M.W.D. Cooper

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.

Development of Xe and Kr empirical potentials for CeO2, ThO2, UO2 and PuO2, combining DFT with high temperature MD

The development of embedded atom method (EAM) many-body potentials for actinide oxides and associated mixed oxide (MOX) systems has motivated the development of a complementary parameter set for gas-actinide and gas-oxygen interactions. A comprehensive set of density functional theory (DFT) calculations were used to study Xe and Kr incorporation at a number of sites in CeO2, ThO2, UO2 and PuO2. These structures were used to fit a potential, which was used to generate molecular dynamics (MD) configurations incorporating Xe and Kr at 300 K, 1500 K, 3000 K and 5000 K. Subsequent matching to the forces predicted by DFT for these MD configurations was used to refine the potential set. This fitting approach ensured weighted fitting to configurations that are thermodynamically significant over a broad temperature range, while avoiding computationally expensive DFT-MD calculations. The resultant gas potentials were validated against DFT trapping energies and are suitable for simulating combinations of Xe and Kr in solid solutions of CeO2, ThO2, UO2 and PuO2, providing a powerful tool for the atomistic simulation of conventional nuclear reactor fuel UO2 as well as advanced MOX fuels.

Investigation of oxygen self-diffusion in PuO2 by combining molecular dynamics with thermodynamic calculations

In the present work, the defect properties of oxygen self-diffusion in PuO2 are investigated over a wide temperature (300–1900 K) and pressure (0–10 GPa) range, by combining molecular dynamics simulations and thermodynamic calculations. Based on the well-established cBΩ thermodynamic model which connects the activation Gibbs free energy of diffusion with the bulk elastic and expansion properties, various point defect parameters such as activation enthalpy, activation entropy, and activation volume were calculated as a function of T and P. Molecular dynamics calculations provided the necessary bulk properties for the proper implementation of the thermodynamic model, in the lack of any relevant experimental data. The estimated compressibility and the thermal expansion coefficient of activation volume are found to be more than one order of magnitude greater than the corresponding values of the bulk plutonia. The diffusion mechanism is discussed in the context of the temperature and pressure dependence of the activation volume.

Pipe and grain boundary diffusion of He in UO2

Molecular dynamics simulations have been conducted to study the effects of dislocations and grain boundaries on He diffusion in [Formula: see text]. Calculations were carried out for the {1 0 0}, {1 1 0} and {1 1 1} [Formula: see text] edge dislocations, the screw [Formula: see text] dislocation and Σ5, Σ13, Σ19 and Σ25 tilt grain boundaries. He diffusivity as a function of distance from the dislocation core and grain boundaries was investigated for the temperature range 2300-3000 K. An enhancement in diffusivity was predicted within 20 Å of the dislocations or grain boundaries. Further investigation showed that He diffusion in the edge dislocations follows anisotropic behaviour along the dislocation core, suggesting that pipe diffusion occurs. An Arrhenius plot of He diffusivity against the inverse of temperature was also presented and the activation energy calculated for each structure, as a function of distance from the dislocation or grain boundary.

Oxygen self-diffusion in ThO2 under pressure: connecting point defect parameters with bulk properties

ThO2 is a candidate material for use in nuclear fuel applications and as such it is important to investigate its materials properties over a range of temperatures and pressures. In the present study molecular dynamics calculations are used to calculate elastic and expansivity data. These are used in the framework of a thermodynamic model, the cBΩ model, to calculate the oxygen self-diffusion coefficient in ThO2 over a range of pressures (–10–10 GPa) and temperatures (300–1900 K). As a result, increasing the hydrostatic pressure leads to a significant reduction in oxygen self-diffusion. Conversely, negative hydrostatic pressure significantly enhances oxygen self-diffusion.

Activation volumes of oxygen self-diffusion in fluorite structured oxides

Fluorite structured oxides are used in numerous applications and as such it is necessary to determine their materials properties over a range of conditions. In the present study we employ molecular dynamics calculations to calculate the elastic and expansivity data, which are then used in a thermodynamic model (the cBΩ model) to calculate the activation volumes of oxygen self-diffusion coefficient in ThO2, UO2 and PuO2 fluorite structured oxides over a wide temperature range. We present relations to calculate the activation volumes of oxygen self-diffusion coefficient in ThO2, UO2 and PuO2 for a wide range of temperature (300–1700 K) and pressure (−7.5 to 7.5 GPa).

