Showing papers on "Cluster (physics) published in 1986"

Clusters of transition-metal atoms

Abstract: Functions of Size: The Approach to the Bulk A. Ionization Potentials, Electron Affinities, and the Development of Band Structure B. Response of Clusters to External Fields: Magnetic Moments and Electric Polarizabilities C. Metal Cluster Structure and Interatomic Distances 0. Dissociation of Multiply Charged Clusters: Coulomb Explosions E. Chemical Reactions of Neutral Clusters F. Chemical Reactions of Ionized Clusters 111. Properties of Transition-Metal Clusters as

Quantum size effects in metal particles

Abstract: The subject of small metallic particle properties is outlined with emphasis on quantum electronic effects. The theoretical background for interpretation of experiments is discussed beginning with the work of Kubo. More recent amendments to this have been included, taking into account the techniques of random matrix theory and effects of the spin-orbit interaction. A general review of experimental work is presented in order to permit a comprehensive evaluation of current understanding of the quantum size effect on the electronic spectrum. This survey includes magnetic susceptibility, nuclear magnetic resonance, electron spin resonance, heat capacity, optical, and infrared absorption measurements. These are discussed in many instances from the point of view of there being competing size effects arising from a reduced volume contrasted with those from the surface. A number of stimulating and provocative results have led to the development of new areas of research involving metallic clusters such as cluster beam techniques, far-infrared absorption by particle clusters, adsorbate NMR, and particle-matrix composites. Although there is little question that the experiments themselves indicate the existence of quantum effects, there are as yet, insufficient results to test the theoretical predictions for electron-level distribution functions based on fundamental symmetries of the electron Hamiltonian. A new suggestion for measurement of the electron-level correlation function is made using the magnetic field dependence of the NMR Knight shift. Particle preparation methods are also reviewed with commentary on the problems and advantages of these techniques for investigation of quantum electronic effects.

Classically exact overlayer dynamics: Diffusion of rhodium clusters on Rh(100)

Abstract: A new method is presented for describing the classical dynamics (e.g., diffusion, desorption) of adsorbed overlayers of atoms or molecules, starting from arbitrary interatomic potentials. Provided that a certain dynamical criterion is met, the method yields classically exact results, but with many orders of magnitude less computation than direct molecular dynamics. The approach provides, for what we believe to be the first time, a connection between stochastic lattice-gas dynamical methods and the interatomic potential function. As a sample application, the diffusion constants are computed for two-dimensional rhodium clusters of up to 75 atoms on the Rh(100) surface at T = 2000 K. For clusters larger than n = 15 atoms, the diffusion constant scales as n/sup -1.76//sup +- //sup 0.06/, and the dominant mechanism for the diffusion is found to be atoms running along the edges of the cluster blocks.

Theoretical study of small silicon clusters: Equilibrium geometries and electronic structures of Sin (n=2–7,10)

Abstract: The geometries and energies of small silicon clusters have been investigated in a systematic manner by means of accurate ab initio calculations. The effects of polarization functions and electron correlation have been included in these calculations. Several geometrical arrangements and electronic states have been considered for each cluster. All the geometries considered have been completely optimized within the given symmetry constraints with several basis sets at the Hartree–Fock level of theory. Single point calculations have been performed at these geometries using complete fourth‐order perturbation theory with the polarized 6‐31G* basis set. The effects of larger basis sets including multiple sets of polarization functions have been considered for Si2 and Si3. Singlet ground states are found for Si3–Si7 with the associated geometries corresponding to a triangle, a planar rhombus, a trigonal bipyramid, an edge‐capped trigonal bipyramid, and a tricapped tetrahedron, respectively. The best calculated structure for Si10 corresponds to a tetracapped octahedral arrangement where alternate faces of the octahedron have been capped to yield a structure with overall tetrahedral symmetry. All the geometries are considerably different from those derived from microcrystal fragments. Binding energies have been computed for all clusters and used to interpret the distribution and fragmentation patterns of small silicon cluster ions observed recently.

Noncrystalline structure of argon clusters. II. Multilayer icosahedral structure of ArN clusters 50<N<750

Abstract: In a preceding paper, we have described the polyicosahedral structure of small argon clusters containing less than about 50 atoms which were produced in a free jet expansion. Going on with this study, we describe presently the multilayer icosahedral structure of larger argon clusters containing up to about 750 atoms, a value for which the transition to the fcc crystalline bulk structure is found to occur. Cluster models are used in order to study the third icosahedral layer construction, and the transition from a twin to a regular surface arrangement, which is expected to take place around 75 atoms, is observed on experimental patterns. The good agreement between experimental and calculated diffraction functions leads to an estimate of mean cluster sizes, cluster size distributions, and temperature (32±2 K) of clusters containing several hundreds of atoms.

