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DOE OSTI2025

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↗

DOE OSTI2026

Part-scale evolution of fine-scale microstructural heterogeneity in solid-state additive manufacturing

Current solid-state additive manufacturing methods, refined through costly and time-consuming trial and error, have spurred interest in computational models that replicate material behavior under typical thermomechanical conditions (e.g., strain-rate ~ 102 s−1). These models, however, struggle to capture time-dependent microstructural evolution. In this work, Additive Friction-Stir Deposition (AFSD) is used as a representative case study for part-scale quantification of microstructure evolution at a fine spatial resolution (200 μm) by examining a liquid-nitrogen-cooled stop-action build via energy-dispersive X-ray diffraction coupled with a multi-channel detector. These results inform modeling efforts by linking process asymmetry to stored plastic strain, residual elastic strain, and texture development, and unlike current state-of-the-art characterization methods (e.g., EBSD or neutron diffraction), this approach provides both the spatial resolution and collection efficiency necessary to quantify fine-scale microstructural heterogeneity over large component volumes. As such, this technique provides essential validation data for computational models, e.g., crystal plasticity, enabling future prediction of heterogeneous behavior in AFSD and other additive manufacturing processes.

Franz, Cole [ORNL] (ORCID:0000000213465881)↗

DOE OSTI2025

Long-term thermal aging behavior and strength reduction in a laser powder bed fusion 316H stainless steel

The long-term thermal stability of structural alloys is essential for ensuring the safe and reliable operation of nuclear reactors and other power plants. While extensive research has explored the effects of thermal aging on conventional stainless steels, the behavior of additively manufactured (AM) alloys remains less understood. This study examines the thermal aging response of laser powder bed fusion (LPBF) 316H stainless steel (SS) at temperatures ranging from 550 °C to 750 °C over durations of up to 10,000 h (approximately 1.14 years). Advanced characterization techniques, including electron microscopy and synchrotron X-ray diffraction, were used to investigate dislocation recovery and phase evolution. Based on these findings, a time-temperature-precipitation (TTP) diagram was developed for LPBF 316H SS, revealing a 10- to100-fold acceleration in precipitation kinetics compared to wrought 316H SS. A physics-informed model was calibrated using the short-term experimental data, enabling predictions of average precipitate sizes, volume fractions of M 23 C 6 and Laves phases, and changes in molybdenum solute concentration for aging up to 1 × 10⁶ h (114 years). These microstructural insights were further utilized to estimate yield strength and extrapolate strength reduction factors over the extended aging period. Despite the accelerated aging kinetics, LPBF 316H SS demonstrated superior yield strength retention compared to its wrought counterpart. In conclusion, this study establishes a framework for evaluating long-term performance using short-term experimental data and supports the accelerated qualification of AM materials for high-temperature structural applications.

Laser powder bed fusion↗

DOE OSTI2020

Defect cluster and nonequilibrium gas bubble associated growth in irradiated UMo fuels – a cluster dynamics and phase field model

Irradiation examination shows that gas bubble swelling kinetics is much faster after irradiation-induced recrystallization than that prior recrystallization in UMo fuels. It implies that gas bubbles in coarse grains and small recrystallized grains have different growth behavior. In this work, a phase-field model of gas bubble evolution integrating microstructure dependent cluster dynamics has been developed, for the first time, to study the gas bubble swelling behavior in the recrystallization zone of UMo fuels. Generation, diffusion, reaction, sink, emission and clustering of vacancies and interstitials are described by the cluster dynamics model while a phase-field model is used to describe the evolution of non-equilibrium gas bubbles including nucleation and growth. With the coupled model, the effect of defect generation rate, clustering rate, interstitial emission and sink rates on grain boundaries on the gas bubble evolution are systematically simulated. A set of model parameters (defect generation rate, clustering rate, interstitial emission and sink rates) is determined by comparing measured and simulated gas bubble swelling kinetics. The results demonstrate that interstitial clustering is one of the important physical mechanisms which results in a fast gas bubble swelling kinetics in the recrystallization zone. The developed model can also be extended to study the associated growth of defect and second phase precipitates often observed in irradiated materials.