Thermal transport in UO2 with defects and fission products by molecular dynamics simulations

The importance of the thermal transport in nuclear fuel has motivated a wide range of experimental and modelling studies. In this report, the reduction of thermal transport in UO2 due to defects and fission products has been investigated using non-equilibrium MD simulations, with two sets of empirical potentials for studying the degregation of UO2 thermal conductivity including a Buckingham type interatomic potential and a recently developed EAM type interatomic potential. Additional parameters for U5+ and Zr4+ in UO2 have been developed for the EAM potential. The thermal conductivity results from MD simulations are then corrected for the spin-phonon scattering through Callaway model formulations. To validate the modelling results, comparison was made with experimental measurements on single crystal hyper-stoichiometric UO2+x samples.

Atomistic model of xenon gas bubble re-solution rate due to thermal spike in uranium oxide

Atomistic simulations are performed to study the response of Xe gas bubbles in UO2 to ionizing fission products through the thermal spike approximation. A portion of the total electronic stopping power (Se) is taken as the thermal spike energy through a ratio variable ζ. The thermal spike energy causes extreme melting within the fission track cylindrical region. Molecular dynamics is employed to quantify the probability of a Xe gas atom to be re-solved (re-dissolved) back into the UO2 matrix. Subsequently, a re-solution model is developed and parametrized as a function of bubble radius (R), off-centered distance (r), and thermal spike energy ( ζSe). The off-centered distance measures the shift of the thermal spike axis from the bubble center. To evaluate the re-solution model, independent fission product yield of U-235 fission due to thermal neutrons (0.0253 eV), taken from the JEFF-3.3 database, is used. The kinetic energy of the fission products is taken from the EXFOR database. Subsequently, the decay of Se over distance for each fission product is simulated. Finally, the evaluated re-solution rate (re-solution probability per second) is presented as a function of bubble radius for a range of ζ.Atomistic simulations are performed to study the response of Xe gas bubbles in UO2 to ionizing fission products through the thermal spike approximation. A portion of the total electronic stopping power (Se) is taken as the thermal spike energy through a ratio variable ζ. The thermal spike energy causes extreme melting within the fission track cylindrical region. Molecular dynamics is employed to quantify the probability of a Xe gas atom to be re-solved (re-dissolved) back into the UO2 matrix. Subsequently, a re-solution model is developed and parametrized as a function of bubble radius (R), off-centered distance (r), and thermal spike energy ( ζSe). The off-centered distance measures the shift of the thermal spike axis from the bubble center. To evaluate the re-solution model, independent fission product yield of U-235 fission due to thermal neutrons (0.0253 eV), taken from the JEFF-3.3 database, is used. The kinetic energy of the fission products is taken from the EXFOR database. Subsequently, the decay ...

The thermal conductivity of mixed fuel UxPu1-xO2: molecular dynamics simulations

Mixed oxides (MOX), in the context of nuclear fuels, are a mixture of the oxides of heavy actinide elements such as uranium, plutonium and thorium. The interest in the UO2-PuO2 system arises from the fact that these oxides are used both in fast breeder reactors (FBRs) as well as in pressurized water reactors (PWRs). The thermal conductivity of UO2 fuel is an important material property that affects fuel performance since it is the key parameter determining the temperature distribution in the fuel, thus governing, e.g., dimensional changes due to thermal expansion, fission gas release rates, etc. For this reason it is important to understand the thermal conductivity of MOX fuel and how it differs from UO2. Here, molecular dynamics (MD) simulations are carried out to determine quantitatively, the effect of mixing on the thermal conductivity of UxPu1-xO2, as a function of PuO2 concentrations, for a range of temperatures, 300 – 1500 K. The results will be used to develop enhanced continuum thermal conductivity models for MARMOT and BISON by INL. These models express the thermal conductivity as a function of microstructure state-variables, thus enabling thermal conductivity models with closer connection to the physical state of the fuel.