Monomer Adsorption-Desorption Processes

We propose an adsorption-desorption model for a deposit growth system, in which the adsorption and desorption of particles coexist. By means of the generalized rate equation we investigate the cluster （island） size distribution in the dynamic equilibrium state. The results show that the evolution behaviour of the system depends crucially on the details of the rate kernels. The cluster size distribution can take the scale-free power-law form in some cases, while it grows exponentially with size in other cases.     

熔融Cu55团簇在Cu(010)表面上凝固过程的分子动力学模拟

采用基于嵌入原子方法的分子动力学,模拟了熔融Cu₅₅团簇在Cu衬底（010）表面上以两个不同降温速率降温过程中结构的变化.模拟结果表明,降温速率对团簇结构的变化有很大影响.较快的降温速率使得降温过程中团簇原子具有较低的能量;较慢的降温速率有助于高温时位于衬底内的原子向衬底表面扩散,排列形成面心立方结构. 关键词： 团簇 凝固 分子动力学 表面     

熔融Cu55团簇在Cu(010)表面上凝固过程的分子动力学模拟

采用基于嵌入原子方法的分子动力学,模拟了熔融Cu55团簇在Cu衬底(010)表面上以两个不同降温速率降温过程中结构的变化.模拟结果表明,降温速率对团簇结构的变化有很大影响.较快的降温速率使得降温过程中团簇原子具有较低的能量;较慢的降温速率有助于高温时位于衬底内的原子向衬底表面扩散,排列形成面心立方结构.     

A Solvable Symbiosis-Driven Growth Model

We introduce a two-species symbiosis-driven growth model, in which two species can mutually benefit for their monomer birth and the self-death of each species simultaneously occurs. By means of the generalized rate equation, we investigate the dynamic evolution of the system under the monodisperse initial condition. It is found that the kinetic behaviour of the system depends crucially on the details of the rate kernels as well as the initial concentration distributions. The cluster size distribution of either species cannot be scaled in most cases; while in some special cases, they both consistently take the universal scaling form. Moreover, in some cases the system may undergo a gelation transition and the pre-gelation behaviour of the cluster size distributions satisfies the scaling form in the vicinity of the gelation point. On the other hand, the two species always live and die together.     

Kinetics of Catalysis-Driven Aggregation Processes with Sequential Input of Catalyst

We investigate the kinetic behavior of a two-species catalysis-driven aggregation model, in which coagulation of species A occurs only with the help of species B. We suppose the monomers of species B are stable and cannot selfcoagulate in reaction processes. Meanwhile, the monomers are continuously injected into the system. The model with a constant rate kernel is investigated by means of the mean-field rate equation. We show that the Mneties of the system depends crucially on the details of the input term. The injection rate of species B is assumed to take the given time- dependent form K（t） -t^λ, and the sealing solution of the duster size distribution is then investigated analytically. It is found that the cluster size distribution can satisfy the conventional or modified scaling form in most cases.     

Diffusion and Growth of Metal Clusters in Nanocomposites: A Kinetic Monte Carlo Study

Noble metals that are deposited on a polymer surface exhibit surface diffusion and diffusion into the bulk. At the same time the metal atoms tend to form clusters because their cohesive energy is about two orders of magnitude higher than the cohesive energy of polymers. To selfconsistently simulate these coupled processes, we present in this paper a Kinetic Monte Carlo approach. Using a simple model with diffusion coefficients taken as input parameters allows us to perform a systematic study of the behavior of a large ensemble of metal atoms on a polymer surface eventually leading to polymer nanocomposites. Special emphasis is placed on the cluster growth, cluster size distribution and the penetration of clusters into the substrate. We also study the influence of surface defects and analyze how the properties of the resulting material can be controlled by variation of the deposition rate (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A partition function model for nucleation on surfaces

Using a procedure to minimize the total Helmholtz free energy of a system composed of an idealized substrate, a collection of surface clusters, and a vapor in contact with the surface, an expression is derived for the concentration of clusters of a given size on the substrate. The result is based on several assumptions about the system, the most important being that the surface clusters do not interact and that the substrate remains intact. The expression for the concentration of surface clusters together with the conventional form for the growth rate of clusters on a surface can be used to calculate surface nucleation rates.     