Hu, Shenyang↗

DOE OSTI2020

Beyond Idealized Models of Nanoscale Metal Hydrides for Hydrogen Storage

Metal hydrides are attractive for compact, low-pressure hydrogen storage, yet a foundational understanding of factors governing their thermodynamics and kinetics is still lacking. Predictive modeling from the atomic to the microstructural scale plays a critical role in addressing these gaps, particularly for nanoscale materials, which promise improved performance but are difficult to probe. In this paper, we summarize strategies being developed within the Hydrogen Materials—Advanced Research Consortium (HyMARC) for going beyond conventional models to incorporate more complex physics, more realistic structures, and better approximation of operation conditions in simulations of nanoscale metal hydrides. We highlight four beyond-ideal factors that influence predicted performance: (1) surface anharmonic dynamics, (2) interface and surface energy penalties, (3) mechanical stress under confinement, and (4) the presence of native surface oxide. Approaches for addressing these factors are demonstrated on model materials representative of high-capacity hydrogen storage systems, and implications for understanding performance under operating conditions are discussed.

08 HYDROGEN↗

DOE OSTI2021

Integrated Multiscale Modeling for Design of Robust 3D Solid-State Lithium Batteries - FY21 Annual Report

This project is developing a multiscale, multi-physics modeling framework for probing the effects of materials microstructure and device architecture on ion transport within 3D ceramic solid-state battery materials, with the goal of enhancing performance and reliability. The project has three primary objectives: (1) integrate multi physics and multiscale model components; (2) understand interface- and microstructure-derived limitations on ion transport; and (3) derive key structure-performance relations for enabling future optimization.

25 ENERGY STORAGE↗

DOE OSTI2022

Phase-field simulations of fission gas bubbles in high burnup UO2 to inform engineering-scale fuel performance modeling

To improve the economics of commercial nuclear energy generation, U.S. utilities are currently seeking licensing approval to operate UO2 fuel to higher burnups. One significant safety issue that must be addressed to obtain approval is the potential for fine fragmentation/pulverization of the fuel during a loss-of-coolant accident (LOCA). The cause of pulverization has been hypothesized to be the rapid increase of pressure in fission gas bubbles in the high burnup region of the fuel during a LOCA. To better understand this phenomenon, a novel phase-field model of the fission gas bubble microstructure in UO2 has been developed and implemented in Idaho National Laboratory (INL)'s Marmot application for phase-field simulation of nuclear materials. Simulations of the bubble response to steady-state and transient conditions were conducted. Simulation results were used to inform a mechanistic model of pulverization in BISON, INL’s fuel performance simulation code.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Cluster Dynamics Modeling Needs for the Advanced Materials and Manufacturing Technologies Program

This milestone report aims to identify and assess the cluster dynamics (CD) modeling requirements within the Department of Energy's Office of Nuclear Energy (DOE-NE) Advanced Materials and Manufacturing Technologies (AMMT) program and to communicate these needs to the DOE-NE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. The goal is to ensure NEAMS is well-informed about the CD modeling requirements to support AMMT's mission of accelerating the development, qualification, demonstration, and deployment of advanced structural materials and manufacturing for nuclear energy applications. CD modeling is an essential tool for predicting the degradation of structural materials under irradiation, which is a key component of AMMT's accelerated qualification process. The AMMT program focuses on both additively manufactured and wrought structural alloys, such as laser powder-bed fusion 316H austenitic stainless steel, alloy 709, Haynes 244, and alloy 617. These materials require a generalized CD modeling framework to facilitate rapid model development and computational simulation. A flexible, generalized CD software, similar to the Multiphysics Object-Oriented Simulation Environment (MOOSE) finite element framework, would enable modeling of various cluster types, including defect clusters, defect-solute clusters, and multicomponent clusters, incorporating thermodynamics and kinetics parameters. Radiation effects, microstructural feature evolution, and multi-dimensional modeling are critical considerations for the CD model. The usability of the CD code should allow for easy modification and coupling with MOOSE-based simulations. Additionally, the software should adhere to Nuclear Quality Assurance-1 standards, include a testing suite for verification and validation, and be version-controlled within a national laboratory-managed Git repository. Benchmark problems are needed to assess code predictions and performance.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Machine learning insights into microstructural origins of transport and mechanical properties in porous microstructures

