Bulk Limit Research Articles

Local binding trend and local electronic structures of 4d transition metals.

The local binding properties and electronic structures of 4d transition metals are studied by using a cluster model within the frame of density-functional theory. The equilibrium structures of all 4d transition-metal clusters are obtained by maximizing the binding energy of each cluster. The obtained mechanical properties, binding energies, and bond lengths well reproduced the trends displayed by corresponding set of bulk solids, which reveal that local interactions play a significant role in determining variations of binding properties of 4d transition metals. The bond lengths of clusters are found to converge more rapidly with cluster size toward their bulk limits than the binding energies. The relative stabilities of all clusters are discussed in terms of their ground-state electronic configurations. The contraction effect in valence-band widths (VBW's) is founded in clusters. The variation trend of VBW's for one cluster relative to another also bears analogs to the trend displayed by bulk solids. A striking correlation between magnetic moments and the magnitude of exchange splittings is found and elaborated. The mechanism leading to nonzero magnetizations and giant magnetic moments in some clusters is discussed in detail. \textcopyright{} 1996 The American Physical Society.

Analytic solution for the ground-state energy of the extensive many-body problem.

A closed form expression for the ground state energy density of the general extensive many-body problem is given in terms of the Lanczos tri-diagonal form of the Hamiltonian. Given the general expressions of the diagonal and off-diagonal elements of the Hamiltonian Lanczos matrix, $\alpha_n(N)$ and $\beta_n(N)$, asymptotic forms $\alpha(z)$ and $\beta(z)$ can be defined in terms of a new parameter $z\equiv n/N$ ($n$ is the Lanczos iteration and $N$ is the size of the system). By application of theorems on the zeros of orthogonal polynomials we find the ground-state energy density in the bulk limit to be given in general by ${\cal E}_0 = {\rm inf}\,\left[\alpha(z) - 2\,\beta(z)\right]$.

Excited states in metal voids.

Based on a variational model, we obtain the spectra of excited states in metallic voids. Void plasmons are seen to have a peculiar behavior, concerning the radius of the cavity, which can be ascribed to a delay in the onset of collectivity. This is further demonstrated by the electronic currents and transition densities obtained. One of the major features of the developed method is that it enables us to describe arbitrarily large voids, up to the bulk limit. \textcopyright{} 1996 The American Physical Society.

Size dependences of model nanostructure sound velocity

We study by means of numerical simulations the size dependences for sound velocity of model nanostructures. We use molecular dynamics to obtain the zero temperature size dependences of the propagation velocity of mechanical perturbation for rod-shaped nanostructures with free surfaces. The particles interact with the Stillinger–Weber potential for silicon. We consider the longitudinal sound propagation in the (001) direction only. The bulk limit is reached very quickly and the longitudinal velocity is already independent of the cross section for a nanofiber larger than 40×40 Å. We also study velocity for structures without free surfaces and the effect of changing the magnitude of the triplet interaction potentials.

Reply to ‘‘Comment on: ‘Multiband coupling effects on electron quantum well intersubband transitions’ ’’ [J. Appl. Phys. 80, 600 (1996)

It is shown that the 14 band k⋅p analysis of TE (x,y)-polarized quantum well intersubband transitions can be categorized as (i) second order (bulk limit), and (ii) first order (quantum limit) perturbation depending on the structures. In the quantum limit, TE-active intersubband transition prevails. This explains the recent reports of normal incident quantum well photodetectors made of InGaAs/GaAs, InGaAs/AlGaAs, and GaAs/AlGaAs.

MAGNETISM IN TRANSITION-METAL CLUSTERS FROM THE ATOM TO THE BULK

Molecular beam deflection measurements of small iron, cobalt, and nickel clusters show how magnetism develops as the cluster size is increased from several tens to several hundreds of atoms for temperatures from 80 and 1000 K. Cluster magnetization is found to be superparamagnetic for rotationally warm clusters, where it follows the Langevin function. The magnetization of rotationally cold clusters is anomalous: it is strongly reduced and nonlinear with the applied field. For superparamagnetic clusters, the magnetic moments can be determined from the magnetization. We find that ferromagnetism occurs even for the smallest sizes: for clusters with less than about 30 atoms the magnetic moments are atom-like and as the size is increased up to 700 atoms they approach the bulk limit, with oscillations probably caused by surface-induced spin-density waves. The trends are explained in a magnetic shell model. The magnetic properties of iron cluster show anomalies, suggesting that a high moment to low moment crystallographic phase transition in Fe clusters occurs at relatively low temperatures.

