Electronic Shell Structure Research Articles

Shell structure in large nonspherical metal clusters.

Electronic shell structure of icosahedral and cuboctahedral sodium clusters with 300 to 1500 atoms has been studied using a potential-well approximation for the effective one-electron potential. The results show that icosahedral clusters yield the same shell structure as spherical clusters up to the cluster size of about 500 atoms and that similarities persist until the cluster has about 1000 atoms. The shell structure of a cuboctahedral geometry begins to deviate from that of a sphere when the cluster size is about 100. A study on quadrupole deformations of large clusters shows that surface fluctuations in liquid clusters cannot destroy the shell structure even in the largest clusters.

Metal clusters as giant atoms

M12X-type metal clusters of icosahedral symmetry are discussed in terms of the giant atom concept on the basis of the electronic shell structures in free-electron-like metal clusters. The first-principles calculations for Au12,13, Ag12,13, Al12,13, Au12Cr, and Al12Si clusters have been done by the self-consistent local density functional scheme using the norm-conserving pseudopotential in the linear combination of atomic orbitals method. Electronic shell structures in icosahedral clusters are formed by 6s, 5s and 3p orbitals or peripheral atoms in Au, Ag, and Al clusters, respectively. By doping Cr into Au12 and Si into Al12 clusters M13 clusters are stabilized by about 0.7 eV atom-1 (Au12Cr) and 0.2 eV atom-1 (Al12Si) because of the closed shell formation. Interactions between clusters, cluster and surface, and cluster and metal tip used in the atomic force microscope are discussed based on the Harris functional scheme. Dimers of Au12Cr and Al12Si are weakly bound, and the Au13 cluster on Si(111) has two kinds of binding, but Al13 does not. The repulsive or attractive nature of the force between the cluster and Pt tip is considerably dependent on the cluster-tip distance.

Shell Structure in Photoionization Spectra of Trivalent Metal Clusters

AbstractPhotoionization mass spectra of large AlN and InN clusters, produced by laser vaporization technique, have been recorded via standard TOF spectroscopic methods. Ionization potentials are measured in the size range N = 37–112 for aluminum and N = 31–132 for indium. Comparison between these two trivalent simple metals is presented, as well as with the electronic shell structure predictions of the spherical jellium model. In the large size range N = 200–1400, regular oscillations are observed in the AlN mass spectra. This oscillating behaviour, which is a manifestation of the electronic shell structure of the Ne = 3N valence electrons, is analyzed within the semiclassical theory of single‐particle quantum level density. The oscillation period as a function of Ne3, two times shorter than the period obtained in alkali cluster experiments, is well explained by the classical two‐turn star orbit contribution, whereas for alkali metals the electronic structure near the Fermi energy is governed by the single‐turn triangular and square orbit contributions.

Shell Dependent Chemical Reactivity of Large Sodium Clusters

It has been shown in the past that sodium clusters possess an electronic shell structure characteristic of a nearly spherical, finite Fermi system. For this reason they might be expected to behave like giant atoms. In fact, closed shell clusters are known to have particularly high ionization energies. In this paper, we report variations in the reactivity of Nan for 100 ≤ n ≤ 800 with molecular oxygen. Clusters with completely filled electron shells are found to be relatively unreactive.

Evidence for classical star orbit in large AlN clusters.

Mass spectra of ${\mathrm{Al}}_{\mathit{N}}$ clusters produced by a laser vaporization source have been recorded via standard time-of-flight spectroscopic methods. Regular signal oscillations are observed in the size range N=200--900 when low-power near-threshold ionization is performed. This striking feature, which is a manifestation of the electronic shell structure of the aluminum clusters, is analyzed with the semiclassical theory of single-particle level density. The oscillation frequency is found to be well explained by the classical star orbit contribution.

Electronic shell structure in the ionization potentials of copper clusters

The ionization potentials (IPs) of copper clusters (Cu n ) up to 150 atoms have been bracketed using laser photoionization. Large decreases in IP at n = 2, 8, 20, 30, 34, 40 and 60 atoms are observed, as well as a strong odd—even alternation extending beyond 100 atoms. These features correspond to electronic shell and subshell closings predicted for systems of n valence electrons confined to spherical or spheroidal potentials. The decreases in IP expected to accompany shell closings at n = 58 and 92 are absent, however, and a new set of local extrema are observed, including local maxima at n = 57 and 88–91 and minima at n = 49 and 92. The possibility of perturbations to the electronic energy level structure due to geometric packing constraints is discussed.

