First-principles theory for helium and xenon diffusion in uranium dioxide

The diffusion properties of He and Xe in UO₂ have been investigated, using density-functional calculations employing the projector-augmented-wave (PAW) method and the generalized gradient approximation (GGA). The migration energies corresponding to both interstitial and vacancy-assisted mechanisms have been calculated and the results for the two noble gas atoms are compared with each other. We suggest that He likely diffuses by hopping through a single vacancy with computed low migration energies smaller than 0.79 eV and its diffusivity is much higher than that of Xe. Xe has a quite large migration energy compared to He; the strain energy plays a key role in Xe diffusion in UO₂.     

Theory of He trapping, diffusion, and clustering in UO2

We have performed ab initio total energy calculations to investigate the behavior of helium and its diffusion properties in uranium dioxide (UO₂). Our investigations are based on the density functional theory within the generalized gradient approximation (GGA). The trapping behavior of He in UO₂ has been modeled with a supercell containing 96-atoms as well as uranium and oxygen vacancy trapping sites. The calculated incorporation energies show that for He a uranium vacancy is more stable than an oxygen vacancy or an octahedral interstitial site (OIS). Interstitial site hopping is found to be the rate-determining mechanism of the He diffusion process and the corresponding migration energy is computed as 2.79 eV at 0 K (with the spin-orbit coupling (SOC) included), and as 2.09 eV by using the thermally expanded lattice parameter of UO₂ at 1200 K, which is relatively close to the experimental value of 2.0 eV. The lattice expansion coefficient of He-induced swelling of UO₂ is calculated as 9 × 10⁻². For two He atoms, we have found that they form a dumbbell configuration if they are close enough to each other, and that the lattice expansion induced by a dumbbell is larger than by two distant interstitial He atoms. The clustering tendency of He has been studied for small clusters of up to six He atoms. We find that He strongly tends to cluster in the vicinity of an OIS, and that the collective action of the He atoms is sufficient to spontaneously create additional point defects around the He cluster in the UO₂ lattice.     

An atomistic approach to self-diffusion in uranium dioxide

The formation and mobility of point defects in UO₂ 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 5f 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 UO₂ than uranium atoms. Those results are discussed in the light of experimentally determined activation energies for diffusion.     

Ab initio study of solution energy and diffusion of caesium in uranium dioxide

The behaviour of caesium in nuclear fuels is investigated using density functional theory (DFT). In a first step, the incorporation and solution energies of Cs in pre-existing trap sites of UO₂ (vacancies, interstitials, U-O di-vacancy and Schottky trio defects) are calculated using the projector-augmented-wave (PAW) derived pseudopotentials as implemented in the Vienna ab initio simulation package (VASP). Correlation effects are taken into account within the DFT + U approach. The solubility of caesium is found to be very low, in agreement with experimental data. The migration of Cs is found to be highly anisotropic, it is controlled by uranium diffusion with an Arrhenius activation energy of 4.8 eV in hyperstoichiometric UO_2+x, in good agreement with experimental values.     

Temperature accelerated dynamics study of migration process of oxygen defects in UO2

We studied the migration dynamics of oxygen point defects in UO₂ which is the primary ceramic fuel for light-water reactors. Temperature accelerated dynamics simulations are performed for several initial conditions. Though the migration of the single interstitial is much slower than that of the vacancy, clustered interstitial shows faster migration than those. This observation gives us important insight on the formation mechanism of high-burnup restructuring, including planar defects and grain sub-division (the rim structure), found in UO₂.     

