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Comparative study between experimental measurements and model predictions of bubble rise velocity in molten LiCl-KCl

This research investigated the shape and rise velocities of gas bubbles (helium, nitrogen, argon, and krypton) in molten LiCl-KCl at 500 °C using a specialized optical visualization apparatus. The apparatus features a custom quartz rectangular prism cell housed in a furnace, enabling the application of the shadowgraph measurement technique. Bubbles with diameters between 0.45 and 3.2 mm were produced via a capillary, and their equivalent diameters and rise velocities were analyzed using high-resolution imaging and centroid tracking algorithms. Important non-dimensional parameters were calculated to characterize behavior. Bubbles with 0.03 < Eo < 1.32, 17 < Re < 718, and Mo order of 10 -11 were generated in the molten LiCl-KCl, revealing that bubbles with diameters less than 1.46 mm remain spherical, whereas those with larger diameters are ellipsoidal. The transition and oscillation onset for bubble shape occurred at larger diameters than those previously observed in air–water systems. Comparative analysis of the gas-molten salt data against existing air–water bubble rise velocity correlations highlighted inaccuracies in predictions, particularly across the different bubble regimes. An existing correlation was calibrated to the molten salt data to improve the bubble velocity predictions. In conclusion, this study contributes essential experimental data for the design and safety evaluation of molten salt reactors and offers insights for the optimization of sparge systems for fission product removal.

Bubble rise velocity

MOSCATO Development and Integration in Fiscal Year 2025: Implementation of Multiphase, Multiphysics Modeling Capabilities for Molten Salt Systems

MOSCATO (Molten Salt Chemistry and Transport) is a multiphysics code that provides high-fidelity, coupled simulations of fluid flow, heat transfer, mass transfer, chemistry, electrochemical phenomena, and alloy corrosion for molten salt systems. In FY25, significant developments were made to the code package, enhancing its capabilities for modeling all relevant phenomena within operating moltens salt reactors (MSRs). The developments and activities in FY25 included: 1. Implementation of Level-Set methods to enable modeling of single-bubble behavior in molten salts. In FY25, the Level-Set two-phase flow modeling implementation was improved to simulate single bubble behavior with molten salt media. The large density and viscosity ratios between typical gases and molten salt liquids present challenges for these types of numerical solvers. With enhancements to the pressure projection method, MOSCATO’s Level-Set solver was able to be successfully validated to experiments related to helium bubble rise in stagnant molten salt. The simulated bubble rising velocity showed reasonable good agreement with experimental measurements. The bubble shape and dynamics were also visually compared with experimental snapshots, demonstrating a good qualitative match. 2. Generation of mass transfer correlations for multiphase flow systems. To enable calculations of the tritium transport across the interface between gas bubbles and salt, we modeled high- Schmidt-number mass transfer around a sphere across a broad range of Reynolds numbers. The mesh near the sphere surface was highly refined to resolve steep concentration gradients caused by the low diffusion coefficient. Literature-based mass transfer correlations were compared with the numerical results, and modifications were proposed to improve agreement, particularly at higher Schmidt numbers. These mass transfer correlations were subsequently provided to other national laboratories to help enable high quality mass transfer simulations using lower-order solvers under development within the NEAMS program. 3. Preliminary implementation of a bubbly flow solver. To model bubbly flow in molten salt, we implemented a bubbly flow solver for void fractions less than 5%. To do so, an algebraic relative velocity model that assumes small bubbles with rapid momentum equilibration was added to MOSCATO to compute bubble velocities. Preliminary comparisons with experimental data showed reasonable agreement, and further improvements are underway. 4. Generation of mass transfer correlations for MSRE subchannel The Molten-Salt Reactor Experiment (MSRE) was a landmark historical project that demonstrated the feasibility of molten-salt reactor technology. The MSRE campaign also generated a significant body of experimental data and reports that continue to support molten-salt–related research. In this report, the MSRE core subchannel was used as the reference geometry for a mass transfer study performed with MOSCATO. The geometry and computational mesh were adapted from a previous study, providing adequate resolution for the relatively low Reynolds number in this case. Additional mesh refinement was applied to reach higher Schmidt numbers, enabling the derivation of a reliable mass-transfer correlation for the present scenario. 5. Simulations of oxygen ingressions into molten salt. In the previous fiscal year, we initiated a study to simulate oxygen ingression in stagnant salt. As oxygen enters the salt through its surface, it reacts with Ce 3+ to form solid CeO 2 and other reaction products. To more fully capture the complex diffusion-convection-reaction mechanisms, capabilities for modeling natural convection in the salt vessel were added. These were needed as the flow of the ingressed gas induced flow in the salt caused by surface shear and non-isothermal effects. With these updated physics in place, we were able to successfully reproduce the experimental results for the rate of change of CeCl 3 concentrations versus time. 6. Flow corrosion model validation. In FY24, MOSCATO’s corrosion model was validated against static corrosion experiments. In FY25, this work was extended to a flow corrosion experiment, where FLiNaK salt was driven by natural convection, with initial salt impurities to initiate corrosion. Despite uncertainties in parameters such as elemental diffusion coefficients in the alloy and unknown H + concentrations, the simulations achieved good agreement with experimental results, especially in predicting sample mass losses.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Additively manufactured refractory high-entropy alloys with superior radiation resistance

