Kinetic Monte Carlo Method Research Articles

Applying multi-scale simulations to materials research of nuclear fuels: A review

Computational simulation is an important technical means in research of nuclear fuel materials. Since nuclear fuel issues are inherently multi-scopic, it is imperative to study them with multi-scale simulation scheme. At present, the development of multi-scale simulation for nuclear fuel materials calls for a more systematic approach, in which lies the main purpose of this article. The most important thing in multi-scale simulation is to accurately formulate the goals to be achieved and the types of methods to be used. In this regard, we first summarize the basic principles and applicability of the simulation methods which are commonly used in nuclear fuel research and are based on different scales ranging from micro to macro, i.e. First-Principles (FP), Molecular Dynamics (MD), Kinetic Monte Carlo (KMC), Phase Field (PF), Rate Theory (RT), and Finite Element Method (FEM). And then we discuss the major material issues in this field, also ranging from micro-scale to macro-scale and covering both pellets and claddings, with emphasis on what simulation method would be most suitable for solving each of the issues. Finally, we give our prospective analysis and understanding about the feasible ways of multi-scale integration and relevant handicaps and challenges.

Correlation Between Microstructure and Macroscopic Properties of Solid Oxide Fuel Cell Composite Anode: Mesoscale Modeling and Deep Learning with Convolutional Neural Network

In this paper, we propose a framework for studying the linkage between microstructure and performance of Ni-YSZ anode in solid oxide fuel cells (SOFCs) by using meso-scale modeling and deep learning. The discrete element method (DEM) and the mesoscale kinetic Monte Carlo (KMC) method were respectively used to model the particle packing and sintering of composite Ni-YSZ anodes. Anodes with various microstructures were numerically synthesized by varying volume fraction, sizes and size distributions of solid phases and pores. Then, representative volume elements (RVEs) of anode microstructures were meshed for finite element modeling of the effective elastic modulus and thermal coefficient of expansion of the anode based on the homogenization theory. The triple phase boundary length density ( L TPB), tortuosity factor for each phase were also calculated based on RVEs. Based on a large dataset which consists of various anode microstructures (represented as ternary image stacks) and corresponding macroscopic properties, a deep convolutional neural network (CNN) was trained to capture the nonlinear functional relationship between anode microstructures and macroscopic properties. The deep learning CNN model was finally well validated against extra new samples with excellent predictive performances. This indicates that the CNN model can be used as a surrogate model for rapid direct access to macroscopic properties of composite anodes, if the microstructure of the anode is known. The macroscopic properties can be further used for continuum modeling of SOFCs. This framework is highly extendable for other single-phase or composite electrodes of SOFCs. In addition, the proposed framework provides a new ideal for multiscale and multiphysics modeling of SOFCs.

Correlation Between Microstructure and Macroscopic Properties of Solid Oxide Fuel Cell Composite Anode: Mesoscale Modeling and Deep Learning with Convolutional Neural Network

In this paper, we propose a framework for studying the linkage between microstructures and macroscopic properties of Ni-YSZ anode in solid oxide fuel cells (SOFCs) by using meso-scale modeling and deep learning. The discrete element method and the mesoscale kinetic Monte Carlo method were used to generate Ni-YSZ anodes with various microstructures. Then, effective mechanical properties of the representative anodes were evaluated using finite element modeling and the homogenization theory. The triple phase boundary length density (L TPB) was also calculated. The convolutional neural network (CNN) based deep learning model was trained to obtain the functional relationship between the microstructures and the mechanical properties and L TPB. The deep learning model was finally well validated against new samples with excellent predictive performances. This indicates that the CNN model can be used as a surrogate model for rapid direct access to macroscopic properties of composite anodes and for macroscale continuum modeling of SOFCs.

KMC-based POM flash cell optimization and time-dependent performance investigation

The beneficial characteristics of polyoxometalate (POM) molecule-based flash memory cells provide interesting opportunities for scaling beyond the limitations of conventional flash cells. In this paper, we study the write, erase, and retention times of POM flash cells using a kinetic Monte Carlo method implemented in the multi-scale Nano-Electronic Simulation Software simulation framework. The POM flash structure is optimized by studying the tradeoffs between program/erase time and retention time. Based on the optimized POM flash structure, the POM molecular layer charging and discharging processes as well as the corresponding threshold voltage variation are analyzed. The distributions of write, erase, and retention times are simulated and analyzed when studying the POM flash dynamic charging and discharging characteristics.

