MULTIPLE CLUSTER GROWTH OF ULTRA-THIN FILMS WITH ANISOTROPIC EDGE DIFFUSION

The multiple cluster growth of ultra-thin films on a hexagonal substrate with fractal, dendritic and compact morphology has been studied by computer simulation. The influence of the different diffusion processes along island edges on the island shape has been investigated. The results show that the anisotropic corner diffusion induces the dendritic growth, and the anisotropic step diffusion can promote the anisotropic growth and cause the ramified islands growing in three directions. In the case of compact growth, the island shape is mainly determined by the anisotropic corner crossing process. The nonuniform distribution of the multiple cluster formation can be described quantitatively by multifractal. With patterns changing from fractal to compact islands, the width and height of the bell-like or hook-like multifractal spectra increase, while the top f(α) decreases.     

Diffusion on two-dimensional percolation clusters with multifractal jump probabilities

By means of Monte Carlo simulations we studied the properties of diffusion limited recombination reactions (DLRR's) and random walks on two dimensional incipient percolation clusters with multifractal jump probabilities. We claim that, for these kind of geometric and energetic heterogeneous substrata, the long time behavior of the particle density in a DLRR is determined by a random walk exponent. It is also suggested that the exploration of a random walk is compact. It is considered a general case of intersection ind euclidean dimension of a random fractal of dimension D_F and a multifractal distribution of probabilities of dimensionsD _q (q real), where the two dimensional incipient percolation clusters with multifractal jump probabilities are particular examples. We argue that the object formed by this intersection is a multifractal of dimensionsD' _q =D _q +D _F -d, for a finite interval ofq.     

Effects of Monomer Size Distribution on the fractal dimensionality of diffusion-limited aggregates

Computer simulations of diffusion-limited aggregation (DLA) for monomers to investigate the effects of size and of lognormal distribution on the fractal dimensionality of the aggregates were conducted on a two-dimensional lattice. The results show the DLA clusters posses multifractal characteristics. For clusters consisting of monodisperse monomers, the bifurcation point on the graph of the pair correlation function (PCF) for each cluster is located right at the monomers size under investigation The textural dimension (D_f1) has a stable value of about 1.65, whereas the structural dimension (D_f2) decreased with increase in monomer size. For the cases with monomers in log-normal distributions, the textural dimension is around 1.67; however, the structural dimension decreases with increasing polydispersity of monomer size.     

超薄膜多中心生长过程的计算机模拟

利用计算机模拟了不同的允许扩散步数下超薄膜的多中心分形生长和团状生长现象,研究了成核及长大的动力学过程．分形生长时分形维数随团簇大小的增大而增加．分形生长和团状生长时成核率随扩散步数的增大而减小,随时间的增大而急速下降．团簇长大过程可用团簇大小S和生长时间t-t₀的幂函数(t-t₀)^κ描述．由于团簇间的分流作用,生长指数κ比经典理论值1略小,并且存在着非线性现象,即长得较大的团簇的生长指数Κ也较大. 关键词：     

SIMULATION OF FRACTAL GROWTH OF THIN FILMS AT LOW TEMPERATURE

Fractal growth of thin films at low temperature (50－175 K) is simulated by Monte Carlo method. It is shown that the thin film growth is quite different from the diffusion-limited aggregation (DLA) model when the coverage is larger than 0.1 ML. The average branch width of clusters increases with increasing temperature and it usually larger than the branch width (1.9 atom) in the classic DLA model. The average fractal dimension of clusters increases also with increasing coverage while the fractal dimension of DLA model remains constant. This difference comes from the weak screening effect during the late stage of thin film growth. The relationship between the saturation island number n_s and deposition interval Δt is described in a power law: n_s∝Δt^γ, where γ=-0.332 is very close to the theoretical value -1/3 of rate equations from nucleation theory.     

Fractal Aggregation Under Rotation

By means of the Monte Carlo simulation, a fractal growth model is introduced to describe diffusion-limited aggregation (DLA) under rotation. Patterns which are different from the classical DLA model are observed and the fractal dimension of such clusters is calculated. It is found that the pattern of the clusters and their fractal dimension depend strongly on the rotation velocity of the diffusing particle. Our results indicate the transition from fractal to non-fractal behavior of growing cluster with increasing rotation velocity, i.e. for small enough angular velocity ω; thefractal dimension decreases with increasing ω;, but then, with increasing rotation velocity, the fractal dimension increases and the cluster becomes compact and tends to non-fractal.     

