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Phase-field modeling has increasingly been used to study microstructural evolution in fission gas bubbles in nuclear fuel to improve understanding of fission gas release. To improve computational efficiency, often only vacancies and gas atoms are included as defect species. In this case, the net effects of vacancy and interstitial production, recombination, and biased sink absorption are included as a net vacancy source, or net vacancy source combined with an effective sink. However, there has been a lack of clarity on what parameter values should be used for these approaches to best match the more complete physical picture that includes interstitials and vacancies. Here, we compare a phase-field model of void growth to analytical models for the source-only and source plus sink approach to gain insight into how the phase-field models can be parameterized effectively. The source-only approach provides greater flexibility to match growth rates determined from the full vacancy-interstitial picture. A strategy was developed for determining the value of the net vacancy source term by comparing to an analytical model that includes vacancy and interstitial production, recombination, and biased sink absorption. This strategy can be used to parameterize phase-field models of fission gas bubble growth. • Net vacancy production can be approximated by vacancy source-only and source+sink approaches. • Quasi-steady state analytical models explain behavior of phase-field models. • Vacancy source-only models have more flexibility to match vacancy-interstitial models. • Fitting source term in source-only model provides a good approximation to full vacancy-interstitial model. [ABSTRACT FROM AUTHOR]

Constituent redistribution in U–Zr fuels produces radially-distributed phase fields, each with different material properties and behaviors. The location and composition of the phase fields evolve dynamically due to the influence of swelling, fission gas release, and sodium infiltration on the thermal conductivity of the fuel. Gaps in the understanding of these processes limit the ability to model higher-level behaviors such as fuel-cladding chemical interaction and perform design and safety analyses with confidence. In the current work, we developed a quantitative phase-field model of macroscale constituent redistribution in the U–Zr system. Model parameters were optimized, and the model was validated against an independent dataset. No modification of the phase transition temperatures was necessary, but diffusion needed to be enhanced to reproduce the observed behaviors. Sensitivity analysis was then used to investigate gaps in the understanding of the system and identify the most impactful parameters and behaviors. The mobile interface between the γ and β + γ phase fields was found to be particularly influential in forming the Zr bathtub. The β and γ kinetic parameters scale the overall magnitude of constituent redistribution, while parameters associated with swelling and sodium infiltration influence the size, shape, and location of the Zr bathtub. These findings were used to justify specific recommendations for improving U–Zr modeling capability, which will expedite fuel development and qualification. • Constituent redistribution models must account for swelling and sodium infiltration. • Swelling and sodium infiltration influence Zr bathtub size, shape, and location. • Phase kinetic parameters scale the magnitude of constituent redistribution. • Constituent redistribution profiles are most sensitive to fuel surface temperature. [ABSTRACT FROM AUTHOR]

Abstract The Included Phase Model (IPM) is a mesoscale technique, which describes the morphology of phase-phase interfaces as a parametric surface to reduce computational costs while preserving the important features of phase-field type models. The IPM is extended to include a fluid species (fission gas) occupying vacancies. System evolution is driven by interfacial energy, elasticity of the surrounding matrix, and internal energy of the fluid. The model is extended to multiple grains using a symmetry condition and applied to a network of hexagonal grains. The model is applied to investigate fission gas accommodation and percolation as a function of the distance to a free surface and distribution of high fission density areas corresponding to heterogeneity resulting from the manufacturing processes of mixed oxide fuels. [ABSTRACT FROM AUTHOR]

The initial phase separation and coarsening of the Cr-enriched α′ phase in Fe–Cr alloys were studied by utilizing phase field model. The phase separations of the α′ phase via non-classical nucleation and growth, the transition state from nucleation and growth to spinodal decomposition, and the spinodal decomposition were investigated at 700 K for the alloys containing 25, 28 and 35 at.% Cr. The time exponent of the average radius of α′ phase decreases from the growth and coarsening stage to the steady-state coarsening stage for the nucleation growth mechanism, the slope of number density of α′ phase increases at the steady-state coarsening stage with the increased Cr concentration. The velocity of phase separation in 25 at.% Cr alloy with a nucleation growth mechanism are slower than that in high Cr alloys with a spinodal decomposition mechanism. The results indicate that a low concentration alloy is more stable at high temperature, and the phase separation is fast at the early stage, which supply a reference for the alloy composition selection, and for the analysis of the relationship of property and morphology. [ABSTRACT FROM AUTHOR]