Study of magnetization relaxation in molecular spin clusters using an innovative kinetic Monte Carlo method

Modeling blocking temperature in molecular magnets has been a long standing problem in the field of molecular magnetism. We investigate this problem using a kinetic Monte Carlo (kMC) approach on an assembly of 100,000 short molecular magnetic chains (SMMCs), each of six identical spins with nearest neighbour anisotropic ferromagnetic exchange interactions. Each spin is also anisotropic with an uniaxial anisotropy. The site spin on these SMMCs take values $1$, $3/2$ or $2$. Using eigenstates of these SMMCs as the states of Markov chain, we carry out a kMC simulation starting with an initial state in which all SMMCs are completely spin polarized and assembled on a one-dimensional lattice so as to experience ferromagnetic spin-dipolar interaction with each other. From these simulations we obtain the relaxation time $\tau_r$ as a function of temperature and the associated blocking temperature. We study this for different exchange anisotropy, on-site anisotropy and strength of dipolar interactions. The magnetization relaxation times show non-Arrhenius behaviour for weak on-site interactions. The energy barrier to magnetization relaxation increases with increase in on-site anisotropy, exchange anisotropy and strength of spin dipolar interactions; more strongly on the last parameter. In all cases the barrier saturates at large on-site anisotropy. The barrier also increases with site spin. The large barrier observed in rare-earth single ion magnets can be attributed to large dipolar interactions due to short intermolecular distances, owing to their small size and large spin of the rare earth ion in the molecule.

Capture efficiency and bias from the defect dynamics near grain boundaries in BCC Fe using mesoscale simulations

The capture efficiency describes the capability of a sink, such as a grain boundary (GB), dislocation, and void, to absorb point defects (PDs). The bias defines the difference in capture efficiency between the absorption of a vacancy and dumbbell at a sink. Complete kinetic information on PDs, including diffusion barriers and diffusion orientations, as well as accurate saddle points, are needed to determine the capture efficiency and bias at a sink accurately, which is computationally demanding. In the present study, the Self-Evolving Atomistic Kinetic Monte Carlo (SEAKMC) method was used to investigate the defect dynamics of PDs near different types of grain boundaries (GBs) (with both 〈100〉 and 〈110〉 families) accurately in body-centered cubic (BCC) iron (Fe). The capture efficiency, sink strength, and bias factor of different types of GBs were determined in Fe, which, different from traditional rate theory estimation, showed a distinct capture efficiency, sink strength, and bias in different GBs. The results demonstrate a strong positive correlation between the capture efficiency and the GB strain width, instead of the GB misorientation, GB energy, or GB-PD binding energy, which have been investigated previously. This work provides valuable insight into the radiation-induced microstructural evolution of GBs.

Application of the evolutionary kinetic Monte Carlo method for the simulation of anisotropic wet etching of sapphire

In this paper, the simple, rejection-based kinetic Monte Carlo simulation method is applied for the approximate simulation of the etch rates and three-dimensional etch structures during anisotropic wet etching of sapphire. Based on the analysis of the composition of the atomic structure of sapphire, a model of the simplified atomic structure of sapphire is proposed, which reduces the difficulty of classifying types of surface atoms on the different crystallographic planes. This enables adopting a previously proposed six-index classification method (to differentiate effectively between the various surface atoms of sapphire) and a previously proposed removal probability function (RPF) (to link the removal probability of the surface atom with the configuration of its neighbors). By reducing errors between simulated rates and experimental rates of 11 typical crystallographic planes in the <−1 1 0 0> and <1 1 −2 0> crystallographic zones continuously with an evolutionary algorithm, reasonable values of nine energy parameters of the RPF are obtained. The simulated results describe approximately the experimental counterparts.

Modeling and Experimental Investigations of Nanostructured Ag Thin Films Produced by Oblique-Angle Deposition and Its SERS Performance

The growth mechanism of nanocolumnar silver thin film deposited on a smooth silicon substrate using electron beam evaporation process at an oblique angle was simulated with the Kinetic Monte Carlo method. Following the simulated silver nanostructured thin film, a further computational simulation was done using COMSOL for surface-enhanced Raman scattering effects. The simulation results were compared against corresponding experimental results, which demonstrated high agreement between simulation results and experimental data. It was found that as the incident deposition angle increased, the density of the Ag thin film significantly decreased and the surface roughness increased. When the incident deposition angle was at 75° and 85°, the resulting nanocolumnar structure was significantly tilted. For Ag thin films deposited at all investigated angles, surface-enhanced Raman scattering effects were observed. Particularly, the Ag nanocolumns deposited at 85° showed remarkable Surface-enhanced Raman Scattering effects. This was seen in both COMSOL simulations and experimental results: Enhancement factors were 2 × 107 in COMSOL simulation and 3.3 × 105 in the experiment.

