Tracer diffusion of dimers on correlated heterogeneous surfaces

The diffusion of a single dimer adsorbed on highly correlated heterogeneous substrates is studied through Monte Carlo simulations. The topography has been characterized by patches of weak and strong adsorbing sites, arranged in a chessboard-like ordered structure. The time behavior of the mean-square displacement of the dimer is analyzed for different temperatures and patch size. Based on this analysis, a possible method for the characterization of the correlated heterogeneous topography from dimer diffusion measurements is discussed.     

Diffusion of interacting particles in one-dimensional heterogeneous systems

The equilibrium and transport properties of interacting ad-particles on bivariate heterogeneous chains are studied by combining analytical and simulation approaches. Heterogeneity is introduced in the way of patches of shallow and deep adsorbing sites distributed in a deterministic alternating way. Adsorption isotherms and mean-square fluctuations of the surface coverage, as well as the jump and collective diffusion coefficients, are calculated for different values of lateral interactions between ad-particles and substrate heterogeneity. In addition, different elementary jump mechanisms are introduced and their influence in the coverage dependence of the collective diffusion coefficient is investigated.     

Adsorption of interacting monomers on spanning clusters of polyatomic species

The adsorption-desorption process occurring on heterogeneous surfaces is studied by considering a special case where a fractal is used as adsorbent. The fractal surface is the spanning cluster corresponding to the random deposition of objects that occupy more than one site (k-mers) on a square lattice. Such a surface is characterized according to the deposited k-mer. Then, the adsorption of repulsively interacting particles adsorbed on the fractal surface is studied by using Monte Carlo simulations. Different thermodynamic quantities (adsorption isotherms, coverage susceptibility, etc.) are calculated and explained in terms of the characteristics of the substrate. A scheme to characterize the structure of the substrate by just considering the adsorption isotherm is presented and discussed.     

Adsorption thermodynamics of a lattice-gas model with non-additive lateral interactions on triangular and honeycomb lattices

Adsorption thermodynamics of a lattice-gas model with non-additive interactions between adsorbed particles for triangular and honeycomb lattices is discussed in the present study. The model used here assumes that the energy which links a certain atom with any of its nearest-neighbors strongly depends on the state of occupancy in the first coordination sphere of that adatom. By means of Monte Carlo simulations in the grand canonical ensemble the adsorption isotherms and isothermal susceptibility (or equivalently the mean square density fluctuations of adparticles) were calculated and their striking behavior was analyzed and discussed in terms of the low temperature phases formed in the system.     

Sequential desorption of dimers from square lattices: A novel mechanism for phase transitions

This work describes a novel mechanism for phase transitions during desorption, involving the formation of lattice size dependent intermediate states when there is enough adsorbate mobility. Monte Carlo simulations are performed to analyze the mechanism of the thermal desorption for adsorbed homonuclear dimers on two-dimensional square lattices. The lattice-gas model with nearest-neighbor repulsive interactions between particles is implemented to study the cases of mobile (with diffusion) and immobile desorption. The number of peaks for the immobile desorption spectra is related to the connectivity of the adsorbed species for both monomer and dimer molecules. However, for the case of mobile desorption, the spectra give information about the desorption mechanism, which differs significantly for monomers and dimers, particularly when the initial temperatures correspond to the critical region.     

XPK程序包：扩展唯象动力学方法(XPK)与常规动力学蒙特卡罗(KMC)方法的比较

在常规的动力学蒙特卡罗方法(KMC)中,扩散过程的速率往往远大于化学反应,因而造成KMC方法在模拟表面化学体系演化时效率非常低下. 为了解决这一时间尺度分离问题,本文最近发展了扩展唯象动力学方法(XPK). 本文基于加氢反应体系模型,利用新发展的XPK程序包,对XPK方法与常规的KMC方法进行了细致的对比. 为了更全面地说明问题,测试中包含了两条不同的势能曲线,以及多种吸附物之间的相互作用. 对比的内容包括计算消耗、并行效率以及稳态的收敛行为等. 测试结果表明,相比于常规的KMC方法,XPK方法在兼顾精度的同时大大提高了模拟效率. 因而可以预期,XPK方法将成为多相催化理论研究的强有力工具. 特别是在表面吸附物种相互作用有决定性影响的情况下,XPK方法的优势尤其突出.     

Emergence of complex networks from diffusion on fractal lattices. A special case of the Sierpinski gasket and tetrahedron

A new approach to the assemblage of complex networks displaying the scale-free architecture is proposed. While the growth and the preferential attachment of incoming nodes assure an emergence of such networks according to the Barabási–Albert model, it is argued here that the preferential linking condition needs not to be a principal rule. To assert this statement a simple computer model based on random walks on fractal lattices is introduced. It is shown that the model successfully reproduces the degree distributions, the ultra-small-worldness and the high clustering arising from the topology of scale-free networks.     

