Kinetic Monte Carlo Model Research Articles

Effect of nanoglass grain size investigated by a mesoscale variable characteristic strain model

Severe shear localization in metallic glasses (MGs) significantly limits their mechanical performance. Nanoglass (NG), composed of heterogeneous glassy domains created by introducing interfaces into MGs at the nanoscale, could be a promising strategy against severe shear localization, as demonstrated by numerous atomistic simulations. This study introduces a novel mesoscale kinetic Monte Carlo (kMC) model with a variable characteristic strain (VCS) to investigate the grain size effect in NGs. This model captures the complex evolution of shear bands during deformation, revealing a surprising transition from inhomogeneous to homogeneous deformation as the NG grain size decreases to approximately 10 nm. This transition is attributed to the impediment of shear band formation by the small grain size, facilitated by softer interfaces guiding early shear transformation zone (STZ) activities across the entire sample. Furthermore, a progressive reduction of elastic constants simulates the failure response observed in experiments. Our model predicts a critical grain size for the transition in agreement with molecular dynamics simulations and experiments, highlighting its potential for designing NGs with enhanced shear resistance. This mesoscale model enables the investigation of NG deformation with microstructural features on an experimentally-relevant spatial-temporal scale. This paves the way for tailoring NG microstructures to achieve enhanced mechanical performance, and opens new avenues for exploring the influence of interfaces in controlling shear localization.

A multi-scale framework for predicting α-cyclodextrin assembly on polyethylene glycol axles.

Controlling the distribution of rings on polymer axles, such as α-cyclodextrin (αCD) on polyethylene glycol (PEG), is paramount in imparting robust mechanical properties to slide-ring gels and polyrotaxane-based networks. Previous experiments demonstrated that the functionalization of polymer ends could modulate the coverage of αCDs on PEG. To explore the design rule, we propose a multi-scale framework for predicting αCD assembly on bare and functionalized PEG. Our approach combines all-atom molecular dynamics with two-dimensional (2D) umbrella sampling to compute the free energy landscapes of threading αCDs onto PEG with ends functionalized by various moieties. Together with the predicted free energy landscapes and a lattice treatment for αCD and polymer diffusion in dilute solutions, we construct a kinetic Monte Carlo (kMC) model to predict the number and intra-chain distribution of αCDs along the polymer axle. Our model predicts the effects of chain length, concentration, and threading barrier on the supramolecular structure of end-functionalized polypseudorotaxane. With simple modifications, our approach can be extended to explore the design rule of polyrotaxane-based materials with advanced network architectures.

CryoEM reveals the complex self-assembly of a chemically driven disulfide hydrogel.

Inspired by the adaptability of biological materials, a variety of synthetic, chemically driven self-assembly processes have been developed that result in the transient formation of supramolecular structures. These structures form through two simultaneous reactions, forward and backward, which generate and consume a molecule that undergoes self-assembly. The dynamics of these assembly processes have been shown to differ from conventional thermodynamically stable molecular assemblies. However, the evolution of nanoscale morphologies in chemically driven self-assembly and how they compare to conventional assemblies has not been resolved. Here, we use a chemically driven redox system to separately carry out the forward and backward reactions. We analyze the forward and backward reactions both sequentially and synchronously with time-resolved cryogenic transmission electron microscopy (cryoEM). Quantitative image analysis shows that the synchronous process is more complex and heterogeneous than the sequential process. Our key finding is that a thermodynamically unstable stacked nanorod phase, briefly observed in the backward reaction, is sustained for ∼6 hours in the synchronous process. Kinetic Monte Carlo modeling show that the synchronous process is driven by multiple cycles of assembly and disassembly. The collective data suggest that chemically driven self-assembly can create sustained morphologies not seen in thermodynamically stable assemblies by kinetically stabilizing transient intermediates. This finding provides plausible design principles to develop and optimize supramolecular materials with novel properties.

A Method Probing High-Temperature Oxidation Behavior of Crystalline Materials.