Refractory high-entropy alloys (RHEAs) are promising candidates for next-generation nuclear and high-temperature applications. Among many approaches to manufacture RHEAs, additive manufacturing (AM) represents the most recent and advanced metal manufacturing method which allows near-net-shape manufacturing to reduce material waste and post-processing time. However, performance of AM RHEAs under complex irradiation conditions remains largely unexplored. Here, in this study, we demonstrate for the first time the response of directed energy deposition (DED) AM quaternary RHEAs (HfTaVW, CrTaVW) subjected to sequential dual-beam ion irradiation, consisting of helium pre-implantation followed by high-dose heavy ion bombardment. Compositions of DED AM RHEAs were selected using Monte Carlo (MC) simulations based on a cluster expansion (CE) Hamiltonian parameterized by density functional theory (DFT). Post-irradiation microstructural characterization revealed that the AM RHEA maintained remarkable stability, with suppressed helium bubble growth and reduced defect accumulation compared to conventional alloys. Even at high doses (∼100 dpa), the alloy exhibited no void swelling, a low density of dislocation loops, and no evidence of severe degradation. These results highlight the intrinsic ability of AM-derived microstructures and multicomponent chemistry to synergistically mitigate irradiation effects. Our findings establish AM RHEAs as a class of materials with superior resistance to radiation damage under conditions relevant to advanced fusion and fission environments and demonstrate the importance of sequential ion beam studies in evaluating their long-term performance.

36 MATERIALS SCIENCE

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

2024 Second Half Semi Annual Report: Modeling plasticity-mediated flow in metals with pressurized cavities

The objective is to better predict the bulk-scale mechanical behavior of porous metals that have over pressurized cavities (e.g., irradiated metals with helium bubbles) by quantifying the complex coupling among cavity aspects (e.g., size distribution, inhomogeneous overpressure values, spatial arrangement) and metal properties (e.g., rate-dependency, crystallographic lattice). This requires up-scaling local mechanical fields from the single crystal scale and will be accomplished using a homogenization approach that combines full-field numerical simulations, analytical formalisms, and physics-informed machine learning to produce symbolically-defined constitutive equations (e.g., gauge functions). These equations will satisfy the objective because they enable computationally efficient predictions that approach the accuracy of computationally expensive full-field numerical simulations, abide by theoretical requirements (e.g., conservation of energy, work conjugacy), and retain the transparency of analytical models.

