Fission Gas Atoms Research Articles

Development of a multiscale thermal conductivity model for fission gas in UO2

Accurately predicting changes in the thermal conductivity of light water reactor UO2 fuel throughout its lifetime in reactor is an essential part of fuel performance modeling. However, typical thermal conductivity models from the literature are empirical. In this work, we begin to develop a mechanistic thermal conductivity model by focusing on the impact of gaseous fission products, which is coupled to swelling and fission gas release. The impact of additional defects and fission products will be added in future work. The model is developed using a combination of atomistic and mesoscale simulation, as well as analytical models. The impact of dispersed fission gas atoms is quantified using molecular dynamics simulations corrected to account for phonon-spin scattering. The impact of intragranular bubbles is accounted for using an analytical model that considers phonon scattering. The impact of grain boundary bubbles is determined using a simple model with five thermal resistors that are parameterized by comparing to 3D mesoscale heat conduction results. When used in the BISON fuel performance code to model four reactor experiments, it produces reasonable predictions without having been fit to fuel thermocouple data.

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.

Diffusion of Zr, Ru, Ce, Y, La, Sr and Ba fission products in UO2

The diffusivity of the solid fission products (FP) Zr (Zr4+), Ru (Ru4+, Ru3+), Ce (Ce4+), Y (Y3+), La (La3+), Sr (Sr2+) and Ba (Ba2+) by a vacancy mechanism has been calculated, using a combination of density functional theory (DFT) and empirical potential (EP) calculations. The activation energies for the solid fission products are compared to the activation energy for Xe fission gas atoms calculated previously. Apart from Ru, the solid fission products all exhibit higher activation energy than Xe. For all solid FPs except Y3+, the migration of the FP has lower barrier than the migration of a neighboring U atom, making the latter the rate limiting step for direct migration. An indirect mechanism, consisting of two successive migrations around the FP, is also investigated. The calculated diffusivities show that most solid fission products diffuse with rates similar to U self-diffusion. However, Ru, Ba and Sr exhibit faster diffusion than the other solid FPs, with Ru3+ and Ru4+ diffusing even faster than Xe for T<1200K. The diffusivities correlate with the observed fission product solubility in UO2, and the tendency to form metallic and oxide second phase inclusions.

Radiation re-solution of fission gas in non-oxide nuclear fuel

Renewed interest in fast nuclear reactors is creating a need for better understanding of fission gas bubble behavior in non-oxide fuels to support very long fuel lifetimes. Collisions between fission fragments and their subsequent cascades can knock fission gas atoms out of bubbles and back into the fuel lattice. We showed that these collisions can be treated as using the so-called “homogenous” atom-by-atom re-solution theory and calculated using the Binary Collision Approximation code 3DOT. The calculations showed that there is a decrease in the re-solution parameter as bubble radius increases until about 50nm, at which the re-solution parameter stays nearly constant. Furthermore, our model shows ion cascades created in the fuel result in many more implanted fission gas atoms than collisions directly with fission fragments. This calculated re-solution parameter can be used to find a re-solution rate for future bubble simulations.

Atomistic modeling of intrinsic and radiation-enhanced fission gas (Xe) diffusion in [formula omitted]: Implications for nuclear fuel performance modeling

Based on density functional theory (DFT) and empirical potential calculations, the diffusivity of fission gas atoms (Xe) in UO2 nuclear fuel has been calculated for a range of non-stoichiometry (i.e. UO2±x), under both out-of-pile (no irradiation) and in-pile (irradiation) conditions. This was achieved by first deriving expressions for the activation energy that account for the type of trap site that the fission gas atoms occupy, which includes the corresponding type of mobile cluster, the charge state of these defects and the chemistry acting as boundary condition. In the next step DFT calculations were used to estimate migration barriers and internal energy contributions to the thermodynamic properties and calculations based on empirical potentials were used to estimate defect formation and migration entropies (i.e. pre-exponentials). The diffusivities calculated for out-of-pile conditions as function of the UO2±x non-stoichiometry were used to validate the accuracy of the diffusion models and the DFT calculations against available experimental data. The Xe diffusivity is predicted to depend strongly on the UO2±x non-stoichiometry due to a combination of changes in the preferred Xe trap site and in the concentration of uranium vacancies enabling Xe diffusion, which is consistent with experiments. After establishing the validity of the modeling approach, it was used for studying Xe diffusion under in-pile conditions, for which experimental data is very scarce. The radiation-enhanced Xe diffusivity is compared to existing empirical models. Finally, the predicted fission gas diffusion rates were implemented in the BISON fuel performance code and fission gas release from a Risø fuel rod irradiation experiment was simulated.