沉积在硅油表面上的Ag原子分形凝聚体

研究了沉积在硅油表面上的Ag原子团簇,经过随机扩散和转动,最终形成大尺度分形凝聚体的凝聚过程．研究结果表明：Ag原子团簇在这种液体基底上的转动为随机转动,转动角位移的方均值<(Δθ)²>和测量时间间隔Δt满足广义爱因斯坦关系<(Δθ)²>=4D_θΔt．随机转动系数D_θ与凝聚体面积S满足指数关系D_θ∝S^{－γ_θ,其中指数γ_θ＝2.4±0. 关键词：}     

Formation of an ensemble of nanoclusters under rapid deposition of atoms on a surface

The results of an experimental study of the formation of nanometer-size Au clusters on NaCl(100) and HOPG(0001) surfaces under pulsed laser deposition are presented. No clusters of small sizes (d ≤ 1 nm) have been found in the cluster size distribution. The distribution itself at d < 5 nm has the form of a percolation distribution. It has been established that the perimeter of clusters with sizes d < 5 nm has a fractal structure. The fractal dimension of clusters is different for NaCl(100) and HOPG(0001) surfaces with different symmetries; it decreases with increasing cluster size from D _f ≈ 1.2–1.4 at d ≈ 1.5 nm to D _f ≈ 1 at d ≈ 5 nm. A physical mechanism of nanocluster formation is suggested. Under pulsed laser deposition, the attainable densities of adatoms are close to the percolation threshold in the region of thermodynamically unstable states and many-particle correlation regions are formed in a spatially inhomogeneous adsorbate. Clusters are formed on the surface from many-particle correlation regions in several diffusion jumps. The suggested mechanism allows the fractal dimension of the clusters forming on surfaces with different symmetries, its dependence on cluster size, and the cluster size distribution functions to be calculated.     

FORMATIONS OF FRACTAL ISLANDS AGGREGATED WITH DISCS IN GAUSSIAN DISTRIBUTION ON NONLATTICE SUBSTRATES

The growth mechanism of fractal islands on a two-dimensional nonlattice substrate with periodic boundary conditions has been investigated by using Monte Carlo technique. Results show that the fractal dimension d_f of the final ramified islands is almost independent of the diffusion step length, mobility and rigid rotation of the islands. The characteristics of the size distribution of the discs in an island do not change the dimension d_f of the island. However, we find that d_f increases linearly with the surface coverage ρ of the system and its slope decreases with the increase of the mean diameter of the discs.     

各向异性扩散DLA集团的豪斯道夫维数与标度性质

讨论了DLA集团的各向异性扩散效应.计算机模拟证实了具有各向异性扩散规则的DLA集团有严格的菱形结构.导出了一个粒子的各向异性扩散的新方程，计算了各向异性扩散DLA集团的豪斯道夫维数，结果表明，有效外半角β_eff=min(β_ix,β_iy).讨论了各向异性扩散DLA集团的广义维数，使用修改的楔模型得到了广义维数D_q的表达式. 关键词：     

基于分形多孔介质三维网络模型的非混溶两相流驱替数值模拟

提出了一个描述多孔介质孔隙尺寸分布的三维分形网络模型,利用该模型对多孔介质中的非混溶两相流驱替进行了数值模拟,研究了孔隙尺寸分布分维D_f和两相流黏滞比M对驱替前沿指进型的影响,结果表明指进型容量维数D_h随着孔隙尺寸分布分维D_f以及黏滞比M的增大而减少,并通过曲线拟合得到了它们之间的定量关系. 关键词： 多孔介质 三维网络 黏滞指进 非混溶两相流     

A study of radiative properties of fractal soot aggregates using the superposition T-matrix method

