Kinetic Monte Carlo

The problem of plasma-wall interaction requires multiscale methods (molecular dynamics and kinetic Monte Carlo) for both the material and the plasma. One possible concept for such multiscale modelling is presented, including validation strategies.

We present a kinetic Monte Carlo model for boron diffusion, clustering and activation in i o n implanted silicon. The input to the model is based on a combination o f experimental data and ab i n i t i o calculations. The model shows that boron diffusion and activation are low while vacancy clusters are present in the system. As the vacancy clusters dissociate, boron becomes substitutional and the active fraction increases rapidly. At the same time, the total boron diffusion length also increases rapidly while interstitial clusters ripen. The final burst of boron diffusion occurs a s the large interstitial clusters d i s s o l v e , but most of the transient diffusion of the implanted boron has already taken place by this time. We show that these results are in excellent agreement with experimental data on annealed dopant profiles and dopant activation as a function of annealing time.

The authors investigate quantitatively the self-organization of step bunching instability during epitaxy of Si on vicinal Si(001). They show that growth instability evolution can be fitted by power laws L~tα and A~tβ (where L is the correlation length and A is the instability amplitude) with critical exponents α~0.3 and β~0.5 in good agreement with previous studies and well reproduced by kinetic Monte Carlo simulation. They demonstrate that the main phenomenon controlling step bunching is the anisotropy of surface diffusion. The microscopic origin of the instability is attributed to an easier adatom detachment from SA step, which can be interpreted as a pseudoinverse Ehrlich-Schwoebel barrier [J. Appl. Phys. 37, 3682 (1967); J. Chem. Phys. 44, 1039 (1966)].

The efficiency of different technological processes where nanoporous carbons are used depends on their storage capacity and an appropriate gas transport. Different experimental and theoretical works that relate storage to global structural parameters of the solid such as specific surface area (SSA) or total pore volume (V t ) can be found in literature. The structure-transport relationships have been less studied. The combined use of the truncated pore network model (TPNM) and the kinetic Monte Carlo (KMC) method is proposed in this work to find hydrogen and methane effective self-diffusivities (D eff ) and to delve into those relationships. It was found that for Knudsen and free molecular diffusion in the simulated materials, the D eff /V t vs. SSA graphic nearly follows a power law. The KMC/TPNM approach was also used to predict the self-diffusion coefficients of hydrogen in Vulcan XC-72 and of methane in a carbon aerogel. The obtained values are within the expected range. KCM/TPNM is computationally fast and it allows a study of the diffusion synchronously and globally in the network, avoiding thus its fractionation in single pores and the use of just one geometric model to describe the porous spaces.

The microscopic spatial kinetic Monte Carlo (KMC) method has been employed extensively in materials modeling. In this review paper, we focus on different traditional and multiscale KMC algorithms, challenges associated with their implementation, and methods developed to overcome these challenges. In the first part of the paper, we compare the implementation and computational cost of the null-event and rejection-free microscopic KMC algorithms. A firmer and more general foundation of the null-event KMC algorithm is presented. Statistical equivalence between the null-event and rejection-free KMC algorithms is also demonstrated. Implementation and efficiency of various search and update algorithms, which are at the heart of all spatial KMC simulations, are outlined and compared via numerical examples. In the second half of the paper, we review various spatial and temporal multiscale KMC methods, namely, the coarse-grained Monte Carlo (CGMC), the stochastic singular perturbation approximation, and the τ -leap methods, introduced recently to overcome the disparity of length and time scales and the one-at-a time execution of events. The concepts of the CGMC and the τ -leap methods, stochastic closures, multigrid methods, error associated with coarse-graining, a posteriori error estimates for generating spatially adaptive coarse-grained lattices, and computational speed-up upon coarse-graining are illustrated through simple examples from crystal growth, defect dynamics, adsorption-desorption, surface diffusion, and phase transitions.

We present an algorithm for the simulation of vicinal surface growth. It combines a lattice gas anisotropic Ising model with a phase-field model. The molecular behavior of individual adatoms is described by the lattice gas model. The microstructure dynamics on the vicinal surface are calculated using the phase-field method. In this way, adsorption processes on two different length scales can be described: nucleation processes on the terraces (lattice gas model) and step-flow growth (phase field model). The hybrid algorithm that is proposed here, is therefore able to describe an epitaxial layer-by-layer growth controlled by temperature and by deposition rate. This method is faster than kinetic Monte Carlo simulations and can take into account the stochastic processes in a comparable way.

