Magic Sizes Research Articles

Blue light emitting diodes based on fluorescent CdSe∕ZnS nanocrystals

The authors report on the blue electroluminescence from CdSe∕ZnS core/shell nanocrystals prepared from ultrasmall, magic size CdSe clusters that have a diameter of less than 2nm. The light emitting device consists of an active layer of nanocrystals blended with 4,4′,N,N′- diphenylcarbazole and an evaporated electron transporting/hole blocking layer made of 2,9-dimethyl-4,7-diphenyl-1,10-phenanthroline. A blue, stable electroluminescence at 485nm from the hybrid device was observed, in good agreement with the photoluminescence spectra of a solid film of the same nanocrystals used for the device.

Collapse of Transient Nucleation Fluxes in a Cold Ising Ferromagnet

We report the time-dependent nucleation fluxes and associated nucleation rates in a metastable Ising ferromagnet on square lattice with Metropolis (Glauber-type) dynamics. It is discovered that, with lowering of the temperature, fluxes collapse into several representative transient curves corresponding to magic cluster sizes. Those can be associated with physical droplets, i.e., long-lived configurations which provide a link with the classical Becker-Döring picture.

Structure of small clusters of parahydrogen molecules

The ground state energies and the one-body densities of parahydrogen clusters have been systematically calculated by the diffusion Monte Carlo technique in steps of one molecule from $3\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}50\phantom{\rule{0.3em}{0ex}}\text{molecules}$. These calculations show that parahydrogen clusters exhibit a clear geometrical order which excludes any liquidlike structure. A definite confirmation of the magic size for the cluster with $13\phantom{\rule{0.3em}{0ex}}\text{molecules}$ is also obtained.

The dynamics of small excitable ion channel clusters

Through computational modeling we predict that small sodium ion channel clusters on small patches of membrane can encode electric signals most efficiently at certain magic cluster sizes. We show that this effect can be traced back to algebraic features of small integers and are universal for channels with a simple gating dynamics. We further explore physiologic conditions under which such effects can occur.

Molecular-dynamics study of possible packing sequence of medium size gold clusters: Au 2–Au 43

Growing pattern, structural stability, energetics and magic sizes of gold clusters, Au n ( n = 2 –43), have been investigated by using molecular-dynamics simulations. Starting from the dimer configuration, following rearrangement collision of the system in fusion process, and absorbing its energy step by step up to 0 K, possible stable structures of the clusters have been identified via an empirical model potential energy function. It has been found that gold clusters prefer to form three-dimensional compact structures and five-fold symmetry appears on the spherical medium clusters. This approach serves an efficient alternative to the growing path determination and the global optimization techniques.

Fabrication of uniform Au silicide islands on the Si(1 1 1)-(7 × 7) substrate

The Au silicide islands have been fabricated by additional deposition of Au on the prepared surface at 270 °C where the Si islands of magic sizes were formed on the Si(1 1 1)-(7 × 7) dimer-adatom-stacking fault substrate. The surface structure on the Au silicide islands shows the Au/Si(1 1 1)-√3 × √3 reconstructed structure although the substrate remains 7 × 7 DAS structure. The size of the Au silicide islands depends on the size distribution of the preformed Si islands, because the initial size and shape of the Si islands play important roles in the formation of the Au silicide island. We have achieved the fabrication of the Au silicide islands of about the same size (∼5 nm) and the same shape by controlling the initial Si growth and the additional Au growth conditions.

Numerical dispersion and numerical loss in explicit finite-difference time-domain methods in lossy media

The numerical dispersion relations of finite-difference time-domain (FDTD) methods have been analyzed extensively in lossless media. This paper investigates numerical dispersion and loss for Yee's FDTD in lossy media. It is shown that: the numerical velocity can be smaller or larger than the physical velocity; there is no magic time step size in lossy media; and the numerical loss is smallest at the Courant limit. It is shown that the numerical loss is always larger than its physical value, and so Yee's FDTD overestimates the absorption of electromagnetic energy in lossy media. The numerical velocity anisotropy can be positive or negative, but the numerical loss anisotropy is always positive. The anisotropies in the three-dimensional (3-D) case are usually larger than those in the 2-D case. Numerical experiments in 1-D are shown to agree with the theoretical prediction.

