Constituent Redistribution Research Articles

A neutronics-fuel coupling model for the simulation of constituent redistribution in U–Zr fuel

Simulating the dynamic redistribution of elements within metallic fuels, such as U–10Zr (wt.%), is a complex challenge in nuclear power research. While existing models can adequately simulate constituent redistribution throughout the fuel pin, they rely heavily on pre-known power history data or power calculated a priori. Furthermore, existing models do not calculate an accurate actinide inventory throughout the fuel pin. This limitation leads to less precise power distribution calculations, which can negatively affect the efficiency and safety of fuel design and performance. This work aims to introduce a new approach to modeling constituent redistribution for U–10Zr (wt.%) fuel by developing a new code called PFPS that accounts for the depletion and diffusion of Zr throughout the fuel pin during burnup through an explicit coupling method. The approach independently calculates the power distribution by coupling with the reactor physics code, Serpent 2, thereby eliminating the need for externally supplied power history data. The main contribution of this study lies in this coupling to obtain a more accurate history of the compositional evolution of U–Zr fuel and its fission products. This procedure can enhance the understanding of constituent redistribution by calculating a more accurate power distribution and lays the foundation for future attempts to simulate the compositional and microstructural evolution of all materials in the fuel.

Exploring constituent redistribution in irradiated U-19Pu-14Zr fuel via electron probe microanalysis

The phenomena of constituent redistribution, wherein a previously homogeneous metallic fuel forms discrete, radially concentric compositional zones upon irradiation was investigated by examining an irradiated U-19Pu-14Zr fuel (where numbers represent wt. %) with a burnup of 11.5 at.% with electron probe microanalysis (EPMA) and quadruple inductively coupled plasma mass spectroscopy (Q-ICP-MS).EPMA-generated U, Pu, and Zr compositional data obtained from a diameter traverse of the sample was converted to mass and was used to: 1) compare the overall fuel element analysis results between the two methods, 2) determine the number of compositionally distinct zones forming as a result of constituent redistribution; and 3) quantify the post-irradiation loss or gain of U, Pu, and Zr atoms in each distinct compositional zone.Weight percent concentrations of U, Pu, and Zr for the overall cross section compare favorably between the two analytical methods, suggesting that the spatially resolved EPMA analysis complements bulk chemical analysis.Among the four identified compositional zones, post-irradiation quantification of U, Pu, and Zr elemental atom content changes shows that the quantity of U atoms lost from the innermost zone is slightly less than the quantity of U atoms gained by the middle two zones, and the quantity of Zr atoms lost from the high-U third zone is slightly less than is gained by the two innermost zones. Pu is lost from all four zones, although the innermost zone and the high-U third zone lose a significantly higher percentage (> 22 %) of their initial Pu atoms than the other two zones. For all three elements, EPMA cannot distinguish between atoms lost due to transport to a different zone from atoms lost due to nuclear processes; however, the insight gained from using this process can be used to experiment with new modeling techniques to predict constituent redistribution in U-Pu-Zr fuels.

Fission accelerated steady-state post irradiation examinations - Part II

The Advanced Fuels Campaign's Fission Accelerated Steady State Testing (FAST) approach at Idaho National Laboratory creates a benchmark for evaluating accelerated irradiation via control rodlets and advanced metal fuel alloys for sodium-cooled fast reactors (SFRs). FAST experiments have been developed to generate prototypic temperature conditions during steady state irradiations of scaled geometric fuel pins. This approach helps to attain higher burn ups at a much faster rate than previous irradiation tests. For this study, the results from profilometry, fission gas release, and metallography of a FAST experiment are presented. Profilometry determined 0 % effective strain in the rodlets. The fission gas release fraction was measured from puncture/collection analysis. Constituent redistribution was observed in two specimens despite the peak fuel temperatures being below the normal ranges in which redistribution is expected. Metallography of the two higher temperature specimens showed typical swelling with the solid pin closing the fuel-cladding gap and the annular specimen having a fully closed annulus. Additionally, metallography indicated no swelling, no redistribution, and a homogenous microstructure for specimens with lower irradiation temperature. Post irradiation examination of FAST rodlets generally showed the expected representative behavior of metallic fuels within SFRs.

