aggregation

Abstract: A hierarchical model is introduced to describe chemically limited cluster-cluster aggregation. The fractal dimension of the clusters, D, as well as an exponent characterising the number of active sites per cluster are evaluated numerically for d=2,3,4. The relevance of the model to realistic physical situation is discussed.

Chemically limited versus diffusion limited aggregation

Abstract: In realistic growth processes, both kinetic and chemical factors determine the structure of the aggregates. Here, a model is proposed which interpolates between a purely diffusive and a purely chemical situation. There is crossover from a new, chemically limited growth model, with fractal exponents D=1.55±0.05 (2.00±0.08) in two (three) dimensions, to diffusive cluster aggregation Proposition d'un modele qui tient compte des facteurs cinetiques et chimiques pour la determination de la structure des agregats formes par croissance. Calcul de l'exposant fractal de l'agregat chimique a 2 et 3 dimensions. Comportement de crossover entre les regimes d'agregation chimique et diffusive

Effects of cluster trajectories on cluster-cluster aggregation: A comparison of linear and Brownian trajectories in two- and three-dimensional simulations

Abstract: Recent computer simulation studies have shown that diffusion-limited particle-cluster aggregation leads to structures with a considerably smaller effective fractal dimensionality than particle-cluster aggregation via linear particle trajectories. Here it is shown that Brownian motion has a much smaller effect on the structure of aggregates formed as a result of cluster-cluster aggregation. In particle-cluster diffusion-limited aggregation, it is the particle trajectory which prevents the particles from penetrating and filling in the fractal cluster. In cluster-cluster aggregation, the clusters cannot penetrate each other by means of any trajectory so the particle trajectory is of much less importance.

A proposal for the proper use of pseudopotentials in molecular orbital cluster model studies of chemisorption

Abstract: The interaction of CO with Cu5, Ni5, and Al4 are treated as model systems for molecular adsorption on metal surfaces. The effect of the use of pseudopotentials for the metal atoms is studied by considering three types of clusters. In the first case, all of the metal electrons are explicitly included in the wave function; an all electron (AE) treatment. In the second case, the metal atom which directly interacts with the CO is described by as AE but the remaining metal atoms include a pseudopotential for their core electrons. Finally, in the third case, all of the metal atoms in the cluster have a pseudopotential treatment for the core electrons. The AE cluster results are taken as reference values for the two pseudopotential treatments. The mixed cluster results are in excellent agreement with those of the all AE clusters; however, the results for the all pseudopotential cluster of Ni5CO or of Cu5CO are qualitatively different. The pseudopotential treatment for all of the metal atoms often leads to results that contain serious errors and it is not a reliable approach.

Diffusion-limited aggregation in three dimensions: Results from a new cluster-cluster aggregation model

Abstract: Diffusion-limited aggregation has been investigated using three-dimensional lattice models in which both particles and clusters can move and stick together. The final state consists of a single cluster or network of occupied lattice sites with a fractal dimensionality of about 1.75. Two versions of the model have been investigated. In Model 1, the cluster diffusion coefficient is independent of cluster size, and in Model 2, only the smallest clusters are allowed to “diffuse.” Both models give final states which are identical within the accuracy of the simulations. However, the cluster size dispersion at intermediate stages is distinctly different for Model 1 and Model 2. The results taken together with more extensive simulations in two dimensions indicate that a fractal dimensionality of ≈ 1.75 will be obtained for all versions of the model in which the diffusion coefficient of small clusters is equal to or greater than the diffusion coefficient for larger clusters. A number of the geometric properties which characterize final state and intermediate clusters are analyzed. Some of these properties should be amenable to measurement in real systems. The results of the simulations are in good agreement with measurements of the fractal dimensionality of metal particle aggregates.

Application of EXAFS in Catalysis. Structure of Bimetallic Cluster Catalysts

Abstract: In recent years the utility of extended x-ray absorption fine structure (EXAFS) as a probe for the study of catalysts has been clearly demonstrated [1–13]. Measurements of EXAFS are particularly valuable for very highly dispersed catalysts. Supported metal systems, in which small metal clusters or crystallites are commonly dispersed on a refractory oxide such as alumina or silica, are good examples of such catalysts. The ratio of surface atoms to total atoms in the metal clusters is generally high and may even approach unity in some cases. With such catalysts it is difficult or impossible to obtain structural information by conventional x-ray diffraction methods [14].

Compound clusters produced by the reaction of elemental vapors

Abstract: Cesium clusters containing up to 15 atoms were allowed to react with a variety of gases and vapors (O2, H2O, S8, Cl2) and the products were observed in a mass spectrometer. For example, using a cluster source containing two ovens, it was possible to produce and detect CsS clusters of all conceivable compositions, from (CsS48)+ to (Cs14S)+. Certain clusters, however, stand out particularly strongly in the mass spectra. These clusters are assumed to be unusually stable. Where meaningful, the structures of the stable clusters were determined by minimizing the total binding energy assuming a pair potential.

Relations Between Spatial Correlations of Rich Clusters of Galaxies

Abstract: The authors express the N-point rich cluster correlation function in terms of the two-point rich cluster correlation function in a model where rich clusters formed wherever suitably averaged primordial energy density fluctuations are unusually large. The validity of the results is not restricted to regions where the connected (reduced) N-point correlation functions are small compared with unity.

The photoionization of oxidized metal clusters

Abstract: Oxidized metal clusters (NaxO and KxO for 2≤x≤4) were formed in a gas phase reaction between metal clusters and an oxidizing gas using a double expansion technique. Their appearance potentials were measured using a molecular beam‐photoionization mass spectrometer system. These first photoionization data for oxidized clusters provide information on trends of ionization potentials as a function of the degree of aggregation. The ionization potentials do not differ greatly from the analogous metallic species, but in the case of the sodium tetramer the value does fall below that of the bare metal cluster. This finding is in accord with what has been observed as an influence of impurities on the work function of the bulk sodium. The results are also of interest concerning questions of octet rule violations and hypervalency.

Electronic structure and charge-transfer-induced cluster formation in alkali-group-IV alloys

Abstract: In this paper the authors apply model tight-binding calculations to the electronic structure of systems in which there are essentially two covalent interactions: the intracluster interaction U and the intercluster interaction V. The atomic structure is simulated by a modified Bethe lattice which incorporates closed loops as a possibility. The ratio alpha =V/U is an important parameter to be varied. At a distinct value, alpha crit, a metal-non-metal transition takes place. The results are applied to the electronic structure and chemical stability of anion cluster in liquid and solid alkali-group-IV alloys. The physical parameters which govern the process of clustering are discussed.

Vibrational predissociation spectra of nitrous oxide clusters

Abstract: A colour-centre laser has been used in conjunction with a molecular-beam apparatus to study the infrared vibrational predissociation spectra of nitrous oxide clusters near the ν1 + ν3 vibrational combination band of the momomer. These spectra were recorded as a function of source pressure in order to measure their dependence on cluster size. A frequency shift, corresponding to a gradual transition from the vapour to the solid state, is observed as the cluster size increases. The cluster-size distributions were estimated using both quadrupole and ion time-of-flight mass spectrometry. The latter technique shows cluster sizes well in excess of (N2O)100. Semiclassical studies based on Monte Carlo simulations and local mode analysis of representative cluster configurations are used to account for line profiles and shifts.