Computer Simulation of Quantum Melting in Hydrogen Clusters

We introduce a new criterion, based on multipole dynamical correlations calculated within reptation quantum Monte Carlo, to discriminate between a melting versus freezing behavior in quantum clusters. This criterion is applied to small clusters of para-hydrogen molecules (both pristine and doped with a CO chromophore), for cluster sizes of around twelve molecules. This is a magic size at which para-hydrogen clusters display an icosahedral structure and a large stability. Despite the similar geometric structure of CO@(pH2)12 and (pH2)13, the first system has a rigid, crystalline, behavior; the second behaves more like a superfluid (or, possibly, a supersolid).

Nanoscale lead and noble gas inclusions in aluminum: Structures and properties

Transmission electron microscopy has been used for structural and physical characterization of nanoscale inclusions of lead and noble gases in aluminum. When the inclusion sizes approach nanoscale dimensions, many of their properties are seen to deviate from similar properties in bulk and in most cases the deviations will increase as the inclusion sizes decrease. Binary alloys of lead and noble gases with aluminum are characterized by extremely low mutual solubilities and inclusions will, therefore, exist as practically pure components embedded in the aluminum matrix. Furthermore, the thermal vacancy mobility in aluminum at and above room temperature is sufficiently high to accommodate volume strains associated with the inclusions thus leading to virtually strain free crystals. The inclusions grow in parallel cube alignment with the aluminum matrix and have a cuboctahedral shape, which reflects directly the anisotropy of the interfacial energies. Inclusions in grain boundaries can have single crystalline or bicrystalline morphology that can be explained from a generalized Wulff analysis such as the xi-vector construction. The inclusions have been found to display a variety of nanoscale features such as high Laplace pressure, size-dependent superheating during melting, deviations from the Wulff shape displaying magic size effects, a shape dependence of edge energy, and so on. All these effects have been observed and monitored by TEM using conventional imaging conditions and high-resolution conditions in combination with in-situ analysis at elevated temperatures.

Atomic scale friction of nanoscale clusters

We study both the activation energy for diffusion and dynamics of nanoscale clusters of a Frenkel–Kontrova chain subject to the microscopic friction, in connection with atomic friction phenomena. We clarify the atomistic mechanism for the presence of a magic size for diffusion and show how the magic size effects appear in the friction. When a cluster is pulled by a constant driving force, the critical force strength of depinning depends crucially on the cluster size, and it is smallest at the magic size. When a cluster is pulled by a spring at a constant velocity below the critical value, clusters show a stick-and-slip motion, and the maximum force of a spring also becomes smallest at the magic size.

Photodissociation and photoionization of sodium coated C $_\mathsf{60}$ clusters

(C60) m Na n clusters are produced in a tandem laser vaporization source and analyzed by photoionization and photofragmentation time-of-flight mass spectroscopy. At low sodium coverage, the special behavior of (C60) m=1,2Na n clusters $(n\leq 6m)$ is consistent with a significant electron transfer from the first six adsorbed atoms towards each of the C60 fullerenes and an ionic-like bonding in this size range. However, the stability of the (C60)Na3 + cation is found much more pronounced than the one of (C60)Na7 + predicted to be a magic size under the hypothesis of a full charge transfer from the metal atoms to the C60 molecule. When more sodium atoms are present, metal-metal bonds tend to become preponderant and control the cluster properties. Relative to the number of sodium atoms, an odd-even alternation in their stability is explained by the high dissociation rates for even-numbered clusters. The even clusters evaporate neutral sodium atoms whereas odd ones prefer to evaporate Na2 molecules. The hypotheses for the growth of a sodium droplet that does not wet the fullerene surface or for the formation of a concentric metallic layer are discussed in the light of this study.

