Spheroidal cap configurations of atomic clusters on planar surfaces

Deposited atomic cluster configurations are investigated under the hypothesis of spheroidal cap shapes being a stable geometry. The macroscopic-microscopic method is employed to calculate the deformation energy. A new specialized single-particle model is developed in order to account for the quantum effects, and the liquid-drop approach is used to calculate the macroscopic part of the energy. The minima within the total deformation energy are interpreted as equilibrium states of atomic clusters on surfaces. Calculations have been performed for the metallic clusters of Na with atom numbers N = 20, 70 and 200.     

Shape evolution for Sm isotopes in relativistic mean-field theory

The evolution of shape from the spherical to the axially deformed shapes in the Sm isotopes is investigated microscopically in relativistic mean-field theory. The microscopic and self-consistent quadrupole deformation constrained relativistic mean-field calculations show a clear shape change for the even-even Sm isotopes with N = 82-96. The potential surfaces for ¹⁴⁸Sm, ¹⁵⁰Sm and ¹⁵²Sm are found to be relatively flat, which may be the possible critical-point nuclei. By examining the single-particle spectra and nearest-neighbor spacing distribution of the single-particle levels, one finds that the single-particle levels in ¹⁴⁸Sm , ¹⁵⁰Sm, and ¹⁵²Sm distribute more uniformly.     

Landau fragmentation and deformation effects in dipoSe response of sodium clusters

Recent experimental data on the dipole plasmon in axial sodium clusters Na _N ⁺ with 11 ≤ N ≤ 57 are analyzed within a self-consistent separable random-phase approximation (SRPA) based on the deformed Konh-Sham functional. Good agreement with the data is achieved. The calculations show that, while in light clusters plasmon properties (gross structure and width) are determined mainly by deformation splitting, in medium clusters with N τ 50 the Landau fragmentation becomes decisive. Moreover, in medium clusters shape isomers come to play with contributions to the plasmon comparable with the ground state one. As a result, commonly used methods of the experimental analysis of cluster deformation become useless and correct treatment of cluster shape requires microscopic calculations.     

Rotational consequences of stable octupole deformation in nuclei

The characteristic features of high-spin spectra of octupole-deformed nuclei are demonstrated by means of Woods-Saxon-Bogolyubov cranking calculations. The rotational spectra of Ra and Th nuclei are studied. The experimental data suggests shape changes with increasing neutron number from N ? 130 (nearly spherical shapes) through N ? 134 (octupole-deformed shapes) to N ? 140 (well-deformed reflection-symmetric shapes). The octupole mixing between the high-j intruder states and normal-parity orbitals leads to specific patterns of quasiparticle spectra characterised by a quantum number referred to as simplex. The influence of octupole deformation on high-spin properties of nuclear spectra like spin alignment, band interaction, etc. are discussed.     

The reaction πN → ππN in a meson-exchange approach

A resonance model for two-pion production in the pion-nucleon reaction is developed that includes information obtained in the analysis of pion-nucleon scattering in a meson-exchange model. The baryonic resonances Δ(1232), N^*(1440), N^*(1520), N^*(1535), and N^*(1650) are included. The model reproduces the total cross-sections up to kinetic energies of the incident pion of 400MeV and obtains the shapes of the differential cross-sections in reasonable agreement with the data.     

Implantation of size-selected silver clusters into graphite

We report on a systematic study of the implantation of size-selected Ag_N ⁺ clusters on a graphite sample, for different cluster sizes (N = 1,3,7,9,13) and different impact energies (E = 1-30 keV). Results show that the implantation depth scales linearly with the momentum of the cluster, with a stopping power which depends on cluster size. We have particularly investigated the effects of the size and the geometry of the cluster on the implantation into the graphite substrate. A sort of universal behavior, which unifies different elements and different cluster geometries, can be recognized by scaling the momentum with the cluster projected surface. The stopping power of the cluster while penetrating the HOPG surface has been investigated for each cluster size, and a molecular effect is recognized, meaning that the stopping power is not additive in the number of atoms of the cluster.Received: 24 November 2003, Published online: 10 February 2004PACS: 61.46. + w Nanoscale materials: clusters, nanoparticles, nanotubes, and nanocrystals - 68.55.Ln Defects and impurities: doping, implantation, distribution, concentration, etc. - 79.20.Rf Atomic, molecular, and ion beam impact and interactions with surfaces - 81.05.Uw Carbon, diamond, graphite     

Vibrational Feshbach resonances in electron attachment to carbon dioxide clusters

