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Computational Modeling of Molten Salt Infiltration and Oxidation in Nuclear Graphite

Graphite is utilized as a moderator and reflector in advanced nuclear reactor designs due to its high thermal conductivity, neutron moderation properties, and resistance to radiation damage. However, its longterm performance and reliability are challenged by degradation mechanisms such as molten salt infiltration in molten salt reactors (MSRs) and oxidation in gas-cooled reactors (GCRs). These mechanisms can compromise the structural integrity and operational lifetime of graphite components, necessitating a more detailed assessment of their physical behavior. This report focuses on the development of computational models for molten salt infiltration and oxidation of graphite to aid the design and performance analysis of graphite components. For molten salt infiltration, a computational framework is developed that couples incompressible Navier-Stokes and phase-field model to simulate the penetration of molten salt into graphite?s interconnected pore structure. Initial model verification is performed using two-phase flows in two dimensions, demonstrating the models ability to capture fundamental physical behavior and agree with analytical solution. This framework is then applied to a realistic IG110 nuclear graphite , where a computed tomography extracted pore geometry is used to analyse the infiltration behavior of FLiNaK molten salt. This model provides insights into how the microstructure and other relevant parameters influence the transport pathways of molten salt into graphite, potentially offering a means to rapidly evaluate a graphite grade?s resistance to infiltration. For oxidation, the report details pore-scale mass and heat transport models, describing the diffusion of gases, reaction kinetics, and thermal effects. Additionally, this report highlights inconsistencies in the existing volume-averaged macroscopic model, particularly in upscaling of reaction kinetics and flux terms, and surface to volume transformations. These inconsistencies suggest that current formulations may not accurately capture the experimentally observed graphite oxidation process, highlighting the need for improved model development. This work advances the development of physics-based computational models for graphite degradation, contributing to improved predictive models for next-generation nuclear reactor designs. Future efforts will focus on refining the infiltration model to address non-physical behaviors and enhance its robustness. Additionally, for oxidation, further studies will employ the principles of volume averaging to rigorously derive the upscaled equations, potentially in collaboration with subject matter experts.

Computational Modeling of Molten Salt Infiltration

Low-energy measurement of the 25 Mg ⁢(𝛼,𝑛)⁢ 28 Si reaction via neutron spectroscopy

During core helium and carbon burning in massive stars, neutrons are produced mainly by the 22 Ne⁢ (𝛼,𝑛) ⁢25 Mg reaction. Some of these released neutrons are captured by heavy seed nuclei from previous nucleosynthesis events, resulting in the slow production of many of the elements between masses 60 ≤ 𝐴 ≤ 90 via the weak 𝑠 process. Determining the overall neutron flux available in this environment is one of the main challenges in modeling its contributions to heavy element production. Not only must the reaction rate be well defined for the primary neutron source, but the rates of neutron poison and recycling reactions must also be well determined. One critical reaction in the simulation network is 25 Mg ⁢(𝛼,𝑛) ⁢ 28 Si. This reaction, together with 25 Mg ⁢(𝑛,𝛾)⁢ 26 Mg and 25 Mg⁢ (𝛼,𝛾) ⁢ 29 Si, determine how 25 Mg nuclei affect the available neutron flux. Past attempts to measure the 25 Mg ⁢(𝛼,𝑛)⁢ 28 Si cross section using neutron moderator counters have been greatly hindered by lower-𝑍 background reactions. Here, in the present work, neutron spectroscopy with deuterated liquid scintillator detectors has been used. The experimental spectra have been analyzed by applying spectrum unfolding techniques to achieve improved background discrimination for the 25 Mg⁢ (𝛼,𝑛)⁢ 28 Si reaction at low energies, down to 𝐸 𝛼 = 1.75 MeV. The separation of the different background contributions gives further insight into the results of previous moderator counter measurements and the measurements lead to a revised and more reliable determination of the reaction rate.

hydrostatic stellar nucleosynthesis

Degradation of Be 2 C at conditions expected in molten salt environments

This technical report is in submission of completion of the Level 4 milestone number M4AT-25OR1101021, titled “Degradation of Be 2 C at conditions expected in molten salt environments”, for the AT-25OR110102 “Beryllium Carbide as moderator for MSRs—ORNL” WBS number 2.04.11.01 within the larger Advanced Reactor Technologies program at Oak Ridge National Laboratory. This effort is an initial study of the viability of Be 2 C as a future neutron moderator for molten salt reactors and other high-temperature reactors. The research was awarded funding in September 2022, and this Level 4 milestone presents the work that completed by the end of July 2025. This work is a collaboration between Oak Ridge National Laboratory and the University of Michigan.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Back to functional hydrides: Effects of neutron-irradiated microstructure on hydrogen retention in yttrium hydride