To date, the oxidation behavior of crystal materials is not fully understood; additional research is needed to understand the oxidation of materials. Herein, density functional theory (DFT) calculations and a 3D kinetic Monte Carlo (KMC) model are used to investigate the infiltration and diffusion behaviors of oxygen atoms within the crystal. Oxygen molecules readily adsorbes on crystal surfaces of the material and rapidly dissociates, verified by both first-principles calculations and energy-dispersive spectrometer (EDS) results. The infiltration ability of oxygen atoms into the inner crystal layers is affected by the surrounding oxygen atom, lattice compactness, and other factors. Energy-barrier calculations show that crystal thin/dense layers have significant effects on the crystal oxidation process, so high-pressure technology is used to investigate this correlation experimentally. KMC calculations and thermogravimetric analyses (TGA) show the infiltration behavior of oxygen atoms in the main crystal plane (211) toward the inner layers has the highest proportion to the actual high-temperature oxidation behavior of the title material. The results of both the KMC calculations and thermal experiments show the material peeled off upon further oxidation, which accelerates oxidation. At the same time, high-pressure treatment increases the oxidation resistance of materials at lower temperatures (<600°C).

Investigation of the Large Variability of HfO2‐Based Resistive Random Access Memory Devices with a Small Current Compliance by a Kinetic Monte Carlo Model

While scaling down resistive random access memory devices can bring many benefits, it also introduces uncertainties during operation. One example is the wide distribution of the resistances in the low‐resistance state (LRS) when the device is connected by a small current compliance () in the microampere range. During the operation under such small , it is believed that the stochastic migration of oxygen vacancies in the oxide layer plays an important role for the variability. To this regard, the model where oxygen vacancies are treated as point defects and the kinetic Monte Carlo method is applied for the stochastic migration of vacancies is extended. The relation between the macroscopic observations in measurements and the microscopic vacancy distribution are discussed. It turns out that three representative configurations are sufficient to describe the vacancy distribution in the LRS. The large spread of the resistance seen in the cycle‐to‐cycle statistics is then due to the change from one of the configuration to the other. The origin for the change between configurations is discussed in terms of the anisotropic zero‐field energy barrier of the diffusion of vacancies.

Reliability Aspects of 28 nm BEOL‐Integrated Resistive Switching Random Access Memory

Approaching the application of redox‐based resistive switching random access memory (ReRAM), the research focus shifts more and more toward different aspects of reliability. Herein, it is vital to account for the statistics in large memory blocks, as certain failure mechanisms are observed to only affect a few bits per million. In a cooperation between RWTH Aachen and Infineon Technologies, the variability, retention, and endurance of filamentary valence change memory, integrated into 28 nm CMOS on Mbit scale are comprehensively studied. This article reviews the main findings of this project. It is found that the programmed states follow characteristic normal or log‐normal statistics based on dynamic equilibrium in the random walk of oxygen vacancies in the switching layer, experimentally observed as read noise. On long timescales, these statistics are remarkably stable, providing high data retention. However, the existing long‐term degradation can be characterized by shifting and broadening of the programmed high resistive state distributions. A high endurance of more than 500 k cycles is demonstrated on the Mbit scale. Only a tail of a few devices appears to fail to reset. Via kinetic Monte Carlo modeling, the voltage divider of ReRAM cell and periphery has been identified as the origin of this failure.

