Showing papers on "Cluster (physics) published in 1971"
TL;DR: In this article, the potential energy surfaces for clusters of some three to sixty atoms under Lennard-Jones forces have been systematically explored using numerical optimization techniques, and three particularly compact non-lattice growth schemes emerge showing tetrahedral, pentagonal (D5 h ) and icosahedral symmetry respectively.
Abstract: The potential energy surfaces for clusters of some three to sixty atoms under Lennard-Jones forces have been systematically explored using numerical optimization techniques. In searching for minimum-energy configurations three particularly compact non-lattice growth schemes emerge showing tetrahedral, pentagonal (D5 h ) and icosahedral symmetry respectively. All these systems were found to be appreciably more stable than microcrystallites based on the face-centred cubic structure while certain lattice elements were shown to be metastable for small numbers of atoms. Some qualitative conclusions are then drawn concerning the occurrence of saddle-points for delocalized motion and the contribution of these to the generation of configurational entropy in small clusters. A crucial feature of the energy surfaces examined is the breakdown of strict local symmetry in compact clusters of more than two ‘shells’ of atoms and the possibility of delocalized motion of surface atoms around a solid-like core. The...
421 citations
TL;DR: In this article, the steady state rate of homogeneous nucleation in a vapor of Lennard-Jones spheres has been calculated using statistical mechanical techniques to compute the equilibrium concentrations of clusters in the vapor.
Abstract: The steady state rate of homogeneous nucleation in a vapor of Lennard‐Jones spheres has been calculated using statistical mechanical techniques to compute the equilibrium concentrations of clusters in the vapor. All degrees of freedom of the clusters are explicitly considered. The harmonic approximation is used in the calculation of vibrational contributions to the cluster partition functions and the rigid body approximation is used in the calculation of rotational contributions. The Gibbs free energy of cluster formation as a function of cluster size is calculated and its dependence on temperature is examined. Size effects on the vibrational free energy are found to be mainly energetic rather than entropic. The rate of nucleation as a function of pressure is calculated at four temperatures and found to have a behavior similar to what would be expected from “liquid drop” model calculations.
130 citations
125 citations
TL;DR: In this article, the authors describe the geometrical features of the clustering of small numbers of interacting particles, and present an approach that is quite different from others which consider the problem as one of finding dense packings of spheres.
Abstract: This article describes the chief geometrical features of the clustering of small numbers of interacting particles. The approach is quite different from others which consider the problem as one of finding dense packings of spheres.
76 citations
TL;DR: It is shown that cholesterol inhibits the chain motion of lecithin above its gel-liquid crystal transition temperature (T,), completely removing the transition when present in equimolar quantities.
71 citations
TL;DR: In this paper, the influence of crystal growth conditions on the formation of vacancy clusters was studied. But vacancy clusters could not be detected in crystals grown by floating zone technique. And the authors proposed methods for the prevention of vacancy cluster formation during growth, based on a nucleation model.
Abstract: In dislocation‐free silicon crystals grown by the floating‐zone technique vacancy clusters are formed. The influence of crystal growth conditions on the cluster formation is studied. Methods for the prevention of vacancy cluster formation during growth, based on a nucleation model, are discussed. In crystals grown by one of these methods vacancy clusters could not be detected.
68 citations
54 citations
TL;DR: In this paper, the applicability of the extended Huckel method for the calculation of the electronic properties of point defects in diamond-type crystals is discussed and the results obtained depend upon the size of the cluster chosen and the approximations made at the boundary of the system Clusters with up to 47 host lattice atoms are considered.
Abstract: The applicability of the extended Huckel method for the calculation of the electronic properties of point defects in diamond-type crystals is discussed A detailed study of the isolated vacancy in both the diamond and silicon lattice shows that the results obtained depend upon the size of the cluster chosen and the approximations made at the boundary of the system Clusters with up to 47 host lattice atoms are considered A cluster of 41 atoms, which includes all atoms directly bonded to the second neighbours from the point defect, is considered to be the most suitable system On the basis of a comparison of ab initio and extended Huckel calculations for small molecules, it is argued that studies involving distortions are beyond the validity of the simple method used here At best, the results from extended Huckel studies for point defects in diamond type crystal should be considered to be semiquantitative
51 citations
Nera1
TL;DR: In this article, a way to deal with cluster effects in disordered alloys is given through an extension of the coherent-potential-approximation theory, and an explicit expression is derived for pair effects and is shown to give the exact ${c}^{2}$ term in the lower concentration limit.
Abstract: A way to deal with cluster effects in disordered alloys is given through an extension of the coherent-potential-approximation theory. An explicit expression is derived for pair effects and is shown to give the exact ${c}^{2}$ term in the lower concentration limit.
41 citations
41 citations
TL;DR: In this article, a generalized Einstein model was developed for calculating the thermodynamic properties of small crystalline clusters of atoms, and the validity of the model was established through molecular dynamics calculations by Dickey and Paskin.
Abstract: We develop a generalized Einstein model for calculating the thermodynamic properties of small crystalline clusters of atoms. The validity of the model is established through the molecular dynamics calculations by Dickey and Paskin and the numerical normal mode analysis by Burton for certain cluster packings. The rapid computational procedure and low computer storage requirements for our model calculations enable us to easily compute thermodynamic quantities for cluster configurations and sizes beyond those previously studied. Polyhedron cluster packings and “approximately spherical” cluster packings are used to generate clusters of various configurations. The Einstein theory is used to study the Helmholtz free energy, vibrational energy, and entropy for the various cluster configurations and for cluster sizes up to ∼ 1000 atoms. The model calculations are compared with the predictions based on the capillarity approximation used in nucleation theory. The simplicity of the method enables one to calculate th...
