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Bayesian calibration of irradiated graphite property models under high temperatures

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.

36 - MATERIALS SCIENCE↗

Review of Graphite Properties Relevant to Micro-Reactor Design

Microreactors are advanced reactors that are designed to be small, scalable, and portable with up to 20 MW power. These reactors could operate independently, or as part of a microgrid, without need of a frequent refueling. Micro-reactors are designed to be deployable to provide electric power in remote locations, therefore providing greater flexibility. Several micro-reactors are under development in the US. These reactors are based on advanced gas-cooled or heat-pipe concepts. While Graphite can be found in various applications, some high-temperature reactors plan to employ Graphite in their core components due to its role as a moderator and its ability to maintain its structural integrity when subjected to elevated temperatures and high neutron fluence. Although there is significant experience with use of Graphite in nuclear applications, there are still unknowns that should be addressed. Graphite properties depend on the graphite type and affected by the fabrication procedures. Material properties are functions of the temperature and irradiation dose. The fundamental properties also affected by the oxidation environment. Therefore, in-depth understanding of graphite properties, including the effect of irradiation, oxidation and other influencing parameters are required to evaluate the design accurately. This draft aims to provide a comprehensive review of material properties for Graphite relevant to micro reactor design. For this work, two distinct grades of graphite were considered, namely IG-110 and Mersen-2114. Physical, thermal, and mechanical properties for these grades were comparatively evaluated. The properties that are discussed in this draft aim to serve as a basis for design and safety analysis.

42 ENGINEERING↗

Fully Bayesian Analysis With Model Inadequacy Correction For Nuclear Graphite Property Models With Hierarchical Variance Structure

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.

Dhulipala, Som Lakshmi NarasimhaLakshmi Narasimha ↗

Bayesian Calibration of Nuclear Graphite Property Models Accounting for Model Inadequacy and Impacts on Component Performance

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.

36 - MATERIALS SCIENCE↗

Defect formation and bending properties in graphite under He atom implantation investigated by molecular dynamics method

The formation and evolution of radiation defects and their effects on bending property of a single graphite under low energy helium atom implantation have been studied at atomic scale through molecular dynamics simulations. Various simple interstitial and vacancy defects are observed during the implantation process, which is a function of incident energy and cross section of helium-carbon interaction. Large defects are observed after continuous helium atom implantations. The effects of incident energy on the density, size and distribution of defects are analyzed in detail. Furthermore, the kinetic evolution process of radiation defects at different annealing temperatures have also been simulated, including the migration, aggregation, transformation, coalescence, and self-healing. Here, the large defect clusters, crossing several carbon layers, have been confirmed to be the primary reasons that affect the bending property of graphite. All these results provide a new understanding for further applications of graphite in nuclear reactors.

Atomic implantation↗

Probing the Influence of Multiscale Heterogeneity on Effective Properties of Graphite Electrodes

Graphite electrodes in the lithium-ion battery exhibit various particle shapes, including spherical and platelet morphologies, which influence structural and electrochemical characteristics. It is well established that porous structures exhibit spatial heterogeneity, and the particle morphology can influence transport properties. The impact of the particle morphology on the heterogeneity and anisotropy of geometric and transport properties has not been previously studied. Herein, this study characterizes the spatial heterogeneities of 18 graphite electrodes at multiple length scales by calculating and comparing the structural anisotropy, geometric quantities, and transport properties (pore-scale tortuosity and electrical conductivity). We found that the particle morphology and structural anisotropy play an integral role in determining the spatial heterogeneity of directional tortuosity and its dependency on pore-scale heterogeneity. Our analysis reveals that the magnitude of in-plane and through-plane tortuosity difference influences the multiscale heterogeneity in graphite electrodes.