Molecular Clusters: Structure and Dynamics of Weakly Bound Systems

Weakly bound atomic and molecular clusters can be viewed as finite-size “pieces” of the condensed phases of matter. From both the experimental and theoretical points of view, the finite size of these clusters is of great advantage in simplifying the system, permitting molecular level characterization of solvent effects on the solute spectroscopy and chemical reaction dynamics. In addition, the ability to vary the number of atoms or molecules in the cluster enables us to observe how its various structural and dynamical properties evolve with size, from those typical of isolated gas phase molecules toward the bulk limit. By far the most detailed information has been obtained for binary complexes, where the issues of interest are the determination of intermolecular potential energy surfaces and understanding the vibrational dynamics of these complexes. Considerable progress has also been made in the characterization of higher-order complexes, which provide information on many-body interactions and more realistically approximate solvated systems. Since the breadth of this field precludes a complete review, we attempt here only to give some examples that illustrate the important issues and convey some of the excitement.

Molecules of jellium dimers

A simple tight-binding-like model of the electronic structure of simple metal clusters is presented which relies on the special stability of the first shell closures atNel=2 andNel=8. The wavefunctions, energy levels, and ground state deformations of the “ultimate jellium model”, which is based on a full Kohn-Sham treatment of the electrons, can be explained relying on a simple geometrical growth pattern complemented by an extremely simplified Hamiltonian matrix. The bulk and surface limits of the model also yield reasonable results.

Low damping of micron capillary waves on superfluid 4He.

Capillary waves (ripplons) in the wavelength range 3.3--20 \ensuremath{\mu}m on a superfluid ${}^{4}$He layer of continuously controllable thickness are generated and detected with coplanar interdigital capacitors. In the bulk limit, the waves propagate over several centimeters at low temperature and the attenuation factor is compatible with a ${T}^{4}$ power law in the temperature interval 300--700 mK. The damping is about 6 orders of magnitude smaller than previous theoretical estimates of ripplon-ripplon scattering. The results point instead to scattering of ripplons by phonons, in accord with a revised calculation.

Systematics of pure and doped 4He clusters.

Optimized variational calculations have been carried out for pure and doped clusters of $^{4}\mathrm{He}$ atoms up to a cluster size of N=1000 particles. For small cluster sizes with less than or equal to 112 particles, where comparisions with existing diffusion Monte Carlo results are possible, we find excellent agreement for the ground-state energy, correlation, and structure functions. For larger clusters our ground-state energies extrapolate smoothly toward a bulk limit of -7.2 K with a surface energy of 0.272 K A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}2}$. The resulting ground-state densities show unmistakable oscillations, confirming our earlier conclusions based on diffusion Monte Carlo studies. The present study of large clusters allows us to bridge the gap between finite systems and the bulk limit. Specifically, we show how the bulk limit of collective energies is reached as well as how the bulk Feynman spectrum is reproduced in the S-wave component of the dynamic structure function in large droplets. By plotting the collective excitation energy of higher multipole modes as a function of an effective wave number k=\ensuremath{\surd}scrl(scrl+1)/R, we show that the resulting spectrum can be directly compared with experimental excitation energies determined for plane liquid surfaces and films. By summing up to scrl=50 partial wave components, we show that the full dynamic structure function simultaneously displays the phonon-roton and the ripplon excitation spectrum. In the case of helium droplets doped with impurities such as rare gas atoms or the ${\mathrm{SF}}_{6}$ molecule, we show that the dipole collective mode becomes unstable with increased droplet size, strongly indicating that these impurities are delocalized inside large droplets. The microscopic character of the instability is revealed in the excitation functions and transition densities of the dipole mode. The introduction of impurities also profoundly alters the dynamic structure function, severely ``fragments'' the Feynman spectrum, and obliterates landmark structures such as the maxon and the roton.

