Kinetic Monte Carlo Simulations Research Articles

Does Zn mimic diffusion of Al in the HCP Al-Sc-Hf-Ti-Zr high entropy alloys?

The presence of Al in the hexagonal close-packed (HCP) Al-Sc-Hf-Ti-Zr high-entropy-alloy system was previously found to be a primary reason for partial D019 ordering. Since tracer measurements of Al self-diffusion are extremely challenging due to the absence of a suitable radioisotope, in this work, diffusion of Zn as a solute element is investigated for two HCP Al-Sc-Hf-Ti-Zr alloys. The experimental results on diffusion of the 65Zn radioisotope are benchmarked against Al diffusion rates predicted by kinetic Monte Carlo simulations using ab initio-informed calculations of the vacancy formation and migration energies. Furthermore, the partitioning of Zn and the mechanism of Zn diffusion are evaluated. Similarities between Zn and Al diffusion in the investigated HCP Al-Sc-Hf-Ti-Zr alloys are traced back to correlations between the corresponding chemically resolved site substitution energies and migration barriers.

Ethane Dehydrogenation over the Core–Shell Pt-Based Alloy Catalysts: Driven by Engineering the Shell Composition and Thickness

Pt-based catalysts as the commercial catalysts in ethane dehydrogenation (EDH) face one of the main challenges of realizing the balance between coke formation and catalytic activity. In this work, a strategy to drive the catalytic performance of EDH on Pt-Sn alloy catalysts is proposed by rationally engineering the shell surface structure and thickness of core-shell Pt@Pt3Sn and Pt3Sn@Pt catalysts from a theoretical perspective. Eight types of Pt@Pt3Sn and Pt3Sn@Pt catalysts with different Pt and Pt3Sn shell thicknesses are considered and compared with the industrially used Pt and Pt3Sn catalysts. Density functional theory (DFT) calculations completely describe the reaction network of EDH, including the side reactions of deep dehydrogenation and C-C bond cracking. Kinetic Monte Carlo (kMC) simulations reveal the influences of the catalyst surface structure, experimentally related temperatures, and reactant partial pressures. The results show that CHCH* is the main precursor for coke formation, and Pt@Pt3Sn catalysts generally have higher C2H4(g) activity and lower selectivity compared to those of Pt3Sn@Pt catalysts, which is attributed to the unique surface geometrical and electronic properties. 1Pt3Sn@4Pt and 1Pt@4Pt3Sn are screened out as catalysts exhibiting excellent performance; especially, the 1Pt3Sn@4Pt catalyst has much higher C2H4(g) activity and 100% C2H4(g) selectivity compared to those of 1Pt@4Pt3Sn and the widely used Pt and Pt3Sn catalysts. The two descriptors C2H5* adsorption energy and reaction energy of its dehydrogenation to C2H4* are proposed to qualitatively evaluate the C2H4(g) selectivity and activity, respectively. This work facilitates a valuable exploration for optimizing the catalytic performance of core-shell Pt-based catalysts in EDH and reveals the great importance of the fine control of the catalyst shell surface structure and thickness.

Schottky-Contact Formation between Metal Electrodes and Molecularly Doped Disordered Organic Semiconductors

We study using three-dimensional kinetic Monte Carlo (KMC) simulations to what extent the formation of Schottky contacts between a metal electrode and a molecularly doped disordered organic semiconductor can be understood from the theory for crystalline inorganic semiconductors, adapted to include the effects of the localized nature of the states in which the charge carriers reside and the hopping transport in between these states. The thickness of the Schottky-contact depletion region is found to be significantly smaller than as expected when the energetical disorder is neglected. The presence of energetic disorder is also found to influence the voltage dependence of the width of the depletion regions near the contacts of single-layer double-Schottky-contact devices. The voltage drop over the two depletion regions and the remaining charge-neutral bulk layer is shown to be described successfully by a semianalytical model, based on an accurately parameterized bulk mobility function of the dopant concentration, energetic disorder, and the electric field. We furthermore find that the mobility in the depletion regions is drastically reduced. As a result, the depletion-region formation process can be ultraslow, with a characteristic time scale ranging from microseconds to beyond milliseconds.