TL;DR: In this article, the authors showed that the cluster system [(π-C5H5)FeS]4 remains intact in the oxidation states +3, +2, +1, 0, and 1.
Abstract: Electrochemical studies indicate that the cluster system [(π-C5H5)FeS]4 remains intact in the oxidation states +3, +2, +1, 0, and –1 and [(π-C5H5)Fe(CO)]4 in the oxidation states +2, +1, 0, and –1.
TL;DR: In this article, the electrical properties of liquid In-S and Tl-Te mixtures are examined in the light of a cluster model, consisting of small "semiconducting" clusters mixed up with highly conducting random liquid.
Abstract: The electrical properties of liquid In-S and Tl-Te mixtures are examined in the light of a cluster model, consisting of small 'semiconducting' clusters mixed up with highly conducting random liquid. It is found that this model can account for all the electrical properties, and is also applicable to other systems including semiconducting glasses. Evidence on contactless electrical conductivity measurements on glasses tends to support the model.
TL;DR: In this paper, the coordination behavior of the cluster is determined by the apical substituent Y, and the stereochemistry adopted is one which minimizes nonbonded carbonyl interactions.
Abstract: Mono-, di-, and tri-substituted tertiary phosphine and arsine derivatives of methinyltricobalt enneacarbonyls have been prepared The co-ordination behaviour of the cluster is determined by the apical substituent Y, and the stereochemistry adopted is one which minimizes nonbonded carbonyl interactions Thus the majority of mono-substituted complexes have the same structure as MeCCo3(CO)8Ph3P but other MeCCo3(CO)8L compounds adopt a carbonyl-bridged configuration Di- and tri-substituted complexes also have a bridged structure Different types of structural isomerism in solution have been identified
IBM1
TL;DR: In this paper, the authors compared the surface potential energy of different geometrical packings by presenting the dependence of the surface energy for microcrystallites of spherical atoms as a function of the cluster size, cluster packing and interaction range.
TL;DR: In this article, it was shown that the leading low-temperature behavior of the nth cluster coefficient can be calculated without sloving the $n$-body problem, and that there is a $\mathrm{ln}T$ term in the expansion.
Abstract: We show that the leading low-temperature behavior of the nth cluster coefficient ${b}_{n}$ can be calculated without sloving the $n$-body problem, and that there is a $\mathrm{ln}T$ term in the expansion. We illustrate these results particularly for the case of ${b}_{3}$.
TL;DR: In this article, the solvent dependence of nuclear spin coupling constants is studied in terms of a model which assumes a cubic closest packed cluster in which six solvent molecules are arranged around the solute molecule.
Abstract: A theoretical study of the solvent dependence of nuclear spin—spin coupling constants is presented in terms of a model which assumes a cubic closest packed cluster in which six solvent molecules are arranged around the solute molecule. This model is described theoretically by means of a group function modification of self‐consistent perturbation theory. Calculations for individual molecular groups were performed by the semiempirical INDO (intermediate neglect of differential overlap) approximation of self‐consistent‐field molecular orbital theory. Intermolecular integrals associated with solute and solvent molecules were evaluated theoretically. This model provides some improvement over the previous theoretical study in this series, which was based on the reaction field model. The improvement can be attributed to the inclusion of electrostatic effects arising from the real charge distributions of the solvent molecules, especially those which are perpendicular to the solute dipole moment axis. A most impor...
TL;DR: In this paper, the angular and energy distributions in the λ 7 Li → 4 He + 3 He + π − decay were calculated with the use of the initial wave function φ(τ-t-Λ).
TL;DR: In this paper, the self-diffusion coefficient of an isotropic fluid is obtained by means of a cluster expansion of the resolvent operator corresponding to the Liouville operator for the system.
Abstract: A density series of the autocorrelation function for the self‐diffusion coefficient of an isotropic fluid is obtained by means of a cluster expansion (different from that used by Ernst, Haines, and Dorfman) of the resolvent operator corresponding to the Liouville operator for the system. Nonsingular potentials are assumed for the interaction potential between pairs of the particles. It is shown that the self‐diffusion coefficient, and thus transport coefficients in general, can be put into a form similar to that of equilibrium statistical mechanics, when the resolvent operator is expanded in terms of clusters just as the configuration integral is expanded in terms of the cluster integrals in equilibrium statistical mechanics. The cluster functions may also be expanded into irreducible cluster functions. This decomposition of the clusters into the irreducible clusters is derived from the integral equations for the collision operators corresponding to the clusters, and makes it possible to establish formall...
TL;DR: In this paper, the authors confirmed the existence of a new system of acetato-complexes containing the oxygen-centred triangle Ru3O which may undergo reversible reduction reactions.
Abstract: X-ray diffraction and other studies have confirmed the existence of a new systems of acetato-complexes containing the oxygen-centred triangle Ru3O which may undergo reversible reduction reactions.
TL;DR: In this paper, a size-dependent Gibbs-Thomson equation is proposed for Wulff polyhedra, which results in pr, σ≫Pr, and renders the Gibbs Thomson equation increasingly inaccurate for r < 30 A. The authors concluded that the atomistic theory describes more reliably the formation of nuclei consisting of only a few atoms.
TL;DR: In this article, a soft core central potential is used to calculate independently 6Li ground state and excited state wave functions in the refined cluster model and charge density, elastic formfactor and transition formfactor to the 3+ state are derived and agree reasonably well with experiment.
Abstract: A soft core central potential is used to calculate independently6Li ground state and excited state wave functions in the refined cluster model. Charge density, elastic formfactor and transition formfactor to the 3+ state are derived and agree reasonably well with experiment.
TL;DR: The Hall resistivity of polycrystalline samples of Au Fe, Ag Mn, Cu Fe and Cu Mn shows to varying degrees a contribution which at 4.2°K saturates in a few kG as mentioned in this paper.