高背压超声气体团簇喷流中团簇平均尺寸沿喷流方向演化研究

本文通过对高背压(50 bar, 1 bar = 1.0×10⁵ Pa)氩气经长锥型喷嘴(长度L=30 mm)向真空绝热膨胀所形成的超声气体团簇喷流的数值模拟, 分析比较了由喷嘴喉口起沿喷流方向在喷流中心轴线上团簇平均尺寸的演化情况. 结果表明: 沿喷流方向团簇平均尺寸显示先增长后趋于饱和的变化趋势, 具有较大尺寸团簇的区域出现在距离喷嘴喉口大约20 mm. 据此本文再结合关于喷流中原子密度沿喷流方向变化的模拟结果开展了锥形喷嘴长度的优化研究. 针对由常见构型的锥形喷嘴(喉径～ 0.5 mm, 半张角～ 8.5°)在高背压下形成的团簇喷流, 20 mm左右的长度为锥形喷嘴的适宜长度.     

Analytical results for the cluster size distribution in controlled deposition processes

This paper proposes a controlled particle deposition model for cluster growth on the substrate surface and then presents exact results for the cluster (island) size distribution. In the system, at every time step a fixed number of particles are injected into the system and immediately deposited onto the substrate surface. It investigates the cluster size distribution by employing the generalized rate equation approach. The results exhibit that the evolution behaviour of the system depends crucially on the details of the adsorption rate kernel. The cluster size distribution can take the Poisson distribution or the conventional scaling form in some cases, while it is of a quite complex form in other cases.     

Typical cluster size for two-dimensional percolation processes

The typical cluster size for two-dimensional percolation models is discussed. It is shown that, forW ₀={xZ ²0x}, [–lim _n(1/n) logP _p (W ₀=n)]^–1p–p _c ^– aspp _c , provided thatE _p (W ₀²)/E _p (W ₀)p–P _c ^– aspp _c . Furthermore, we introduce a new quantityf _s (p), which may be thought of as the singular part of the free energy, and show thatf _s (p)¦p–p _c ¦^2v provided that the correlation length ¦p–p _c ¦^–v aspp _c .     

Lower bounds on the cluster size distribution

We rigorously prove that the probabilityP _n that the origin of ad-dimensional lattice belongs to a cluster of exactlyn sites satisfiesP _n > exp(–n ^(d–1)/d ) whenever percolation occurs. This holds for the usual (noninteracting) percolation models for any concentrationp > p _c , as well as for the equilibrium states of lattice spin systems with quite general interactions. Such a lower bound applies also if no percolation occurs, but if it appears in some other phase of the system.     

Spatiotemporal distribution of nucleation events during crystal growth

We consider irreversible second-layer nucleation that occurs when two adatoms on a terrace meet. We solve the problem analytically in one dimension for zero and infinite step-edge barriers, and numerically for any value of the barriers in one and two dimensions. For large barriers, the spatial distribution of nucleation events strongly differs from rho(2), where rho is the stationary adatom density in the presence of a constant flux. Theories of the nucleation rate omega based on the assumption that it is proportional to rho(2) are shown to overestimate omega by a factor proportional to the number of times an adatom diffusing on the terrace visits an already visited lattice site.     

A monte carlo method for approximating critical cluster size in the nucleation of model systems

A formalism is presented for estimating critical cluster size as defined in classical models for nucleation phenomena. The method combines Bennett's Monte Carlo technique for determining free-energy differences for clusters containingn andn- 1 atoms with the steady state nucleation rate formalism. A simple form for the free energy of formation of then cluster [including a termA (n)n ^2/3] is used to predict critical cluster size and critical supersaturation ratio, S^*. This approach is applied to Lennard-Jones vapor clusters at 60 K. Results for free-energy differences for the 13, 18, 24, and 43 clusters predict a critical cluster size of 70 ± 5 atoms at a critical supersaturation ratio given bylnS ^*=2,45 0.15. This method is intended to provide estimates of critical cluster size for more ambitious attempts to calculate cluster free energies or for initializing conditions in microscopic simulations of nucleating systems.This material is based upon work supported by the National Science Foundation under Grant No. ATM80 15790 and the National Aeronautics and Space Administration under Grant No. NAS8-31150.     