The reactor pressure vessel (RPV) steels used in current nuclear power plants embrittle as a consequence of the continuous irradiation with neutrons. Among other radiation effects, the experimentally observed formation of copper-rich defects is accepted to be one of the main causes of embrittlement. Therefore, an accurate description of the nucleation and growth under irradiation of these and other defects is fundamental for the prediction of the mechanical degradation that these materials undergo during operation, with a view to guarantee a safer plant life management. In this work we describe in detail the object kinetic Monte Carlo (OKMC) method that we developed, showing that it is well suited to investigate the evolution of radiation damage in simple Fe alloys (Fe, Fe-Cu) under irradiation conditions (temperature, dose and dose-rate) typical of experiments with different impinging particles and also operating conditions. The still open issue concerning the method is the determination of the mechanisms and parameters that should be introduced in the model in order to correctly reproduce the experimentally observed trends. The stateof-the-art, based on the input from atomistic simulation techniques, such as ab initio calculations, molecular dynamics (MD) and atomic kinetic Monte Carlo, is critically revised in detail and a sensitivity study on the effects of the choice of the reaction radii and the description of defect mobility is conducted. A few preliminary, but promising, results of favorable comparison with experimental observations are shown and possible further refinements of the model are briefly discussed.

Catalytic conversion of biomass-derived synthesis gas to ethanol and other C2+ oxygenates has received considerable attention recently due to the strong demands for alternative, renewable energy sources. Combining experimental measurements with first-principles-based kinetic modeling, we investigated the reaction kinetics of ethanol synthesis from CO hydrogenation over SiO2 -supported Rh/Mn alloy catalysts. We find that an Mn promoter can exist in

The growth of hydrocarbon molecules up to sizes of incipient soot is computed in premixed laminar flames using kinetic Monte Carlo and molecular dynamic methodologies (AMPI code). This approach is designed to preserve atomistic scale structure (bonds, bond angles, dihedral angles) as soot precursors evolve into three-dimensional structures. Application of this code to aliphatic (acetylene) and aromatic (benzene) flame environments is able to explain results in the literature on the differences in properties of soot precursors from these two classes of flames, particularly relating to H/C ratio, particle sphericity, and depolarization ratio.

We present here a summary of some recent techniques used for atomistic studies of thin film growth and morphological evolution. Specific attention is given to a new kinetic Monte Carlo technique in which the usage of unique labeling schemes of the environment of the diffusing entity allows the development of a closed data base of 49 single atom diffusion processes for periphery motion. The activation energy barriers and diffusion paths are calculated using reliable manybody interatomic potentials. The application of the technique to the diffusion of 2-dimensional Cu clusters on Cu(111) shows interesting trends in the diffusion rate and in the frequencies of the microscopic mechanisms which are responsible for the motion of the clusters, as a function of cluster size and temperature. The results are compared with those obtained from yet another novel kinetic Monte Carlo technique in which an open data base of the energetics and diffusion paths of microscopic processes is continuously updated as needed. Comparisons are made with experimental data where available.

A hybrid algorithm that combines a phase-field model and a lattice gas model evolving according to a kinetic Monte-Carlo (KMC) simulation scheme is used to investigate the dynamics of vicinal surface growth during vapor phase epitaxy. The algorithm is computationally far more efficient than pure KMC schemes, and this gain in efficiency does not correspond to a loss in information on the kinetics of individual atoms. We present numerical studies on the temperature dependence of macroscopic properties of the growing surface, evaluating the relevant stochastic processes (attachment, detachment, diffusion and island dynamics) as a function of their rates. We show that the temperature at which step flow is replaced by island nucleation depends on incoming flux, diffusion parameters and interstep distance. Moreover, we validate these finding by comparison to experiments and by analytical investigations.

