Kinetic Monte Carlo Model Research Articles

Insights from an OKMC simulation of dose rate effects on the irradiated microstructure of RPV model alloys

This work studies the defect features in a dilute FeMnNi alloy by an Object Kinetic Monte Carlo (OKMC) model based on the "grey-alloy" method. The dose rate effect is studied at 573 K in a wide range of dose rates from 10−8 to 10−4 displacement per atom (dpa)/s and demonstrates that the density of defect clusters rises while the average size of defect clusters decreases with increasing dose rate. However, the dose-rate effect decreases with increasing irradiation dose. The model considered two realistic mechanisms for producing <100>-type self-interstitial atom (SIA) loops and gave reasonable production ratios compared with experimental results. Our simulation shows that the proportion of <100>-type SIA loops could change obviously with the dose rate, influencing hardening prediction for various dose rates irradiation. We also investigated ways to compensate for the dose rate effect. The simulation results verified that about a 100 K temperature shift at a high dose rate of 1 × 10−4 dpa/s could produce similar irradiation microstructures to a lower dose rate of 1 × 10−7 dpa/s irradiation, including matrix defects and deduced solute migration events. The work brings new insight into the OKMC modeling and the dose rate effect of the Fe-based alloys.

Effect of Deposition Flux on Polytypic Competitive Growth of SiC Crystal by Kinetic Monte Carlo Method

A competitive kinetic Monte Carlo (KMC) model for gas‐phase epitaxy growth of 4H‐SiC and 6H‐SiC crystals is established based on polytype transformation and the Monte Carlo algorithm. The competitive growth processes of the two polytypes are simulated, and the effect of deposition flux on the polytype competition is analyzed. The 4H‐SiC competitive growth is promoted by the increase in deposition rate, and the effect of the Si/C ratio on polytypic competition is suppressed by the high deposition rate. Moreover, competitive growth is affected by deposition flux by changing the ratio of diffusion rate to deposition rate.

Object kinetic Monte Carlo modelling of irradiation microstructures with elastic interactions

Elastic interactions between point defects and sinks, such as dislocations and cavities, affect the diffusion of point defects and are responsible for some of the features observed in microstructures under irradiation. It is therefore necessary to include elastic interactions in kinetic simulations for a quantitative prediction of material properties. In this work a method is presented to accurately and efficiently evaluate the strain field in object kinetic Monte Carlo simulations. It can handle any strain field which is biharmonic, such as the one generated by a dislocation segment or a cavity in isotropic elasticity. A speed-up of several orders of magnitude is obtained compared to the direct summation over strain sources, so that simulations over experimental time scales can be performed within reasonable computation times. The case of a thin foil containing a high density of loops under irradiation is investigated. Loop growth rates are found to depend on the loop radius, as shown experimentally, but more complex effects due to the surrounding microstructure are also highlighted.

An atomistic modeling framework for valence change memory cells

We present a framework dedicated to modeling the resistive switching operation of Valence Change Memory (VCM) cells. The method combines an atomistic description of the device structure, a Kinetic Monte Carlo (KMC) model for the creation and diffusion of oxygen vacancies in the central oxide under an external field, and an ab initio quantum transport method to calculate electrical current and conductance. As such, it reproduces a realistically stochastic device operation and its impact on the resulting conductance. We demonstrate this framework by simulating a switching cycle for a TiN/HfO2/TiN VCM cell, and see a clear current hysteresis between high/low resistance states, with a conductance ratio of one order of magnitude. Additionally, we observe that the changes in conductance originate from the creation and recombination of vacancies near the active electrode, effectively modulating a tunneling gap for the current. This framework can be used to further investigate the mechanisms behind resistive switching at an atomistic scale and optimize VCM material stacks and geometries.

