Showing papers on "Cluster (physics) published in 1994"

Clusters and colloids : from theory to applications

Abstract: General Introduction Electronic Structure of Metal Clusters and Cluster Compounds Physics and Chemistry of Isolated Clusters Ligand Stabilized Metal Clusters Clusters in Cages Condensed Metal Clusters Colloids Perspectives.

Structure and parameters of clusters in traffic flow.

Abstract: The nonlinear theory of the cluster effect in a traffic flow [B. S. Kerner and P. Konh\"auser, Phys. Rev. E 48, 2335 (1993)], i.e., the effect of the appearance of a region of high density and low average velocity of vehicles in an initially homogeneous flow, is presented. The structures of a stationary moving cluster are derived. It is found that the density, the average velocities of vehicles inside and outside the cluster, and also the velocity of the cluster are the characteristic parameters of the traffic flow. The dependencies of the cluster structure and parameters on the density of vehicles in the initially homogeneous flow and on the length of the road are investigated. It is found that the cluster can appear within regions of density of vehicles which correspond to a stable homogeneous flow. It is shown that an appearance of a localized perturbation, having a finite amplitude, in the stable homogeneous flow can lead to a self-formation of a local cluster of vehicles which is surrounded by the homogeneous traffic flow. The parameters of the local cluster do not depend on the amplitude of this perturbation but only on the parameters of the flow.

Filling of micron‐sized contact holes with copper by energetic cluster impact

Abstract: A completely ionized and clustered beam of Mo or Cu is deposited with variable kinetic energy on a substrate, and the filling of micron‐sized contact holes on semiconductor devices is studied. An excellent hole filling is obtained for the impact of charged copper clusters, if they contain 1000–3000 Cu atoms and impinge with a kinetic energy of about 10 eV per atom on a substrate having a temperature of 500 K. The morphology of small hole fillings by slow and energetic cluster impact is discussed.

Magnetism in 4d-transition metal clusters.

Abstract: We present the results of a study of magnetism in rhodium, ruthenium, and palladium clusters. We report values for the magnetic moments of rhodium clusters which are free from a systematic error present in our previous measurements [Phys. Rev. Lett. 71, 923 (1993)] and show that their magnetic moments decrease to the bulk value of zero as the cluster sizes increase. Ruthenium and palladium clusters are nonmagnetic.

The structure of the Virgo cluster of galaxies from Rosat X-ray images

Abstract: THE Virgo cluster1–10 is the nearest large concentration of galaxies to us, and therefore plays a critical role in calibrating the cosmological distance scale11. Unfortunately, the cluster is very irregular, making it difficult to model the distribution of mass within it, and therefore impossible to determine its content of dark matter. X-ray observations offer a way around this problem, by revealing the hot, diffuse gas that is thought to fill the cluster's gravitational potential well in a way that closely matches the total distribution of mass12. Here we report X-ray images of Virgo, obtained with the Rosat observatory, which show hot luminous gas extending over most of the optically visible cluster. The data show that a large part of the mass of the cluster is centred on the galaxy M87, with smaller concentrations around M86 and M49. Our results for M86 support the recent suggestion3 that it is part of a small group of galaxies that is merging with the main cluster.

Path integral simulations of mixed para‐D2 and ortho‐D2 clusters: The orientational effects

Abstract: A recently suggested computational scheme [Buch and Devlin, J. Chem. Phys. 98, 4195 (1993)] is extended to describe orientational phenomena in systems containing assemblies of odd‐J and even‐J hydrogen and deuterium molecules. Nuclear symmetry and rotational effects are incorporated in the path integral Monte Carlo algorithm. The scheme is employed in a study of the (para‐D2)3(ortho‐D2)10 and (para‐D2)13 clusters in the 1–3 K temperature range. In the (para‐D2)3(ortho‐D2)10 cluster at 1 K, the three J=1 molecules form a ‘‘cluster within cluster,’’ held together by the anisotropic quadrupole–quadrupole interactions. At 3 K the three molecule J=1 cluster is dissolved within the (D2)13 cluster. The orientational structure of the (para‐D2)13 cluster at 1 K is composed of two distinct distorted‐T pair configurations of neighboring J=1 molecules. Upon heating to 3 K the orientational structure changes, and a clear separation between the two pair geometries is no longer obtained. Moreover at 3 K thermal distortion of the cluster structure from icosahedral relaxes the extent of orientational frustration of the system, and thus contributes to the lowering of the rotational energy.

