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Covariate Dependent Sparse Functional Data Analysis

This study proposes a method to incorporate covariate information into sparse functional data analysis. The method aims at cases where each subject has a limited number of longitudinal measurements and is associated with static covariates. This research is motivated by several use cases in practice. One representative example is void swelling, a nuclear-specific material degradation mechanism. Void swelling is affected by many covariates, including alloy composition and irradiation type. How to accurately model the complicated joint effects of such covariates on the swelling process is the key to mitigating the effect of swelling and ensuring safe operation. Unlike most of the existing methods, the proposed method can handle high-dimensional covariates with the informative covariate identification procedure and sparse and irregularly spaced measurements, that is, does not require complete or dense observations. The main innovation of the proposed method is that we model the variation coming from covariates and the variation left conditioned on covariates, such that the functional principal component analysis and Gaussian process can be conducted in a unified manner. Further, we also propose a systematic approach to identify important covariates in the hypothesis testing context. The methodology is demonstrated on applications in nuclear engineering and healthcare and simulation studies.

42 ENGINEERING↗

A Rate Theory Model of Radiation-Induced Swelling in an Austenitic Stainless Steel

Many rate theory models of cavity (void) swelling have been published over the past 50 years, all having the same, or similar, structures. A rigorous validation of the models has not been possible because of the dearth of information concerning the microstructures that correspond with the swelling data. Whereas the lack of microstructure information is still an issue for historical swelling data, in the past 10–20 years data have been published on the evolution of the microstructure (point defect yields from collision cascades, cavity number densities, and dislocation densities/yield strengths) allowing certain gaps in information to be filled when considering historic swelling data. With reasonable estimates of key microstructure parameters, a standard rate theory model can be applied, and the model parameter space explored, in connection with historical swelling data. By using published data on: (i) yield strength as a function of dose and temperature (to establish an empirical expression for dislocation density evolution); (ii) cavity number densities as a function of temperature; and (iii) freely migrating defect (FMD) production as a function of primary knock-on atom (PKA) spectrum, the necessary parameter and microstructure inputs that were previously unknown can be used in model development. This paper describes a rate-theory model for void swelling of 316 stainless steel irradiated in the EBR-2 reactor as a function of irradiation temperature and neutron dose.

36 MATERIALS SCIENCE↗

High radiation tolerance of an ultrastrong nanostructured NiCoCr alloy with stable dispersed nanooxides and fine grain structure

The present paper reports the irradiation behavior of nanostructured NiCoCr medium entropy alloy enhanced by Y-Hf-O nanooxides and fine grains produced by powder metallurgy. Ion beam irradiation to a peak dose of 130 dpa at 580°C produced neither detectable void swelling nor irradiation-induced hardening, in contrast to significant void swelling and property degradation of single phase NiCoCr concentrated solid-solution alloy under the similar irradiation condition. The dispersed nanooxides and high density of grain boundaries act as defect sinks that effectively annihilate irradiation-induced interstitials and vacancies. Furthermore, high-density nanooxides maintain their crystalline structures and stabilize the grain boundaries during irradiation.

36 MATERIALS SCIENCE↗

Ni coating on 316L stainless steel using cage plasma treatment: Feasibility and swelling studies

A modified cage plasma nitriding technique is used to coat a Ni film onto a 316L substrate as a protective layer for austenitic steels in molten fluoride salts. The coating is achieved by deposition of Ni atoms sputtered from a Ni cage with a 316L substrate floated at the same potential as the cage to reduce plasma sputtering on the substrate. The Ni coating is porosity-free and precipitation-free and forms a γ-(Fe, Ni) phase due to interdiffusion from the substrate. Beneath the interdiffusion layer exists a thick γ-phase layer mainly affected by long-range nitrogen diffusion along the grain boundary. This layer develops grain boundary Cr nitride precipitates. Ion irradiation on the polished cross-section of the plasma-treated sample shows no void swelling in the surface-deposited Ni layer, very limited void formation in N diffusion layer, and significant void swelling in bulk unaffected by nitrogen. The studies demonstrate the feasibility of the technique for Ni coating and show good swelling resistance of the coating layer and N diffusion-affected layer. Mechanisms are discussed in this paper.

