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The role of irradiation-enhanced interstitial diffusion in over-pressurizing fission gas bubbles in UO 2
Fission gas bubbles in UO 2 nuclear fuel have been observed to exhibit pressures in excess of the equilibrium bubble pressure; however, the cause of bubble over-pressurization has not yet been demonstrated. The mechanical interaction between a bubble and the surrounding matrix or grain boundary depends on the internal pressure of the bubble and local stress state, such that over-pressurized bubbles are thought to be responsible for fragmentation and pulverization, when exposed to a temperature ramp. Here, in this work, we investigate the role of U interstitials, produced through irradiation, in over-pressurizing bubbles by using a combined molecular dynamics (MD) and cluster dynamics approach. Firstly, the energies for the capture of interstitials and vacancies by bubbles have been determined from MD as a function of the ratio of gas atoms to vacancies that make up the bubble. Secondly, these reaction energies have been implemented in the cluster dynamics code Centipede to predict bubble over-pressurization as a function of temperature for typical fission rates. It was found that there is a transition from low pressure bubbles (at high temperatures) to high pressure bubbles (at lower temperatures). The cause of this behavior was shown to be the creation of irradiation-induced interstitials that are highly mobile relative to vacancies at low temperature; whereas, vacancies are sufficiently mobile at high temperatures to limit bubble pressures. This result supports the hypothesis that over-pressurized bubbles form during steady-state operation and that this behavior is highly sensitive to the local pellet temperature.
Predicting images for the dynamics of stellar clusters ( π-DOC ): a deep learning framework to predict mass, distance, and age of globular clusters
ABSTRACT Dynamical mass estimates of simple systems such as globular clusters (GCs) still suffer from up to a factor of 2 uncertainty. This is primarily due to the oversimplifications of standard dynamical models that often neglect the effects of the long-term evolution of GCs. Here, we introduce a new approach to measure the dynamical properties of GCs, based on the combination of a deep-learning framework and the large amount of data from direct N-body simulations. Our algorithm, π-DOC (Predicting Images for the Dynamics Of stellar Clusters) is composed of two convolutional networks, trained to learn the non-trivial transformation between an observed GC luminosity map and its associated mass distribution, age, and distance. The training set is made of V-band luminosity and mass maps constructed as mock observations from N-body simulations. The tests on π-DOC demonstrate that we can predict the mass distribution with a mean error per pixel of 27 per cent, and the age and distance with an accuracy of 1.5 Gyr and 6 kpc, respectively. In turn, we recover the shape of the mass-to-light profile and its global value with a mean error of 12 per cent, which implies that we efficiently trace mass segregation. A preliminary comparison with observations indicates that our algorithm is able to predict the dynamical properties of GCs within the limits of the training set. These encouraging results demonstrate that our deep-learning framework and its forward modelling approach can offer a rapid and adaptable tool competitive with standard dynamical models.
Investigating bubble pressures in irradiated UO 2 for understanding fragmentation of high burnup structure
This report summarized work carried out to investigate mechanisms relevant to fragmentation of high burnup UO 2 fuel. High pressure bubbles that form in high burnup structure are thought to be responsible for fragmentation and pulverization, when exposed to a temperature ramp during a transient. The over-pressurization of the bubbles during normal operation is a pre-requisite for this mechanism to occur. Therefore, in this work we investigate the role of interstitials, produced through irradiation, in over-pressurizing the bubbles by using a combined molecular dynamics (MD) and cluster dynamics approach. Firstly, the energies for the annihilation of interstitials and vacancies at bubbles have been determined from MD as a function of bubble pressure. Secondly, these reaction energies have been implemented in the cluster dynamics code Centipede to determine the steady-state defect concentrations and bubble pressure under irradiation. It was found that there is a transition from low pressure bubbles, at high temperature, to high pressure bubbles, at low temperatures. This indicates the formation of over-pressurized bubbles in the low temperature periphery of the pellet, where high burnup structure forms. This result supports the hypothesis that over-pressurized bubbles form during steady-state operation and can then contribute to fragmentation during a transient. Future work will examine the influence of bubble pressure on Xe diffusion and study the impact of other sinks (e.g. grain boundaries and dislocations) that are relevant to high burnup structure. Ultimately, the goal is to provide predictions of the bubble pressure as a function of burnup that can be used to derive a more mechanistic fragmentation threshold for use in BISON.
