Kinetic Monte Carlo Model Research Articles

Temperature and Stress Dependence of Screw Dislocation Mobility in Nb-V-Ta Alloys Using Kinetic Monte Carlo Simulations

In this work we present simulations of thermally-activated screw dislocation motion in Nb-Ta-V alloys for two distinct scenarios, one where kink propagation is solely driven by chemical energy changes, i.e., thermodynamic energy differences, and another one where a migration barrier of 1.0 eV is added to such changes. The simulations have been performed using a kinetic Monte Carlo model for screw dislocation kinetics modified for complex lattice-level chemical environments. At low stresses, we find that dislocation motion in the case with no barrier is controlled by long waiting times due to slow nucleation rates and extremely fast kink propagation. Conversely, at high stress, the distribution of sampled time steps for both kink-pair nucleation and kink propagation events are comparable, resulting in continuous motion and faster velocities. In the case of the 1.0-eV kink propagation energy barrier, at low stresses kink motion becomes the rate-limiting step, leading to slow dynamics and large kink lateral pileups, while at high stresses both kink pair nucleation and kink propagation coexist on similar time scales. In the end, dislocation velocities differ by more than four orders of magnitude between both scenarios, emphasizing the need to have accurate calculations of kink energy barriers in the complex chemical environments inherent to these alloys.

A three dimensional kinetic Monte Carlo defect-free crystal dissolution model for biological systems, with application to uncertainty analysis and robust optimization

The objective of this study was to construct a novel kinetic Monte Carlo (kMC) model to predict the complete dissolution of nanoscale crystals. The developed framework was designed to predict the dissolution of a wide variety of crystalline minerals, regardless of their composition and crystal structure. The proposed framework was used to explore ways of enhancing crystal dissolution processes by assessing the variability from environmental uncertainties and by performing robust optimization to improve the dissolution performance. The approach was used to simulate calcium carbonate dissolution within the human gastrointestinal system. Polynomial chaos expansions (PCEs) were used to propagate the parametric uncertainty through the kMC model. Robust optimization was subsequently performed to determine the crystal design parameters that achieve target dissolution specifications using low-order PCE coefficient models. The results showcased the applicability of the kMC crystal dissolution model and the need to account for dissolution uncertainty within key biological applications.

Effects of surface diffusion in electrocatalytic CO2 reduction on Cu revealed by kinetic Monte Carlo simulations.

Kinetic Monte Carlo (KMC) methods are frequently used for mechanistic studies of thermally driven heterogeneous catalysis systems but are underused for electrocatalysis. Here, we develop a lattice KMC approach for electrocatalytic CO2 reduction. The work is motivated by a prior experimental report that performed electroreduction of a mixed feed of 12CO2 and 13CO on Cu; differences in the 13C content of C2 products ethylene and ethanol (Δ13C) were interpreted as evidence of site selectivity. The lattice KMC model considers the effect of surface diffusion on this system. In the limit of infinitely fast diffusion (mean-field approximation), the key intermediates 12CO* and 13CO* would be well mixed on the surface and no evidence of site selectivity could have been observed. Using a simple two-site model and adapting a previously reported microkinetic model, we assess the effects of diffusion on the relative isotope fractions in the products using the estimated surface diffusion rate of CO* from literature reports. We find that the size of the active sites and the total surface adsorbate coverage can have a large influence on the values of Δ13C that can be observed. Δ13C is less sensitive to the CO* diffusion rate as long as it is within the estimated range. We further offer possible methods to estimate surface distribution of intermediates and to predict intrinsic selectivity of active sites based on experimental observations. This work illustrates the importance of considering surface diffusion in the study of electrochemical CO2 reduction to multi-carbon products. Our approach is entirely based on a freely available open-source code, so will be readily adaptable to other electrocatalytic systems.

Kinetic Monte Carlo Tool for Kinetic Modeling of Linear Step‐Growth Polymerization: Insight into Recycling of Polyurethanes

AbstractA kinetic Monte Carlo model of polyurethane polymerization which explicitly tracks the polymer sequences is developed and shared. This model is benchmarked against theoretical and experimental polyurethane data and used to investigate the effect on oligomer distributions of unequal reactivity of the first and second isocyanate to react. The reverse reactions using thermodynamic consistency are then added to the framework, and analogous to the addition polymerization concept of ceiling temperature, equilibrium chain length distributions at various temperatures are calculated. For a mixture of three monomers AA, BB, and CC, where BB and CC do not react with one another, are present in stoichiometric proportions, and have different enthalpies of reaction with AA, an odd‐even effect emerges. Odd length chains are more likely than even length chains for temperatures at which BB and CC have significantly different equilibrium conversions. The concept of ceiling temperature that is typically cited for addition polymers is extended here to provide a measure of conditions under which depolymerization for recycling is favored.

