Uranium Self-diffusion Research Articles

First-principles study of intrinsic point defects and Xe impurities in uranium monocarbide

Based on density functional theory (DFT) calculations, we perform an extensive investigation of intrinsic point defects and Xe impurities in uranium monocarbide (UC). The DFT calculations involve both the conventional generalized gradient approximation (GGA) and the GGA+U approach with the Hubbard parametric term (U), using up to 5×5×5 supercells. GGA calculations for the formation energy of intrinsic defects demonstrate the significant effect of using larger supercells than in previous studies. Results confirm that the ⟨111⟩ and ⟨100⟩ dumbbell interstitials are the most stable interstitial configurations for U and C, respectively. The interstitial mechanisms are favored for self-diffusion of both uranium and carbon and diffusion of Xe under equilibrium conditions. Calculations also reveal that the Xe substitutional defect at the C lattice site tends to adopt an off-site configuration, which can be interpreted as a Xe interstitial–C vacancy complex. We also utilize GGA+U to assess the impact of effective U parameter (Ueff) on the results. Moreover, we introduce a method to estimate the carbon chemical potential by fitting the phase diagram composition data and propose a selection Ueff=1.25 eV based on the experimental Xe diffusion activation energy. With this approach, GGA+U calculations reproduce the available experimental data for the formation energy of the carbon Frenkel pair and can explain the stepwise recovery of intrinsic properties and burst Xe release behavior in UC observed in annealing experiments.

Cluster dynamics simulation of uranium self-diffusion during irradiation in UO2

As fission fragments pass through UO2 nuclear fuel, a considerable concentration of Frenkel pair defects (i.e. vacancies and interstitials) are created. The steady-state concentration of these defects leads to enhanced uranium self-diffusion, one of several fundamental kinetic parameters that control key engineering properties such as creep and fission gas swelling in UO2 nuclear fuel. A cluster dynamics method to track point defects and defect clusters has been implemented in the MARMOT phase-field code in order to predict as-measured out-of-pile and irradiation enhanced thermal diffusivity. The calculated uranium self-diffusion coefficient compares well with non-irradiated fuel measurements, and shows similar trends to those observed in irradiated fuel, which is a good result given the complexities introduced by non-stoichiometric compositions.

Carbon diffusion in molten uranium: an ab initio molecular dynamics study

In this work we used ab initio molecular dynamics within the framework of density functional theory and the projector-augmented wave method to study carbon diffusion in liquid uranium at temperatures above 1600 K. The electronic interactions of carbon and uranium were described using the local density approximation (LDA). The self-diffusion of uranium based on this approach is compared with literature computational and experimental results for liquid uranium. The temperature dependence of carbon and uranium diffusion in the melt was evaluated by fitting the resulting diffusion coefficients to an Arrhenius relationship. We found that the LDA calculated activation energy for carbon was nearly twice that of uranium: 0.55 ± 0.03 eV for carbon compared to 0.32 ± 0.04 eV for uranium. Structural analysis of the liquid uranium–carbon system is also discussed.

First-principles calculations of uranium diffusion in uranium dioxide

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.

On the nuclear oxide fuel densification, swelling and thermal re-sintering

A method of calculating the fuel densification and swelling as a result of only the initial fuel porosity has been developed. Well-characterized UO 2 fuel pellets, from the Romanian CANDU type fuel fabrication route, were used to fit the specific pore volume distribution resulted from the sintering process to a lognormal distribution function and thermal re-sintering tests up to 280 h at 1700 °C were done to fit the coefficients of vacancies diffusion and the self-diffusion of uranium, required by the model. Careful analyses proved that the irradiation-induced resolution is strongly dependent of the hydrostatic pressure and a corrected formula has been proposed. Analyses of the time evolution of the pore size distribution during re-sintering tests and annealing tests similar with some as described in the open literature were also done.

The diffusion of iodine and caesium in the UO 2± x lattice

The migration activation enthalpies of caesium and iodine in UO 2± x predicted using atomistic simulation methodology, depend greatly on fuel stoichiometry. The mechanisms for stoichiometric and non-stoichiometric fuel require uranium self-diffusion, with the exception of iodine in UO 2− x which employs an anion vacancy mechanism. The iodine post-irradiation results compare very well with the predicted activation enthalpy. In-pile iodine release experiments suggest a reduced activation enthalpy for iodine migration. The diffusion model presented allows for this result if uranium diffusion were greatly affected by the irradiation conditions.

First study of uranium self-diffusion in UO 2 by SIMS

Uranium self-diffusion coefficients were measured in UO 2 single crystals through an original methodology based on the utilization of 235U as tracer and depth profiling by secondary ion mass spectrometry (SIMS). The values of the self-diffusion coefficients measured in this work, between 1498 and 1697°C, in H 2 atmosphere, can be described by the following Arrhenius relation: D (cm 2/s)=8.54 × 10 −7exp[−4.4(eV)/kT], and are lower than those previously determined by other authors in `nearly stochiometric' UO 2 in the same temperature range.