36 MATERIALS SCIENCE↗

In situ observation of short- and long-timescale material property evolution under extreme conditions

Directly observing the evolution of material performance in-situ under extreme conditions remains a great challenge. Emergent behavior, such as the transition from incubation to steady state void swelling, is often difficult to capture in these conditions. To fill this gap, transient grating spectroscopy (TGS) has been used to collect multi-property information in-situ under high temperature exposure to ion beam irradiation. This all-optical method returns elastic and thermal transport properties with second-scale time resolution. Here, recent work using this methodology to track the evolution of Ni-based solid-solution alloys using the in situ ion irradiation TGS (I3TGS) beamline will be described. Tracking material property evolution during long exposure times (hours) provides a clear indication of when void swelling has occurred. On short timescales (seconds to minutes), observing rapid changes in thermoelastic properties as defect generation is initiated allows a unique window into bulk transient defect populations which are otherwise difficult to observe.

36 MATERIALS SCIENCE↗

Development of a U-19Pu-10Zr fuel performance benchmark case based on the IFR-1 experiment

Metallic nuclear fuels are subject to research and development for use in advanced reactors. Robust, accurate metallic fuel performance models are important for the design, safety analysis, and licensing of these reactors. However, metallic fuel performance models require additional development; they are not as mature as UO 2 fuel performance models. A benchmark case based on the IFR-1 experiment was developed to better gauge the accuracy of existing models, identify models for high-priority development, and potentially quantify any future improvements made by further model development.This work collected publicly available information on the IFR-1 experiment and used it to develop the benchmark case. Fuel behavior during the IFR-1 irradiation was simulated by using the fuel performance code BISON, and the predicted results were compared with postirradiation examination data from the IFR-1 experiment. Furthermore, a sensitivity study and tuning studies were performed as a preliminary investigation into the causes of inaccurate temperature and dimensional change predictions.The benchmark predicted reasonably accurate values for the burnup and fission gas release. There was error in the predicted temperatures, which could be explained by uncertainty in the input parameters and legacy temperatures. BISON over-predicted dimensional changes in the fuel and cladding. The sensitivity study showed that the dimensional changes were most sensitive to the fuel swelling anisotropy and the cladding void swelling model. Future benchmark and model development should focus on cladding swelling behaviors to improve dimensional change predictions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

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↗

Evaluation of the effects of neutron irradiation on first-generation corrosion mitigation coatings on SiC for accident-tolerant fuel cladding

In this work, high purity SiC and SiC/SiC composites coated with commercial TiN, Cr, CrN, or CrN/Cr multilayer coatings were irradiated in Ar or flowing PWR water in the Massachusetts Institute of Technology Nuclear Reactor Laboratory (MITR). Irradiation in Ar was performed in the core. In the water environment, identical samples were placed in one of three different locations: in-core, providing exposure to neutron damage and radiolysis-affected water; above-core, where samples were exposed to radiolysis-affected water but not neutron damage, or outside of the core, where samples were exposed to the coolant water without the effects of radiation. Radiation in Ar revealed significant cracking of all but the TiN coatings, attributed to differential swelling between the coating and substrate. Lattice swelling was not observed in any of the coatings, but 0.2% void swelling was observed in the Cr coating. All of the coatings failed during water exposures in the core. Likewise, CrN/Cr spalled in each condition. Cr was protective, except under radiation damage as a result of cracking, and TiN severely degraded in the core with no coating was found following exposure. A SiC/coating ATF cladding system is anticipated to perform adequately following improvements in coating ductility and purity.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Generalized rate theory for void and bubble swelling and its application to δ -plutonium