HybridPDE‐kMCmodeling approach to simulate multivalent lectin‐glycan binding process

AbstractGlycans are the major components of the cellular membranes and mediate many cellular processes via their interactions with lectins. A kinetic Monte Carlo (kMC) model was proposed previously to incorporate the key features of glycan‐lectin interactions such as multivalency and glycan diffusion, and its accuracy has been validated by experiments. However, computational cost of the kMC model is its major bottleneck. In this study, a hybrid model combining a partial differential equation (PDE) with the kMC model is proposed to greatly reduce the computational cost while preserving the accuracy. Specifically, glycan diffusion is simulated by the PDE for improving computational efficiency since the glycan diffusion execution through the kMC is computationally expensive. The hybrid PDE‐kMC model is employed to simulate the binding dynamics between cholera toxin subunit B and gangliosides on cellular membranes. The accuracy and efficiency of the proposed model was demonstrated by comparing with the sole kMC model.

Modeling study of porosity’s effect on grain evolution during directed energy deposition

In this work, porosity’s influence on grain evolution during Directed Energy Deposition was studied with the developed Kinetic Monte Carlo model. In the first case, grain evolution was simulated in a purely solid domain without any porosity. In the second case, some internal spheres were inlaid in the simulation domain as internal pores. The porosity’s effect on grain evolution was investigated by comparing the predicted grain morphologies in both cases. This study is the first work focused on porosity’s influence on additive manufacturing microstructure.

Combined density functional theory/kinetic Monte Carlo investigation of surface morphology during cycling of Li-Cu electrodes

We employed a combined density functional theory and kinetic Monte Carlo approach in order to investigate the nanoscale behavior of lithium stripping and plating on lithium-copper nanoalloys. Density functional theory calculations were used to develop an atom-by-atom understanding of the nucleation behavior of lithium on copper surfaces with different surface morphologies. We found that nanometric pits resulted in significantly more favorable lithium deposition when compared to pristine or lightly-defective Cu surfaces, which is in agreement with previous experimental studies. We then used density functional theory and constrained ab initio molecular dynamics to develop interaction and reaction parameters for a larger-scale kinetic Monte Carlo model in order to provide insight into the stripping and plating behavior of nanostructured Li-Cu nanoalloy anodes. Substantial losses in capacity and strong indications of morphological change were observed for a wide range of Cu:Li ratios over 100 cycles. We observed a complex relationship between the nanoparticle composition and the properties of the formed solid-electrolyte interphase.

An Object Kinetic Monte Carlo Simulation for Defect Evolution of Neutron‐Irradiated Reactor Pressure Vessel Steels: Carbon Sensitive Study

Herein, the defect evolution in the FeCMnNi model alloy is investigated by the gray‐alloy method in an object kinetic Monte Carlo (OKMC) model. Based on the parameters of the Fe–C system, the influence of Mn and Ni is implicitly considered, and the migration energy of mobile defects is modified. The number density of interstitial clusters and vacancy clusters in simulation has a good agreement with experimental results. The defect evolution features versus carbon and solutes concentration are also studied. The simulation results show that the number density of defect clusters increases with increasing carbon or solutes concentration. The average size of interstitial clusters decreases, while the average size of vacancy clusters is hardly affected by increasing impurity/solutes concentration. The defect features do not show a saturation tendency with increasing carbon/solutes concentrations. It also seems the influence of solutes concentration is more sensitive on defect features than carbon concentration in this FeCMnNi alloy.

Conformational Variations for Surface-Initiated Reversible Deactivation Radical Polymerization: From Flat to Curved Nanoparticle Surfaces