Monte Carlo simulation of the effect of atomic diagonal transition on cluster diffusion

The effect of atomic diagonal transition on the cluster diffusion and its size dependence is simulated by kinetic Monte Carlo method. The thresholds of atomic diagonal transition barriers E_{dt} are found to be 0.2eV and 0.4eV, corresponding to with and without evaporation and condensation mechanism, respectively. The results indicate that the cluster diffusion is controlled primarily by the atomic diagonal transition, and the cluster diffusion coefficient D decreases drastically with increasing E_d when E_dE_{dt}, and the relationship between D and N changes into D∝N^{-1.08±0.027}.     

The effect of three-body interactions on thermal desorption spectra

Thermal desorption spectra are calculated for a one-dimensional chain and for a two-dimensional square lattice using the transfer-matrix technique and Monte Carlo simulations. Lateral interactions of adsorbed particles cause a splitting of spectra. The repulsive three-body interactions are shown to lead to an inequality of the integral intensities of the thermal desorption peaks.     

Percolation of interacting particles on heterogeneous surfaces

The percolation problem of interacting particles on square lattices with two kinds of energetically different sites is studied. Square lattices formed by collections of either randomly or orderly distributed sites are generated. The system is characterized by two parameters, namely, the interaction between adjacent particles, ω, and the energy difference between the two kinds of sites, . Particles are adsorbed at equilibrium on the lattice. By means of Monte Carlo simulations and finite-size scaling analysis the critical coverage is determined. The percolative behavior of the system is presented and discussed in terms of the mentioned parameters, ω and .     

Simulations of germanium epitaxial growth on the silicon (1 0 0) surface incorporating intermixing

We present kinetic lattice Monte Carlo simulations of Ge deposition onto a reconstructed Si (1 0 0) surface. We account for the exchange of Ge with Si atoms in the substrate, considering two different exchange mechanisms: a dimer exchange mechanism whereby Ge–Ge dimers on the surface become intermixed with substrate Si atoms, and the exchange of Ge atoms below the surface to relieve misfit strain. We examine how Si–Ge exchange affects the interface between the materials when the growth simulations are done at different temperatures.     

Random alloy diffusion kinetics for the application to multicomponent alloy systems

In this paper, extensive Monte Carlo simulation results are reported on tracer and collective diffusion correlation effects in the random ternary alloy, as an example of a multicomponent alloy system. The problem of analytically describing both collective and tracer diffusion kinetics is also addressed for the random multicomponent alloy by application of a combination of the Manning theory and Holdsworth and Elliott theory. It is found that the overall results from the combined theory agree reasonably well with Monte Carlo results. This combined approach is much more accurate than Manning’s approach itself and much more manageable than the almost exact, but unfortunately difficult to use, self-consistent theory of Moleko, Allnatt and Allnatt. Some relations between the Onsager phenomenological coefficients and tracer diffusion coefficients are derived and are tested with our Monte Carlo data. Good agreement is found.     

Configurational entropy of adsorbed rigid rods: Theory and Monte Carlo simulations

The configurational entropy of straight rigid rods of length k (k-mers) adsorbed on square, honeycomb, and triangular lattices is studied by combining theory and Monte Carlo (MC) simulations in grand canonical and canonical ensembles. Three theoretical models to treat k-mer adsorption on two-dimensional lattices have been discussed: (i) the Flory-Huggins approximation and its modification to address linear adsorbates; (ii) the well-known Guggenheim-DiMarzio approximation; and (iii) a simple semi-empirical model obtained by combining exact one-dimensional calculations, its extension to higher dimensions and Guggenheim-DiMarzio approach. On the other hand, grand canonical and canonical MC calculations of the configurational entropy were obtained by using a thermodynamic integration technique. In the second case, the method relies upon the definition of an artificial Hamiltonian associated with the system of interest for which the entropy of a reference state can be exactly known. Thermodynamic integration is then applied to calculate the entropy in a given state of the system of interest. Comparisons between MC simulations and theoretical results were used to test the accuracy and reliability of the models studied.     

Kinetics versus thermodynamics in materials modeling: The case of the di-vacancy in iron

Monte Carlo models are widely used for the study of microstructural and microchemical evolution of materials under irradiation. However, they often link explicitly the relevant activation energies to the energy difference between local equilibrium states. We provide a simple example (di-vacancy migration in iron) in which a rigorous activation energy calculation, by means of both empirical interatomic potentials and density functional theory methods, clearly shows that such a link is not granted, revealing a migration mechanism that a thermodynamics-linked activation energy model cannot predict. Such a mechanism is, however, fully consistent with thermodynamics. This example emphasizes the importance of basing Monte Carlo methods on models where the activation energies are rigorously calculated, rather than deduced from widespread heuristic equations.     