Readdressing nanocavity diffusion in tungsten

In nuclear fusion (ITER and the future DEMO), those components that face the plasma are exposed to high temperature and irradiation which, in the long term, modifies their thermal and mechanical properties and tritium retention. Tungsten is a candidate material and is the subject of many studies of microstructure evolution under various irradiation and temperature conditions. One milestone is the characterization of its defect properties. We here readdress the diffusion of nanocavities on broad ranges of size and temperature and compare it with dissociation, a competing process during nanocavity growth. First, at the atomic scale, we used molecular dynamics to explore the variety of elementary events involved in the nanocavity diffusion. Second, an experimental study of ion-irradiated samples, annealed at different temperatures up to 1,773 K, revealed the creation and growth of nanocavities on transmission electron microscopy images. Third, we performed multi-objective optimization of the nanocavity diffusion input of our object kinetic Monte Carlo model to reproduce the experimental results. Finally, we applied a sensitivity analysis of the main inputs of our model developed for these particular conditions—the source term which combines two cascade databases and the impurities whose interaction with the defects is characterised with a supplemented database of density functional theory calculations. Three domains of nanocavity size were observed. The first is the small vacancy clusters, for which atomistic calculations are possible and dissociation is negligible. The second is the small nanocavities, for which we provide new diffusion data and where a competition with the dissociation can take place. The third domain is the large nanocavities, for which, in any case, the dissociation prevents their existence above 1,500 K in the absence of a stabilizing interface.

Microscopic study of submonolayer nucleation characteristics during GaN (0001) homoepitaxial growth

An on-lattice kinetic Monte Carlo model is constructed to investigate microscopic nucleation behavior during the submonolayer epitaxial growth of GaN islands, where the Ga and N atoms are treated as the basic particles. The input kinetic parameters of Ga and N, including their surface diffusion energy barriers, were obtained from previous ab initio calculations. Furthermore, a simple and effective bond counting rule is applied in our kinetic Monte Carlo model, and the statistics of the GaN islands on the surface are realized via the application of the Hoshen–Kopelman algorithm. The growth temperature range covers the typical growth temperatures used in the molecular beam epitaxy of GaN. The results obtained show that triangular GaN flakes are observed and that the shapes of the GaN islands remain triangular when the growth temperature is changed. Additionally, the power law for the maximum density of islands versus the ratio of the effective diffusion to the deposition rate is obtained; the exponent of this law is −0.506 ± 0.006, indicating that these triplets represent the seeds required for further nucleation. Finally, the coexistence of the Ga-edge and N-edge types of triangular GaN islands is observed. The island formation mechanism is attributed to a local monomer density misbalance, and it is also shown that a slight variation in the Ga/N ratio in the deposition flux changes the proportion of the Ga-edge and N-edge type triangles; this represents a further indication that controllable GaN morphologies can be obtained by tuning the chemical potentials of the constituent elements.

Temperature dependence of the strength of Nb-Mo-Ta-W alloys due to screw dislocations

The Nb-Mo-Ta-W system has attracted significant attention as a model alloy of the refractory multi-principal element alloy family. Nb-Mo-Ta-W crystallizes as a single phase in the body-centered cubic (bcc) structure and possesses exceptional mechanical properties at high temperature. However, unlike in standard bcc metals, the ground-state configurations of screw dislocations in Nb-Mo-Ta-W are highly twisted, with dislocation lines displaying a high concentration of kinks and cross-kinks at all temperatures. This gives rise to a strengthening of chemical nature associated with overcoming this intrinsic line roughness. In this paper we quantify the contribution to the total strength of this ‘self-pinning’ effect using a kinetic Monte Carlo model of screw dislocation lines that is not subjected to some of the traditional limitations of atomistic simulations. We find that the self-pinning stress remains even at high temperatures due to the balance of two competing effects: strengthening due to higher concentrations of kinks on multiple glide planes, and softening associated with the thermal dissolution of cross-kinks.

KINETIC MODEL OF THE STELLAR WIND FORCING ON THE EXTENDED HYDROGEN ATMOSPHERE OF THE EXOPLANEt π Men c

In this paper, an extension of the kinetic model of the aeronomy of the upper atmosphere of an exoplanet is performed by including the processes of the effect of stellar wind plasma on the extended hydrogen corona of a hot sub-neptune. For this purpose, previously developed kinetic Monte Carlo models were used to study the precipitation of protons and hydrogen atoms with high energies into planetary atmospheres. The kinetic model is adapted to the upper atmospheres of hot sub-neptunes, which made it possible to calculate the rate of absorption of stellar wind plasma energy in the planetary corona and to refine estimates of the non-thermal loss rate of the atmosphere due to the influence of the stellar wind. The calculations carried out for the hot sub-neptune π Men c showed that the energy of a flux of energetic neutral hydrogen atoms (ENA H) penetrating the atmosphere, formed during the charge exchange of stellar wind protons with thermal hydrogen corona atoms, mainly goes to heating the hydrogen corona of a hot exoplanet.

