Showing papers on "Cluster (physics) published in 1976"

Structural and Bonding Patterns in Cluster Chemistry

Abstract: Publisher Summary This is one of two articles in this volume that is concerned with the borane-carborane structural pattern. In the other, Williams has shown how the pattern reflects the coordination number preferences of the various atoms involved. The purpose of the present article is to note some bonding implications of the pattern, and to show its relevance to a wide range of other compounds, including metal clusters, metal-hydrocarbon 7∼ complexes, and various neutral or charged hydrocarbons. Boranes and carboranes may be regarded as cluster compounds in the sense defined by Cotton; they contain a finite group or skeleton of atoms held together entirely, mainly, or at least to a significant extent by bonding directly between those atoms, even though some other atoms may be associated intimately with the cluster. Examples of their structural pattern, however, can be found far beyond the confines of what is normally regarded as cluster chemistry, so this survey includes many systems not commonly referred to as clusters.

Energy spectra of X-ray clusters of galaxies

Abstract: A procedure for estimating the ranges of parameters that describe the spectra of X-rays from clusters of galaxies is presented. The applicability of the method is proved by statistical simulations of cluster spectra; such a proof is necessary because of the nonlinearity of the spectral functions. Implications for the spectra of the Perseus, Coma, and Virgo clusters are discussed. The procedure can be applied in more general problems of parameter estimation.

A cluster model for the transition from the short-range order to the long-range order state in f.c.c. based binary systems and its study by means of electron diffraction

Abstract: The 'transition' state in binary f.c.c. based systems is assumed to be characterized by the repetition of interpenetrating polyhedral clusters of atoms occupying lattice sites and having the macroscopic composition. Its mathematical formulation leads to relations between the short-range order (SRO) coefficients, which in turn impose conditions on the distribution in reciprocal space of the diffuse intensity as observed in electron diffraction patterns. It follows that for a given cluster type the diffuse intensity can only differ from zero along certain surfaces or curves. The effect of deviations from the ideal composition of the clusters is briefly discussed. The theory allows an explanation of available diffraction data on certain binary alloys in the initial stages of ordering i.e. in the 'transition' state between the SRO state and the long-range order (LRO) state.

Aggregation effect on the infrared absorption spectrum of small ionic crystals

Abstract: The frequency spectrum of clusters of small ionic particles is calculated when the particle mutual interaction is described by a dipole-dipole interaction Hamiltonian. The crystallites are spheres of known bulk dielectric properties. The actual geometry of the cluster is taken into account. Clusters of increasing size (pair, triplet, quadruplet, etc.) have been solved analytically. As expected, the dipolar broadening of the frequency spectrum of (optically active or inactive) surface modes increases with cluster size and compactness. From the spectrum of few-particle clusters, one obtains the long-wavelength modes of large linear or planar aggregates of such clusters by application of the Bloch-Floquet theorem.Application is made to ir optical absorption of NiO. The present approach is intermediate between the continuum model of a structureless powder on the one hand and microscopic calculations for single microcrystals of prescribed shape on the other hand.

Molecular-orbital calculations on cluster compounds of gold

Abstract: Molecular-orbital calculations on [Au6]2+ and [Aug9]3+ clusters have shown that the overlap of the gold 6s orbitals makes a dominant contribution to the bonding. Co-ordination of ligands to these ‘ bare ’ metal clusters encourages a more favourable hybridisation of the metal orbitals and results in stronger radial metal–metal bonding. The electronic factors responsible for the breakdown of the Polyhedral Skeletal Electron Pair rules when applied to the gold clusters are discussed.