ON THE BOUNDARY MAGNETIZATION OF SOME LAYERED MODEL

In the present letter we generalize a previous exact result for the boundary magnetization of the two-dimensional layered Ising model, obtaining an expression in which the bulk limits of the interactions do not appear explicitly. The formula we have obtained is applicable even when such limits are not defined, as is for aperiodic systems, which are briefly discussed. The methods used, developed for Ising-like models, are then extended to quantum antiferromagnetic chains at zero temperature.

A microscopic coupled‐cluster treatment of electronic correlations in Hubbard models

AbstractWe recently applied the coupled‐cluster method (CCM) with considerable success to several novel quantum spin‐lattice systems in the infinite bulk limit. In this article, we extend our CCM analysis to the electronic Hubbard models. In particular, based on a systematic approximation scheme within the CCM, we investigate the zero‐temperature properties of Hubbard models at half‐filling and with a single hole on a general bipartite lattice. Our aim was to provide the CCM framework for a systematic calculation of the properties of Hubbard models. © 1995 John Wiley & Sons, Inc.

Directed compact percolation near a wall. II. Cluster length and size

For paper I, see ibid., vol.27, p.3743-50 (1994). The mean cluster size and length for the unbiassed growth of compact clusters near a dry wall are considered. In the case of the cluster size below pc an exact expression is obtained for a seed of arbitrary width and distance from the surface. It is found that the critical exponent gamma =1 for any finite distance from the surface. Crossover to the bulk value gamma =2 as the distance from the surface tends to infinity is observed. This extends an existing result for the exponent beta of the percolation probability which changes from a value of 2 in the presence of a surface to 1 in the bulk limit. The value Delta =3 of the scaling size exponent is unchanged by the introduction of the surface. The cluster size above pc and the mean cluster length are investigated using differential approximants from which we conjecture that these functions satisfy second-order differential equations. Accepting this conjecture gives a mean size exponent the same as below pc and a logarithmic divergence of the mean length from both sides of the critical point. The latter result together with scaling theory predicts that the exponent v/sub /// has the value 2, the same as for the bulk problem.

Static Crossover of Critical Behavior in Polymer Blend Solutions: Scaling Analysis of the Ginzburg Number

By means of light scattering, the static critical behavior was investigated for symmetrical polymer blend solutions of polystyrene/poly(methyl methacrylate)/deuterated benzene and polystyrene/poly(2-chlorostyrene)/deuterated benzene with different polymeric indices N and polymer concentrations c. The temperature dependence of the isothermal susceptibility S T and the correlation length ξ t near the stability limit showed the static crossover from the mean-field to the three-dimensional Ising behavior in all solutions. The Ginzburg number Gi BK was evaluated with the aid of the crossover function of Belyakov and Kiselev. As c increases from the semidilute region to the bulk limit, the scaled Ginzburg number gi BK = Gi BK N decreased, with the power α of gi BK ∞ c α being -1.25 to -2 as expected by the theory based on the blob concept. The values of gi BK (bare) evaluated by the bare interactions were smaller than experimental values.

Mutual-induction measurement of the AC penetration depth in HTSC's theory of calibration function for flat samples under axial symmetry

A contribution to find optimum mutual-induction arrangements for investigating the linear AC response properties of the pinned vortices in the mixed state of HTSC is given. In particular, the complex calibration function (mutual-induction coefficient L 12 as a function of the complex AC penetration depth λ) is analyzed, strictly axial symmetry and flat sample geometries provided (finite disk and its limiting case of infinite platelet) assuming the radius of at least one induction coil is smaller than the sample radius. Because the sample is positioned transverse to the AC induction B , the mutual inductance becomes, in general, strongly modified by distortions of B around the sample, which results in a strong dependence of L 12(λ) upon certain geometry parameters and an enhanced sensitivity to λ for selected |λ| intervals. The analysis is based upon powerful analytic approximation formulae for elementary arrangements derived in a separate paper. Also, formulae to estimate the errors from irregular (eccentric) sample shapes, from the field enhancement near the disk edges as well as from treating the finite-disk problem in the limit of an infinite platelet are given. Except for ultrathin films with thickness much smaller than |λ|, arrangements with both the coils at the same sample side and with the loop radii sufficiently smaller than the disk radius are favored for measurements of small λ with |D/λ| ≳ 1 ( D is the sample thickness), which also includes the possibility of a λ measurement in the bulk limit | D/λ| → ∞.