A rate theory for void and bubble swelling is derived that allows both vacancies and self-interstitial atoms to be generated by thermal activation at all sinks. In addition, they can also be produced by displacement damage from external and internal radiation. This generalized rate theory (GRT) is applied to swelling of gallium-stabilized δ-plutonium in which α-decay causes the displacement damage. Since the helium atoms produced also become trapped in vacancies, a distinction is made between empty and occupied vacancies. The growth of helium bubbles observed by transmission electron microscopy in weapons-grade and in material enriched with Pu238 is analyzed, using different values for the formation energy of self-interstitial atoms (SIA) and two different sets of relaxation volumes for the vacancy and for the SIA. One set allows preferential capture of SIA at dislocations, while the other set gives equal preference to both vacancy and SIA. It is found that the helium bubble diameters observed are in better agreement with GRT predictions if no preferential capture occurs at dislocations. Therefore, helium bubbles in δ-plutonium will not evolve into voids. Furthermore, the helium density within the bubbles remains sufficiently high to cause thermal emission of SIA. Based on a helium density between two to three helium atoms per vacant site, the sum of formation and migration energies must be around 2.0 eV for SIA in δ-plutonium.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

The effect of heat treatment on the defect evolution in LPBF 316H stainless steel

This work investigates the effect of processing and heat treatment on defect evolution and irradiation response of laser powder bed fusion (LPBF) 316H stainless steel, with comparisons to LPBF 316L and wrought 316L/316H. Using in-situ and ex-situ ion irradiations across a wide parameter space—temperature (300–675 °C), dose (0.2–25 dpa), dose rate (10 -3 –10 -5 dpa/s), and helium co-implantation (20–2500 appm)—we correlated void swelling, dislocation loop evolution, and segregation behavior with pre-irradiation microstructures (as-built, stress-relieved, solution-annealed, and cold-worked). Results show that swelling is strongly controlled by dislocation density: intermediate densities maximize swelling, while solution annealing or cold working reduce susceptibility to levels comparable to wrought alloys. Low dose rates and helium both promote cavity nucleation and lower the incubation barrier, with helium suppressing the role of dislocation density and driving swelling behavior toward wrought-like response. Loop evolution in SA LPBF 316H resembles wrought 316L but shows localized denuded zones near low-angle grain boundaries. STEM-EDS mapping further revealed Ni segregation at voids and sparse Al-rich oxides, without evidence of Ni–Si precipitates. Collectively, these findings identify dislocation density, helium content, and dose rate as the factors governing swelling in LPBF 316H and provide mechanistic datasets for model validation, supporting LAIN and the qualification of AM austenitic steels for nuclear service.

316 stainless steel↗

Recent Studies on Void Shrinkage in Metallic Materials Subjected to In Situ Heavy Ion Irradiations

The continuous formation and growth of voids induced by radiations in metallic materials may lead to significant microstructure damage and degradation of mechanical properties. In sharp contrast to the void swelling commonly observed in irradiated metallic materials, nanovoids in nanoporous metallic materials are found to shrink during radiation and thus nanovoids enhance the radiation tolerance of metallic materials. This article reviews recent studies on size-dependent void shrinkage in metallic materials subject to in situ heavy ion irradiation. Furthermore, we demonstrate the capability of machine learning in identifying and tracking the evolution of nanovoids. Finally, the physical mechanisms of radiation induced void shrinkage revealed by simulation studies are briefly summarized.

36 MATERIALS SCIENCE↗

Development of Corrosion Resistant Coatings for Structural Materials for Liquid Fueled Molten Salts Reactors Applications (Final Report)

