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Overview of graphite model development. Discuss graphite in motel salt, potential degradation mechanisms, stress due to volumetric heating, and the role of different parameters. Also wear modeling, modeling salt infiltration into graphite, oxidation modeling, and the existing graphite models.
Graphite anisotropic microstructure Graphite crystal structure and basal planes Response to irradiation and temperature C-axis and a-axis behavior The effect of porosity Nano-and micro-length scale Microscopic to macroscopic response Material property changes Defect length-scale factors Internal stress build-up Irradiation induced dimensional change Temperature effects Stress increases & property changes
Graphite microstructure and oxidation Graphite crystal structure and basal planes Reactive surface area sites Zig-zag and Arm-chair Pore microstructure effects Interconnectivity Reactivity and oxygen transport Oxygen-graphitereaction Not C-O reaction! Temperature effects Oxygen diffusion to graphite Diffusion into the microstructure High temperature vs low temperature diffusion Oxidation: It’s a gradient of factors
The fundamental process in non-aqueous redox flow battery (NRFB) operation revolves around electron transfer (ET) between a current collector electrode and redox-active organic molecules (redoxmers) in solution. Here, we present an approach utilizing scanning electrochemical microscopy (SECM) to evaluate interfacial ET kinetics between redoxmers and various electrode materials of interest at desired locations. This spot-analysis method relies on the measurement of heterogeneous electron transfer rate constants (k f or k b ) as a function of applied potential (E-E 0 '). As demonstrated by COMSOL simulations, this method enables the quantification of Butler-Volmer kinetic parameters, the standard heterogeneous rate constant, k 0 , and the transfer coefficient, α. Our method enabled the identification of inherent asymmetries in the ET kinetics arising during the reduction of ferrocene-based redoxmers, compared to their oxidation which displayed faster rate constants. Similar behavior was observed on a wide variety of carbon electrodes such as multi-layer graphene, highly ordered pyrolytic graphite, glassy carbon, and chemical vapor deposition-grown graphite films. However, aqueous systems and Pt do not exhibit such kinetic effects. Our analysis suggests that differential adsorption of the redoxmers is insufficient to account for our observations. Displaying a greater versatility than conventional electroanalytical methods, we demonstrate the operation of our spot analysis at concentrations up to 100 mM of redoxmer over graphite films. Looking forward, our method can be used to assess non-idealities in a variety of redoxmer/electrode/solvent systems with quantitative evaluation of kinetics for applications in redox-flow battery research.
A graphite component in a nuclear reactor core is subjected to variety of stresses and can experience degradation during normal and off-normal operation. Understanding how a graphite component will behave in service is essential to ensuring core structural stability and safe reactor operation. This report summarizes a graphite modeling tool currently under development at Idaho National Laboratory. The model incorporates several of the anticipated stresses during service and includes the effects of oxidation and irradiation prior to turnaround. This tool is intended to be used to help assess the design of graphite components by utilizing design code rules found in Section III, Division 5 of the American Society of Mechanical Engineering Boiler and Pressure Vessel Code. Specifically, the tool uses the methodologies found within the Full and Simplified assessments from Article HHA-3000 to verify that a graphite component has an acceptably low probability of failure.
Nuclear-grade graphites are extensively utilized in the core designs of various advanced nuclear reactors. Within the reactor environment, graphite is subjected to prolonged exposure to extreme conditions, including high temperatures, radiation, and potentially molten salt and oxygen. Such exposure can induce several degradation mechanisms in graphite, such as nonuniform volumetric strains caused by irradiation and thermal expansion, leading to stresses that may compromise the performance of graphite components. Assessing component integrity, forecasting component performance over the reactor's lifespan, and developing design standards necessitate robust tools for predicting fracture initiation and propagation in graphite structural components within nuclear reactors. This code enables the Bayesian calibration of properties for nuclear-grade graphites. Using a hierarchical Bayesian approach, multiple experimental data sources are combined to develop Gaussian process models for the properties. Using the Kennedy O'Hagan framework, the uncertainties due inadequacies in the model and the inherent spread in the experimental data are quantified.
Graphite under high temperatures and irradiation is central to advanced reactors. We develop a Bayesian calibration framework for graphite property models that explicitly represents model-data mismatch via a Gaussian-process discrepancy. The approach propagates uncertainty from parameters, experimental noise, and model form, with a hierarchical variance structure to capture group and cross-group noise. Using two predictive models across five grades (IG-110, NBG-18, PCEA, NBG-17, 2114) and four properties-irradiation-induced dimension change, creep, Young’s modulus change ratio, and coefficient of thermal expansion change ratio-we obtain average predictive-error reductions of 54%, 65%, 17%, and 17% when discrepancy is included. We illustrate engineering impact with a multiphysics model of a very-high-temperature reactor prismatic reflector brick, analyzing stresses under high fluence and temperature. Accounting for model discrepancy markedly improves predictive accuracy and provides a robust basis for reliable graphite component design in advanced reactors.