Transmission electron microscopy investigation of phase transformation and fuel constituent redistribution in neutron irradiated U-10wt.%Zr fuel

Uranium-10 wt.% zirconium (U-10 wt.%Zr) is a primary candidate for fast reactor nuclear fuels. However, there is a lack of data characterizing the crystallographic phases and chemistry of the neutron irradiated fuel. In the current study, the microstructural evolution of a U-10 wt.%Zr fuel neutron irradiated to a burnup of 5.7 at.% was investigated using scanning transmission electron microscopy, energy dispersive X-ray spectroscopy, and selected area electron diffraction to determine the major phases, alterations in microstructure, and variations in local chemical composition at different localities of a fuel cross-section. The current study revealed that the irradiated U-10 wt.%Zr fuel was comprised of various major phases, including α-U, β-U, and δ-UZr2, as well as amorphous and crystalline solid fission product (FP) precipitates within different regions of the fuel cross-section. Regions A and A/B in the center of the fuel were comprised of U-rich, U-intermediate, and U-lean localities with α-U and δ-UZr2 composing the major phases. Regions B and C in the intermediate and peripheral fuel localities, respectively, were comprised of α-U grains, U-rich (β-U) grains with Zr-rich precipitates, U-intermediate grains (δ-UZr2), and solid FP precipitates. The major phases identified were associated with the nanoscopic chemical concentrations, the phase diagram, and the as-characterized specimen temperature, with the exception of the non-equilibrium β-U phase identified in Region B. The U-lean localities in Regions A, A/B, B, and C were Zr-enriched pathways along subgrain/grain boundaries, suggesting that Zr is susceptible to radiation-induced segregation in U-Zr fuels and indicating a new mechanism for constituent redistribution.

Testing fast reactor fuels in a thermal reactor: Comparison of transmutation metallic fuel alloys behavior by scanning electron microscopy

To optimize nuclear waste repository performance, the destruction of minor actinide elements, particularly Np and Am, in a neutron fast spectrum reactor is possible by incorporating these elements into nuclear fuel. Evaluating the performance of minor actinide containing fuel is of paramount importance to enabling this technology. However, such a task is challenging without an available domestic fast spectrum test reactor. A comparison of fuel performance tested in an available domestic thermal reactor at the Idaho National Laboratory, the Advanced Test Reactor, and in a fast spectrum reactor in France (Phénix) is presented in this study. This study evaluates the capability of using a cadmium shrouded test position to mimic the power profile along the fuel radius present in fast spectrum reactors so that thermally driven phenomenon (e.g., constituent redistribution) can be evaluated in a thermal reactor and determined to be prototypical of a fast reactor. Thus, optical microscopy and scanning electron microscopy has been performed on irradiated 35U-29Pu-4Am-2Np-30Zr fuel samples (where the number preceding the element is the weight percent concentration) from the two mentioned reactors that present similar irradiation temperatures and power conditions. The results indicate that fuel performance phenomena are reproducible in the two irradiation conditions. The redistribution of Zr occurred in the same manner for the two samples. Similar partitioning of U-Pu-Zr phases was observed, and the behavior of Am was similar in the analyzed specimens. Finally, the overall microstructure evolution seems not to be affected by minor actinides addition compared to expected behavior of conventional U-19Pu-10Zr ternary metal fuels for both specimens. Slight differences in fuel cladding chemical interaction were, however, observed. This difference is likely driven by difference in cladding composition rather than irradiation conditions.