Current structural alloys, code certified for the MSRs temperature ranges, contain high levels of chromium, making them highly susceptible to molten halide salt corrosion. One potential solution to circumvent the need for code certification of novel alloys, which is expensive and time consuming, is to design claddings that will protect the underlying code certified materials from corrosion damage during operation. In this work, we examined the corrosion of Ni and Cu electroplated, Ni and CuNi weld overlay, Mo-laser clad, and carburized claddings on SS316H for use in molten salt reactor environments. After characterization of the cladded materials (Task 1), static corrosion tests were used to assess corrosion resistance of the claddings in typical molten fluoride salts (Task 2). The corrosion tests were performed in molten FLiNaK at 700°C up to 1000 hours. Pre- and post-corrosion Scanning Electron Microscopy (SEM), energy-dispersive-spectroscopy (EDS), Transmission Electron Microscopy (TEM), X-ray Diffraction (XRD) and glow-discharge-optical-emission-spectroscopy (GDOES) were performed on cladding cross-sections and surfaces to evaluate degradation. The Cu and Ni electroplated samples, as well as the carburized samples, showed excellent corrosion resistance relative to the bare SS316H. To assess high temperature cladding stability, ageing experiments were performed at temperatures up to 900 C in inert atmosphere for the electroplated and carburized samples and a diffusion model was developed to predict long term cladding behavior (Task 3). It was found that the Cu cladding was basically insensitive to the high temperature ageing, except for small secondary phases forming at the interface. On the other hand, the Ni electroplated cladding experienced significant interdiffusion. Nevertheless, the gain in corrosion resistance for a 100μm Ni electroplated cladding is phenomenal, with more than 50% reduction in chromium dissolution from the substrate material for the first 15 years of salt exposure at 700°C. To assess radiation resistance and phase stability, high-temperature 4MeV Ni heavy ion irradiation was performed across the cladding/substrate interface up to 50 displacement-per-atom (DPA) at 500°C and 700°C to assess the phase stability and irradiation behaviors of the electroplated systems (Task 4). The Ni and Cu electroplated systems did not experience void swelling at the contrary to the SS316H substrate due to their nanocrystalline nature. Some level of recrystallization was observed in the cladding, as well as radiation induced segregation and enhanced diffusion. The interface acted as a potent sink for point defects with the presence of a void denuded zone. The mechanical properties of the claddings were assessed using thermal shock, micro-indentation, nano-indentation, and four-point bend testing experiments (Task 5). These experiments were performed on the claddings in as-received, corroded, irradiated, and thermally aged states to determine the effects of typical molten salt reactor environments on cladding integrity. No significant mass loss was observed after repeated thermal shocks. While the electroplated samples softened after high-temperature ageing, irradiation hardening compensate this effect, such that there is little different with the as-received materials. The results of these experiments suggest that the electroplated (copper/nickel) show the greatest promise for application in molten salt reactor development. These claddings prevented any chromium dissolution from occurring during the static corrosion experiments. Additionally, they demonstrated favorable properties for high temperature diffusion, phase stability, interfacial mechanical properties, and irradiation resistance. Weld-overlay cladding are also of great interest and could reach properties similar to the electroplated samples upon optimization (especially with multiple weld passes). The carburized SS316H showed excellent behavior as well, but more work needs to be done to assess their long-term stability. Finally, the Mo-laser clad system was not pursued further due to the manufacturing challenges. It is also worth noting that the Ni cladding systems should behave relatively well in terms of weldability since the Ni-weld overlay microstructure and associated corrosion rate are sound. While the NiCu weld-overlay has even lower corrosion rates than the Ni-weld overlay, more studies on welding of Cu-electroplated systems are necessary since Cu clusters are known to embrittle steels.

