Dynamics of transition-metal clusters

The atomic structure and thermodynamic properties of transition-metal 6- and 7-atom clusters are investigated using the molecular dynamics method, where Gupta's potential taking into account many-body interaction is employed. The caloric and the structural fluctuations are studied. The “fluctuating state” is found forN=6 in the region of the temperature near and below the melting point, where clusters undergo structural transition from one isomer to others without making any topological change. The fluctuating state differs from the “coexistence state” found in Ar clusters [1] i.e. the former involves no liquid state. In the liquid state the motion of atom-permutation occurs besides the breathing motion. On the other hand, the fluctuating state is not found forN=7 but only the motion of atom-permutation in the liquid state. The coexistence state is found in both cases of 6- and 7-atom clusters. We also discuss a possibility of larger clusters displaying the fluctuating state.     

Determination of structural transitions of atomic clusters from local and global bond orientational order parameters

Designing an effective order parameter for the identification of geometries in atomic clusters is an important step toward understanding the structural transitions occurring in these systems. We propose a method that simultaneously utilizes the local and global bond orientational order parameters for structural transitions. When applied to Lennard-Jones clusters at finite temperature over the size range 30< or =N< or =146, this method identified all the major geometries: icosahedra with Mackay overlayers, icosahedra with anti-Mackay overlayers, decahedra, octahedra, and tetrahedra. From the distributions of these geometries as a function of temperatures on clusters containing 38, 75, and 98 atoms, we are able to interpret all transition types without ambiguity.     

Structure and dynamics of Lennard-Jones clusters with impurities

Molecular dynamics simulations and Lennard-Jones potentials have been used to study binary mixed clusters. The low temperature structures, impurity solvation and the melting and freezing transitions for different values of the relative atomic size and interaction energy have been studied forA ₁₃ B,A ₁₂ B,A ₅₅ B andA ₁₃ B ₁₃ clusters. ForA ₁₃ B large impurities do not solvate even for high interaction energy. ForA ₅₅ B larger impurities remain on the surface for low interaction energies but solvate as the energy of interaction increases. The presence of the impurity very strongly affects the solid-liquid transition. Icosahedral structures remain as the minimum energy configurations forA ₁₃ B ₁₃ clusters with atoms of the same size and different interaction energies. ForA ₁₃ B ₁₃ clusters with atoms of the same interaction energy and different size, smaller atoms go inside surrounded by the bigger surface atoms.     

Photoabsorption spectra of Cs n O and Cs n clusters

Photoabsorption spectra of several Cs _N+2O and Cs _N clusters were obtained by means of laser-induced beam-depletion techniques. The strong absorption of clusters withN≥3 in the near infrared indicates that collective motion might play an important role. Dipole transitions between molecular orbitals, enhanced by plasmon oscillations, generate remarkably distinct spectra for(a) closed-shell clusters atN=8 and(b) geometrically symmetric clusters like Cs₆O and Cs₁₄O.     

Structure of silver clusters with magic numbers of atoms by data of molecular dynamics

The behavior of silver clusters (cubic octahedron habit) with magic numbers of atoms N = 13, 55, 146, 309, 561, 923, 1415, and 2057 in the 0–1300 K temperature range is studied for the embeded atom model by the molecular dynamics method. The structural method for the analysis of the dynamics of local configurations of atoms based on the construction of angular characteristics of simplexes of the Delone partition of a cluster is proposed. Structural transitions of clusters with a cubic octahedron habit to the stable clusters with an icosahedron habit are revealed. Motions of atoms in clusters with an icosahedron habit are transformed into the stationary vibration mode. Middle positions of atoms in clusters tend to form shells with a regular structure. At N = 561, there are 15 such shells. The cluster with N = 561 at 650 K is characterized by a reduced density close to that of silver melt.     