“Magic size” effect in the packing of n-alkanes on Au(1 1 1): evidence of lowered sliding force for molecules with specific length

Molecular structure of monolayers formed at the interface between Au(111) surfaces and solutions containing n-alkanes has been studied by in situ scanning tunneling microscopy at room temperature. Increasing the CnH2n+2 length from n=10 up to 50 with even n numbers alternates rectangular and tilted arrangement of alkanes within the self-organized layers. This alternation is related to the dramatically lowered sliding force for molecules with a length close to mT (m-integer), where T is the period of commensurability between the CH2–CH2–CH2 period along alkyl chains and the interatomic distance along Au〈110〉 direction.

'Magic-size' GeSi and Si nanocrystals created by ion bombardment of hexagonal SiC; a molecular dynamics study

We recently showed that GeSi and Si nanocrystals created after Ge- and Si-ion implantation into hexagonal SiC and subsequent annealing contain a high percentage of hexagonality. Here we demonstrate that the nanocrystals are of 'magic sizes' and are microtwinned. Both these features are explained by molecular dynamics calculations.

Real-time heat capacity measurement during thin-film deposition by scanning nanocalorimetry

The scanning nanocalorimetry technique is utilized to characterize thin-film growth in real-time. The technique generates three-dimensional heat capacity data as a function of temperature and thickness that show the continuous change of indium film during deposition. The measurement interval is ∼4×10−3 nm in thickness. Indium thin films form nanoparticles on silicon nitride surfaces that show the phenomena of melting point depression and the formation of magic number size particles. The measured increment of the heat capacity ΔCp is ∼30 pJ/K and the temperature resolution is better than 0.5 K.

Non-crystalline structures in the growth of silver nanoclusters

The growth of nanometer-size free Ag clusters is studied by Molecular Dynamics simulations. The morphology transition from the icosahedron at the magic size of N = 55 atoms to the Marks truncated decahedron at N = 75 is analyzed in details, in order to single out kinetic trapping and entropic effects. At very low T, the cluster is kinetically trapped in an icosahedral structure. At intermediate T the transition takes place sharply at N≃ 65. At higher T, the transition is smeared out and finally, around 550 K no transition is found because the 75 decahedron is melted.

Electronic and geometric properties of exohedral sodium- and gold-fullerenes

The electronic and geometric properties of gas-phase exohedral C60NaN−, C70NaN−, and C60AuN− cluster anions are investigated. Time-of-flight mass spectrometry and photoelectron spectroscopy (PES) reveal complex-specific arrangements of the sodium and the gold atoms on the fullerene cage. The electron affinity of C60AuN clearly shows even–odd alternation with the number of Au atoms, which suggests a “dry” structure where Au atoms aggregate as a cluster on the C60. In contrast, C60NaN and C70NaN show a “wet” structure having the Na atoms packed into stable trimers on the surface. For C60NaN (N=0 to 4), PES experiments at a high photodetachment energy (5.81 eV) allow us to deduce the net charge transferred from the sodium atoms to the lowest unoccupied molecular orbital of the fullerene. For larger C60NaN, moreover, a metallic transition is shown to occur at N∼13, and analysis of the adiabatic electron affinity variations allows the identification of the first magic sizes corresponding to electronic shell closure in the sodium layer.

