Surface diffusion of k-mers in one-dimensional systems

The surface diffusion of interacting k-mers is studied both through analytical and Monte Carlo simulation methods in one-dimensional systems. Adsorption isotherms, jump diffusion coefficients and collective diffusion coefficients are obtained for attractive and repulsive k-mers, showing a variety of behaviors as a function of the size of particles, k. The following main results are found: (a) diffusion coefficients increase with k for non-interacting particles; (b) for fixed k, diffusion coefficients increase as the interaction energy increases from negative (attractive) to positive (repulsive) values; (c) for attractive interactions diffusion coefficients increase with k in the whole range of coverage; (d) for repulsive interactions diffusion coefficients decrease with k up to moderately high coverage and increase with k at high coverage. Results are rationalized in terms of the behavior of the vacancy probability distribution.     

A dynamical mean field theory for the study of surface diffusion constants

We present a combined analytical and numerical approach based on the Mori projection operator formalism and Monte Carlo simulations to study surface diffusion within the lattice-gas model. In the present theory, the average jump rate and the susceptibility factor appearing are evaluated through Monte Carlo simulations, while the memory functions are approximated by the known results for a Langmuir gas model. This leads to a dynamical mean field theory (DMF) for collective diffusion, while approximate correlation effects beyond DMF are included for tracer diffusion. We apply our formalism to three very different strongly interacting systems and compare the results of the new approach with those of usual Monte Carlo simulations. We find that the combined approach works very well for collective diffusion, whereas for tracer diffusion the influence of interactions on the memory effects is more prominent.     

On the theory of surface diffusion: kinetic versus lattice gas approach

The present paper extends the results of a recent analytic kinetic theory of particle-on-substrate diffusion. The approach treats explicitly the molecule–surface interaction and takes into account inter-molecular interaction within the hard particle approximation. The physics influencing the diffusion pre-exponential factor and mechanisms determining the density dependence of collective diffusivity are discussed. The kinetic results are compared with those of the traditional lattice gas hopping models. Analytical expressions for jump rates in the low density limit are derived, and the density dependence of effective jump rates at finite occupancy is discussed. It is shown how the traditional hopping model oversimplifies the picture of diffusion by neglecting the collision part of the hopping process.     

Diffusion of particles over triangular inhomogeneous lattice with two non-equivalent sites

We investigate the diffusion of particles adsorbed on a triangular lattice with deep and shallow sites. It is shown that the character of the particle migration depends substantially on the relative jump rates from the deep and shallow sites. The site inhomogeneity imposes specific correlation betweeen successive jumps: particles perform pairs of slow and fast jumps. General analytical expressions have been derived for the chemical and jump diffusion coefficients. We have calculated coverage dependencies of the diffusion coefficients and some thermodynamic quantities for different lateral interactions between the particles. The analytical data have been compared with the numerical data obtained by kinetic Monte Carlo simulations. The agreement between the results obtained by these quite different approaches is found to be very satisfactory.     

Surface diffusion of particles adsorbed on an inhomogeneous lattice with two non-equivalent sites

We investigate surface diffusion in a system of particles with the nearest neighbor pairwise lateral interaction adsorbed on a two-dimensional inhomogeneous lattice of square symmetry with deep and shallow sites. General analytical expressions for the chemical and jump diffusion coefficients have been derived in case of strong inhomogeneity. The expressions are valid for the inhomogeneous lattices with different geometries and dimensionalities. We have calculated the coverage dependencies of the tracer, jump and chemical diffusion coefficients for different temperatures using the real-space renormalization group (RSRG) method and compared the data with the numerical results obtained by the MC simulations. The coincidence between the data obtained by these quite different methods is rather good.     

Mössbauer spectroscopy to investigate jump mechanisms on an atomic scale: Fast diffusion studies

The fast diffusion of transition‐metal impurities in metals and semiconductors provides us with a challenging research field, because the jump frequencies and the concentration of the “diffusion vehicles” (probably interstitials) contributing to the fast diffusion are always close to the detection limit of Mössbauer spectroscopy. Therefore, several new experimental set‐ups have to be developed in order to achieve a direct observation of the fast diffusing vehicles and to study the jump mechanism on an atomic scale. High temperature UHV‐furnaces and the in‐beam Mössbauer spectrometers, which have been constructed in different institutes in different countries, are introduced and the new experimental results obtained by these apparatus are presented.     

Diffusion of particles on a heterogeneous surface: A case of adsorption-induced surface reconstruction

The influence of surface reconstruction on diffusion of particles adsorbed on the surface is investigated in the framework of symmetrical four-position model. The analytical expressions for free energy and diffusion coefficients are obtained assuming the lateral interaction between particles is negligibly small.The critical behavior of the system is described by the Ising spin model. The coverage dependencies of the tracer, jump and chemical diffusion coefficients are calculated for some representative temperatures. The dependencies show clearly strong influence of the surface reconstruction on the thermodynamic and kinetic phenomena: diffusion coefficients become anisotropic on the reconstructed surface. To check the analytical results we have used Monte Carlo simulations of the diffusion on this lattice.     

