Growth Of Fission Gas Bubbles Research Articles

Parameterization of vacancy production rate in phase-field models of fission gas bubble evolution in nuclear fuel

Phase-field modeling has increasingly been used to study microstructual evolution in fission gas bubbles in nuclear fuel to improve understanding of fission gas release. To improve computational efficiency, often only vacancies and gas atoms are included as defect species. In this case, the net effects of vacancy and interstitial production, recombination, and biased sink absorption are included as a net vacancy source, or net vacancy source combined with an effective sink. However, there has been a lack of clarity on what parameter values should be used for these approaches to best match the more complete physical picture that includes interstitials and vacancies. Here, we compare a phase-field model of void growth to analytical models for the source-only and source plus sink approach to gain insight into how the phase-field models can be parameterized effectively. The source-only approach provides greater flexibility to match growth rates determined from the full vacancy-interstitial picture. A strategy was developed for determining the value of the net vacancy source term by comparing to an analytical model that includes vacancy and interstitial production, recombination, and biased sink absorption. This strategy can be used to parameterize phase-field models of fission gas bubble growth.

Scaling dynamics and universality of fission-gas-bubble growth in amorphous systems

ABSTRACT We present a generalised approach for describing the universal dynamics and statistical properties of fission gas bubble growth in amorphous systems, using as an example. We examine the scaling properties of both the growth and coalescence regimes of bubble growth, and find that the scaling exponents in these regimes are controlled by the fission rate and temperature. The nucleation regime is characterised by a growth exponent close to 1/2, while the coalescence regime is characterised by a growth exponent around 1/3. We show that the statistical distribution over bubble size is of a universal character. Analytical results are verified by numerical simulations and clarified with experimental data. This study provides insight into the kinetics of fission gas bubble growth in amorphous systems.

Skeleton-creep based bubble growth model and multi-scale mechanical constitutive model for U-10Mo fuels under irradiation

The macroscale irradiation swelling deformations of nuclear fuels induced by the solid and gas fission products are one of the most concerned problems in nuclear reactor core design. Based on continuum mechanics, an innovative macroscale volume growth strain model is proposed for U-10Mo fuels, with the coupling contributions of irradiation creep, fission solid swelling and thermal expansion of fuel skeleton. Correspondingly, new three-dimensional mechanical constitutive models and stress update algorithms are also developed for the multi-scale irradiation-deformation and stress analysis. Good agreements of the predictions with diverse experimental data validate the effectiveness of newly developed models. It is obtained that the growth of fission gas bubbles is dominated by the creep deformations of the surrounding fuel skeleton, depending on the external hydrostatic pressure and the internal bubble pressure related to the intra-granular fission gas atom diffusion; the influences of temperature, external hydrostatic pressure and fuel-skeleton creep rate coefficient are found to become prominent at higher burnup levels, dominantly induced by the coupling of fuel-skeleton creep and local porosity. This study provides a new insight into the mechanism of bubble growth in the solid skeleton, revealing the coupling of irradiation swelling with fuel-skeleton creep.

Phase-field simulations of fission gas bubble growth and interconnection in U-(Pu)-Zr nuclear fuel

The growth and interconnection of fission gas bubbles in the hotter central regions of U-(Pu)-Zr nuclear fuel has been simulated with a phase-field model. The Cahn-Hilliard equation was used to represent the two-phase microstructure, with a single defect species. The volume fraction of the bubble phase and surface area of the bubble-matrix interface were determined during growth and interconnection. Surface area increased rapidly during the initial stages of growth, then slowed and finally decreased as bubble interconnection began and coarsening acted to reduce surface area. The fraction of the bubbles vented to a simulation domain boundary, fV, was quantified as a measure of the microstructure’s interconnectivity and plotted as a function of porosity p. The defect species diffusivity was varied; although changes in diffusivity significantly affected the microstructure, the plots of fV vs. p did not change significantly. The percolation threshold pc was calculated to be approximately 0.26, depending on the assumed diffusivity and using an initial bubble number density based on experimental observations. This is slightly smaller than the percolation threshold for continuum percolation of overlapping 3D spheres. The simulation results were used to parameterize two different engineering-scale swelling models for U-(Pu)-Zr in the nuclear fuel performance code BISON.