Introduction to graphite Fabrication of graphite Unique features of nuclear grade graphite Providing the properties As-fabricated material properties of interest Thermal diff, thermal stability, mechanical strength, etc. General graphite behavior and degradation Microstructure: key to behavior Crystallographic structure Basal plane (covalent) bonding Porosity and pore microstructure Degradation Irradiation behavior Oxidation behavior Molten salt issues
Graphite has historically been extensively used in power reactor cores and will be used in multiple types of advanced reactors currently under development. These graphite structural components can experience significant stresses due to nonuniform volumetric strains induced by irradiation and thermal expansion, which can lead to fracture. Robust tools for predicting fracture initiation and propagation in graphite structural components in nuclear reactors are important for evaluating component integrity, developing design standards, and interpreting experimental results to characterize graphite performance. The U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation program has been developing degradation models for other structural components in nuclear reactors within the Grizzly and BlackBear codes. This report documents an effort to develop initial capabilities for modeling graphite fracture within these codes, building on prior efforts to model fracture in other materials. Major elements of this effort include developing a new system for modeling fracture nucleation and growth in two dimensions using the extended finite element method and incorporating a damage and plasticity model. These capabilities are applied here to model a representative graphite component and a splitting disc experiment used to obtain tensile strength.
Nuclear-grade structural graphite is extensively utilized in the core designs of various advanced nuclear reactors. In the reactor environment, graphite is subjected to prolonged exposure to extreme conditions, including high temperatures, radiation, and potentially molten salt and oxygen. Such exposure can induce several degradation mechanisms in graphite, including nonuniform volumetric strains caused by irradiation and thermal expansion, leading to stresses that may compromise the performance of graphite components. Assessing component integrity requires accurate models of graphite's thermomechanical response. This report documents the Bayesian calibration of thermomechanical properties for nuclear-grade graphite and their application to graphite component modeling and simulation using the Grizzly code. As part of this work, uncertainty-quantified models were developed for the elastic modulus, coefficient of thermal expansion, irradiation-induced dimensional change, and irradiation-induced creep for graphite grades IG-110, NBG-18, NBG-17, PCEA, and 2114. Using a hierarchical Bayesian approach, multiple experimental data sources were combined to develop Gaussian process models for the properties. Using the Kennedy O'Hagan framework, the uncertainties due to inadequacies in the model and the inherent spread in the experimental data were quantified for three different models. These uncertainty-quantified models, with a model-form correction, were subsequently applied to a coupled-physics simulation of representative graphite components, revealing that the uncertainties have a large impact on the components' deformation.
Oxidation modeling importance ASME consideration Effect on graphite properties Model Overview Numerical Model Oxidation Diffusion Reaction Kinetics Model Parameterization Example problems Editing the model Simple problem example Conclusions Coupling to stress analysis Oxidation result analysis
Molten-salt reactors (MSRs) represent a promising next-generation reactor design, with graphite serving as a moderator and/or reflector in several designs. However, due to limited experimental data and operational experience, a technical understanding of the structural integrity of graphite in molten salt environments remains incomplete. This report presents a modeling-based evaluation of graphite degradation in MSR environments, focusing on the effects of salt infiltration in fuel salt-based designs and surface wear in pebble bed reactor designs. The objective of this study is to enhance understanding of the structural integrity challenges posed by these degradation mechanisms and to provide a framework for assessing graphite behavior in MSRs. The first part of the report investigates the phenomenon of molten salt infiltration into graphite. This infiltration occurs when molten salt permeates the interconnected pore structure of the graphite moderator, driven by factors such as pressure differentials and the physical properties of both the salt and graphite. The infiltration process is influenced by characteristics of the pore structure, viscosity of the molten salt, and the interfacial energies between the graphite, salt, and the atmosphere within the graphite pore. Utilizing a coupled multiphysics modeling approach with Grizzly software, the study evaluates the stress induced by internal heat sources due to infiltration, which can lead to structural concerns. This evaluation is crucial for understanding how infiltration affects the mechanical integrity of graphite components in MSRs. The study considers the Molten-Salt Reactor Experiment (MSRE) graphite stringer geometry due to the availability of relevant data. Through detailed finite element analysis, the study examines stress distributions at varying infiltration percentages, revealing that stress levels increase with higher amounts of infiltration. Rare-event simulations, using the parallel subset simulation (PSS) framework, further quantify the failure probabilities under input uncertainties, with a user-specified failure metric. The PSS framework also identifies critical input parameters that significantly affect the stress values, including infiltration amount, thermal conductivity, and power density. Additionally, considering realistic reactor scenarios, the analysis was performed to account for the combined effects of radiation and infiltration, and modeling strategies on how to analyze new reactor designs or new graphite grades are discussed. The second part of the report focuses on wear mechanisms in pebble bed-based MSRs. As graphite fuel pebbles interact with the graphite reflector block, wear can result in material loss and the formation of surface defects, which may act as stress concentrators. A similar multiphysics modeling framework is employed to assess the impact of wear on the structural integrity of graphite components. This study considers a generic fluoride-cooled high-temperature reactor (gFHR) design due to the availability of comprehensive data. Worst-case scenario dimensions of the reflector blocks were analyzed under thermal and radiation conditions. Subsequently, wear in the form of idealized pits and grooves is modeled on the inner surface of the graphite block, with the maximum stress from previous simulations. The simulations show that groove-type defects are more detrimental than pits, leading to higher stress concentrations. Considering worst-case simulation scenarios and experimental wear rates, it was determined that the formation of a surface defect critical enough to affect the stress may not be possible in a gFHR design. Overall, the findings of this research contribute to the development of robust modeling tools for predicting graphite behavior under various operational conditions in MSRs.
