Effect of cationic chemical disorder on defect formation energies in uranium-plutonium mixed oxides

At the atomic scale, uranium-plutonium mixed oxides (U,Pu)O_2 are characterized by cationic chemical disorder, which entails that U and Pu cations are randomly distributed on the cation sublattice. In the present work, we study the impact of disorder on point-defect formation energies in (U,Pu)O_2 using interatomic-potential and Density Functional Theory (DFT+U) calculations. We focus on bound Schottky defects (BSD) that are among the most stable defects in these oxides. As a first step, we estimate the distance R_D around the BSD up to which the local chemical environment significantly affects their formation energy. To this end, we propose an original procedure in which the formation energy is computed for several supercells at varying levels of disorder. We conclude that the first three cation shells around the BSD have a non-negligible influence on their formation energy (R_{D} = 7.0 \{AA}). We apply then a systematic approach to compute the BSD formation energies for all the possible cation configurations on the first and second nearest neighbor shells around the BSD. We show that the formation energy can range in an interval of 0.97 eV, depending on the relative amount of U and Pu neighboring cations. Based on these results, we propose an interaction model that describes the effect of nominal and local composition on the BSD formation energy. Finally, the DFT+U benchmark calculations show a satisfactory agreement for configurations characterized by a U-rich local environment, and a larger mismatch in the case of a Pu-rich one. In summary, this work provides valuable insights on the properties of BSD defects in (U,Pu)O_2, and can represent a valid strategy to study point defect properties in disordered compounds.Comment: 33 pages, 20 figure

Study of point defect and thermodynamics properties coupling electronic structure and empirical interatomic potential calculations

En réacteur, le combustible MOX (U,Pu)O_2 est soumis à des conditions extrêmes qui créent des défauts ponctuels et qui modifient ses propriétés, ayant pour conséquence d'altérer ses performances. Une détermination précise des propriétés thermodynamiques et des défauts dans le MOX est donc nécessaire pour prédire son comportement en réacteur. A l'échelle des atomes, les cations U et Pu sont distribués de manière aléatoire sur un même sous-réseau de la structure cristalline du MOX. Dans cette étude, nous avons étudié l'effet de ce désordre chimique sur les propriétés thermodynamiques et des défauts ponctuels de (U,Pu)O_2 en utilisant une approche numérique couplant les calculs de structure électronique et les potentiels interatomiques empiriques. Les résultats obtenus en potentiels empiriques montrent que la capacité calorifique C_p de (U,Pu)O_2 en phase solide présente un pic associé à une transition de phase dite de Bredig. Cette transition a été confirmée dans le cas de UO_2 et PuO_2 à l'aide des méthodes de structure électronique. Une loi analytique du C_p de (U,Pu)O_2 a été ajustée sur les données des potentiels empiriques et mise en \oe{}uvre dans le code de performance GERMINAL. Par ailleurs, nous avons déterminé, à l'aide des potentiels empiriques, la distance autour des défauts de Schottky (BSD) jusqu'à laquelle les configurations cationiques de U et Pu affectent l'énergie de formation des BSD ainsi que l'effet du désordre chimique sur cette propriété. Cette étude a été confirmée par des calculs de structure électronique et ouvre la voie à des études complémentaires des propriétés des défauts et de transport atomique dans (U,Pu)O_2.(U,Pu)O_2 MOX fuel is subjected in pile to extreme conditions that create point defects and that influence its properties, resulting in the alteration of its performance. Therefore, an accurate determination of thermodynamic and defects properties of (U,Pu)O_2 is required to predict its behaviour during its life in reactor. At the atomic scale, U and Pu cations are distributed randomly on a single common sublattice of the fluorite structure. In this study, we have investigated the effect of this cationic chemical disorder on thermodynamic and point defect properties of (U,Pu)O_2 using an approach coupling electronic structure and empirical potential calculations. Concerning thermodynamic properties, the results of empirical potential calculations show that the heat capacity of (U,Pu)O_2 exhibits a peak below the melting temperature associated with the Bredig phase transition. This transition was confirmed in the case of UO_2 and PuO_2 using electronic structure calculations. An analytical law for (U,Pu)O_2 heat capacity was fitted on the empirical potentials data and implemented in the GERMINAL performance code. This new law only has a significant effect on transient power simulations involving large and rapid temperature variations. Concerning point defect properties, we have determined using empirical potentials the distance around Schottky defects (BSD) up to which the cationic configurations affect the BSD formation energy and the energy interval induced by the chemical disorder. This energy interval was confirmed using electronic structure calculations. This study opens the path to further studies of defect and transport properties in (U,Pu)O_2

Atomic scale investigation of thermodynamic and defect properties of (U,Pu)O2 mixed oxide

International audienceOne way of increasing significantly the efficiency in designing and qualifying innovative fuels is to enhance the predictive capability of fuel behaviour simulation by developing a more physically based description of nuclear fuels. Basic research approaches combining multiscale modelling and separate effect experiments can bring significant insight into materials properties and key phenomena involved in the evolution of fuels in reactor.We will show the results obtained using state-of-the art electronic structure and empirical calculations on the uranium-plutonium mixed oxide. In particular, the thermal expansion, enthalpy increments and specific heat of (U,Pu)O2 as a function of Pu content will be presented. The defect properties of (U,Pu)O2 and the impact of the disorder on the cationic sublattice will also be discussed

Finite frequency noise: an original probe for topological superconductors

International audienceTopological superconductor nanowires constitute a strong candidate for the observation of Majorana bound states, which are expected to lie at each of its ends. Here, we suggest that current-current correlations probed at finite frequency offer a promising and original tool for the further characterization of the presence of such states in condensed matter systems, complementary to properties studied thus far. Focusing on a voltage-biased junction between a normal metal and a topological superconductor nanowire, we use the nonequilibrium Keldysh formalism to compute the finite frequency emission and absorption noise. Our results suggest that the presence of a Majorana bound state leads to a characteristic behavior of the noise spectrum at low frequency. While more work is still required to ensure that this constitutes an unambiguous signature, we could already check that different features arise for a nontopological system with a resonant level, exhibiting a zero-energy Andreev bound state

Semi-supervised generative approach to point-defect formation in chemically disordered compounds: application to uranium-plutonium mixed oxides

Machine-learning methods are nowadays of common use in the field of material science. For example, they can aid in optimizing the physicochemical properties of new materials, or help in the characterization of highly complex chemical compounds. An especially challenging problem arises in the modeling of chemically disordered solid solutions, for which some properties depend on the distribution of chemical species in the crystal lattice. This is the case of defect properties of uranium-plutonium mixed oxides nuclear fuels. The number of possible configurations is so high that the problem becomes intractable if treated with direct sampling. We thus propose a machine learning approach, based on generative modeling, to optimize the exploration of this large configuration space. A probabilistic, semi-supervised approach using Mixture Density Network is applied to estimate the concentration of thermal defects in (U, Pu)O2. We show that this method, based on the prediction of the density of states of formation energy of a defect, is computationally much more cost-efficient compared to other approaches available in the literature.Comment: The performed calculations require re-verificatio

Carbon stable isotope ratio of phloem sugars in mature pine trees throughout the growing season: comparison of two extraction methods

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Seasonal dynamics of the carbon isotope composition of phloem sap and CO2 fluxes in a mature pine forest

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