The coupling of a new radiation transport (RT) solver with an existing multimaterial fluid dynamics code (ARWEN) using Adaptive Mesh Refinement named DAFNE, has been completed. In addition, improvements were made to ARWEN in order to work properly with the RT code, and to make it user-friendlier, including new treatment of Equations of State, and graphical tools for visualization. The evaluation of the code has been performed, comparing it with other existing RT codes (including the one used in DAFNE, but in the single-grid version). These comparisons consist in problems with real input parameters (mainly opacities and geometry parameters). Important advances in Atomic Physics, Opacity calculations and NLTE atomic physics calculations, with participation in significant experiments in this area, have been obtained. Early published calculations showed that a DT x fuel with a small tritium initial content (x53%) could work in a catalytic regime in Inertial Fusion Targets, at very high burning temperatures (4100 keV). Otherwise, the cross-section of DT remains much higher than that of DD and no internal breeding of tritium can take place. Improvements in the calculation model allow to properly simulate the effect of inverse Compton scattering which tends to lower T e and to enhance radiation losses, reducing the plasma temperature, T i . The neutron activation of all natural elements in First Structural Wall (FSW) component of an Inertial Fusion Energy (IFE) reactor for waste management, and the analysis of activation of target debris in NIF-type facilities has been completed. Using an original efficient modeling for pulse activation, the FSW behavior in inertial fusion has been studied. A radiological dose library coupled to the ACAB code is being generated for assessing impact of environmental releases, and atmospheric dispersion analysis from HIF reactors indicate the uncertainty in tritium release parameters. The first recognition of recombination barriers in SiC, modify the understanding of the calculation of displacement per atom, dpa, to quantify the collisional damage. An important analysis has been the confirmation, using Molecular Dynamics (MD) with an astonishing agreement, of the experimental evidence of low-temperature amorphization by damage accumulation in SiC, which could modify extensively its viability as a candidate material for IFE (fusion in general) applications. The radiation damage pulse effect has also been assessed using MD and Kinetic Monte Carlo diffusion of defects, showing the dose and driver frequency dependences. #

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Vacancy migration energies as functions of the local atomic configuration (LAC) in Fe-Cu alloys have been systematically tabulated using an appropriate interatomic potential for the alloy of interest. Subsets of these tabulations have been used to train an artificial neural network (ANN) to predict all vacancy migration energies depending on the LAC. The error in the prediction of the ANN has been evaluated by a fuzzy logic system (FLS), allowing a feedback to be introduced for further training, to improve the ANN prediction. This artificial intelligence (AI) system is used to develop a novel approach to atomistic kinetic Monte Carlo (AKMC) simulations, aimed at providing a better description of the kinetic path followed by the system through diffusion of solute atoms in the alloy via vacancy mechanism. Fe-Cu has been chosen because of the importance of Cu precipitation in Fe in connection with the embrittlement of reactor pressure vessels of existing nuclear power plants. In this paper the method is described in some detail and the first results of its application are presented and briefly discussed.

Pulsed laser deposition (PLD) is a popular growth method, which has been successfully used for fabricating thin films. Compared to continuous deposition (like molecular beam epitaxy) the pulse intensity can be used as an additional parameter for tuning the growth behavior, so that under certain circumstances PLD improves layer-by-layer growth. We present kinetic Monte-Carlo simulations for PLD in the submonolayer regime and give a description of the island distance versus intensity. Furthermore we discuss a theory for second layer nucleation and the impact of Ehrlich-Schwoebel barriers on the growth behavior. We find an exact analytical expression for the probability of second layer nucleation during one pulse for high Ehrlich-Schwoebel barriers.

Atoms and molecules adsorbed on metals affect each other indirectly even over considerable distances. Via systematic density-functional calculations, we establish the nature and strength of such interactions, and explain for what adsorbate systems they critically affect important materials properties. This is verified in kinetic Monte Carlo simulations of epitaxial growth, which help rationalize a number of recent experimental reports on anomalously low diffusion prefactors. PACS numbers: 68.35.Fx, 68.35.Bs, 68.35.Ja Besides forming direct chemical bonds at short separations, atoms and molecules interact indirectly over large distances via relaxations in the lattice of substrate atoms on which they are adsorbed. In metals, polarization of the electron gas gives rise to a supplementary form of indirect adsorbate interactions . Because almost nothing is known about the relative and absolute strengths of these long-ranged elastic and electronic interactions for real metals, it is unclear in general how they modify adsorbate behavior and affect materials properties.