A phase-field model with irradiation-enhanced diffusion for constituent redistribution in U-10wt%Zr metallic fuels

Constituent redistribution is a unique phenomenon to metal fuels that threatens the safety of such fuel forms. Therefore, it is imperative to establish models to understand the intrinsic mechanisms and predict the redistribution kinetics. In this work, we derived the conservative field equations of the phase-field model from near-equilibrium thermodynamic theory. A macroscopic constituent redistribution phase-field model was developed by introducing the effect of irradiation on the atom mobility and the effect of temperature on the interface mobility. An expression of phase boundary width, applicable to both microscopic and macroscopic scenarios was proposed. The interfacial parameters of the model and the Zr concentration distribution near the fuel surface were discussed at last. These works may help understand constituent redistribution characteristics and promote the application of the phase-field method in studying constituent redistribution in macroscopic scenarios.

Investigation of constituent redistribution in U-Pu-Zr fuels and its dependence on varying Zr content

This contribution investigates fuel constituent segregation and fuel-cladding chemical interactions (FCCI) in three U-Pu-Zr fuel pins irradiated to ∼11% burnup in Experimental Breeder Reactor-II as part of the X441 DP-1 experiment. In examined pins, Zr content ranged from 6 to 10 and 14 wt.%, while Pu concentration was constant at 19 wt.% Pu. The primary goal of the investigation was to determine the role Zr content plays in fuel performance and this manuscript provides assessment of both constituent redistribution and FCCI as a function of axial position. FCCI was observed in all pins, though no cladding failure was noted. Optical and scanning electron microscopy (SEM) results show that variation in Zr content alters the number and relative size of constituent redistribution zones in the fuel. For example, larger Zr-rich central regions and smaller U-rich intermediate regions were observed in 14 wt.% Zr fuels. More importantly, all examined fuels have four or more discrete constituent redistribution regions, where each region has dissimilar morphological features. The existence of four to six distinctive regions deviates from traditionally accepted three region redistribution model , highlights complexity of constituent redistribution in this metal fuel , and identifies the need to conduct additional studies using state-of-the-art instrumentation.

Recent trends in metallic fast reactor fuels research

Metallic nuclear fuels have been extensively investigated for more than 60 years. Early studies noted that metallic fuels exhibit characteristic irradiation behaviors that set them apart from oxide fuels. By performing a critical review of historical data, the current gaps in the understanding of metallic U-Zr and U-Pu-Zr fuels (e.g., constituent redistribution, swelling and fission gas release) and recommendations for future research direction can be identified. This paper reviews and highlights the key aspects of the metallic fuel irradiation behaviors, with respect to the gaps in current understanding, based on the research performed in the past 3 years.

A CALPHAD-informed approach to modeling constituent redistribution in Zr-based metallic fuels using BISON

A CALPHAD-informed (Computer Coupling of Phase Diagrams and Thermochemistry) constituent redistribution model was developed for Zr-based metallic fuels and incorporated into the BISON fuel performance code. Three uncertain model parameters associated with β and γ phase kinetics were calibrated using integral test data from U-Zr fuel elements irradiated in Experimental Breeder Reactor II. The calibrated constituent redistribution model was shown to predict the behavior of U-Zr fuels with excellent accuracy. Model predictions for U-Pu-Zr fuels were physically reasonable but less accurate. Reduction of uncertainties in the ternary phase transition temperatures and collection of kinetic data for the ζ phase are expected to improve the model’s ternary predictions. Finally, the new model was coupled to existing thermomechanics models in BISON to simulate irradiation of an entire U-Zr fuel element, demonstrating its ability to accurately predict the behavior of U-Zr fuels with realistic geometries and mesh resolutions at the engineering scale.