Exact distribution of cluster size and perimeter for two-dimensional percolation

Exact series expansion data of Sykes et al. are used to calculate the average numberc _n and perimeters _n of clusters of sizen20 in the site percolation problem for the triangular, square, and honeycomb lattice. At the percolation thresholdp _n we find a sharply peaked distribution of perimeterss _n with mean s _n =((1–p _n )/p _c )n+O(n ) and width s _n ² –S _n ²n ^1.6 where1/=0.39. This perimeter s _n should not be interpreted as a cluster surface in the usual sense. Two tests confirm the universality hypothesis with reasonable accuracy. The asymptotic decay of the cluster numbersc _n withn is consistent with the postulated asymmetry aboutp _c : logc _n –n forn with1 forp<p _c and1/2 forp>p _c .     

Plume propagation through a buffer gas and cluster size prediction

A mixed-propagation picture for the expansion of an ablation plume through a buffer gas at different pressures is proposed after a brief discussion of the available analytical expansion models. Using parameter values deduced by the model the size of carbon clusters formed during plume propagation in helium is evaluated and compared with experimental data. Starting from experiments on silver plume propagation through molecular oxygen the size of silver clusters is predicted.     

A stochastic model of deposition processes with nucleation

We study an interacting particle system on a one-dimensional infinite lattice and one-dimensional lattices with a periodic boundary. In this system, each site of the lattice may be either empty or occupied and initially all the lattice sites are empty. The evolution of the system is defined as follows: an empty site waits an exponential time with mean 1 and becomes occupied, and an occupied site becomes empty at a time which is distributed exponentially with mean _k, wherek is the number of occupied neighboring sites of this site in the current state of the system. We show that the mean number of the occupied sites of the lattice, considered as a function of time, may possess a convex part. A sufficient condition for this is that ₀ is large and _k,k1, are small. The studied system has been proposed recently as a mathematical model of certain deposition processes, in particular those which exhibit nucleation caused by lateral attractive interaction between the deposited molecules. Our research was motivated by the observation that the density of deposited molecules contains a convex part, over some time interval, if the attractive forces are strong, while this density is a concave function of time if these forces are weak or absent. Our result agrees with this observation.     

Scaling function for cluster size distribution in two-dimensional site percolation

Exact cluster size distributions of Sykes et al. in the square and triangular lattice for cluster sizes up to 17 are used to extrapolate the scaling function in the site percolation problem. Also the amplitude ratioC ₊/C _- of the second moment is determined.     

Estimation of particle size distributions obtained by gas phase processes

Nanoparticles intended for high value added applications often require special size distributions. Based on model calculations, this article compares the particle size distributions obtained with conventional and plasma processes. The model is based on an estimation of the probability for collisions; either for neutral or equally charged particles, whereas the growth of the particles is calculated using a model derived from Markov chains. The results of these calculations confirm the empirical knowledge that, under the special conditions of particles carrying electric charges of equal sign, plasma processes deliver products with the narrowest particle size distribution. Synthesis of extremely small particles with conventional processes leads to a significant residue of unreacted precursor. This finding is important in cases of expensive educts. The results of these model calculations are in perfect agreement with experimental findings.     

The evolution of the cluster size distribution in a coagulation system

The coagulation equation with kernelK _ij =A+B(i+j)+C _ij and arbitrary initial conditions is studied analytically and a simple expression for the solution is found. For monodisperse initial conditions, we recover the known size distribution expressed in terms of a degeneracy factorN _k, which is determined by a recursion relation. For polydisperse initial conditions, a similar solution form is found, which includes a degeneracy factorN _kl, also determined by a recursion relation. The physical meaning ofN _kl and the recursion relation is given. A method to get explicit expressions forN _k andN _kl is illustrated. Finally, the pre-gel solution is given explicitly and a general method to get the post-gel solution is proposed.     