Multifunctional porous materials are increasingly needed across various fields, but their complex microstructures create significant challenges due to the intricate microstructure-property relationships. This complexity, combined with limitations of traditional analysis methods, hinders efforts to understand and optimize microstructure–property relationships. Here, to address this, we integrate physics-based mesoscale modeling with interpretable machine learning (ML) to uncover how microstructural features govern effective diffusivity and elastic modulus. At constant porosity, we show diffusivity varies by over 150 × and modulus by ∼50 ×, highlighting the power of microstructure engineering. Statistical analysis reveals bimodal behavior in diffusivity and unimodal in modulus. ML identifies connectivity as the dominant factor, while modulus is also sensitive to domain size and feature interactions. Controlled simulations further highlight domain shape as a critical feature for modulus. This framework enables efficient exploration of microstructure-property correlations, offering new insights to guide the design of advanced porous materials.

Bicontinuous microstructure↗

DOE OSTI2025

Machine learning approaches for intentional materials engineering

In this article, the development of nanoporous metals and metallic composites through dealloying processes presents significant opportunities in materials engineering. However, designing multicomponent precursor alloys and establishing corresponding processing methods that yield predictable compositions and nanostructures remain a complex challenge. This article explores how machine learning (ML)-augmented computational and experimental methodologies can tackle these challenges by predicting precursor alloy compositions, final nanoporous structures, and mechanical properties, while integrating ML-enabled autonomous experimentation for material design and quantification. We highlight recent advancements in applying ML to nanostructured materials design via dealloying and discuss how techniques from other nanomaterial designs can be adapted for improved control over morphological and compositional outcomes in nanoporous and nanocomposite materials. Furthermore, we explore the role of ML in autonomous synchrotron x-ray experimentation, enabling real-time feedback between modeling and experimental setups. ML-driven approaches to microstructure characterization and mechanical property prediction are also examined, with a focus on modeling and advanced imaging techniques such as three-dimensional nanotomography. Finally, this article outlines future directions for ML-enhanced materials science, emphasizing the exploration of high-dimensional parameter spaces and the incorporation of materials kinetics into processing and property evaluation, ultimately advancing the design of nanoporous structures and materials science.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Microstructural evolution and strengthening mechanisms in a heat-treated additively manufactured Al–Cu–Mn–Zr alloy

In this report the microstructural and strength evolution of an additively manufactured Al-8.6Cu-0.5Mn-0.9Zr alloy upon aging at 300, 350, and 400 °C is investigated. The strengthening phases of the alloy evolve significantly upon aging, with breakdown and spheroidization of the interconnected θ-Al 2 Cu network, dissolution of metastable θ'-Al 2 Cu precipitates, and precipitation of nanometric L1 2 -Al 3 Zr from a matrix supersaturated in Zr. In the peak-aged states, the alloy displays a favorable combination of strength and ductility, with a room-temperature yield strength of 314–341 MPa and ductility of 11–13%. The measured yield strengths for microstructures with different aging treatments are compared to predictions of yield strengths from grain boundary, solid solution, and particle strengthening contributions. The observed strain hardening behavior is related to fundamental precipitate and dislocation interactions. Comparison between predicted and measured strength values indicates a continued need for strengthening models specifically developed for the heterogeneous microstructures of additively manufactured alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Multi-scale simulation of high burnup UO2 nuclear fuel during loss-of-coolant accident conditions

To improve the economics of commercial nuclear energy generation, U.S. utilities are currently seeking licensing approval to operate UO2 fuel to higher burnups. One significant safety issue that must be addressed to obtain approval is the potential for fine fragmentation/pulverization of the fuel during a loss-of-coolant accident (LOCA). It has been hypothesized that pulverization is caused by the rapid increase of pressure in fission gas bubbles in the high burnup region of the fuel during a LOCA. To better understand this phenomenon, a novel phase-field model of the fission gas bubble microstructure in UO2 has been developed and implemented in Idaho National Laboratory (INL)'s Marmot application for phase-field simulation of nuclear materials. Simulations of the bubble response to steady-state and transient conditions were conducted, and the results were used to inform a mechanistic model of pulverization in BISON, INL’s fuel performance simulation code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2017