Diffusion coefficient of Xe-133 in a SIMFUEL with a low burnup

Post irradiation annealing tests were performed to obtain the Xe-133 diffusion coefficients in a SIMFUEL which was a simulated irradiated UO₂ fuel with a burnup of 27,300 MWd/t U. Specimens were fabricated as cubic polycrystals with the same composition for a given burnup. Each 300 mg specimen was irradiated in the HANARO research reactor for up to a 0.1 MWd/t U burnup. Post irradiation annealing tests were carried out at 1400 °C, 1500 °C and 1600 °C. The xenon diffusion coefficients for the SIMFUEL were lower than those for UO₂ in near stoichiometric UO₂ due to a relatively higher concentration of the tri-valent additives, which is related to the concentration of a cation vacancy. The activation energy in the SIMFUEL was also lower than that in UO₂ due to the lower formation energy of a cation vacancy and the migration energy. The xenon diffusion coefficient for the SIMFUEL increased with an increasing oxygen potential of the ambient gas.     

On the solution and migration of single Xe atoms in uranium dioxide - An interatomic potentials study

Atomic scale simulation techniques based on empirical potentials have been considered in the present work to get insight on the behaviour of single Xe atoms in the uranium dioxide matrix. In view of the high activation energies commonly observed for Xe migration, this work has focused on the so-called “static calculations” (i.e. energy minimization based calculation) of incorporation and migration energies of Xe in UO₂, using empirical interatomic potentials to describe atom interactions. A detailed study of these results enables to determine the solution and the migration properties of Xe in the different stoichiometry regimes, and can be applied as well for the in-pile behaviour of xenon.     

Kinetic Monte Carlo model of defect transport and irradiation effects in La-doped CeO2

A generalized Kinetic Monte Carlo code was developed to study oxygen mobility in UO₂ type nuclear fuels, using lanthanum doped CeO₂ as a surrogate material. Molecular Statics simulations were performed using interatomic potentials for CeO₂ developed by Gotte, Minervini, and Sayle to calculate local configuration-dependent oxygen vacancy migration energies. Kinetic Monte Carlo simulations of oxygen vacancy diffusion were performed at varying lanthanum dopant concentrations using the developed generalized Kinetic Monte Carlo code and the calculated configuration-dependent migration energies. All three interatomic potentials were found to confirm the lanthanum trapping effect. The results of these simulations were compared with experimental data and the Gotte potential was concluded to yield the most realistic diffusivity curve.     

Atomistic modeling of the vibrational and thermodynamic properties of uranium dioxide, UO2

Modeling the thermal properties of uranium oxide is of immense interest to the nuclear industry. UO₂ belongs to the family of superionic conductors whose solid-state diffusion coefficients at high temperatures are comparable to that of liquids. We report lattice dynamics and molecular dynamics studies carried out on oxide UO₂ in its normal as well as superionic phase. Lattice dynamics calculations have been carried out using shell model in the quasiharmonic approximation. The calculated equilibrium structure, elastic constants, bulk modulus, phonon frequencies and specific heat are in excellent agreement with the reported experimental data. Pressure variation of the phonon dispersion and equation of state have also been predicted. Molecular dynamics simulations have been carried out to study the diffusion behavior and the thermodynamic properties in UO₂. The diffusion constant of O in UO₂ has been determined. The pair correlation functions, O-U-O bond angle and thermal amplitude of vibration for the oxygen atom provide a microscopic picture of the local structure thereby throwing light on the gradual increase in the disorder of the oxygen sub-lattice which is a signature of superionic transition. The calculated transition temperature of UO₂ is 2300 K, which compares well with experimental value of about 2600 K.     

The response of fission gas bubbles to the dynamic behavior of point defects

A model has been developed to investigate the response of fission gas bubbles to the dynamic behavior of uranium point defects in uranium oxide. Simple thermodynamics is used to calculate the thermal equilibrium concentrations of both anion and cation point defects in UO_2±x and fully dynamic rate theory has been extended to estimate the dynamic concentrations of uranium vacancies and interstitials and the enhanced self-diffusion of uranium during constant temperature and thermal transient irradiations.During low temperature irradiations, fission production of uranium Frenkel pairs is dominant and the slow migration rate of the vacancies leads to long start-up transients (~10⁶ s in stoichiometric UO₂ at 1000 K) as the vacancies reach a quasisteady state with the microstructure. Thermal ramp behavior of the point defects and fission gas cavities depends primarily upon the initial concentration of point defects, and the temperature at which the thermal production of point defects becomes dominant. Our results indicate that non-equilibrium fission gas behavior is important for both constant temperature and thermal transient irradiations and that fission gas bubble behavior models must consider fuel stoichiometry. Below about 2200 K the dynamic behavior of the point defects should be incorporated as well.     