Although progress in surface-initiated reversible deactivation radical polymerization (SI-RDRP) has already enabled the production of increasingly novel and advanced polymer structures on solid surfaces, fundamental kinetic questions remain regarding the impact of reaction conditions on the molecular properties of synthesized tethered chains. In the current work, we put forward a matrix-based kinetic Monte Carlo (kMC) model, which is based on an implicit SI-RDRP reaction scheme and continuous three-dimensional (3D) representations, capable of following the temporal evolution of the molecular properties of individual free and surface-tethered polymer chains. This is uniquely possible for variable surface curvature (nanoparticle radii from 4.5 to 32 nm; 353 K; monomer: methyl methacrylate), also including the comparison with the limiting case of a flat surface and addressing various (average) RDRP initiator surface coverages. For the tethered chains, we emphasize the prediction of the variation of the molecular height, monomer occupancy, and radius of gyration and also focus on the simulation of the chain length distribution (CLD) to enable a comparison with solution RDRP results. It is shown that confinement effects on the surface lead to the formation of heterogeneous polymer layers with a marked bimodality in the number CLD. This bimodality is, however, wiped out in experimental analysis based on log-molar mass distributions. It is also shown that an increase in the size of the spherical particles and, hence, a decrease in their curvature results in a deterioration of the control over molecular properties, leading to behavior more similar to that of flat surfaces. Average molecular heights and monomer occupancies can vary with a factor of 2. The impact of the targeted chain length is shown to be of lower importance.

Characterization of Monte Carlo Dynamic/Kinetic Properties of Local Structure in Bond Fluctuation Model of Polymer System.

We report the results of the characterization of local Monte Carlo (MC) dynamics of an equilibrium bond fluctuation model polymer matrix (BFM), in time interval typical for MC simulations of non-linear optical phenomena in host-guest systems. The study contributes to the physical picture of the dynamical aspects of quasi-binary mosaic states characterized previously in the static regime. The polymer dynamics was studied at three temperatures (below, above and close to the glass transition), using time-dependent generalization of the static parameters which characterize local free volume and local mobility of the matrix. Those parameters play the central role in the kinetic MC model of host-guest systems. The analysis was done in terms of the probability distributions of instantaneous and time-averaged local parameters. The main result is the characterization of time scales characteristic of various local structural processes. Slowing down effects close to the glass transition are clearly marked. The approach yields an elegant geometric criterion for the glass transition temperature. A simplified quantitative physical picture of the dynamics of guest molecules dispersed in BFM matrix at low temperatures offers a starting point for stochastic modeling of host-guest systems.

Investigating the formation mechanism of void lattice in tungsten under neutron irradiation: from collision cascades to ordered nanovoids

The “void lattice” formed by periodic arrangements of voids, usually replicating the symmetry and crystallographic orientation of the host matrix, is an interesting phenomenon in materials under neutron irradiation. In this work, taking tungsten (W) as an example, we explore the formation mechanism of the void lattice using an object kinetic Monte Carlo (OKMC) model together with the collision cascades simulated by the molecular dynamics method. The entire formation processes from the chaotic neutron irradiation defects to the observable void lattice are reproduced via OKMC simulation, which could be divided into three stages: nucleation, incubation and growth. It is found that both the one-dimensional (1D) migration of SIAs and the fraction of clustered vacancies in cascades play a critical role in the formation of the void lattice. On the one hand, the 1D migration of SIAs leads to the mutual protection of voids aligned in <111> directions. The self-shielded voids may therefore grow faster than the unaligned ones. On the other hand, a moderate fraction of clustered vacancies in cascades guarantees the stable nucleation and growth rates of voids. Once the density of the <111> aligned voids reaches a critical value, the shrinkage rate of the unaligned voids will overwhelm their growth rate, leading to the formation of void-free channels and thus the void lattice. Our results reveal the synergistic effects of the fraction of clustered vacancies in cascades and 1D migration of SIAs for the formation of the void lattice in W under neutron irradiation, which improves the fundamental understanding of the self-assembled microstructures in irradiated materials.

Multiscale modeling of dendrite formation in lithium-ion batteries

The commercialization of Lithium-ion batteries (LIBs) with Li metal anode has reached an impasse due to the unpredictable dendrite growth, which significantly deteriorates the battery performance. Previous studies show that dendrite growth is affected by the interplay among many factors, but the complex interaction between these factors has not been adequately addressed in the literature. In this work, we fill this knowledge gap by proposing a multiscale model for LIBs. Specifically, a kinetic Monte Carlo model describing dendrite formation at microscopic level is integrated with a macroscopic electrochemical model. Overall, the proposed model can (a) generate the evolution of macroscopic variables such as current density, Li-ion concentration, cell voltage, and state of charge, (b) explain their effects on the evolution of microscopic variables such as dendrite growth on the Li anode, and (c) provide a platform for optimal operation of LIBs to mitigate dendrite growth.