25 ENERGY STORAGE↗

GIF-VHTR Materials (Graphite) Project Plan: Progress since September 2021

¦1: Data, Design Methodology and Construction 1.1: Graphite Selection and Acquisition Strategy (Original tasks completed) 1.2: Graphite Properties (Virgin Materials) 1.3: Graphite Fracture Behaviour(Original tasks completed) 1.4: Graphite Oxidation Behaviour(Original tasks completed) 1.5: Graphite Component Testing 1.6: Graphite Irradiation Effects 1.7: Graphite Irradiation Induced Creep 1.8: Graphite Codes and Standards Development (ASME & ASTM) 1.9: Graphite BehaviourModels Development 1.10: Links to Existing Graphite Irradiation BehaviourDatabases 1.11: Materials Database ¦2: Operation and Inspection 2.1: Methodologies for determining requirements for inspection of graphite cores 2.2: Methodologies for ISI of graphite cores ¦3: Decommissioning and Disposal (New task added 2021) 3.1: Technical data for decommissioning and disposal issues

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Initial Developments in Modeling Graphite Behavior

Graphite is used in High Temperature Reactor designs as a moderator, reflector and core material responsible for protecting the fuel and maintaining structural stability. From a safety perspective, it is imperative to be able to predict how graphite will behave under reactor operating conditions which may compromise the core’s structural integrity or fuel’s safety performance. The following report summarizes recent modeling work undertaken at Idaho National Laboratory which focuses on graphite degradation behavior. One phenomenon which is explored in this report and can cause significant degradation to graphite properties is oxidation. Oxidation behavior in graphite is highly temperature dependent. At low temperatures, oxygen can fully penetrate a component and cause a homogeneous damage profile. At high temperatures, only the graphite near the surface of a component is affected. Understanding and modeling this temperature dependence is essential to predicting graphite behavior. In this report, three graphite models are discussed. The first model is used to investigate strength loss after low temperature oxidation. It does this by generating an approximate graphite microstructure then determining the required load to cause crack propagation. It has been shown that the model reproduces the quasi brittle stress versus strain relationship observed in graphite. Strength loss results from the model are shown to match experimental values. The second model investigates strength loss under high temperature oxidation conditions. This model is more applicable to full scale graphite components where the oxidation damage is often inhomogeneous throughout a component. The third model computes stresses in graphite under reactor conditions. Specifically, the model incorporates the effect of creep, irradiation dose, thermal strains, and oxidation in order to predict internal stresses in a component. All of these models are implemented in the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open source, parallel finite element framework.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

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↗

Graphite Oxidation Modeling

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

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Structure–property relations in graphitic pebbles for nuclear applications

This work presents an analytical approach for holistically characterizing graphitic matrix pebbles for nuclear applications whereby the macrostructure, microstructure, and thermophysical properties of pebbles are determined. A systematic sectioning method was applied to several pebbles to describe the regional properties of the samples. Intact matrix-only spheres and sections of spheres fabricated by Kairos Power were characterized via optical imaging, x-ray computed tomography, x-ray diffraction, and ellipsometry to determine 2D and 3D macrostructure and anisotropy. The thermophysical properties of these materials were determined via measurements of density, specific heat, thermal expansion, and thermal diffusivity. The results of this study indicate that the pebble fabrication methods and their resultant effect on microstructure have a nontrivial effect on thermophysical properties, confirming the importance of robust characterization of these components. A discussion of the characterization approach and its applicability to nuclear fuel development activities is also included.