A Fast Parallel Particle Filter for Shared Memory Systems

Particle Filters (PFs) are Sequential Monte Carlo methods which are widely used to solve filtering problems of dynamic models under Non-Linear Non-Gaussian noise. Modern PF applications have demanding accuracy and run-time constraints that can be addressed through parallel computing. However, an efficient parallelization of PFs can only be achieved by effectively parallelizing the bottleneck: resampling and its constituent redistribution step. A pre-existing implementation of redistribute on Shared Memory Architectures (SMAs) achieves $O(\frac{N}{T}log_2N)$ time complexity over $T$ parallel cores. This redistribute implementation is, however, highly computationally intensive and cannot be effectively parallelized due to the inherently limited number of cores of SMAs. In this paper, we propose a novel parallel redistribute on OpenMP 4.5 which takes $O(\frac{N}{T} + log_2N)$ steps and fully exploits the computational power of SMAs. The proposed approach is up to six times faster than the $O(\frac{N}{T}log_2N)$ one and its implementation on GPU provides a further three-time speed-up vs its equivalent on a 32-core CPU. We also show on an exemplary PF that our redistribution is no longer the bottleneck.

Reexamination of a U-Zr diffusion couple experiment using quantitative phase-field modeling and sensitivity analysis

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.

Assessment of swelling and constituent redistribution in uranium-zirconium fuel using phenomena identification and ranking tables (PIRT)

Metallic alloy U-Zr nuclear fuels remain a candidate for future US fast reactors. However, with more than 30 years of investigation into the system, U-Zr fuel remains unqualified and lacks predictive modeling capabilities. Phenomenon identification and ranking tables (PIRT) were developed for U-Zr fuels to prioritize the study of microstructural phenomena related to fuel performance and to aid predictive models. Two areas of emphasis, fuel swelling and constituent redistribution, were identified with PIRT and were evaluated in detail. The analysis identified influencing parameters that should be considered during future studies including: external mechanical constraint, temperature, composition, crystallographic texture, temperature gradient, fabrication constraints, fission density, fission rate, initial porosity, and pre-irradiation grain size. The PIRT results support the need for a comprehensive study that focus on the decoupling of fission rate, irradiation temperature, and alloy composition to independently investigate the microstructural evolution in the multiple phases typical of advanced reactor conditions.

Defect production and segregation induced by collision cascades in U-10Zr alloy

Swelling and constituent redistribution of uranium-zirconium (U-Zr) alloys under irradiation will hinder their further application as feasible nuclear fuels. It is necessary to explore the primary irradiation damage induced by collision cascades in U-Zr alloys due to its profound effect on subsequent swelling and constituent redistribution. Herein, we perform molecular dynamic simulations to investigate the irradiation characteristic in the collision cascade of U-10Zr (U with 10 wt% Zr). It is found that, compared with pure U, the addition of Zr can reduce the peak number and increase the surviving number of Frenkel pairs, which should be attributed to the huge atomic mass difference between U and Zr. In U-10Zr alloy, the formation of Zr interstitials is found to be suppressed by analyzing the solute interstitial production efficiency, which is caused by the higher formation energy of Zr interstitials than that of U interstitials in a U matrix. Our simulations also indicate that the solute separation phenomenon actually happens in the collision cascade of U-10Zr. In addition, secondary peaks appear in the curves of defect number, which is induced by the interaction between shock waves and periodic boundaries. The present simulation data and insights would be significant for understanding the irradiation damage behavior of U-Zr alloy in collision cascades.

A study of constituent redistribution in U–Zr fuels using quantitative phase-field modeling and sensitivity analysis

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.

Development and verification of a phase-field model for the equilibrium thermodynamics of U-Pu-Zr