Electronic energy loss assessment in theoretical modeling of primary radiation damage in tungsten

Reliable electronic energy loss needs to be accounted for to accurately estimate primary radiation damage of materials in theory. By introducing four types of electronic stopping cross-sections ([Formula: see text]) into the Monte Carlo (MC) code (IM3D) of collision cascade, and using an object kinetic MC model of short-term defect evolution, we studied the complete process of production and annealing of primary defects in tungsten (W) under high-energy ([Formula: see text] MeV) self-ion and low-energy ([Formula: see text] keV - hundreds keV) neutron-primary knock-on atom (PKA) irradiation. Different [Formula: see text] and their effects were evaluated to accurately estimate primary radiation damage. The difference in electronic energy loss changes the fraction of damage energy, affecting the number of primary defects and their spatial/size distributions. This effect is even pronounced with increasing initial energy, with deviations up to 40% and 60% for damage range and defect number, respectively. The simulation results with [Formula: see text] calculated by time-dependent density functional theory (TDDFT) are quantitatively consistent with experimental damage peaks in self-ion irradiated W and molecular dynamics simulated number of survival defects in neutron-PKA irradiated W. Thus, we recommend using [Formula: see text] calculated by TDDFT to estimate primary radiation damage in W with relative accuracy. It helps understand primary damage behaviors, further accurately simulate long-term defect evolution and predict properties of materials under irradiation.

Kinetic Monte Carlo method for epitaxial 3C-SiC (0001) growth on vicinal surfaces

A kinetic Monte Carlo model has been developed to predict island nucleation and step flow growth on vicinal surface during epitaxial growth of 3C-SiC. In the model, the crystal lattice is represented by a structured mesh which retains fixed atom positions and bond partners of the 3C-SiC crystal lattice. The events considered in the model are the deposition, evaporation and diffusion of atoms, and the attachment and detachment of adsorbed atoms. Both the incorporation energy barrier and Ehrlich-Schwoebel (ES) barrier are taken into account in the model when an adatom migrates to a step or island. The growth parameters such as growth temperature, coverages and terrace width can be selected freely, and the cross process of step flow growth and island nucleation can be simulated. The simulation results show that lower growth temperatures lead to a larger number of islands forming on the vicinal surfaces. There is also an observed coupling between island nucleation and steps at higher temperature. For smaller coverages, the islands and step patterns grow independently, and the steps and islands begin eventually to coalesce over the time. Furthermore, a decrease in terrace width leads to adatoms preferentially attaching to steps and the system to go to a step flow growth system. The results are consistent with predictions for the case of the epitaxial growth on vicinal surfaces.

The role of oxygenated species in the growth of graphene, fullerenes and carbonaceous particles

The growth of carbonaceous materials was studied using a Kinetic Monte Carlo model that captures the growth and oxidation of six-member and partially-embedded five-member rings. A novel algorithm was used to resolve the migration of partially-embedded five-member rings. Circumcoronene molecules were grown at 1500 K and 1 atm in the presence of varying mole fractions of atomic and molecular oxygen and constant mole fractions of hydrogen and acetylene. Four regions of carbon growth associated with different carbonaceous products were identified. Graphene was formed in the presence of high mole fractions of atomic oxygen 10−4<XO≤10−2. Fullerenes were formed in the presence of low mole fractions of atomic oxygen and high mole fractions of molecular oxygen (XO ≤ 10−4 and 10−2 < XO2 ≤ 10−1). Low mole fractions of both atomic and molecular oxygen (XO ≤ 10−4 and XO2 ≤ 10−2) resulted in structures that became curved as time progressed. Small structures were found at the highest mole fractions of atomic oxygen (XO > 10−2). The production and consumption of partially-embedded five-member rings appear to explain the formation of the observed structures. The oxidation of partially-embedded five-member rings produces armchair sites that grow to form flat graphenic structures. Formation and subsequent embedding of partially-embedded five-member rings result in curved structures that resemble fullerenes.

A modeling approach for unveiling adsorption of toxic ions on iron oxide nanocrystals

The era of advanced computer simulations in materials science enables a great potential to design in silico computational experiments for (nano-)material performance. The adsorption efficiency of nanoparticles in various environments can be unveiled by atomistic models and computer simulations. Arsenic (As) is one of the important globally distributed contaminants with a hazardous impact on human health and environment, and it can strongly bind with iron nanocrystals (e.g., hematite (Fe2O3)) depending on their shape and size. Here, we developed a novel Kinetic Monte Carlo (KMC) model capable of exploring and delineating shape-efficiency dependence for Fe2O3 nanocrystals in contact with arsenate-contaminated water. This newly designed model demonstrated the performance of nanocrystals for removal of toxic (As) ions on their surface. The current model opens new avenues for designing further advanced KMC models for nanoparticles-toxic ions interactions, under varying environmentally relevant situations, e.g., groundwater, wetlands, and water treatment systems. In addition to bidentate adsorption complexes, implemented in the model presented, monodentate and outer-sphere adsorption complexes should be incorporated into the KMC model. Detailed environmental controls can be addressed by implementation of pH and background ions.