The cores and reflectors in high-temperature gas-cooled reactors (HTGRs) are made of graphite materials, with the graphite acting as a moderator, a fuel host matrix, or the foundation for various structural components. This study aims to survey the models in the literature for graphite materials being used as host matrices in pebble/fuel compacts and to implement those surveyed models into Bison to conduct an early assessment of graphite's thermo-mechanical response under various reactor conditions. In this study, thermal (e.g., thermal conductivity, and specific heat capacity) and mechanical (e.g., elastic properties, thermal expansion, irradiation-induced dimensional changes, and irradiation-induced creep) material models for various graphite grades (e.g., H-451, IG-110, G-348, 2020, A3-3, and A3-27) are incorporated into Bison. Two benchmark problems are then exercised utilizing these new graphite-related capabilities: (1) modeling an Advanced Gas Reactor (AGR)-2 fuel compact, and (2) modeling the debonding of a particle-matrix interface.
Molten salt reactors (MSRs) often employ graphite as a moderator and reflector. An important challenge for deploying graphite in these reactors is that, due to limited experimental data, our understanding of graphite’s structural integrity in molten salt environments remains incomplete. Here, this study addresses heat generation from fuel-bearing salt that has infiltrated open pores in the graphite, driven primarily by pressure differentials. This is one of multiple identified physical and chemical mechanisms through which molten salt could potentially degrade graphite. Thermally driven stresses are quantified using the Molten-Salt Reactor Experiment (MSRE) graphite moderator elements as a case study. Finite element simulations predict stress distributions at varying infiltration levels, indicating that thermal stresses increase with higher infiltration. Rare-event simulations using the parallel subset simulation framework identify the combinations and corresponding ranges of input parameters that lead to stresses above a specified threshold. In particular, combinations involving high infiltration amounts, high power density, and low thermal conductivity tend to induce the highest stresses. Under the inputs and assumptions considered in this work, the magnitudes of the thermally driven stresses are quite low, with a very low likelihood of causing failure due to exceeding the graphite’s tensile strength. Additionally, rare-event simulations were performed for two more scenarios: a scaled-up moderator geometry and a localized hotspot in the original geometry. Both cases resulted in increased susceptibility to failure, though not to a detrimental extent. Furthermore, the combined effects of irradiation and infiltration-induced thermal stresses were evaluated. The results showed that thermal stresses from infiltration were negligible compared to those caused by irradiation. The findings of such a study are inherently component-specific, but the methodology presented here could be used for similar assessments of salt-infiltration effects in other graphite components.
The development of reference standard problems based on prototypical reactor designs is of particular importance to verify the adequacy of computer codes and evaluation models for specific reactor types. To support the multiphysics coupled simulation of molten-salt-fueled reactor (MSR) using SAM and Griffin computer codes for safety and licensing analysis, much efforts have been put into enhancing code capabilities and developing reference models for the MSR primary loop in SAM. In this work, a previously developed Molten Salt Reactor Experiment (MSRE) primary loop model was updated to include a two-dimensional (2-D) core region and external core components in one-dimension (1-D) or zero-dimension (0-D). To ensure accurate feedback calculation in multi-physics simulations, the delayed neutron precursor tracking model and solid graphite model were added in the SAM model. In addition, the 2-D and 1-D domains are tightly coupled using the recently developed single-solve approach in SAM. The updated model has been tested under both steady-state and transient scenarios to demonstrate its potential for the multi-physics simulation of MSRE with coupled SAM and Griffin.