Computational and experimental study of the cluster size distribution in MAPLE

A combined experimental and computational study is performed to investigate the origin and characteristics of the surface features observed in SEM images of thin polymer films deposited in matrix-assisted pulsed laser evaporation (MAPLE). Analysis of high-resolution SEM images of surface morphologies of the films deposited at different fluences reveals that the mass distributions of the surface features can be well described by a power-law, Y(N) ∝ N^−t, with exponent −t ≈ −1.6. Molecular dynamic simulations of the MAPLE process predict a similar size distribution for large clusters observed in the ablation plume. A weak dependence of the cluster size distributions on fluence and target composition suggests that the power-law cluster size distribution may be a general characteristic of the ablation plume generated as a result of an explosive decomposition of a target region overheated above the limit of its thermodynamic stability. Based on the simulation results, we suggest that the ejection of large matrix-polymer clusters, followed by evaporation of the volatile matrix, is responsible for the formation of the surface features observed in the polymer films deposited in MAPLE experiments.     

Grain size distributions for competitive growth with nucleation

The paper introduces and discusses an idealized competitive growth model with nucleation for the microstructure formation during dense branching phase separation in thin Al/Ge films. Grain size and grain length distributions for the new model are obtained analytically and by simulation. These distributions exhibit a characteristic scaling form similar to cluster size distributions in many other growth models. The cutoff functions in these scaling forms and their influence on the determination of effective exponents are studied in detail. It is found that nucleation introduces a new length scale into the other-wise selfsimilar competitive growth model. This length scale appears only inside the cutoff function and diverges algebraically as the nucleation rate vanishes. We find both analytically and by simulation that the cutoff functions can exhibit stretched exponential behaviour exp(–x ) for large arguments. Our analytical and simulation results for grain size and grain length distributions are in excellent quantitative agreement.     

The scales of brane nucleation processes

The scales associated with Brown–Teitelboim–Bousso–Polchinski processes of brane nucleation, which result in changes of the flux parameters and the number of D-branes, are discussed in the context of type IIB models with all moduli stabilized. It is argued that such processes are unlikely to be described by effective field theory.     

The probability distribution of the velocities of gas molecules after collision with a rapidly moving rigid body

The above problem is met, for example, in the case of the collision of molecules of the atmosphere with an artificial earth satellite and leads to the problem of determining the probability distribution of the absolute value of the vector sum of a constant vector and a Maxwell vector (the latter being a vector, whose rectangular components are distributed normally, with the same standard deviation and mean value zero). The resultant probability density is given by equation (18), the complement to the distribution function by (24), the mean value by (27) and the variance by (31). These results are obtained by transforming the corresponding three-dimensional normal distribution to spherical co-ordinates and integrating over the co-ordinate angles and , which yields the required probability density; the other results are then obtained from it by the usual methods.

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, , (. . , ). (18), -(24), -(27) (31). , ; .

     

Essential singularity in percolation problems and asymptotic behavior of cluster size distribution

It is rigorously proved that the analog of the free energy for the bond and site percolation problem on in arbitrary dimension (> 1) has a singularity at zero external field as soon as percolation appears, whereas it is analytic for small concentrations. For large concentrations at least, it remains, however, infinitely differentiable and Borel-summable. Results on the asymptotic behavior of the cluster size distribution and its moments, and on the average surface-to-size ratio, are also obtained. Analogous results hold for the cluster generating function of any equilibrium state of a lattice model, including, for example, the Ising model, but infinite-range andn-body interactions are also allowed.Supported by the Fonds National Suisse de la Recherche Scientifique (to HK).     

气体凝聚团簇源中团簇形成的DSMC研究

利用直接模拟蒙特卡洛方法(DSMC) ,模拟了气体凝聚团簇源的引出口尺寸和中心位置不同的条件下,Cu团簇的尺寸分布以及模拟了随着时间的增长,腔内团簇数目的变化.模拟结果表明:引出口的直径越大,产生大团簇的比例越小;在引出口的直径相同的情况下,引出口的中心位置偏离坐标原点比在原点产生的大团簇的比例要大;随着时间的增长,腔内团簇数目先变多后变少.