Electronic and atomic structure of Na,Mg, Al and Pb clusters

Density functional theory is used to study the electronic and atomic structure of small clusters of Na, Mg, Al and Pb. We study the quantityE _N?1–E _N , which has relevance to the processes of cluster growth and evaporation (E _N is the total energy of the cluster withN atoms). By comparing the results of the jellium model with those of a more realistic model (although still simple) we are able to appreciate “structural” effects beyond the “electronic-shell effects” which form the essence of the predictions of the jellium model. The calculations predict formation of atomic shells and appreciable reconstruction as the cluster grows.     

Anomalous coherence functions in collective resonance fluorescence

The anomalous coherence functions (ACF) of collective resonance fluorescence are calculated analytically forN two-level atoms, coherently driven by a strong laser field and distributed in a region much smaller than the resonant wavelength. It is shown that the anomalous coherence functions are nonzero for transient as well as steady-state resonance fluorescence. The values of ACF are dependent on the number of atoms and the initial atomic populations. For one-atom resonance fluorescence, the one-time ACF vanishes whereas the two-time ACF differ from zero irrespective of the number of atoms. Moreover, it is found that information about the higher-order resonance at 2Θ, where Θ is the Rabi frequency, is conveyed by the ACF's only in the transient régime of resonance fluorescence. For steady-state resonance fluorescence, the ACF's carry information similar to that carried by the correlation function that yields the fluorescent spectrum. We also discuss the possibility of measuring the ACF's using photon-counting techniques.     

Stability and structure of singly-charged xenon-argon clusters [Xe1Arn−1]+,n=3–27

Monte-Carlo calculations have been performed for positively charged xenon-argon clusters in the temperature range between 10K and 40K for cluster sizes up ton=27. The argon-argon interaction potential stems from empirical data, the Xe⁺-Ar potential is determined by ab initio MRD-CI calculations and a semi-empirical treatment of spin-orbit effects. Special stability is found for cluster sizesn=10, 13, 19 and less pronounced forn=23 and 25 fairly independent of the temperature. The geometrical structure of the clusters are given and the construction principle is discussed in light of the interactions among neutral argon atoms and the xenon ion — argon interaction. Comparison with measured mass spectra for mixed rare-gas clusters and [Xe_n]⁺ clusters is made and shows a consistent picture for the building principle.     

Size effects in the solid phase transition of SF6 clusters

The structure of SF₆ clusters produced in a free jet expansion is studied by electron diffraction methods. A solid phase transition is known to occur when clusters are warmed up by changing several experimental conditions in the expansion of a Ne + SF₆ mixture. In the present study, the total stagnation pressure and the SF₆ mole fraction are varied in order to understand how these parameters influence the structural state of the clusters and further to observe the phase transition for different cluster sizes. When the stagnation pressurep ₀ is larger than about 10 bar, a given mole fraction results in clusters with identical structure and probably identical temperature. Whenp ₀ is decreased below 10 bar, identical structures are found for lower and lower mole fractions. This structural behaviour suggests that for small clusters, containing less than about 500 molecules, the transition steps occur at temperatures lower than those observed for larger clusters. The possibility of detecting a temperature variation in the diffraction patterns of small cubic clusters is discussed.     

Structural transformations in silver nanoparticles

A molecular dynamics simulation was performed for silver clusters of 147, 309, and 561 atoms with the initial cuboctahedral habit in the temperature range 0–1000 K with an embedded atom potential for silver. Structural transitions of the silver clusters to complex twins (icosahedral habit) with coherent (111)/(111) boundaries over all edges of icosahedra were found, which started at temperatures of 50 K, 350 K, and 700 K, respectively. To analyze the structural transformations in nanoparticles, an algorithm is proposed based on a simplicial Delaunay decomposition (Delaunay triangulation). It was found that after the transition of silver nanoparticles to complex twins, the atomic motion becomes vibrational; the atoms vibrate around the sites that correspond to the vertices of the regular polyhedra. In the case of the 147-atom silver nanoparticle, the polyhedra are arranged in the following sequence, starting from the center of mass: icosahedron (12 atoms), icosododecahedron (30 atoms), icosahedron (12 atoms), dodecahedron (20 atoms), truncated icosahedron (60 atoms, isostructural with fullerene C₆₀), icosahedron (12 atoms), and one atom at the center of mass.     