Reagent-Triggered Isomerization of Fluxional Cluster Catalyst via Dynamic Coupling
Metallic cluster catalysts have many thermodynamically accessible isomers with diverse active sites and low reaction barriers, and lately a strong hypothesis emerged that the many catalyst states collectively drive the catalysis. Furthermore, it remained a hypothesis that catalyst isomerization is actually kinetically feasible under the current reaction conditions. Using high-temperature dynamics simulations and sampling, a range of orientations, and vibrational energy distributions, we probe how thermal effects and molecular events affect cluster catalyst dynamics. We show that even such a delicate affair as the dissociation or scattering of a methane molecule on the heavy and thus slow Pt 13 cluster triggers substantial isomerization of the catalyst, far beyond thermal at 700 K. A kinetic coupling between the methane activity and cluster catalyst dynamics is observed. In return, the thermal dynamics of the cluster affects the methane reaction and scattering probabilities. Hence, molecular events at the surfaces of fluxional cluster catalysts should facilitate the population of an ensemble of catalyst states under the current reaction conditions, with implications for available active sites, reaction mechanisms, and apparent rates.
Scalable edge clustering of dynamic graphs via weighted line graphs
Timestamped relational datasets consisting of records (or connections) between pairs of entities are ubiquitous in network science. For applications like peer-to-peer communication, email, various social network interactions, and computer network security, it is useful to organize these records into groups based on how and when they are occurring. Weighted line graphs offer a natural way to model how records are related in such datasets but for large real-world graph topologies, building and utilizing the line graph is prohibitively expensive. Here, we present the framework to cluster the edges of a dynamic graph via the associated line graph that contains two major contributions. The first is a method to work with the line graph implicitly and the second is a distributed scale implementation of an agglomerative hierarchical graph clustering algorithm. We outline a novel hierarchical dynamic graph edge clustering approach that efficiently breaks massive relational datasets into small sets of edges containing events at various timescales. This is in stark contrast to traditional graph clustering algorithms that prioritize highly connected (clique-like) community structures. Our approach relies on constructing a sufficient subgraph of a weighted line graph and applying a hierarchical agglomerative clustering. This approach is related to scalable techniques from spatial clustering, nonlinear-dimension reduction, topological data analysis, and draws particular inspiration from HDBSCAN. As an edge clustering, this method yields an overlapping node clustering. Our algorithm is parallelizable and we demonstrate efficient clustering of a billion-scale, real-world dynamic graph into small edge sets that correlate in topology and time. The entire clustering process for a graph with tens of billions of edges takes just a few minutes of run time on 256 nodes of a distributed compute environment. We argue how the output of the edge clustering is useful for a multitude of data visualization and powerful machine learning tasks, both involving the original massive dynamic graph data and metadata associated with the nodes and edges. Finally, we describe how this approach can be extended to dynamic hypergraphs and dynamic graphs/hypergraphs with unstructured data living on vertices and edges.
Fission gas diffusion and release for Cr 2 O 3 -doped UO 2 : From the atomic to the engineering scale
Here, the anticipated benefits of large grains in Cr 2 O 3 -doped UO 2 pellets include improved mechanical and fission gas retention properties. To support the assessment of fission gas release (FGR) from doped pellets, the impact of doping on fission gas diffusivity for in-reactor conditions must be understood. In this work, we tackle this issue by informing the fission gas model within the BISON fuel performance code using material models developed at the atomic scale. The investigation of intra-granular fission gas diffusivity in Cr 2 O 3 -doped UO 2 is carried out by adapting a cluster dynamics model that, accounting for UO 2 thermochemistry, is capable of describing Xe diffusion under irradiation in undoped UO 2 as the starting point. Using a thermodynamic analysis, it is shown that in stoichiometric UO 2 with additions of Cr 2 O 3 the oxygen potential is defined by the Cr-Cr 2 O 3 two-phase equilibrium. Using the cluster dynamics model, the predicted Xe diffusivity in doped UO 2 was significantly increased in both the intrinsic and irradiation-enhanced regimes compared to undoped UO 2 as a result of higher concentrations of uranium and oxygen vacancies, respectively. This is a consequence of the more oxidizing conditions at high temperature, and more reducing conditions at low temperature, as a result of doping. Arrhenius functions have been fitted to the cluster dynamics results to enable implementation of the new diffusivities in the BISON fission gas behavior model. BISON simulations were carried out, showing the competing effects of the enlarged grains and the new fission gas diffusivity model, which act to suppress and enhance fission gas release, respectively. The new physics-informed model was validated against in-reactor experimental measurements under normal operation. Additionally, benchmarking was carried out for power ramp conditions. The predicted fission gas release agreed well with the experimental data, showing noticeable improvements over the standard UO 2 model.