Simplified semiclassical theory for the electronic shell structure of metallic clusters

We present a simplified theory for the electronic shell structure of large metallic clusters by extending the semiclassical analysis by Gutzwiller, Balian and Bloch. Thus analytical results are given for the shell effect in the Fermi energy and cohesive energy. In particular, results for the temperature dependence of the shell structure are given. New results are presented for the shell structure in the ionization potential and photoyield and for the existence of electronic- versus atomic shell structure as a function of cluster size and temperature. We obtain good quantitative agreement with previous numerical calculations and with experiments on Na clusters.

Magic numbers for metallic clusters and the principle of maximum hardness.

It is shown that for relatively more stable metallic clusters (those with magic number of atoms) the chemical hardness (I-A) too is relatively larger. Thus the occurrence of magic numbers for metal clusters whose stability is determined by their electronic shell structure can be understood as a manifestation of the principle of maximum hardness. This may also represent a possible way of delineating clusters with stability dominated by their electronic shell structure from those for which the magic numbers occur as a result of their geometric structure.

Quantum size effects in the attractive hubbard model

We investigate superconducting pair correlations in the attractive Hubbard model on a finite square lattice. Our aim is to understand the pronounced size dependence which they display in the weak and intermediate coupling regimes. These size effects originate from the electronic shell structure of finite systems and severely complicate a reliable extrapolation of numerical simulation data from small systems to the thermodynamic limit. To analyze the size effects in detail, we use the BCS approximation, as well as a particle number conserving modification of it and compare the results with those of quantum Monte Carlo simulations. As an application, we explore the possibility of reducing the shell effects in simulation data by changing the shape of the system and the imposed boundary conditions and by making use of the size dependence of corresponding BCS data.

Temperature dependence of supershells in large sodium clusters.

We present self-consistent calculations of the electronic shell and supershell structure of sodium clusters with up to N\ensuremath{\sim}1600 atoms at finite temperatures and N\ensuremath{\sim}2800 at zero temperature, employing the spherical jellium model in the local-density approximation and numerically solving the Kohn-Sham equations. The finite temperature of the valence electrons is included by treating them as a canonical subsystem embedded in the heat bath of the ions. We present sensitive quantities for the effects of temperature and self-consistency on the supershell structure, and compare our results with recent experiments and former calculations based on phenomenological mean-field potentials.

Electronic shell structure of laser-warmed Na clusters

Mass spectra are reported for large sodium clusters warmed by a continuous laser beam prior to ionization. During the 1 ms warming period, the clusters lose more than 10% of their mass by single-atom evaporation. The resulting size distribution reveals what appears to be electronic shell structure for clusters containing up to 2500 atoms.

On the shell structure and geometry of monovalent metal clusters

The Huckel model is used to study the electronic structure of monovalent metal clusters. In an fcc cluster the Huckel model gives an estimate to the electronic structure of a free electron cluster. It is shown that the surface faceting of the fcc cluster can destroy the electronic shell structure already when the cluster has about 100 electrons. In the Huckel model the icosahedral structure has smaller total energy than the fcc structures, from which the Wulff construction has the smallest energy already when the cluster has 600 atoms.

Electron attachment to niobium clusters and the condensation process

Condensation and electron attachment processes of niobium clusters and superfine particles (NSFP) are presented. These particles were formed under 0.2–0.5 Torr argon pressure by using a magnetron sputtering system. The morphology of the condensed particles strongly depended on argon pressures. A small amount of oxygen was needed for the formation of NSFPs. Energy distributions of sputtered particles were measured by using the retarding potential method to investigate the condensation process of NSFPs. The magnetic field ( H∼1 kG) was applied to the sputtered particles extracted into the growth chamber for electron attachment. When the magnetic field was applied to the sputtered beam, five peaks appeared at 2.7, 6.7,13.9,19.5 and 46.3 eV. These values approximately coincide with electron shell structures N = 8, 20, 40, 58 and 138, respectively, when an elemental particle has the energy 0.34 eV. These clusters seem to play roles as nuclei in the condensation process and as indexes of electronic structures.

Copper clusters: The interplay between electronic and geometrical structure

Copper clusters in the 50- to 100-atom size range are found to exhibit electronic shell structure as well as icosahedral geometry. Clusters corresponding to filled shells have minimum intensity in near-threshold photoionization mass spectra, implying that they have locally higher ionization potentials than other cluster sizes. The chemical stability of these clusters is illustrated by a reduced reactivity towards O2. Cluster geometry is probed via the equilibrium reactions with H2O: Clusters having one copper atom more than closed icosahedral subshells show an enhanced binding of water. The relative importance of electronic and geometrical structure in determining cluster chemical properties is discussed.

