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DOE OSTI2024

Adaptive tau-leaping methods for microscopic-lattice kinetic Monte Carlo simulations

Traditional Kinetic Monte Carlo (KMC) approaches, rooted in Gillespie’s stochastic simulation algorithm, become computationally demanding in systems with a large range of timescales. The goal of this work is to propose and study new adaptive lattice-KMC time integration strategies for spatially non-uniform systems. To that end, two novel adaptive tau-leaping methods and their corresponding time integration strategies are developed based on the idea of the “n-fold” direct KMC method. These strategies allow for the simultaneous execution of multiple reactions, advancing time by adaptively selected coarse increments. We present numerical experiments comparing the proposed methods with existing approaches in a catalytic surface kinetics application involving ammonia decomposition.

Bimolecular reactions↗

NASA NTRS2003

Kinetic Monte Carlo Simulations of Rod Eutectics and the Surface Roughening Transition in Binary Alloys

In this paper we report on two related topics: Kinetic Monte Carlo simulations of the steady state growth of rod eutectics from the melt, and a study of the surface roughness of binary alloys. We have implemented a three dimensional kinetic Monte Carlo (kMC) simulation with diffusion by pair exchange only in the liquid phase. Entropies of fusion are first chosen to fit the surface roughness of the pure materials, and the bond energies are derived from the equilibrium phase diagram, by treating the solid and liquid as regular and ideal solutions respectively. A simple cubic lattice oriented in the {100} direction is used. Growth of the rods is initiated from columns of pure B material embedded in an A matrix, arranged in a close packed array with semi-periodic boundary conditions. The simulation cells typically have dimensions of 50 by 87 by 200 unit cells. Steady state growth is compliant with the Jackson-Hunt model. In the kMC simulations, using the spin-one Ising model, growth of each phase is faceted or nonfaceted phases depending on the entropy of fusion. There have been many studies of the surface roughening transition in single component systems, but none for binary alloy systems. The location of the surface roughening transition for the phases of a eutectic alloy determines whether the eutectic morphology will be regular or irregular. We have conducted a study of surface roughness on the spin-one Ising Model with diffusion using kMC. The surface roughness was found to scale with the melting temperature of the alloy as given by the liquidus line on the equilibrium phase diagram. The density of missing lateral bonds at the surface was used as a measure of surface roughness.

Bentz, Daniel N.↗

NASA NTRS2013

Kinetic Monte Carlo Simulation of Cation Diffusion in Low-K Ceramics

Low thermal conductivity (low-K) ceramic materials are of interest to the aerospace community for use as the thermal barrier component of coating systems for turbine engine components. In particular, zirconia-based materials exhibit both low thermal conductivity and structural stability at high temperature, making them suitable for such applications. Because creep is one of the potential failure modes, and because diffusion is a mechanism by which creep takes place, we have performed computer simulations of cation diffusion in a variety of zirconia-based low-K materials. The kinetic Monte Carlo simulation method is an alternative to the more widely known molecular dynamics (MD) method. It is designed to study "infrequent-event" processes, such as diffusion, for which MD simulation can be highly inefficient. We describe the results of kinetic Monte Carlo computer simulations of cation diffusion in several zirconia-based materials, specifically, zirconia doped with Y, Gd, Nb and Yb. Diffusion paths are identified, and migration energy barriers are obtained from density functional calculations and from the literature. We present results on the temperature dependence of the diffusivity, and on the effects of the presence of oxygen vacancies in cation diffusion barrier complexes as well.

Good, Brian↗

DOE OSTI2023

Electrochemical Degradation of Pt 3 Co Nanoparticles Investigated by Off-Lattice Kinetic Monte Carlo Simulations with Machine-Learned Potentials

In fuel cell applications, the durability of catalysts is critical for large-scale industrial implementation. However, limited synthesis controllability and spectroscopic resolution impede a comprehensive understanding of degradation mechanisms at the atomic level. In this study, we develop a machine-learned potential (MLP) to simulate the degradation processes for Pt3Co nanoparticles. The precision of MLP is determined to be comparable to that of density functional theory calculations. Using off-lattice kinetic Monte Carlo simulations with MLP, we successfully replicate established experimental trends and offer a logical resolution to ongoing debates regarding atomic orderings. Based on the simulation results, we suggest design principles for Pt3Co nanoparticles that combine high activity and durability. Finally, we validate the wide applicability of our method by successfully applying it to Pt3Ni and Pt3Co0.5Ni0.5 nanoparticles. The research serves as a guideline for developing MLPs for alloy electrochemical catalysts and lays the foundation for designing more durable and active fuel-cell catalysts.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Machine learning force field model for kinetic Monte Carlo simulations of itinerant Ising magnets