The structure of small nickel clusters. I. Ni3–Ni15

Abstract: The geometrical structure of small nickel clusters is probed via molecular adsorption of nitrogen on their surfaces. Nitrogen uptake patterns can be rationalized with the proposed structures if it is assumed that N2 binds to every exposed nickel atom, that the binding energies decrease with increasing metal—metal coordination, and that atoms that are four or less coordinate can bind two nitrogen molecules. In some cases nitrogen adsorption causes a change in cluster structure, usually to one that can accommodate more nitrogen molecules. Cluster structures are proposed for all clusters (bare and nitrogenated) in the 3–15‐atom size range except Ni4 and Ni11. The nitrogen uptake for Ni4 is consistent with virtually any structure, and the data for Ni11 could not be interpreted in terms of a specific structure. In general, nickel cluster structures are different from those found for rare gas clusters as well as those derived from bulk packing. A comparison of the experimental results with existing theoretical ...

Annealing Carbon Cluster Ions: A Mechanism for Fullerene Synthesis

Abstract: We describe studies of the annealing and dissociation of even-numbered carbon cluster ions containing 50-70 atoms. The polycyclic polyyne ring isomers for cluster ions in this size regime can be annealed almost entirely into the fullerene geometry, with a small fraction being converted into an isomer which appears to be a large monocyclic ring. Surprisingly, we find that C[sub 60][sup +] behaves essentially the same as other similarly-sized clusters (such as C[sub 58][sup +]). This has important implications for understanding the mechanism of these structural transformations, as well as the overall scheme for fullerene synthesis. The activation energies for conversion of the polycyclic rings to fullerenes are low and relatively independent of cluster size, though the efficiency of forming a fullerene (rather than a large monocyclic ring) increases with cluster size. Based on our experimental results, a detailed mechanism is proposed to account for conversion of the polycyclic polyyne rings into fullerenes. According to this mechanism, a fullerene fragment is prepared by a Bergman enediyne cyclization followed by a radical-induced ring closure and a retro [2 + 2] process. The polyyne chains are then configured to spiral around the fullerene fragment and zip up to form a spheroidal fullerene. Wemore » also consider how these processes fit into an overall scheme for fullerene synthesis from small carbon fragments and describe a scheme that is consistent with the experimental results presented here. 36 refs., 14 figs., 1 tab.« less

The galactic globular cluster system

Abstract: We explore correlations between various properties of Galactic globular clusters, using a database on 143 objects. Our goal is identify correlations and trends which can be used to test and constrain theoretical models of cluster formation and evolution. We use a set of 13 cluster parameters, 9 of which are independently measured. Several arguments suggest that the number of clusters still missing in the obscured regions of the Galaxy is of the order of 10, and thus the selection effects are probably not severe for our sample. Known clusters follow a power-law density distribution with a slope approximately -3.5 to -4, and an apparent core with a core radius approximately 1 kpc. Clusters show a large dynamical range in many of their properties, more so for the core parameters (which are presumably more affected by dynamical evolution) than for the half-light parameters. There are no good correlations with luminosity, although more luminous clusters tend to be more concentrated. When data are binned in luminosity, several trends emerge: more luminous clusters tend to have smaller and denser cores. We interpret this as a differential survival effect, with more massive clusters surviving longer and reaching more evolved dynamical states. Cluster core parameters and concentrations also correlate with the position in the Galaxy, with clusters closer to the Galactic center or plane being more concentrated and having smaller and denser cores. These trends are more pronounced for the fainter (less massive) clusters. This is in agreement with a picture where tidal shocks form disk or bulge passages accelerate dynamical evolution of clusters. Cluster metallicities do not correlate with any other parameter, including luminosity and velocity dispersion; the only detectable trend is with the position in the Galaxy, probably reflecting Zinn's disk-halo dichotomy. This suggests that globular clusters were not self-enriched systems. Velocity dispersions show excellent correlations with luminosity and surface brightness. Their origin is not well understood, but they may well reflect initial conditions of cluster formation, and perhaps even be used to probe the initial density perturbation spectrum on a approximately 10(exp 6) solar mass scale. Core radii and concentrations play a role of a 'second parameter' in these correlations. While a global manifold of cluster properties has a high statistical dimensionality (D greater than 4), a subset of structural, photometric, and dynamical parameters forms a statistically three-dimensional family, as expected from objects following King models; we propose to call this set of quantities the King Manifold. Some of the observed correlations may be usable as distance indicator relations for globular clusters.