Electronic shell structure in multiply charged silver clusters

Silver clusters are generated by standard laser vaporization technique and ionized via multiphoton ionization. Time-of-flight mass spectrometry reveals singly, doubly and triply charged clusters, Agnz+ (z=1,2,3). The spectra show, for all charge states, intensity variations, indicating enhanced stabilities for cluster sizes with closed electronic configurations in accord with the spherical jellium model.

Electronic shell structure in large metallic clusters.

The investigation of shell structure in the ground states of atoms is limited to values of the angular momentum quantum number l\ensuremath{\le}3. In atomic nuclei, shells with l\ensuremath{\le}6 can be observed. We present evidence for shell structure in the electronic states of metal clusters for l\ensuremath{\le}12.

A Mössbauer study of57Fe vibration dynamics in substituted YIG

The NGR probabilityf′ dependence on57Fe3+ nuclei in YIG a- and d-sublattices, with Fe3+ and Y3+ substituted by other cations Me3+ (Gd3+, Ga3+, Al3+, In3+) of different massm, ion radiusr, and electron shell structure, was studied.f′ was found to be practically unaffected by either concentration,m, r or electron shell structure of Me3+ introduced into YIG c-, a-, and d-sublattices. For YIG:Al3+ and YIG:In3+ systemsf′ was found to increase with Me3+x-concentration if the absolute value of lattice parameter change per formula unit |Δa(Me3+)/x|≥8×10−2 A due to oxygen polyhedra deformation caused by substitution. For all YIG:Me3+ compositions investigated, atT>Tc there was a Fe3+ (a,d) vibration anisotropy due to O2− polyhedra being elongated along their figure axis.

Electronic shell structure and metal clusters: the self-consistent spheroidal jellium model

The electronic properties of small metal particles within the recently proposed self-consistent spheroidal jellium model [1] are further explored and compared to recent experimental data. Physical properties investigated include ionization potentials, electron affinities and the binding energy of neutral monomers to cationic clusters. The formalism is applied within the size-range 2≦N≦41, but could easily be extended beyondN=41. Finally, we discuss briefly the implications for the study of the dynamical response of open-shell clusters. In sharp contrast to earlier studies the functional is now corrected for self-interaction error, in a way first proposed by Pedew and Zunger [2]. This enables us to calculate reliable values for the electron affinities within ajellium-based model. This has the advantage, that we can calculate the affinities for Cu for all particle numbers for which experimental data are available. In all cases investigated we obtain excellent agreement with experiment, with pronounced shell-effects both for the electron affinities and for the binding energies, confirming in this way that the abundances map the relative stability of (Me) N clusters, with Me being a sp-metal atom (Na, K, Li, Cu, Ag, Au etc.).

Thomas-fermi approach to the theory of optical constants in the XUV range

The theory of many-electron atoms and ions and their interaction with XUV radiation is one of the fundamental aspects of X-ray laser physics. The topic of this paper is the theory of optical constants of many-electron atoms in the XUV which define the dielectric susceptibility of materials in this wavelength range. We use the statistical description of atomic electrons and, as a starting point, develop the rigorous theory of the dynamical response of a Thomas-Fermi atom. The equations obtained are used with proper boundary conditions to find the dynamical polarizability and photoabsorption of many-electron atoms. The results are employed for an analysis of existing experimental data on optical constants of Ar and Si. A procedure is suggested to include into the theory the effects of atomic electron shell structure. This leads to more reasonable results and better agreement with experiment. In particular, the effect of the Cooper minimum in the atomic photoionization cross-section can be described.

Studies on the electron structure reconstruction in intense shock waves

Abstract Shock-wave studies have made it possible to obtain data on the compressibility of more than 200 materials at standard conditions, in solid, liquid and gaseous states, including about 50 It has been found that the functions of atomic volumes of elementary substances versus the atomic number have a periodic forms. This periodicity is related with the electron shell structure of atoms. A flattening of curves versus a pressure increase and growth of compressibility of substances with large atomic volumes are observed. This phenomenon is related with the reconstruction of the electron structure: the atoms are drawing together under compression and the energy exchange is increasing. It leads to broadening and overlapping of electron energy levels. The pressure range up to several megabars has been studied in detail under laboratory conditions. At these pressures electron structure changes of substances having an inverse population may take place. Transitions of outer A-electrons into vacant d-levels ar...