Here, we present a scalable machine learning (ML) framework for large-scale kinetic Monte Carlo (kMC) simulations of itinerant electron Ising systems. As the effective interactions between Ising spins in such itinerant magnets are mediated by conducting electrons, the calculation of energy change due to a local spin update requires solving an electronic structure problem. Such repeated electronic structure calculations could be overwhelmingly prohibitive for large systems. Assuming the locality principle, a convolutional neural network (CNN) model is developed to directly predict the effective local field and the corresponding energy change associated with a given spin update based on Ising configuration in a finite neighborhood. As the kernel size of the CNN is fixed at a constant, the model can be directly scalable to kMC simulations of large lattices. Our approach is reminiscent of the ML force field models widely used in first-principles molecular dynamics simulations. Applying our ML framework to a square-lattice double-exchange Ising model, we uncover unusual coarsening of ferromagnetic domains at low temperatures. Our work highlights the potential of ML methods for large-scale modeling of similar itinerant systems with discrete dynamical variables.

machine learning↗

DOE OSTI2025

Kinetic Monte Carlo simulations of aging in δ -Pu

We have developed a first-passage kinetic Monte Carlo approach for materials aging to investigate the sensitivity of void swelling to model parameters, including helium bubble density and size distribution. In addition to explicitly accounting for the spatial distribution of individual point defects, bubbles, and voids, our approach can simulate total doses equivalent to 100 years of natural aging on statistically representative volumes of materials. This technique enables us to study the effects on swelling and radiation damage evolution due to temperature and dose rate (as altered in artificially aged experiments), differences in effective interaction radii between vacancies and interstitials, and varying defect diffusion activation energies, while providing more detailed information than previous rate-equation based approaches. In conclusion, our results indicate that spatial effects that are not modeled in mean-field rate theories could play a significant role in void swelling initiation and growth for certain regimes of model parameters.

Actinides↗

DOE OSTI2024

A DFT-based kinetic Monte Carlo simulation of multiphase oxide-metal thin film growth

Functional thin films of nanoscale metal pillars in oxide or nitride matrices known as vertically aligned nanocomposite (VAN) have gained much interest owing to their unique strain-coupled and highly anisotropic properties. So far, the deposition of these films has been explored mostly experimentally. In this work, a density functional theory (DFT)-based kinetic Monte Carlo simulation model using Bortz–Kalos–Lebowitz algorithm was developed to understand the growth of VAN films deposited by pulsed laser technique on mismatching substrates. The model has been parameterized and applied to understand the kinetics of growth thin films consisting of Au pillars in CeO2 matrix deposited on SrTiO3 substrates. The effects of pulsed laser deposition (PLD) conditions including the pulse frequency, deposition flux, and substrate temperature were explored. The simulations indicate that the Au pillar size and shape exhibit significant dependence on the PLD conditions. Namely, increasing the temperature increases the average pillar size and lowers the pillar density, and vice versa. In addition, the simulations revealed that increasing the deposition rate results in lowering the average pillar size and increasing the density. Particularly, the DFT results suggest that Au pillar size can be tuned during the initial growth of the first monolayer due to the significantly low activation barrier. Our analysis showed that the relationship between the average pillar size and pillar density is influenced by the kinetics. Furthermore, autocorrelation analysis showed that pillars self-organize in quasi-ordered patterns at certain windows of the deposition conditions, which is attributed to the complex nature of the chemical interactions in the system, the kinetics, and the deposition parameters.

Physics↗

NASA NTRS2015

Kinetic Monte Carlo Simulation of Oxygen Diffusion in Ytterbium Disilicate

Ytterbium disilicate is of interest as a potential environmental barrier coating for aerospace applications, notably for use in next generation jet turbine engines. In such applications, the transport of oxygen and water vapor through these coatings to the ceramic substrate is undesirable if high temperature oxidation is to be avoided. In an effort to understand the diffusion process in these materials, we have performed kinetic Monte Carlo simulations of vacancy-mediated and interstitial oxygen diffusion in Ytterbium disilicate. Oxygen vacancy and interstitial site energies, vacancy and interstitial formation energies, and migration barrier energies were computed using Density Functional Theory. We have found that, in the case of vacancy-mediated diffusion, many potential diffusion paths involve large barrier energies, but some paths have barrier energies smaller than one electron volt. However, computed vacancy formation energies suggest that the intrinsic vacancy concentration is small. In the case of interstitial diffusion, migration barrier energies are typically around one electron volt, but the interstitial defect formation energies are positive, with the result that the disilicate is unlikely to exhibit experience significant oxygen permeability except at very high temperature.

