Small Atomic Clusters Research Articles

Random walk of single atoms and small atom-clusters on solid surfaces

Using atomic resolution microscopy, it is now possible to observe directly discrete random walks of single atoms and small atom-clusters, nucleation and dissociation of clusters and surface layers, etc. on solid surfaces. Such information is needed for understanding atomic interactions, mechanisms of growth of thin films and crystals, and the dynamic behavior of surfaces. In this type of experiment, data analysis is very direct without the need of relying on uncertain physical modeling. For analyzing data, all we need usually are some of the equations available in mathematical theory of random walks. Some of the mathematical problems we still have to solve are the finite size effect of the small surfaces, how the jump length distribution of the atomic jump is related to the mean square displacement and displacement distribution, and how the random walk of a simple cluster is related to the coupled but otherwise still random jumps of each of the atoms in the cluster, etc. In the past, one focused on equilibrium statistics of infinite systems and their universal behavior. Recent interest shifts to small and steady state systems where fiite size and quantum effects are important. They may exhibit universal behavior also.

Tensor LEED for the approximation of nondashspherical atomic scattering

We present a new approach to consider nondashspherical atomic charge densities for the computation of intensities in low energy electron diffraction (LEED). This might be important for covalently bonded atoms for example in adsorbed molecules, semiconductors or compound materials. In a first step the nondashspherical charge distribution of a surface atom is approximated by Hartree-Fock calculations applied to a small atomic cluster surrounding the atom under consideration. Then, starting with a LEED reference calculation for spherical scatterers as usual, the deviation from the spherical charge distribution is taken into account by means of the corresponding change of the atomic scattering matrix which becomes nondashdiagonal. Eventually, this is made to enter the perturbation scheme tensor LEED. This procedure allows easy access to trial structures with realistic atomic scattering. We applied the method to an example of practical importance, i.e. to the unreconstructed Si(100) surface. A rough estimation neglecting multiple scattering between the nondashspherical and spherical part of the atomic potential proves, however, that the influence of nondashspherical scattering on intensities in a typical energy range (20–150 eV) is practically negligible.

Dynamic behaviour of a small atomic cluster on an Ir(001) surface

Abstract The dynamic behaviour of small atomic clusters consisting of eight atoms and ten atoms on an Ir(001) surface has been studied using a field ion microscope. It has been found that eight-atom and ten-atom clusters are energetically favoured to form ring configurations with central lattice vacancies in the clusters. The fact that the atomic-ring configurations with fewer nearest-neighbour bonds are more thermally stable than those dense cluster structures with more nearest-neighbour bonds demonstrates convincingly the general believed non-additivity of bond energies at the metal surface.

Electrochemical characteristics of LaNi 4.7Al 0.3 alloy activated by alkaline solution containing hydrazine

The electrochemical characteristics of LaNi 4.7Al 0.3 alloy treated with an alkaline solution containing hydrazine (N 2H 4·H 2O) have been investigated under various treatment conditions. Hydrazine solution can activate LaNi 4.7Al 0.3 alloy effectively to attain high initial discharge capacity at fast charge and discharge rates and at low polarization. The treated electrode has initial capacity C 0 before charging. In alkaline media the alloy surface disproportionates into La(OH) 3 and small clusters of Ni atoms which posses high catalytic activity. The strong reducing agent N 2H 4 is beneficial to maintain the high catalytic activity.

Nanodispersed silicon in pregraphitic carbons

Using chemical-vapor deposition nanodispersed silicon has been prepared in carbon at temperatures between 850 and 1050 °C. Samples with up to 11% atomic silicon in carbon show the same pregraphitic x-ray-diffraction pattern as those without silicon. X-ray-absorption spectroscopy shows that the silicon is bonded mostly to carbon neighbors and that large clusters of silicon are not found. It is believed that silicon atoms, or small clusters of a few silicon atoms, are located in regions of ‘‘unorganized carbon’’ which separate small regions of organized graphene layers. These materials may have application as electrode materials in advanced rechargeable lithium batteries.

Two-particle correlations in finite low-dimensional Hubbard-like lattices

The ground-state properties of two particles (or two holes) with different masses in finite low-dimensional lattices with periodic boundary conditions is investigated rigorously in a Hubbard-like model with external field. A sufficient strong field results in ferromagnetic ordering, and we found the conditions, when the creation of two holes near half-filling for hypercubes in d = 1, 2, 3 dimensions with even numbers of atoms (for bipartite lattices) and with odd numbers of atoms (for non-bipartite lattices), leads to instability of the ferromagnetic Nagaoka state against spin-flip in the strong interaction limit. The criteria for ferromagnetic stability in lattices consisting of different numbers (odd or even) of particles and lattice sites are also found and represent a qualitative explanation of the strong spontaneous ferromagnetism sometimes seen in small clusters of atoms, such as in rhodium.