Molecular dynamics study of the point defects in bcc uranium

Thermodynamic properties of bcc uranium with point defects are studied using ab initio molecular dynamics (MD) simulations at 1100 K. The simulations were performed with canonical ensembles of ${\mathrm{U}}_{127}{\mathrm{M}}_{1}$, ${\mathrm{U}}_{128}{\mathrm{M}}_{1}$, and ${\mathrm{U}}_{126}{\mathrm{M}}_{1}{\ensuremath{\square}}_{1}$ for M = $\ensuremath{\square}$, He, Ne, Ar, Kr, Xe, Sr, Zr, I, Cs, and Pu disposed on a bcc lattice lying within a $4\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4$ cubic supercell. This work provides formation energies of substitutional, self, and solute interstitial atom defects as well as binding energies of M-$\ensuremath{\square}$ pair defects. This work demonstrates that our computational scheme based on MD simulations gives reliable formation and binding energies of atomic defects in bcc uranium compared to conventional density functional theory calculations. The equilibrium volume, bulk modulus, and thermal expansion coefficient of pure bcc uranium obtained from our MD simulations compare very well with corresponding experimental results. The vacancy formation energy is predicted to be 0.88 eV. The experimental vacancy formation energy remains uncertain. Experimental study of the formation and binding energies of other point defects as well as the bulk modulus and thermal expansion coefficients of uranium with these defects is also not found in the literature. This work shows that point defects tend to decrease the bulk modulus and increase the thermal expansion coefficient of bcc uranium. The solute formation energies of noble gas atoms show a bearing on their size. A large solute (Xe) has a high formation energy, and vice versa. This size effect is not quite evident for the chemically reactive solutes, namely, Sr, Zr, I, Cs, and Pu. Our MD simulations further show that vacancies are the favorable point defects in bcc uranium rather than both vacancies and self interstitials as predicted by earlier calculations. The formation energies of self interstitial atoms are found to be lower than those of solute interstitial atoms, each calculated in six different basic interstitial dumbbell configurations. That is, bcc U accommodates self interstitials more easily than decay or fission gas interstitials (He, Kr, and Xe). Further, He atoms are found to have comparable formation energies in the substitutional and interstitial locations. The fission product atoms Kr and Xe prefer to occupy vacant substitutional lattice sites rather than interstitial sites. Binding energies of divacancy and solute-vacancy pairs (0.31 vs $\ensuremath{-}0.69$ eV for the Xe-$\ensuremath{\square}$ pair, for instance) from our MD simulation show that nucleation and growth of fission gas bubbles are supported by a thermodynamic driving force, whereas vacancies tend to stay apart. This is in agreement with literature reporting that bcc uranium softens and swells mainly by agglomeration of noble gas bubbles.

Phase-field modeling of fission gas bubble growth on grain boundaries and triple junctions in UO2 nuclear fuel

A phase-field model of fission gas bubble evolution was developed and applied to gain an improved understanding of the microstructure-level processes leading to fission gas release from nuclear fuel, and to inform engineering-scale fission gas release models. The phase-field model accounts for multiple fuel grains and fission gas bubbles and tracks the local concentration of vacancies and gas atoms. The model was used to simulate the growth of grain boundary and triple junction bubbles in a hexagonal periodic 3D grain structure. The fractional coverage of the triple junctions and the number of fully saturated triple junctions (that is, triple junctions fully covered by the gas phase) was calculated, and correlations were developed between these quantities and the grain boundary coverage. The effects of initial triple junction bubble density, vacancy source strength, and bubble semi-dihedral angle on triple junction coverage and saturation were evaluated. High initial triple junction coverage and high bubble semi-dihedral angle can lead to triple junction saturation well before grain boundary percolation. The implications of these findings for engineering-scale fuel performance modeling are discussed.

