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A modified Embedded-Atom Method interatomic potential for uranium-silicide

Uranium-silicide (U-Si) fuels are being pursued as a possible accident tolerant fuel (ATF). U-Si fuels benefit from higher thermal conductivity and higher fissile density compared to UO2. In order to perform engineering scale nuclear fuel performance simulations, the material properties of the fuel must be known. Currently, the experimental data available for U-Si fuels is rather limited. Thus, multiscale modeling efforts are underway to address this gap in knowledge. In this study, a semi-empirical Modified Embedded Atom Method (MEAM) potential is presented for the description of the U-Si system. The potential accurately describes not only the primary phase of interest (U3Si2), but also a variety of U-Si phases across the composition spectrum.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Radiation Re-solution Calculation in Uranium-Silicide Fuels

The release of fission gas from nuclear fuels is of primary concern for safe operation of nuclear power plants. Although the production of fission gas atoms can be easily calculated from the fission rate in the fuel and the average yield of fission gas, the actual diffusion, behavior, and ultimate escape of fission gas from nuclear fuel depends on many other variables. As fission gas diffuses through the fuel grain, it tends to collect into intra-granular bubbles, as portrayed in Figure 1.1. These bubbles continue to grow due to absorption of single gas atoms. Simultaneously, passing fission fragments can cause collisions in the bubble that result in gas atoms being knocked back into the grain. This so called “re-solution” event results in a transient equilibrium of single gas atoms within the grain. As single gas atoms progress through the grain, they will eventually collect along grain boundaries, creating inter-granular bubbles. As the inter-granular bubbles grow over time, they will interconnect with other grain-face bubbles until a pathway is created to the outside of the fuel surface, at which point the highly pressurized inter-granular bubbles will expel their contents into the fuel plenum. This last process is the primary cause of fission gas release. From the simple description above, it is clear there are several parameters that ultimately affect fission gas release, including the diffusivity of single gas atoms, the absorption and knockout rate of single gas atoms in intra-granular bubbles, and the growth and interlinkage of intergranular bubbles. Of these, the knockout, or re-solution rate has an particularly important role in determining the transient concentration of single gas atoms in the grain. The re-solution rate will be explored in the following sections with regards to uranium-silicide fuels in order to support future models of fission gas bubble behavior.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

High Flux Isotope Reactor Low-Enriched Uranium Low Density Silicide Fuel Design Parameters

High Flux Isotope Reactor (HFIR) highly enriched uranium (HEU) to low-enriched uranium (LEU) conversion activities are ongoing as part of the Department of Energy (DOE) National Nuclear Security Administration (NNSA)’s nuclear nonproliferation mission. Design activities studying the conversion of HFIR from HEU to LEU fuel explored different fuel design features and shapes with a low density uranium-silicide dispersion (U 3 Si 2 -Al) fuel, which has a uranium density of 4.8 gU/cm 3 . The goal of these studies is to generate several HFIR LEU fuel designs of varying fuel fabrication complexity that meet the current HEU performance metrics and safety requirements. The documented designs will serve as references for fuel fabrication and qualification activities. Recent advancements in modeling and simulation tools enable quick prototyping of fuel designs. Shift, a Monte Carlo neutron transport and depletion tool optimized for high-performance computing (HPC) architectures, is used for efficient fuel cycle and performance metrics calculations. The HFIR Steady State Heat Transfer Code (HSSHTC) is used to vet the thermal safety margin. Also, a new automation tool that connects all fuel design analysis steps, named Python HFIR Analysis and Measurement Engine (PHAME), has been developed to expedite the design study in an efficient and reproducible manner. Leveraging these tools, several candidate fuel designs were selected for varying fabrication complexity. This report provides design feature details for four selected HFIR LEU low density U 3 Si 2 -Al fuel designs and their corresponding performance and safety metrics. Nominal, best-estimate design parameters and irradiation conditions, including fission rate densities, power densities, heat fluxes, and cumulative fission densities are provided for candidate fuel designs relevant to framing irradiation experiments to support fuel qualification efforts. Simulations show that the low density U 3 Si 2 -Al, with design features to enhance safety, can meet HEU core performance metrics and safety requirements if the reactor power is increased from 85 MW (HEU) to 95 MW (LEU) and if the active fuel length is increased from 50.80 cm (HEU) to 55.88 cm (LEU).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Phase equilibria of advanced technology uranium silicide-based nuclear fuel