Nanoporosity evolution during dealloying: Interplay between chemical dissolution, material defects, coarsening and local structural rearrangements over long timescales

Selective dissolution/dealloying of metal alloys is commonly used to synthesize nanoporous structures. During dealloying, the morphological evolution over minutes timescales involves an interplay between chemical dissolution, ligament formation, coarsening of ligaments, local collapse within ligaments, and material defect formation. Ligament relaxation (collapse, defect-formation, etc.) events happen at picosecond-nanosecond timescales, whereas dissolution events proceed at seconds timescales. To resolve the underlying materials phenomena in unprecedented detail, we introduce a novel multiscale framework that combines lattice kinetic Monte Carlo (KMC) and molecular dynamics (MD) with an appropriate handshaking algorithm. Our algorithm exploits the underlying separation of timescales to capture several key features: (i) no breakage of ligaments occurs during dissolution, (ii) coarse ligaments with diameter ~10 times larger than the ones from standard KMC models are obtained, (iii) a maximum in surface area is observed at 50-60% dissolution, (iv) particle shrinkage happens due to ligament collapse, (v) constant porosity is obtained beyond ~50% dissolution, and (vi) dislocation density increases as more electroactive atoms are dissolved. The effect of particle size, temperature, alloy composition, and overpotential are also captured. This study underscores the need to incorporate continuous ligament relaxation while modeling selective dissolution of metal alloys.

Noble gas bubbles in bcc metals: Ab initio-based theory and kinetic Monte Carlo modeling

Understanding the interactions of noble gases with metals is of fundamental importance for the design of radiation-resistant structural materials for fission and fusion nuclear reactors. Here we present a unified theory for describing the energetics of He, Ne, Ar, and Kr bubbles in bcc metals in group 5B (V, Nb, Ta), 6B (Cr, Mo, W) and 8B (Fe). Our predictive analytical model is based on the effective-medium and isotropic elasticity theories, and is parameterized using density functional theory (DFT) calculations of small gas-vacancy clusters. By performing kinetic Monte Carlo (KMC) simulations driven by our analytical model, we have predicted the lifetimes of noble gas bubbles and their coarsening by Ostwald ripening. Our most notable finding is the exceptionally higher thermal stability of Ne, Ar and Kr bubbles than He bubbles in bcc metals, conferring them outstanding resistance to Ostwald ripening. The physical origin of the unexpected stability of bubbles formed by large noble gas atoms has been further elucidated. Our theoretical finding is consistent with the experimental observation of He gas bubble superlattice (GBS) coarsening under thermal annealing, and provides new insights on the exceptional stability of fission GBS in bcc U-Mo up to a high homologous temperature of 0.78. The present calculated results also compare favorably with the existing thermal helium desorption spectrometry experiments in the literature.

A multiscale model for CVD growth of silicon carbide

Thin film deposition is a complex process of chemical and physical phenomena occurring at different time and length scales. A thorough knowledge of the deposition mechanism is necessary to design chemical vapor deposition (CVD) reactors and optimize CVD processes. CVD of (111)- and (100)-oriented SiC films was studied by a multiscale approach, which was designed to describe the fluid dynamics and local composition in the reactor through the solution of the mass, energy, and momentum conservation equations with the inner doubly-iterative efficient algorithm for linked equations (IDEAL) algorithm and finite volume method (FVM). At the atomic scale, a kinetic Monte Carlo model is adopted, and the parameters are taken from the reliable sources. The coupling between the reactor and the atomic scale is realized by applying the continuity of gas phase concentration and flux at the common boundary. The predicted growth rate, film texture, and grain quality of the simulation results were qualitatively compared with corresponding experimental data. This method allows us to optimize the operating conditions of the reactor scale, which in turn can control the performance of the final film.

Monte Carlo and Kinetic Monte Carlo Models for Deposition Processes: A Review of Recent Works

Monte Carlo (MC) and kinetic Monte Carlo (kMC) models are widely used for studying the physicochemical surface phenomena encountered in most deposition processes. This spans from physical and chemical vapor deposition to atomic layer and electrochemical deposition. MC and kMC, in comparison to popular molecular methods, such as Molecular Mechanics/Dynamics, have the ability to address much larger time and spatial scales. They also offer a far more detailed approach of the surface processes than continuum-type models, such as the reaction-diffusion models. This work presents a review of the modern applications of MC/kMC models employed in deposition processes.