Modelling multi-scale material growth and erosion under energetic atomic deposition

ABSTRACT We study crystalline surface evolution in extreme environments, where high-energy atoms impinge on a crystalline surface to cause sputtering, growth and surface roughening. For our model system, we study the evolution of the Ni(111) surface under Ni atom bombardment, using Molecular Dynamics (MD) simulation and a Sutton-Chen force field, where the uppermost surface layers are free to move, supported by thermostatically controlled layers above a rigid template. The MD statistics of sputtering and sticking are used to aid the development of a computationally efficient kinetic Monte Carlo (KMC) code. Comparisons between the simulation surface morphologies are used to tune the KMC growth rules so that the key statistical features of the MD structures are captured by the KMC model. This model is then employed to explore the predicted behaviour over length and times scales much larger than those accessible to MD. While the MD-KMC approach is well known, this application to the complex surface growth encountered in energetic atomic bombardment illuminates the complexities of relating atomistic events to morphological evolution. The work shows how simulation methodology can be extended to provide predictive capabilities, paving the way for design tools for engineering processes such as plasma deposition film growth.

Accelerating off-lattice kinetic Monte Carlo simulations to predict hydrogen vacancy-cluster interactions in [formula omitted]-Fe

We present an enhanced off-lattice kinetic Monte Carlo (OLKMC) model, based on a new method for tolerant classification of atomistic local-environments that is invariant under Euclidean-transformations and permutations of atoms. Our method ensures that environments within a norm-based tolerance are classified as equivalent. During OLKMC simulations, our method guarantees to elide the maximum number of redundant saddle-point searches in symmetrically equivalent local-environments. Hence, we are able to study the trapping/detrapping of hydrogen from up to five-vacancy clusters and simultaneously the effect hydrogen has on the diffusivity of these clusters. These processes occur at vastly different timescales at room temperature in body-centred cubic iron. We predict the diffusion pathways of clusters/complexes without a priori assumptions of their mechanisms, not only reproducing previously reported mechanisms but also discovering new ones for larger complexes. We detail the hydrogen-induced changes in the clusters’ diffusion mechanisms and find evidence that, in contrast to mono-vacancies, the introduction of hydrogen to larger clusters can increase their diffusivity. We compare the effective hydrogen diffusivity to Oriani’s classical theory of trapping, finding general agreement and some evidence that hydrogen may not always be in equilibrium with traps, when the traps are mobile. Finally, we compute the trapping atmosphere of meta-stable states surrounding non-point traps, opening new avenues to better understand and predict hydrogen embrittlement in complex alloys.

Influence of the Composition and Vacancy Concentration on Cluster Decomposition Behavior in Al-Si-Mg Alloy: A Kinetic Monte Carlo Study.

The influence of cluster composition and the addition of vacancies on the decomposition behavior of clusters during artificial aging in Al–Si–Mg alloys were analyzed according to the kinetic Montel Carlo model. Clusters with a balanced composition (Mg/(Mg + Si) = 0.5) were the most difficult to decompose. In addition, the cluster decomposition was slower when more vacancies were added to the cluster. Among Si, Mg, and vacancies, vacancies most significantly affect decomposition. The clusters with Mg/(Mg + Si) ≤ 0.4 strongly trap vacancies, which can be classified as hardly decomposable vacancy-rich clusters. The clustering behavior during natural aging and the effect of pre-aging were analyzed using the Kinetic Monte Carlo model. Pre-aging slows down cluster formation due to the lowered vacancy concentration. In addition, the overall composition of the clusters changes to easily decomposable clusters after pre-aging. Thus, not only is the number of clusters reduced but also the clusters are more easily decomposable when pre-aging is performed.