36 MATERIALS SCIENCE

Impact of position and density of nanoscale voids on fracture initiation in iron from phase field fracture simulation

Understanding the impact of these bubbles on crack propagation, like that of helium bubble-induced cracking in irradiated materials is incredibly complex. A useful first study towards understanding bubble effects on fracture is to examine how voids impact fracture first. In this work, we used phase-field fracture simulations to examine the influence of voids and their distribution on Mode I fracture in Fe. Assuming brittle fracture, two simulation configurations were considered: (1) nanoscale systems with one or two voids, and (2) nanoscale systems with an experimentally relevant distribution of voids, with up to 20% void area. Results from simulations with one and two voids showed that voids within 10 nm of a crack tip reduce the stress required for crack growth, with the magnitude of reduction depending on void-to-crack orientation. Comparisons with linear elastic fracture mechanics and evaluation of one versus two void systems revealed deviations from linear superposition, implying complex interactions between void and crack tip stress fields. In multi-void simulations, as void sizes increase, the nearest void to the crack tip exerts a greater influence on fracture stress than the overall porosity. Furthermore this study provides valuable insights into the relationship between void size and concentration, and the stress necessary for crack growth, marking a step forward towards understanding He bubble-induced fracture in ferrous materials.

36 MATERIALS SCIENCE

Influence of implantation temperature and He implantation-induced defects on morphological evolution of co-deposited Cu-Mo nanocomposites

Here, we investigate the effect of high-temperature helium (He) implantation on microstructural evolution in physical-vapor-co-deposited nanocomposite thin films of copper (Cu) and molybdenum (Mo). The microstructure morphologies of He-implanted and He-free domains are characterized using transmission electron microscopy and statistical analysis. High implantation temperatures (500°C and 750°C) lead to coarsening of Cu and Mo domains and their eventual reorientation. The microstructure evolution in He-implanted and He-free domains is comparable, indicating that implantation-induced defects do not accelerate the coarsening of the nanocomposite as compared to annealing alone. This observation contrasts with previously reported effects of implantation-induced defects on single-phase nanocrystalline metals, which include enhancement of grain growth by increasing self-diffusivity or its inhibition by pinning of grain boundaries.

36 MATERIALS SCIENCE

Compositionally-driven surface nanostructuring on refractory compositionally complex alloys under low energy helium bombardment

Additive manufacturing enables user-defined control of the compositional complexity, opening new design spaces for complex concentrated alloys (CCAs). Refractory CCAs may offer enhanced performance in the divertor region of a fusion reactor environment where plasma-facing materials will be subject to high temperatures, low energy He and D particles, and 14 MeV neutrons. In this work, specimens with the nominal composition of NbTaMoTi, NbTaMo, NbTaTi, and NbTa were fabricated via directed energy deposition (DED) then bombarded with 40 eV He ions to a fluence of 2x10 26 m −2 at ∼ 1000 K. Post irradiation, the surface morphology and composition were examined with electron microscopy and x-ray photoelectron spectroscopy to offer information on the spatial distribution of surface nano-structuring. Sub-surface He bubbles driving the nano-structuring were examined with electron microscopy techniques. Analysis indicates the local composition directly influences the He bubble and tendril size, while the region with the highest complexity showed the shortest nano-structuring. Molecular Dynamics simulations complement the experimental results, showing comparable helium bubble growth and migration as a function of compositional complexity. This work demonstrates the compositional dependence of surface nanostructure formation of compositionally complex alloys, important for future design of complex plasma facing materials in fusion reactors.

Complex concentrated alloys

MX precipitate behavior in an irradiated advanced Fe-9Cr steel: Helium sequestration and cavity swelling performance

This work is the third and final part in an initial series on addressing the behavior of MX precipitate stability in an advanced Fe-9Cr reduced activation ferritic/martensitic (RAFM) alloy under fusion-relevant ion irradiation conditions. Here, the helium trapping properties of MX precipitates are investigated across varying damage levels (15–100 dpa), temperatures (400–600 °C), and helium doses (10–25 appm He/dpa) using sophisticated dual ion beam experiments and electron microscopy. Results indicate that individual MX precipitates efficiently sequester helium in the form of nanoscale bubbles at the precipitate-matrix interfaces near the peak swelling temperature (∼5 bubbles/precipitate at 500 °C). Swelling was primarily due to matrix cavities. The Fe-9Cr alloy reached 2% swelling by 100 dpa, suggesting a shift to steady-state swelling around 50 dpa at 500 °C. Furthermore, MX precipitate dissolution beginning at 15 dpa did not coincide with this onset of steady-state swelling.