Nucleation of catalyst clusters during the growth of carbon nanotubes

The formation of cluster in the course of pyrolysis of ferrocene is studied experimentally and theoretically, and the parameters of the clusters are determined. The thermodynamics of homogeneous formation of catalyst clusters is developed. It is shown that the surface tension and sizes of the clusters substantially depend on the temperature and the properties of the substrate. Surface tension coefficients, as well as the characteristic sizes of clusters, are calculated. The resultant dependences and parameters make it possible to reconstruct the size distribution function for the clusters growing on a certain substrate by setting the temperature in the working zone. This permits the prediction of the cluster size depending on the synthesis conditions.     

气体团簇离子束装置的设计及其在表面平坦化、自组装纳米结构中的应用

根据超声膨胀原理,n(10-10^4)个气体原子可以绝热冷却后凝聚在一起形成团簇,经过离化后,形成带一个电荷量的团簇离子,比如Arn^+.当团簇离子与固体材料相互作用时,由于平均每个原子携带的能量(~eV)较低,仅作用于材料浅表面区域,因此,气体团簇离子束是材料表面改性的优良选择.本文介绍了一台由武汉大学加速器实验室自主研制的气体团簇离子束装置,包括整体构造、工作原理及实验应用.中性团簇束由金属锥形喷嘴(F=65-135μm,q=14°)形成,平均尺寸为3000 atoms/cluster,经离化后,其离子束流达到了50μA.Ar团簇离子因其反应活性较低,本文运用Ar团簇离子(平均尺寸为1000 atoms/cluster)进行了平坦化和自组装纳米结构的研究.单晶硅片经Ar团簇离子束处理后,均方根粗糙度由初始的1.92 nm降低到0.5 nm,同时观察到了束流的清洁效应.利用Ar团簇离子束的倾斜(30°-60°)轰击,在宽大平坦的单晶ZnO基片上形成了纳米波纹,而在ZnO纳米棒表面则形成了有序的纳米台阶,同时,利用二维功率谱密度函数分析了纳米结构在基片上的表面形貌和特征分布,并计算了纳米波纹的尺寸和数量.     

Revision of single atom local density and capture number varying with coverage in uniform depletion approximation and its effect on coalescence and number of stable clusters

In vapour deposition,single atoms (adatoms) on the substrate surface are the main source of growth.The change in its density plays a decisive role in the growth of thin films and quantum size islands.In the nucleation and cluster coalescence stages of vapour deposition,the growth of stable clusters occurs on the substrate surface covered by stable clusters.Nucleation occurs in the non-covered part,while the total area covered by stable clusters on the substrate surface will gradually increase.Carefully taking into account the coverage effect,a revised single atom density rate equation is given for the famous and widely used thin-film rate equation theory,but the work of solving the revised equation has not been done.In this paper,we solve the equation and obtain the single-atom density and capture number by using a uniform depletion approximation.We determine that the single atom density is much lower than that evaluated from the single atom density rate equation in the traditional rate equation theory when the stable cluster coverage fraction is large,and it goes down very fast with an increase in the coverage fraction.The revised equation gives a higher value for the ’average’ capture number than the present equation.It also increases with increasing coverage.That makes the preparation of single crystalline thin film materials difficult and the size control of quantum size islands complicated.We also discuss the effect of the revision on coalescence and the number of stable clusters in vapour deposition.     

Analytical Results of a Two-Species Predator-Prey Model

We propose a sequential monomer reaction model for a two-species predator-prey system, in which the aggregates of either species can spontaneously produce or lose one monomer and meanwhile, a type-B aggregate can prey upon one monomer of a type-A aggregate when they meet. Using the mean-field rate equation approach, we analytically investigate the kinetic behavior of the system. The results show that the evolution of the system depends crucially on the details of the rate kernels. The aggregate size distribution of either species approaches the conventional or modified scaling form in most cases. Moreover, the total size of either species grows exponentially with time in some cases and asymptotically retains a constant quantity in other cases, while it decays with time and vanishes finally in the rest cases.     