Self diffusion of europium, neodymium, thorium, and uranium in haplobasaltic melt: The effect of oxygen fugacity and the relationship to melt structure

We report new measurements of self diffusion coefficients ( D) for Mg, Nd, Eu, Th, and U in a haplobasaltic (Fo 15Di 40An 45) melt at 1 atm, 1400–1500°C, and oxygen fugacities corresponding to air and the FeFeO buffer. Diffusion couples consisted of isotopically distinct melts of the same chemical composition, and isotopic concentration profiles in quenched couples were measured with an ion probe. The valence state distributions of Eu and U were determined from absorption spectroscopy and model calculations, which demonstrate a shift from Eu 3+ and U 5.5+ in air to Eu 2.5+ and U 4+ at FeFeO. D Mg, D Nd, and D Th are independent of oxygen fugacity and agree well with our previous measurements. D Eu = D Nd in air and increases by 42% at FeFeO, while D U = D Th in air and shows a possible small increase of ∼20% at FeFeO. The change in D Eu with oxygen fugacity matches the established ionic radius and charge dependence for Mg, Ca, Ba, Nd, Yb, Ti, and Zr, while diffusion coefficients for Zr, Th, U 4+, and U 5.5+ are independent of ionic radius and charge. Activation energies for all cations are approximately equal, independent of oxygen fugacity, and approximately match the activation energy for viscous flow. In addition, activation energies and diffusion coefficients recently measured for O and Si in basalt agree well with the present values. The good agreement between the various activation energies and between network modifier and network former diffusivities is consistent with a model in which diffusion of network modifying cations in low viscosity melts is controlled largely by the extrinsic influence of the melt network reorganization, with an additional influence from the intrinsic mobilities of the individual cations. The constant diffusion coefficient defined by the high ionic radius and charge elements is interpreted to represent the characteristic network diffusivity for this composition, which dominates over the intrinsic diffusivities for these elements. Elements with faster intrinsic diffusivities still display a small ionic radius and charge dependence. Diffusion coefficients in high viscosity melts are expected to be decoupled from the network, and thus may display a much greater dependence on ionic radius and charge.

Uranium-plutonium interdiffusion at 750°C

An isothermal diffusion couple between pure uranium and a uranium-27 at% plutonium alloy was annealed at 750°C for 25 h. Composition profiles were determined from electron microanalyses, from which interdiffusion fluxes and interdiffusion coefficients were evaluated. The presence of plutonium greatly increases diffusion at this temperature over what would be predicted from uranium self-diffusion studies. Moreover, diffusivities in the body centered cubic U(γ) phase increase with increasing plutonium concentration, unlike interdiffusion in the orthorhombic U(α) phase at lower temperatures. The diffusion results suggest that plutonium has a greater intrinsic diffusivity than uranium at 750°C.

Uranium self-diffusion in UC doped with Y, Zr, La or Ce

Metal diffusion in UC and (U, Pu) C is increased at intermediate temperatures (e.g. 1200 to 1600°C) by factors of between 10 and 1000 by small additions of impurities (e.g. 0.1 to 2% of Fe, Ni, Ta). This can be explained by impurityvacancy interactions. All impurities studied so far had smaller atomic sizes than the substituted U and Pu atoms. In the present work, the effect of the bigger impurity atoms La and Ce on uranium self-diffusion in UC 1 ± x is studied. Further data are reported on Zr and Y as additives. The results show that Zr, Ce, and possibly Y can decrease metal atom self-diffusion rates. This effect can, however, easily be overcompensated by other impurities such as Fe and W which increase uranium self-diffusion. There is no obvious relation between the enhancement or diminution factor of the impurities and the lattice parameter of the doped carbide or the atomic size of the impurity atom.

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 (~10 6 s in stoichiometric UO 2 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.

Observations on the low-temperature creep properties of uranium carbide under irradiation

The creep behaviour of 97% dense hyperstoichiometric UC has been examined during irradiation in three-point bend tests carried out at 450°C up to a dose of 1.65 × 10 26 fissions/m 3 . A rapid decrease in measured strain rate with dose was observed at each stress level, nominally steady-state creep being established above ≈ 1 × 10 26 fissions/m 3 when the creep rate was a factor of 8 lower than that observed in UO 2 irradiated under identical conditions. Creep rates were found to be directly proportional to stress at high doses. Comparison of results from this test with data from other experiments up to 2 × 10 25 fissions/m 3 in compression and tension indicates little variation in the radiation-creep constant between 450°C and 800°C. The creep rate for UC, much lower than that observed in UO 2, is consistent with recently reported determinations of the effective uranium self-diffusion coefficients under irradiation in those materials.

The effect of Fe, Ni and W impurities on uranium diffusion in uranium monocarbide

The self-diffusion of uranium with U-233 as tracer was measured in stoichiometric UC which was doped with Fe, Ni or W impurities. The impurities were added by flash evaporation on the UC and subsequent diffusion into the UC. Uranium diffusion was increased in the doped samples as compared to undoped UC at all temperatures studied (1380 to 2200°C). The increase was most pronounced (more than a factor of 100) at low temperatures. Simultaneously, pronounced grain-boundary penetration was observed at low temperatures, possibly due to eutectic formation at the grain boundaries. The ratio of grain boundary to lattice diffusion coefficients at 1380°C was of the order of 3 × 10 4. The present data serve to explain some of the scatter of the literature data and correlate well with the known increased rate of sintering of Ni-doped UC.