The intrinsic electrostatic dielectric behaviour of graphite anodes in Li-ion batteries—Across the entire functional range of charge

Lithium–graphite intercalation compounds (Li-GICs) are by far the most common anode material for modern Li-ion batteries. However, the dielectric response of this material in the electrostatic limit and its variation depending on the state of charge (SOC) has not been investigated to a satisfactory degree – neither by means of theory nor by experiment – and especially not for the higher range of SOC. In this work, we – for the first time – predict a mostly linear dependency of the relative permittivity ϵr on the SOC, from ≈7 at SOC 0% to ≈25 at SOC 100%. This is achieved by making use of our recently published DFTB parametrization for Li-GICs based on a machine-learned repulsive potential in order to overcome the computational hurdles of sampling the long-ranged Coulomb interactions within this material. In doing so, we provide novel insight into a property which is highly desired, particularly as an input parameter for charged kinetic Monte Carlo simulations.

Dynamics of Poly(3-hexylthiophene) Monolayers at Solution/Graphite Interfaces.

We have studied the dynamics of poly(3-hexylthiophene) (P3HT) monolayers at the interfaces between highly oriented pyrolytic graphite (HOPG) and P3HT solutions in 1,2,4-trichlorobenzene, using scanning tunneling microscopy (STM). Real-time STM observation at room temperature reveals that P3HT molecules adsorbed on graphite are substantially mobile even in densely packed conditions, causing significant fluctuations of the self-organized monolayer of P3HT. We find that in the monolayers, the orientational order is limited to a short range comparable to the polymer chain length. We show that our observations can be understood based on a 2D semiflexible lattice polymer model by performing kinetic Monte Carlo simulations.

Kinetic Monte Carlo simulations for AlN and AlGaN epitaxial growth on AlN

With increasing availability of AlN substrates, growth of AlN and AlGaN epitaxial layers on AlN(0001) has become a subject of extended experimental investigations. For a deeper understanding of the growth process, we developed a kinetic Monte Carlo (KMC) model for the adsorption, desorption, and diffusion on a stepped Al(001) surface under MOVPE conditions. Nitrogen is provided via ammonia and we assumed that the surface is covered by N in a 2 × 2 N reconstruction. This reconstruction could be obtained in our calculations for a flat surface. We performed several runs for a vicinal AlN(0001) surface with a miscut of 3° in m-direction [11¯00] direction. The results are analysed in detail both for AlN and AlGaN epitaxial layers. In addition, we investigate the influence of dislocations by a simple approach for bond and diffusion energies.

Carrier Capture Dynamics of Deep-Level Defects in Neutron-Irradiated Si With Improved Intracascade Potential

Defect–carrier interactions, especially carrier capture of defects (defect charging), are crucial for understanding displacement damage and failure mechanisms of semiconductor devices under irradiation. A multiscale model is thus developed to study the charging behaviors of deep-level defects in neutron-irradiated semiconductors. The model combines Monte Carlo and object kinetic Monte Carlo (OKMC) simulations for defect annealing, with improved rate equations based on the Shockey–Read–Hall (SRH) theory for defect charging. Especially, the rate equations newly include the improved intracascade electrostatic potential without adjustable parameters, acquired via a proposed effective polarized region model with annealed defect distributions. This model is applied to simulate the collector of the 2N2222 n-p-n silicon (Si) bipolar transistor under pulse-neutron irradiation. We found that the decrease in electron density under irradiation results from both the reduction of effective dopant concentration and the indirect electron trapping of stable vacancy–oxygen pairs (VO) and divacancies (V2). Moreover, two important mechanisms are revealed, including the cocharging of both V2(=/−) and VO(−/0) at 130 K, which corrects the traditional knowledge of single charging of V2(=/−) and the suppressed occupation of V2(=/−) due to the intracascade electrostatic potential formed by V2(−/0) charging. It is very helpful to understand the key mechanisms of the defect–carrier interactions and resolving performance failures of neutron-irradiated semiconductors.