36 MATERIALS SCIENCE↗

Dynamic observation of dual-beam irradiated Fe and Fe-10Cr alloys at 435 °C

The attractive mechanical properties and superior resistance to void-swelling make ferritic/martensitic alloys a promising structural material for advanced nuclear reactors. However, one anomaly that has intrigued researchers for more than 50 years is the proportion of two types of dislocation loops in Fe and Fe-Cr alloys with Burger vectors b=½<111> and b=<100>. Although the possible mechanisms responsible for the presence of <100> loops continue to be the subject of intense modeling studies, there remains incomplete experimental understanding of fundamental irradiation processes in Fe(Cr) alloys. Here, the dose dependence of the irradiation-induced microstructural evolution was examined from 0 to 20 displacement per atom (dpa) in high purity Fe and Fe-10Cr during simultaneous dual-beam (1 MeV Kr + 10 appm He/dpa) irradiation at 435 °C. We experimentally revealed that the mechanism for the formation of <100> loops may not follow the conventional simple dislocation reaction between two 1½<111> loops. Real-time dynamic formation and evolution of defects including black dot loops, loop coarsening, loop decoration, network dislocations, and cavities were demonstrated. Several results indicated that the addition of Cr and He could impede dislocation loop motion. The evolution of the defect size/density and relative fraction of ½<111> vs <100> loops were quantitatively summarized. With increasing dose, ½<111> loops became the dominant type of loop in both materials. Notably, <100> loops were predominantly observed near grain boundaries only for pure Fe, while arrays of nanoscale black dot defects composing the <100> loop strings were observed in plenty in Fe-10Cr.

36 MATERIALS SCIENCE↗

Formation of misfit dislocation arrays and helium nanochannels near copper surface assisted by high-temperature graphene deposition

Misfit dislocation arrays (MDAs) at semi-coherent heterogeneous interface have been demonstrated effectiveness to trap and then outgas helium (He) for alleviating void swelling in metals, but limited by atomic-level thin film deposition that is difficult to scale-up for industrial production. In this work, we proposed an innovative strategy that could generate semi-coherent homophase interfaces in a same grain by varying surface energy density assisted by high-temperature graphene (Gr) deposition. This strategy transforms strain energy and surface energy, two originally distinctive processes into successive processes, and demonstrates experimentally and theoretically by introducing {111} copper (Cu) in a {100} Cu grain. Subsequent He implantation and electrical resistivity measurement results suggest that high-density MDAs originated at this {111}/{100} interface could form stable He nanochannels near Cu surface with Gr assistance, manifesting by ultra-low increased ratio of the electrical resistivity (i.e. ~3800% of Cu vs. ~90% of Gr/Cu) after He implantation. Finally, the present findings may provide a new strategy for efficiently managing He and achieving surface protection of advanced metals, merely by depositing a super-rigid material on metal surface to greatly reduce surface energy density.

36 MATERIALS SCIENCE↗

Local chemical ordering of a neutron-irradiated CrFeMnNi compositionally complex alloy

While ion-irradiation studies are a critical first step in studying compositionally complex alloys (CCAs) for nuclear applications, they do not capture all the microstructural changes occurring under the low irradiation dose rates and different particles’ scattering patterns experienced in a nuclear reactor setting. To explore these phenomena in reactor-relevant conditions for the first time in CCA, the single-phase solid-solution Cr 10 Fe 30 Mn 30 Ni 30 was neutron irradiated up to 6.61 displacements per atom at 395 and 579 °C. Irradiation-enhanced local chemical ordering (LCO) well beyond the range of short range ordering was observed, and is predicted to be the precursor to the precipitation of a coherent Ni-Mn L1 0 phase and a Cr-rich α’ phase, though TEM analysis did not indicate the presence of either in any irradiation condition. The line density of faulted dislocation loops decreased from 6.47 to 1.69 ∙ 10 15 m -2 from 3.43 to 6.61 dpa at 579 °C despite no appreciable faulted loop content in the unirradiated material. LCO is expected to increase the complexity of the energy landscape within this alloy, restricting interstitial point defect mobility and creating local regions of greater stacking fault energy. These contribute to the negative correlation between irradiation dose and faulted dislocation loop density in this study, as well as the lack of void swelling observed.