Random-walk Monte Carlo simulation of intergranular gas bubble nucleation in UO2 fuel

Using a random-walk particle algorithm, we investigate the clustering of fission gas atoms on grain boundaries in oxide fuels. The computational algorithm implemented in this work considers a planar surface representing a grain boundary on which particles appear at a rate dictated by the Booth flux, migrate two dimensionally according to their grain boundary diffusivity, and coalesce by random encounters. Specifically, the intergranular bubble nucleation density is the key variable we investigate using a parametric study in which the temperature, grain boundary gas diffusivity, and grain boundary segregation energy are varied. The results reveal that the grain boundary bubble nucleation density can vary widely due to these three parameters, which may be an important factor in the observed variability in intergranular bubble percolation among grain boundaries in oxide fuel during fission gas release.

Verification of FEMAXI-7 code by using irradiation test in Halden reactor for He-pressurization effect on FGR of BWR fuels under power transient

Power ramp test for He-pressurization effect on fission gas release (FGR) of about 42GWd/tUO2 boiling water reactor (BWR) fuel rods was analyzed by the fuel performance code FEMAXI-7. The experimental data were obtained with the two rods, which were base irradiated in the Halden reactor for 12 years (IFA-409), then subjected to the power ramp tests (IFA-535) to investigate the He-pressurization effect. The FEMAXI-7 calculations were performed by inputting rod specifications and experimental conditions in both the baseand test irradiations. The results showed that the calculations reasonably followed the trends of measured cladding elongation and FGR during the power ramp test, depending on the pellet temperature and fission gas atoms diffusion rate. Based on the calculated results, the reason that no apparent He-pressurization effect was observed in the experiment was considered to be caused by insufficient gas communication during strong pellet–clad mechanical interaction (PCMI) and enhanced gap thermal conductance by the solid–solid contact due to gap closure.

Free energy of Xe incorporation at point defects and in nanovoids and bubbles inUO2

Intra- and intergranular fission gas bubbles in nuclear fuels are known to have a deleterious effect on fuel performance, particularly at high levels of burnup. The mechanisms by which randomly distributed fission gas atoms agglomerate to form larger fission bubbles are not well understood. Therefore, this paper aims to examine the thermodynamics of bubble nucleation from isolated point defects to nanovoids and ultimately to bubbles of $\ensuremath{\approx}\phantom{\rule{-0.16em}{0ex}}2.0\phantom{\rule{0.28em}{0ex}}\mathrm{nm}$ using molecular-dynamics simulations employing empirical pair potentials. A thermodynamic driving force for bubble nucleation from point defects is highlighted by the substantial reduction in the free energy of Xe atoms contained within larger bubbles relative to accommodation at point defects. The simulations also illustrate the processes that the lattice surrounding a fission gas bubble undergoes in order to prevent thermal resolution, clearly indicating the thermodynamic imperative to ensure the Xe remains in the bubble.

Molecular dynamics simulation of Xe bubble nucleation in nanocrystalline UO 2 nuclear fuel

We have performed molecular dynamics (MD) simulations to investigate the dynamical interactions between vacancy defects, fission gas atoms (Xe), and grain boundaries in a model of polycrystalline UO 2 nuclear fuel with average grain diameter of about 20 nm. We followed the mobility and aggregation of Xe atoms in the vacancy-saturated model compound for up to 2 ns. During this time we observed the aggregation of Xe atoms into nuclei, which are possible precursors to Xe bubbles. The nucleation was driven by the migration of Xe atoms via vacancy-assisted diffusion. The Xe clusters aggregate faster than grain boundary diffusion rates and are smaller than experimentally observed bubbles. As the system evolves towards equilibrium, the Xe atom cluster growth slows down significantly, and the lattice relaxes around the cluster. These simulations provide insights into fundamental physical processes that are inaccessible to experiment.

Fission product induced swelling of U–Mo alloy fuel

Fuel swelling of U–Mo alloy was modeled using the measured data from samples irradiated up to a fission density of ∼7 × 10 27 fissions/m 3 at temperatures below ∼250 °C. The overall fuel swelling was measured from U–Mo foils with as-fabricated thickness of 250 μm. Volume fractions occupied by fission gas bubbles were measured and fuel swelling caused by the fission gas bubbles was quantified. The portion of fuel swelling by solid fission products including solid and liquid fission products as well as fission gas atoms not enclosed in the fission gas bubbles is estimated by subtracting the portion of fuel swelling by gas bubbles from the overall fuel swelling. Empirical correlations for overall fuel swelling, swelling by gas bubbles, and swelling by solid fission products were obtained in terms of fission density.