The stochastic models method applied to the critical behavior of Ising lattices

The stochastic models (SM) computer simulation method for treating manybody systems in thermodynamic equilibrium is investigated. The SM method, unlike the commonly used Metropolis Monte Carlo method, is not of a relaxation type. Thus an equilibrium configuration is constructed at once by adding particles to an initiallyempty volume with the help of a model stochastic process. The probability of the equilibrium configurations is known and this permits one to estimate the entropy directly. In the present work we greatly improve the accuracy of the SM method for the two and three-dimensional Ising lattices and extend its scope to calculate fluctuations, and hence specific heat and magnetic susceptibility, in addition to average thermodynamic quantities like energy, entropy, and magnetization. The method is found to be advantageous near the critical temperature. Of special interest are the results at the critical temperature itself, where the Metropolis method seems to be impractical. At this temperature, the average thermodynamic quantities agree well with theoretical values, for both the two and three-dimensional lattices. For the two-dimensional lattice the specific heat exhibits the expected logarithmic dependence on lattice size; the dependence of the susceptibility on lattice size is also satisfactory, leading to a ratio of critical exponents/=1.85 ±0.08. For the three-dimensional lattice the dependence of the specific heat, long-range order, and susceptibility on lattice size leads to similarly satisfactory exponents:=0.12 ±0.03,=0.30 ±0.03, and=1.32 ±0.05 (assuming =2/3).     

Influence of the spacing between metal particles on the kinetics of reaction with spillover on the supported metal catalyst

The influence of the spacing between active metal particles placed on the supported metal catalyst on the kinetics of the catalytic reaction with spillover was investigated. The 2A+B₂→2AB reaction, modelling the CO oxidation on Pd/Al₂O₃ catalyst, was studied using Dynamic Monte Carlo simulations. It was shown that there exists an optimal spacing, that provides the maximum reaction rate. It was postulated that this optimum is a consequence of both competition and cooperative effects occurring between metal particles.     

Surface diffusion during decay of nano-island on Si(1 0 0) at high temperature

Surface diffusion during decay of a two-dimensional nano-island formed on Si(1 0 0) surface at 750-800 K is studied using STM and a kinetic Monte Carlo simulation. From a surface diffusion point of view, decay proceeds so that the total diffusion rate of atoms on a surface decreases. Atoms at step edges move more frequently than terrace atoms, which results in decay from step edges of the island. In addition, a terrace atom takes part in surface diffusion in the same way as an atom from steps of the island once it hops up on a terrace leaving a vacancy. The mass transport is not a specific atom process but terrace atoms and vacancies on the terrace are involved. Repeated upward and downward hops of atoms and their difference are combined with surface diffusion, which leads to the mass transport. Some tracks of atom using simulation show random walk with preferential diffusion along step edges, re-entering to the island, exchange of diffusing atom and filling in a vacancy on the terrace. The motion of the center of the island to the upper side of the terrace observed by STM is also well reproduced in the simulation.     

Study of oscillations and pattern formation in the CO + O2 reaction on Pt(1 0 0) surfaces through dynamic Monte Carlo simulation

Oscillations and pattern formation driven by a surface reconstruction are studied for the catalytic oxidation of CO on Pt(1 0 0) single-crystal surfaces through dynamic Monte Carlo simulations at low pressure and relatively high temperatures conditions. Sustained, modulated, irregular and damped oscillations are observed in our analysis as well as the formation of cellular, target, double spiral, spiral wave and turbulent patterns. The effect and the importance of the hex ? 1 × 1 surface phase transition and partial pressure of the reactants in the gas phase on the behavior of the system are discussed.     

Monte Carlo simulation for temperature dependence of Ga diffusion length on GaAs(0 0 1)

Diffusion length of Ga on the GaAs(0 0 1)-(2×4)β2 is investigated by a newly developed Monte Carlo-based computational method. The new computational method incorporates chemical potential of Ga in the vapor phase and Ga migration potential on the reconstructed surface obtained by ab initio calculations; therefore we can investigate the adsorption, diffusion and desorption kinetics of adsorbate atoms on the surface. The calculated results imply that Ga diffusion length before desorption decreases exponentially with temperature because Ga surface lifetime decreases exponentially. Furthermore, Ga diffusion length L along and [1 1 0] on the GaAs(0 0 1)-(2×4)β2 are estimated to be and L_[110]200 nm, respectively, at the incorporation–desorption transition temperature (T860 K).     

Usage of pattern recognition scheme in kinetic Monte Carlo simulations: Application to cluster diffusion on Cu(1 1 1)

We have invoked a simple pattern recognition scheme in kinetic Monte Carlo simulations of post-deposition evolution of two dimensional islands on fcc(1 1 1) surfaces. On application of the technique to the diffusion of small Cu clusters (8-100 atoms) on Cu(1 1 1) we find that, at room temperature, clusters with certain magic numbers show stick-slip type of motion with striking patterns rather than the random paths followed by the others. At higher temperatures all clusters display random motion. The calculated diffusion coefficients show dependence on size and temperature with an effective barrier ranging between 0.62 eV and 0.84 eV. Small asymmetries in diffusion barriers lead to a large difference in the frequencies of adatom diffusion along the two types of micro-facetted steps on Cu(1 1 1) leading to consequences in their shape evolution. The pattern recognition scheme revealed 49 basic periphery single atom diffusion processes whose activation energy barriers were calculated using the nudged elastic band technique and interatomic potentials from the embedded atom method.