Theory and molecular simulations of plasma sputtering, transport and deposition processes

The present review provides an overview of the basic theory of sputtering with recent models, focusing in particular on sputtered atom energy distribution functions. Molecular models such as Monte-Carlo, kinetic Monte-Carlo, and classical Molecular Dynamics simulations are presented due to their ability to describe the various processes involved in sputter deposition at the atomic and molecular scale as required. The sputter plasma, the sputtering mechanisms, the transport of sputtered material and its deposition leading to thin film growth can be addressed using these molecular simulations. In all cases, the underlying methodologies and some selected mechanisms are highlighted.

Toward an Automated Convergence Tool for Kinetic Monte Carlo Simulation of Conversion, Distributions, and Their Averages in Non-dispersed Phase Linear Chain-Growth Polymerization

The time evolution of (bio)chemical processes, specifically those involving distributed species as in polymer synthesis and recycling, can be obtained using Gillespie-based kinetic Monte Carlo simulations, provided that a sufficiently high (Monte Carlo) control volume is utilized with respect to the simulation targets (e.g., focus on only conversion/yield or a combination of the former and average molar masses, or even the combination with complete distributions with accurate tail prediction). For more detailed kinetics and more demanding simulations targets, currently, simulation results are mostly visually checked to decide which control volume to practically use, taking into account user time constraints. The present work puts forward a convergence strategy that avoids relying on subjective visual analysis to set the minimum control value that guarantees the minimization of the stochastic noise for several simulation target combinations to acceptable values. The strategy is illustrated for two (for simplicity, intrinsic) non-dispersed phase bulk chain-growth polymerization processes, one with high average chain lengths and a broad chain length distribution (CLD), that is, free-radical polymerization (FRP), and one with low average chain lengths and a narrow CLD, that is, nitroxide-mediated polymerization (NMP). It is showcased that the monomer conversion profile converges the fastest, with even the occurrence of noise-free simulation results in the absence of numerical convergence. A sufficiently accurate representation of the tail of the (number) CLD in FRP demands a sufficiently high control volume so that relative errors below 0.5% result for the z-based average chain length or molar mass (Mz). This need to inspect Mz convergence further holds under NMP, in general, reversible deactivation radical polymerization (RDRP) conditions, in which it is uncommon to report such higher order averages. An automated convergence check beyond threshold values is recommended to minimize the impact of possible fluctuations in certain simulation targets, specifically peak representations, for example, the initial spike in the dispersity plot in RDRP. The convergence results are supported by the number of radicals in the control volume with values much higher than 2 to accurately represent termination kinetics for specifically CLD prediction, already under intrinsic conditions.

Shape Transformation Mechanism of Gold Nanoplates

Shape control is of key importance in utilizing the structure-property relationship of nanocrystals. The high surface-to-volume ratio of nanocrystals induces dynamic surface reactions on exposed facets of nanocrystals, such as adsorption, desorption, and diffusion of surface atoms, all of which are important in overall shape transformation. However, it is difficult to track shape transformation of nanocrystals and understand the underlying mechanism at the level of distinguishing events on individual facets. Herein, we investigate changes of individual surface-exposed facets during diverse shape transformations of Au nanocrystals using liquid phase TEM in various chemical potentials and kinetic Monte Carlo simulations. The results reveal that the diffusion of surface atoms on nanocrystals is the governing factor in determining the final structure in shape transformation, causing the fast transformation of unstable facets to truncated morphology with minimized surface energy. The role of surface diffusion introduced here can be further applied to understanding the formation mechanism of variously shaped nanocrystals.

Modeling of Masked Droplet Deposition for Site-Controlled Ga Droplets.