Clusters of atoms and molecules : theory, experiment, and clusters of atoms

Abstract: Clusters of Atoms and Molecules I is devoted to theoretical concepts and experimental techniques important in the rapidly expanding field of cluster science. Cluster properties are dicussed for clusters composed of alkali metals, semiconductors, transition metals, carbon, oxides and halides of alkali metals, rare gases, and neutral molecules. The book contains several well-integrated treatments, all prepared by experts. Each contribution starts out as simple as possible and ends with the latest results, so that the book can serve as a text for a course, an introduction into the field, or as a reference book for the expert.

Structural transitions in size-selected germanium cluster ions.

Abstract: Injected ion drift tube techniques have been used to probe the geometries of germanium cluster ions. Clusters with \ensuremath{\sim}(10-40) atoms appear to follow a one-dimensional growth sequence to give prolate geometries. At \ensuremath{\sim}40 atoms the clusters stop following this growth sequence, and clusters with \ensuremath{\sim}(40-70) atoms appear to retain roughly the same aspect ratio. At \ensuremath{\sim}70 atoms the clusters abruptly reconstruct to a more spherical geometry. Dissociation energies, measured for the germanium clusters, suggest that clusters with $nl70$ can be thought of as loosely bound assemblies of small strongly bound fragments (such as ${\mathrm{Ge}}_{7}$ and ${\mathrm{Ge}}_{10}$). It appears that the structural transition at \ensuremath{\sim}70 atoms may reflect a change to a more bulklike bonding arrangement.

Cooling flows and the X-ray luminosity–temperature relation for clusters

Abstract: The luminosity-temperature relation for clusters has a wide dispersion which has been explained as being due to a range of gas density or mass. We show here that the offset of a cluster from the mean relation is proportional to the strength of its cooling flow. We also confirm a similar effect on the metallicity-temperature relation. Since the cooling flow itself cannot produce such large effects, we propose that they are due to a more widespread difference between the intracluster media of cooling flow and non-cooling flow clusters. We suggest that the effects may be due to the inhomogeneity of the intracluster medium that is required in cooling flows to explain the distributed mass deposition. The effects have implications for the cluster temperature function and for the evolution of clusters

High-Resolution, Direct Infrared Laser Absorption Spectroscopy in Slit Supersonic Jets: Intermolecular Forces and Unimolecular Vibrational Dynamics in Clusters

Abstract: A long-standing goal in the field of cluster research has been to elucidate the transition between the properties of isolated monomer species in the gas phase and the corresponding properties in the condensed phase. Some of the most exacting methods of studying small clusters in this transition region are offered by high resolution spectroscopies (1-6), particularly in the nearand far-IR, which have succeeded in providing the first detailed glimpses of the quantum level structure that corresponds to both low frequency van der Waals motion and high frequency intramolecular motion in the molecular aggregates. In a very tangible sense, we are beginning to realize one of the long-standing dreams of the physical chem­ ist-that of watching molecules in the process of a collision by measuring

Dissociation pathways and binding energies of lithium clusters from evaporation experiments

Abstract: The unimolecular dissociation of energy rich lithium cluster ions shows that Li+n dissociate by sequential atom or dimer loss. The binding energies of Li+n (n=4–42) generated in an evaporative ensemble are determined from unimolecular decay, within a well defined time window, and energy constraint. They present a sawtooth behavior vs cluster size less pronounced that it should be from a simple metal model. Odd–even alternation is superimposed on the sawtooth behavior, with odd sized cluster ions being more stable. Cohesive energies per atom of Li+n are deduced from these dissociation energies up to n=40 and from extended photo‐induced measurements up to n=95. Cohesive energies per atom of neutral clusters Lin are derived by combining these ionic cohesive energies with the literature ionization potentials. The linearity of the neutral cluster cohesive energy vs the cluster surface to volume ratio permits a volume and a surface energy to be deduced. These values are compared to the bulk values.

