Statistical measures and magic numbers in metal clusters

In this work, a shell model for metal clusters up to 220 valence electrons is used to obtain the fractional occupation probabilities of the electronic orbitals. Then, the calculation of a statistical measure of complexity and the Fisher-Shannon information is carried out. An increase of both magnitudes with the number of valence electrons is observed. The shell structure is reflected by the behavior of the statistical complexity. The magic numbers are indicated by the Fisher-Shannon information. So, as in the case of atomic nuclei, the study of statistical indicators also unveil the existence of magic numbers in metal clusters.     

传统中子幻数稳定性的研究

在考虑了BCS理论的相对论平均场模型框架内,通过系统研究N=8,20,28,50,82和126六条同中子素链中每个元素费米面附近的单粒子能级间隔、粒子数占有概率比以及原子核体系的粒子数偏离随质子数的变化规律,讨论了传统中子幻数的壳结构在从中子滴线区到质子滴线区整个核谱上的稳定性,预言只有在轻核的丰中子区域,传统的中子幻数效应才可能消失,并把计算结果和最近的文献报道作了比较. 关键词： 相对论平均场模型 能级间隔 占有概率 粒子数偏离     

Mapping the magic numbers in binary Lennard-Jones clusters

Using a global optimization approach that directly searches for the composition of greatest stability, we have been able to find the particularly stable structures for binary Lennard-Jones clusters with up to 100 atoms for a range of Lennard-Jones parameters. In particular, we have shown that just having atoms of different sizes leads to a remarkable stabilization of polytetrahedral structures, including both polyicosahedral clusters and at larger sizes structures with disclination lines.     

Structures of inert atomic clusters and their magic numbers of geometry

The optimal configurations of all atoms in atomic microclusters of an inert element have been obtained from their arbitrary positions and shapes by means of a Lennard-Jones interaction potential between atoms in the clusters, calculating the binding energies of the clusters with the numbers of atoms N ⩽ 14, which have shown the magic numbers of geometry in accordance with the experimental results. The structural pictures of such clusters are also presented.     

Equilibrium geometries,magic numbers and electronic structure of small carbon clusters

A carbon tetramer in the form of a distorted tetrahedron has been discovered to exist in a metastable spin-triplet excited state with an activation barrier of 0.5 eV. This state is 2.5 eV above the spin-singlet rhombus shaped ground state. These results are based on fully self-consistent all electron molecular orbital calculations. We also illustrate the processes leading to the carbon trimer as a “magic number”. Implications of the present discovery for future industrial applications are pointed out.     

Tetrahedra packings — Observation of magic numbers for clusters from antimony-tetramers

Sb_n-clusters have been generated by condensation of tetramer units in LN₂-cooled He-gas. Electronic time-of-flight spectra show resolved mass peaks of clusters from tetramers up to n = 240 with pronounced size dependent structure. The observed magic numbers $\text{n}{}^1\text{= 8, 36, 52}\text{and}\text{84}$ are explained by a tetrahedra packing model.     

New magic numbers in metallic clusters: an unexpected metal dependence

Using a many-body tight-binding potential within the second moment approximation in a quenched molecular dynamics simulation, we calculate the internal energy of free Cu, Ag and Au clusters of various sizes and morphologies. We find that the icosahedral structure, which is the equilibrium shape for small sizes at least for Cu and Ag, adopts a very inhomogeneous atomic relaxation. More surprisingly, introducing a vacancy at the center lowers the mean energy per atom for sufficiently large size icosahedra. This means that above a critical size, which decreases from Cu to Au, the icosahedron admits a constitutional vacancy. Taking into account the stability domain of the icosahedron relative to the fcc structure (namely the Wulff polyhedron), we find that there is a stability range of size for Cu and Ag icosahedra with a central vacancy, but not for Au icosahedra. This trend along the noble metal column is discussed in view of tight-binding potential parameters.     

Geometric magic numbers of sodium clusters: Interpretation of the melting behaviour

Putative global minima of sodium clusters with up to 380 atoms have been located for two model interatomic potentials in order to identify the structures responsible for the size-dependence of the thermodynamic properties in experiments. Structures based upon the Mackay icosahedra predominate for both potentials, and the magic numbers for the Murrell-Mottram model show excellent agreement with the sizes at which maxima in the latent heat and entropy change at melting have been found in experiment. In particular, the magic numbers at sizes intermediate between the complete Mackay icosahedra are due to unusual twisted icosahedral structures.     