Calculations of the trapping and migration of vacancies and nickel self-interstitials in the presence of rare gases and dislocations

Recent models of swelling, void growth, and solute segregation under irradiation all require knowledge of the trapping and migration of vacancies and self-interstitials in the presence of lattice defects. The present calculations include trapping of both vacancies and nickel self-interstitials to substitutional and interstitial rare gas atoms. The results show a systematic dependence on rare gas atom size. It is found for example, that a vacancy is bound to a small fixed rare gas interstitial (He) by ～0.5 eV and to a large fixed interstitial (Xe) by ≥3 eV. In addition, a fixed substitutional rare gas or rare gas interstitial is found to be a strong trap for a self-interstitial. It is found that a single vacancy can significantly affect the migration energy of another vacancy. For example, a 0.4 eV decrease in migration energy is found at a distance of three half-lattice constants. However, this interaction is of limited range; at distances greater than five half-lattice constants vacancy migration is unaffected. The migration of vacancies near the core of a partial dislocation was also investigated. This partial is found to provide a 1 eV (compared to 1.4 eV in the bulk) path for the pipe diffusion of vacancies. In addition, the activation energy for vacancy migration along the slip plane is reduced by as much as 0.2 eV.     

Plutonium diffusion in hyperstoichiometric mixed uranium-plutonium dioxides

The diffusion behaviour of plutonium in hyperstoichiometric mixed uranium (15%) plutonium dioxides was investigated as a function of temperature and oxygen/ metal ratio. At O/M = 2.10 an activation energy of 86 kcal/mole is found in good agreement with recent results on uranium self-diffusion in UO_{2 + x}. At constant temperature (1400 °C) and varying O/M ratios the diffusion coefficients are found to increase proportional to xⁿ, with n being equal to 2.77. The results are discussed in the light of recent theoretical models and experimental results on cation diffusion in uranium dioxide. Comparison is made to earlier results obtained on nearly stoichiometric mixed oxide.     

Interaction between uranium sulphides and oxygen

Study of the oxidation of uranium monosulphide shows that certain phenomena occur at three temperatures: 350–380, 480, and 720°C. In the temperature range 350–380°C, an intensive incorporation of oxygen begins, accompanied by loss of SO₂ and S. Simultaneously UO_2+0.45 and UO₂SO₄ are formed. As the temperature increases, the amount of sulphur remains constant and only oxygen is incorporated. At 540°C the X-ray pattern of the product corresponded to that of U₃O₈, but the composition was UO_3.50 + UO₂SO₄. At higher temperatures the remaining sulphur was burnt and U₃O₈ was obtained. The reaction between uranium disulphide and oxygen proceeds in a similar way, except that at 345°C preferential oxidation of sulphur occurs. Investigation of the isothermal oxidation of US and US₂ at temperatures 250–305° C and under an oxygen pressure of 400 Torr showed that the rate law was initially exponential (lateral growth of oxide film), and that it later became parabolic (diffusion of oxygen through the oxide layer).     