Thermal conductivity of fresh and irradiated U-Mo fuels

The thermal conductivity of fresh and irradiated U-Mo dispersion and monolithic fuel has been investigated experimentally and compared to theoretical models. During in-pile irradiation, thermal conductivity of fresh dispersion fuel at a temperature of 150 °C decreased from 59 W/m·K to 18 W/m·K at a burn-up of 4.9·1021 f/cc and further to 9 W/m·K at a burn-up of 6.1·1021 f/cc. Fresh monolithic fuel has a considerably lower thermal conductivity of 15 W/m·K at a temperature of 150 °C and consequently its decrease during in-pile irradiation is less steep than for dispersion fuel. For a burn-up of 3.5·1021 f/cc of monolithic fuel, a thermal conductivity of 11 W/m·K at a temperature of 150 °C has been measured by Burkes et al. (2015).The difference of decrease for both fuels originates from effects in the matrix that occur during irradiation, like for dispersion fuel the gradual disappearance of the Al matrix with increased burn-up and the subsequent growth of an interaction layer (IDL) between the U-Mo fuel particle and Al matrix and subsequent matrix hardening. The growth of fission gas bubbles and the decomposition of the U-Mo crystal lattice also affect both dispersion and monolithic fuel.

Multiscale simulation of xenon diffusion and grain boundary segregation in UO2

In light water reactor fuel, gaseous fission products segregate to grain boundaries, resulting in the nucleation and growth of large intergranular fission gas bubbles. The segregation rate is controlled by diffusion of fission gas atoms through the grains and interaction with the boundaries. Based on the mechanisms established from earlier density functional theory (DFT) and empirical potential calculations, diffusion models for xenon (Xe), uranium (U) vacancies and U interstitials in UO2 have been derived for both intrinsic (no irradiation) and irradiation conditions. Segregation of Xe to grain boundaries is described by combining the bulk diffusion model with a model for the interaction between Xe atoms and three different grain boundaries in UO2 (Σ5 tilt, Σ5 twist and a high angle random boundary), as derived from atomistic calculations. The present model does not attempt to capture nucleation or growth of fission gas bubbles at the grain boundaries. The point defect and Xe diffusion and segregation models are implemented in the MARMOT phase field code, which is used to calculate effective Xe and U diffusivities as well as to simulate Xe redistribution for a few simple microstructures.

Extended fuel swelling models and ultra high burn-up fuel behavior of U–Pu–Zr metallic fuel using FEAST-METAL

Computational models in FEAST-METAL U–Pu–Zr metallic fuel behavior code have been upgraded to improve fission gas, solid fission product swelling, and pore sintering behavior in a microstructure dependent form. First, fission gas bubble growth is modeled by selecting small and large bubble groups according to a fixed number of gas atoms per bubble group. Small bubbles nucleated at phase boundaries grow via gas migration and turn into large bubbles. Furthermore, bubble morphology for each phase structure is captured by selecting the number of atoms per bubble and the shape of the bubbles in a phase dependent form. The gas diffusion coefficients for the single gamma phase and effective dual (α+δ) and (β+γ) phase structures are modeled separately, using the activation energy of the corresponding phase structure. In this study, it is found that pressure sintering of the interconnected porosity in dual phases should be less effective than the reference model in order to match clad strain and fission gas release behavior. In addition to these improvements, a probabilistic approach is taken to verify the fission gas-swelling threshold at which interconnected porosity begins. This fracture problem is treated as a function of critical crack length formed via bubble coalescence. It was found that a 10% gas-swelling threshold is appropriate for a wide range of gas bubble sizes. The new version of FEAST-METAL predicts the burn-up, smear density, and axial variation of the clad hoop strain and fission gas release behavior satisfactorily for selected test pins under EBR-II conditions. The code is used to predict ultra-high burn-up U–Pu–6Zr vented metallic fuel behavior with HT9 cladding for fast breeder reactor applications for 20 years of irradiation. It is assumed that HT9 clad will retain its fracture toughness and creep properties for this simulation. It appears that the increased dose on the cladding, increased solid fission product swelling, and low operating fuel temperature requires lower fuel smear density (∼60%) in order to ensure acceptable clad hoop strain at high burn-up (∼35at.%). Furthermore, keeping the peak clad temperature below 550°C seems to control lanthanide migration and clad inner wastage at a reasonable level. Possible design concerns and improvements are discussed.