• A mesoscale model for structural alloy corrosion in molten salts is developed. • Model is implemented using the MOOSE framework. • Sensitivity analysis, verification, and validation are performed on the model. • Quantitatively predicts mass-loss and captures selective Cr depletion. [Display omitted] Understanding the impact of microstructure on corrosion rates can aid the development of corrosion-resistant alloys for molten salt reactors. In this work, we develop an electrochemical phase-field model for capturing the microstructure-dependent corrosion of structural alloys by molten salts. As a demonstration problem, we apply this model to capture the selective depletion of Cr from Ni-Cr grain boundaries during corrosion in molten FLiBe salt. We perform sensitivity analysis and model verification on 1D simulations to confirm that the model predicts diffusion-limited kinetics. The model is validated using 1D, 2D, and 3D simulations against experimental data for Ni-5Cr and Ni-20Cr corrosion in molten FLiBe. The 1D simulations predict the corrosion behavior with reasonable accuracy when using an effective diffusion coefficient that accurately represents the grain boundary diffusion. 2D simulations that represent the grain structure underpredict the corrosion. 3D simulations that represent the grain structure predict the corrosion with reasonable accuracy. The corrosion rate predicted by the 3D simulations is proportional to the average grain size at the alloy/salt interface. [ABSTRACT FROM AUTHOR]

Incident neutrons in irradiated W can cause the formation of solid transmutation elements, of which Rhenium (Re) is the most abundant. We apply the phase-field method to investigate the clustering and growth of the Re-rich precipitate in irradiated W based on the spinodal decomposition mechanism, and their effects on the mechanical and thermal properties of W. Needle-like precipitates are reproduced and comparable to experimental observations. We then vary the irradiation dose and temperature to study their influences on the microstructure evolution of the Re-rich precipitate. Simulation results show that the average diameter, the number density, and the coverage rate of the precipitates significantly increase with the increase of the irradiation doses but slightly increase with the increase of the temperature. The effects of the Re-rich precipitate on the mechanical and thermal properties of W are also investigated. Results show that the Vickers hardness increase and the thermal conductivity degrade due to the formation of the Re-rich precipitate, especially at high irradiation doses. Conventional simulation methods can hardly handle the effect of the needle-like precipitates on the mechanical and thermal properties. In this work, we compare these two properties by using needle-like precipitates and circular precipitates. Our results clearly show that the needle-like precipitates give a better consistency with experimental results of the Vickers hardness increase, and reveal the anisotropic ability of the heat transfer in neutron-irradiated W. The current results can provide a systematic understanding of the Re clustering behavior from the microstructure evolution to its influences on the mechanical and thermal properties of W materials. [ABSTRACT FROM AUTHOR]

The time-evolution of an intergranular bubble population is considered using the Included Phase Model (IPM). The model considers the generation and coupled transport of vacancies and gas atoms driven by interfacial energy, elasticity, and internal energy in a framework that admits complex interface morphology. The model predicts overpressure, bubble growth, coarsening, and coalescence leading to the formation of interconnected high-aspect-ratio bubbles on the grain face. The computational efficiency of this model is leveraged to simulate sets of 250 bubbles over time, which compare well with the CAGR-UOX-SWELL SEM measurements and the established SIFGRS model. Analysis of the simulation results highlights the importance of the bubble density as an indicator of bubble structure formed by coalescence and suggests that the two-point autocorrelation function captures the formation of an interconnected network which could improve release thresholds. [ABSTRACT FROM AUTHOR]

Uranium Dioxide (UO 2) fuel powers almost all commercial Nuclear Power Plants (NPPs) worldwide, generating carbon-free energy and contributing to the fight against climate change. UO 2 fuel incurs damage and fractures due to large thermal gradients that develop across the fuel pellet during normal and transient operating conditions. A comprehensive understanding of the underlying mechanisms by which these processes take place is still lacking. A combined experimental and computational approach is utilized here to quantify the behavior of UO 2 fuel fracture induced by thermal shock. This work introduces both (1) an experimental study to understand the fuel fracturing behavior of sintered UO 2 pellets when exposed to thermal shock, and (2) a Multiphysics phase-field fracture model capable of simulating this process. Parametric studies were conducted to evaluate the effects of uncertainties in fracture properties on the fracture behavior of UO 2 due to thermal shocking. A set of energy release rate (or equivalently fracture toughness) and contract area (the part of the fuel pellet in direct contact with the cold bath) were able to capture the overall fracture trends of the corresponding experimental data. Our combined approach presents a new method for accounting for the effects of microstructure and sample size on the energy release rate/fracture toughness. The experimental data were collected from multiple experiments that exposed UO 2 pellets to high-temperature conditions (589–676 ∘ C) followed by a quench in sub-zero water. This work demonstrates that joint experimental and computational efforts are able to advance the understanding of thermal fracture in the primary fuel source for existing and future NPPs. [ABSTRACT FROM AUTHOR]