Functional hydrides are promising candidates for advanced nuclear reactors, particularly in portable or transportable applications, due to their high hydrogen-retention capabilities, enabling efficient neutron moderation, and compact reactor design. However, hydrogen mobility in hydrides at elevated irradiation temperatures poses significant technological challenges, necessitating a comprehensive understanding of their irradiation behavior. Furthermore, this study investigated the microstructural and chemical stability of neutron-irradiated yttrium hydrides to assess their hydrogen-retention capacity. A targeted literature review was also conducted to contextualize neutron-irradiation effects on functional hydrides with regards to structural stability and hydrogen retention. Experimental characterizations revealed that, at high temperatures, irradiated hydrides retained their phase stability, which was likely enhanced by irradiation-induced microstructure evolution. Notably, an amorphous yttrium and oxygen -rich surface layer was present at the free surface of the hydride. Its thickness decreased while a continuous crystalline Y-O-rich layer was formed with increasing neutron damage. Additionally, the number density of dislocation loops and cavities generally increased as a function of neutron dose. First-principles calculations of hydrogen behavior within yttrium vacancy clusters in yttrium hydrides demonstrated vacancy-size-dependent hydrogen stability and configuration, highlighting the role of vacancy geometry in regulating hydrogen retention. Thus, the presence of irradiation-induced dislocation loops and cavities were hypothesized to improve hydrogen retention. Collectively, these findings advance the understanding of hydride behavior under neutron irradiation as well as their technological readiness for portable or transportable nuclear reactors.

Defect clusters

Nuclear-pumped CW lasing of the He-Ne system

The gain for the 6328-A laser line for the nuclear excited He-Ne system has been measured to 300 Torr pressure at thermal neutron flux levels from 2 x 10 to the 7th to 1 x 10 to the 14th n/sq cm sec. In order to estimate small:signal gain, the gain was also measured as a function of input intensity. For demonstration of feasibility of CW operation of nuclear pumped lasers, a cavity was operated and lasing was observed. Although the laser output was small, it is concluded that lasing in a CW mode has been achieved with He-Ne using moderate neutron flux levels.

Carter, B. D.

Postirradiation Examination of HFIR-Irradiated Yttrium Hydrides

The US Department of Energy Microreactor Program is developing compact, high-temperature microreactors that require robust neutron moderators. Known for its high hydrogen retention and structural stability, YH x is a leading candidate for this purpose. As part of an ongoing evaluation, Oak Ridge National Laboratory conducted post-irradiation examinations on YH x specimens irradiated in the High Flux Isotope Reactor under the legacy Transformational Challenge Reactor program, focusing on their structural integrity, hydrogen retention, and thermal properties. The post-irradiation examination campaign primarily examined specimens from two irradiation campaigns, covering a range of hydrogen-to-yttrium atomic ratios (H/Y), neutron damage levels (0.1–2 displacements per atom), and targeted irradiation temperature of 600°C. The investigations included electron microscopy, high-energy x-ray diffraction, laser flash analysis, differential scanning calorimetry, and SiC thermometry analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Direct NeTS sampling of nuclear graphite $S(α, β, T)$ in Serpent