The effects of heat treatment and purity on the mechanical properties of monocrystalline NiAl

The yield stress, σ y, strain to fracture, ε f, and thickness-compensated fracture load of monocrystalline NiAl were investigated as functions of purity, annealing treatment and cooling rates. A miniaturized disk bend test was employed to test disks 3 mm in diameter and approximately 250 μm thick. Specimens in the soft (110) orientation from commercial purity (CP) and high-purity (HP) alloys were tested. The annealing treatments affected σ y more strongly than the other mechanical properties. The yield stresses of both of the as-received alloys increased significantly after annealing at 1300 °C followed by furnace cooling. Subsequent annealing at 400 °C for 2 h resulted in a reduction of σ y. This behavior is attributed to the role of excess vacancies retained during cooling, which annealed out at the lower temperature. The mean values of the yield strength also tended to decrease with increasing cooling rate from 400 °C, but the effect was small. A substantial increase in σ y of the CP alloy was found on prolonged aging at 400 °C, whereas σ y of the HP alloy was unaffected. We attribute this behavior to the precipitation of very small particles or solute atom clusters in the CP alloy. The ductility of the CP alloy, and the thickness-compensated fracture loads of both alloys, were relatively insensitive to the heat treatments.

An FIM and STM study of the dynamical behavior of solid surfaces

Atoms at the surface are by no means static. When the temperature of a solid is increased gradually, surface atoms may start to dissociate from their lattice sites and diffuse on the surface around or slightly above the room temperature. This diffusion involves with single adatoms on terraces and ledge atoms along lattice steps. It may involve with small atomic clusters or even large islands. At a higher temperature, collective effects may become important and step as well as surface roughening, structure phase transitions and collective movements of surface atoms may start to occur. A similar behavior can occur for atoms condensed on the surface. This dynamical behavior of the solid surface can be described by the occurence of a series of elementary atomic processes or steps which are common to different surface phenomena involving the transport and movement of surface atoms. These phenomena include epitaxial growth of thin films, crystal growth, changes of the shape of crystals and surface layers, surface atomic reconstructions, and surface enhanced chemical reactions, etc. We have been studying in atomic details both the mechanisms and energetics of various surface atomic processes using the field ion microscope. Recently we have also started to use the scanning tunneling microscope and molecular dynamics to study the same problem. Our very recent works include finding a new atomic-exchange-displacement mechanism in adatom diffusion on the Ir(001) and the formation as well as two diffusion modes of and Ir-Re dimer-vacancy complex on the Ir(001). We have also measured the dissociation energies of step edge atoms at the Ir(001), binding energies of Ir atoms in kink sites and adsorption sites of the Ir(001) surface, and the formation energies of single- and di-vacancies at the Si(111) (7 × 7) surface etc. Details of these studies can be found in the papers listed in the references below and some of our upcoming papers. These works were done in collaboration with Chonglin Chen, Jiang Liu, C.S. Chang, R.L. Lo and others

Study of Oxygen Diffusion and Clustering in Silicon Using an Empirical Interatomic Potential

AbstractThe diffusion path and diffusivity of oxygen in crystalline silicon are computed using an empirical interatomic potential which was recently developed [1] for modelling the interactions between oxygen and silicon atoms. The diffusion path is determined by constrained energy minimization, and the diffusivity is computed using jump rate theory. The calculated diffusivity D=0.025 exp(-2.43eV/kBT) cm2/sec is in excellent agreement with experimental data. The same interatomic potential also is used to study the formation of small clusters of oxygen atoms in silicon. The structures of these clusters are found by NPT molecular dynamics simulations, and their free energies are calculated by thermodynamic integration. These free energies are used to predict the temperature dependence of the equilibrium partitioning of oxygen atoms into clusters of different sizes. The calculations show that, for given total oxygen concentration, most oxygen atoms are in clusters at temperature below 1300K, and that the average cluster size increases with decreasing temperature. These results are in qualitative agreement with the effects of thermal annealing on oxygen precipitation in silicon crystals.