Variability of Radionuclide Sorption Efficiency on Muscovite Cleavage Planes

AbstractIn deep geological repositories for nuclear waste, the surrounding rock formation serves as an important barrier against radionuclide migration. Multiple potential host rocks contain phyllosilicates, which have shown high efficiency in radionuclide sorption. Recent experimental studies report a heterogeneous distribution of adsorbed radionuclides on nanotopographic mineral surfaces. In this study, the energetic differences of surface sorption sites available at nanotopographic structures such as steps, pits, and terraces are investigated. Eleven important surface sites are selected and the energies of ad‐ and desorption reactions are obtained from density functional theory calculations. The adsorption energies are then used for the parameterization of a kinetic Monte Carlo model simulating the distribution of adsorbed europium on a typical nanotopographic muscovite surface. On muscovite, silicon step sites are favorable for europium sorption and lead to an increased adsorption in regions with high step concentrations. Under identical chemical conditions, sorption on typical nanotopographic surfaces is increased by a factor of three compared to atomically flat surfaces. Desorption occurs preferentially at terrace sites, leading to an overall 2.5 times increased retention at nanotopographic structures. This study provides a mechanistic explanation for heterogeneous sorption on nanotopographic mineral surfaces due to the availability of energetically favorable sorption sites.

Studying of threshold switching behavior based on programmable metallization cells selector by KMC method

Programmable metallization cells (PMCs) selectors are considered with great potential in various properties including suppressing the current and mimicking the neurons while its mechanism is still difficult to study by direct observation. In this work, a Kinetic Monte Carlo (KMC) model was established to understand the mechanism of selector with the W/Ag/HfO2/Pt structure, which performed typical threshold switching characteristics. By comparing experiment and simulation of threshold switching behavior, the model was verified and the morphological change of conductive filaments (CF) was displayed. The interfacial energy and migration of ions had a great influence on the formation and rupture of the filament and the threshold switching (TS) behavior. Moreover, the mechanism of TS property was studied by analyzing the dynamic changes of CF in switching and cycling processes. This work provided a KMC model of PMC selectors which was possibly helpful for predicting the performance of the device and guided further optimization of selectors.

Efficient global sensitivity analysis of kinetic Monte Carlo simulations using Cramérs-von Mises distance.

Typically, the parameters entering a physical simulation model carry some kind of uncertainty, e.g., due to the intrinsic approximations in a higher fidelity theory from which they have been obtained. Global sensitivity analysis (GSA) targets quantifying which parameter uncertainties impact the accuracy of the simulation results, e.g., to identify which parameters need to be determined more accurately. We present a GSA approach based on the Cramérs-von Mises distance. Unlike prevalent approaches, it combines the following properties: (i) it is equally suited for deterministic as well as stochastic model outputs, (ii) it does not require gradients, and (iii) it can be estimated from numerical quadrature without further numerical approximations. Using quasi-Monte Carlo for numerical integration and a first-principles kinetic Monte Carlo model for the CO oxidation on RuO2(110), we examine the performance of the approach. We find that the results agree very well with what is known in the literature about the sensitivity of this model and that the approach converges in a modest number of quadrature points. Furthermore, it appears to be robust against even extreme relative noise. All these properties make the method particularly suited for expensive (kinetic) Monte Carlo models because we can reduce the number of simulations as well as the target variance of each of these.