Mesoscale modeling of intergranular bubble percolation in nuclear fuels

Phase-field simulations are used to examine the variability of intergranular fission gas bubble growth and percolation on uranium dioxide grain boundaries on a mesoscopic length scale. Three key parameters are systematically varied in this study: the contact angle (or dihedral angle) defining the bubble shape, the initial bubble density on the grain boundary plane, and the ratio of the gas diffusivity on the grain boundary versus the grain interiors. The simulation results agree well with previous experimental data obtained for bubble densities and average bubble areas during coalescence events. Interestingly, the rate of percolation is found to be highly variable, with a large dependency on the contact angle and the initial bubble density and little-to-no dependency on the grain boundary gas diffusivity.

Analysis of mechanical load on cladding induced by fuel swelling during power ramp in high burn-up rod by fuel performance code FEMAXI-6

Mechanical load on cladding induced by fuel swelling in a high burn-up BWR type rod was analyzed by a fuel performance code FEMAXI-6. The code was developed for the analysis of LWR fuel rod behaviors in normal operation and transient conditions using finite element method (FEM). During a power ramp for the high burn-up rod, instantaneous pellet swelling can significantly exceed the level that is predicted by a “steady-rate” swelling model, causing a large circumferential strain in cladding. This phenomenon was simulated by a new swelling model to take into account the fission gas bubble growth. As a result it was found that the new model can give reasonable predictions on cladding diameter expansion in comparison with PIE data. The bubble growth model assumes that the equilibrium state equation holds for a bubble under external pressure, and simultaneous solution is obtained with both bubble size determination equation and diffusion equation of fission gas atoms. In addition, a pellet-clad bonding model which has been incorporated in the code to assume solid mechanical coupling between pellet outer surface and cladding inner surface predicted the generation of bi-axial stress state in the cladding during ramp.

Dynamics of irradiation-induced grain subdivision and swelling in U 3Si 2 and UO 2 fuels

Observations on low-temperature swelling of irradiated uranium silicide dispersion fuels have shown that the growth of fission-gas bubbles is strongly affected by fission rate. The plot of swelling versus fuel burnup exhibits a distinct “knee” that shifts to higher fission density with increased fission rate. State-of-the-art models of fission-gas behavior do not predict such a dependence. Below the knee, no gas bubbles can be detected by scanning electron microscopy. Just at the knee, gas bubbles are seen to form in a heterogeneous fashion. Above the knee, the bubble population rapidly multiplies and the bubble size increases with fission density. “Subdivision” of the original grains has been observed in high-burnup uranium dioxide. In addition, the peripheral region of LWR fuel pellets reveals an increasingly porous microstructure with burnup. Observations of this “rim effect” show that an extremely fine-grained structure formed by subdivision of the original fuel grains is associated with the porous microstructure. The singular observation that gas-bubble swelling is strongly dependent on fission rate has led us to speculate that a dense network of subgrain boundaries forms in UO 2 and U 3Si 2 at high burnup. Fission-gas bubbles nucleate at the newly formed boundaries and then grow at an accelerated rate relative to that of fission-gas bubbles in the bulk material. A theoretical formulation is presented wherein the stored energy in the material is concentrated on a network of sink-like nuclei that diminish with dose due to interaction with radiation-produced defects. Grain subdivision is induced when the energy per nucleus is high enough that the creation of grain-boundary surfaces is offset by the creation of strain-free volumes, with a resultant net decrease in the free energy of the material. This formulation, applied within the context of a mechanistic treatment of fission-gas-bubble behavior, is shown to provide a plausible interpretation of the observed phenomenon.

Mechanistic model of fission gas behavior in metallic fuel

A mechanistic model of fission gas swelling and release has been developed for metallic fuel under operational conditions. This swelling model is based on gas bubble coalescence and growth by gas bubble random and/or biased migration occurring in grain boundaries. The gas release is modeled by open bubbles and tunnel formation. Experimental data are analyzed by this model. The result suggests that the model can predict fission gas bubble growth of metallic fuel.