Ab initio molecular dynamical investigation of the finite temperature behavior of the tetrahedral Au19 and Au20 clusters

Density functional molecular dynamics simulations have been carried out to understand the finite temperature behavior of Au19 and Au20 clusters. Au20 has been reported to be a unique molecule having tetrahedral geometry, a large HOMO-LUMO energy gap, and an atomic packing similar to that of the bulk gold (Li, J.; et al. Science 2003, 299, 864). Our results show that the geometry of Au19 is exactly identical with that of Au20 with one missing corner atom (called a vacancy). Surprisingly, our calculated heat capacities for this nearly identical pair of gold clusters exhibit dramatic differences. Au20 undergoes a clear and distinct solid-like to liquid-like transition with a sharp peak in the heat capacity curve around 770 K. On the other hand, Au19 has a broad and flat heat capacity curve with continuous melting transition. This continuous melting transition turns out to be a consequence of a process involving a series of atomic rearrangements along the surface to fill in the missing corner atom. This results in a restricted diffusive motion of atoms along the surface of Au19 between 650 to 900 K during which the shape of the ground state geometry is retained. In contrast, the tetrahedral structure of Au20 is destroyed around 800 K, and the cluster is clearly in a liquid-like state above 1000 K. Thus, this work clearly demonstrates that (i) the gold clusters exhibit size sensitive variations in the heat capacity curves and (ii) the broad and continuous melting transition in a cluster, a feature that has so far been attributed to the disorder or absence of symmetry in the system, can also be a consequence of a defect (absence of a cap atom) in the structure.     

The influence of shells,electron thermodynamics,and evaporation on the abundance spectra of large sodium metal clusters

Measurements of the mass abundance spectra of sodium clusters containing up to 600 atoms are presented. The clusters are produced in a seeded supersonic expansion of Ar or Kr gas, and the spectra are obtained by a time-of-flight technique. The sawtooth features in the spectra are interpreted as evidence of a regular spherical shell structure with magic numbers,N ₀, scaling approximately with the cube root of the number of sodium atoms. Altogether twelve shell closings are observed,N ₀=2, 8, 20, 40, 58, 92, 138, 196, 260, 344, 440 and 558. There is also a pronounced odd-even staggering all the way up toN=70. The experimentally observed intensity changes for the clusters around the magic numbers are discussed in terms of the electronic free energy,F(N), calculated at finite temperature, and the second differences of the free energy Δ₂ F(N)=F(N?1)?2F(N)+F(N+1). The processes behind the non-uniform abundance distributions, and the thermodynamics of finite electron systems with non-uniform level spacings are discussed on this basis.     

Structural and electronic properties of compound metal clusters

The equilibrium geometries, relative stabilities, and vertical ionization potentials of compound clusters involving Li _n , Na, Mg, and Al atoms have been calculated using ab initio self-consistent field linear combination of atomic orbitals — molecular orbital (SCF-LCAO-MO) method. The exchange energies are calculated exactly using the unrestricted Hartree-Fock (UHF) method whereas the correlation correction is included within the framework of configuration interaction involving pair excitations of valence electrons. While the later correction has no significant effect on the equilibrium geometries of clusters, it is essential for the understanding of relative stabilities. Clusters with even numbers of electrons are found to be more stable than those with odd numbers of electrons regardless of their charge state and atomic composition. The equilibrium geometries of homo-nuclear clusters can be significantly altered by replacing one of its constituent atoms with a hetero-nuclear atom. The role of electronic structure on the geometries and stabilities of compound clusters is discussed.     