Cluster expansion for abstract polymer models

Abstract: A new direct proof of convergence of cluster expansions for polymer (contour) models is given in an abstract setting. It does not rely on Kirkwood-Salsburg type equations or “combinatorics of trees.” A distinctive feature is that, at all steps, the considered clusters contain every polymer at most once.

Noble- and transition-metal clusters: The d bands of silver and palladium.

Abstract: A comparison of x-ray photoemission from Ag and Pd clusters grown on amorphous carbon substrates highlights the importance of the unfilled 4d band in Pd clusters. In both cases, the valence-band spectra show the d-band narrowing with decreasing cluster size, as expected. In both cases, also, there is a positive shift of the binding energies of the d-band centroids and of the core levels, primarily due to the unit positive charge that remains on the cluster in the photoemission final state, as occurs for other metal clusters on amorphous carbon. In Ag clusters the core-level shift is smaller than the valence-band shift because in small clusters the Coulomb energy of the charged cluster suppresses the conduction electron screening of the core hole. By contrast, in Pd clusters the increased localization causes a reduction in the d-electron density of states at ${E}_{F}$, resulting in a transition to s-electron screening and hence a core-level shift that is larger than the valence-band shift.

Peer Cluster Theory: Drugs and the Adolescent.

Abstract: The authors review several theories advanced to explain adolescent drug use to provide background for describing peer cluster theory. Peer clusters, small subsets of peer groups, including pairs, dictate the shared beliefs, values, and behaviors that determine where, when, and with whom drugs are used and the role that drugs play in defining cluster membership. Peer cluster theory incorporates those psychosocial factors that promote or inoculate against drug use in youth.

Higher excited electronic states in clusters of ZnSe, CdSe, and ZnS: Spin‐orbit, vibronic, and relaxation phenomena

Abstract: Metal selenide clusters have been made and characterized, using the arrested precipitation colloidal technique. A comparison of sulfide and selenide spectra enables observation of the effect of changes in the highest occupied molecular orbitals upon cluster electronic properties. The first and second excited electronic states are both observed as a function of size in ZnSe clusters. The systematic dependence of the spectra lead to assignment of the higher state to a 1S‐type hole based upon the split‐off valence band. It is shown that the energy spectrum of discrete hole states is controlled by the spin‐orbit energy and the isotropic hole mass in small, highly symmetrical clusters. This result contrasts with the heavy hole and light hole states observed for planar confinement. In ≂ 20 A diameter ZnS clusters, there is a strong vibronic temperature dependence in the excited state spectra, while in clusters of smaller gap materials such vibronic effects are very minor. We conjecture that lifetime broadening ...

Supersonic cluster beams of III–V semiconductors: GaxAsy

Abstract: Supersonic beams of semiconductor clusters with the formula GaxAsy were generated by laser vaporization of a disc of pure GaAs mounted on the side of a pulsed supersonic nozzle. These cluster beams were characterized by laser photoionization with various fixed-frequency lasers followed by time-of-flight mass spectrometry. Mass analysis of the clusters with x+y>10 showed all clusters in the composition range from Gax+y through GaxAsy to Asx+y to be present in roughly the amount expected from a binomial distribution. In the smaller clusters strong variations were observed from this expected binomial distirbution as a result of kinetic effects in the cluster formation process. Photoionization with an ArF excimer laser at very low pulse energy revealed a pronounced even/odd alternation in the photoionization cross section of the GaxAsy clusters, depending only on the total number of atoms in the cluster. Clusters in the 5–21 atom range with an odd number of atoms were one-photon ionized by the 6.4 eV ArF excimer laser photons. This even/odd alternation in ionization properties of the clusters supports the view that the even clusters have fully paired singlet ground states with no dangling bonds. At higher ArF excimer laser fluences, the observed mass spectrum became increasingly affected by fragmentation. As is true with bulk GaAs surfaces, these GaxAsy clusters evaporate largely by the loss of arsenic (probably As2) when heated by the laser, leaving behind clusters which are richer in gallium.