Uranium self-diffusion in stoichiometric uranium monocarbide

Uranium-233 self-diffusion was studied in stoichiometric uranium monocarbide; the diffusion coefficients can be represented by the expression D ∗ U = (2.58 +4.54 −1.64) × 10 3exp(− 157000 ± 5000 RT )cm 2/s in the temperature range from 1900 to 2260°C. Self-diffusion of uranium and carbon, in stoichiometric and hypostoichiometric uranium carbides occurs by a vacancy mechanism. It is shown that the kinetics and mechanism are similar to those for self-diffusion in the group IVb and Vb transition element monocarbides; for these B1 (fcc) type carbides in general, the activation energy for diffusion is empirically correlated to the congruent melting temperature: for carbon ΔH C m∼- 31 T m and for the metal, (ΔH M f + ΔH M m) ∼-54 T m . In addition, the activation entropies correlate well to the temperature derivative of the shear modulus; this behaviour is consistent with the familiar Zener model. Microstructural effects have probably been the principal underlying cause of the preponderant discordance in the results of other investigators.

Fission-enhanced self-diffusion of uranium in UO 2 and UC

In-pile self-diffusion measurements in stoichiometric UO 2 sinters and single crystals and in arc-cast stoichiometric UC have been performed using the thin layer condition and 233U as tracer. The nominal irradiation temperature was 900°C. The resulting diffusion coefficients D∗ of 1.5 × 10 −16 cm 2 · sec −1 for UO 2 and 2.2 × 10 −17 cm 2 · sec −1 for UC for a fission rate S of 1 × 10 13f/cm 3 · sec represent radiation enhanced diffusion and are higher by factors of 10 3 to 10 4 than (extrapolated) coefficients of thermal diffusion. The data are of immediate relevance for understanding and predicting such important quantities as in-pile sintering and densification, diffusion controlled creep and fission gas behavior in the outer zones of the fuel. They are at the upper limit of expected values.

Self-diffusion of uranium in uranium dicarbide UC 2

The self-diffusion of uranium in uranium dicarbide, UC 2, was measured between 1670 and 2500 K using the α-energy degradation method with the thin layer condition and U-233 as tracer. The activation enthalpy was 5.7 ± 0.2 eV. A discontinuity was indicated at ≈ 2050 K, the transition temperature of α-UC 2 to β-UC 2.

Crystallographic shear and ordered reduction of UO2

Abstract Electron microscopy was used to study the surfaces (with replicas) and the near surface regions (with transmission) of UO2 annealed under reducing conditions. Parallel striations were observed with both techniques following isothermal or pulse annealing to temperatures between 1480° and 1950°c, and simultaneously a splitting of the spots in the diffraction patterns occurred. These observations are consistent with the formation of planar faults in a crystallographic shear structure of partly reduced UO2. A reduction to UO1·98 is indicated for regions near the surface on annealing UO2 to 1500°c in H2. The surface structure is probably due to additional etching to minimize the misfit. Implications of the ordered reduction on physical measurements sensitive to surface conditions (especially of uranium self-diffusion), and on the understanding of the defect structure of UO2, are discussed.

Actinide diffusion in uranium monocarbide

Uranium self-diffusion has been investigated in uranium carbide of controlled compositions, UC 1.07 and UC 0.96, within a temperature range between 1700 and 2300 °C. The respective temperature functions are: [Display omitted] [Display omitted] [Display omitted] Comparative measurements of actinide diffusion (Pa, Pu, Am) in UC 1.07 yielded quite similar results, the deviations between the respective activation energies being within the range of experimental errors. From the change in activation energies in the hyperstoichiometric material at 2050 °C it is concluded that the phase-boundary between UC 1 + x and β-UC 2 does not agree with the presently accepted U-C phase diagram.

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 x n , 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.

Uranium and oxygen self-diffusion in UO2

Uranium self-diffusion coefficients in hyperstoichiometric uranium dioxide UO2 + x (0.005 ⩽ x ⩽ 0.217) were determined in the temperature range 1275–1650 °C by means of the alpha spectrum degradation method. The results can be fitted, in the composition range 0.03 <x < 0.20, with the Arrhenius equation: D = 0.13 x2 [1 + 103x3] exp (−85 000/RT)cm2/sec.Oxygen self-diffusion in massive UO2 samples has been studied by means of mass spectrometry (using a spark or laser source), proton 18O (p, α) 15N reaction and ionic mass analyzer. In the temperature range 780–1250 °C, oxygen diffusion in stoichiometric samples can be represented by the equation: D = 0.26 exp (−59 300/RT) cm2/sec.A considerable enhancement of D with small stoichiometry deviations has been evidenced at 800 °C.