36 MATERIALS SCIENCE↗

Perspectives and challenges of ultra-high temperature ceramics for fusion plasma-facing applications

Ultra-high temperature ceramics (UHTCs) offer several potential advantages as plasma-facing components (PFCs) in fusion reactors due to their extreme melting points, tailorable thermal conductivity, and attractive unirradiated mechanical properties including fracture toughness comparable or superior to tungsten. Here, recent developments and material properties of UHTCs are briefly reviewed, along with an overview of limited studies on their responses to neutron irradiation and an evaluation of plasma-surface interactions. Five key research pathways, primarily focused on irradiation effects, for advancing UHTCs in PFC applications are discussed: (1) assessing irradiation effects on the coupled thermal–mechanical performance (2) addressing the lack of studies on irradiation, plasma-surface interactions, and their synergistic effects; (3) investigating high-temperature (>1000 °C) neutron irradiation effects critical for PFC performance; (4) optimizing multi-component UHTC compositions or composites to improve thermal or mechanical properties; (5) enhancing radiation resistance to mitigate microcracking and void swelling through strategies such as increasing sink strength by reducing grain size, introducing fine particles, and leveraging complex concentrated alloy concepts.

36 MATERIALS SCIENCE↗

Radiation response of FeCrAl-coated Zircaloy-4

Coating the surface of Zircaloy-4 light water reactor fuel cladding tube is of considerable interest for enhancing its accident tolerance. In this study, thermal annealing of FeCrAl-coated Zircaloy-4 at 725 °C for 500 h, was used to induce interfacial reactions between Zircaloy-4 and FeCrAl. The interface zones were then irradiated by 3.5 MeV Zr ions at 400 °C, up to 50, 100, 150 peak dpa values. Transmission electron microscopy (TEM) and scanning TEM were used to characterize microstructural and composition changes before and after ion irradiation. Three interfacial phases were identified: FeZr 3 , (Fe,Cr) 2 Zr, and ZrC. The widest intermetallic layer, FeZr3, had large grains. The narrower phases, (Fe,Cr)2Zr and ZrC, contained small grains and were often mixed. The unexpected observation of the ZrC phase was attributed to the presence of very small impurity level concentrations of carbon in the powder material. No void swelling was observed in any of the phases, including the FeCrAl coating and Zircaloy-4 substrate. (Fe,Cr) 2 Zr, however, fully amorphized after irradiation, even at the lowest dpa.

36 MATERIALS SCIENCE↗

Microstructural characterization of cold-worked 316 stainless steel flux thimble tubes irradiated up to 100 dpa in a commercial Pressurized Water Reactor

Two flux thimble tubes (FTT) made of 15% cold-worked 316 stainless steel (SS) were harvested from Ringhals Pressurized Water Reactor (PWR) Unit 2, with peak damages of 76 and 100 displacements per atom (dpa) after 29 and 34 years’ service, respectively. Specimens sectioned from parent tubes were comprehensively characterized with nominal damage levels of ~0, ~41, ~74, 76, and 100 dpa at a nominal temperature range of 285-323 °C. Both FTTs contained helium and hydrogen gases as transmutation products. The helium follows a production rate of ~9.8 appm/dpa, while environmental factors complicate hydrogen production obscuring an exact H/dpa ratio. Irradiation-induced dislocation loops, nano-cavities, solute clusters, and microsegregation were all observed. The dislocation loops and nano-cavities indicated saturation at 41 dpa. The solute clusters continued to evolve with Ni-Si clusters formed at 41 dpa, and Ni-Si-Mn-P clusters formed at 74 and 100 dpa, but neither clusters exhibited distinct diffraction patterns at any damage levels. Solute clusters were observed to frequently be co-located with dislocation loops, but fully decorated loops were rarely detected. Significant radiation-induced segregation (RIS) was observed around grain boundaries at all damage levels. The modified inverse Kirkendall (MIK) model captured the RIS behavior of major elements. Large cavities within or around an Mn-S rich region were observed for the first time. Through all the damage levels, void swelling is always below 0.05%, making significant dimensional change unlikely in core internals when used at similar conditions. Meanwhile, the role of overwhelming nanocavities, presumably helium bubbles, should be considered in other potential degradation mechanisms, including irradiation-assisted stress corrosion cracking, embrittlement, and loss of fracture toughness, which remain the concerns for extended operation of nuclear power plants.

Post Irradiation Examination, Isotope Dilution Mas↗