Melting of (Ar-Xe)13 Clusters: Surface-Core Effects

Potential energy fluctuations in the liquid phase of small atomic clusters (e.g. Ar 13 ) have been seen to have long-range temporal correlations. This is manifest in a power-law decay for the power spectrum, which has a characteristic 1/f dependence on the frequency,f. (More precisely, the dependence is 1/f(alpha), with alpha approximate to 1.) In order to understand the origin of this behavior, we study the melting of mixed rare-gas clusters Ar 12 Xe and Xe 12 Ar (via molecular dynamics simulations). Substitution of atomic impurities introduces widely differing time scales in the dynamics, and we show that long-lived memory-effects have their origins in hierarchical relaxation processes arising in the motion of the atoms from the surface to the core and vice versa.

Scanning tunnelling microscopy observations of the evolution of small-scale topography on gold surfaces following irradiation with low-energy argon ions

Abstract Room-temperature irradiation of atomically flat gold films has been observed, using scanning tunnelling microscopy, to give rise to small faceted islands and pits (about 10 nm in lateral dimension and a few monolayers in height) which subsequently evolve by surface diffusion over a period of hours. The evolution on grains with different surface orientations is observed to be markedly different and, in particular, on what appears from symmetry consideration to be a (100) grain, the surface features are apparently in dynamic equilibrium under irradiation and subsequently thermally dissociate by the emission of small mobile clusters of atoms.

Cluster-solid interactions: A molecular dynamics investigation

Abstract The interaction of small energetic clusters of metal atoms with surfaces has been investigated by molecular dynamics computer simulations. A wide variety of cluster-solid combinations have been studied so that the effects of the energy, size, and angle of incidence of the cluster, and the relative elastic properties of the cluster and substrate could be elucidated. ‘Soft landings’ were also investigated. From these studies, a mechanism map for cluster-solid interactions is developed. The results have particular importance for cluster beam deposition of thin films. The simulations are fully dynamical and 3-dimensional; they employ embedded-atom method potentials, which have been modified for interactions at close separations. A scheme for reducing the CPU time that is required for these and other simulations of radiation effects is described.

Angular momentum stability of small atomic clusters

The limits of stability of small atomic clusters with angular momentum are investigated as a function of the size and charge of the aggregates. Critical angular momenta are obtained in a di-cluster picture from the balance of a cohesive surface-surface interaction and the disruptive centrifugal and electric interactions. The calculation scheme incorporates the mass and charge asymmetry degrees of freedom and it is thus particularly suited to explore cluster-cluster reaction processes. Deformation of the fragments is taken into account.

The ?-? phase transition in AlPO4 cristobalite: Symmetry analysis, domain structure and transition dynamics

Despite their crystallographic differences, the mechanisms of the α-β phase transitions in the cristobalite phases of SiO2 and AlPO4 are very similar. The β→α transition in AlPO4 cristobalite is from cubic (\(\left( {F\bar 43m} \right)\)) to orthorhombic (C2221), whereas that in SiO2 cristobalite is from cubic (\(\left( {Fd\bar 3m} \right)\)) to tetragonal (P43212 or P41212). These crystallographic differences stem from the fact that there are two distinct cation positions in AlPO4 cristobalite as opposed to one in SiO2 cristobalite and the ordered (Al,P) distribution is retained through the phase transition. As a result, there are significant differences in their crystal structures, domain configurations resulting from the phase transition and Landau free energy expressions. A symmetry analysis of the “improper ferroelastic” transition from \(F\bar 43m \to C222_1\)in AlPO4 cristobalite has been carried out based on the Landau formalism and the projection operator methods. The six-component order parameter, η driving the phase transition transforms as the X5 representation of \(F\bar 43m\)and corresponds to the simultaneous translation and rotation of the [AlO4] and [PO4] tetrahedra coupled along 110. The Landau free energy expression contains a third order invariant, the minimization of which requires a first-order transition, consistent with experimental results. The tetrahedral configurations of twelve α phase domains resulting from the β→α transition in AlPO4 cristobalite are of two types: (1) transformation twins from a loss of the 3-fold axis, and (2) antiphase domains from the loss of the translation vectors 1/2[101] and 1/2[011] (F→C). In contrast to α-SiO2 cristobalite, the α-AlPO4 cristobalite (C2221) does not have chiral elements (43, 41) and hence, enantiomorphous domains are absent. These transformation domains are essentially macroscopic and static in the α phase and microscopic and dynamic in the β phase. The order parameter, η couples with the strain components, which initiates the structural fluctuations causing the domain configurations to dynamically interchange in the β phase. An analysis of the MAS NMR data (29Si, 17O, 27Al) on the α α-β transitions in SiO2 and AlPO4 cristobalites (Spearing et al. 1992, Phillips et al. 1993) essentially confirms the dynamical model proposed earlier for SiO2 cristobalite (Hatch and Ghose 1991) and yields a detailed picture of the transition dynamics. In both cases, small atomic clusters with the configuration of the low temperature α phase persist considerably above the transition temperature, T0. The NMR data on the β phases above T0 cannot be explained by a softening of the tetrahedral rotational and translational modes alone, but require the onset of an order-disorder mechanism resulting in a dynamic averaging due to rapidly changing domain configurations considerably below T0.