Inductive response of HTSC platelets and disks due to AC conductivity analytic theory for axial symmetry

The electrodynamic boundary-value problem which is basic for the AC penetration depth and conductivity measurement of HTSC samples by means of the mutual-induction technique is re-examined, and novel analytic solutions are presented. In particular, the vector potential from the exciting current in a circular driving loop and its perturbation due to the induced currents in the neighboring HTSC sample is studied, axial symmetry provided. This paper is mainly concerned with arrangements characterized by a strong field perturbation from the sample, combined with a field concentration in certain sample regions, but far from the sample edges, namely disk-shaped samples with radius larger than the driving loop radius. Both the limiting case of the infinite platelet, and/or the AC penetration depth much smaller than the sample thickness (bulk limit) are included. Powerful asymptotic methods are used to evaluate the complicated integral representations for the infinite-platelet problem. Asymptotic methods are also introduced to solve the integral equations for the finite disk. Remainders are given to estimate the correctness of the analytic approximations.

Strange hadronic matter

Recent investigations of regions of stability for multi-strange hadronic systems, made up of nucleons and hyperons {p, n, Λ, Ξ 0, Ξ −}, are reviewed. Relativistic mean field calculations, designed to reproduce the observed binding energies of ordinary nuclei and of Λ, Ξ and ΛΛ hypernuclei, predict a large class of such objects which are stable against strong decay, including the bulk limit A → ∞, with binding energies per baryon as large as E B A ∼ −22 MeV , large strangeness per baryon f s ∼ 1–1.2, small charge per baryon f q ∼ −0.1 to 0 and with baryon densities 2–3 times that of ordinary nuclear matter. A straightforward extension of the Bethe-Weizsäcker mass formula into the strange domain accounts satisfactorily for all of these features.

Boundary magnetization of a two-dimensional Ising model with inhomogeneous nearest-neighbor interactions.

An explicit formula for the boundary magnetization of a two-dimensional Ising model with a strip of inhomogeneous interactions is obtained by means of a transfer matrix mean-field method introduced by Lipowski and Suzuki. There is clear numerical evidence that the formula is exact By taking the limit where the width of the strip approaches infinity and the interactions have well defined bulk limits, I arrive at the boundary magnetization for a model which includes the Hilhorst--van Leeuwen model. The rich critical behavior of the latter magnetization is thereby rederived with little effort.

Magnetism from the Atom to the Bulk in Iron, Cobalt, and Nickel Clusters

Molecular beam deflection measurements of small iron, cobalt, and nickel clusters show how magnetism develops as the cluster size is increased from several tens to several hundreds of atoms for temperatures between 80 and 1000 K. Ferromagnetism occurs even for the smallest sizes: for clusters with fewer than about 30 atoms the magnetic moments are atomlike; as the size is increased up to 700 atoms, the magnetic moments approach the bulk limit, with oscillations probably caused by surface-induced spin-density waves. The trends are explained in a magnetic shell model. A crystallographic phase transition from high moment to low moment in iron clusters has also been identified.

Excitonic wave function, correlation energy, exchange energy, and oscillator strength in a cubic quantum dot.

We present a variational calculation of the envelope wave function of an exciton inside a cube. We show that all sixfold integrals can be reduced to threefold integrals with a change of variables which shortens tremendously the computer calculations. Then (i) we calculate numerically the Bohr radius, the correlation energy (the difference between the energy of the exciton and of the uncorrelated electron-hole pair), the exchange energy, and the oscillator strength of the exciton for any value of the cube side and (ii) we obtain asymptotic expression of these four quantities for a large cube. This allows one to discern the difference between a large but finite cubic semiconductor and an infinite semiconductor. We show that the correlation energy tends to its bulk limit value in infinite volume as the inverse of the cube side while the effective Bohr radius and the exchange energy tend to their limiting value as the inverse of the square of the side. Finally our results are applied to porous silicon: the experimental exchange energy 10 meV corresponds to a cube of side 28 \AA{} which is quite reasonable in this compound.