The phases in uranium-silicide binary system were evaluated in regards to their stabilities, phase boundaries, crystal structures, and phase transitions. The results from this study were used in combination with a well assessed literature to optimize the U-Si phase diagram using the CALPHAD method. A thermodynamic database was developed, which could be used to guide nuclear fuel fabrication, could be incorporated into other nuclear fuel thermodynamic databases, or could be used to generate data required by fuel performance codes to model fuel behavior in normal or off-normal reactor operations. The U 3 Si 2 and U 3 Si 5 phases were modeled using the Compound Energy Formalism model with 3 sublattices to account for the variation in composition. The crystal structure used for the USi phase was the tetragonal with an I4/mmm space. Above 450°C, the U 3 Si 5 phase was modeled. The composition of the USi 2 phase was adjusted to USi 1.84 . The calculated invariant reactions and the enthalpy of formation for the stoichiometric phases were in agreement with experimental data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Development of molecular dynamics potential for uranium silicide fuels

The use of uranium-silicide (U-Si) in place of uranium dioxide (UO{sub 2}) is one of the promising concepts being proposed to increase the accident tolerance of nuclear fuels for light water reactors. First-principles based density functional theory (DFT) electronic structure calculations may provide the most reliable information. However, it is probably not possible to obtain kinetic information such as amorphization under irradiation directly from DFT simulations due to size and time limitations. Thus, a more feasible way may be to employ molecular dynamics (MD) simulation. Unfortunately, so far no MD potential is available for U-Si to discover the underlying mechanisms. Here, we present our recent progress in developing a U-Si potential. The development is based on the Tersoff type potentials for single element U and Si. The Si potential is taken from the literature and a Tersoff type U potential is developed in this project. With the primary focus on the U{sub 3}Si{sub 2} phase, some other U-Si systems such as U{sub 3}Si are also included as a test of the transferability of the potentials for binary U-Si phases. Based on the potentials for unary U and Si, two sets of parameters for the binary U-Si system are developed using the Tersoff mixing rules and the cross-term fitting, respectively. The cross-term potential is found to give better results on the enthalpy of formation, lattice constants and elastic constants than those produced by the Tersoff mixing potential, with the reference data taken from either experiments or DFT calculations. In particular, the results on the formation enthalpy and lattice constants for the U{sub 3}Si{sub 2} phase and lattice constants for the high temperature U{sub 3}Si (h-U{sub 3}Si) phase generated by the cross-term potential agree well with experimental data. Reasonable agreements are also reached on the elastic constants of U{sub 3}Si{sub 2}, on the formation enthalpy for the low temperature U{sub 3}Si (m-U{sub 3}Si) and h-U{sub 3}Si phases, and on the lattice constants of m-U{sub 3}Si phase. All these phases are predicted to be mechanically stable. The unary U potential is also tested for three metallic U phases (α, β, γ). The potential is found capable to predict the cohesive energies well against experimental data for all three phases. It matches reasonably with previous experiments on the lattice constants and elastic constants of αU. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A Modified Embedded-Atom Method Interatomic Potential for U-Si

Uranium-silicide (U-Si) fuels are being pursued as a possible accident tolerant fuel (ATF). This uranium alloy fuel benefits from higher thermal conductivity and higher fissile density compared to UO{sub 2}. In order to perform engineering scale nuclear fuel performance simulations, the material properties of the fuel must be known. Currently, the experimental data available for U-Si fuels is rather limited. Thus, multiscale modeling efforts are underway to address this gap in knowledge. In this study, a semiempirical modified Embedded Atom Method (MEAM) potential is presented for the description of the U-Si system. The potential accurately describes not only the primary phase of interest (U{sub 3}Si{sub 2}), but also a variety of U-Si phases across the composition spectrum.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Mechanical Properties of Uranium Silicides by Nanoindentation and Finite Elements Modeling

Three methods were used to measure the mechanical properties of U 3 Si, U 3 Si 2 , and USi. Quasi-static and continuous stiffness measurement nanoindentation were used to determine hardness and Young’s modulus, and microindentation was used to evaluate the bulk hardness. Hardness and Young’s modulus of the three U-Si compounds were both observed to increase with Si content. In conclusion, finite elements modelling was used to validate the nanoindentation data calculated for U 3 Si 2 and estimate its yield strength.

36 MATERIALS SCIENCE↗