Chemical probes of metal cluster structure - Fe,Co, Ni and Cu

Chemical reactivity is one of the few methods currently available for investigating the geometrical structure of isolated transition metal clusters. In this paper we summarize what is currently known about the structures of clusters of four transition metals, Fe, Co, Ni, and Cu, in the size range from 13 to 180 atoms. Chemical probes used to determine structural information include reactions with H₂ (D₂), H₂O, NH₃ and N₂. Measurements at both low coverage and at saturation are discussed.     

Thermal behaviour of carbon clusters and small fullerenes

The structural and thermal properties of small carbon clusters (C _N , N = 13, 20, and 32) are investigated by constant energy Molecular Dynamics simulations over a wide range of temperatures, i.e., from T = 0K to above the melting point of graphitic carbon. The Tersoff interatomic potential [6] is used to mimic the covalent bond between the carbon atoms in the cluster. We find that small carbon clusters start to fragment or to evaporate atoms or C₂ or C₃ units before fully developing a liquidlike phase. As a consequence, some relevant isomers (such as rings, bowls, hollow cages) are thermally isolated from each other i.e., there are no thermally activated isomerization transitions between them. Possible implications of our results on the growth mechanism of fullerenes are discussed.     

Stability of relaxed Lennard-Jones models made of 500 to 6000 atoms

We present a study of the stability of clusters models made of a numberN of atoms in the range 500 to 6000 atoms, freely interacting through the Lennard-Jones potential. The potential energy per atom, calculated for relaxed models, shows that stable models belong to an icosahedral sequence whenN<1600 and to a decahedral sequence beyond. A coexistence size range of both structures is discussed in connection with experimental results on argon clusters in free jet expansions.     

Evolution of photoionization spectra of metal clusters as a function of size

Electronic structure effect in small metallic clusters up ton=15 are investigated through three series of experiments performed on one-valence-electron-atom clusters and two-valence-electron ones. In these experiments the cluster molecular beam is probed by photoionization mass spectroscopy, either by using a tunable laser source for alkali clusters or by synchrotron radiation for mercury ones. With alkali clusters the results are related to fragmentation effects, ionization potential measurements and photoionization efficiency curve profile analysis in the threshold region. The similar behavior of the homogeneous and heterogeneous clusters and the comparison with theoretical models suggest that forn≧3 the valence electrons are partially delocalized. This similarity against the electronic structure is not found in the nucleation process which generates homogeneous and heterogeneous clusters with a strong difference in their respective abundances. For mercury clusters the evolution with size for excitation spectra of two autoionizing lines is obtained up ton=8. Results show that they do not have a metallic character. This is also supported by the observation of small doubly charged mercury clusters forn≧5 which are stable against the Coulomb explosion.     

Phase change of Lennard-Jones nano clusters containing non magic numbers

Phase changes of Lennard-Jones clusters containing 4N ³ (N= 1?20) identical atoms in terms of solid and liquid phase-like forms have been studied by performing molecular dynamics (MD) simulation at sharply-bounded range of temperatures between freezing temperature (T _f) and melting temperature (T _m) and at constant pressure. The small differences between the free energies of clusters in different phase-like forms and also the non-rigidity of the cluster (0 ≤ γ ≤ 1) as an order-parameter, which characterizes the phase transition, have been calculated. Plots of the free energy of phase change versus the non-rigidity indicate that the free energy is a continuous function of the non-rigidity and also different crystalline-like cores with different free energies correspond to the same non-rigidity factor at any given temperature.     

Neutron inelastic scattering spectra and phase transition of 1,2-dichloroethane crystal

Neutron inelastic scattering spectra of 1,2-dichloroethane crystal have been measured at three temperatures above and below 177°K where the crystal undergoes a broad phase transition. Two and three peaks have been observed in the high and low temperature phases, respectively. The frequency distribution g(v) has been calculated in the first Brillouin zone for the low temperature phase and is compared with the observed spectra. The results show that the phase transition at 177°K is associated with rotational motion of the molecule around the axis passing through two chlorine atoms.