Dual ion irradiation

Test Report for the Regulatory Testing of the Welded Isotek-SFC-W-3 Special Form Capsule

Two prototypes the welded ISOTEK-SFC-W-3 special form capsules (SFCs) of the same design were evaluated to determine if the requirements of Title 49, Code of Federal Regulations (CFR), Part 173.469, Tests for Special Form Class 7 (Radioactive) Materials, were met. The results of the special form tests are documented in this test report. This report describes the special form testing activities performed on the two welded ISOTEK-SFC-W-3 capsules. The test units were designated as TU-1 and TU-2. TU-1 was subjected to leak testing, percussion testing, and impact testing. TU-1 was leak tested using the leak rate test specified in 49 CFR 173.469(a)(4)(i). The impact test on TU-1 was conducted according to the requirements in 49 CFR 173.469 (b)(1). The percussion test that was carried out on TU-1 was conducted in accordance with 49 CFR 173.469 (b)(2). TU-2 was subjected to a leak rate test as specified in 173.469(a)(4)(i) and a heat test as specified in 49 CFR 173.469(b)(4). Each test unit was leak tested before and after these respective tests. The leak rate tests performed were helium back-pressure tests and bubble tests, as specified in American National Standards Institute (ANSI) N14.5-2014. The measured leak rates were converted to standard condition leak rates as specified in American Society for Testing and Measurement (ASTM) E 493. The determined standardized leak rates obtained from the test and the calculations for all the test units met the requirements for special form certification. The testing was performed under the direction of the Oak Ridge National Laboratory (ORNL) Package Testing Program (PTP).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Assessment of simulated and observed cavitation-induced erosion damage in Spallation Neutron Source target vessels

Cavitation-induced erosion damage in different Spallation Neutron Source (SNS) target designs are simulated using explicit finite element–based techniques and compared with observations of erosion in targets after operation. The efficacy of the previously developed method, called saturation time, was evaluated using erosion-damaged samples from new target designs. A new metric called maximum bubble size was implemented under the rationale that larger cavitation bubbles will collapse more intensely. The maximum cavitation bubble size over 1 ms of simulated time was calculated based on the Rayleigh–Plesset equation for each element integration point and presented as a contour map at the vessel surface for assessing with erosion observations. SNS targets are now operated with helium gas injection to reduce cavitation damage. A simulation method using a material model for the mixture of mercury and gas bubbles was recently developed and used to account for the effect of small gas bubbles on the structural response of the target vessel. Furthermore, this work compares the new method's results with observed cavitation damage. Maps of the calculated maximum bubble size for targets operated with and without gas injection were compared with photographs of erosion damage observed in SNS targets. The patterns in maximum bubble size maps correlated well with observations of erosion patterns in target vessels after service. Advantages and challenges of the maximum bubble size simulation technique are provided, and differences between results from the previous and the newly proposed metric are discussed.

Jiang, Hao

Microstructurally informed synchrotron x-ray analysis revealing helium defect transitions in ultrafine grained tungsten