Simulation removal of sulfamethazine, ciprofloxacin, sulfathiazole and amoxicillin via photo-Fenton process in by Monte Carlo modeling

Kinetic Monte Carlo modeling was employed as a powerful tool to kinetically investigate of antibiotics removal by photo-Fenton process (iron(III) citrate/ hydrogen peroxide in the presence of UV irradiation). Sulfamethazine, ciprofloxacin, sulfathiazole and amoxicillin are the antibiotics which were studied in this investigation. The kinetic mechanism of the photo-Fenton degradation was found by Monte Carlo simulation for several studied antibiotics including sulfamethazine, ciprofloxacin, sulfathiazole and amoxicillin. Also the rate constants values of each step in the suggested mechanism were acquired for these antibiotics through the simulation. Optimized values of Fe(III) citrate and hydrogen peroxide were attained through obtaining the effect of their initial amounts on the rate of antibiotics elimination by utilizing kinetic Monte Carlo simulation. The perfect agreement is observed between the simulation results and the experimental photo-Fenton data for the systems above.

Kinetic Monte Carlo modeling of the interface heterogeneous catalysis effect based on machine learning

<p indent="0mm">Heterogeneous catalysis in a high-enthalpy environment has a remarkable influence on the aerodynamic heating of hypersonic aircraft, and modeling this multiscale effect is an important prerequisite for the lightweight and low-redundancy design of an aircraft thermal protection system. A mesoscale interface heterogeneous catalysis model applicable to macroscale flow field calculation was established by the Monte Carlo method. By the radial basis function neural network algorithm, a machine learning-based reaction kinetics analytical surrogate model was constructed, by which fast and accurate prediction of the catalytic recombination coefficient was realized. The results showed that the machine learning model predicted a recombination coefficient similar to the kinetic Monte Carlo method while reducing the magnitude of the calculation time to that of the traditional macroscale method. Coupled with the macroscale CFD solver, the proposed model can efficiently predict surface heat flux with a multiscale heterogeneous catalysis effect. Modeling of microscale results by the machine learning method and its application in macroscale simulation not only covers the heterogeneous catalytic kinetics but also improves computational efficiency. This modeling provides a theoretical basis for multiscale modeling of complicated high-temperature effects on hypersonic aircraft surfaces.

Towards the modeling of the interplay between radiation induced segregation and sink microstructure

Excess point defects created by irradiation in metallic alloys diffuse and annihilate at sinks available in the microstructure, such as grain boundaries, dislocations, or point defect clusters. Fluxes of defects create fluxes of alloying elements, leading to local changes of composition near the sinks and to a modification of the properties of the materials. The direction and the amplitude of this radiation-induced segregation, its tendency to produce an enrichment or a depletion of solute, depend on a set of transport coefficients that are very difficult to measure experimentally. The understanding of radiation-induced segregation phenomena has, however, made significant progress in recent years, thanks to the modeling at different scales of diffusion and segregation mechanisms. We review here these different advances and try to identify the key scientific issues that limit the development of predictive models, applicable to real alloys. The review addresses three main issues: the calculation of the transport coefficients from ab initio calculations, the modeling of segregation kinetics at static point defects sinks—mainly by kinetic Monte Carlo or diffusion-reaction models—and the more challenging task of modeling the dynamic interplay between radiation-induced segregation and sink microstructure evolution, especially when this evolution results from annihilation of point defects. From this overview of the current state-of-the-art in this field, we discuss still-open questions and guidelines for what constitutes, in our opinion, the desirable future works on this topic.

The Kinetic Monte Carlo Model of the Auroral Electron Precipitation into N2-O2 Planetary Atmospheres

Auroral events are the prominent manifestation of solar/stellar forcing on planetary atmospheres. They are closely related to the energy deposition by and evolution of planetary atmospheres, and their observations are widely used to analyze the composition, structure, and chemistry of the atmosphere under study, as well as energy fluxes of the precipitating particles that affect the atmosphere. A numerical kinetic Monte Carlo model had been developed, allowing us to study the processes of precipitation of high-energy auroral electrons into the N2-O2 atmospheres of the rocky planets in the Solar and exosolar planetary systems. This model describes on a molecular level the collisions of auroral electrons and atmospheric gas, taking into account the stochastic nature of collisional scattering at high kinetic energies. The current status of the kinetic model is illustrated in the applications to the auroral events on the Earth such as the production of suprathermal nitrogen atoms due to the electron impact dissociation of N2. It was found that electron impact dissociation of N2 can potentially be an important source of suprathermal N atoms in the auroral regions of the N2-O2 atmosphere of terrestrial-type planets. Such research will allow us to study the odd nitrogen chemistry as an atmospheric marker of the N2-O2 atmosphere of rocky exoplanets.