We present some recent applications of the atomistic diffusion model and of the kinetic Monte Carlo (KMC) algorithm to systems of industrial interest, i.e. Al-Zr-Sc and Fe-Nb-C alloys, or to model systems. These applications include study of homogeneous and heterogeneous precipitation as well as of phase transformation under irradiation. The KMC simulations are also used to test the main assumptions and limitations of more simple models and classical theories used in the industry, e.g. the classical nucleation theory. Fig. 5. Variation with the nominal concentration and the temperature of the steadystate nucleation rate J st for Al 3 Zr precipitation. Symbols correspond to KMC simulations and lines to CNT.

This paper reviews our recent studies of the fundamentals of growth morphology evolution in Pulsed Laser Deposition in two prototypical growth modes: metal-oninsulator island growth and semiconductor homoepitaxy. By comparing morphology evolution for pulsed laser deposition and thermal deposition in the same dual-use chamber under identical thermal, background, and surface preparation conditions, and varying the kinetic energy by varying the laser fluence or using an inert background gas, we have isolated the effect of kinetic energy from that of flux pulsing in determining the differences between morphology evolution in these growth methods. In each growth mode analytical growth models and Kinetic Monte Carlo simulations for thermal deposition, modified to include kinetic energy effects, are successful at explaining much of what we observe experimentally.

We present here a summary of some recent techniques used for atomistic studies of thin film growth and morphological evolution. Specific attention is given to a new kinetic Monte Carlo technique in which the usage of unique labeling schemes of the environment of the diffusing entity allows the development of a closed data base of 49 single atom diffusion processes for periphery motion. The activation energy barriers and diffusion paths are calculated using reliable manybody interatomic potentials. The application of the technique to the diffusion of 2-dimensional Cu clusters on Cu(111) shows interesting trends in the diffusion rate and in the frequencies of the microscopic mechanisms which are responsible for the motion of the clusters, as a function of cluster size and temperature. The results are compared with those obtained from yet another novel kinetic Monte Carlo technique in which an open data base of the energetics and diffusion paths of microscopic processes is continuously updated as needed. Comparisons are made with experimental data where available.

Nanoscience is an area with increasing interest both in the physicochemical phenomena involved and the potential applications such as silicon carbide films, carbon nanotubes, quantum dots, MEMS etc. These materials exhibit very interesting properties (electronic, optical, mechanical) at various length/time scales necessitating better insight. Modern fabrication techniques, such as CVD, also require better understanding in a wide range of length/time scales, in order to achieve better process control. Multiscale modeling is a new, fast developing and challenging scientific field with contributions from many scientific disciplines in an effort to assure materials simulation across length/time scales. In this paper we present a brief review of recent advances in multiscale materials modeling. First, a classification of existing simulation methods based on time and length scales is presented along with basic principles of the multiscale approach. More specifically, we focus on electronic structure calculations, classical atomistic simulation with molecular dynamics or monte carlo methods at the nano/micro scale, Kinetic Monte Carlo for larger system/ time scales and finite elements for very large scales. Then, we present the hierarchical and the hybrid strategies of multiscale modeling to couple these methods. Finally, we deal with selected applications concerning thin film CVD deposition and mechanical behavior of carbon nanotubes and we conclude presenting an overview of future trends of multiscale modeling.

Simulations of displacement cascade annealing were carried out using object kinetic Monte Carlo based on an extensive MD database including various primary knock-on atom energies and directions. The sensitivity of the results to a broad range of material and model parameters was examined. The diffusion mechanism of interstitial clusters has been identified to have the most significant impact on the fraction of stable interstitials that escape the cascade region. The maximum level of recombination was observed for the limiting case in which all interstitial clusters exhibit 3D random walk diffusion. The OKMC model was parameterized using two alternative sets of defect migration and binding energies, one from ab initio calculations and the second from an empirical potential. The two sets of data predict essentially the same fraction of surviving defects but different times associated with the defect escape processes. This study provides a comprehensive picture of the first phase of long-term defect evolution in bcc iron and generates information that can be used as input data for mean field rate theory (MFRT) to predict the microstructure evolution of materials under irradiation. In addition, the limitations of the current OKMC model are discussed and a potential way to overcome these limitations is outlined.