The formation of insoluble gaseous defects in materials due to nuclear transmutation or ion implantation involves the diffusion of impurity atoms to form atomic defect clusters that coalesce into bubbles or cavities and ultimately degrade the material properties. Transmission electron microscopy (TEM) is limited in its ability to resolve sub-nanometer gas clusters whereas X-ray diffraction (XRD) provides information pertaining to local atomic changes. Here, in this study, helium (He) implanted ultrafine grained tungsten is explored through a multimodal defect characterization campaign combining TEM-informed Small Angle X-ray Scattering (SAXS) analysis, XRD lattice parameter measurements, and nanoscale He cluster quantification from a region of reciprocal space accessible via Wide Angle X-ray Scattering (WAXS). Moderate elevated temperature implantations are shown to produce high concentrations of sub-nanoscale He clusters and small, homogeneously distributed cavities, which collectively are linked to lattice expansion and further substantiated through complementary atomistic simulations. Increased implantation temperatures encourage the diffusion of these defects to the grain boundaries (GBs), leading to lattice relaxation and the growth of large GB cavities manifesting as bimodal size distributions in the SAXS analysis. Overall, our results demonstrate the utility of multimodal synchrotron X-ray analysis in bridging the gap between microscale He cavity quantification and atomic-scale defect analysis.

36 MATERIALS SCIENCE

Radiation damage in tungsten under high-energy He-ion irradiation

Tungsten (W) is a primary candidate for plasma-facing components (PFCs) in fusion reactors and hybrid fission-fusion reactors. However, W suffers from severe microstructural damage under Helium (He) ion irradiation in operation conditions. Key irradiation parameters, including incident ion energy, fluence, and irradiation temperature, are known to determine the formation of He bubbles and dislocation loops, which ultimately lead to the degradation of mechanical properties, such as radiation hardening and ductile-to-brittle transition temperature (DBTT) shifts. Various strategies, for instance, interface engineering and alloying, have been developed to enhance He irradiation tolerance in W to address these challenges. Studies in the recent two decades have enhanced the understanding of the underlying mechanisms that drive defect evolution and mechanical performance degradation, thereby offering more insights into the design of more resilient W-based materials for extreme environments.

Liu, Yinghang [Purdue University]

Radiation damage effects in beryllium for next generation neutrino beam targetry (Final Technical Report)

Current and future high-power accelerators put severe requirements on materials used for target and beam windows and target facilities have been recognized as a critical challenge in development of future particle accelerators. In accelerators, window and target materials are exposed to extreme conditions, which include bombardment with very high energy protons (1- 100 GeV) and thermomechanical shock waves. Radiation can cause direct damage in the material, and it leads to production of transmutation products (especially helium), both phenomena having a potential adverse effect on the stability and durability of the target/window material. At high enough temperatures, He can aggregate to form gas bubbles, which in turn cause significant dimensional changes (swelling), enable easy crack propagation, and eventually cause failure by fracture. On the other hand, if the temperature is too low, radiation damage accumulates in the form of internal defects (e.g., dislocations), leading to hardening and a decreased ductility of the material. In this project, we will focus on beryllium since it is considered to be one of the candidate materials for beam windows and targets in the next-generation proton accelerators, e.g., the Long Baseline Neutrino Facility (LBNF). Radiation effects in Be have been studied in the context of nuclear fusion reactor applications. However, key differences exist between reactor and accelerator conditions, including neutron vs. proton irradiation, continuous vs. pulsed beam flux, much higher energies of bombarding particles in accelerators, and higher operating temperatures for typical reactors. For example, the impact of beam pulsing on the radiation damage and the He bubble kinetics is largely unknown. While results obtained on Be from fusion research might not be directly transferrable to understanding target materials, there is an opportunity to bring state-of-the-art tools from materials research in nuclear reactors to aid design of target and beam window materials in high-power accelerators. To this end, the overarching goal of this project are to develop an experimentally-validated computational framework capable of predicting radiation damage evolution in beryllium relevant to beam window and target conditions, focusing on He bubble formation and growth as a function of irradiation temperature. Our model will be based on the cluster dynamics formalism, where size distribution of defects and He bubbles is simulated as a function of time, temperature, and radiation dose. Parameters for the model will be taken from published experiments and from high-fidelity atomistic simulations proposed in this project. In addition, we will carry out a series of targeted ex-situ and in-situ dual-beam experiments using low-energy protons to provide critical data for validation of the model on the effects of radiation on He clustering, He bubble distribution, and dislocation loop density/size in proton irradiated Be.