Molecular dynamics simulation of intragranular Xe bubble re-solution in UO 2

The homogeneous re-solution of Xe fission gas bubbles in UO 2 is investigated by combined Monte Carlo and molecular dynamics simulations. Using a binary collision model, based on the Ziegler–Littmark–Biersack potential [J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Stopping and Ranges of Ions in Matter, vol. 1, Pergamon Press, New York, 1984], the recoil energy distribution of fission gas atoms is obtained. An extensive library of fission gas atom displacement cascades is then compiled using molecular dynamic simulations. It used for calculating recoil spectrum averaged quantities. The calculations yield a re-solution parameter for homogeneous re-solution and a displacement distribution of fission gas atoms around the fission gas bubbles. The results disagree considerably from past estimates. The importance of channeling and threshold energy for fission gas escape are discussed.

Re-solution of fission gas – A review: Part I. Intragranular bubbles

Theories of fission-fragment-driven re-solution of fission-gas atoms from intragranular bubbles in irradiated UO 2 nuclear fuel are reviewed. Two mechanisms of re-solution are generally accepted: the heterogeneous process destroys entire bubbles in the path of fission fragments and returns the gas to the solid as individual atoms; the homogeneous process re-solves fission-gas atoms singly by scattering collisions with fission fragments and uranium recoils whose paths intersect the bubbles. Coupling of these two re-solution models with the bubble nucleation analogs determines the size and number density of the intragranular bubble population. Two approaches are reviewed: the single-size theory, in which all bubbles are accorded one size, and the bubble distribution theory, which seeks to determine the variation of bubble number density with size.

Effect of Replacing Helium with a Liquid Metal in the Fuel-Cladding Gap on Fission Gas Release

In light water reactors, a helium-filled gap between the fuel and the cladding accommodates fuel swelling and cladding creepdown. However, the low thermal conductivity of helium results in a large ΔT over the gap before closure occurs. To remedy this situation, Wright et al. proposed the use of a liquid metal (LM) bond in the fuel-cladding gap. The LM (33 wt% each of lead, tin, and bismuth) was chosen for its low melting point (~120°C), its lack of chemical reactivity with UO2 and water, and its high thermal conductivity (~100 times that of He). The thermal resistance of the LM-bonded gap is nil.Prior to closure of a helium-bonded gap, the centerline fuel temperature can be hundreds of degrees hotter than that with an LM-bonded gap at the same linear heat rating. Since the diffusion of fission gas atoms depends strongly upon temperature, it is expected that with the high thermal conductivity pellet-cladding gap, the incubation time to fission gas release should be considerably delayed. A modified Booth Sphere model, which takes into account re-solution, is adopted. The amount of fission gas atoms collected at the grain boundary is calculated using realistic time-temperature histories taken from a recent U.S. Nuclear Regulatory Commission review. The saturation value of gas at the grain boundary proposed by Dowling to fission gas release is adopted. The results show that although the temperature in the LM-bonded case is substantially lower than the He-filled case when the gap is open, the temperatures in the two cases equalize when the gap vanishes. Correspondingly, the two cases exhibit a comparable amount of fission gas at the grain boundary. Calculated differences between the times to saturation with LM and He in the gap are as high as ~1 yr and as low as 1 to 2 days.

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.

Formation of Nanostructures in UO2Fuel at High Burn-ups

In the present paper it is assumed that above a limiting value of fission fluency (burn-up) a more intensive process of irradiation induced chemical interaction occurs. A significant part of fission gas product is thus expected to be chemically bounded in the matrix of UO 2 fuel. The fission gas atoms substituting, for example, uranium atoms in the crystallographic lattice can form weak facets. At a certain saturation condition, division of the grains can occur at the weak facets and the increase in fission-gas-products release may be expected. The fact that the process of grain division for high burn-ups (70-80 MWd/kgU) forms an extremely fine structure up to a temperature as high as 1100°C and simultaneously the observed decrease in fission gas concentration in the fuel supports this concept. The analysis of fission gas concentration change due to the formation of nanostructures in UO 2 fuel at high burn-ups in terms of total surface area change in a function of burn-up and knock-out process is presented.

Fission-gas release in a spinel-based fuel used for actinide transmutation

The present paper discusses the fission-gas release as measured from three fuels considered for the transmutation process. The releases were measured in spinel-based fuels from the EFTTRA-T3 irradiation [1,2]. Gas puncturing and EPMA data are discussed for three different inert-matrix concepts. The differences in the fission-gas release for the three spinel-based fuel concepts are most likely connected with the concentrations of fission-gas atoms in the fissile phase and in the spinel phase. The present data suggest that homogeneously distributing the fission-gas atoms over the various phases, as would arise from micro-dispersed fuel, gives a lower release than implanting the fission-gas only in the fissile phase.