ABSTRACT An atomistic kinetic Monte Carlo (AKMC) method has been applied to study the stability and mobility of copper–vacancy clusters in Fe. This information, which cannot be obtained directly from experimental measurements, is needed to parameterise models describing the nanostructure evolution under irradiation of Fe alloys (e.g. model alloys for reactor pressure vessel steels). The physical reliability of the AKMC method has been improved by employing artificial intelligence techniques for the regression of the activation energies required by the model as input. These energies are calculated allowing for the effects of local chemistry and relaxation, using an interatomic potential fitted to reproduce them as accurately as possible and the nudged-elastic-band method. The model validation was based on comparison with available ab initio calculations for verification of the used cohesive model, as well as with other models and theories.

The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applying it to materials modeling problems of interest to Sandia. In this report we give an overview of the methods and algorithms developed, and describe our new open-source code called SPPARKS, for Stochastic Parallel PARticle Kinetic Simulator. We also highlight the development of several Monte Carlo models in SPPARKS for specific materials modeling applications, including grain growth, bubble formation, diffusion in nanoporous materials, defect formation in erbium hydrides, and surface growth and evolution. The Kinetic Monte Carlo method provides a simple yet powerful and flexible tool for exercising the concerted action of fundamental, stochastic, physical mechanisms to create a model of the phenomena that they produce. This manuscript contains an overview of the theory behind the method, some simple examples to illustrate its implementation, and a technologically relevant application of the method to model the refinement of grains during polycrystalline thin film deposition. The objective is to provide an introduction to the method and its basics, and to present useful examples that might be followed to achieve its implementation for solving practical problems.

Groups of displacement cascades calculated independently with different simulation models and computer codes are compared on a statistical basis. The parameters used for this comparison are the number of Frenkel pairs (FP) produced, the percentages of vacancies and self-interstitial atoms (SIAs) in clusters, the spatial extent and the aspect ratio of the vacancies and the SIAs formed in each cascade. One group of cascades was generated in the binary collision approximation (BCA) and all others by full molecular dynamics (MD). The MD results differ primarily due to the empirical interatomic potentials used and, to some extent, in code strategies. Cascades were generated in simulation boxes at different initial equilibrium temperatures. Only modest differences in the predicted numbers of FP are observed, but the other cascade parameters may differ by more than 100%. The consequences of these differences on long-term cluster growth in a radiation environment are examined by means of object kinetic Monte Carlo (OKMC) simulations. These were repeated with three different parameterizations of SIA and SIA cluster mobility. The differences encompassed low to high mobility, one-and three-dimensional migration of clusters, and complete immobility of large clusters. The OKMC evolution was followed until 0.1 dpa was reached. With the range of OKMC parameters used, cluster populations after 0.1 dpa differ by orders of magnitude. Using the groups of cascades from different sources induced no difference larger than a factor of 2 in the OKMC results. No correlation could be identified between the cascade parameters considered and the number densities of vacancies and SIAs predicted by OKMC to cluster in the long term. However, use of random point defect distributions instead of those obtained for displacement cascades as input for the OKMC modeling led to significantly different results.

Changes in microstructure and mechanical properties of nuclear materials are governed by the kinetics of defects produced by irradiation. The population of vacancies, interstitials and their clusters can however be followed only indirectly, for example by macroscopic resistivity measurements. The information on the mobility, recombination, clustering or dissociation of defects provided by such experiments is both extremely rich and diffi cult to interpret. By combining ab initio and kinetic Monte Carlo methods, we successfully reproduce the abrupt resistivity changes-so-called recovery stagesobserved upon annealing at increasing temperatures after electron irradiation in α-iron. New features in the mechanisms responsible for these stages are revealed.

We introduce a discrete event kinetic Monte Carlo ( KMC ) simulation program that is capable of reproducing thermal desorption data. The KMC program is suitable for the analysis of both, desorption in 2D quasi-equilibrium and desorption influenced by kinetic effects. Whereas the KMC simulation exhibits a clear advantage over approaches using rate equations regarding kinetic influences, the well-known quasi-equilibrium desorption provides a crucial test for the KMC simulation. Under the appropriate circumstances, the KMC simulation is, indeed, in full agreement with the quasi-equilibrium analysis based on the Polanyi-Wigner equation.