Coatings↗

NASA NTRS2017

Kinetic Monte Carlo Simulations of Oxygen Diffusion in Environmental Barrier Coating Materials

Good, Brian S.↗

NASA NTRS2017

Kinetic Monte Carlo Simulations of Oxygen Diffusion in Environmental Barrier Coating Materials

Ceramic Matrix Composite (CMC) materials are of interest for use in next-generation turbine engine components, offering a number of significant advantages, including reduced weight and high operating temperatures. However, in the hot environment in which such components operate, the presence of water vapor can lead to corrosion and recession, limiting the useful life of the components. Such degradation can be reduced through the use of Environmental Barrier Coatings (EBCs) that limit the amount of oxygen and water vapor reaching the component. Candidate EBC materials include Yttrium and Ytterbium silicates. In this work we present results of kinetic Monte Carlo (kMC) simulations of oxygen diffusion, via the vacancy mechanism, in Yttrium and Ytterbium disilicates, along with a brief discussion of interstitial diffusion. An EBC system typically includes a bond coat located between the EBC and the component surface. Bond coat materials are generally chosen for properties other than low oxygen diffusivity, but low oxygen diffusivity is nevertheless a desirable characteristic, as the bond coat could provide some additional component protection, particularly in the case where cracks in the coating system provide a direct path from the environment to the bond coat interface. We have therefore performed similar kMC simulations of oxygen diffusion in this material.

Good, Brian S.↗

NASA NTRS2017

Kinetic Monte Carlo Simulations of Diffusion in Environmental Barrier Coating Materials

Ceramic Matrix Components (CMC) components for use in turbine engines offer a number of advantages compared with current practice. However, such components are subject to degradation through a variety of mechanisms. In particular, in the hot environment inside a turbine in operation a considerable amount of water vapor is present, and this can lead to corrosion and recession. Environmental Barrier Coating (EBC) systems that limit the amount of oxygen and water reaching the component are required to reduce this degradation and extend component life. A number of silicate-based materials are under consideration for use in such coating systems, including Yttterbium and Yttrium di- and monosilicates. In this work, we present results of kinetic Monte Carlo computer simulations of oxygen diffusion in Yttrium disilicate, and compare with previous work on Yttterbium disilicate. Coatings may also exhibit cracking, and the cracks can provide a direct path for oxygen to reach the component. There is typically a bond coat between the coating and component surface, but the bond coat material is generally chosen for properties other than low oxygen diffusivity. Nevertheless, the degree to which the bond coat can inhibit oxygen diffusion is of interest, as it may form the final defense against oxygen impingement on the component. We have therefore performed similar simulations of oxygen diffusion through HfSiO4, a proposed bond coat material.

Computer Simulation↗

NASA NTRS2015

Kinetic Monte Carlo Simulation of Oxygen Diffusion in Ytterbium Disilicate

Silicon-based ceramic components for next-generation jet turbine engines offer potential weight savings, as well as higher operating temperatures, both of which lead to increased efficiency and lower fuel costs. Silicon carbide (SiC), in particular, offers low density, good strength at high temperatures, and good oxidation resistance in dry air. However, reaction of SiC with high-temperature water vapor, as found in the hot section of jet turbine engines in operation, can cause rapid surface recession, which limits the lifetime of such components. Environmental Barrier Coatings (EBCs) are therefore needed if long component lifetime is to be achieved. Rare earth silicates such as Yb2Si2O7 and Yb2SiO5 have been proposed for such applications; in an effort to better understand diffusion in such materials, we have performed kinetic Monte Carlo (kMC) simulations of oxygen diffusion in Ytterbium disilicate, Yb2- Si2O7. The diffusive process is assumed to take place via the thermally activated hopping of oxygen atoms among oxygen vacancy sites or among interstitial sites. Migration barrier energies are computed using density functional theory (DFT).

Computer Simulation↗

NASA NTRS2011

Kinetic Monte Carlo Simulation of Oxygen and Cation Diffusion in Yttria-Stabilized Zirconia

Yttria-stabilized zirconia (YSZ) is of interest to the aerospace community, notably for its application as a thermal barrier coating for turbine engine components. In such an application, diffusion of both oxygen ions and cations is of concern. Oxygen diffusion can lead to deterioration of a coated part, and often necessitates an environmental barrier coating. Cation diffusion in YSZ is much slower than oxygen diffusion. However, such diffusion is a mechanism by which creep takes place, potentially affecting the mechanical integrity and phase stability of the coating. In other applications, the high oxygen diffusivity of YSZ is useful, and makes the material of interest for use as a solid-state electrolyte in fuel cells. The kinetic Monte Carlo (kMC) method offers a number of advantages compared with the more widely known molecular dynamics simulation method. In particular, kMC is much more efficient for the study of processes, such as diffusion, that involve infrequent events. We describe the results of kinetic Monte Carlo computer simulations of oxygen and cation diffusion in YSZ. Using diffusive energy barriers from ab initio calculations and from the literature, we present results on the temperature dependence of oxygen and cation diffusivity, and on the dependence of the diffusivities on yttria concentration and oxygen sublattice vacancy concentration. We also present results of the effect on diffusivity of oxygen vacancies in the vicinity of the barrier cations that determine the oxygen diffusion energy barriers.