Influence of helium on the evolution of irradiation-induced defects in tungsten: An object kinetic Monte Carlo simulation* *Project supported by the Science Challenge Project (Grant No. TZ2018002), the National Natural Science Foundation of China (Grant No. 11905135), and the National MCF Energy R&D Program of China (Grant No. 2018YFE0308103).

Understanding the evolution of irradiation-induced defects is of critical importance for the performance estimation of nuclear materials under irradiation. Hereby, we systematically investigate the influence of He on the evolution of Frenkel pairs and collision cascades in tungsten (W) via using the object kinetic Monte Carlo (OKMC) method. Our findings suggest that the presence of He has significant effect on the evolution of irradiation-induced defects. On the one hand, the presence of He can facilitate the recombination of vacancies and self-interstitial atoms (SIAs) in W. This can be attributed to the formation of immobile He-SIA complexes, which increases the annihilation probability of vacancies and SIAs. On the other hand, due to the high stability and low mobility of He-vacancy complexes, the growth of large vacancy clusters in W is kinetically suppressed by He addition. Specially, in comparison with the injection of collision cascades and He in sequential way at 1223 K, the average sizes of surviving vacancy clusters in W via simultaneous way are smaller, which is in good agreement with previous experimental observations. These results advocate that the impurity with low concentration has significant effect on the evolution of irradiation-induced defects in materials, and contributes to our understanding of W performance under irradiation.

Atomistic modeling of meso-timescale processes with SEAKMC: A perspective and recent developments

On-the-fly kinetic Monte Carlo (kMC) methods have recently garnered significant attentions after successful applications to various atomic-scale problems using a timescale outside the reach of classical molecular dynamics. These methods play a critical role in modeling atomistic meso-timescale processes, and it is therefore essential to further improve their capabilities. Herein, we review one of the on-the-fly kMC methods, Self-Evolving Atomistic kinetic Monte Carlo (SEAKMC) and propose two schemes that considerably enhance the efficiency of saddle point searches (SPSs) during the simulations. The performance of these schemes is tested using the diffusion of point defects in bcc Fe. In addition, we discuss approaches to significantly mitigate limitations of these schemes, which further improves their efficiencies. Importantly, these schemes improve the SPS efficiency not only for SEAKMC but also for other on-the-fly kMC methods, broadening the applications of on-the-fly kMC simulations to complex meso-timescale problems.

Adsorption time scales of cluster-forming systems.

A microscopic model of adsorption in cluster forming systems with competing interaction is considered. The adsorption process is described by the master equation and modelled by a kinetic Monte Carlo method. The evolution of the particle concentration and interaction energy during the adsorption of particles on a plane triangular lattice is investigated. The simulation results show a diverse behavior of the system time evolution depending on the temperature and chemical potential and finally on the formation of clusters in the system. The characteristic relaxation times of adsorption vary in several orders of magnitude depending on the thermodynamic parameters of the final equilibrium state of the adsorbate. A very fast adsorption of particles is observed for highly ordered adsorbate equilibrium states.

Diffusion mechanism of bound Schottky defect in magnesium oxide

In simple ionic crystals, intrinsic point defects must satisfy electrical neutrality and exist as Schottky defects. In magnesium oxide (MgO), a Schottky defect is then a combination of anionic and cationic vacancies. Since vacancies are charged, the stable configuration of the Schottky defect corresponds to a bound pair of vacancies of opposite signs. In this study, we investigate the kinetics of formation and migration of such a bound pair on long timescales reaching in some cases thousands of seconds using the kinetic activation-relaxation technique, an off-lattice kinetic Monte Carlo method with an event catalog built on-the-fly during static molecular simulations. We show that the diffusion of this bound Schottky defect involves the migration of vacancies bounded to the first and third neighbor sites of the crystal structure with an apparent migration energy which cannot be inferred from the migration energies expected from isolated defects. Overall, this study gives insights and constraints on the oxygen diffusion mechanism reported experimentally in high-purity MgO samples.

