Kinetic Monte Carlo Model Research Articles

Predicting isotopologue abundances in the products of organic catagenesis with a kinetic Monte-Carlo model

Thermal cracking of complex organic matter can occur under many geological settings. However, the role of thermal cracking vs. other chemistries (e.g., metallic catalysis or Fischer-Tropsch-type reactions) in petroleum formation remains controversial. Realistic modeling of isotope effects in chemical reaction networks involving thermal cracking might shed light on this problem, especially given the recent progress on measurements of intramolecular stable isotope distributions in organic compounds. Previously published models of thermal cracking in petroleum formation are incapable of predicting the intramolecular isotope patterns of products because they do not incorporate realistic precursors, elementary reactions and patterns of inheritance. In this study, we develop a kinetic Monte-Carlo (kMC) model to address this problem. We simulate thermal breakdown of different types of organic matter that is represented by molecular models. At the onset of each simulation, we initialize the model parent organic molecules with isotopic substitutions, and then subject them to free radical chain reactions in a many-step process. Every simulation captures a possible route of thermal degradation and tallies the numbers of each unique isotopologue of all product molecules at the end. Although this model produces data that contain information for all molecules and isotopic forms, in this study we focus on the proportions of many of the isotopologues of all of the C1-C7n-alkanes. We use two chemistry schemes that differ in complexity. The basic scheme (scheme A) includes only homolytic cleavage and capping of metastable radicals by hydrogen atoms. The more sophisticated scheme (scheme B) includes most reactions of importance in the free radical chain mechanism of thermal cracking. We find significant differences between the schemes A and B in predicted molecular and isotopic compositions of products. Scheme B is more consistent with natural data than scheme A, suggesting that full radical mechanisms should be considered in models of thermal cracking in natural hydrocarbon formation. Our model is further validated by reproducing results from hydrous pyrolysis experiments. For simulating natural petroleum formation, we found that the kMC model is acceptable at low maturity, but cannot match compositions and time estimates of mature gas formation, suggesting the influence of alternative mechanisms in late-stage, high-thermal-maturity catagenesis. Using our model, we provide mechanistic explanations for some of the existing observations, such as the evolution of intramolecular and intermolecular carbon isotope compositions with thermal maturity. Our study also makes predictions of intramolecular isotope compositions for higher-order alkanes (C4+) that have been little studied to date but present attractive targets for future measurements.

Microscopic origins of anisotropy for the epitaxial growth of 3C-SiC (0001) vicinal surface: A kinetic Monte Carlo study

In order to investigate the microscopic evolution of the step flow growth process and reveal the microscopic origins of crystalline anisotropy during the epitaxial growth of 3C-SiC (0001) vicinal surface, a three-dimensional Kinetic Monte Carlo model is established, in which Si and C are considered individually. The helicoidal boundary condition is applied to the direction perpendicular to the step, and the periodic boundary condition is used in the direction along the step. Then, the effects of crystalline anisotropy on lateral growth rate, morphologies of step patterns, and growth mode are studied. The results show that the lateral growth rate in [1−210] is larger than that in ⟨1−100⟩, and the zigzag and meandering patterns of step are constructed in [1−210] and ⟨1−100⟩ directions, respectively, which is consistent with the experimental observations. Two possible origins of anisotropy are also revealed: one is the higher concentration of the edge sites of the step and the larger bonding energy in the [1−210] direction and another is the adatom diffusion along the edge of the step. Finally, a larger area of pure step flow growth mode is obtained in the [1−210] direction, which is good for lowering the cost for 3C-SiC epitaxial layers.