36 MATERIALS SCIENCE

Isolated vesicles in submarine pumice: insights from the 2019 Volcano F eruption, Kingdom of Tonga

No reliable method can distinguish between subaerial and submarine pumice, but recent work shows that highly vesicular (total porosity, φ > 65%) submarine pumice from the 2012 Havre and 2021 Fukutoku Oka-no-Ba eruptions contains abundant isolated porosity (connectivity, C < 0.6). This differs from textural measurements of subaerial pumice with similarly high vesicularities, where high connectivities (C > 0.8) are often measured. To investigate the implications of this under-studied texture for bubble nucleation, growth, and coalescence dynamics at submarine eruptions, we analyze the textural characteristics of rafted pumice clasts from the 2019 submarine eruption of Volcano F, located along the Tonga-Kermadec Arc. We examined clasts collected while floating near the vent (50–200 km) and distally on the shores of Fiji (900 km). Using helium pycnometry and X-ray tomography (XRT), we quantified porosity and connectivity in 45 pumice lapilli, classifying them by vesicle macrotexture and edge morphology. Microvesicular clasts, the majority of which have breadcrust and cauliflower textures, exhibit the lowest connectivities (C = 0.61 ± 0.2), while macrovesicular clasts have high connectivities with C ~ 1. We propose that isolated porosity abundance varies according to clast location in the eruption column post-fragmentation. Microvesicular clasts erupted on the edges of the column and experienced high levels of seawater ingestion and subsequent quenching of the entire clast. Macrovesicular clasts, in contrast, erupted in the center of the eruption column and were thus thermally insulated, allowing magmatic bubbles in the molten pumice to nucleate, grow, and coalesce for longer. Our results and interpretation imply that low connectivity, microvesicular clasts preserve pre and syn-eruptive bubble processes at the 2019 Volcano F eruption.

Permeability

Lithium–Divertor Interactions and Helium/Hydrogen Trapping in Lithiated Metals (Final Technical Report)

The goal of this project was to develop a fundamental understanding of helium and hydrogen behavior in lithium, both in bulk and at interfaces with tungsten, in order to inform the design of lithium based plasma facing components for fusion devices. Over the course of the award, the project produced the first comprehensive, peer reviewed dataset describing helium energetics, migration behaviors, and defect interactions in lithium. The research demonstrated that helium behaves in ways not previously observed in any other body centered cubic (BCC) metal: its interstitial configurations are more stable than substitutional ones, and its migration barriers are extraordinarily low, in some cases more than an order of magnitude below those in tungsten or iron. These discoveries reveal that helium in lithium diffuses so rapidly that its transport may be dominated by translational motion rather than the vibrationally activated mechanisms that underpin conventional solid state diffusion. This work lays a scientific foundation for understanding gas retention, bubble formation, and wall evolution in lithium based fusion environments and provides new computational tools, most notably a newly developed Li–He interatomic potential, for advancing future modeling efforts.

36 MATERIALS SCIENCE

Effect of thermal oxidation on helium implanted pure iron

The impact of thermal oxidation on Helium (He) implanted pure iron (Fe) was investigated to experimentally evaluate how thermal oxidation influences the diffusion and distribution of He within the material. In case of the sample with the lowest dose (2 × 10 17 ions/cm 2 ), the thinnest oxide layer was observed compared to the non-implanted pure Fe. It is due to He nano bubbles implanted in the material, which hinder the diffusion of Fe ions necessary for forming the oxide layer. For the medium dose sample (5 × 10 17 ions/cm 2 ), the oxide layer was slightly thicker than that of the lowest dose, however it had more porous structure due to the numerous nano He bubbles. In addition, a large bubble region around 150–200 nm depth was generated. Here, the highest dose sample (1 × 10 18 ions/cm 2 ) was observed that the escape of He was accelerated by the large amount of nano He bubbles from within the metal, forming a porous Fe matrix on the top surface and an oxide layer that is very porous but thicker than those of lower doses.

He implantation