Using a high resolution ( meV) laser photoelectron attachment method, we have studied the formation of (CO ₂) _q ⁻ ions (q = 4−22) in collisions of low energy electrons (1−180 meV) with (CO₂) _N () clusters. The previously reported “zero energy resonance”, observed at much larger electron bandwidths, actually consists of several narrow vibrational Feshbach resonances of the type [(CO ₂) _{N −1}CO which involve a vibrationally-excited molecular constituent ( denotes vibrational mode) and a diffuse electron weakly bound to the cluster by long range forces. The resonances occur at energies below those of the vibrational excitation energies of the neutral clusters [(CO ₂) _{N −1}CO ]; the redshift rises with increasing cluster ion size q by about 12 meV per unit; these findings are recovered by a simple model calculation for the size dependent binding energies. The size distribution in the cluster anion mass spectrum, resulting from attachment of very slow electrons, mainly reflects the amount of overlap of solvation-shifted vibrational resonances with zero energy; the cluster anion size q is identical with or close to that of the attaching neutral cluster. Received 11 January 2000 and Received in final form 10 April 2000     

B12N12纳米笼：潜在的二氧化氮检测传感器

利用密度泛函理论通过计算吸附能量、HOMO/LUMO能隙变化、电荷转移、结构扭曲等研究二氧化氮分子在B12N12纳米笼的吸附．此外,通过计算B₁₂N₁₂的电子结合能、Gibbs自由能、态密度和分子表面的静电势研究其稳定性和其它特性．B₁₂N₁₂纳米笼吸附二氧化氮显示三种构型．B₁₂N₁₂团簇的HOMO/LUMO能隙变化对二氧化氮分子的存在非常敏感,从自由团簇的6.84 eV降为NO₂/团簇稳定团簇的3.23 eV．团簇的导电性被极大地提高,表明B₁₂N₁₂纳米簇可能是潜在的二氧化氮气体分子检测传感器.     

Phase transitions between axisymmetric and nonaxial nuclear shapes

Within the interacting-boson model, phase transitions between different nuclear shapes are considered in the space of three control parameters. Depending on the values of these parameters, the equilibrium shape of a nucleus can be spherical, axially deformed, or nonaxial. It is shown that the phase transition from an axisymmetric to a nonaxial deformation is a second-order phase transition. Within the Bohr-Mottelson model, an approximate solution is found that describes a nucleus in the vicinity of the critical point of a phase transition from a spherical to nonaxially deformed shape. The results obtained for the energies and E2-transition probabilities are close to experimental data for the ¹³⁴Ba nucleus.     

Nucleation and stability of defect clusters: New energetic model in the case of substituted wustites

Abstract

For wüstite Fe_1?z O (z < 0.08) an energetic model accounts for the stability of cubic defect clusters (m/n) which are partly ordered in the crystal. The Gibbs energy G_T (N) associated with clusters, including their distorted envelope, is expressed as a sum of a volume term in N ³ and of surface terms in N ⁴; N is the number of bonds characteristic of the cluster size. In the case of a (10/4) type cluster, this energy is negative and minimum for N_m ranging between 4 and 5, when the volume and surface energies range between specific values. Using simple assumptions, a volume energy ?0.80 eV per vacancy is found in accordance with the value of stabilization energy calculated by theorists for the (10/4) cluster. The substitution of Fe²⁺ by Ca²⁺ should lead to a decrease of cluster size; this has been recently suggested by neutron diffraction studies.     

Ab-initio Study of Small Silver Nanoclusters

We explore the lowest energy structures and investigate the structural and electronic properties of small Ag_N (N = 1–10) clusters by employing an ab-initio self-consistent density functional method in the local density approximation. The calculation of binding energy, bond length and the energy difference of HOMO–LUMO states have been carried out in a large energy interval for different isomeric forms of Ag clusters. The cluster binding energies increases rapidly with cluster size, which is consistent with the size dependence properties of clusters but our values are slightly higher than the other calculations.     

Ga6N6团簇结构性质的理论计算研究

在密度泛函理论的基础上，对Ga₆N₆团簇进行了第一性原理、全电子、从头计算，得到了10种可能的三维空间结构及其电子结构.其中最稳定结构的一对GaN原子的平均结合能为9.748 eV，因此是可能存在的.但与他人计算的Ga₃N₃和Ga₅N₅相比，Ga₆N₆团簇可能不属于“幻数”团簇.最稳定结构的Ga₆N_{6 关键词： GaN 团簇 电子结构}     

Mean shape of large semi-flexible tethered vesicles

The mean shapes of decorated icosahedron models for closed semi-flexible tethered networks are determined using molecular dynamics simulation techniques. It is found that the radii of curvature at center of the edges of the icosahedron both scale asN ^1/2 for the system sizes studied, whereN is proportional to the area of the surface. The radius of curvature at center of triangular faces is also found to scale asN ^1/2. Results for the mean vesicle shape are compared to those of minimum energy solutions of networks of similar size and elastic moduli. It is argued that system sizes several orders of magnitude larger than those studied here are necessary in order to observe the asymptotic scaling behavior predicted by Witten and Li.Dedicated to Prof. H. Wagner on the occasion of his 60th birthday     