Metal Clusters in Catalysis

Abstract: Part 1. Molecular Metal Clusters. Chapter 1. Synthesis of Mono- and Multimetallic Metal Clusters (G.L. Geoffroy). 2. Structures of Metal Clusters (G.L. Geoffroy). 3. Thermochemical Properties and Bond Energies of Transition Metal Clusters (J.A. Connor). 4. Reactivities of Metal Clusters (E. Lavigne, H.D. Kaesz). 5. Homogeneous Catalysis by Metal Clusters (L. Marko, A. Vizi-Orosz). Part II. Metal Clusters in and on Supports. 6. Characterization by Physical Methods (H. Knozinger, L. Guczi, R.F. Pettifer). 7. Dispersed Metal Clusters from Metal Vapor Chemistry (G.A. Ozin, M.P. Andrews). 8. Metal Clusters and Zeolites (P.A. Jacobs). 9. Supported Metal Catalysts Prepared from Molecular Metal Clusters: Organometallic Surface Chemistry (B.C. Gates, R. Psaro, R. Ugo, G. Maire, H. Knozinger). 10. Supported Bimetallic Catalysts Derived from Molecular Metal Clusters (L. Guczi). Part III. Relations Between Molecular Clusters and Metal Surfaces. 11. Relations between Metal Clusters and Metal Surfaces (G. Ertl). Part IV. Summary and Evaluation (B.C. Gates, L. Guczi and H. Knozinger). Cluster Index. Subject Index. ``The editors are to be congratulated for this thorough and critical assessment of molecular metal clusters in catalysis. The strength of this book is the critical coverage of each topic making it very valuable within the field. Close to 2000 carefully selected literature references provide the reader with key information to metal clusters. Without any doubt this is the most authoritative work written today on this subject.''

Multiple-quantum NMR study of clustering in hydrogenated amorphous silicon.

Abstract: Multiple-quantum nuclear-magnetic-resonance techniques are used to study the distribution of hydrogen in hydrogenated amorphous silicon. Using the fact that multiple-quantum excitation is limited by the size of the dipolar-coupled spin system, we show that the predominant bonding environment for hydrogen is a cluster of four to seven atoms. For device quality films, the concentration of these cluster defects increases with increasing hydrogen content. At very high hydrogen content, the clusters are replaced with a continuous network of silicon-hydrogen bonds.

Aluminum clusters: Magnetic properties

Abstract: We report the first measurement of the magnetic moments of gas phase aluminum clusters ranging in size from 2 to 25 atoms. Aluminum clusters are produced by pulsed laser vaporization of an aluminum rod inside the throat of a high pressure pulsed nozzle. The highly collimated cluster beam is passed through a Stern–Gerlach magnet and the deflected beam is analyzed by spatially resolved photoionization time‐of‐flight mass spectrometry. Aluminum clusters less than nine atoms in size are found to have magnetic moments generally consistent with those predicted from spin and orbital moments of the ground electronic states. As expected, a general trend toward reduced magnetic moment per atom with increasing cluster size is observed.

On the manifestation of electronic structure effects in metal clusters

Abstract: Potasium (K x x<40) and sodium(Na x , x<66) clusters were generated in molecular beams and probed by photoionizationmass spectroscopy. Results obtained include measurements of neutral cluster abundances and determinations of ionization potentials. The I. P. values can be rationalized in terms of a global electrostatic model which extrapolates to the bulk work function. This model also applies to transition metals as can be shown by comparng it to the limited experimental data sets available. The I. P.’s of small clusters exhibit ‘‘quantum size’’ effects which can be understood by individual quantum chemical calculations. As previously found for sodium clusters, photoionization mass spectra obtained for potassium, mixed potassium/sodium and potassium/lithium exhibit abundance maxima at M+ 8 and M+ 20, where M is an alkali metal. This has been interpreted in terms of increased thermodynamic stability of the corresponding neutrals relative to neighboring clusters. We present data which show that a spherical jellium model, while providing a set of numbers correlating well with those of preferred stability in alkali clusters, is less successful in explaining other properties.

Enhanced stability of ion–clathrate structures for magic number water clusters

Abstract: The near threshold vacuum‐UV photoionization of water clusters has been performed by using a resonance line emission of argon at 1183 eV The well‐known intensity anomaly at the cluster ion (H2O)21H+ is observed even in this threshold photoionization, for the first time, with very small excess energy Structures for the water cluster ions (H2O)21H+ and (H2O)28H+ which exhibit enhanced structural stability (magic number), are presented based on Monte Carlo simulations as well as on the analogy of our previous study on the stability of the (H2O)20NH+4 ion The Monte Carlo calculations are carried out at the temperatures of 200, 150, 100, and 50 K for the ionized water clusters (H2O)nH+ around n=21 and also around n=28, which includes the ionic hydrogen‐bond interactions between an H3O+ ion and neutral H2O molecules The clusters (H2O)21H+ and (H2O)28H+ have greater binding energies per molecule than their neighbors although the enhancement of the latter is somewhat temperature dependent The calculations s

Electron binding and chemical inertness of specific Nbx clusters

Abstract: Photoionization threshold measurements on niobium clusters Nbx x=4–29, reveal an unprecedentedly strong dependence on x, the number of atoms in the cluster. Major maxima in threshold energies occurring at x=8, 10, and 16 correspond to those clusters recently shown to be unreactive toward molecular deuterium.