Molecular, Brownian, kinetic and stochastic models of the processes in photosynthetic membrane of green plants and microalgae.

The paper presents the results of recent work at the Department of Biophysics of the Biological Faculty, Lomonosov Moscow State University on the kinetic and multiparticle modeling of processes in the photosynthetic membrane. The detailed kinetic models and the rule-based kinetic Monte Carlo models allow to reproduce the fluorescence induction curves and redox transformations of the photoactive pigment P700 in the time range from 100ns to dozens of seconds and make it possible to reveal the role of individual carriers in their formation for different types of photosynthetic organisms under different illumination regimes, in the presence of inhibitors, under stress conditions. The fitting of the model curves to the experimental data quantifies the reaction rate constants that cannot be directly measured experimentally, including the non-radiative thermal relaxation reactions. We use the direct multiparticle models to explicitly describe the interactions of mobile photosynthetic carrier proteins with multienzyme complexes both in solution and in the biomembrane interior. An analysis of these models reveals the role of diffusion and electrostatic factors in the regulation of electron transport, the influence of ionic strength and pH of the cellular environment on the rate of electron transport reactions between carrier proteins. To describe the conformational intramolecular processes of formation of the final complex, in which the actual electron transfer occurs, we use the methods of molecular dynamics. The results obtained using kinetic and molecular models supplement our knowledge of the mechanisms of organization of the photosynthetic electron transport processes at the cellular and molecular levels.

Gaining Insight into the Electrochemical Interface Dynamics in an Organic Redox Flow Battery with a Kinetic Monte Carlo Approach.

Finding low-cost and nontoxic redox couples for organic redox flow batteries is challenging due to unrevealed reaction mechanisms and side reactions. In this study, a 3D kinetic Monte Carlo model to study the electrode-anolyte interface of a methyl viologen-based organic redox flow battery is presented. This model captures various electrode processes, such as ionic displacement and degradation of active materials. The workflow consists of input parameters obtained from density functional theory calculations, a kinetic Monte Carlo algorithm to simulate the discharging process, and an electric double layer model to account for the electric field distribution near the electrode surface. Galvanostatic discharge is simulated at different anolyte concentrations and input current densities, which demonstrate that the model captured the formation of the electrical double layer due to ionic transport. The simulated electrochemical kinetics (potential, charge density) are found to be in agreement with the Nernst equation and the obtained EDL structure corresponded with published molecular dynamics results. The model's flexibility allows further applications of simulating the behavior of different redox couples and makes it possible to consider other molecular-scale phenomena. This study paves the way for computational screening of active species by assessing their potential kinetics in electrochemical environments.

(Invited) The Impact of Interface Layer on Li Plating and Stripping Morphology

Li metal is the preferred anode material for high energy Li batteries. However, a stable plating and stripping of Li metal at the anode−solid electrolyte interface (SEI) remains a significant challenge, particularly at practically feasible current densities. The formation of the SEI layer can significantly change the Li-nucleation density and growth morphology. With multiscale modeling, these factors can be investigated in more detail. Upon, lithiation, while a classical nucleation and growth model can describe the nucleation density of Li clusters and the charging rates in ultrahigh vacuum, a trace amount of reactive gas (oxygen for example) can change Li growth morphology. Reactive molecular dynamics simulations revealed that the fine balance between Li growth rate and the reaction rate of the thin lithium-oxide shell on the surface of the metallic Li can lead to Li nanowire formation. During delithiation, the accumulation of Li vacancies can lead to void generation and interface delamination. A DFT-informed kinetic Monte Carlo (KMC) model was developed to investigate the impact of the SEI layer, stack pressure, and alloying effects. The contact area is then incorporated into a 1D Newman battery model to simulate the impact of the contact area on the battery performance.