Sub-system quantum dynamics using coupled cluster downfolding techniques
In this paper, we discuss extending the sub-system embedding sub-algebra coupled cluster (SES-CC) formalism and the double unitary coupled cluster (DUCC) ansatz to the time domain. As we demonstrated in earlier studies, it is possible, using these formalisms, to calculate the energy of the entire system as an eigenvalue of downfolded/effective Hamiltonian in the active space, that is identifiable with the sub-system of the composite system. In these studies, we demonstrated that downfolded Hamiltonians integrate out Fermionic degrees of freedom that do not correspond to the physics encapsulated by the active space. We extend these results to the time-dependent Schrödinger equation, showing that a similar construct is possible to partition a system into a sub-system that varies slowly in time and a remaining subsystem that corresponds to fast oscillations. This time dependent formalism allows coupled cluster quantum dynamics to be extended to larger systems and for the formulation of novel quantum algorithms based on the quantum Lanczos approach, which have recently been considered in the literature.
Modeling of fission gas diffusion and release for Gd 2 O 3 doped UO 2
Uranium dioxide (UO 2 ) is the primary nuclear fuel in light water reactors, and its excess neutronic reactivity can be controlled by adding burnable absorbers, such as Gd 2 O 3 . This burnable absorber has a large neutron absorption cross-section, lowering the high reactivity of the reactor's initial fuel load. However, there needs to be more understanding of how added Gd 2 O 3 influences the properties of UO 2 under irradiation. To understand the behavior of defects and fission gas in the UO 2 /Gd 2 O 3 system under irradiation, we use cluster dynamics modeling supported by density functional theory calculations. First, we calculate the formation energies of Gd point and cluster defects, and evaluate the temperature-dependent defect concentrations using the defect formation energies and entropies. We show that Gd is soluble in UO 2 , introducing a negative charge in the system. Using this information, we adapted the cluster dynamics code Centipede to model the influence of Gd on U self-diffusion and Xe diffusion in UO 2 with 10 wt% Gd 2 O 3 . Also, we analyzed the Xe diffusion as a function of Gd 2 O 3 concentration, showing that the Xe diffusivity is decreased, which means that the athermal diffusivity due to electronic stopping persists at higher temperatures. In conclusion, the decrease in Xe diffusion means that more Xe stays in the matrix, decreasing the Xe release, and lowering its influence of fission gas release on the thermomechanical properties of UO 2 .
Development of a MOOSE-based crystal plasticity model with irradiation defect evolution for irradiation creep in 316
Irradiation creep and irradiation swelling are two of the lifetime limiting factors for structural materials in nuclear reactors. These mechanical effects are driven by irradiation defect evolution and the interaction of those defects with dislocations in the microstructure. We present here a coupled cluster dynamics – crystal plasticity approach to model irradiation swelling and creep behavior in 316 SS. The time-dependent evolution of irradiation defects is calculated with a cluster dynamics approach and passed to the crystal plasticity model to compute the dislocation evolution. We show the impact of the irradiation defect evolution on the stress state in the material, which drives inelastic deformation through dislocation motion. The inelastic deformation in the 316 SS is dependent on the dose rate, where the inelastic deformation driven by the early-stage irradiation defect evolution determines the mechanical behavior of the 316 SS.
Dynamic Atom Clusters on AuCu Nanoparticle Surface During CO Oxidation
Supported alloy nanoparticles are prevailing alternative low-cost catalysts for both heterogeneous and electrochemical catalytic processes. Selective interaction of an alloy component with a specific reactant induces a dynamic structural change of alloy nanoparticles under reaction conditions and largely controls their catalytic properties. However, such a multi-component dynamic-interaction-controlled evolution, both structural and chemical, remains far from clear. Herein, by using state-of-the-art environmental TEM, we directly visualize, in-situ at the atomic scale, the evolution of an AuCu alloy nanoparticle supported on CeO2 during CO oxidation. We find that gas molecules can “free” metal atoms on the {001} surface and form highly mobile atom clusters. Remarkably, we discover that CO exposure induces Au segregation and activation on nanoparticle surface, while O2 exposure leads to the segregation and oxidation of Cu on the particle surface. The as-formed Cu2O/AuCu interface may facilitate CO-O interaction corroborated by DFT calculations. These findings provide insights into the atomistic mechanisms on alloy nanoparticles during catalytic CO oxidation reaction, and to a broad scope of rational design of alloy nanoparticle catalysts.
