Thermal Energy Transport in Oxide Nuclear Fuel.

To efficiently capture the energy of the nuclear bond, advanced nuclear reactor concepts seek solid fuels that must withstand unprecedented temperature and radiation extremes. In these advanced fuels, thermal energy transport under irradiation is directly related to reactor performance as well as reactor safety. The science of thermal transport in nuclear fuel is a grand challenge as a result of both computational and experimental complexities. Here we provide a comprehensive review of thermal transport research on two actinide oxides: one currently in use in commercial nuclear reactors, uranium dioxide (UO2), and one advanced fuel candidate material, thorium dioxide (ThO2). In both materials, heat is carried by lattice waves or phonons. Crystalline defects caused by fission events effectively scatter phonons and lead to a degradation in fuel performance over time. Bolstered by new computational and experimental tools, researchers are now developing the foundational work necessary to accurately model and ultimately control thermal transport in advanced nuclear fuels. We begin by reviewing research aimed at understanding thermal transport in perfect single crystals. The absence of defects enables studies that focus on the fundamental aspects of phonon transport. Next, we review research that targets defect generation and evolution. Here the focus is on ion irradiation studies used as surrogates for damage caused by fission products. We end this review with a discussion of modeling and experimental efforts directed at predicting and validating mesoscale thermal transport in the presence of irradiation defects. While efforts in these research areas have been robust, challenging work remains in developing holistic tools to capture and predict thermal energy transport across widely varying environmental conditions.

Determination of Krypton Diffusion Coefficients in Uranium Dioxide Using Atomic Scale Calculations.

We present a study of the diffusion of krypton in UO2 using atomic scale calculations combined with diffusion models adapted to the system studied. The migration barriers of the elementary mechanisms for interstitial or vacancy assisted migration are calculated in the DFT+U framework using the nudged elastic band method. The attempt frequencies are obtained from the phonon modes of the defect at the initial and saddle points using empirical potential methods. The diffusion coefficients of Kr in UO2 are then calculated by combining this data with diffusion models accounting for the concentration of vacancies and the interaction of vacancies with Kr atoms. We determined the preferred mechanism for Kr migration and the corresponding diffusion coefficient as a function of the oxygen chemical potential µO or nonstoichiometry. For very hypostoichiometric (or U-rich) conditions, the most favorable mechanism is interstitial migration. For hypostoichiometric UO2, migration is assisted by the bound Schottky defect and the charged uranium vacancy, VU4-. Around stoichiometry, migration assisted by the charged uranium-oxygen divacancy (VUO2-) and VU4- is the favored mechanism. Finally, for hyperstoichiometric or O-rich conditions, the migration assisted by two VU4- dominates. Kr migration is enhanced at higher µO, and in this regime, the activation energy will be between 4.09 and 0.73 eV depending on nonstoichiometry. The experimental values available are in the latter interval. Since it is very probable that these values were obtained for at least slightly hyperstoichiometric samples, our activation energies are consistent with the experimental data, even if further experiments with precisely controlled stoichiometry are needed to confirm these results. The mechanisms and trends with nonstoichiometry established for Kr are similar to those found in previous studies of Xe.

Machine learning molecular dynamics simulations toward exploration of high-temperature properties of nuclear fuel materials: case study of thorium dioxide.

Predicting materials properties of nuclear fuel compounds is a challenging task in materials science. Their thermodynamical behaviors around and above the operational temperature are essential for the design of nuclear reactors. However, they are not easy to measure, because the target temperature range is too high to perform various standard experiments safely and accurately. Moreover, theoretical methods such as first-principles calculations also suffer from the computational limitations in calculating thermodynamical properties due to their high calculation-costs and complicated electronic structures stemming from f-orbital occupations of valence electrons in actinide elements. Here, we demonstrate, for the first time, machine-learning molecular-dynamics to theoretically explore high-temperature thermodynamical properties of a nuclear fuel material, thorium dioxide. The target compound satisfies first-principles calculation accuracy because f-electron occupation coincidentally diminishes and the scheme meets sampling sufficiency because it works at the computational cost of classical molecular-dynamics levels. We prepare a set of training data using first-principles molecular dynamics with small number of atoms, which cannot directly evaluate thermodynamical properties but captures essential atomistic dynamics at the high temperature range. Then, we construct a machine-learning molecular-dynamics potential and carry out large-scale molecular-dynamics calculations. Consequently, we successfully access two kinds of thermodynamic phase transitions, namely the melting and the anomalous [Formula: see text] transition induced by large diffusions of oxygen atoms. Furthermore, we quantitatively reproduce various experimental data in the best agreement manner by selecting a density functional scheme known as SCAN. Our results suggest that the present scale-up simulation-scheme using machine-learning techniques opens up a new pathway on theoretical studies of not only nuclear fuel compounds, but also a variety of similar materials that contain both heavy and light elements, like thorium dioxide.

Thermophysical and anion diffusion properties of (U x ,Th1-x )O2.

Using molecular dynamics, the thermophysical properties of the (U x ,Th1-x )O2 system have been investigated between 300 and 3600 K. The thermal dependence of lattice parameter, linear thermal expansion coefficient, enthalpy and specific heat at constant pressure is explained in terms of defect formation and diffusivity on the oxygen sublattice. Vegard's law is approximately observed for solid solution thermal expansion below 2000 K. Different deviations from Vegard's law above this temperature occur owing to the different temperatures at which the solid solutions undergo the superionic transition (2500-3300 K). Similarly, a spike in the specific heat, associated with the superionic transition, occurs at lower temperatures in solid solutions that have a high U content. Correspondingly, oxygen diffusivity is higher in pure UO2 than in pure ThO2. Furthermore, at temperatures below the superionic transition, oxygen mobility is notably higher in solid solutions than in the end members. Enhanced diffusivity is promoted by lower oxygen-defect enthalpies in (U x ,Th1-x )O2 solid solutions. Unlike in UO2 and ThO2, there is considerable variety of oxygen vacancy and oxygen interstitial sites in solid solutions generating a wide range of property values. Trends in the defect enthalpies are discussed in terms of composition and the lattice parameter of (U x ,Th1-x )O2.