Site-controlled Ga droplets on AlGaAs substrates are fabricated using area-selective deposition of Ga through apertures in a mask during molecular beam epitaxy (MBE). The Ga droplets can be crystallized into GaAs quantum dots using a crystallization step under As flux. In order to model the complex process, including the masked deposition of the droplets and a reduction of their number during a thermal annealing step, a multiscale kinetic Monte Carlo (mkMC) simulation of self-assembled Ga droplet formation on AlGaAs is expanded for area-selective deposition. The simulation has only two free model parameters: the activation energy for surface diffusion and the activation energy for thermal escape of adatoms from a droplet. Simulated droplet numbers within the opening of the aperture agree quantitatively with the experimental results down to the perfect site-control, with one droplet per aperture. However, the model parameters are different compared to those of the self-assembled droplet growth. We attribute this to the presence of the mask in close proximity to the surface, which modifies the local process temperature and the As background. This approach also explains the dependence of the model parameters on the size of the aperture.

Novel effects of grain size and ion implantation on grain boundary segregation in ion irradiated austenitic steel

Nuclear reactor environments are extreme in nature due to the combination of exposure to corrosive coolant, mechanical stresses, and neutron irradiation damage. This combination of environments can lead to irradiation induced/assisted precipitation, segregation, and embrittlement coupled with enhanced creep and stress corrosion cracking. While nanostructured materials are of interest in a variety of applications due to their unique properties including high mechanical strength, for nuclear applications nanostructured materials have the added benefit of irradiation resistance due to the high volume density of sinks for irradiation-induced defects. In this study, we show unique radiation-induced segregation (RIS) behavior in nanocrystalline 304 stainless steel (SS304). Typical RIS in austenitic steels includes Ni enrichment and Cr depletion within the grain boundaries. In nanostructured SS304 this RIS is reduced. Furthermore, interestingly, some grain boundaries in the nanocrystalline SS304 in this study were found to be enriched in Cr after Fe2+ ion irradiation at 500 °C up to 50 displacements per atom (dpa). To understand this unique observation, lattice-based atomic kinetic Monte Carlo simulations were performed to investigate the effects of grain size, thermal segregation, as well as injected interstitials (introduced as Fe self-ions). The results indicate that the Cr enrichment at grain boundaries may be caused by combined effects of grain size, self-ion injection and preferential Cr diffusion via the interstitial mechanism. The findings also suggest a possible difference in RIS between ion and neutron irradiations.

Circular depolarization spectroscopy: A new tool to study photo-imprinting of chirality.

When irradiating a molecular material containing photo-isomerizable groups with pure circularly polarized light, a particular handedness may get imprinted into the material. To study the mechanism and kinetics of this process in situ and operando, we have developed a new chiroptical tool where the circular polarization of the incident circularly polarized light is monitored after transmission through the photoactive layer. Practical limits to the resolution and sensitivity of the measurements as well as its calibration are discussed. To aid interpretation of experimental results, we present kinetic Monte Carlo simulations on a model for the active material involving photo-induced reorientation of molecules in a cholesteric organization. The simulations support the interpretation of a transient minimum in the degree of circular polarization of the transmitted light in terms of a nematic transient state during photo-inversion of a cholesteric organization in the molecular material.

Mechanisms of ethanol dehydration to ethylene on γ-Al2O3（100）and (110C): A combined DFT and KMC study

Periodic density function theory (DFT) and kinetic Monte Carlo (KMC) method are carried out to investigate ethanol dehydration to ethylene on γ-Al2O3 surface. Data on the adsorption energy, adsorption sites and heat of reaction of key species for the reaction of ethanol dehydration to ethylene on γ-Al2O3(100) , (110C) and (110D) surfaces were obtained by the DFT method. Subsequently, KMC simulations are performed with DFT results employed as database. The kinetics of ethanol dehydration from γ-Al2O3(100) surface to ethylene was studied by KMC. The effects of water-alcohol ratios on the reaction process were investigated. Under the process conditions of 750 K, 1 MPa, and water-ethanol ratio ratios in the range of 1 to 3, appropriate reducing the water-alcohol ratio can effectively inhibit carbon build-up without having a significant impact on the rate of ethylene production, providing a theoretical basis for extending catalyst life and reduce the industrial production cost.

Multiscale modeling of solute diffusion in triblock copolymer membranes.