A novel approach to inulin depolymerization: A Monte Carlo based model

• Monte Carlo model for inulin depolymerization. • End-biting/internal random cleavage mechanism was adopted. • The detailed molecular weight distribution can be simulated. • The model can distinguish between two scission mechanisms. • The obtained kinetic parameters are in line with literature. Modelling the depolymerization of natural and synthetic polymers is still a challenge in the field of chemical reaction engineering, as the classical approaches based on complex consecutive/parallel reaction mechanisms show limited capabilities in predicting phenomena that nature would do statistically. A Kinetic Monte Carlo model is proposed, which assumes that polymers can be cleaved following two parallel reaction mechanisms: (i) end-biting (i.e., unzipping), (ii) internal random cleavage. The model was studied via a systematic parametric investigation, and it showed high flexibility in predicting detailed product distribution and concentration profiles of monomers as a function of reaction time. The model was applied to a industrially interesting case: inulin hydrolysis, giving mostly fructose as reaction product. A very good fit was obtained and the model was capable to explain the often-overlooked details observed in the experimental results, e.g., the sigmoidal kinetics in the early stages of the hydrolysis and its dependence on experimental conditions.

Dynamic strain aging and the role of the Cottrell atmosphere

We have developed an atomistic kinetic Monte Carlo (kMC) model describing carbon diffusion, trapping and detrapping in the stress field generated by a 1/2[111] screw dislocation in bcc iron. By performing long time scale carbon diffusion simulations we study the formation of carbon Cottrell atmospheres around screw dislocations at different temperatures and background carbon concentrations. The kMC simulations allow us to predict the rate of formation and strength of carbon atmospheres which control the dislocation's behavior resulting in dynamic strain aging in steel. From the kMC simulations of carbon diffusivity in a block of iron crystal containing a screw dislocation we extract the effective diffusion constants. Our results show that except at low carbon concentrations the diffusivity resulting from carbon transport inside the dislocation core dominates the effective diffusivity, which indicates that pipe diffusion in a screw dislocation is likely. The kMC approach, which explicitly accounts for the behavior of individual carbon atoms, offers an atomistic view of the carbon drag mechanism by which mobile dislocations can collect and transport carbon within their cores. We simulate the carbon drag mechanism at different temperatures, background carbon concentrations, and dislocation velocities and estimate the maximal dislocation velocity at which the atmosphere of carbon atoms can follow a moving screw dislocation.

The sintering behavior of ellipsoidal particles

AbstractThe sintering behavior of ellipsoidally shaped particles, particularly spheroids, was studied using a numerical kinetic Monte Carlo model for solid‐state sintering. Compact packings of spheroids with five different aspect ratios from 0.5 to 2.0, thus comprising oblate, spherical, and prolate particles, were generated by simulating the pouring of such particles into a cubic container. For each spheroid particle aspect ratio, five different packings were generated to provide statistics on the sintering properties. The sintering behavior was quantified by the densification rate, relative density, anisotropic strain, grain size, and grain coordination number, as determined from the kinetic Monte Carlo model. The spherical particles were found to sinter to a relative density of 0.87 before grain growth occurs, whereas the oblate and prolate particles reach a relative density of 0.91 before grain growth sets in, with the prolate particles sintering slightly better compared to oblate particles. The more extreme the particle aspect ratio, the more anisotropic the strain is. Finally, the oblate and prolate spheroids have a slightly higher mean grain coordination number and a slightly higher initial relative density compared to the spherical particles.

Kinetic Monte Carlo modeling of oxide thin film growth.