U-Pu-Zr is a promising metallic fuel candidate. However, fuel selection and qualification will require the ability to accurately predict its behavior. Unfortunately, the system’s complex phase behaviors promote formation of heterogeneities that cannot be adequately described using bulk properties. This work presents an equilibrium phase-field model capable of resolving these heterogeneities spatially so that their effects on reactor safety and fuel performance can be understood and predicted. Development of the twelve-phase model is presented beginning with derivation of its CALPHAD free energies. Verification tests show that the model predicts the equilibrium concentrations and overall phase fractions of stable mixtures consistent with analytical methods. Additional assessments show that the model predicts phase transition temperatures with reasonable accuracy. The model is shown to resolve heterogeneities in ternary alloys that could affect composition-dependent properties like neutron cross-sections, thermal conductivities, and melting temperatures. Finally, the model is used to demonstrate that equilibrium thermodynamics has a significant role in constituent redistribution by modeling the formation of radial zones in the presence of a temperature gradient. These zones are qualitatively consistent with those exhibited by EBR-II Fuel Element T179, but results indicate that at least one other significant mechanism must be taken into account to model these behaviors. Overall, the model shows promise and will serve as a thermodynamic foundation onto which more sophisticated models will be built.

Simulated Microstructural and Compositional Evolution of U-Pu-Zr Alloys Using the Potts-Phase Field Modeling Technique

U-Pu-Zr alloys are considered ideal metallic fuels for experimental breeder reactors because of their superior material properties and potential for increased burnup performance. However, significant constituent redistribution has been observed in these alloys when irradiated, or subject to a thermal gradient, resulting in inhomogeneity of both composition and phase, which, in turn, alters the fuel performance. The hybrid Potts-phase field method is reformulated for ternary alloys in a thermal gradient and utilized to simulate and predict constituent redistribution and phase transformations in the U-Pu-Zr nuclear fuel system. Simulated evolution profiles for the U-16Pu-23Zr (at. pct) alloy show concentric zones that are compared with published experimental results; discrepancies in zone size are attributed to thermal profile differences and assumptions related to the diffusivity values used. Twenty-one alloys, over the entire ternary compositional spectrum, are also simulated to investigate the effects of alloy composition on constituent redistribution and phase transformations. The U-40Pu-20Zr (at. pct) alloy shows the most potential for compositional uniformity and phase homogeneity, throughout a thermal gradient, while remaining in the compositional range of feasible alloys.

Temperature and composition dependent thermal conductivity model for U-Zr alloys

Uranium-zirconium (U-Zr) based metallic fuels are promising fuel forms for next-generation fast reactors. The presence of temperature gradient and constituent redistribution in U-Zr based fuels can induce the formation of different phases that have different physical properties such as thermal conductivity. In this work, a semi-empirical model is developed to predict the thermal conductivities of U-Zr alloys for the complete composition range and a wide range of temperatures. The model considers the effects of different electron scattering mechanisms on the electronic thermal resistivity in pure metals and the model's parameters are empirically determined by fitting to the experimental data. A new mixing rule is used to predict the effective thermal conductivity in U-Zr alloys by taking the alloying effects into account. The thermal conductivity predictions by the new model show good agreement with many available experimental data. In comparison with previous models, the new model has further improvement, in particular for high-U alloys that are relevant to reactor fuel compositions and at the low-temperature regime for the high-Zr alloys.

Microstructure of α-U and δ-UZr2 phase uranium–zirconium alloys irradiated with 140-keV He+ ion-beam

Ion-beam irradiation has been conducted to demonstrate and assess solid phase dependence of fission gas bubble nucleation and growth in metallic nuclear fuels. Differential formation and growth of irradiation-induced voids and bubbles were observed from as-cast uranium-zirconium (U–Zr) alloys including 0.1 and 40 wt% zirconium. The U–Zr alloys were irradiated with 140-keV He+ ions with fluences ranged from 1 × 1014 ions/cm2 to 5 × 1016 ions/cm2. Several larger spherical bubbles (<∼70 nm) were revealed from an irradiated single α-U phase alloy (U–0.1Zr) in which observed bubbles were mobile under 200-keV electron beam of transmission electron microscope (TEM). In-situ mergence and leakage of the bubbles in the uranium-rich alloy was also evident during the observation. In contrast, numerous number of small (∼6 nm) angular voids, or low pressure bubbles, were found in an irradiated δ-UZr2 phase alloy (U–40Zr), in which the radiation-induced nanostructure was stationary throughout the observation. This study may reaffirm higher radiation-susceptibility of the α-U phase than the δ-UZr2 phase, which could strengthen the needs of separate accounting of solid phase effects for metallic fuel performance modeling particularly regarding the fuel restructuring phenomena, such as fission gas swelling and constituent redistribution, since conventional models are commonly adopted homogeneous medium assumption, not in accordance with the results of post-irradiation examinations of used metallic nuclear fuel in which the formation of several concentric phase zone was distinct corresponding to a steep radial temperature gradient in the fuel pin and multiple isotherm lines in the binary phase diagram of U–Zr alloy system.