Atom deposition on surface clusters: thin film growth on Pd(111)

We have studied the vapor phase deposition of single metal atoms on two-dimensional clusters at the Pd(111) surface. The system considered here are heptamers and dodecamers for the substrate temperature of 100 K. Using molecular dynamics simulations with the corrected effective medium potentials for Pd, Cu and Rh, we have found that an adatom either diffuses on the cluster or incorporates itself into the cluster depending on the size of clusters and the kind of metals in the gas/cluster system. We also discovered that incorporation of a deposited gas atom into a surface cluster at 100 K was not a consequence of the reduction of the barrier heights at the step edges and that the type of post-impact dynamics for hexagonal heptamers depends on the impact point.     

分子动力学模拟Cu(010)基体对负载Co-Cu双金属团簇熔化过程的影响

纳米团簇负载到基体上的结构演化和热稳定性是其走向技术应用的关键. 本文用分子动力学结合嵌入原子方法模拟了具有二十面体初始结构的Co₂₈₁Cu₂₈₀ 混合双金属团簇在Cu(010)基体上的熔化过程, 考察了基体的Cu原子可以自由移动(自由基体)和固定(固定基体)两种条件对负载团簇熔化的影响. 发现基体条件对团簇的熔化有明显的影响. 在自由基体上团簇原子的温度-能量曲线存在明显的团簇熔化时的能量突变点, 熔点为1320 K, 低于固定基体上团簇的熔点1630 K. 在升温过程中团簇的二十面体结构会在基体表面发生外延生长. 外延团簇随着温度增加发生表面预熔, 预熔原子会逐渐向基体表面扩散形成薄层, 直至完全熔化. 自由基体上团簇原子的嵌入行为会使原子的分布状态产生不同于固定基体上的演变.     

Evolution of imitation networks in Minority Game model

The Minority Game is adapted to study the “imitation dilemma”, i.e. the tradeoff between local benefit and global harm coming from imitation. The agents are placed on a substrate network and are allowed to imitate more successful neighbours. Imitation domains, which are oriented trees, are formed. We investigate size distribution of the domains and in-degree distribution within the trees. We use four types of substrate: one-dimensional chain; Erd?s-Rényi graph; Barabási-Albert scale-free graph; Barabási-Albert 'model A' graph. The behaviour of some features of the imitation network strongly depend on the information cost epsilon, which is the percentage of gain the imitators must pay to the imitated. Generally, the system tends to form a few domains of equal size. However, positive epsilon makes the system stay in a long-lasting metastable state with complex structure. The in-degree distribution is found to follow a power law in two cases of those studied: for Erd?s-Rényi substrate for any epsilon and for Barabási-Albert scale-free substrate for large enough epsilon. A brief comparison with empirical data is provided.     

Experimental studies of complex crater formation under cluster implantation of solids

The results of a systematic study of surface defect formation after energetic Ar_n⁺ (n = 12, 22, 32, 54) and Xe_n⁺ (n = 4, 16) cluster ion implantation into silicon and sapphire are presented. Implantation energies vary from 3 to 18 keV/ion. Two cases of comparative studies are carried out: the same cluster species are implanted into two different substrates, i.e. Ar_n⁺ cluster ions into silicon and sapphire and two different cluster species Ar_n⁺ and Xe_n⁺ are implanted into the same kind of substrate (silicon). Atomic force, scanning electron and transmission electron microscopies (AFM, SEM and TEM) are used to study the implanted samples. The analysis reveals the formation of two types of surface erosion defects: simple and complex (with centrally positioned hillock) craters. It is found that the ratio of simple to complex crater formation as well as the hillock dimensions depend strongly on the cluster species, size and impact energy as well as on the type of substrate material. Qualitative models describing the two comparative cases of cluster implantation, the case of different cluster species and the case of different substrate materials, are proposed.     