Diffusion of adsorbates on random alloy surfaces

In this work the diffusion of non-interacting adsorbates on a random AB alloy surface is considered. For this purpose a simple cubic (sc), body-centered cubic (bcc) or face-centered cubic (fcc) auxiliary metal lattice is introduced. The auxiliary lattice is truncated parallel to its (100) plane in such a way that the fourfold hollow positions of the metal surface form a regular net of adsorption sites with square symmetry. The adsorption energy of each adsorption site is determined by its own environment, i.e. by the numbers of direct A or B neighbors. The Monte-Carlo method has been utilized to simulate surface diffusion of adsorbates on such energetically heterogeneous alloy surfaces and to calculate the tracer, jump and chemical diffusion coefficients. The chemical diffusion coefficient was calculated via two different approaches: the fluctuation and the Kubo-Green method. The influence of energetical heterogeneities on the surface diffusion is largely pronounced at low temperatures and low surface coverages, where most of the adatoms are trapped by deep adsorption sites. It was found that at low temperatures the sequential occupation of the different types of adsorption sites can be observed. Received: 24 October 1997 / Accepted: 17 December 1997     

New model for tracer-diffusion in amorphous solid

The tracer-diffusion and structure of polymorphic states of amorphous solid is studied by mean of the statistic relaxation technique and simplex analysis. Several different metastable states of amorphous iron have been constructed based on the model containing 2 × 10⁵ atoms. All models have almost the same pair radial distribution functions, but they differ in the potential energy per atom and the density. We found a large number of vacancy-simplexes which varies according to the relaxation and serves as a diffusion vehicle. New diffusion mechanism for tracer-diffusion is found of which the elementary diffusion process likes a collapse of “microscopic bubble” in amorphous matrix. This includes a jump of diffusing atom and the collective movement of a large number of neighboring atoms. The diffusion constant D determined in accordance with considered diffusion mechanism is in reasonable agreement with experimental data. The decrease in diffusion constant D upon thermal annealing is explained by the reducing vacancy-simplex concentration which is caused by both the local atomic rearrangement and the elimination of excess free volume.     

Theoretical description of adatom migration in two-dimensional highly-ordered states

Analytical expressions for chemical, jump, and tracer diffusion coefficients are obtained for interacting lattice gases on a square lattice. Strongly repulsive nearest neighbor interactions cause the formation of a highly-ordered c() state in the vicinity of half coverage. It is shown that only strongly correlated successive adatom jumps contribute to the particle flow. This allows to describe the adatom kinetics by considering an almost ideal lattice gas of defects. Two types of defects are considered, adatoms in the empty sublattice and vacancies in the filled sublattice of the c() ordered state. The diffusion equations for these defects are developed considering the generation and recombination of defects. In addition we have considered adatom transport caused by the motion of defect pairs (dimers). Dimer transport mechanism prevails in the high coverage region. The characteristic features of the various diffusion coefficients near half coverage are analyzed and discussed. The theory is compared with the results of sophisticated Monte-Carlo simulations which have been executed with the use of a fully parallelized algorithm on a Cray T3E (LC784-128). The agreement between theoretical and MC results is excellent if the motion of dimers at is taken into account. Received 24 June 1998     

A jump diffusion model for spot electricity prices and market price of risk

We construct a jump-diffusion model with seasonality, mean-reversion, time-dependent jump intensity and heteroskedastic disturbance for electricity spot prices, while keeping the analytical tractability of futures prices. We find that the jump component plays a considerably larger role than the diffusion component in the variance of spot prices. Moreover, the jump intensity is much higher during summer and winter. We also explore the seasonal market price of risk (MPR) with different maturities, from one month to five months. Our results show that the diffusion risk and the jump risk are priced quite differently.     

Collective and single particle diffusion on surfaces

We review in this article the current theoretical understanding of collective and single particle diffusion on surfaces and how it relates to the existing experimental data. We begin with a brief survey of the experimental techniques that have been employed for the measurement of the surface diffusion coefficients. This is followed by a section on the basic concepts involved in this field. In particular, we wish to clarify the relation between jump or exchange motion on microscopic length scales, and the diffusion coefficients which can be defined properly only in the long length and time scales. The central role in this is played by the memory effects. We also discuss the concept of diffusion under nonequilibrium conditions. In the third section, a variety of different theoretical approaches that have been employed in studying surface diffusion such as first principles calculations, transition state theory, the Langevin equation, Monte Carlo and molecular dynamics simulations, and path integral formalism are presented. These first three sections form an introduction to the field of surface diffusion. Section 4 contains subsections that discuss surface diffusion for various systems which have been investigated both experimentally and theoretically. The focus here is not so much on specific systems but rather on important issues concerning diffusion measurements or calculations. Examples include the influence of steps, diffusion in systems undergoing phase transitions, and the role of correlation and memory effects. Obviously, the choice of topics here reflects the interest and expertise of the authors and is by no means exhaustive. Nevertheless, these topics form a collection of issues that are under active investigation, with many important open questions remaining.     