For advanced reactor applications, Neural Thermal Scattering (NeTS) modules were developed to predict the thermal scattering law (TSL or $S(α, β, T)$) of a nuclear graphite neutron moderator. NeTS are multi-layer, feedforward artificial neural networks, which act as universal function approximators designed for TSL datasets. In this case, a 4-layer neural network with 164 neurons per layer is trained using FLASSH evaluated data in PyTorch and serialized as a torchscript dictionary to predict $S(α, β, T)$ on-the-fly. Relative, absolute and maximum percent deviations of NeTS from File 7 data generated using the FLASSH code are on the order of 0.01%, 0.1% and 1%, respectively, with low inference latencies of 0.000172 s per $S(α, β, T)$ at a given temperature. Capturing the full dimensionality of possible inelastic neutron-lattice interactions, NeTS functionality is embedded in the Serpent Monte Carlo code, where $S(α, β, T)_{NeTS}$ sampling is conducted on-the-fly and compared to ACE look-up-tables for predicting TREAT criticality. k-eff differences between sampling algorithms of 6 pcm are observed and are within the order of Monte Carlo uncertainty. Compared to discrete and continuous-energy ACE files (30 MB and 131 MB per temperature), the NeTS format is on the order of 200–300 kB for a continuous-temperature, interpolation-free representation of $S(α, β, T)$ and cross sections. NeTS-in-Serpent runtimes comparable with ACE look-up tables are achieved by scaling NeTS for high performance computing architectures with hybrid OpenMP + MPI parallelization. This work validates a novel, self-contained reactor physics framework for predictive cross sections, and demonstrates a general methodology for embedding modern machine learning libraries within existing neutronic analysis frameworks.

Nuclear Criticality Safety Program (NCSP)

Historic and modern nuclear graphite impurities: Pathways to improved waste strategies

Graphite has been used in large volumes as a structural material and neutron moderator since the earliest days of nuclear fission. However, no international consensus exists on the disposal of irradiated graphite, leaving much of the historic radioactive graphite inventory in interim vault or silo storage. With several new graphite-moderated reactors planned or under construction, the issue of graphite waste management is becoming increasingly urgent. This paper reviews and quantifies impurities in both historic and modern nuclear graphite, with emphasis on nitrogen—responsible for much of the 14 C inventory—and chlorine, which plays a critical role in repository performance and design. Modern graphites, benefitting from stringent quality-control measures developed for non-nuclear industries, meet or exceed the ASTM Ultra-High Purity nuclear standards, even without halide purification. Both chlorine and nitrogen concentrations have declined over time. For chlorine, identified as a key impurity influencing U.S. waste repository design, we propose a target of 0.1 appm in as-fabricated billets as a reasonable benchmark. Nitrogen sources are traced throughout the graphite production process, with surface and bulk concentrations characterized for all materials studied. Modern graphites commonly exhibit nitrogen levels below 5 appm, with values approaching 1 appm achievable. Using such reduced-nitrogen grades is critical to keeping graphite-induced radioactivity below the greater-than-Class-C waste threshold, thereby avoiding disposal cost penalties of nearly an order of magnitude.

Chlorine

Physical and thermal property changes under uniform oxidation in nuclear graphite

Material property changes of fine- and medium-grain nuclear graphite grades were measured after subjection to uniform oxidation. The cores of high temperature reactors are composed of large nuclear graphite block components. Here, these large core components are designed to provide neutron moderation and reflection, create a large thermal sink to assist in operational control, and form the solid core structure containing the nuclear fuel, coolant channels, and the safety critical channels for control rod insertion. Oxidation is a principle degradation mechanism affecting all aspects of the nuclear graphite component functions. This study addresses the underlying physical property changes of nuclear-graphite components for oxidized mass loss ranges beyond the current recommended ASME code rule limits to ensure structural integrity within the graphite components (a maximum mass loss = 10%).

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Sensitivity study of hydrogen Soret transport in yttrium Hydride-Based nuclear fuel

Yttrium hydride is an excellent solid neutron moderator material for high temperature nuclear reactor applications due to its high hydrogen density and exceptional hydride stability at high temperatures. Despite these attractive characteristics, the details of how hydrogen behaves within yttrium hydride while temperature gradients exist are still not well understood. The evolution of the hydrogen composition profile resulting from a temperature gradient requires knowledge of hydrogen’s heat of transport, a critical parameter that has not yet been measured for this material. In this work, we perform hydride redistribution, hydrogen dissociation, and hydrogen leakage calculations while varying the Soret heat of transport of hydrogen in yttrium hydride to elucidate the sensitivity of hydride stability under temperature gradients to this parameter. This study analyzes hydride stability of a hypothetical uranium-yttrium hydride nuclear fuel design during operation of a high temperature liquid metal-cooled nuclear reactor. Assuming U-YH x could be fabricated in a physically stabilized manner, this fuel system can likely maintain hydride stability while operating at very high power densities and temperatures. We find that even though the hydrogen dissociation pressure in the gas gap does vary by several percent as the heat of transport temperature parameter is varied, the hydrogen content in the U-YH x fuel meat is relatively insensitive to this parameter over the course of a high burnup fuel cycle; this is due to yttrium hydride’s excellent hydrogen retention under the high temperature conditions considered here. Here, this suggests that hydride stability analyses are insensitive to the value of the Soret heat of transport in U-YH x under steady state liquid metal-cooled reactor conditions. However, the susceptibility to internal gas overpressurization-induced stress-rupture of the cladding during a high temperature transient is more sensitive to this parameter due to the non-linear dependence of hydrogen gas dissociation pressure vs. composition and temperature.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Superionic-like diffusion in yttrium dihydride