We employ the numerically exact superposition T-matrix method to perform extensive computations of scattering and absorption properties of soot aggregates with varying state of compactness and size. The fractal dimension, D_f, is used to quantify the geometrical mass dispersion of the clusters. The optical properties of soot aggregates for a given fractal dimension are complex functions of the refractive index of the material m, the number of monomers N_S, and the monomer radius a. It is shown that for smaller values of a, the absorption cross section tends to be relatively constant when D_f<2 but increases rapidly when D_f>2. However, a systematic reduction in light absorption with D_f is observed for clusters with sufficiently large N_S, m, and a. The scattering cross section and single-scattering albedo increase monotonically as fractals evolve from chain-like to more densely packed morphologies, which is a strong manifestation of the increasing importance of scattering interaction among spherules. Overall, the results for soot fractals differ profoundly from those calculated for the respective volume-equivalent soot spheres as well as for the respective external mixtures of soot monomers under the assumption that there are no electromagnetic interactions between the monomers. The climate-research implications of our results are discussed.     

FRACTAL VISCOUS FINGERING AND ITS SCALING STRUCTURE IN RANDOM SIERPINSKI CARPET

Viscous fingering (VF) in random Sierpinski carpet is investigated by means of successive over-relaxation technique and under the assumption that bond radii are of Rayleigh distribution. In the random Sierpinski network, the VF pattern of porous media in the limit M→∞ (M is the viscosity ratio and equals to η₂/η₁ where η₁ and η₂ are the viscosities of the injected and displaced fluids, respectively) is found to be similar to the diffusion-limited aggregation (DLA) pattern. The interior of the cluster of the displacing fluid is compact on long length scales when M=1, and the pores in the interior of the cluster have been completely swept by the displacing fluid. For finite values of M such as M≥10, the pores in the interior of the cluster have been only partly swept by the displacing fluid on short length scales. But for values of M in 1f(α) sites have velocites scaling as L^-α; and the scaling function f(α) is measured and its variation with M is found.     

非均质基底表面上团簇生长的Monte Carlo模拟

Monte Carlo方法模拟了在非均质基底表面上团簇的生长过程.非均质基底由规则分布的A，B两类不同性质的物质(不同材料、不同温度等)组成.沉积粒子的初动能为E₀，在不同相基底上单位长度扩散的能耗为E_A,E_B，粒子从A经过相界扩散到B的能耗为E_AB.模拟中粒子的初动能E₀.远大于E_A,E_B，粒子从B过相界到A能耗E_BA取为0.结果表明，沉积在此类基底表面的粒子凝聚成具有分形结构的团簇.当E_AB远大于E_A,E_B时，团簇的数目、团簇的回旋半径、团簇的分形维数均随E₀/E_AB呈周期性变化. 关键词： 分形团簇 非均质基底 Monte Carlo模拟 周期性     

Surface characterization and microstructure of ITO thin films at different annealing temperatures

In this study, the electron beam evaporation method is used to generate an indium tin oxide (ITO) thin film on a glass substrate at room temperature. The surface characteristics of this ITO thin film are then investigated by means of an AFM (atomic force microscopy) method. The influence of postgrowth thermal annealing on the microstructure and surface morphology of ITO thin films are also examined. The results demonstrate that the film annealed at higher annealing temperature (300 °C) has higher surface roughness, which is due to the aggregation of the native grains into larger clusters upon annealing. The fractal analysis reveals that the value of fractal dimension D_f falls within the range 2.16-2.20 depending upon the annealing temperatures and is calculated by the height-height correlation function.     

Thermal and chemical nanofractal relaxation

We studied shape relaxation of nano-fractal islands, during annealing, after their growth from antimony cluster deposition on graphite surface. Annealing at 180^°C shows evidence of an increase of the fractal branch width with time followed by branch fragmentation, without changing the fractal dimension. The time evolution of the width of the arm suggests the surface self-diffusion mechanism as the main relaxation process. With Monte Carlo simulations, we confirmed the observed behavior. Comparison is done with our previous results on fragmentation of nano-fractal silver islands when impurity added to the incident cluster promotes rapid fragmentation by surface self-diffusion enhancement [1].     