Hydrogen bonded and non‐hydrogen bonded van der Waals clusters: Comparison between clusters of pyrazine, pyrimidine, and benzene with various solvents

Abstract: Solute–solvent clusters of pyrazine, pyrimidine, and benzene (solutes) and CnH2n+2 (n=1,2), NH3, and H2O (solvents) are studied by the techniques of supersonic molecular jet spectroscopy and two‐color time‐of‐flight mass spectroscopy (two‐color TOFMS) Spectral shifts, van der Waals (vdW) modes, dissociation energies, and vdW mode–solute mode vibronic couplings are characterized for most of the observed clusters Based on these data and previous results for hydrocarbon systems, cluster geometries can be suggested Lennard‐Jones potential (6‐12‐1) calculations are also performed for these clusters and in all instances for which comparisons can be readily made, calculated and experimentally estimated geometries and binding energies agree completely Clusters of N‐heterocyclic solutes and H2O are not observed experimentally Systematics and trends among the clusters reported herein and those previously reported are discussed and analyzed

Simulated annealing of silicon atom clusters in Langevin molecular dynamics.

Abstract: We have performed simulated annealing of silicon clusters with a Langevin molecular-dynamics approach. The silicon atoms interact through two- and three-body potentials and are connected to a heat bath that provides a stochastic force and a viscous friction. The simulated annealing is substantially better than any steepest-descent method, and produces low-lying energy states of the clusters that are insensitive to the initial cluster configuration or the details of the cooling schedule. Systematics of the simulated annealing process are discussed.

Kinetics of cluster formation in the laser vaporization source: Carbon clusters

Abstract: A general model of cluster formation in the laser vaporization source starting from the atomic vapor is developed and applied to carbon clusters. Two limiting cases of cluster growth exist: the diffusion‐limited regime, in which the cluster distribution is essentially featureless, and the reaction‐limited regime, in which the most stable clusters show as magic numbers in the cluster distribution. An approximate theory of the aggregation kernel allows for calculation of the cluster distribution in the reaction‐limited regime from the formation energies of the reacting clusters. Heat released in cluster fusion allows small and medium size clusters to attain their lowest or almost lowest energy configurations in both the diffusion‐ and reaction‐limited regimes. For larger clusters, crystalline structures are expected for transition metals, while network‐forming materials are likely to exibit a multitude of structures. An application to carbon clusters in the n=1–25 range reproduce the experimentally observed cluster distributions and the magic numbers in the n=10–25 regime. The equilibrium structures of the small carbon clusters formed in the nozzle are found to be chains and monocyclic rings. At the reaction temperature, the transition between the chain and ring structures occurs around n=10 for the neutral and the positively charged clusters.

Clusters in solution: Growth and optical properties of layered semiconductors with hexagonal and honeycombed structures

Abstract: Transmission electron microscopy and optical absorption were used to examine small clusters of the layered semiconductors, PbI2 and BiI3. In both systems, a layer of metal is sandwiched between two hexagonally closed‐packed layers of iodine. We describe a simple solution preparation which gives rise to clusters corresponding to single layer sandwiches, roughly 7 A thick, whose lateral dimensions vary from 12 to 90 A depending on the solvent and the nature of the growing cluster interface. The cluster size distributions are markedly different for PbI2 and BiI3 reflecting the different structure in the metal planes of these systems. PbI2 cluster sizes are determined by hexagonal symmetry, with cluster growth achieved by placement of lead atoms symmetrically about a smaller cluster. In BiI3, whose metal plane has a honeycombed structure like graphite, clusters grow to be much larger with their sizes determined by the closure of six‐membered rings. The optical absorption spectra of PbI2 and BiI3 can be quantitatively understood in terms of the measured cluster size distributions.

Photodetachment studies of metal clusters: Electron affinity measurements for Cux

Abstract: Laser photodetachment studies have been performed on silver and copper cluster negative ion beams extracted from a supersonic metal cluster source. This source involves the use of laser vaporization within a pulsed nozzle to prepare the neutral cluster jet, followed by ArF excimer irradiation of the nozzle orifice as the copper clusters emerge into the expansion. Photoelectrons ejected from the aluminum nozzle by the excimer radiation are entrained in the supersonic flow and attach to the neutral copper clusters, producing negative ions which stabilize and extensively cool in the subsequent supersonic expansion. Laser photolysis of mass‐selected negative copper cluster ions extracted from this source reveals efficient photodetachment to produce a free electron in the absence of measurable fragmentation. The laser fluence dependence of the photodetachment process at different photon energy permits a rough experimental determination of the electron affinities of copper metal clusters as a function of cluster size for the first time.