Early stage nucleation mechanism for SiC(0001) surface epitaxial growth

Due to the complexity of the binary component system and the difficulty of tracing individual particles in experiments, it is highly desirable to develop simulation tools and models to further reveal the microscopic nucleation behavior of Si and C atoms. In this article, self-consistent rate equations (SCRE) theory combined with the Kinetic Monte Carlo (KMC) model are used to study the nucleation mechanism in the early stage of SiC(0001) surface epitaxial growth under a constant deposition flux. A set of rate equations describing the time evolution of the density of monomers, dimers, and islands are established. By introducing the effective absorption length, the rate equations can be solved self-consistently. In the KMC model, a set of crystal lattices of SiC, including the coordinates of individual Si and C particles and the bond indication, are established. In this model, deposition, adatom diffusion, attachment to and detachment from the clusters of Si or C, and their diffusion along the edge of clusters are considered, and the Hoshen–Kopelman algorithm is implemented to identify and label the clusters. The results show that the time evolution of the density of monomers, dimers, and islands and their dependences on the deposition flux, which are obtained from the SCRE theory, are consistent with the results of the KMC model. The nucleation rate of the dimer increases with the increase in the deposition flux until the number of islands becomes saturated, which leads to a higher density of stable clusters at higher flux. Two regimes governing the absorption length of the monomer are presented. First, before the appearance of the nucleus, the absorption length of the monomer is mainly dominated by monomer density and the diffusion coefficient of adatom. Second, with the growth process, the total capture rate of stable islands gradually plays a dominant role, which is responsible for the further reduction in absorption length and the equal absorption length of Si and C.

In vitro corrosion response of CoCrMo and Ti-6Al-4V orthopedic implants with Zr columnar thin films

This study focuses on the functionalized modification of Ti-6Al-4V and CoCrMo alloys substrates widely used by the biomedical domain as total joint replacements (TJRs) of the hip and knee. To improve the corrosion resistance of these devices, nanostructured columnar zirconium (Zr) thin films were produced by oblique angle deposition (OAD) using DC magnetron sputtering to model the particular design of the joint. The influence of the angular distribution of the incoming particle flux on the resulting film morphology (column tilt angle, porosity) and electrochemical behavior was studied by varying the substrates inclination angle θ from 15 to 90°. The experimental deposition process was reproduced by kinetic Monte Carlo (kMC) models. With the increase of the flux incidence angle α from 0 to 70°, the film thickness and the column tilt angle β vary in agreement with the theoretical models. Additionally, the corrosion behavior of uncoated and Zr-coated alloys (CoCrMo and Ti-6Al-4V) was compared through open circuit potential chronopotentiometry and electrochemical polarization test in NaCl 0.9% solution at 37 °C. It was found that the corrosion protection was successfully improved by the presence of the films. The variation of the corrosion behavior with the flux incidence angle is explained by the changes in the film density.

Reaction–drift–diffusion models from master equations: application to material defects

We present a general method to produce well-conditioned continuum reaction–drift–diffusion equations directly from master equations on a discrete, periodic state space. We assume the underlying data to be kinetic Monte Carlo models (i.e. continuous-time Markov chains) produced from atomic sampling of point defects in locally periodic environments, such as perfect lattices, ordered surface structures or dislocation cores, possibly under the influence of a slowly varying external field. Our approach also applies to any discrete, periodic Markov chain. The analysis identifies a previously omitted non-equilibrium drift term, present even in the absence of external forces, which can compete in magnitude with the reaction rates, thus being essential to correctly capture the kinetics. To remove fast modes which hinder time integration, we use a generalized Bloch relation to efficiently calculate the eigenspectrum of the master equation. A well conditioned continuum equation then emerges by searching for spectral gaps in the long wavelength limit, using an established kinetic clustering algorithm to define a proper reduced, Markovian state space.

Monte Carlo simulation of ultrafast nonequilibrium spin and charge transport in iron

Spin transport and spin dynamics after femtosecond laser pulse irradiation of iron (Fe) are studied using a kinetic Monte Carlo model. This model simulates spin dependent dynamics by taking into account two interaction processes during nonequilibrium: elastic electron–lattice scattering, where only the direction of the excited electrons changes, and inelastic electron–electron scattering processes, where secondary electrons are generated. An analysis of the spin dependent particle kinetics inside the material shows that a smaller elastic scattering time leads to a larger spatial spread of electrons in the material, whereas generation of secondary electrons extends the time span for superdiffusive transport and increases the spin current density.