Experimental studies of U-Pu-Zr fast reactor fuel pins in the experimental breeder reactor-ll

Argonne National Laboratory’s Integral Fast Reactor (IFR) concept has been under demonstration in the Experimental Breeder Reactor II (EBR-II) since February 1985. Irradiation tests of U-Zr and U-Pu-Zr fuel pins to >15 at. pct burnup have demonstrated their viability as driver fuel prototypes in innovative design liquid metal reactors. A number of technically challenging irradiation effects have been observed and are now under study. Microstructural changes in the fuel are dominated early in exposure by grain boundary cavitation and fission gas bubble growth, producing large amounts of swelling. Irradiation creep and swelling of the austenitic (D9) and martensitic (HT-9) candidate cladding alloys have been measured and correlate well with property modeling efforts. Chemical interaction between the fuel and cladding alloys has been characterized to assess the magnitude of cladding wastage during steady-state irradiation. Significant interdiffusion of the uranium and zirconium occurs producing metallurgically distinct zones in the fuel.

Effects of Annealing under High Static Pressure on Precipitation Behavior of Fission Gas Bubbles in Irradiated UO2

Annealing experiments were carried out on irradiated UO2 in argon gas under high pressure (600 and 1,000 kg/cm2) as well as atmospheric, at temperatures of 1,400°–1,600°C. The effects of high external pressure on the behavior of fission gas bubbles in the irradiated UO2 were studied by comparing replica electron micrographs of fractured surfaces of specimens annealed under different temperatures and pressures. The results indicate that high pressures such as above 600 kg/cm2 can be effective in surpressing the growth of fission gas bubbles in both intergranular and intragranular zones, and in inhibiting the joining together of intergranular bubbles to form direct passages for fission gas release.

85Kr release during the oxidation and self-heating of irradiated uranium in air

The behaviour of the fission gas 85Kr has been studied during the oxidation of irradiated uranium in air. Over the temperature range 220–320 °C there is a direct proportionality between the extent of isothermal oxidation and the amount of 85Kr released. Above 300 °C the irradiated metal can self heat and although well defined ignitions do not occur a thermal cycling reaction is observed, which with unirradiated uranium is initiated at a temperature at least 200 °C higher. During thermal cycling the 85Kr release curve follows with considerable sensitivity the irradiated metal temperature curve. The degree of self heating is insufficient for fission gas bubble growth to play a significant role during the oxidation and it is concluded that the solid fission product concentration in the oxide and oxide stoichiometry are important parameters in the initiation and continuation of the temperature cycling reactions.

The growth of fission gas bubbles in irradiated uranium dioxide

Abstract The growth of fission gas bubbles from supersaturated solution in irradiated uranium dioxide has been studied by electron microscopy under isothermal annealing conditions between 1300° and 1500°C. Measurements of the kinetics of bubble growth have enabled the diffusion coefficients of atomic xenon and krypton in irradiated uranium dioxide to be determined. The diffusion coefficients obtained may be expressed by the equation: The results obtained from the current experiments are believed to be more precise than most of those obtained using the Booth model for gas released from solid samples of irradiated uranium dioxide during a post-irradiation anneal.

The post-irradiation annealing behaviour of fission gas bubbles in various purities of uranium

The gas bubble distribution in irradiated uranium foils subjected to a wide range of annealing treatments has been studied by transmission electron microscopy. The results show that: 1. 1. In the absence of stress, the growth of fission gas bubbles ~ 100 Å diameter in the alpha phase is extremely slow for both pure and adjusted uranium for times up to 1000 h. 2. 2. Post-irradiation annealing at 600 °C of material irradiated at low temperature is not equivalent to irradiation at 600 °C. 3. 3. In the absence of stress, the migration of fission gas bubbles ~ 100 Å diameter at 800 °C for pure and adjusted uranium is slow but measurable. 4. 4. The application of stress during annealing of ~ 100 Å bubbles in the α phase at 600 °C does not noticeably affect the coarsening rate. 5. 5. The gas bubble density increases with dose when the gas bubbles are formed after irradiation but is independent of dose (after very small doses) for high-temperature irradiations.