Recently there has been interest in developing efficient ways to model heterogeneous surface reactions with hybrid computational models that couple a kinetic Monte Carlo (KMC) model for a surface to a finite-difference model for bulk diffusion in a continuous domain. We consider two representative problems that validate a hybrid method and show that this method captures the combined effects of nonlinearity and stochasticity. We first validate a simple deposition-dissolution model with a linear rate showing that the KMC-continuum hybrid agrees with both a fully deterministic model and its analytical solution. We then study a deposition-dissolution model including competitive adsorption, which leads to a nonlinear rate, and show that in this case the KMC-continuum hybrid and fully deterministic simulations do not agree. However, we are able to identify the difference as a natural result of the stochasticity coming from the KMC surface process. Because KMC captures inherent fluctuations, we consider it to be more realistic than a purely deterministic model. Therefore, we consider the KMC-continuum hybrid to be more representative of a real system.

This paper gives a summary of basic concepts of density-functional theory (DFT) and its use in state-of-the-art computations of complex processes in condensed matter physics and materials science. In particular we discuss how microscopic growth parameters can be determined by DFT and how on this basis macroscopic phenomena can be described. To reach the time and length scales of realistic growth conditions, DFT results are complemented by kinetic Monte Carlo simulations.

Cement hydration kinetics is a complex problem involving dissolution, nucleation and growth and is still not well understood, particularly in a quantitative way. While cement systems are unique in certain aspects, they are also comparable to natural mineral systems. Therefore, geochemistry and particularly the study of mineral dissolution and growth may be able to provide insight and methods that can be utilized in cement hydration research. Here, we review mainly what is not known or what is currently used and applied in a problematic way. Examples are the typical Avrami approach, the application of Transition State Theory (TST) to overall reaction kinetics and the problem of reactive surface area. Finally, we suggest an integrated approach that combines vertical scanning interferometry (VSI) with other sophisticated analytical techniques such as atomic force microscopy (AFM) and theoretical model calculations based on a stochastic treatment.

We present a novel application of the Zobrist hashing method, known in the computer chess literature, to simulation of diffusional phase transformations in metal alloys. A history of previously visited states can be easily maintained, allowing very fast lookup of energies and transition rates calculated earlier in the simulation. The method has been applied to the simulation of a Fe-1at.%Cu system, with simple potentials and a transition rate for diffusional events approximated from the difference in internal energy between trial states. In this simple model at temperatures of 1073 K we find that 61.2% of the states considered during the simulation have been seen previously, and that this proportion rises to 85.1% at 773 K and even to 99.9% at 373 K. Rapid recall of these states reduces the computational time taken for the same sequence of atom-vacancy exchange moves by a factor of 6.3 at 773 K rising to over 100 at 373 K. We suggest that a similar speedup factor will be found using more sophisticated models of diffusion and that the method can, with small modifications, be applied to a wide range of kinetic Monte Carlo simulations of atomistic diffusion processes.

We present a detailed description of the kinetic activation-relaxation technique (k-ART), an off-lattice, self-learning kinetic Monte Carlo (KMC) algorithm with on-the-fly event search. Combining a topological classification for local environments and event generation with ART nouveau, an efficient unbiased sampling method for finding transition states, k-ART can be applied to complex materials with atoms in off-lattice positions or with elastic deformations that cannot be handled with standard KMC approaches. In addition to presenting the various elements of the algorithm, we demonstrate the general character of k-ART by applying the algorithm to three challenging systems: self-defect annihilation in c-Si (crystalline silicon), self-interstitial diffusion in Fe, and structural relaxation in a-Si (amorphous silicon).

We have developed a two-band model of Fe-Cr, fitted to properties of the ferro-magnetic alloy. Fitting many-body functionals to the calculated mixing enthalpy of the alloy and the mixed interstitial binding energy in iron, our potential reproduces changes in sign of the formation energy as function of Cr concentration. When applied in Kinetic Monte Carlo simulations, the potential correctly predicts decomposition of initially random Fe-Cr alloys into the α-prime phase as function of Cr concentration.