Diffraction of neutral helium clusters: evidence for "magic numbers"

The size distributions of neutral 4He clusters in cryogenic jet beams, analyzed by diffraction from a 100 nm period transmission grating, reveal magic numbers at N=10-11, 14, 22, 26-27, and 44 atoms. Whereas magic numbers in nuclei and clusters are attributed to enhanced stabilities, this is not expected for quantum fluid He clusters on the basis of numerous calculations. These magic numbers occur at threshold sizes for which the quantized excitations calculated with the diffusion Monte Carlo method are stabilized, thereby providing the first experimental confirmation for the energy levels of 4He clusters.     

Spherical clusters of simple metals: Madelung energies and structures

The Madelung energies of simple metal spheres are calculated for bcc, fcc, and hcp structures as well as for fully relaxed structures. It is found that for clusters of up to 40 atoms the structure generally does not have the symmetry of any simple lattice. The variation of the structural part of the total energy is shown to be slightly smaller than the variation arising from the filling of discrete single-electron energy levels.     

Structure determination of surface magic clusters

The structure of a type of surface magic cluster is determined by a combination of scanning tunneling microscopy, density-functional calculations, and dynamical low energy electron diffraction. The diffraction method is applicable because these clusters created through hierarchical self-organization of Ga deposited onto a Si(111)-7x7 surface have identical size and structure and form an ordered array with exact translational symmetry. The unprecedented detailed structure information provided by the diffraction measurement is consistent with direct microscopic imaging and theoretical calculations.     

Evidence for magic numbers of free lead-clusters

Microclusters Pb_n have been generated by condensation of lead atoms in cold He-gas. Electronic time-of-flight mass spectra show resolved peaks up to n ≈ 110 with pronounced size dependent structure up to n = 20. The magic numbers $\text{n}{}^1\text{= 7, 10, 13, 17}\text{and}\text{19}$ are deduced from the spectra.     

Cluster growing process and a sequence of magic numbers

We present a new theoretical framework for modeling the cluster growing process. Starting from the initial tetrahedral cluster configuration, adding new atoms to the system, and absorbing its energy at each step, we find cluster growing paths up to the cluster sizes of more than 100 atoms. We demonstrate that in this way all known global minimum structures of the Lennard-Jones (LJ) clusters can be found. Our method provides an efficient tool for the calculation and analysis of atomic cluster structure. With its use we justify the magic number sequence for the clusters of noble gas atoms and compare it with experimental observations.     

Magic numbers of sodium clusters

The cohesive energy E_c of crystalline-like b.c.c. and f.c.c. sodium clusters is calculated as a function of the number of atoms in the cluster using the density functional formalism. The maxima of E_c define the theoretical magic numbers for crystalline clusters. A comparison with theoretical results using the jellium background model and with experimental magic numbers obtained by Knight and co-workers suggests that sodium clusters prepared in those expeiments are in a disordered liquid-like or amorphous state.     

Shell corrections,magic numbers,and mean field

It is shown that the positions of deep local minima of shell corrections associated with magic numbers in the region of superheavy nuclei depend on the parameters of the central and spin-orbit mean-field potentials. The accuracy of nuclear-mass predictions made within various models for superheavy nuclei is analyzed.     

Different magic number behaviors in supported metal clusters

Two different magic number behaviors in supported metal clusters, which contain several to hundreds of atoms, are revealed on a series of fcc(001) metal surfaces based on the calculations with the tight-binding potential. The magic number sequence persists on some surfaces while gradually disappears on the others with the increasing cluster size. A theory is proposed to explain these behaviors in terms of atomic interactions. We find in surprise that the different magic number behaviors are triggered by the relatively weak adatom–adatom interactions between next nearest-neighbor (NNN) atoms, although the closed shell of the magic cluster is enhanced by nearest-neighbor interactions. For an attractive NNN interaction, the closed shell of the magic cluster is gradually destabilized and eventually broken, leading to the disappearance of the magic number sequence with increasing cluster size. For a repulsive one, the closed shell and magic number sequence persists. Besides, our theory also allows a good understanding of the equilibrium shape of Cu islands on the Cu(001) surface.     

Interplay between magic number stabilities and superfluidity of small parahydrogen clusters

The interplay between magic number stabilities and superfluidity of small parahydrogen clusters with sizes N=5 to 40 and temperatures 0.5 K相似文献