For the next-generation high temperature microreactors, yttrium dihydride (YH 2 ) is an attractive solid state neutron moderator. Despite a number of recent investigations, the mechanism of hydrogen transport remains poorly understood. Experimental evaluations of diffusivity are inconclusive with large variations in diffusivities and activation energies. In this work, we perform ab initio molecular dynamics (AIMD) simulations on YH 2 for temperatures spanning 300 K to 1200 K. Our main finding is that YH 2 shows a superionic-like behavior with hydrogen atoms hopping from one native site to another above a characteristic temperature of 800 K. This correlated motion results in quasi-one-dimensional string-like displacements that enable the hydrogen atoms to diffuse rapidly. We confirm that the octahedral sites are mostly unoccupied, although channeling through them is the most favored pathway between lattice hops above 800 K. At the highest temperature of 1200 K, the string relaxation time is merely of the order of a few picoseconds, which indicates a liquid-like diffusive behavior. Based on the formation of spontaneous thermal vacancies, an order-disorder crossover temperature T α ~ 800 K is established for YH 2 with an activation energy of 0.83 eV for hydrogen diffusion in the superionic-like state.

Superionic-like Diffusion

Investigation of High-Temperature Compatibility of Select Oxides with Yttrium Hydride for Micro and Space Reactor Applications

Yttrium hydride is a promising material for a high-temperature neutron moderator in advanced micro and space reactors due to its high hydrogen density and relative thermal stability compared to other metal hydrides. However, yttrium hydride desorbs hydrogen rapidly at temperatures above 800°C, which is below the operational temperature range of some reactor designs. A hydrogen barrier coating of oxide on the hydride surface may inhibit hydrogen loss at 800°C and beyond, but the high-temperature compatibility between yttrium hydride and many oxides is currently unknown. The high-temperature compatibility of Al 2 O 3 , MgO, and Y 2 O 3 with YH 1.92 was examined by subjecting mixed oxide–hydride pellets to a 1200°C heat treatment then using a combination of diffractometry, microscopy, and spectroscopy to determine changes in the pellet composition as a result. Yttrium scavenged oxygen from both Al 2 O 3 and MgO to form Y 2 O 3 , resulting in significant loss of YH 1.92 . Yttrium reacted with reduced aluminum to form YAl 2 and several other compounds. Reduced magnesium volatilized above 1091°C and vacated the pellet. Only Y 2 O 3 did not appreciably react with YH 1.92 . Of the three oxides tested, only Y 2 O 3 was compatible with YH 1.92 at 1200°C based on the experimental criteria.

compatibility

Assessing the Impact of Large Removable Beryllium Reflector Experiments on HFIR Performance and Safety Metrics

This study investigated the effect of various removable beryllium (RB) experiment configurations on High Flux Isotope Reactor (HFIR) metrics to address increasing interest in these facilities for materials and fuels irradiation research. The RB reflector contains eight large and four small irradiation experiment facilities that offer excellent neutron flux conditions to perform fission and fusion reactor materials and fuels irradiation research. This work aims to outline acceptable RB configurations based on safety, performance, and programmatic metrics. This study assessed experiment effects on reactivity, cycle length, fission rate density distributions, and neutron flux distributions using the Shift, HFIRCON, and SCALE ORIGEN codes. Initial evaluations focused on generic experiment materials including aluminum plugs, stainless steel plugs, molybdenum plugs, and aluminum plugs with gadolinium shields. Subsequent analyses of MiniFuel experiments were performed to evaluate a heterogenous experiment, consisting of a more complex geometry and bearing several materials, and to test the correlations developed with the generic materials on a real experiment. Furthermore, the effects of neutron poison concentrations in the standard beryllium plugs were evaluated. When assuming a reference RB configuration with eight large fresh beryllium plugs, perturbed configurations with three aluminum plugs, one stainless steel plug, one molybdenum plug, one gadolinium-shielded aluminum plug, and one MiniFuel experiment resulted in a cycle length reduction of less than 1.3 days, the current threshold before requiring additional approvals. Configurations with five aluminum plugs, one stainless steel plug, one molybdenum plug, one gadolinium-shielded aluminum plug, and two MiniFuel experiments meet the 1.3 day limit if irradiated beryllium plugs are considered. Fuel element fission rate density distributions remained within safety limits, with maximum local increases under 9%. Neutron flux calculations revealed large thermal flux depressions inside and around the perturbed RB facilities, while epithermal and fast neutron fluxes increased because of reduced neutron moderation by the perturbed materials. These findings provide valuable guidance for optimizing RB configurations to balance safety and performance at HFIR.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS

Non-destructive structural characterization of graphite components using mechanical resonance and deep learning

As compared to conventional nuclear reactors, microreactors have the potential to significantly reduce construction timelines and capital costs, decreasing the barriers for advanced nuclear reactor technologies. However, the lower power output of these microreactors (typically < 20 MWe) creates challenging economics if operation and maintenance costs cannot be sufficiently reduced. The compact size of these designs presents an opportunity for comprehensive in-situ structural health monitoring to provide real-time feedback in order to reduce operational costs associated with maintenance and downtime. Many microreactor concepts use graphite for both in-core neutron moderation and as a structural material, which has typically required some form of periodic and laborious inspection. This report provides a description and assessment of recent work with graphite to couple acoustic-based experimental measurements and characterization with machine learning models to mature structural health monitoring capabilities and generate benefits for the nuclear microreactor industry. With resilient embedded sensors in development in other programs funded by the US Department of Energy’s Office of Nuclear Energy and elsewhere, the work described herein builds upon previously funded efforts to mature non-destructive testing technology that relates measured vibrational signatures to structural changes, using a combination of new experimental measurements and machine learning processing. Building on past successful demonstrations of predictive workflows to identify structural changes in a hexagonal stainless steel test article with excellent acoustic propagation, we first performed baseline characterization on graphite samples with canonical geometries to ensure compatibility and confidence in the applied techniques for a material with distinctly different mechanical properties. In contrast to efforts in previous years, we worked exclusively with unidirectional vibration data that is more comparable to those expected from the existing embedded sensor technologies which are suitable for deployment in a reactor setting. Established acoustic and modern machine-learning-based characterization approaches were applied to the resulting datasets from these simple geometries. Both approaches were found to be highly capable of detecting even small geometric irregularities amongst nominally identical samples. As such, we then moved to testing these approaches for detection of artificial local stress perturbations introduced into a more complex geometry: a hexagonal block with drilled holes. A main outcome of this work is that a generalizable ML workflow can be used to detect and predict the characteristics of small artificial anomalies in a graphite component with a relevant geometry. While this work was performed using surficial vibration data, we expect the approach to be flexible and viable for other monitoring scenarios, such as those with different arrangements or types of sensor arrays. As compared to previously funded efforts, an existing ML workflow based on neural networks was enhanced through the addition of recently developed Fourier neural operators. As applied to previously collected and new vibration datasets, prediction accuracies of anomaly characterizations were greatly improved with minimal added computational cost. As trained on small durations of vibration data (tens of seconds) collected over a realistic number of locations, the model was able to reliably determine the presence of a subtle stress anomaly and begin to provide location estimates. Such an approach is likely to be viable for more relevant reactor damage scenarios for graphite components, such as progressive crack growth or creep.

36 MATERIALS SCIENCE

Nuclear pumped laser modeling

A model for an indirectly nuclear pumped laser experiment was developed. The apparatus consists of the usual cylindrical neutron moderator enclosing a gas filled quartz cell. The quartz cell in this case has two concentric compartments; the larger output compartment is filled with He-3 and fluorescent gases which are coupled radiatively to the inner compartment which is filled with a lasing gas for efficient optical pumping. The fluorescent gas in this study was a mixture of Ar, Kr and F2. Perfluoroalkyliodide was chosen as the lasant material of the inner compartment. The degree of photoabsorption in the lasant gas was calculated. The kinetic efficiencies of various gas combinations in the outer fluorescence tube were then evaluated in order to maximize the fluorescence output in the iodine pump band.

Wilson, J. W.