Comprehensive study of conductivity in the series of monoclinic oxymolybdates: Ln2MoO6 (Ln = Sm, Gd, Dy)

The conductivity in the monoclinic polymorphs of Ln2MoO6 (Ln = Sm, Gd, Dy) oxymolybdates was investigated by theoretical and experimental methods. A theoretical approach consisted of geometrical-topological analysis, bond valence site energy, kinetic Monte-Carlo (KMC) modeling and density functional theory (DFT) calculations. The theoretical results have shown that oxygen ionic conductivity is possible in all oxymolybdates with DFT migration energy <1.39 eV. We also calculated oxygen ionic conductivity at various temperatures (500–800 °C) using KMC modeling and found values higher than 10–3.5 S/cm at 800 °C, which was in agreement with the experimental measurements. The total conductivity achieved ~10−5 S/cm for Sm2MoO6, ~10−4 S/cm for Gd2MoO6 and ~10−3 S/cm for Dy2MoO6 at 800 °C according to impedance spectroscopy data. The oxygen pressure isotherms in the Ln2MoO6 (Ln = Sm, Gd, Dy) indicated electronic conductivity contribution in the temperature range of 500–800 °C. The experimental electromotive force (EMF) method also showed an increase in the contribution of electronic conductivity with the temperature growth. The activation energy of oxygen ionic diffusion according to EMF data was in the range of 0.78–1.27 eV.

Lithium-ion battery multi-scale modeling coupled with simplified electrochemical model and kinetic Monte Carlo model

The multi-scale modeling of lithium-ion battery (LIB) is difficult and necessary due to its complexity. However, it is difficult to capture the aging behavior of batteries, and the coupling mechanism between multiple scales is still incomplete. In this paper, a simplified electrochemical model (SEM) and a kinetic Monte Carlo (KMC)-based solid electrolyte interphase (SEI) film growth model are used to study the multi-scale characteristics of LIBs. The single-particle SEM (SP-SEM) is described for macro scale, and a simple and self-consistent multi-particle SEM (MP-SEM) is developed. Then, the KMC-based SEI model is established for micro-scale molecular evolution. And, the two models are coupled to construct the full-cycle multi-scale model. After modeling, validation is performed by using a commercial 18650-type LIB. Finally, the effect of parameters on the SEI model is studied, including qualitative trend analysis and quantitative sensitivity analysis. The growth of SEI film with different particle sizes is studied by MP-SEM coupling simulation.

In silico studies of OLED device architectures regarding their efficiency

Simulations have become increasingly important to understand and design organic optoelectronic devices, such as organic light emitting diodes (OLEDs) and to optimize their performance by selecting appropriate materials and layer arrangements. To achieve accurate device simulations, it is crucial to consider the interplay between material properties, device architecture, and operating conditions and to incorporate physical processes such as charge injection, transport, recombination, and exciton decay. Simulations can provide insights into device bottlenecks and streamline optimization cycles, eliminating the need for physical prototyping and rationalizing OLED design. In this study, we investigated three heuristic OLED architectures with a 3D kinetic Monte Carlo (kMC) model and compared their quantum efficiency at different operation voltages. Our investigation focused on examining the effects of various layer arrangements on charge and exciton dynamics in OLED devices and establishing design principles for achieving high efficiency, which are consistent with experimental observations. Notably, we find that increasing the thickness of the emissive layer (EML) led to higher luminance efficiency, and that an emitter concentration of approximately 5% results in optimal performance. By using this model, it is possible to rapidly study the influence of many device parameters and explore a broad range of parameter and architecture space within a reasonable time-frame.

Kinetic simulation of early-stage precipitation behavior in Mg-RE binary alloys during aging process

The precipitation behavior of magnesium-rare earth (Mg-RE) alloys plays a crucial role for their properties. However, the precipitation happens at small-length and long-time scales, making it challenging to be analyzed by state-of-the-art experimental techniques. Here, we combine the advantages of both molecular dynamic force fields on describing atom interactions and Monte Carlo method on describing diffusive events to develop an embedded atom method (EAM) potential based kinetic Monte Carlo (KMC) model. Using the proposed model, we simulated the formation and evolution of Y clusters in Mg-Y alloy formed by the vacancy mechanism, and rationalize the simulation results using aberration-corrected scanning transmission electron microscopy characterize. We conducted a systematic analysis of the atomic structure, the evolution kinetics and path of the Y cluster by tracing Y atoms and comparing with density function theory (DFT) calculations. Our work reveals that, all solute columns in a same cluster trend to grow along the [0001]Mg direction synchronously. The method presented is not only used for the Mg-Y alloy but also other Mg-RE alloys such as Mg-Gd as illustrated in the last part of the paper.