Electron correlation in small metal clusters. Application of a theory of self‐consistent electron pairs to the Be4 system

Abstract: A knowledge of the properties of small metal particles is essential to the understanding of catalysis on a molecular level. In this regard, one particularly important property is the rate at which the dissociation energy of a small metal cluster approaches the bulk cohesive energy. The present research concerns the effect of electron correlation on the dissociation energy of a particularly stable beryllium cluster, the tetrahedral Be4 system. A contracted Gaussian basis set of size Be(9s 4p/5s 2p) was adopted in conjunction with the recently developed theory of self‐consistent electron pairs (SCEP). Several new theoretical and computational wrinkles are discussed, including the incorporation of the SCEP/coupled electron pair approximation (SCEP/CEPA). The Be4 results provide strong evidence for the reliability of the Hartree–Fock approximation for alkaline earth cohesive energies. As suggested earlier the Be4 dissociation energy appears to be ∼40 kcal/mole. Analogous studies of the Be2 molecule are reported.

Structures, binding energies, and charge distributions for two to six atom Ti, Cr, Fe, and Ni clusters and their relationship to nucleation and cluster catalysis

Abstract: In a low spin molecular orbital approximation, binding energies and optimized structures for various two to six atom clusters of Ti, Cr, Fe, and Ni are calculated. Ti, with few d electrons, shows a preference for tightly packed clusters with positively charged corner atoms while Ni favors open and ringlike clusters with negatively charged corner atoms; Cr and Fe, with nearer to half‐filled d shells, prefer tightly packed configurations, but charge distributions are less predictable. The parameterization and spin models used in the theoretical procedure are considered. The binding energies, structures, and charge distributions are discussed in relation to transition metal cluster catalysis and experimental Fe nucleation studies. The photoemission spectra for O and CO on a nine atom Fe (100) model cluster are calculated and are found to be similar, within calculational and experimental resolution, to those for the Fe(100) surface.

Percolation and Cluster Distribution. I. Cluster Multiple Labeling Technique and Critical Concentration Algorithm

Abstract: A new approach for the determination of the critical percolation concentration, percolation probabilities, and cluster size distributions is presented for the site percolation problem The novel "cluster multiple labeling technique" is described for both two- and three-dimensional crystal structures Its distinctive feature is the assignment of alternate labels to sites belonging to the same cluster These sites are members of a simulated finite random lattice An algorithm useful for the determination of the critical percolation concentration of a finite lattice is also presented This algorithm is especially useful when applied in conjunction with the cluster multiple labeling technique The basic features of this technique are illustrated by applying it to a small planar square lattice Numerical results are given for a triangular subcrystal containing up to 9 000 000 sites These results compare favorably with the exact value of the infinite lattice critical percolation concentration

Migration of platinum adatom clusters on tungsten (110) surfaces

Abstract: Field-ion microscopy was used to study the migration of individual adatoms and clusters of two, three and four platinum adatoms over tungsten (110) surfaces. Mobility decreased with increasing cluster size and the activation energies for motion were 65+or-6 kJ mol-1 for Pt and Pt2, 77+or-15 kJ mol-1 for Pt3 and 84+or-15 kJ mol-1 for Pt4. The probability of reorientation in observable elementary displacements was high (0.67) for Pt2 and low (<0.1) for the linear-chain clusters Pt3 and Pt4. It is shown that with physically reasonable assumptions about the energies of unobserved cluster configurations, sequential movement of one adatom at a time accounts satisfactorily for the two-dimensional migration of the clusters.

Molecular dynamics study of the effects of ions on water microclusters

Abstract: We report a molecular dynamics study of water ion microclusters. This study concerns clusters containing Na+, Rb+, Br−, and I− and up to eight water molecules, and larger clusters containing Cs+ and F− and up to 29 water molecules. For each cluster we calculated the total cluster energy, radial density functions, dipole orientations of water molecules around the ion, and effective ionic radii. The ion lowers the cluster energy by a considerable amount, depending to a great extent on the ionic radius. The ion strongly orients all of the water molecules in the cluster. The coordination numbers of the ions depend primarily on ion size and to a lesser extent on charge sign. Our calculated effective ionic radii are in reasonable agreement with the Pauling radii.