Electronic properties of assembled islands of hydrogen-saturated silicon clusters on Si(111)-(7 x 7) surfaces studied by scanning tunneling spectroscopy

We present results of scanning tunneling spectroscopy (STS) measurements of hydrogen-saturated silicon clusters islands formed on Si(111)-( 7×7) surfaces. Nanometer-size islands of Si₆H₁₂ with a height of 0.2-4 nm were assembled with a scanning tunneling microscope (STM) using a tip-to-sample voltage larger than 3 V. STS spectra of Si₆H₁₂ cluster islands show characteristic peaks originating in resonance tunneling through discrete states of the clusters. The peak positions change little with island height, while the peak width shows a tendency of narrowing for the tall islands. The peak narrowing is interpreted as increase of lifetime of electron trapped at the cluster states. The lifetime was as short as 10^-13 s resulting from interaction with the dangling bonds of surface atoms, which prevents charge accumulation at the cluster islands. Received 30 November 2000     

Off lattice simulations of cluster-cluster aggregation in dimensions 2–6

Cluster-cluster aggregation has been simulated in dimensions two to six using both linear and brownian cluster trajectories. Relatively efficient off lattice algorithms have allowed large clusters to be generated and values for the fractal dimensionalities of the aggregates have been obtained without finite concentration effects. The values for the fractal dimensionality are in good aggreement with lattice model simulations for euclidean dimensionalities 2–4. The effective dimensionality (D_β) obtained from the dependence of the radius of gyration on cluster size increases with increasing cluster size for all of our models (particularly for d ≥ 4). For clusters in the accessible size range (up to 10³-10⁴) D_β is slightly larger for cluster-cluster aggregation via linear trajectories than for brownian trajectories. For cluster-cluster aggregation via brownian trajectories, the limiting (large cluster size) fractal dimensionality is estimated to be 1.46 ± 0.04 for d=2,1.82 ± 0.10 for d = 3, 2.10 ± 0.15 for d = 4, 2.35 ± 0.15 for d = 4, 2.65 ± 0.25 for d = 6. For cluster- cluster aggregation via linear trajectories, the limiting fractal dimensionality is estimated to be 1.55 ± 0.04 for d = 2, 1.91 ± 0.10 for d = 3≥ 2.5 ± 0.06 for d = 5 and ≥2.64 ± 0.05 for d = 6.     

Dynamic behavior of non-uniform granular gases system with the fractal characteristic in one dimension

A one-dimensional dynamic model of polydisperse granular mixture with a power-law size distribution is presented, in which the particles are subject to inelastic mutual collisions and driven by Gaussian white noise. The particle size distribution of the mixture has the fractal characteristic, and a fractal dimension D as a measurement of the inhomogeneity of the particle size distribution is introduced. We define the global granular temperature and the kinetic pressure of the mixture, and obtain their expressions. By molecular dynamics simulations, we have mainly investigated how the inhomogeneity of the particle size distribution and the inelasticity of collisions influence the steady-state dynamic properties of the system, focusing on the global granular temperature, kinetic pressure, velocity distribution and distribution of interparticle spacing. Some novel results are found that, with the increase of the fractal dimension D, the global granular temperature and the kinetic pressure decrease, the velocity distribution deviates more obviously from the Gaussian one and the particles cluster more pronouncedly at the same value of the restitution coefficient e (0<e<1). On the other hand, as the restitution coefficient e decreases, the dynamic behavior has the similar evolution as above at the fixed fractal dimension D. The dynamic behavior changing with e and D is, respectively, presented.     

纳米团聚生长的多重分形谱

采用小角x射线散射（SAXS）方法，对两类具有代表性的纳米团聚的生长分形进行了表征.一 类为用化学方法 (水合肼溶液还原法) 制备的纳米金属Ni粉；另一类通过物理方法(纳米晶 化处理)，由非晶基体相中生长纳米晶相、形成非晶/纳米晶双相结构的Finemet (Fe_{73 .5} Cu₁Nb₃Si_13.5B₉) 合金.上述两 类材料的纳米团聚在生长过程中都存在 明显元素扩散迁移，形成在1—100 nm范围内的元素分布非均匀区域.这些元素分布的非均匀 区域具有多重质量生长分形特征，其尺度大小和分布方式对最终的材料的物理性能至关重要 .SAXS方法是表征这类具有分形生长特征的纳米团聚微观结构信息的强有力手段.从方法论的 角度详述了从SAXS测量到获得多重分形谱的处理过程，这一实验研究分析手段对于定量考察 纳米微结构形貌的生长机理和性能的其他研究课题有一定的帮助作用. 关键词： 纳米材料 分形生长 小角x射线散射 磁性材料