A modeling approach to understanding OLED performance improvements arising from spatial variations in guest:host blend ratio.

Phosphorescent organic light emitting diodes (OLEDs) suffer from efficiency roll off, where device efficiency rapidly decays at higher luminance. One strategy to minimize this loss of efficiency at higher luminance is the use of non-uniform or graded guest:host blend ratios within the emissive layer. This work applies a multi-scale modeling framework to elucidate the mechanisms by which a non-uniform blend ratio can change the performance of an OLED. Mobility and exciton data are extracted from a kinetic Monte-Carlo model, which is then coupled to a drift diffusion model for fast sampling of the parameter space. The model is applied to OLEDs with uniform, linear, and stepwise graduations in the blend ratio in the emissive layer. The distribution of the guests in the film was found to affect the mobility of the charge carriers, and it was determined that having a graduated guest profile broadened the recombination zone, leading to a reduction in second order annihilation rates. That is, there was a reduction in triplet-triplet and triplet-polaron annihilation. Reducing triplet-triplet and triplet-polaron annihilation would lead to an improvement in device efficiency.

Modelling of zirconium growth under irradiation and annealing conditions

Modelling zirconium growth under irradiation is a difficult task due to the different types of defects formed which all contribute to the macroscopic deformation. An Object Kinetic Monte Carlo model parameterized using state-of-the-art atomic-scale calculations and experimental data is presented. It is able to reproduce a good macroscopic deformation, the coexistence of all types of defects: 〈a〉 interstitial and vacancy loops, 〈c〉 vacancy loops and the alignments of 〈a〉 loops parallel to the basal plane. A large parametric study is performed in order to understand thoroughly in which conditions these microstructural features can be observed. The model is then applied to study flux effects and the microstructure evolution during annealing. It can be concluded that 〈a〉 loop alignments are phenomena which are very sensitive to the flux. During annealing, the defects can recover in a non-monotonous way and 〈a〉 loops inside the alignments disappear at last, which illustrates their strong stability.

Utilizing Data-Driven Optimization to Automate the Parametrization of Kinetic Monte Carlo Models.

Kinetic Monte Carlo (kMC) simulations are a popular tool to investigate the dynamic behavior of stochastic systems. However, one major limitation is their relatively high computational costs. In the last three decades, significant effort has been put into developing methodologies to make kMC more efficient, resulting in an enhanced runtime efficiency. Nevertheless, kMC models remain computationally expensive. This is in particular an issue in complex systems with several unknown input parameters where often most of the simulation time is required for finding a suitable parametrization. A potential route for automating the parametrization of kinetic Monte Carlo models arises from coupling kMC with a data-driven approach. In this work, we equip kinetic Monte Carlo simulations with a feedback loop consisting of Gaussian Processes (GPs) and Bayesian optimization (BO) to enable a systematic and data-efficient input parametrization. We utilize the results from fast-converging kMC simulations to construct a database for training a cheap-to-evaluate surrogate model based on Gaussian processes. Combining the surrogate model with a system-specific acquisition function enables us to apply Bayesian optimization for the guided prediction of suitable input parameters. Thus, the amount of trial simulation runs can be considerably reduced facilitating an efficient utilization of arbitrary kMC models. We showcase the effectiveness of our methodology for a physical process of growing industrial relevance: the space-charge layer formation in solid-state electrolytes as it occurs in all-solid-state batteries. Our data-driven approach requires only 1-2 iterations to reconstruct the input parameters from different baseline simulations within the training data set. Moreover, we show that the methodology is even capable of accurately extrapolating into regions outside the training data set which are computationally expensive for direct kMC simulation. Concluding, we demonstrate the high accuracy of the underlying surrogate model via a full parameter space investigation eventually making the original kMC simulation obsolete.