Calculation method for diffusional gas release with grain boundary resolution

The problem of diffusional release of stable fission gas atoms in nuclear fuel including grain boundary resolution is described. A numerical method for solving the set of resulting non-linear differential equations in time varying conditions is presented. The method is an extension to the locally accurate method (LOAM) published earlier. The extended LOAM accounts for the kinetic evolution of the gas content in the grain boundary. The fission gas release and the time to reach the saturation concentration at the grain boundaries by the extended method are compared to analytical solutions under steady state conditions. The results of this comparison show the excellent capability of the extended LOAM. The performance of the extended method in time varying conditions is tested by calculating the fission gas release for hundreds of complicated temperature–power histories. The extended LOAM is found to be able to calculate the fission gas release with ±1% accuracy in time varying conditions by using only three equal volume nodes. The computing time of the extended LOAM is less than twice the time needed by the LOAM without grain boundary resolution.

Modelling of fission gas release and gaseous swelling of light water reactor fuels

Modelling to investigate the behavior of fission gas atoms of light water reactor fuels is elaborated. The model features the treatment of the grain boundary assumed to consist of two zones for solute gas atoms and intergranular bubbles. This, along with the athermal diffusion of fission gas atoms, enables the retention of gas during the base irradiation and the instantaneous release at temperature rise. The number density of intergranular bubbles varies upon interlinkage to express the saturation of the gaseous swelling after the gas release. Gas release at power reduction is dealt with considering the effective tensile stress acting on the grain boundary. The model is verified with four kinds of data from the irradiated fuels with known temperatures and confirmed to simulate fission gas release in a wide range of burnup, the time-dependency of gas release and porosity change in pellet, the decrease of gas release onset temperature with burnup, and the gas release at the power reduction.

Modeling and parametric studies of the effect of Pu-mixing heterogeneity on fission gas release from mixed oxide fuels of LWRs and FBRs

A simple, practical method has been proposed for evaluation of the effect of heterogeneity in Pu-mixing on fission gas release (FGR) behavior in mixed oxide (MOX) fuels. In contrast to the usual PuO 2 spherical particle model, the proposed model uses the measurable (by electron probe microanalysis, etc.) statistical frequency distribution of local Pu-content in as-fabricated MOX fuels in combination with the usual fission gas release model based on the diffusion theory for homogeneous UO 2 fuel. From parametric studies using a binomial distribution model for the expression of the statistical frequency distribution of local Pu-content, it was confirmed that the enhancement of FGR in MOX fuels is caused by the simultaneous effects of (a) the fission-rate-enhanced diffusion of fission gas atoms and (b) the local (on the scale of fission fragment range) fission rate peaking in the fuel matrix, resulting from the Pu-mixing heterogeneity. The degree of FGR enhancement is greater in the MOX fuels of lower average Pu fraction under a given average power density, and is more apparent at lower operating temperatures as long as the temperature is high enough to cause the FGR. Since FBR-MOX fuels are of high average Pu fraction (~ 20 wt%) and are used at relatively high operating temperatures compared with LWR-MOX fuels, the FGR enhancement due to their heterogeneity is insignificant.

Fission Gas Behavior during Postirradiation Annealing of Large Grained UO2 Fuels Irradiated to 23GWd/t.

Abstract Fission gas behavior of UO2 fuel pellets with controlled microstructure irradiated to 23 GWd/t in a test reactor has been studied by using a postirradiation annealing experiment. Four types of fuel pellets with or without additives were examined : (1) un-doped standard (grain size: 16/μm), (2) un-doped large grained (43μm), (3) 0.7 wt% Nb2O5-doped large grained (110/μm), (4) 0.2wt% TiO2-doped large grained (85μm) fuels. The annealing was conducted at 1,600 or 1,800°C for 5 h in reducing or oxidizing atmospheres. Fission gas release and bubble swelling caused by the high temperature annealing for the two un-doped fuels were reduced to about 1/3–1/2 by increasing the grain size from 16 to 43 μm, which roughly corresponded to the ratio of their grain sizes. By contrast, the performance of the two large grained fuels doped with Nb2O5 or TiO2 was roughly equivalent to, or rather inferior to that of the standard fuel, despite their large grain sizes of 110 and 85 μm. The fission gas behavior of un-doped fuels was aggravated by increasing the oxygen potential in the annealing atmosphere, while that of additive doped fuels did not depend on it. The effects of grain size, additive doping and oxygen potential on fission gas release and bubble swelling were discussed in connection with the diffusivities of fission gas atoms and cation vacancies.