A procedure for bypassing metastable states in local basis set DFT+U calculations and its application to uranium dioxide surfaces

We present a study of the bulk and the (100), (110) and (111) surfaces of uranium dioxide (UO2) using DFT+U in combination with a mixed Gaussian and plane waves basis set method, as implemented in the CP2K program package. A novel scheme is presented which reliably allows the system to escape the lower-lying metastable states that arise from the improved treatment of the strongly correlated 5f electrons of uranium. Based on the electronic configurations obtained by an f-occupation smearing combined with U ramping, this method relaxes the local energy minima by averaging the f-occupation matrices used to calculate the corrections in DFT+U. Various surface terminations are investigated and their calculated formation energies are found to be consistent with the experimentally observed morphologies. The direction of the antiferromagmentic ordering in relation to the surfaces exerts little influence on the results of the calculations while surface reconstructions can induce significant structural changes extending well into the bulk.JRC.E.3-Materials researc

A DFT Investigation of the Interactions of Pd, Ag, Sn and Cs with silicon carbide

With a view to understanding the diffusion of radionuclides through the silicon carbide layers in Tristructural Isotropic (TRISO) coated fuel particles, density functional theory (DFT) calculations are applied to palladium, silver, tin and caesium with silicon carbide. The silicon carbide molecule (Si2C2), crystalline cubic silicon carbide (β-SiC) and the (120) Σ5 grain boundary of β-SiC are investigated to elucidate the differences in the interactions of silicon carbide with these elements. The calculations show that the electronic interactions have a significant effect on the way these elements interact with the silicon and carbon atoms of silicon carbide. The lowest energy structure of the AgSi2C2 complex is unique to silver, although for all these elements low energy structures are formed where the metal atom lies to one side of a C-Si bond. By comparing the incorporation energies in the solid phases, it is possible to group these elements by similarities in the patterns of incorporation energies. Silver and palladium form a group with carbon, tin is grouped with silicon and caesium is on its own.JRC.E.3-Materials researc

Steam flows in concrete cracks: Pressure differentials and flow rates

International audienc

DFT-based Metadynamics Simulation of Proton Diffusion in Tetragonal Zirconia at 1500K.

The diffusion rate of hydrogen in zirconium oxides is a factor in both the steam oxidation and the hydriding of zirconium alloys. It has been suggested that the measured rates of hydrogen uptake in zircaloys exposed to high-temperature steam can be explained by the diffusion of protons through the surface oxide layers, since the measured uptake and diffusion of neutral hydrogen species in zirconium oxides is very low. This paper investigates the diffusion of protons in tetragonal zirconia at 1500K using denstity functional theory based molecular dynamics and metadynamics simulations. A mean calculated diffusion rate of 5×10-9 / m2s-1 is obtained, which compares well with the value of 3.2×10-10 / m2s-1 obtained by fit to experimentally determined diffusivities of hydrogen in yttrium stabilised zirconia. The simulations show that the "proton" is present as the hydrogen atom in a hydroxide ion and analysis of the electronic structure reveals that the diffusion of the proton is mediated by two-electron-three-centre bonds that form between hydroxide and adjacent oxide ions.JRC.E.3-Materials researc

Steam flows in concrete cracks: Design of an experiment

International audienc

Density Functional Theory Metadynamics of Silver, Caesium and Palladium diffusion at β-SiC Grain Boundaries