Evaluating the benefits of kinetic Monte Carlo and microkinetic modeling for catalyst design studies in the presence of lateral interactions

Popular computational catalyst design strategies rely on the identification of reactivity descriptors, which can be used along with Brønsted−Evans−Polanyi (BEP) and scaling relations as input to a microkinetic model (MKM) to make predictions for activity or selectivity trends. The main benefit of this approach is related to the inherent dimensionality reduction of the large material space to just a few catalyst descriptors. Conversely, it is well documented that a small set of descriptors is insufficient to capture the intricacies and complexities of a real catalytic system. The inclusion of coverage effects through lateral adsorbate-adsorbate interactions can narrow the gap between simplified descriptor predictions and real systems, but mean-field MKMs cannot properly account for local coverage effects. This shortcoming of the mean-field approximation can be rectified by switching to a lattice-based kinetic Monte Carlo (kMC) method using cluster expansion representation of adsorbate−adsorbate lateral interactions.Using the prototypical CO oxidation reaction as an example, we critically evaluate the benefits of kMC over MKM in terms of trend predictions and computational cost when using only a small set of input parameters. After confirming that in the absence of lateral interactions the kMC and MKM approaches yield identical trends and mechanistic information, we observed substantial differences between the two kinetic models when lateral interactions were introduced. The mean-field implementation applies coverage corrections directly to the descriptors, causing an artificial overprediction of the activity of strongly binding metals. In contrast, the cluster expansion in kMC implementation can differentiate among the highly active metals but it is very sensitive to the set of included interaction parameters. Considering that computational screening relies on a minimal set of descriptors, for which MKM makes reasonable trend predictions at a ca. three orders of magnitude lower computational cost than kMC, the MKM approach does provide a better entry point for computational catalyst design.

Electrodeposition of lithium metal on lithium anode surface, a simulation study by: Kinetic Monte Carlo-embedded atom method

In this paper by using Kinetic Monte Carlo (KMC) method along with the embedded atom method (EAM), the electrodeposition of lithium metal on the lithium anode surface in lithium-ion batteries (LIBs) is investigated. The purpose of this research is to demonstrate how the operating condition, of a LIB, such as temperature, electrolyte concentration, and voltage change across the Li-anode surface and electrolyte may affect the Li-anode behavior due to diffusion, deposition, crystal orientation, and double layer formation by Li-atom on the anode surface. Analyses of the obtained results and their agreement with the available experimental data confirm the validity of employed simulation procedure and indicate that surface morphology is influenced significantly by surface diffusion which is governed by hopping, bulk-atom exchange, step edge and grain boundary mechanisms, and consequently, the performance of the LIB would be controlled by the crystalline structure of the Li-anode. Considering the overall results reveals that by adjusting the LIB operating condition and modifying its anode surface chemistry, it is possible to achieve a smooth crystal structure on the Li-anode surface and prevent the formation of undesirable deposits such as Li-dendrite structures, and thereby promote the efficiency of the LIB.

A study of MgF2 thin film growth in the atomic layer deposition process by multi-scale simulations

Metal fluoride thin film enhances cyclability and capacity retention of a battery by protecting electrodes and reducing side reactions at the interface. In this work, growth mechanism for MgF2 thin film by ALD is investigated by multi-scale approach of density functional theory (DFT) and the kinetic monte carlo (KMC) method. Bis(ethylcyclopentadienyl)magnesium, Mg(EtCp)2, and hydrogen fluoride, HF, are selected as a precursor and reactive gas, respectively. DFT is adopted to reveal and find dominant reaction pathways calculating adsorption and activation energies of surface reactions. F on a clean MgF2 surface is a major reaction site for the precursor adsorption, and sequential and concurrent ligand decompositions are equally predicted during HF pulse. The KMC model is developed to reproduce the MgF2 deposition process with calculated energetics from DFT. Mass gain of the film, growth rate, and surface HF coverage calculated by KMC show a good agreement with experimentally measured values. Ligand molecules remaining on the surface are suggested to be a critical factor for a low surface HF coverage and carbon impurity. We believe the multi-scale simulation presented in this work can be a useful guide for the fundamental understanding of the reaction mechanism as well as the optimization of film quality.

Modelling of ceramic coatings grow during Arc-PVD deposition

This paper presents the results of modeling the growth of ceramic coatings obtained by the kinetic Monte Carlo method. In the considered model, the possibility of forming misoriented grains in the direction of coating growth and in the plane of coating is realized. To verify the model, three coatings of different compositions were prepared, and their structure and composition was studied by TEM and EDS.