Improved kinetic Monte Carlo models for computational and analytical investigations of the magnetic properties of finite-size atomic chains

Two improved kinetic Monte Carlo (kMC) models for investigations of the magnetic properties of finite-size atomic chains are presented. These models take into account the possible noncollinearity of magnetic moments. The spontaneous remagnetization of ferromagnetic Co chains on the Pt(997) surface and antiferromagnetic Fe chains on the surface is investigated in the framework of our models. The results are compared with the results of the simple kMC model. It is also shown that a single domain-wall approximation can be successfully used to estimate the reversal time of the magnetization. Therefore, the improved kMC models can be used for analytical calculations as well as for computer simulations.

Engineering defect energy landscape of CoCrFeNi high-entropy alloys by the introduction of additional dopants

The concept of high-entropy alloys (HEAs) focusing on tuning the overall chemical complexity represents a novel alloy design strategy. In contrast, alloying of a metallic matrix with minor doping elements with limited and localized tunability has been a common practice to improve material performance. Combining the idea of globally engineering defect energy landscape in HEAs and the localized doping strategy in dilute alloys, in this work, we explore doping effects of minor elements in a HEA matrix to further enhance the overall and localized chemical tunability, aiming to improve its irradiation resistance. Specifically, we study the influence of minor Al, Cu, Ti, and Pd substitutional doping elements on defect energetics in a CoCrFeNi model HEA based on density-functional theory (DFT) calculations. The DFT results indicate that the formation and migration energies of vacancies can be strongly influenced when a dopant is introduced at the first nearest neighbor shells around a vacancy. On the other hand, interstitial energetics are only slightly affected. Among the four elements, Ti and Pd generally decrease vacancy formation energies and increase vacancy migration energies more significantly than Al and Cu. The doping effects become more pronounced when the concentration of the substitutional dopants increases. Based on the energy distributions obtained from DFT, we build a kinetic Monte Carlo (kMC) model to assess the impact of dopants on vacancy-mediated diffusivity in the doped HEAs. Our results suggest that Ti and Pd can lower the tracer diffusivity in the considered HEAs and act as trapping sites, whereas Cu may enhance the atomic transport. This work indicates that substitutional doping in HEAs is an effective strategy in metallurgy to further tune the defect and transport properties of complex alloys.

3D kinetic Monte-Carlo simulations of diamond growth on (1 0 0) surfaces

A 3D Kinetic Monte-Carlo (KMC) model is implemented and used to simulate the growth of (1 0 0)-oriented diamond films. The model considers four processes: adsorption and desorption of CH3 radicals, etching of carbon atoms and migration of adsorbed radicals. The atomic structure of diamond is taken into account including the formation of dimer rows on the surface. The model correctly reproduces the step-flow growth mechanism of diamond (1 0 0) surfaces and the obtained growth rates are close to experimental data. The propagation of the steps shows a clear anisotropy. Steps are usually two atomic layers high but step bunching can be observed in presence of defects. The model thus can be used as a predictive tool to obtain growth rates and to understand the effect of atomic interactions on the film morphology.

Systematic kMC Study of Doped Hole Injection Layers in Organic Electronics.

Organic light emitting diodes (OLED) play an important role in commercial displays and are promising candidates for energy-efficient lighting applications. Although they have been continuously developed since their discovery in 1987, some unresolved challenges remain. The performance of OLEDs is determined by a multifaceted interplay of materials and device architectures. A commonly used technique to overcome the charge injection barrier from the electrodes to the organic layers, are doped injection layers. The optimization of doped injection layers is critical for high-efficiency OLED devices, but has been driven mainly by chemical intuition and experimental experience, slowing down the progress in this field. Therefore, computer-aided methods for material and device modeling are promising tools to accelerate the device development process. In this work, we studied the effect of doped hole injection layers on the injection barrier in dependence on material and layer properties by using a parametric kinetic Monte Carlo model. We were able to quantitatively elucidate the influence of doping concentration, material properties, and layer thickness on the injection barrier and device conductivity, leading to the conclusion that our kMC model is suitable for virtual device design.