Impact of Soret effect on hydrogen and helium retention in PFC tungsten under ELM-like conditions
Abstract In our previous work, we have demonstrated using nonequilibrium molecular-dynamics simulations that the fluxes of helium and self-interstitial atoms in the presence of a thermal gradient in tungsten are directed opposite to the heat flux, indicating that species transport is governed by a Soret effect, namely, thermal-gradient-driven diffusion, characterized by a negative heat of transport that drives species transport uphill, i.e. from the cooler to the hot regions of the tungsten sample. In this work, the findings of our thermal and species transport analysis have been implemented in our cluster-dynamics code, Xolotl, which has been used to compute temperature and species profiles over spatiotemporal scales representative of plasma-facing component (PFC) tungsten under typical reactor operating conditions, including extreme heat loads at the plasma-facing surface characteristic of plasma instabilities that induce edge localized modes (ELMs). We demonstrate that the steady-state species profiles, when properly accounting for the Soret effect, vary significantly from those where temperature-gradient-driven transport is not accounted for and discuss the implications of such a Soret effect on the response to plasma exposure of plasma-facing tungsten. Although our cluster-dynamics simulations do not yet include self-clustering of helium or hydrogen blister formation, our simulation results show that the Soret effect substantially reduces helium and hydrogenic species retention inside PFC tungsten.
Microstructure modeling of nuclear structural materials: Recent progress and future directions
Modeling and simulation of microstructures are essential to understand the complex responses and behaviors of nuclear materials in extreme environments. The needs to assess the extended life operation as well as the growing interest in accelerating nuclear materials development and qualification have stimulated the use of high-fidelity multiscale models aided by empirical and ab initio data. This paper reviews the role of various models across different length and time scales in investigating irradiation effects on microstructure evolution and degradation, in particular the embrittlement caused by radiation induced or enhanced formation of nanoscale chemical heterogeneities. The strength and limitations of these models, including classical rate theories, cluster dynamics, phase-field methods, and atomistic models informed by ab initio energies, are discussed with seminal examples. Challenges regarding the lack of thermo-kinetic data and theoretical treatments considering chemical complexities and magnetic excitations, as well as the stabilizing effect by excess point defects in nuclear structural materials are presented, along with potential solutions based on ab initio informed surrogate energy models and statistical sampling by Monte Carlo simulations. Further, the review then highlights the opportunities to leverage the advantages of different methods by establishing hybrid models by shared variables or coupled codes and applications. Finally, the review concludes with forward-looking remarks on how the use of physics-based models can aid the improvement of machine-learning models of property degradation and vice versa.
Impact of amorphous pockets on displacement damage evolution in silicon
Silicon has long been known to exhibit amorphization in response to heavy particle bombardment. For doses below the total amorphization threshold, partial amorphization is observed in the form of scattered amorphous pockets. While extensive research has gone into modeling the formation and evolution of amorphous pockets in response to irradiation, no studies yet investigate their impact on the evolution of other damage such as interstitial supersaturation and clustering. In this study, we survey the impact of amorphous pockets on defect evolution in silicon when treated as static sinks. MD is first used to show that amorphous pockets provide energetically favorable sites for point defects relative to the crystalline bulk, supporting the hypothesis that they act as sinks. A 0-D cluster dynamics model is then constructed, taking an interstitial clustering model from the literature and including amorphous pockets as a sink species. We conduct our survey for temperatures between 30 and 400 °C and sink strengths between 1 to 6 x 10 10 cm −2 . Both implantation- and radiation-induced damage states are investigated using interstitial and vacancy concentrations as initial condition variables. We find that, due to the differing migration rates of the interstitial and the vacancy, amorphous pockets have a non-monotonic impact on the final damage state depending on the effective sink strength of the amorphous pockets, resulting in increased damage formation in regimes of intermediate amorphization. In conclusion, this result emphasizes the important role of amorphous pockets in governing the evolution of damage in partially amorphized crystalline materials.