Comparison of Commonly-Used Microwave Radiative Transfer Models for Snow Remote Sensing

This paper reviews four commonly-used microwave radiative transfer models that take different electromagnetic approaches to simulate snow brightness temperature (T(sub B)): the Dense Media Radiative Transfer - Multi-Layer model (DMRT-ML), the Dense Media Radiative Transfer - Quasi-Crystalline Approximation Mie scattering of Sticky spheres (DMRT-QMS), the Helsinki University of Technology n-Layers model (HUT-nlayers) and the Microwave Emission Model of Layered Snowpacks (MEMLS). Using the same extensively measured physical snowpack properties, we compared the simulated T(sub B) at 11, 19 and 37 GHz from these four models. The analysis focuses on the impact of using different types of measured snow microstructure metrics in the simulations. In addition to density, snow microstructure is defined for each snow layer by grain optical diameter (Do) and stickiness for DMRT-ML and DMRT-QMS, mean grain geometrical maximum extent (D(sub max)) for HUT n-layers and the exponential correlation length for MEMLS. These metrics were derived from either in-situ measurements of snow specific surface area (SSA) or macrophotos of grain sizes (D(sub max)), assuming non-sticky spheres for the DMRT models. Simulated T(sub B) sensitivity analysis using the same inputs shows relatively consistent T(sub B) behavior as a function of Do and density variations for the vertical polarization (maximum deviation of 18 K and 27 K, respectively), while some divergences appear in simulated variations for the polarization ratio (PR). Comparisons with ground based radiometric measurements show that the simulations based on snow SSA measurements have to be scaled with a model-specific factor of Do in order to minimize the root mean square error (RMSE) between measured and simulated T(sub B). Results using in-situ grain size measurements (SSA or D(sub max), depending on the model) give a mean T(sub B) RMSE (19 and 37 GHz) of the order of 16-26 K, which is similar for all models when the snow microstructure metrics are scaled. However, the MEMLS model converges to better results when driven by the correlation length estimated from in-situ SSA measurements rather than D(sub max) measurements. On a practical level, this paper shows that the SSA parameter, a snow property that is easy to retrieve in-situ, appears to be the most relevant parameter for characterizing snow microstructure, despite the need for a scaling factor.

Snow↗

DOE OSTI2021

Influence of geometry on columnar to equiaxed transition during electron beam powder bed fusion of IN718

Correlation between spot-melt scan parameters (linear spot-density aka areal energy density), build geometry, and solidification microstructure evolution (columnar vs equiaxed) in a powder bed fusion technology is investigated. It is shown that to maintain the equiaxed solidification microstructure evolution in electron beam powder bed additive manufacturing (AM), the areal energy density per layer needs to be scaled with respect to the 2D cross-sectional area of the layer being melted. Samples with two different cross-sectional areas (40 × 40 mm and 20 × 20 mm) have been fabricated with varying areal energy densities. For a given square cross-section (20 × 20 mm), increasing the areal energy density (4.8 MJ/sq.m to 14.7 MJ/sq.m) transitioned the solidification microstructure from columnar to equiaxed. The observed microstructure data (Electron Back Scattered Diffraction - EBSD) is quantified by calculating the principal component (PC) score using a spatial statistics methodology. The sample with equiaxed grains is found to have a low PC score while the sample with columnar grain had a high PC score. A semi-analytical model is used to simulate the heat transfer and the local solidification conditions as a function of processing parameters (linear spot-density). The result from the heat transfer model is correlated with previously quantified microstructure data. Space-Time analysis of the melt pattern is done and correlated with the observed microstructure. In addition, from the findings, appropriate parameters have been used to additively manufacture a turbine blade with site-specific or hybrid solidification microstructure (traditional fabrication possible via a patented method of localized cold working and heat treatment).

