Showing papers on "Cluster (physics) published in 1979"

A Cluster Separation Measure

Abstract: A measure is presented which indicates the similarity of clusters which are assumed to have a data density which is a decreasing function of distance from a vector characteristic of the cluster. The measure can be used to infer the appropriateness of data partitions and can therefore be used to compare relative appropriateness of various divisions of the data. The measure does not depend on either the number of clusters analyzed nor the method of partitioning of the data and can be used to guide a cluster seeking algorithm.

Extended x-ray absorption fine structure (EXAFS) of dispersed metal catalysts

Abstract: Extended x‐ray absorption fine structure (EXAFS) studies were made in a series of highly dispersed metal catalysts to obtain structural information on the metal clusters present. Clusters of osmium, iridium, and platinum dispersed on silica or alumina were investigated. The metal clusters in the catalysts constituted 1.0 wt.% of the total mass. Chemisorption measurements indicated that the metal dispersions approached unity, where dispersion is defined as the ratio of surface metal atoms to total metal atoms in the clusters. When EXAFS data on the metal clusters are compared with data on the corresponding bulk metals, the lower average coordination number of the metal atoms in a cluster is evident. The decrease in coordination number is accompanied by an increase in the root mean square deviation of interatomic distance about the equilibrium value.

Sodium tetramolybdenum hexoxide (NaMo4O6). A metallic infinite-chain polymer derived by condensation of octahedral clusters

Abstract: The synthesis and structure of NaMo/sub 4/O/sub 6/, which contains octahedral cluster units welded on opposite edges to form linear chains, were reported. This new compound represents the result of condensation of cluster units, a consequence of progressive lowering of nonmetal/metal ratio. One way to achieve lower nonmetal/metal ratios was by substitution of divalent nonmetal atoms for monovalent atoms in the structure. Intensive examinations of properties are currently being studied. 2 figures.

Orthogonally-spin-adapted coupled-cluster theory for closed-shell systems including triexcited clusters

Abstract: The orthogonally-spin-adapted form of the nonlinear system of equations for the extended coupled-pair many-electron theory, which involves the monoexcited, biexcited, and triexcited states and cluster components, is derived. A diagrammatic approach, based on second quantization, the time-independent Wick theorem, and the graphical methods of spin algebras, is employed. The advantages of using the orthogonally-spin-adapted states and cluster components, rather than the nonorthogonally-spin-adapted ones which have been previously employed, particularly in the triexcited case, are also discussed. It is also shown that the formulas for the direct configuration-interaction method can easily be obtained in compact form from the linear part of the system of extended coupled-pair equations.

The structure and evolution of X-ray clusters.

Abstract: Observations of the structure of the X-ray emission from 12 nearby rich clusters of galaxies are presented and interpreted in terms of dynamic cluster evolution. X-ray structures revealed by the Einstein Observatory imaging proportional counter in the range 0.25 to 3.0 keV were analyzed and used to classify the clusters based on their X-ray morphologies. Four categories are observed, consisting of spiral-rich clusters with low X-ray temperatures and velocity dispersions with broad and highly clumped emission, spiral-poor clusters with high X-ray temperatures and velocity dispersions with smoothly varying emission broadly or sharply peaked around a dominant galaxy, and clusters with emission typical of a cD galaxy in a poor cluster or group. The broad, highly clumped cluster emission is interpreted as a result of an early evolutionary stage, while the cD and centrally enhanced emissions represent successive later stages in X-ray galactic cluster evolution.

Theory of the Surface Electronic Structure and Defect States of Rutile by the DV–Xα Cluster Calculation

Abstract: The discrete-variational (DV)-X α calculations are applied to the surface clusters Ti 4 O 16,15 and the bulk cluster Ti 3 O 15,14 of rutile (TiO 2 ) with and without the oxygen vacancy. For the clusters with the defect, an occupied localized state is obtained, whose orbital is mainly composed of the d states of the nearest Ti ions. The defect state energy for the surface cluster agrees with that obtained by UPS and ELS experiments. The change in the state density at the valence band calculated for (Ti 3 O 15,14 ) 18- cluster explains satisfactorily the change in the UPS spectra on the Ar or electron bombardment of the ordered (110) surface.