Irradiation dose-rate effect in Fe-C system: An Object Kinetic Monte Carlo simulation

Herein, the defect features under irradiation in the Fe-C system are studied by an Object Kinetic Monte Carlo (OKMC) model. The model was based on recent parameters and was validated by comparing the numerical estimates with the experimentally obtained defect features in neutron-irradiated iron. Systematic simulations of defects evolution at 70 °C in a wide range of dose rates from 10−8 to 10−4 dpa/s were carried out. The simulation results demonstrate that at the lower dose range (< 0.02 dpa), a higher dose rate irradiation leads to a higher interstitial-loop density and irradiation hardening. In contrast, the dose rate does not obviously influence the defect features at the high dose range. Defect features under two carbon concentrations 50 and 100 appm show a similar dose-rate effect, and a higher carbon concentration leads to a higher interstitial loop density and irradiation hardening. We attribute the dose rate effect change with dose to the competition between sinks absorption and SIAs-vacancies annihilation. Based on the interaction model of <100> production, the ratio of <100>-type interstitial loops is higher at the higher dose rate irradiation, consistent with the experimental results.

OKMC simulation of matrix defect evolution of Fe-C Alloy under irradiation

The effects of carbon traps in Fe-C alloys on matrix defects and the evolutions of matrix defects in Fe-C alloys under irradiation are investigated in this paper. The object kinetic Monte Carlo (OKMC) modeling is used to establish a bridge between the micro-computational simulation data and the macro-experimental data. The simulation results verify the evolution of the carbon (C)-vacancy (Vac) complex under ideal conditions, and at relatively low temperatures, the complex is mainly C-Vac&lt;sub&gt;2&lt;/sub&gt;. Under the assumption of complex traps, the evolution of matrix defects in Fe-C systems under irradiation is simulated in this work. It is verified that the carbon vacancy complex has an obvious trapping effect on matrix defects, and the simulation results of evolution simulation of matrix defects in the Fe-C system under irradiation are consistent with the experimental results. Furthermore, the effective approximate parameters used in the simulation are compared and discussed. The present research can provide a basic support for the research on the evolution of iron-based alloy irradiation defects.

Endurance of 2 Mbit Based BEOL Integrated ReRAM

In this work, we experimentally characterize the endurance of 2 Mbit resistive switching random access memories (ReRAMs) from a 16 MBit test-chip. Here, very rare failure events where the memory cells become stuck in the low-resistive state (LRS) are observed. As this failure mechanism is the limiting one concerning the endurance of this ReRAM implementation, extensive investigations are conducted and presented. The experimental findings are detailed via a voltage divider model, illustrating why memory cells can become stuck in the LRS. It is proposed, that an insufficient voltage dropping over the cell due to an unfavorable combination of cell- and transistor resistances is responsible for stuck-at-LRS bits. Furthermore, we give predictions for the origin of these suboptimal combinations. Additionally, a one-dimensional Kinetic Monte Carlo (KMC) model that allows a statistical investigation of large numbers of cells with regard to rare random events has been developed. Here, we fortify our proposed explanation for the observed failure mechanism by the simulation and evaluation of the switching process of the memory. All simulations are in very good agreement with the experimental data. Finally, based on our findings, we give suggestions for the improvement of switching algorithms.