The dependence of in-reactor UO2 densification on temperature and microstructure

The in-reactor changes in size of sintered UO₂ are analyzed by superposing matrix swelling and pore shrinkage. At first pore shrinkage dominates and results in densification, an effect which has been known for a few years. With regard to shrinkage mechanisms one should distinguish between very fine pores and coarser pores, the latter being responsible for the majority of total porosity in well sintered UO₂. For this coarser porosity a two-step mechanism is postulated: first, the generation of vacancies by the fission fragments traversing the pores, second, the migration of these vacancies to effective sinks (grain boundaries) producing densification. Based on this assumption the dependence of densification on fission rate, temperature, pore size distribution and grain size is evaluated. There is a transient temperature above which the generation of vacancies is rate controlling and below which the vacancy migration becomes the rate controlling mechanism. At temperatures much lower than the transient temperature no densification should be observed.     

Uranium oxide weathering: spectroscopy and kinetics

Particles of UO_2+x (x≅0.16 ± 0.06) exposed to the atmosphere react by oxidation and formation of complexes (hydrates, hydroxides and carbonates). Surface reactions alter and erode the UO₂ particles. This paper outlines results for measurements of oxidation rates on uranium oxide particles using in situ photoluminescence spectroscopy (PL), X-ray photoelectron spectroscopy (XPS) and secondary ion mass spectrometry (SIMS). Phosphorescence spectra observed during oxidation of UO_2+x were attributed to U(VI) in uranyl-type coordination and in octahedral coordination. Uranyl-type spectra formed during wet oxidation of UO_2+x, and U(VI) octahedral spectra formed during dry oxidation of UO_2+x. The uranyl-type species, although more stable, is more kinetically labile for vacuum reduction than is the octahedral U(VI). Oxidation of U(IV) species are diffusion controlled. Vacuum reduction of uranyl U(VI) in UO₃ follows a field-enhanced cationic diffusion rate law, while re-oxidation follows a diffusion rate law. Post-oxidation core and valence band XPS and SIMS measurements provided qualitative and quantitative measures of uranium oxidation states near uranium oxide surfaces.     

Electrochemical Properties of Uranyl Ion in Ionic Liquids as Media for Pyrochemical Reprocessing

We have proposed a new reprocessing process by using ionic liquids (ILs) instead of molten salts of alkali chlorides in pyrochemical process. In the proposed process, spent nuclear fuels are dissolved in ILs by using Cl₂ as an oxidant, and UO₂ ²⁺ and PuO₂ ²⁺ ions in ILs are recovered as UO₂ and PuO₂ by electrochemical reduction. In order to examine applicability of ILs as media for reprocessing, we have studied electrochemical behavior of UO₂ ²⁺ in 1-butyl-3-methylimidazolium chloride (BMICl), 1-butyl-3-methylimidazolium tetrafluoroborate (BMIBF₄), and 1-butyl-3-methylimidazolium nonafluorobutanesulfonate (BMINfO). Electrochemical properties of uranyl chloride dissolved into ILs were examined by cyclic voltammetry. In BMICl, an almost reversible redox couple was observed, and the formal potential and the diffusion coefficient were evaluated as _0:758V vs. Ag/AgCl and 4:8 × 10^?8 cm²s^?1, respectively. On the other hand, the electrochemical reactions of UO₂ ²⁺ in BMIBF₄ and BMINfO were irreversible. In BMINfO, some reduction peaks and one sharp oxidation peak were observed in the range of ?0:6～–0:2V and around 0.85V vs. Ag/AgCl, respectively. The reduction and oxidation peaks were assigned to multi step reduction of UO₂ ²⁺ to U(IV) via U(V) and/or direct reduction of UO₂ ²⁺ to U(IV), and the oxidative dissolution of the resulting U(IV) compounds, respectively. The electrochemical reduction of UO₂ ²⁺ in BMINfO at ?1:0V vs. Ag/AgCl produced the deposits on a carbon electrode as a cathode. Analyses of the deposits with the scanning electron microscope and the energy dispersive X-ray spectrometer indicated that the deposits are compounds containing uranium, oxygen, and chlorine. As a result, it is expected that the UO₂ ²⁺ in IL can be recovered electrolytically as uranium compounds such as UO₂ and uranium oxychlorides.     