Modeling constituent redistribution in U–Pu–Zr metallic fuel using the advanced fuel performance code BISON

An improved robust formulation for constituent distribution in metallic nuclear fuels is developed and implemented into the advanced fuel performance framework BISON. The coupled thermal diffusion equations are solved simultaneously to reanalyze the constituent redistribution in post irradiation data from fuel tests performed in Experimental Breeder Reactor-II (EBR-II). Deficiencies observed in previously published formulation and numerical implementations are also improved. The present model corrects an inconsistency between the enthalpies of solution and the solubility limit curves of the phase diagram while also adding an artificial diffusion term when in the 2-phase regime that stabilizes the standard Galerkin finite element (FE) method used by BISON. An additional improvement is in the formulation of zirconium flux as it relates to the Soret term. With these new modifications, phase dependent diffusion coefficients are revaluated and compared with the previously recommended values.The model validation included testing against experimental data from fuel pins T179, DP16 and T459, irradiated in EBR-II. A series of viable material properties for U–Pu–Zr based materials was determined through a sensitivity study, which resulted in three cases with differing parameters that showed strong agreement with one set of experimental data, rod T179. Subsequently a full-scale simulation of T179 was performed to reduce uncertainties, particularly relating to the temperature boundary condition for the fuel. In addition a new thermal conductivity model combining all available data covering 0–100% zirconium concentration and a zirconium concentration dependent linear heat rate solution derived from Monte Carlo N-Particle (MCNP) simulations were developed. An iterative calibration process was applied to obtain optimized diffusion coefficients for U–Pu–Zr metallic fuels. Optimized diffusion coefficients suggest relative improvements in comparison to previous reported values. The most influential or uncertain phase is found to be the gamma phase, followed by alpha phase, and thirdly the beta phase; indicating separate effect testing should concentrate on these phases.

Thermophysical investigations of the uranium–zirconium alloy system

The solid phase transformation behavior of uranium–zirconium (U–Zr) alloys (U–0.1, 2, 5, 10, 20, 30, 40, and 50wt% Zr) was observed using differential scanning calorimetry (DSC) with thermogravimetric analysis (TGA). The phase transformation temperatures and enthalpies were measured from the alloys annealed at 600°C for 72, 168, and 672h. The observations indicated distinctive mismatches between the measured data and the existing U–Zr alloy phase diagram. Most notably, the phase transformation of the (α-U, γ2) phase to the (β-U, γ2) phase at ∼662°C was not evident in Zr-rich (>10wt%) U–Zr alloys, while only two phase transformations were evident in the U–10Zr and U–20Zr alloys compared to the three isotherm lines extended over the two compositions in the current phase diagram. The absence of the phase transformation is rather consistent with the older U–Zr phase diagram that was experimentally assessed in the 1950s. This observation may lead to the conclusion that the (β-U, γ2) phase region is not correctly represented in the Zr-rich portion, or the hyper-monotectoid region, of the current U–Zr alloy phase diagram. It is evident that the phase diagram needs to be experimentally revisited to provide more reliable information for the development of metallic nuclear fuel performance models, if such models are to include phase-relevant effects, such as fuel constituent redistribution and fission gas swelling.