Study on the competitive growth mechanism of SiC polytypes using Kinetic Monte Carlo method

The competitive growth process of the 4H and 6H polytypes of SiC is studied by a competitive Kinetic Monte Carlo model(KMC), which takes the atoms of silicon and carbon as the elementary kinetic particle to fully account for the interaction energy between atoms. In the competitive KMC model, the crystal lattices of two polytypes are represented by a structured mesh which fixed the site positions at the perfect crystal lattice positions. Kinetic events with competitive growth, such as deposition, diffusion are considered in physical criterion in the model. Moreover, the model not only considers the interaction energy between the same kind of atoms (Si-Si), but also considers the interaction energy between different types of atoms (Si-C). Based on the KMC model, the effects of growth conditions on the competitive growth of 4H- and 6H- SiC were studied. The competitive KMC simulation results show that the higher temperature and the larger proportion of Si source in the mixture will promote the preferential growth of 6H polytype during competitive growth. Meanwhile, with the increase of temperature and Si/C ratio, the phenomenon of atom aggregation growth on crystal surface becomes more and more obvious.

Кинетическое Монте-Карло моделирование роста нанокристаллов СdSe

Статья посвящена моделированию кинетики коллоидной кристаллизации наночастиц (NPs) селенида кадмия (CdSe). С учетом вкладов констант скорости реакции отдельных стадий модифицировано кинетическое уравнение, включающее константы скорости реакции, термодинамические и расчетные параметры и физические свойства. Использована модифицированная кинетическая модель на основе уравнения кристаллизации, где учтены вклады адсорбции, десорбции и миграции зародившихся частиц в разное время. Модифицированная модель предполагает, что при кристаллизации NPs CdSe мономерные звенья зависят от частоты переходов присоединения и отрыва комплекса мономер–CdSe. В этом случае превращения предшественника в мономер, формирование эффективного мономера и зародышеобразование переходят в стадию роста нанокристаллов (NC CdSe) с засеянной массой. В процессе полученный нанокластер будет и дальше расти за счет раннего созревания, старения и последующего роста в более крупный NC CdSe. Кинетическим методом Монте-Карло (КМС) аппроксимирована модель процесса зарождение–рост NC с учетом разных вкладов в константы скорости реакции. Модифицированная модель с использованием КМС позволяет описать зависимости кинетических констант скорости от среднего радиуса наночастиц как функцию времени, концентрации и распределения NC CdSe в заданное время. Описаны условия формирования NPs CdSe с эволюционной функцией распределения NC CdSe в пространстве размера. Результаты моделирования кинетики коллоидной кристаллизации CdSe могут быть использованы для управления скоростью зарождения и роста NPs CdSe, а также аналогичных систем при формировании качественных NC.

Atomistic Mechanisms of Binary Alloy Surface Segregation From Nanoseconds to Seconds Using Accelerated Dynamics

Although the equilibrium composition of many alloy surfaces is well understood, the rate of transient surface segregation during annealing is not known, despite its crucial effect on alloy corrosion and catalytic reactions occurring on overlapping timescales. In this work, CuNi bimetallic alloys representing (100) surface facets are annealed in vacuum using atomistic simulations to observe the effect of vacancy diffusion on surface separation. We employ multi-timescale methods to sample the early transient, intermediate, and equilibrium states of slab surfaces during the separation process, including standard MD as well as three methods to perform atomistic, long-time dynamics: parallel trajectory splicing (ParSplice), adaptive kinetic Monte Carlo (AKMC), and kinetic Monte Carlo (KMC). From nanosecond (ns) to second timescales, our multiscale computational methodology can observe rare stochastic events not typically seen with standard MD, closing the gap between computational and experimental timescales for surface segregation. Rapid diffusion of a vacancy to the slab is resolved by all four methods in tens of ns. Stochastic re-entry of vacancies into the subsurface, however, is only seen on the microsecond timescale in the two KMC methods. Kinetic vacancy trapping on the surface and its effect on the segregation rate are discussed. The equilibrium composition profile of CuNi after segregation during annealing is estimated to occur on a timescale of seconds as determined by KMC, a result directly comparable to nanoscale experiments.

Kinetic etch front instability responsible for roughness formation in plasma etching

A universal, kinetic etch front instability responsible for plasma etching induced roughness is proposed. The kinetic process of plasma rough etching is modeled based on Kinetic Monte Carlo method. The basic idea is that adatoms of etching inhibitor preferentially bond with each other rather than the substrate due to the mismatch of binding energies. This ultimately leads to the three-dimensional island growth of etching inhibitor, which, after micro-masking, induces roughness. Numerical simulations give results consistent with experimental findings on morphological characteristics as well as roughness dependencies on various etching conditions. The proposed mechanism provides a new viewpoint for understanding the roughness development in dry etching, meanwhile could be a useful tool for developing the processing recipes for both smooth etching and nano-texturing.