Semiclassical Quasilinear Equation of Turbulent QGP and Non-Abelian Quasilinear Diffusion

After the concept of turbulent QGP is introduced, the quasilinear equations for turbulent QGP are given. Starting from the field equation, we still treat the collective modes as plasmons that satisfy a transport equation. Using the quasilinear equations for quarks and gluons and the transport equation for plasmons, the collisionless diffusion is discussed. We obtain the quasilinear drag coefficient and the diffusion coefficient.     

Multiplicity distributions of charged hadrons at AGS, SPS and RHIC

It is found that Collective Flow Model (CFM) which can successfully analyze charged particle distributions at AGS and lower SPS (less than 20 GeV/n), fails to analyze that of RHIC. The tail of distribution of charged particle at RHIC has a jump away from the collective model calculation as the energy increase. Thermalization Component Model (TCM) is presented basing on collective flow to study the multiplicity distributions at RHIC in this paper. It is realized that the limitation of phase space of collective flow can denote that of thermalization region. By comparing the contributions of particle productions from thermalization region at different energies and different centrality, we can deep our study on the feature of collective movement at RHIC.     

Surface diffusion on heterogeneous correlated substrates

The behaviour of the surface diffusion coefficient on an heterogeneous correlated surface is studied in the framework of the lattice-gas model. Using the multivariate adsorptive energy distribution function the statistical properties of the heterogeneous correlated surface can be appropriately described and the effect of the heterogeneity on the collective diffusion coefficient at finite coverage can be analized through a correlation length. Monte Carlo simulation is also performed to test the analytical results.     

Effect of coverage by carbon on the possibility of forming an interstitial solid solution in Fe(001) and Fe(111) subsurface layers

The interaction between carbon adatoms as a function of the coverage of the Fe(001) and Fe(111) surfaces by carbon has been theoretically investigated using first-principles calculations in terms of the density functional theory. It has been established for the first time that the sequential filling of the upper surface layer by carbon atoms leads to the embedding of a part of atoms in the subsurface iron layer due to the their collective interaction, which provides the possibility of forming the interstitial solid solution. It has been demonstrated that the high coverage of the (001) surface by carbon leads to a considerable decrease in the energy barrier to the diffusion of carbon atoms into the subsurface layer as compared to the diffusion barrier for single atoms.     

Thermal neutron scattering from a hydrogen-metal system in terms of a general multi-sublattice jump diffusion model—I: Theory

A Multi-Sublattice Jump Diffusion Model (MSJD) for hydrogen diffusion through interstitial-site lattices is presented. The MSJD approach may, in principle, be considered as an extension of the Rowe et al.[1] model. Jump diffusion to any neighbours with different jump times which may be asymmetric in space is discussed. On the basis of the model a new method of calculating the diffusion tensor is advanced. The quasielastic, double differential cross section for thermal neutron scattering is obtained in terms of the MSJD model. The model can be used for systems in which interstitial jump diffusion of impurity particles occurs. In Part II the theoretical results are compared with those for quasielastic neutron scattering from the αNbH_x system.     

Continuous time random walk with jump length correlated with waiting time

A coupled continuous time random walk (CTRW) model is proposed, in which the jump length of a walker is correlated with waiting time. The power law distribution is chosen as the probability density function of waiting time and the Gaussian-like distribution as the probability density function of jump length. Normal diffusion, subdiffusion and superdiffusion can be realized within the present model. It is shown that the competition between long-tailed distribution and correlation of jump length and waiting time will lead to different diffusive behavior.     

基底显微结构对薄膜生长影响的Monte Carlo模拟研究

利用Monte Carlo方法研究了基底显微结构对薄膜生长的影响. 对不同显微结构基底上薄膜生长的初始阶段岛的形貌和尺寸与薄膜覆盖度和入射粒子沉积速率之间的关系进行了模拟和分析. 模型中考虑了粒子沉积、吸附粒子扩散和蒸发等过程. 结果表明,基底显微结构对薄膜生长具有明显影响. 当沉积温度为300K、沉积速率为0.005ML/s（Monolayer/second,简称ML/s）、覆盖度为0.05ML时,四方基底上薄膜生长呈现凝聚生长. 随着覆盖度增加,岛的尺寸变大,岛的数目减少. 而对于六方基底,当覆盖度从0.05ML变化到0.25ML时,薄膜生长经历了一个从分散生长过渡到分形生长的过程. 无论是四方还是六方基底,随着沉积速率的增加,岛的形貌由少数聚集型岛核分布状态向众多各自独立的离散型岛核分布状态过渡.