42 ENGINEERING↗

Oxidation Behavior and Property Degradation of Nuclear Graphites

During its multidecade operation in the core of nuclear reactors, graphite components are subjected to aggressive and continuous exposure to a high field of ionizing and neutron irradiation, high temperature, and various types of present and postulated chemical attacks. High density, high crystallinity polygranular synthetic graphite is unique among other materials for its extraordinary capacity of resisting and adapting to the aggression inflicted by high temperature, high energy neutron bombardment and ionizing gamma radiation. But, as a carbonaceous material, even though of very high purity, graphite is reactive towards common oxidizing agents: oxygen, carbon dioxide, water. Safe operation of HTGRs relies, among other aspects, on engineered safeguard systems for efficient and continuous protection of graphite components against oxidation. Graphite oxidation behavior was, and continues to be, an important direction of theoretical and experimental research, engineering analyses, models and simulations, and design and safety regulations. The avalanche of publications, reports, experimental data, computer codes, and regulatory documents related to oxidation behavior of nuclear graphite is now accelerating to new levels, prompted by the increased interest for nuclear energy as a clean, carbon-free energy source. Even though public’s perception of nuclear energy advantages may still be influenced by the memories of past accidents of nuclear reactors from generations II and III, the community of informed scientists and engineers, regulators and statemen knows that generation IV of nuclear reactors is designed at very high safety standards, doubled by great advances of scientific knowledge and technological progress. One of routes of these recent advances is directed at better understanding of graphite oxidation behavior, its relationship with graphite manufacturing and microstructural properties, along with the effects of various environmental factors and process variables. Together, the recent progress in manufacturing, properties characterization, and modeling of intricated physical and chemical processes that concur to the oxidation behavior led to development of powerful simulation codes able to analyze various scenarios of normal operation and hypothetical off-normal events, and thus to clearly specify the allowable parameters envelopes for the designers, constructors, and operators of current and future modular HTGRs. This review begins with an introduction on manufacturing methods, structure, and properties of nuclear graphite, including basic requirements that this specialty graphite type must satisfy for nuclear use. It continues with a chapter on environmental effects on nuclear graphite, where emphasis is placed less on irradiation and much more on oxidation phenomena, their safety implications, and the basic traits of chronic and acute oxidation by air (oxygen) and water (humidity, steam). Particular attention is placed on the three graphite grades of interest for this document (IG-110, NBG-18, PCEA). A chapter on properties degradation induced by oxidation follows, with focus on density, dimensional, and mechanical properties changes. The next chapter is intended as a brief review of various approaches used for modeling of graphite oxidation behavior. It summarizes the progress of oxidation models, from the early attempts to complex computational approaches interfaced with specialized computer codes designed for nuclear reactor simulations. Last, a list is presented of knowledge gaps where more research is needed. A short summary concludes the review.

36 MATERIALS SCIENCE↗

Influence of gadolinium doping on structural, optical, and electronic properties of polymeric graphitic carbon nitride

Polymeric graphitic carbon nitride (gCN) materials have received great attention in the fields of photo and electrocatalysis due to their distinct properties in metal-free systems with high physicochemical stability. Nevertheless, the activity of undoped gCN is limited due to its relatively low specific surface area, low conductivity, and poor dispersibility. Doping Gd atoms in a gCN matrix is an efficient strategy to fine-tune its catalytic activity and its electronic structure. Herein, the influence of various wt% of gadolinium (Gd) doped in melon-type carbon nitride was systematically investigated. Gadolinium-doped graphitic carbon nitride (GdgCN) was synthesized by adding gadolinium nitrate to dicyandiamide during polymerization. The X-ray diffraction (XRD) and transmission electron microscopy (TEM) results revealed that the crystallinity and the morphological properties are influenced by the % of Gd doping. Furthermore, X-ray photoelectron spectroscopy (XPS) studies revealed that the gadolinium ions bonded with nitrogen atoms. Complementary density functional theory (DFT) calculations illustrate possible bonding configurations of Gd ions both in bulk material and on ultrathin melon layers and provide evidence for the corresponding bandgap modifications induced by gadolinium doping.

36 MATERIALS SCIENCE↗

Understanding the effect of specimen size on the properties of fine-grain isotropic nuclear graphite for irradiation studies: Mechanical properties

Programs at Oak Ridge National Laboratory are investigating the effects of neutron irradiation in the High Flux Isotope Reactor (HFIR) on properties of fine-grain isotropic nuclear graphites. Specimens were irradiated in the HFIR flux trap, which requires using specimens that are smaller than the sizes recommended by ASTM standards. Here, this work has investigated whether subsized specimens can be used to reliably predict strength behavior. The results show that (1) tensile strength was loosely coupled to specimen volume, (2) the compression specimens had a slightly higher strength for larger volumes, (3) the uniaxial flexural strength was nearly independent of specimen effective area for one orientation whereas the other orientation showed a slight strength–size scaling Weibull behavior, and (4) equibiaxial flexural strength followed traditional strength–size scaling Weibull behavior. These results suggest that fine-grain graphite is more similar to ceramics than to medium- and large-grained graphite with respect to both the strength-limiting flaws (Griffith theory) and the effect of machining on the strength behavior. This work shows that using specimens that are smaller than ASTM recommendations are suitable for investigating the strength changes caused by neutron irradiation because the primary interest is the relative change in the strength distribution parameters rather than their absolute values.

36 MATERIALS SCIENCE↗