Good, Brian↗

DOE OSTI2025

Self-Learning Kinetic Monte Carlo Simulations of Radiation Damage in Nuclear Fuels

Understanding how irradiation affects the thermo-physical and mechanical properties of nuclear materials, such as thermal conductivity degradation in fuels and embrittlement of structural components, is critical to the safety and efficiency of nuclear reactors. These effects are largely governed by the formation and evolution of atomic-scale point defects and defect clusters. Due to their small sizes, however, these defects are invisible under high-resolution scanning transmission electron microscopy. This project aims to fill this experimental knowledge gap by integrating density functional theory (DFT), machine learning interatomic potential (MLIP), and kinetic Monte Carlo (KMC) techniques to predict longtime evolution of irradiation-induced defects in nuclear fuels.

36 - MATERIALS SCIENCE↗

DOE OSTI2024

Thermal and dynamic partition of dumbbell interstitials in complex concentrated alloys

Complex concentrated alloys (CCAs) are promising candidates for applications in extreme conditions, such as irradiation where interstitial mediated diffusion is important. In CCAs with N principal elements, $\frac{N(N+1)}{2}$ types of dumbbell interstitials exist. Currently, there is no way to predict the thermal partition (fractional concentration at equilibrium) and the dynamic partition (fractional time an interstitial spends during diffusion) of each type of dumbbell interstitial. To mitigate this issue, this work proposes a theoretical model for computing the equilibrium concentrations and thermal partition of dumbbell interstitials in CCAs and validates the model using grand canonical Monte Carlo simulations. Lattice kinetic Monte Carlo simulations show that the thermal partition is equivalent to the dynamic partition, and both are governed by composition and formation energies of dumbbells. As a result, the model proposed provides a foundation for understanding radiation enhanced diffusion and induced segregation in CCAs under irradiation.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Adaptive Tau-Leaping Strategies for Efficient Kinetic Monte Carlo Simulations in Spatially Non-Uniform Systems

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Han, Xiaoying↗

DOE OSTI2024

Tailoring Hierarchical Structure and Rare Earth Affinity of Compositionally Identical Polymers via Sequence Control

Macromolecule sequence, structure, and function are inherently intertwined. While well-established relationships exist in proteins, they are more challenging to define for synthetic polymer nanoparticles due to their molecular weight, sequence, and conformational dispersities. Furthermore, to explore the impact of sequence on nanoparticle structure, we synthesized a set of 16 compositionally identical, sequence-controlled polymers with distinct monomer patterning of dimethyl acrylamide and a bioinspired, structure-driving di(phenylalanine) acrylamide (FF). Sequence control was achieved through multiblock polymerizations, yielding unique ensembles of polymer sequences which were simulated by kinetic Monte Carlo simulations. Systematic analysis of the global (tertiary- and quaternary-like) structure in this amphiphilic copolymer series revealed the effect of multiple sequence descriptors: the number of domains, the hydropathy of terminal domains, and the patchiness (density) of FF within a domain, each of which impacted both chain collapse and the distribution of single- and multichain assemblies. Furthermore, both the conformational freedom of chain segments and local-scale, β-sheet-like interactions were sensitive to the patchiness of FF. To connect sequence, structure, and target function, we evaluated an additional series of nine sequence-controlled copolymers as sequestrants for rare earth elements (REEs) by incorporating a functional acrylic acid monomer into select polymer scaffolds. We identified key sequence variables that influence the binding affinity, capacity, and selectivity of the polymers for REEs. Collectively, these results highlight the potential of and boundaries of sequence control via multiblock polymerizations to drive primary sequence ensembles hierarchical structures, and ultimately the functionality of compositionally identical polymeric materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Catalytic resonance theory for the kinetic signatures of multiple wavelength photocatalysis

Multi-step surface chemistry promoted with one or two wavelengths of light exhibited distinct kinetic signatures indicative of the light-adsorbate interactions and the number of photon-sensitive elementary steps. In this work, kinetic Monte Carlo simulations identified the kinetic response of general surface mechanisms to variation in the per-site photon flux of one or two wavelengths of incident light. Photocatalytic rates were described via a non-dimensional photon flux, identifying multiple kinetic regimes with unique degrees of rate control. Under photon-controlled kinetic conditions, maximum quantum yield and turnover frequency were obtained under constant illumination, while pulsing of one or more light sources was shown to exhibit slower rates and less efficient photocatalytic promotion due to the inherent dynamic nature of light, which comprises a stream of photons. Simulations provided distinct kinetic signatures in catalytic rates and Arrhenius kinetics for specific light-surface-adsorbate interactions corresponding to photocatalytic promotion of specific steps in surface chemistry.

catalytic resonance↗