Interpretation of Ion Irradiation and Neutron Irradiation Damage in Additively Manufactured 316 Stainless Steel using Multiscale Modeling
The accelerated adoption of nuclear energy necessitates advanced manufacturing technologies, such as additive manufacturing, to meet heightened supply chain requirements and support innovative reactor technologies. Due to the unique microstructural characteristics of additively manufactured materials under distinct solidification conditions, comprehensive evaluation of their performance in reactor environments is essential. The Advanced Materials and Manufacturing Technologies program under the Department of Energy's Office of Nuclear Energy focuses on understanding the irradiation performance and damage evolution of laser powder bed fusion 316 stainless steel, with an emphasis on integrating ion and neutron irradiation data to accelerate the development and qualification of materials for advanced nuclear reactor applications. While ion irradiation is a cost- and time-effective method, modeling and simulation are required to interpret the data for the broader range of irradiation conditions encountered in advanced reactors. In fiscal year 2025, integrated multiscale modeling and simulations were conducted to assess irradiation damage in additively manufactured 316 stainless steel. Key outcomes include predictions of chromium enrichment at grain boundaries, nickel enrichment at dislocation cell walls and void surfaces, and heterogeneous void evolution under ion and neutron irradiation conditions. Cluster dynamics simulations revealed the coarsening of voids at high irradiation temperatures and the suppression of void growth by high network dislocation density, while also demonstrating significant growth and coarsening of voids and self-interstitial atom loops at low dose rates. Machine learning-accelerated atomistic simulations highlighted the impact of the local environment and chromium concentration on vacancy diffusivity, providing key insights on the influence of composition on void swelling and radiation-induced segregation. Additionally, molecular dynamics simulations demonstrated the presence of defect production bias and a significant effect of carbon content on defect cluster behavior. These combined efforts aim to predict the performance of additively manufactured materials under various reactor conditions, supporting their qualification for nuclear reactor applications by interpreting ion irradiation data. This report underscores the potential of integrated multiscale modeling to analyze ion irradiation data in the effort to accelerate the qualification of additively manufactured materials for nuclear reactor components.
Atomistically-informed modeling of point defect clustering and evolution in irradiated ThO 2
A cluster dynamics (CD) model has been developed to investigate the nucleation and growth of point defect clusters, i.e., interstitial prismatic loops and nanoscale and sub-nanoscale voids, in ThO 2 during irradiation by energetic particles. The model considers cluster off-stoichiometry due to the asymmetry of point defect generation on the O and Th sublattices under irradiation, as well as the point defect diffusivities and the defect binding energies to clusters. The energies were established using detailed molecular dynamics simulations considering the statistical variability of cluster configuration. A high-order adaptive time-integration has been used to solve the model. The predicted loop density and their average size is in good agreement with reported experimental observations for proton irradiated ThO 2 at 600°C. In conclusion, the model did not predict void evolution due to the sluggish kinetics of cation vacancies, explaining the absence of voids in proton irradiated ThO 2 (and other oxides) at relatively low temperatures.
Velocity dispersions of clusters in the Dark Energy Survey Y3 redMaPPer catalogue
ABSTRACT We measure the velocity dispersions of clusters of galaxies selected by the red-sequence Matched-filter Probabilistic Percolation (redMaPPer) algorithm in the first three years of data from the Dark Energy Survey (DES), allowing us to probe cluster selection and richness estimation, λ, in light of cluster dynamics. Our sample consists of 126 clusters with sufficient spectroscopy for individual velocity dispersion estimates. We examine the correlations between cluster velocity dispersion, richness, X-ray temperature, and luminosity, as well as central galaxy velocity offsets. The velocity dispersion–richness relation exhibits a bimodal distribution. The majority of clusters follow scaling relations between velocity dispersion, richness, and X-ray properties similar to those found for previous samples; however, there is a significant population of clusters with velocity dispersions that are high for their richness. These clusters account for roughly 22 per cent of the λ < 70 systems in our sample, but more than half (55 per cent) of λ < 70 clusters at z > 0.5. A couple of these systems are hot and X-ray bright as expected for massive clusters with richnesses that appear to have been underestimated, but most appear to have high velocity dispersions for their X-ray properties likely due to line-of-sight structure. These results suggest that projection effects contribute significantly to redMaPPer selection, particularly at higher redshifts and lower richnesses. The redMaPPer determined richnesses for the velocity dispersion outliers are consistent with their X-ray properties, but several are X-ray undetected and deeper data are needed to understand their nature.