Metal cluster complexes and heterogeneous catalysis - a heterodox view

Abstract: The properties of clusters investigated, combined with the work of others, indicate that (a) the reactivity of metal clusters toward adsorbate may show very dramatic size dependence, (b) the spectra of adsorbates on small clusters may differ markedly from those on single-crystal surfaces, (c) certain collective phenomena may contribute in subtle ways to the observed frequencies, intensities, and bandwidths of spectra of molecules, (d) the geometries of small clusters are often different from the bulk. The gross features of the chemisorptive bond, as well as that between a molecule and a very small cluster, are adequately described by a local bond. However, the chemistry and the spectroscopy may respond to subtle effects. Catalysis by small, supported-metal aggregates will in general be different from that by stable cluster complexes as a result of the existence of many metastable structures for the bare cluster. 6 figures.

A statistical mechanical theory for activity coefficients of a dilute solute in a binary solvent

Abstract: A statistical mechanical calculation of the activity coefficients of a dilute solute,C, in a binary solvent,A-B, was made using a model for the interactions of a coordination cluster consisting of a solute atom and its neighboring solvent atoms. The derived equations are applicable to a variety of types of ternary solutions including substitutional and interstitial alloys as well as additive and reciprocal molten salts. The theory takes into account the interactions between solute and solvent atoms (ions) as well as changes in interactions of the solvent atoms (ions) which are neighbors of solute atoms (ions). Prior theories such as those of Wagner and the quasi-chemical theories of Alcock and Richardson and Jacob and Alcock can all be shown to be special cases of the present theory. The dependence of the activity coefficients of a solute on the solvent composition is calculated from a knowledge of the activity coefficients of the solvent components, solute activity coefficients in the two pure solvent components, a coordination number, a geometric factor which depends upon the type of solution, and a term which represents the nonadditivity of pair bond interactions within the cluster of a solute atom (ion) and its neighboring solvent atoms (ions). In the model, the thermodynamic properties of the solute are related to the relative concentrations of the different coordination clusters as well as to the thermodynamic properties of the solvent.

Dynoc—A dynamic optimal cluster-seeking technique

Abstract: A new technique for automatic clustering of multivariate data is proposed In this approach a performance index for determining optimal clusters is introduced This performance index is expressed in terms of the ratio of the minimum interset distance to maximum intraset distance The optimal clusters are found when the performance index reaches a global maximum If there are alternative groupings with equal number of clusters, the one with the largest performance index is chosen

Application of fast self-consistent cluster calculations for large systems to the electronic structure of solids

Abstract: Using the multiscattering approach the electron Green's functions of clusters of atoms approximating extended solids are calculated in r space. Exploiting the point symmetries of the system and separating the Green's function into structure- and energy-dependent parts allows calculations for clusters consisting of up to 200 atoms. In these self-consistent calculations the influence of the cluster size on the local densities of states is discussed and the results are compared to those of bandstructure work. As examples the authors discuss the systems BCC Nb the rocksalt structure compound YS and, as a representative for a complex structure, the compound Th4H15. The results are applied to the calculation of superconducting transition temperatures.

Application of cluster analysis for characterization of spatial distribution of particles by stereological methods

Abstract: SUMMARY A method for the detection and characterization of clusters of particles observed in section with the electron microscope is presented. Cluster analysis is performed by the division method described by Berthet et al. (1976). Starting from a single cluster, profiles from each electron micrograph are successively classified in sets containing an increasing number of clusters. The decrease in the mean free distance, Λ, between profiles in the clusters, is used for terminating the subdivision procedure. The function relating the mean free distance with the number of clusters is evaluated in each subdivision set. The actual number of clusters is selected on the basis of the slope of that function, at a point where Λ has a value close to the average profile diameter. The method assumes a convex shape for the clusters; the salient feature is that it provides a physical delineation of clusters in the section. Hence, an evaluation of some characteristics of clusters in the three-dimensional sample may be obtained by using standard stereological procedures. Characterization of the volume to which the individual particles of a population are eventually restricted can as a result be performed. Practical problems in the acquisition of the data needed for cluster analysis are discussed and a system using for that purpose a Quantimet 720 image analyser in a basic configuration, connected on line with a PDP 11/10 minicomputer, is presented. Application of the method is illustrated by the analysis of lysosomes in cultured hepatoma (HTC) cells, at the end of mitosis and during the S phase. Cluster analysis shows that in mitotic cells, lysosomes are confined within 3·7% of the total cellular volume, while in cells actively synthesizing DNA they are grouped in clusters representing 5·7% of the cellular volume. Moreover, the average number of particles per cluster falls from a minimum of thirteen at mitosis to only six at the S phase.