小尺寸铜团簇冷却与并合过程中结构变化的原子尺度研究

研究Cu_N（N=57,58,59）熔融铜团簇在冷却过程以及300 K时两个具有二十面体结构Cu₅₅团簇在并合过程中的结构变化.对这些小尺寸团簇的结构变化采用基于嵌入原子方法的正则系综分子动力学进行计算机模拟.通过对模拟结果的分析表明,小团簇的冷却和并合过程存在阶段变化的特点.降温过程中Cu_N（N=57,58,59）团簇的原子运动及其微观结构变化表现出较大差异,由此导致这三类团簇内原子排布的不同,其中Cu₅₉团簇结构的有序程度最低.在两个Cu₅₅团簇并合早期阶段,这两个团簇相接触后发生变形导致原子位置出现较大改变,在随后的并合过程中,原子扩散引起原子局部位置调整导致所并合体系的结构发生变化.远离两个团簇接触区的原子仍保持其并合前的结构. 关键词： 团簇 分子动力学 计算机模拟 表面     

The NN → NNη reaction close to threshold

The pp → ppη and np → npη reactions at energies near the η production threshold are studied in a non-relativistic one boson exchange model, where the (1535 MeV) S11 resonance is excited through the exchange of π, η, ? and ω mesons and subsequently decays into an ηN pair. Energy integrated cross sections and energy spectra of the out going η's are reported. Providing NN and ηN final state interactions are taken into account coherently, the model reproduces both the scale and energy dependence of the cross section for the pp → ppη reactions up to 100 MeV. Final state interaction corrections due to the nucleon-nucleon and meson-nucleon forces influence strongly the scale and shape of the cross sections. The shape of the energy spectra of the outgoing η's provides a clear signature of the ηN force.     

Interfacial contribution to cluster free energy

The Monte Carlo technique of “overlapping distributions” is used for computing directly the free energy difference F_{N + 1} ?F_N between two clusters containing respectively N + 1 and N solute atoms, in the square and the simple cubic Ising model with nearest neighbour interactions. High accuracy results are obtained within reasonable computer times. The capillarity approximation gives a good fit to the data, provided the following is taken into account: (i) the specific bulk and surface energies are given their macroscopic equilibrium values; (ii) a curvature correction to the surface specific energy has to be introduced: it is positive for two dimensions and negative for three dimensions; (iii) a size independent term is to be added in three dimensions; it may be viewed as a corner contribution; (iv) the coefficient of the logarithmic term is given its more recent value. When introduced in the master equation which describes the kinetics of the cluster population, within the simplifying assumptions of the classical nucleation theory, good agreement is found, for the shapes of the cluster size distributions, with the numerical experiments on the kinetic Ising model in two dimensions. However, the time scales of both computations do not match linearly. Possible reasons for this discrepancy are discussed.     

Theoretical study of small Mo clusters and molecular nitrogen adsorption on Mo clusters

This paper studies the small molybdenum clusters of Mo_n (n=2--8) and their adsorption of N₂ molecule by using the density functional theory (DFT) with the generalized gradient approximation. The optimized structures of Mo_n clusters show the onset of a structural transition from a close-packed structure towards a body-centred cubic structure occurred at n=7. An analysis of adsorption energies suggests that the Mo₂ is of high inertness and Mo₆ cluster is of high activity against the adsorption of N₂. Calculated results indicate that the N₂ molecule prefers end-on mode by forming a linear or quasi-linear structure Mo--N--N, and the adsorption of nitrogen on molybdenum clusters is molecular adsorption with slightly elongated N--N bond. The electron density of highest occupied molecular orbital and lowest unoccupied molecular orbital, and the partial density of states of representative cluster are also used to characterize the adsorption properties of N₂ on the sized Mo_n clusters.     

Controlling X‐ray deformable mirrors during inspection

The X‐ray deformable mirror (XDM) is becoming widely used in the present synchrotron/free‐electron laser facilities because of its flexibility in correcting wavefront errors or modification of the beam size at the sample location. Owing to coupling among the N actuators of an XDM, (N + 1) or (2N + 1) scans are required to learn the response of each actuator one by one. When the mirror has an important number of actuators (N) and the actuator response time including stabilization or the necessary metrology time is long, the learning process can be time consuming. In this work, a fast and accurate method is presented to drive an XDM to a target shape usually with only three or four measurements during inspection. The metrology data are used as feedback to calculate the curvature discrepancy between the current and the target shapes. Three different derivative estimation methods are introduced to calculate the curvature from measured data. The mirror shape is becoming close to the target through iterative compensations. The feasibility of this simple and effective approach is demonstrated by a series of experiments.     

Decay reactions of rare gas cluster ions: Kinetic energy release distributions and binding energies

We have carried out measurements on metastable fragmentation of mass selected argon cluster ions which are produced by electron impact ionization of a neutral argon cluster beam. From the shape of the fragment ion peaks (MIKE scan technique) one can deduce information about the distribution of kinetic energy that is released in the decay reaction. In this study, for Ar ₅ ⁺ to Ar ₁₅ ⁺, it is Gaussian and thus we can calculate from the peak width the mean kinetic energy release 〈KER〉 of the corresponding decay reactions. Using finite heat bath theory we calculate from these data the binding energies of the decaying cluster ions. Received 20 November 2000