Possible routes for cluster growth and particle formation in RF silane discharges

Abstract: After having distinguished five successive steps in the temporal evolution of a powder-forming SiH4 radiofrequency glow discharge, we examine the initial mechanism by which silicon clusters start growing up to the point where they suddenly aggregate into multiply charged particles and modify the discharge regime. This 'induction' period can be much longer than the diffusion time of positive ions and neutral radicals, which implies that cluster growth involves negative ions (anions). We provide a review of basic data concerning anions in SiH4 plasmas and analyse mass spectrometric data showing that anion-molecule reactions SinH2n+1-+SiH4 to Sin+1H2n+3-+H2 at relatively low rate (about 10-12 cm3 s-1), and fast exothermic anion-radical reactions SinHm-+SiHm' to Sin+1Hm+m'-2q-+qH2 at Langevin rates (about 10-9 cm3 s-1), initiate clustering. The effective anion lifetime involves a succession of dissociative attachment to SiH4, detachment or recombination, and attachment to neutral radicals or clusters competing with diffusion out of the plasma. Anion-molecule and anion-radical cluster reactions at Langevin rates probably dominate the cluster growth kinetics below 100 Si atoms whereas anion-neutral and neutral-neutral condensation at size-scaling collision rates govern the subsequent homogenous nucleation regime. At the end of the nucleation period (up to 104 Si atoms) the fraction of singly charged clusters can reach 50%. The reduction of powder formation upon gas heating is attributed to a decrease of the rate of non-dissociative attachment to radicals and neutral clusters.

Collision‐induced dissociation of Co+n (n=2–18) with Xe: Bond energies of cationic and neutral cobalt clusters, dissociation pathways, and structures

Abstract: The kinetic energy dependence of collision‐induced dissociation (CID) of Co+n (n=2–18) with xenon is studied by using a guided ion beam mass spectrometer. Examination of the general dissociation behavior over a broad collision energy range shows that cobalt cluster cations dissociate exclusively by loss of single atoms (cluster ‘‘evaporation’’), with no evidence found for elimination of molecular cluster fragments. Bond dissociation energies for cobalt cluster cations, Co+n (n=2–18), are determined from measurements of the CID thresholds. Bond energies for neutral cobalt clusters, Con (n=4–18), are derived by combining these cationic bond energies with ionization energies for Con from the literature. The dependence of binding energy on cluster size is similar to that observed for iron clusters, and inspires some speculation regarding cluster ion structures.

Free energy barriers to melting in atomic clusters

Abstract: We employ an order parameter approach to investigate melting in clusters bound by the Lennard‐Jones potential containing 13, 55, and 147 atoms. We find well‐defined Landau free energy barriers between solidlike and liquidlike states for the two larger clusters. A barrier is also revealed in an approximate analytical calculation using only information derived from the potential energy surface. For the two smaller clusters the order parameters are calculated for a large number of local minima. This helps us to interpret the Landau free energy calculations and to comment upon the suitability of the various order parameters for the cluster melting process. Systematic quenching offers us further insight into melting events for the 55‐atom cluster. Finally, we elaborate further upon the relationships between S‐bends and probability distributions in different ensembles.

Optical absorption spectra of au7, au9, au11, and au13, and their cations : gold clusters with 6, 7, 8, 9, 10, 11, 12, and 13 s-electrons

Abstract: The optical absorption spectra of a series of small gold clusters and their cations have been measured, between 1.9 and 5.6 eV, using a method based upon the photodepletion of a molecular beam of their van der Waals complexes containing one and two xenon atoms. This method provides size‐specific information even though the molecular beam contains a wide range of cluster sizes. There is little difference between the spectra of complexes containing one or two xenon atoms. However there is a pronounced odd–even alternation in the spectra of gold clusters with differing numbers of valence s electrons. This alternation is described in terms of a simple electron pairing scheme. The spectrum for Au13 is in reasonable agreement with Dirac scattered‐wave molecular orbital considerations for icosahedral Au13 [A. F. Ramos, R. Arratia‐Perez, and G. L. Malli, Phys. Rev. B 35, 3790 (1987)]. This description of the molecular and electronic structure of small gold clusters in terms of localized molecular orbitals is contrasted with other models based upon jellium potentials and delocalized excitations that have been used to describe small clusters of alkali metals and silver. The bonding in gold clusters is influenced by relativistic effects that increase the degree of sd hybridization in the molecular orbitals. Even though gold clusters can be described in this way, some evidence for electron shells is also presented. Thus, it is concluded that structural motifs other than jellium potentials can lead to shell structure in cluster properties.