We develop a multiscale simulation model for diffusion of solutes through porous triblock copolymer membranes. The approach combines two techniques: self-consistent field theory (SCFT) to predict the structure of the self-assembled, solvated membrane and on-lattice kinetic Monte Carlo (kMC) simulations to model diffusion of solutes. Solvation is simulated in SCFT by constraining the glassy membrane matrix while relaxing the brush-like membrane pore coating against the solvent. The kMC simulations capture the resulting solute spatial distribution and concentration-dependent local diffusivity in the polymer-coated pores; we parameterize the latter using particle-based simulations. We apply our approach to simulate solute diffusion through nonequilibrium morphologies of a model triblock copolymer, and we correlate diffusivity with structural descriptors of the morphologies. We also compare the model's predictions to alternative approaches based on simple lattice random walks and find our multiscale model to be more robust and systematic to parameterize. Our multiscale modeling approach is general and can be readily extended in the future to other chemistries, morphologies, and models for the local solute diffusivity and interactions with the membrane.

Unraveling the Surface State Evolution of IrO2 in Ethane Chemical Looping Oxidative Dehydrogenation

Based on the advantages of favorable thermodynamics and coking resistance of ethane oxidative dehydrogenation and the challenge of low ethylene selectivity, chemical looping oxidative dehydrogenation (CL-ODH) over the IrO2 catalyst was examined, including the dehydrogenation and regeneration processes. The stoichiometric S-IrO2 and reduced R-IrO2 catalysts as two extreme states of the IrO2 surface structure with dynamic changes were considered. Density functional theory (DFT) calculations and kinetic Monte Carlo simulations showed that the mechanisms of ethane dehydrogenation over S-IrO2 and R-IrO2 catalysts were quite different. Over the S-IrO2 catalyst, ethane oxidative dehydrogenation to C2H4(g) with H2O(g), CO(g), and CO2(g) taking away surface lattice oxygen, followed by lattice oxygen migration from the bulk to the surface, leads to the reduction of the S-IrO2 catalyst. Over the R-IrO2 catalyst, ethane directly dehydrogenates to C2H4(g) and H2(g). Furthermore, the oxidation degree in the regeneration process is greater than the Ov concentration in the dehydrogenation process, which can easily achieve oxygen replenishment in the regeneration process. More importantly, the IrO2 catalyst can be neither completely reduced in the dehydrogenation process nor completely oxidized in the regeneration process, both S-IrO2 and R-IrO2 simultaneously exist for the IrO2 catalyst, and both 750 K and 0.8 bar C2H6(g) pressure were obtained to be the optimal reaction conditions; thus, for ethane CL-ODH over the IrO2 catalyst, the proposed mechanism starts from the oxidative dehydrogenation process; with the consumption of surface lattice oxygen and the oxygen migration from the bulk to the surface, the oxidative and nonoxidative dehydrogenations occur simultaneously until the regeneration. The present study broadens the understanding of ethane CL-ODH over metal oxide catalysts and provides valuable information for the optimization of the CL-ODH process and the development of other high-performance metal oxide catalysts in other alkane CL-ODH processes.

Aggregation of amphiphilic nanocubes in equilibrium and under shear.

We investigate the self-assembly of amphiphilic nanocubes into finite-sized aggregates in equilibrium and under shear, using molecular dynamics (MD) simulations and kinetic Monte Carlo (KMC) calculations. These patchy nanoparticles combine both interaction and shape anisotropy, making them valuable models for studying folded proteins and DNA-functionalized nanoparticles. The nanocubes can self-assemble into various finite-sized aggregates ranging from rods to self-avoiding random walks, depending on the number and placement of the hydrophobic faces. Our study focuses on suspensions containing multi- and one-patch cubes, with their ratio systematically varied. When the binding energy is comparable to the thermal energy, the aggregates consist of only few cubes that spontaneously associate/dissociate. However, highly stable aggregates emerge when the binding energy exceeds the thermal energy. Generally, the mean aggregation number of the self-assembled clusters increases with the number of hydrophobic faces and decreases with increasing fraction of one-patch cubes. In sheared suspensions, the more frequent collisions between nanocube clusters lead to faster aggregation dynamics but also to smaller terminal steady-state mean cluster sizes. The results from the MD and KMC simulations are in excellent agreement for all investigated two-patch cases, whereas the three-patch cubes form systematically smaller clusters in the MD simulations compared to the KMC calculations due to finite-size effects and slow aggregation kinetics. By analyzing the rate kernels, we are able to identify the primary mechanisms responsible for (shear-induced) cluster growth and breakup. This understanding allows us to tune nanoparticle and process parameters to achieve desired cluster sizes and shapes.