Shapes and sizes of nanoscale Pb inclusions in Al

Al–Pb alloys are monotectic and characterized by a large miscibility gap in the liquid phase area and extremely limited mutual solubility in the solid phase. Due to the extent of the miscibility gap the alloys are difficult to make in conventional processing. However, alloys with relatively homogeneous microstructures of fine Pb inclusions in an Al matrix can be made by metastable processing such as rapid solidification, ion implantation, ball milling and physical vapor deposition. The first two techniques have been employed to make alloys of Al with 0.5–3 at.% Pb. The alloys contain fine dispersions of nanoscale Pb inclusions with sizes in the range from 1 to about 20 nm after ion implantation and from about 10–500 nm after rapid solidification. Inclusions embedded in the Al matrix are single crystalline, and they grow in parallel cube alignment with the matrix. They have cuboctahedral shape with atomically smooth {1 1 1} and {1 0 0} facets determined from a minimization of the interface energy. Using high resolution TEM, two types of deviations from the classical Wulff construction which alter the shape of the inclusions, have been studied. The smallest inclusions, less than about 20 nm in size, adopt a series of magic sizes that can be related to the occurrence of periodic minima in the residual strain energy. Likewise, in this size range, the energy contribution from the cuboctahedral edges becomes non-negligible leading to an increase in the aspect ratio of the inclusions with decreasing size. Inclusions located in grain boundaries in general adopt a single crystal morphology where one part is faceted and grows in parallel cube alignment with the matrix grain, while the other part has a shape approximating a spherical cap. In special cases such as twin boundaries and {1 1 1} twist boundaries, the inclusions are bicrystalline where each part is aligned with the respective grain and the two parts are separated by a boundary similar to that of the matrix. These shapes can be explained using the Cahn–Hoffman ξ-vector construction, which generalizes the Wulff construction to determine equilibrium shapes at anisotropic interfaces and their junctions.

Nuclear isotope shifts within the local energy-density functional approach

The foundation of the local energy-density functional method to describe the nuclear ground-state properties is given. The method is used to investigate differential observables such as the odd–even mass differences and odd–even effects in charge radii. For a few isotope chains of spherical nuclei, the calculations are performed with an exact treatment of the Gor'kov equations in the coordinate-space representation. A zero-range cutoff density-dependent pairing interaction with a density-gradient term is used. The evolution of charge radii and nucleon separation energies is reproduced reasonably well including kinks at magic neutron numbers and sizes of staggering. It is shown that the density-dependent pairing may also induce sizeable staggering and kinks in the evolution of the mean energies of multipole excitations. The results are compared with the conventional mean field Skyrme–HFB and relativistic Hartree–BCS calculations. With the formulated approach, an extrapolation from the pairing properties of finite nuclei to pairing in infinite matter is considered, and the dilute limit near the critical point, at which the regime changes from weak to strong pairing, is discussed.

Tem Investigation Of Precipitate Shapes And New Interface Phenomena In Al-Pb Alloys

Abstract Transmission electron microscopy plays a key role in the investigation of precipitates and inclusions because it provides direct information at high spatial resolution, on their shape, orientation relationship, interface structure and composition. This work has utilized high resolution and in-situ electron microscopy to study the equilibrium shapes and thermal behavior of Pb precipitates in Al. It was found that PB precipitates within Al grains form in parallel-cube orientation relationship, are cuboctahedral in shape, adopt a sequence of magic sizes, and display an increase in aspect ratio with decreasing size. These observations have been explained in terms of interfacial energy and residual strain energy. When the same Pb precipitates form on grain boundaries, their shapes are significantly different. This is apparent from figure 1 which shows a 90° <110> tilt grain boundary in Al with a small cuboctahedral Pb precipitate in the upper grain and a large complex-shaped Pb particle on the grain boundary.

Observation of nanometer silicon clusters in the hot-filament CVD process

Currents of 0.2–5 μA were measured in the hot filament CVD chamber for deposition of silicon. In such a highly ionizing atmosphere with the appreciable supersaturation for precipitation of silicon, it is highly probable that the charged clusters should be formed in the gas phase by ion-induced or photo-induced nucleation. The predicted nanometer silicon clusters were observed by TEM on a carbon membrane, which was placed in the hot-filament CVD chamber in the Si–Cl–H system. The clusters for the filament temperatures of 1800 and 1600°C were ∼2 nm and 5–7 nm, respectively. The film grown by the deposition of these clusters did not show any identity of the individual clusters, making the film indistinguishable from that grown by the atomic unit. In the case of the halogen lamp heating instead of the hot filament, however, the film consists of the large clusters of ∼50 nm and the morphology is similar to the cauliflower structure. The morphological difference between the two heating sources was explained by Fujita's concept of the magic size.