Linear and nonlinear relaxation and cluster dynamics near critical points

Abstract: The critical slowing down of anisotropic magnets, binary mixtures, and systems undergoing structural transitions is interpreted in terms of suitable defined “clusters,” their growth, and their motions (cluster reactions, cluster diffusion, and cluster waves). Our previous studies of the Glauber model are extended considerably by numerical calculations, including the use of the cluster model of Reatto and Rastelli. The behavior of the relaxation function is very insensitive to the details of the models used. A scaling theory of nonlinear response is given, which is far more general than the cluster dynamics treatment. Two different cases occur:(i) at fixed “relative nonlinearity” the critical exponents agree with the corresponding exponents of linear response; (ii) if the initial state is held fixed, different exponents are found, however, which agree with predictions of Racz, and are consistent with Monte Carlo simulations of the nonlinear slowing down of the energy in kinetic Ising models.

X-Ray structures of the hexanuclear cluster complexes [Os6(CO)18]2–, [HOs6(CO)18]–, and [H2Os6(CO)18]

Abstract: X-Ray analyses of three osmium cluster complexes has shown that two, [Os6(CO)18]2– and [HOs6-(CO)18]–, have the approximately regular octahedral structure expected for hexanuclear clusters with 86 valence electrons, but the third, [H2Os6(CO)18], has an unusual monocapped square-pyramidal Os6 arrangement.

Cluster statistics of the lattice gas model in three and two dimensions

Abstract: Cluster statistics in the lattice gas system were evaluated in three dimensions (d=3) below the critical point, and in two dimensions (d=2) above Tc using a Monte Carlo method Defining clusters as sets of l particles connected by nearest‐neighbor bonds, we found remarkable deviation from semiphenomenologic cluster probability formulas below Tc This deviation is attributed to the formation of spongelike noncompact macroclusters near the percolation temperature Tp

Effects of the local configuration on the lattice dynamics of group-IV semiconductors

Abstract: In order to investigate the relative importance of short‐range order and local topology in determining the vibrational properties of group IV semiconductors, we introduce a cluster Bethe lattice method. A cluster of atoms with any desired configuration is treated exactly. The rest of the system is treated within the Bethe Peierls Approximation, which retains the short‐range tetrahedral order. Main features of perfect crystaol density of states are already present in small clusters. A few cases of effects of disorder are studied.

Applications of the Bargmann-Segal transform to nuclear systems of complex clusters

Abstract: The description of the harmonic oscillator cluster model in Bargmann-Segal space is generalized to allow for clusters of different oscillator width and complex clusters. Compact explicit expressions amenable to numerical computation and analytic handling are derived for the interaction kernels of clusters.

Comparison of the Large Unit Cell and Small Periodic Cluster Approaches to the Quasimolecular Calculations of the Band Spectra of Crystals

Abstract: Two recently developed quasimolecular approaches to the calculation of the band spectra of crystals are compared: the “Large Unit Cell” model and the model of “Small Periodic Cluster”. It appears that the first model has an essential advantage allowing to confine by relatively small quasimoleocules in cases where the second model appears to be impracticable. As examples KCl and layered hexagonal BN crystals are considered. [Russian Text Ignored].

On the cluster size distribution for critical percolation

Abstract: A Monte Carlo study of clustering in the vicinity of the critical percolation probability pc has been carried out on the body-centered cubic lattice in which both first- and second-neighbour sites were counted. The total number of clusters shows an inflection point when plotted against concentration of occupied sites in the vicinity of pc suggesting that a characteristic of pc may be a maximum rate of loss of clusters due to aggregation. An empirical form for the cluster size distribution in the critical region has been found which matches the present data as well as previous results on other lattice geometries obtained by Dean and Bird (1966). At large cluster sizes the distribution at pc becomes asymptotically an inverse power law with exponent slightly larger than two. An argument is presented which related this exponent to the linear extent of the cluster.