Complex dynamics of atomic clusters

Potential energy fluctuations in small atomic clusters have long-ranged temporal correlations, which lead to l/f noise in the power spectra. The relaxation dynamics in clusters has a hierarchical organization, resulting from different processes at the surface and core. A cellular dynamical model is proposed to understand the origin of such fluctuations.

The partition functions and thermodynamic properties of small clusters of rare gas atoms

The partition functions Z(T) for the clusters Arn, Krn, and Xen (n=2, 3, and 4) were calculated with the smoothed density of energy levels ρ(E). The latter was determined in the semiclassical approximation by Monte Carlo integration over the phase space and corrected by the rotational asymptotic for the lowest levels and by the trajectory separation method for the bound states above the dissociation threshold. In the temperature range of 5<T<150 K that is of crucial interest for the cluster formation studies in the supersonic jets, the results have an estimated accuracy of about 5%. The structure of the phase space of tetramer (n=4) clusters and their conformational transition dynamics were studied. The possibility of a link between such transitions and clusters melting is discussed.

Structure and Performance of Carbon Aerogel Electrodes

ABSTRACTThe chemistry and physics of small clusters of atoms (1-100 nm) has received considerable attention in recent years because these assemblies often have properties between the molecular and bulk solid-state limits. The different properties can be explained in terms of the large fraction of atoms that are at the surface of a cluster as compared to the interior. Although the synthesis and properties of metal and semiconductor clusters, metallocarbohedrenes, fullerenes, and nanotubes are the subject of extensive investigations, little attention has been paid to cluster-assembled porous materials. This oversight is of particular interest to us since we believe that aerogels are one of the few monolithic materials presently available where the benefits of cluster assembly can be demonstrated. In particular, the unique optical, thermal, acoustic, mechanical, and electrical properties of aerogels are directly related to their nanostructure, which is composed of interconnected particles (3-30 nrm) with small interstitial pores (< 50 nm). This structure leads to extremely high surface areas (400-1100 m2/g) with a large fraction of the atoms covering the surface of the interconnected particles. As a result of these structural features, carbon aerogels are finding applications as electrodes in supercapacitors with high energy and power densities.

Simple rule for complex quantum systems.

The exact rule describing the transformation of spectra of multilevel quantum systems perturbed by a random matrix has been found with the help of the all-order perturbation theory. For systems with a large number of levels this rule has a simple form, resembling the second-order perturbation theory. It immediately gives the well-known semicircle Wigner distribution of the density of states and the double-hump distribution for binary alloys. The spectra of small atomic or molecular clusters resulting from the perturbation of a small number of identical levels are also given among some other examples. Discontinuities of the derivatives of the energy spectra and a nonexponential time evolution are shown to be the typical features of large multilevel systems perturbed by a random matrix.

Atom probe and STEM studies of carbide precipitation in 2 [formula omitted]Cr1Mo steel

Changes in the chemical composition of cementite particles which initially form by a para-equilibrium transformation mechanism are studied using atom probe and scanning transmission electron microscope techniques as a function of tempering heat treatments. Consistent with our theoretical predictions, the enrichment of the substitutional solutes in the carbide at the carbide/matrix interface is not observed to reach the levels required for local equilibrium at the interface. Very small clusters of molybdenum and carbon atoms are found in the ferrite matrix at the early stages of tempering, although more work is needed to verify this observation.

Ab initio investigation of void stabilization: Oxygen in Nickel

We have used the ab initio technique of UHF/LANL 1 MB to study the interactions between absorbed oxygen atoms and molecules with their host nickel lattice. The host lattice is approximated by a small cluster of nickel atoms that are arranged as face-centered-cubic, except for a tubular void described by the absence of three or four lattice elements. The oxygen absorbates are placed, one at time, within this cavity. We conclude that, for tubular cavities, the interaction between the nickel lattice and the oxygen absorbates is stronger than the interactions between pairs of oxygen atoms, suggesting that the absorbates are mostly atomic (as apposed to diatomic) in character, while the (energetically) most preferred number of oxygen atoms to reside inside an n-site, tubular hollow of nickel is simply (n − 1). © 1993 John Wiley & Sons, Inc.