Effective core potential‐configuration interaction study of electronic structure and geometry of small anionic Agn clusters: Predictions and interpretation of photodetachment spectra

Abstract: The ground state geometries of small anionic Ag−n(n=2–9) clusters were determined in the framework of the Hartree–Fock procedure employing a relativistic effective core potential (RECP) accounting for core–valence correlation (CVC) effects. Large scale configuration interaction (CI) calculations for 5s electrons only were carried out in order to determine the ground state energies of anionic and neutral species as well as of excited states of the latter in the geometries of the former. The calculated vertical detachment and excitation energies account for the observed photodetachment spectroscopic patterns and permit an assignment of the cluster geometries. Structural and electronic properties of small Ia and Ib anionic clusters are compared.

The development of the 3p and 4p valence band of small aluminum and gallium clusters

Abstract: Photoelectron spectra of Al−n and Ga−n clusters in the size range n=1–15 are presented. Using 5.0 and 3.68 eV UV light (KrF excimer and nitrogen laser, respectively), electrons from molecular orbitals corresponding to the 3p and 4p orbitals of the atoms are detached. The spectra reveal a rich fine structure not observed in earlier experiments. The data are compared with the results of quantum chemical calculations. A change in the pattern of the spectra near n=6 can be interpreted as a transition from planar to compact 3D structures. The spectrum of Al−13 agrees with the icosahedral structure predicted for this particle. The data do not agree with jellium model predictions. Differences between Al and Ga data can be correlated with the larger binding energy of the Ga 4s band.

Infrared laser spectroscopy of the linear C13 carbon cluster

Abstract: The infrared absorption spectrum of a linear, 13-atom carbon cluster (C13) has been observed by using a supersonic cluster beam-diode laser spectrometer. Seventy-six rovibrational transitions were measured near 1809 wave numbers and assigned to an antisymmetric stretching fundamental in the 1 sigma g+ ground state of C13. This definitive structural characterization of a carbon cluster in the intermediate size range between C10 and C20 is in apparent conflict with theoretical calculations, which predict that clusters of this size should exist as planar monocyclic rings.

Density functional study of phosphorus and arsenic clusters using local and nonlocal energy functionals

Abstract: Previous calculations of the structures of isomers of phosphorus clusters up to P11 (density functional calculations with simulated annealing, local spin density approximation to the exchange‐correlation energy) have been extended to arsenic clusters. The structures of Asn clusters are characterized by an almost uniform expansion (∼ 9%) of the corresponding Pn isomers. All cluster isomers have also been studied using a nonlocal, gradient corrected (Becke–Perdew) energy functional. While the structures are almost unchanged, there are significant improvements in the cohesive energies of all clusters. We present a simple picture to show that the improvements arise from contributions both in the atoms and near the ‘‘surface’’ of the clusters.

Evidence from Gravitational Lensing for a Non-Thermal Pressure Support in the Cluster of Galaxies A2218

Abstract: The central mass distribution of clusters of galaxies can be inferred from gravitationally lensed arcs with known redshifts. For the Abell cluster 2218, this method yields a core mass which is larger by a factor of $2.5 \pm 0.5$ than the value deduced from X-ray observations, under the assumptions that the gas is supported by thermal pressure and that the cluster is spherical. We show that a non-thermal pressure support is the most plausible explanation for this discrepancy. Such a pressure can be naturally provided by strong turbulence and equipartition magnetic fields ($\sim 50\mu$G) that are tangled on small spatial scales (<10 kpc). The turbulent and magnetic pressures do not affect the measured Sunyaev-Zel'dovich effect for this cluster. Intracluster magnetic fields with a comparable magnitude ($\sim 10^{1-2} \mu$G) have already been detected by Faraday rotation in other clusters. If generic, a small-scale equipartition magnetic field should affect the structure of cooling flows and must be included in X-ray determinations of cluster masses.