Enhanced thermal conductivity oxide nuclear fuels by co-sintering with BeO: II. Fuel performance and neutronics

The fuel rod performance and neutronics of enhanced thermal conductivity oxide (ECO) nuclear fuel with BeO have been compared to those of standard UO₂ fuel. The standards of comparison were that the ECO fuel should have the same infinite neutron-multiplication factor k_inf at end of life and provide the same energy extraction per fuel assembly over its lifetime. The BeO displaces some uranium, so equivalence with standard UO₂ fuel was obtained by increasing the burnup and slightly increasing the enrichment. The COPERNIC fuel rod performance code was adapted to account for the effect of BeO on thermal properties. The materials considered were standard UO₂, UO₂ with 4.0 vol.% BeO, and UO₂ with 9.6 vol.% BeO. The smaller amount of BeO was assumed to provide increases in thermal conductivity of 0, 5, or 10%, whereas the larger amount was assumed to provide an increase of 50%. A significant improvement in performance was seen, as evidenced by reduced temperatures, internal rod pressures, and fission gas release, even with modest (5-10%) increases in thermal conductivity. The benefits increased monotonically with increasing thermal conductivity. Improvements in LOCA initialization performance were also seen. A neutronic calculation considered a transition from standard UO₂ fuel to ECO fuel. The calculation indicated that only a small increase in enrichment is required to maintain the k_inf at end of life. The smallness of the change was attributed to the neutron-multiplication reaction of Be with fast neutrons and the moderating effect of BeO. Adoption of ECO fuel was predicted to provide a net reduction in uranium cost. Requirements for industrial hygiene were found to be comparable to those for processing of UO₂.     

Post-irradiation studies on knock-out and pseudo-recoil releases of fission products from fissioning UO2

By using post-irradiation techniques, in-pile releases of ¹³³Xe, ^85mKr, ⁸⁸Kr, ⁸⁷Kr and ¹³⁸Xe from UO₂ fissioning at low temperatures below about 200° C are studied: these are analyzed into a time-dependent knock-out and time-independent pseudo-recoil releases. For the latter, a “self knock-out” mechanism is proposed: when a fission fragment loses thoroughly its energy near the UO₂ surface and stops there, it will knock out the surface substances and accordingly the fragment (i.e. the fission product) will be released. The effective thickness of the layer where the self knock-out occurs is found to be ~7Å. As for the knock-out release, the following is estimated from its dependence on various factors: the knock-out release of fission products occurs from the surface layer with the effective thickness of ~20Å: the shape of UO₂ matrix knocked out by one fission fragment passing through the surface is equivalent to a cylinder ~32Å diameter by ~27Å thick, (i.e. the knock-out coefficient for UO₂ is ~660 uranium atoms per knock-out event). On the basis of the above estimations, the conclusions derived from the past in-pile studies of fission gas releases are evaluated.     

Phase equilibrium of PuO2−x − Pu2O3 based on first-principles calculations and configurational entropy change

Combination of an oxygen vacancy formation energy calculated using first-principles approach and the configurational entropy change treated within the framework of statistical mechanics gives an expression of the Gibbs free energy at large deviation from stoichiometry of plutonium oxide PuO₂. An oxygen vacancy formation energy 4.20 eV derived from our previously first-principles calculation was used to evaluate the Gibbs free energy change due to oxygen vacancies in the crystal. The oxygen partial pressures then can be evaluated from the change of the free energy with two fitting parameters (a vacancy-vacancy interaction energy and vibration entropy change due to induced vacancies). Derived thermodynamic expression for the free energy based on the SGTE thermodynamic data for the stoichiometric PuO₂ and the Pu₂O₃ compounds was further incorporated into the CALPHAD modeling, then phase equilibrium between the stoichiometric Pu₂O₃ and non-stoichiometric PuO_2−x were reproduced.