We present high-temperature thermodynamic properties for graphite from first-principles anharmonic theory. The ab initio electronic structure is obtained from density-functional theory coupled to a lattice dynamics method that is used to model anharmonic lattice vibrations. This combined approach produces free energies and specific heats for graphite that compare well with available experiments and results from models that empirically represent experimental data, such as CALPHAD. We show that anharmonic theory for the phonons is essential for accurate thermodynamic quantities above about 1000 K.
A series of computational and experimental studies were conducted to understand the onset of lithium plating and subsequent quantification of dead lithium on graphite electrodes in the design of fast charging batteries. The experiments include titration and relaxation studies for detecting initiation of lithium metal plating for various SOC and C-rates, which are compared against the thermodynamically consistent phase field computational results. The collaborative study on "model graphite electrode" with 2.18 mAh cm-2 nominal capacity at 25 degrees C demonstrates: (1) the macroscopic voltage response during relaxation studies indicate the reintercalation of plated lithium into the graphite anode; (2) for SOC below 60% and low C-Rates, there is no dead lithium; (3) for SOC between 60% to 80%, and C-Rates in the range of 4C-6C show dead lithium both in experiments and simulations; (4) at 100% SOC and 4C-6C rates, large amounts of dead lithium are observed. The study presented here allows us to evaluate the effects of the physical properties of the electrochemical system on plating and stripping kinetics and the amount of dead lithium on graphite electrodes, which determines the cell capacity loss under fast charge.
The NEAMS Multiphysics Applications team continues to assess code usability and functionality for microreactor design and safety analyses, while demonstrating that NEAMS tools capture both steady-state and transient behavior across distinct microreactor concepts. In FY2025, the team advanced full-core, high-fidelity, multiphysics models that solve more complex problems and strengthen verification/validation for several microreactor systems: heat-pipe microreactor (HPMR), gas-cooled microreactor (GCMR), and the KRUSTY experiment. These models employ the MOOSE MultiApp/Transfers architecture with Griffin for neutronics, BISON for heat conduction/thermomechanics, Sockeye for heat pipes, SAM/THM for coolant channels and loops, and SWIFT for hydride behavior, with meshes generated via the MOOSE Reactor Module. The graphite models available in the Grizzly code were also investigated for future analyses. For the HPMR, a Na-HPMR variant was constructed to align with recently validated heat-pipe experiments and Sockeye’s LCVF capability, enabling mechanistic heat-pipe transients and startup modeling. The Na-HPMR will serve as the primary model for HPMR investigations in upcoming tasks. The load-following and single heat-pipe failure scenarios (Griffin/BISON/Sockeye), which were previously modeled for the K-HPMR, were replicated for the Na-HPMR, showing strong negative temperature feedback and highly localized thermal effects, respectively, while the startup case captured vapor-front progression and heat-removal activation. Solid mechanics was added to the previously built K-HPMR full-core model in BISON, showing minimal impact on steady-state reactivity yet enabling stress-field predictions that prepare the path for full-core TRISO performance analyses. For the GCMR, automated steady-state and four transient scenarios were executed using Griffin/BISON/SAM/SWIFT. Results confirm robust inherent safety: power collapses promptly in loss-of-cooling events, the inlet-temperature drop settles to a new equilibrium, and a single-channel blockage yields only a ~30 K local fuel-temperature rise with <0.4% power decrease. SWIFT-predicted hydrogen redistribution affects reactivity during both steady-state and transient conditions, underscoring its importance. A Brayton-cycle balance of plant (BOP) model in SAM/THM demonstrated stable startup behavior, and xenon-driven reactivity during load following was analyzed. To improve TRISO-compact temperature fidelity, a fast multiscale Heat Source Decomposition (HSD) treatment was implemented. Against heterogeneous benchmarks, HSD reduces underprediction of kernel temperatures and lowers predicted peak powers in reactivity-insertion transients compared to previous homogenized models. KRUSTY warm-critical validation progressed from FY2024 baselines: the 15Ȼ insertion shows excellent agreement in peak power (~2% high) and temperature trends, and the 30Ȼ case was automated via a feedback controller that maintained power near 3 kW for ~150 s with close agreement to data. The successful modeling of the warm critical tests has laid a strong foundation for simulating more complex nuclear system tests in the years ahead. Throughout FY2025, developer feedback was provided (e.g., MOOSE batch mesh generation, distributed pre-split meshes, Griffin sweeper on displaced meshes), several new models were contributed to the Virtual Test Bed, and an OECD-NEA WPRS multiphysics benchmark based on the HPMR was initiated to enable broader cross-comparison and best-practice development with the nuclear community at large.