To improve the economics of commercial light water reactors, increased understanding of UO 2 nuclear fuel with the high burnup structure (HBS) is required in both steady-state and transient conditions. Here, a phase-field model of the fission gas bubble microstructure in nuclear fuel is developed based on the Kim-Kim-Suzuki (KKS) formulation and implemented in Idaho National Laboratory's Marmot application for phase-field simulation of nuclear materials. The model includes the effects of gas pressure and the surface tension of the bubble-fuel matrix interface for arbitrary interfacial curvature. Simulations of bubble growth in the HBS region during steady-state conditions showed that initially overpressurized bubbles decreased in pressure during growth, but still remained above equilibrium pressure. During a loss-of-coolant accident (LOCA) transient, simulations of bubbles in the HBS region showed that bubble size did not change significantly. The bubble pressure in response to the LOCA transient was calculated for a variety of bubble sizes, initial pressures, and external restraint pressures. [ABSTRACT FROM AUTHOR]

The evolution of intergranular fission gas bubbles, including growth, percolation through the fuel matrix, venting and tunnel collapse is simulated using the Included Phase Model (IPM). The model accounts for the effects of vacancy and fission gas species on bubble growth and morphology, which ultimately lead to tunnel formation, venting of fission gas, and subsequent tunnel collapse. A simplified two-dimension bubble model is implemented on a randomly generated irregular, equiangular hexagonal network of grain boundaries and coupled to an intragranular diffusion model. A set of 28 simulations were conducted on a 20 by 15 grid of hexagons with an open surface at one end to permit venting and ensuing tunnel collapse. Results are post-processed and considered statistically to investigate macroscopic fission gas release parameters and the percolation of the network. The behaviors of individual grains and edges are further investigated as a function of edge length, equivalent grain size, and proximity to the free surface. This analysis revealed discrete growth modes corresponding to the number of bubbles on each edge. These modes emerge because edge lengths vary continuously but only an integer number of bubbles precipitate on them, leading to an unequal number of bubbles per unit length for different grains, and corresponding difference in vacancy potential. This result may improve edge percolation conditions utilized in other models. Limitations resulting from the two-dimensional model and avenues future development of more quantitative models are also discussed. [ABSTRACT FROM AUTHOR]

U 3 Si 2 is a potential accident-tolerant fuel that shows promise due to its high thermal conductivity and higher uranium density relative to UO 2. However, its swelling and fission gas release behavior in light water reactor (LWR) conditions is relatively unknown. To provide mechanistic insight and determine parameters for engineering-scale fuel performance modeling of pellet-form U 3 Si 2 , phase-field simulations of the growth, interconnection, and venting of intergranular fission gas bubbles were performed. The fractional coverage of the grain boundary and the fraction of bubble area that is vented were calculated as a function of time. From the simulation data, the fractional grain boundary coverage at saturation, an important parameter needed in engineering-scale modeling of swelling and fission gas release, was determined. Multiple simulations were run to determine the uncertainty in the calculated value. The effect of model assumptions and input parameters that are not well known was evaluated. Simulation results are compared to related theoretical and computational work. Based on the simulation results, a value of 0.60 for the fractional grain boundary coverage at saturation is recommended for U 3 Si 2 fuel. [ABSTRACT FROM AUTHOR]

Interest in U-Zr metallic nuclear fuels has been on the rise, but sparsity in the available diffusion data continues to hinder efforts to model irradiation behaviors like constituent redistribution. In the current work, we develop a quantitative phase-field model for the influential β and γ phases of U-Zr and use it to reexamine data from a published diffusion couple experiment. We optimize the two phases' kinetic parameters and use annealing simulations to show that the optimized model produces more accurate predictions than those obtained using the diffusion parameters currently employed by constituent redistribution models. We then demonstrate how to minimize the impact of user-defined model parameters such that the parameters based on experimental data dominate the model's response. Sensitivity analysis studies confirmed that the phases' kinetic parameters are more influential than the interface energy for this type of problem, and γ phase kinetics were found to be more impactful than β phase kinetics. This observation is believed to be related to differences in phases' solubility ranges and diffusion-limiting behaviors. These findings and the interpretive modeling technique employed in the current work will increase the efficiency of the data collection efforts necessary to reduce uncertainties in U-Zr diffusion parameters, expediting further fuel development. • The diffusion behaviors of U-Zr phases exhibit strong composition dependencies. • Additional experiments are needed to reduce uncertainty in U-Zr interdiffusivities • User-defined phase-field parameters can be selected to maximize model performance. • Data analysis using mechanistic models improves accuracy over empirical smoothing. [ABSTRACT FROM AUTHOR]