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Recently, a combined experimental–theoretical approach to assess the effect of daughter product formation on the stability of crystalline compounds comprised of radioisotopes has been developed. This methodology was motivated by the potential impact on crystalline nuclear waste form stability of a significant fraction of the constituent atoms undergoing transmutation. What is particularly novel about this approach is the experimental use of very short-lived isotopes to accelerate the chemical evolution that occurs during decay. In this paper, we present results of density functional theory (DFT) calculations that have been performed in support of corresponding experiments on the 109 Cd x 109 Ag 1 - x S material system. 109Cd has been selected in order to simulate the decay of important “short-lived” fission products 137Cs or 90Sr (which decay via β - to 137Ba and 90Zr respectively with ≈ 30-year half-lives). By comparison, 109Cd decays by electron capture with a half-life of 109 days to 109Ag. DFT results predict the formation of heretofore unobserved Cd x Ag 1 - x S structures, which support corresponding experiments and ultimately may have implications for waste form stability.

Based on density functional theory (DFT) and empirical potential calculations, the diffusivity of fission gas atoms (Xe) in UO2 nuclear fuel has been calculated for a range of non-stoichiometry (i.e. UO 2 ± x ), under both out-of-pile (no irradiation) and in-pile (irradiation) conditions. This was achieved by first deriving expressions for the activation energy that account for the type of trap site that the fission gas atoms occupy, which includes the corresponding type of mobile cluster, the charge state of these defects and the chemistry acting as boundary condition. In the next step DFT calculations were used to estimate migration barriers and internal energy contributions to the thermodynamic properties and calculations based on empirical potentials were used to estimate defect formation and migration entropies (i.e. pre-exponentials). The diffusivities calculated for out-of-pile conditions as function of the UO 2 ± x non-stoichiometry were used to validate the accuracy of the diffusion models and the DFT calculations against available experimental data. The Xe diffusivity is predicted to depend strongly on the UO 2 ± x non-stoichiometry due to a combination of changes in the preferred Xe trap site and in the concentration of uranium vacancies enabling Xe diffusion, which is consistent with experiments. After establishing the validity of the modeling approach, it was used for studying Xe diffusion under in-pile conditions, for which experimental data is very scarce. The radiation-enhanced Xe diffusivity is compared to existing empirical models. Finally, the predicted fission gas diffusion rates were implemented in the BISON fuel performance code and fission gas release from a Riso fuel rod irradiation experiment was simulated.

The accommodation of trivalent oxides (M2O3) in uranium dioxide has been investigated using atomic scale simulation. Calculations suggest that all trivalent oxides studied preferentially enter UO2 by associating the substitutional ion with an oxygen vacancy, larger cations forming the cluster { 2 M U ′ : V O } × . Solution into hyper-stoichiometric UO2+x was accompanied by the formation of the { M U ′ : U U } × cluster and smaller solution energies than into stoichiometric UO2. Solubility is a particularly strong function of hyper-stoichiometry for smaller cations such as Cr3+, which has implications for the use of Cr2O3 as a grain enlarger but not so for larger cations such s Gd3+.

Ab initio calculations based on the Density Functional Theory are carried out in order to investigate the incorporation of iodine in uranium dioxide. The GGA+U approximation is used to describe the strong correlations of uranium 5f electrons. We studied several defects that are likely to accommodate the incorporation of iodine in the material, such as uranium and oxygen vacancies, divacancy and Schottky defects. We find the iodine atoms to be stable in a neutral Schottky defects, with an incorporation energy of -1.3 eV. This result may account for the solubility of iodine in uranium dioxide observed experimentally. We also notice that the incorporation of iodine involves steric and electronic contributions. The larger the defect iodine is incorporated in, the lower is its incorporation energy. Besides, we find iodine to be charged -1, thus getting the stable electronic configuration of rare gases. We also highlight the fact that the use of GGA+U increases the number of metastable states (non global energy minima), compared to the LDA/GGA approximations. Consequently, special care has to be taken on the 5f electronic occupancies in order to ensure that the absolute energy minimum has been reached.