Bayesian Tuned Kinetic Monte Carlo Modeling of Polystyrene Pyrolysis: Unraveling the Pathways to Monomer, Dimers, and Trimers of Polystyrene

Bayesian Tuned Kinetic Monte Carlo Modeling of Polystyrene Pyrolysis: Unraveling the Pathways to Monomer, Dimers, and Trimers of Polystyrene

New mechanism for autoxidation of polyolefins: kinetic Monte Carlo modelling of the role of short-chain branches, molecular oxygen and unsaturated moieties

Using quantum-chemical calculations and kinetic modelling, we reveal the dominant reaction pathway in polymer autoxidation, (i) whether oxygen promotes or hamper degradation and (ii) how defects in the polymer backbone affect degradation.

Lattice mismatch induced tunable dimensionality of transition metal Di-chalcogenides

Low-dimensional materials have excellent properties which are closely related to their dimensionality. However, the growth mechanism underlying tunable dimensionality from 2D triangles to ID ribbons of such materials is still unrevealed. Here, we establish a general kinetic Monte Carlo model for transition metal dichalcogenides (TMDs) growth to address such an issue. Our model is able to reproduce several key ñndings in experiments, and reveals that the dimensionality is determined by the lattice mismatch and the interaction strength between TMDs and the substrate. We predict that the dimensionality can be well tuned by the interaction strength and the geometry of the substrate. Our work deepens the understanding of tunable dimensionality of low-dimensional materials and may inspire new concepts for the design of such materials with expected dimensionality.

Kinetic Monte Carlo modeling of homogeneous precipitation of Y–O and Y–Ti-O Oxides in bulk alpha iron

Kinetic Monte Carlo modeling of homogeneous precipitation of Y–O and Y–Ti-O Oxides in bulk alpha iron

Modeling ligand crosslinking for interlocking quantum dots in thin-films

Ligand crosslinking in QD systems has shown promise for developing robust QD films for applications in high-resolution displays. The kinetics and mechanism of ligand crosslinking can be described using experimentally validated kinetic Monte Carlo model.

Recurrent Neural-Network-Based Model Predictive Control of a Plasma Etch Process

In this article, we propose the development of a recurrent neural network (RNN)-based model predictive controller (MPC) for a plasma etch process on a three-dimensional substrate using inductive coupled plasma (ICP) analysis. Specifically, the plasma etch process is simulated by a multiscale model: (1) A macroscopic fluid model is applied to simulate the gas flows and chemical reactions of plasma. (2) A kinetic Monte Carlo (kMC) model is applied to simulate the etching process on the substrate. Subsequently, proper orthogonal decomposition (POD) is used to derive the empirical eigenfunctions of the plasma model. Then the empirical eigenfunctions are utilized as basis functions within a Galerkin’s model reduction framework to compute a low-order system capturing dominant dynamics of the plasma model. Additionally, RNN is introduced to approximate dynamics of both the reduced-order plasma system and the microscopic etch process. The training data for the RNN models are generated from discrete sampling of open-loop simulations. A probability distribution function is also involved to present the stochastic characteristic of the kMC model. The trained RNN models are then implemented as the prediction model in the development of MPC to achieve desired control objectives. Closed-loop simulation results are presented to compare the performance of the model predictive controller and a proportional-integral (PI) controller, which show that the proposed MPC framework is effective and exhibits better performance than does a PI controller.

Reduced-order kinetic Monte Carlo model to simulate water diffusion in biodegradable polymers

Water is a driving factor in the degradation process of biodegradable polymers. However, water diffusion is typically not incorporated in the kinetic models of biodegradation such as kinetic Monte Carlo (kMC), because water diffusion events occur at a much shorter time scale than the hydrolysis reactions. As such, there is a need to improve the computational efficiency of water diffusion in the kMC models of diffusion processes in biodegradation. In this work, a new dimensionality reduction scheme for kMC diffusion models is developed to significantly reduce the computation time, where a two-dimensional kMC diffusion model for porous microstructures is reduced to one-dimensional ones. The dimensionality reduction is accomplished by calibrating the model parameters with multi-objective Bayesian optimization. The reduced-order diffusion model shows a 675-fold faster computation compared to the original two-dimensional model.