The use of silicon carbide in coated nuclear fuel particles relies on this materials impermeability towards fission products under normal operating conditions. Determining the underlying factors that control the rate at which radionuclides such as Silver-110m and Caesium-137 can cross the silicon carbide barrier layers, and at which fission products such as palladium could compromise or otherwise alter the nature of this layer, are of paramount importance for the safety of this fuel. To this end, DFT-based metadynamics simulations are applied to the atomic diffusion of silver, caesium and palladium along a Σ5 grain boundary and to palladium along a carbon-rich Σ3 grain boundary in cubic silicon carbide at 1500K. For silver, the calculated diffusion coefficients lie in a similar range (7.04×10-19 – 3.69×10-17 m2s-1) as determined experimentally. For caesium, the calculated diffusion rates are very much slower (3.91×10-23 – 2.15×10-21 m2s-1) than found experimentally, suggesting a different mechanism to the simulation. Conversely, the calculated atomic diffusion of palladium is very much faster (7.96×10-11 – 7.26×10-9 m2s-1) than the observed penetration rate of palladium nodules. This points to the slow dissolution and rapid regrowth of palladium nodules as a possible ingress mechanism in addition to the previously suggested migration of entire nodules along grain boundaries. The diffusion rate of palladium along the Σ3 grain boundary was calculated to be slightly slower (2.38×10-11 – 8.24×10-10 m2s-1) than along the Σ5 grain boundary. Rather than diffusing along the precise plane of the boundary, the palladium atom moves through the bulk layer immediately adjacent to the boundary as there is greater freedom to move.JRC.E.3-Materials researc

Silver and Cesium Diffusion Dynamics at the β‑SiC Σ5 Grain Boundary Investigated with Density Functional Theory Molecular Dynamics and Metadynamics

The diffusion and release of silver-110m, a strong γ-radiation emitter, through silicon carbide in coated nuclear fuel particles has remained an unsolved topic since it was first observed 40 years ago. The challenge remains to explain why, contrary to other elements, silver is capable of escaping the ceramic diffusion barriers. The current work investigates the underlying differences in the diffusion of silver and cesium along a symmetric tilt Σ5 grain boundary of β-SiC through accelerated density functional theory molecular dynamics simulations. The energy barriers extracted from the simulations give diffusion coefficients that are in reasonable agreement with experiment for silver (2.19 × 10−19 to 1.05 × 10−17 m2 s−1), but for cesium the equivalent calculated coefficients for this mechanism are much smaller (3.85 × 10−23 to 2.15 × 10−21 m2 s−1) than those found experimentally. Analysis of the simulated structures and electron densities and comparisons with the calculations of other researchers suggest that diffusion of silver and cesium in β-SiC proceeds via different mechanisms. The mechanisms of cesium diffusion appear to be dominated by its relatively large size and repulsive interactions with the silicon and carbon atoms; β-SiC grain boundaries still offer higher energy barriers to diffusion. Silver, on the other hand, is not only smaller in size but, as we show for the first time, can also participate in weak bonding interactions with the host atoms where favorable geometries allow, thus reducing the energy barrier and enhancing the rate of diffusion.JRC.E.3-Materials researc

Silver and Cesium Diffusion Dynamics at the β‑SiC Σ5 Grain Boundary Investigated with Density Functional Theory Molecular Dynamics and Metadynamics

The diffusion and release of silver-110m, a strong γ-radiation emitter, through silicon carbide in coated nuclear fuel particles has remained an unsolved topic since it was first observed 40 years ago. The challenge remains to explain why, contrary to other elements, silver is capable of escaping the ceramic diffusion barriers. The current work investigates the underlying differences in the diffusion of silver and cesium along a symmetric tilt Σ5 grain boundary of β-SiC through accelerated density functional theory molecular dynamics simulations. The energy barriers extracted from the simulations give diffusion coefficients that are in reasonable agreement with experiment for silver (2.19 × 10^–19 to 1.05 × 10^–17 m² s^–1), but for cesium the equivalent calculated coefficients for this mechanism are much smaller (3.85 × 10^–23 to 2.15 × 10^–21 m² s^–1) than those found experimentally. Analysis of the simulated structures and electron densities and comparisons with the calculations of other researchers suggest that diffusion of silver and cesium in β-SiC proceeds via different mechanisms. The mechanisms of cesium diffusion appear to be dominated by its relatively large size and repulsive interactions with the silicon and carbon atoms; β-SiC grain boundaries still offer higher energy barriers to diffusion. Silver, on the other hand, is not only smaller in size but, as we show for the first time, can also participate in weak bonding interactions with the host atoms where favorable geometries allow, thus reducing the energy barrier and enhancing the rate of diffusion