International audience; The nuclear oxide fuels are submitted ‘in-pile’ to strong structural and chemical modifications due to thefissions and temperature. The diffusion of species is notably the result of a thermal activation and of radiationinduced diffusion. This study proposes to estimate to what extent the radiation induced diffusioncontributes to the diffusion of lattice atoms in UO2. Irradiations are simulated using molecular dynamicssimulation by displacement cascades induced by uranium primary knock-on atoms between 1 and80 keV. As atoms are easier to displace when their vibration amplitude increases, the temperature rangewhich have been investigated is 300–1400 K. Cascade overlaps were also simulated. The material isshown to melt at the end of cascades, yielding a reduced threshold energy displacement. The nuclear contributionto the radiation induced diffusion is compared to thermally activated diffusion under in-reactorand long-term storage conditions.

International audience; This article presents a synthesis of the investigations at the atomic scale of the transport properties of defects and fission gases in uranium dioxide, as well as of the transfer of results from the atomic scale to models at the mesoscopic scale, performed during the F-BRIDGE European project (2008-2012). We first present the mesoscale models used to investigate uranium oxide fuel under irradiation, and in particular the cluster dynamics and kinetic Monte Carlo methods employed to model the behaviour of defects and fission gases in UO$_2$ , as well as the parameters of these models. Second, we describe briefly the atomic scale methods employed, i.e. electronic structure calculations and empirical potential methods. Then, we show the results of the calculation of the data necessary for the mesoscale models using these atomic scale methods. Finally, we summarise the links built between the atomic and mesoscopic scale by listing the data calculated at the atomic scale which are to be used as input in mesoscale modelling. Despite specific difficulties in the description of fuel materials, the results obtained in F-BRIDGE show that atomic scale modelling methods are now mature enough to obtain precise data to feed higher scale models and help interpret experiments on nuclear fuels. These methods bring valuable insight, in particular the formation, binding and migration energies of point and extended defects, fission product local-ization, incorporation energies and migration pathways, elementary mechanisms of irradiation induced processes. These studies open the way for the investigation of other significant phenomena involved in fuel behaviour, in particular the thermochemical and thermomechanical properties and their evolution in-pile, complex microstructures, as well as of more complex fuels.

We report first-principles DFT$\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}U$ calculations of the paramagnetic phases of uranium dioxide (UO${}_{2}$) and (U,Pu) mixed oxides (MOX). We use a combination of two techniques, the first of which enables us to treat the presence of metastable states and the other the random distribution of spins (for paramagnetism) and of plutonium atoms (for MOX). The resulting method is first used to determine the ground-state properties of paramagnetic UO${}_{2}$ and is then applied to MOX with $12.5%$ and $25%$ Pu, for which both experimental and theoretical studies are lacking. We find the paramagnetic phase of fluorite UO${}_{2}$ to be more stable than the antiferromagnetic phase as expected from experimentation, with ground-state properties in excellent agreement with experimental data. Results on MOX show that most of the ground-state properties of UO${}_{2}$ are affected by addition of $12.5%$ Pu and do not seem to be much different when the plutonium content changes, at least for Pu contents below $30%$. For both UO${}_{2}$ and MOX, it is found that the true paramagnetic order has a significant effect on the calculated elastic constants, compared to the antiferromagnetic and ferromagnetic orders. By contrast, we find that regarding energetics, the antiferromagnetic order may be used as a very good approximation of the paramagnetic state.

The present work reports first-principles DFT $+\phantom{\rule{0.16em}{0ex}}U$ calculations of uranium self-diffusion in uranium dioxide (UO${}_{2}$), with a focus on comparing calculated activation energies to those determined from experiments. To calculate activation energies, we initially formulate a point defect model for UO${}_{2\ifmmode\pm\else\textpm\fi{}x}$ that is valid for small deviations from stoichiometry. We investigate five migration mechanisms and calculate the corresponding migration barriers using both the LDA $+\phantom{\rule{0.16em}{0ex}}U$ and GGA $+\phantom{\rule{0.16em}{0ex}}U$ approximations. These energy barriers are calculated using the occupation matrix control scheme that allows one to avoid the metastable states that exist in the DFT $+\phantom{\rule{0.16em}{0ex}}U$ approximation. The lowest migration barrier is obtained for a vacancy mechanism along the $\ensuremath{\langle}110\ensuremath{\rangle}$ direction. This mechanism involves significant contribution from the oxygen sublattice, with several oxygen atoms being displaced from their original position. The $\ensuremath{\langle}110\ensuremath{\rangle}$ vacancy diffusion mechanism is predicted to have lower activation energy than any of the interstitial mechanisms and comparison to experimental data for stoichiometric UO${}_{2}$ also confirms this mechanism.