Equilibrium structure of a dense trimesic acid monolayer on a homogeneous solid surface: from atomistic simulation to thermodynamics.

A general methodology for determining the thermodynamic characteristics of rigid organic crystals on the atomistic level is presented. The proposed approach is based on a combination of grid interpolation of the precalculated intermolecular potential and kinetic Monte Carlo simulation of the gas-crystal system with an explicit interphase. The two-phase system is stabilized in a wide range of external parameters with an imposed external potential and damping field. The damping field reduces the intermolecular potential at the edges of the crystals and turns it off in the gas phase. To determine the thermodynamic characteristics of a crystal the conditions of equality of chemical potentials in coexisting phases are used. The intermolecular pairwise potential can be calculated on the atomistic or quantum level. In the kinetic Monte Carlo simulations, a grid interpolation of the precalculated potential is performed on each iteration of the algorithm. We have applied the approach to the thermodynamic analysis of a dense monolayer of trimesic acid on a homogeneous surface. The calculated free energy and entropy for the dense "superflower" and filled chicken-wire phases obey the Gibbs-Duhem equation, which confirms the thermodynamic consistency of our approach. Using the proposed approach, we have revealed that the dense "superflower" phase becomes metastable at zero pressure and 470-500 K. Under these conditions, the filled chicken-wire structure with partially released hexagonal cages is thermodynamically favourable. The proposed approach is a potentially universal tool for the thermodynamic analysis of crystals formed by "rigid" organic molecules of any complexity on the atomistic level.

Protein charge transfer far from equilibrium: a theoretical perspective.

Potential differences for protein-assisted electron transfer across lipid bilayers or in bio-nano setups can amount to several 100 mV; they lie far outside the range of linear response theory. We describe these situations by Pauli-master equations that are based on Marcus theory of charge transfer between self-trapped electrons and that obey Kirchhoff's current law. In addition, we take on-site blockade effects and a full non-linear response of the local potentials into account. We present analytical and numerical current-potential curves and electron populations for multi-site model systems and biological electron transfer chains. Based on these, we provide empirical rules for electron populations and chemical potentials along the chain. The Pauli-master mean-field results are validated by kinetic Monte Carlo simulations. We briefly discuss the biochemical and evolutionary aspects of our findings.

Topological line defects in hexagonal SiC monolayer.

Defect engineering of two-dimensional (2D) materials offers an unprecedented route to increase their functionality and broaden their applicability. In light of the recent synthesis of the 2D Silicon Carbide (SiC), a deep understanding of the effect of defects on the physical and chemical properties of this new SiC allotrope becomes highly desirable. This study investigates 585 extended line defects (ELDs) in hexagonal SiC considering three types of interstitial atom pairs (SiSi-, SiC-, and CC-ELD) and using computational methods like Density Functional Theory, Born-Oppenheimer Molecular Dynamics, and Kinetic Monte-Carlo (KMC). Results show that the formation of all ELD systems is endothermic, with the CC-ELD structure showing the highest stability at 300 K. To further characterize the ELDs, simulated scanning tunneling microscopy (STM) is employed, and successfully allow identify and distinguish the three types of ELDs. Although pristine SiC has a direct band gap of 2.48 eV, the presence of ELDs introduces mid-gap states derived from the pz orbitals at the defect sites. Furthermore, our findings reveal that the ELD region displays enhanced reactivity towards hydrogen adsorption, which was confirmed by KMC simulations. Overall, this research provides valuable insights into the structural, electronic, and reactivity properties of ELDs in hexagonal SiC monolayers and paves the way for potential applications in areas such as catalysis, optoelectronics, and surface science.