In spite of the increasing interest in and application of ultrathin film oxides in commercial devices, the understanding of the mechanisms that control the growth of these films at the atomic scale remains limited and scarce. This limited understanding prevents the rational design of novel solutions based on precise control of the structure and properties of ultrathin films. Such a limited understanding stems in no minor part from the fact that most of the available modeling methods are unable to access and robustly sample the nanosecond to second timescales required to simulate both atomic deposition and surface reorganization at ultrathin films. To contribute to this knowledge gap, here we have combined molecular dynamics and adaptive kinetic Monte Carlo simulations to study the deposition and growth of oxide materials over an extended timescale of up to ∼0.5ms. In our pilot studies, we have examined the growth of binary oxide thin films on oxide substrates. We have investigated three scenarios: (i) the lattice parameter of both the substrate and thin film are identical, (ii) the lattice parameter of the thin film is smaller than the substrate, and (iii) the lattice parameter is greater than the substrate. Our calculations allow for the diffusion of ions between deposition events and the identification of growth mechanisms in oxide thin films. We make a detailed comparison with previous calculations. Our results are in good agreement with the available experimental results and demonstrate important limitations in former calculations, which fail to sample phase space correctly at the temperatures of interest (typically 300-1000K) with self-evident limitations for the representative modeling of thin films growth. We believe that the present pilot study and proposed combined methodology open up for extended computational support in the understanding and design of ultrathin film growth conditions tailored to specific applications.

Local Temporal Acceleration Scheme to Couple Transport and Reaction Dynamics in Kinetic Monte Carlo Models of Electrochemical Systems.

Kinetic Monte Carlo (kMC) simulations are a well-established tool for investigating the operation of electrochemical systems. Standard kMC algorithms become unfeasible in the presence of processes on vastly different time scales. In electrochemical systems, such time scale disparities often arise between fast transport processes and slow electrochemical reactions. A promising approach to overcome time scale disparities in kMC models is given by temporal acceleration schemes. In this work, we present a local temporal acceleration scheme to bridge the time scale disparity between fast transport and slow reaction dynamics. We combine the superbasin concept with a local, particle-based criterion for the quasi-equilibrium detection and a partitioning of transitions and particles in the system into process chains. Scaling of entire quasi-equilibrated process chains considerably reduces the computational effort without disturbing the relative dynamics of transitions within a process chain. The methodology is outlined for a hybrid organic-aqueous electrolyte device which links fast electronic processes in an organic semiconductor with slow reduction reactions at its interface to the electrolyte. Our approach captures local inhomogeneities such that local physical quantities can be reproduced accurately. Additionally, we show that previous accelerated superbasin algorithms are limited by the presence of spatially varying time scale disparities. Our algorithm achieves an acceleration of several orders of magnitude providing a serious alternative to replace existing multiscale models by stand-alone kMC simulations.

Improved Multibit Storage Reliability by Design of Ferroelectric Modulated Antiferroelectric Memory

In this article, we presented a new concept of ferroelectric (FE) modulated antiferroelectric (AFE) memory with independent two-step state switching and large polarization as a promising option for multibit storage in advanced technology nodes. Based on the Landau–Ginzburg–Devonshire (LGD) theory, four nonvolatile states of AFE with the built-in field can be obtained, and the step-by-step switching among four states was successfully simulated through pulse engineering; then, stable nonvolatile 2-bit storage was experimentally demonstrated in FE/AFE/FE capacitor device, and 0.97-MV/cm bipolar built-in field introduced by FE polarization switching was extracted. The FE + AFE device showed double-peak coercive electric field ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E}_{c}$ </tex-math></inline-formula> ) distribution and large remanent polarization ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${P}_{r}$ </tex-math></inline-formula> ) of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$16.9 ~\mu \text{C}$ </tex-math></inline-formula> /cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> with good process stability. Finally, benefitting from the independently step-by-step switching and large density of effective FE domain, the improved multibit storage reliability was verified by kinetic Monte Carlo (KMC) modeling compared to conventional multibit technology.