36 MATERIALS SCIENCE↗

DOE OSTI2022

A novel approach for tetrahedral-element-based finite element simulations of anisotropic hyperelastic intervertebral disc behavior

Intervertebral discs are microstructurally complex spinal tissues that add greatly to the flexibility and mechanical strength of the human spine. Attempting to provide an adjustable basis for capturing a wide range of mechanical characteristics and to better address known challenges of numerical modeling of the disc, we present a robust finite-element-based model formulation for spinal segments in a hyperelastic framework using tetrahedral elements. We evaluate the model stability and accuracy using numerical simulations, with particular attention to the degenerated intervertebral discs and their likely skewed and narrowed geometry. To this end, 1) annulus fibrosus is modeled as a fiber-reinforced Mooney-Rivlin type solid for numerical analysis. 2) An adaptive state-variable dependent explicit time step is proposed and utilized here as a computationally efficient alternative to theoretical estimates. 3) Tetrahedral-element-based FE models for spinal segments under various loading conditions are evaluated for their use in robust numerical simulations. For flexion, extension, lateral bending, and axial rotation load cases, numerical simulations reveal that a suitable framework based on tetrahedral elements can provide greater stability and flexibility concerning geometrical meshing over commonly employed hexahedral-element-based ones for representation and study of spinal segments in various stages of degeneration.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

A spatially-resolved model of neutron-irradiated tungsten coupling stochastic cluster dynamics and finite deformation plasticity

Structural materials used in nuclear reactors face severe degradation in mechanical properties, such as hardening and embrittlement. At the microscopic scale, this occurs due to creation and accumulation of irradiation-induced defects and their interaction with system dislocations. Although techniques exist which can model evolution of irradiation defects, for instance kinetic transport theory-based models, their interaction with mechanical deformation of the bulk material has not been investigated extensively. In this work, we demonstrate a novel spatially-resolved multiscale coupling between microscopic irradiation defect evolution, modeled using Stochastic Cluster Dynamics (SCD) and macroscopic mechanical deformation modeled using a finite-deformation plasticity model. SCD is used to determine the statistically averaged defect cluster spacing, dependent on operating conditions such as irradiation dose and temperature. This acts as an initial condition that governs the critical resolved shear stress of dislocation glide in the macroscopic plasticity model. This framework is used to predict mechanical behavior in post-mortem test of irradiated Tungsten samples, which has found its importance as structural material used in nuclear reactors. The results obtained using the coupled approach are in good agreement with experimental data of uniaxial tension tests. The model is able to capture the effect of temperature and irradiation dose on the material hardening. Two methods are proposed to estimate hardness – using Tabor's Law relating uniaxial yield stress to hardness and from flat-punch simulations. The results are in reasonable agreement with hardness data from micro-indentation experiments of irradiated Tungsten samples. Finally, the model is also able to reveal microstructural details such as spatial variation in defect density and local stress.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Accelerate microstructure evolution simulation using graph neural networks with adaptive spatiotemporal resolution

Abstract Surrogate models driven by sizeable datasets and scientific machine-learning methods have emerged as an attractive microstructure simulation tool with the potential to deliver predictive microstructure evolution dynamics with huge savings in computational costs. Taking 2D and 3D grain growth simulations as an example, we present a completely overhauled computational framework based on graph neural networks with not only excellent agreement to both the ground truth phase-field methods and theoretical predictions, but enhanced accuracy and efficiency compared to previous works based on convolutional neural networks. These improvements can be attributed to the graph representation, both improved predictive power and a more flexible data structure amenable to adaptive mesh refinement. As the simulated microstructures coarsen, our method can adaptively adopt remeshed grids and larger timesteps to achieve further speedup. The data-to-model pipeline with training procedures together with the source codes are provided.

36 MATERIALS SCIENCE↗

DOE OSTI2023

An Implicit Approach to Phase Field Modeling of Solidification for Additively Manufactured Alloys [Slides]

We are leveraging modern algorithms and computational science to provide a route to predictive simulation of microstructure evolution on emerging exascale architectures. We are utilizing the fastest supercomputers in the world for modeling and simulation of microstructure evolution for generation of data under AM conditions. Solidification conditions in AM can be tailored for the reliable design of materials to specific performance requirements. Developing computational tools to further characterize alloys and correlate the processing-structure-properties-performance (PSPP) relationship.

36 MATERIALS SCIENCE↗