Dimer-anticorrelation-induced stabilization of adsorbate clustering on the Si100-(2 x 1) surface

It is well established that absorbate-absorbate interactions play a key role in determining the distribution of adsorbates on surfaces. In cases where these interactions are repulsive adsorbates frequently arrange so as to minimize these unfavorable interactions. This simple picture, however, neglects the influence of adsorption on the properties on the underlying substrate. Here, using STM, we show that on Si(100) many intrinsically repulsive adsorbates cluster to form surface patches even at low surface coverages. With the aid of density functional theory calculations and Monte Carlo simulations, we show that patch formation is an intrinsic property of the Si(100) surface that is driven by the energy lowering associated with the formation of extended regions of bare dimers. The enhanced attraction between anticorrelated tilted bare dimers is sufficient to offset the repulsions between adsorbates.     

Stimulation of vapor nucleation on perfect and imperfect hexagonal lattice surfaces

Monte Carlo simulations of water vapor nucleation on a perfect crystal surface and on a surface with defects are performed. Mass exchange with the vapor phase is modeled by using an open ensemble. Cluster-substrate interaction is described in terms of conventional atom-atom potentials. The Hamiltonian of the system includes expressions for electrostatic, polarization, exchange, and dispersion interactions. The Gibbs free energy and work of adsorption are calculated by Monte Carlo simulation in the bicano?nical ensemble. The microscopic structure of nuclei is analyzed in terms of pair correlation functions. Periodic boundary conditions are used to simulate an infinite substrate surface. Molecule-substrate and molecule-molecule long-range electrostatic interactions are calculated by summing the Fourier harmonics of the electrostatic potential. Dispersion interactions are calculated by direct summation over layers of unit cells. Nucleation on a surface with matching structure follows a layer-by-layer mechanism. The work of adsorption per molecule of a monolayer on the substrate surface has a maximum as a function of nucleus size. The steady rate of nucleation of islands of supercritical size is evaluated. The work of adsorption per molecule for layer-by-layer film growth is an oscillating function of cluster size. As a function of layer number, it has a minimum depending on the vapor pressure. The electric field generated by a microscopic surface protrusion destroys the layered structure of the condensate and eliminates free-energy nucleation barriers. However, point lattice defects do not stimulate explosive nucleation.     

Tunneling spectroscopy of isolated gold clusters grown on thiol/dithiol mixed self-assembled monolayers

We report a scanning tunneling spectroscopy study on the size-tunable isolated gold nanoclusters grown on thiol/dithiol mixed self-assembled monolayers (SAMs) where the effect of neighboring clusters are practically excluded. The structure forms double tunnel junction system in which the spectra exhibit Coulomb staircases. With increasing cluster size the standard deviation of the offset charge distribution for clusters increases, accompanied with the increase of total capacitance. The results are qualitatively same with the previous ones where clusters are densely grown on the substrate, indicating that this behavior is an intrinsic property for the double tunnel junction structures of tip/vacuum/single cluster/SAMs/Au(1 1 1) systems.     

Influence of surface ordering on the wetting of structured liquids

The substrate is shown to induce substantial ordering in diblock copolymer thin films above the bulk order-disorder transition (ODT) where, thermodynamically, a phase mixed state is favored. Initially, uniform films reorganize to form a hierarchy of transient surface patterns and stable film thicknesses that depend on the initial film thickness and on the substrate. Self-consistent field calculations of the free energy of the system for different situations, depending on the relative tendency for the different block components to be attracted to the substrate and/or free surface, provide an explanation of the formation of the stable film thicknesses. A continuum picture proposed earlier by Brochard et al.rovides an explanation of the wetting characteristics of this system. In some cases the ordering destabilizes the film so that dewetting occurs (wetting autophobicity), whereas in other cases the surface ordering results in a kinetic stabilization of a film that would otherwise dewet. Received 3 August 2001 and Received in final form 1 November 2001