The influence of a static scanning tunneling microscope (STM) tip on the diffusion of xenon atoms adsorbed on a Cu(1 1 0) stepped surface is studied. Semi-empirical potentials for the Xe-surface interaction and a N-body energy based method for the Xe-tip contribution are used to calculate the adsorption energy of adsorbates in the STM junction. First, we analyse the variation of this energy when the adatom is placed near a step edge and for different tip positions. When the tip is situated in the neighbourhood of the step edge, the Ehrlich-Schwoebel barrier experienced by the adatom is lowered. This opens a specific diffusion channel, allowing a possible crossing of the step edge. Second, through a kinetic Monte Carlo approach coupled to the elastic scattering quantum chemistry method, the noisy tunneling current created by the random motion of diffusing atoms in the vicinity of the tip can be analyzed. We show that, by counting the number of diffusion events, we can determine effective barriers related to the most dominant processes contributing to the diffusion at a particular temperature. We also demonstrate that the interaction mode of the tip (attractive or imaging) greatly modifies the diffusion processes.

The surface diffusion of Cu adatoms in the presence of an adisland at FCC or HCP sites on Cu(111) is studied using the EAM potential derived by Mishin et al. (Phys. Rev. B 63 224106 (2001)). The diffusion rates along straight (with close-packed edges) steps with (100) and (111)-type microfacets (resp. step A and step B) are first investigated using

The EAM potential set up by Mishin et al. [Phys. Rev. B 63 224106 (2001)] is used to study some elementary processes in the homoepitaxy of Cu on Cu͑111͒. After having checked its ability to reproduce surface physical quantities, this potential is applied to an investigation of the energetics, the vibrations and the surface diffusion of Cu N close-packed adislands ͑1 ഛ N ഛ 7͒. In each case we determine the most stable configurations, the corresponding activation barriers, the local vibrational spectra, and the Vineyard prefactors. In particular it is found that, at room temperature, dimers and trimers are still very mobile and move by concerted jumps much faster than tetramers while heptamers can be considered as immobile. The very good agreement of our results with scanning tunneling microscopy observations justifies the use of Mishin et al. potential for treating surface diffusion. This allowed us to study in details the influence of the lateral atomic environment of the adatoms along its diffusion path. An effective lateral pair interaction model is set up which is able to predict the existence of a saddle point along the path and to give a very good estimation of the activation barrier height. This model will be very useful in kinetic Monte Carlo simulations of homoepitaxial growth of Cu͑111͒.

Low energy (<100 keV) helium implantation of tungsten has been shown to result in the formation of unusual surface morphologies over a large temperature range (700-2100 °C). Simulation of these macroscopic phenomena requires a multiscale approach to modeling helium transport in both space and time. We present here a multiscale helium transport model by coupling spatially-resolved kinetic rate theory (KRT) with kinetic Monte Carlo (KMC) simulation to model helium bubble nucleation and growth. The KRT-based HEROS Code establishes defect concentrations as well as stable helium bubble nuclei as a function of implantation parameters and position from the implanted surface and the KMC-based Mc-HEROS Code models the growth of helium bubbles due to migration and coalescence. Temperatureand stress-gradients can act as driving forces, resulting in biased bubble migration. The Mc-HEROS Code was modified to simulate the impact of stress gradients on bubble migration and coalescence. In this work, we report on bubble growth and gas release of helium implanted tungsten W/O stress gradients. First, surface pore densities and size distributions are compared with available experimental results for stress-free helium implantation conditions. Next, the impact of stress gradients on helium bubble evolution is simulated. The influence of stress fields on bubble and surface pore evolution are compared with stress-free simulations. It is shown that near surface stress gradients accelerate helium bubbles towards the free surface, but do not increasing average bubble diameters significantly.

The selective deposition of GaAs and InP was investigated using a multiscale approach. Local gas phase composition, temperature, and flow fields were calculated solving mass, energy and momentum conservation equations at the reactor scale with 2D FEM. The growth on patterned wafers was described with a 2D microscale model that includes adsorption and diffusion on mask and feature. Reactor and microscopic models are linked consistently imposing the continuity of gas phase fluxes. The morphology evolution was investigated with 3D KMC using gas phase fluxes calculated with the microscopic scale model. The model is generally in good agreement with experimental data except for high mask/feature ratios, in which case the growth rate is overestimated both for GaAs and InP. We attribute the overestimation to the diffusion of molecular species adsorbed on (1 1 1) facets from feature to mask.