Geng et al. [H. Y. Geng, Y. Chen, Y. Kaneta, M. Kinoshita, and Q. Wu, Phys. Rev. B 82, 094106 (2010)] recently reported $\mathrm{DFT}+U$ calculations of xenon behavior in uranium dioxide UO${}_{2}$. One of the main conclusions of their work is that the quasiannealing (QA) procedure allowed them to avoid metastable states created by the $\text{DFT}+U$ approximation. However, based on a comparison of total energies, they stated that an incomplete implementation of occupation matrix control (OMC) had been done in our previous work [B. Dorado, G. Jomard, M. Freyss, and M. Bertolus, Phys. Rev. B 82, 035114 (2010)] and that we failed to reach the ground state of the perfect UO${}_{2}$ fluorite structure. In this Comment, we show that the discrepancy they observed does not stem from an incomplete implementation of OMC, but from the calculation of the compensation charge used in the projector augmented-wave formalism.

International audience; This work provides an illustration that density functional theory (DFT) + U calculations may quantitatively describe transport phenomena in uranium dioxide. Oxygen diffusion mechanisms are investigated using both ab initio calculations and experimental approaches mainly involving self-diffusion coefficient measurements. The dependences of the experimental data upon oxygen potential and sample impurity content demonstrate, by comparison with basic point defect and diffusion theory, that oxygen migration occurs via an interstitial mechanism. The temperature study provides an estimate of interstitial formation and migration energies which compare very favorably to energies calculated using the DFT+U approximation relating to the interstitialcy mechanism. Also, vacancy migration and Frenkel pair formation energies are shown to agree well with existing data.

The formation and mobility of point defects in UO 2 have been studied within the framework of the Density Functional Theory. The ab initio Projector Augmented Wave method is used to determine the formation and migration energies of defects. The results relative to intrinsic point defect formation energies using the Generalized Gradient Approximation (GGA) and GGA+U approximations for the exchange-correlation interactions are reported and compared to experimental data. The GGA and GGA+U approximations yield different formation energies for both Frenkel pairs and Schottky trios, showing that the 5 f electron correlations have a strong influence on the defect formation energies. Using GGA, various migration mechanisms were investigated for oxygen and uranium defects. For oxygen defects, the calculations show that both a vacancy and an indirect interstitial mechanism have the lowest associated migration energies, 1.2 and 1.1 eV respectively. As regards uranium defects, a vacancy mechanism appears energetically more favourable with a migration energy of 4.4 eV, confirming that oxygen atoms are much more mobile in UO 2 than uranium atoms. Those results are discussed in the light of experimentally determined activation energies for diffusion.

Using classical molecular dynamics simulations, we have studied the first stages of defect cluster formation resulting from 10 keV displacement cascades in uranium dioxide. Nanometre size cavities and dislocation loops are shown to appear as a result of the irradiation process. A specifically designed TEM experiment involving He implanted thin foils have also been carried out to support this modelling work. These results, in conjunction with several other observations taken from the literature of ion implanted or neutron irradiated uranium dioxide, suggest a radiation damage controlled heterogeneous mechanism for insoluble fission product segregation in UO(2). (C) 2010 Elsevier B.V. All rights reserved.

We report a study of the ground state and metastable states of uranium dioxide using ab initio $\text{DFT}+\text{U}$ calculations. We highlight that in order to avoid metastable states and systematically reach the ground state of uranium dioxide with $\text{DFT}+\text{U}$, the monitoring of occupation matrices is crucial, as well as allowing the $5f$ electrons to break the cubic symmetry. For this purpose, we use a method based on the monitoring of the occupation matrix of the correlated orbitals on which the Hubbard term is applied. We observe the presence of numerous metastable states in calculations both with and without taking into account the symmetries of the wave functions. We investigate the influence of metastable states on the total energy, as well as on the electronic and structural properties of uranium dioxide. We show that the presence of metastable states induces large differences in the total energy and explain the origin of the discrepancies observed in the results obtained by various authors on crystalline and defect-containing ${\text{UO}}_{2}$. Finally, in order to check the consistency of the procedure, we determine the structural and electronic properties of the ground state of uranium dioxide and compare them with results obtained in previous studies using the $\text{DFT}+\text{U}$ approximation and hybrid functionals, as well as experimental data.