In studies of island nucleation and growth, the distribution of capture zones, essentially proximity cells, can give more insight than island-size distributions. In contrast to the complicated expressions, ad hoc or derived from rate equations, usually used, we find the capture-zone distribution can be described by a simple expression generalizing the Wigner surmise from random matrix theory that accounts for the distribution of spacings in a host of fluctuation phenomena. Furthermore, its single adjustable parameter can be simply related to the critical nucleus of growth models and the substrate dimensionality. We compare with extensive published kinetic Monte Carlo data and limited experimental data. A phenomenological theory sheds light on the result.

Recent advances in analytical and computational modelling frameworks to describe the mechanics of materials on scales ranging from the atomistic, through the microstructure or transitional, and up to the continuum are reviewed. It is shown that multiscale modelling of materials approaches relies on a systematic reduction in the degrees of freedom on the natural length scales that can be identified in the material. Connections between such scales are currently achieved either by a parametrization or by a 'zoom-out' or 'coarse-graining' procedure. Issues related to the links between the atomistic scale, nanoscale, microscale and macroscale are discussed, and the parameters required for the information to be transferred between one scale and an upper scale are identified. It is also shown that seamless coupling between length scales has not yet been achieved as a result of two main challenges: firstly, the computational complexity of seamlessly coupled simulations via the coarse-graining approach and, secondly, the inherent difficulty in dealing with system evolution stemming from time scaling, which does not permit coarse graining over temporal events. Starting from the Born-Oppenheimer adiabatic approximation, the problem of solving quantum mechanics equations of motion is first reviewed, with successful applications in the mechanics of nanosystems. Atomic simulation methods (e.g. molecular dynamics, Langevin dynamics and the kinetic Monte Carlo method) and their applications at the nanoscale are then discussed. The role played by dislocation dynamics and statistical mechanics methods in understanding microstructure self-organization, heterogeneous plastic deformation, material instabilities and failure phenomena is also discussed.

An accelerated atomistic kinetic Monte Carlo (KMC) approach for evolving complex atomistic structures has been developed. The method incorporates on-the-fly calculations of transition states (TSs) with a scheme for defining active volumes (AVs) in an off-lattice (relaxed) system. In contrast to conventional KMC models that require all reactions to be predetermined, this approach is self-evolving and any physically relevant motion or reaction may occur. Application of this self-evolving atomistic kinetic Monte Carlo (SEAK-MC) approach is illustrated by predicting the evolution of a complex defect configuration obtained in a molecular dynamics (MD) simulation of a displacement cascade in Fe. Over much longer times, it was shown that interstitial clusters interacting with other defects may change their structure, e.g., from glissile to sessile configuration. The direct comparison with MD modeling confirms the atomistic fidelity of the approach, while the longer time simulation demonstrates the unique capability of the model.

We present results from kinetic Monte Carlo ͑KMC͒ simulations of diffusion in a model glass former. We find that the diffusion constants obtained from KMC simulations have Arrhenius temperature dependence, while the correct behavior, obtained from molecular dynamics simulations, can be super-Arrhenius. We conclude that the discrepancy is due to undersampling of higher-lying local minima in the KMC runs. We suggest that the relevant connectivity of minima on the potential energy surface is proportional to the energy density of the local minima, which determines the ''inherent structure entropy.'' The changing connectivity with potential energy may produce a correlation between dynamics and thermodynamics.

An extension of the synchronous parallel kinetic Monte Carlo (pkMC) algorithm developed by Martinez et al [J. Comp. Phys. 227 (2008) 3804] to discrete lattices is presented. The method solves the master equation synchronously by recourse to null events that keep all processors time clocks current in a global sense. Boundary conflicts are rigorously solved by adopting a chessboard decomposition into noninteracting sublattices. We find that the bias introduced by the spatial correlations attendant to the sublattice decomposition is within the standard deviation of the serial method, which confirms the statistical validity of the method. We have assessed the parallel efficiency of the method and find that our algorithm scales consistently with problem size and sublattice partition. We apply the method to the calculation of scale-dependent critical exponents in billion-atom 3D Ising systems, with very good agreement with state-of-the-art multispin simulations.