Intragranular Bubbles Research Articles

The role of xenon/krypton adsorption on the growth of intra-granular bubbles in irradiated UO2

Under transient conditions, rapid fuel swelling in UO2 can occur through fission gas and vacancy capture by intra-granular bubbles. These swellings can lead to significant cladding deformations and clad failure. To understand the mechanisms of intra-granular swelling a number of key experiments have been conducted by the UK in conjunction with the Halden Reactor. Post-irradiation annealing enables the study of the thermal behaviour of the intra-granular bubbles in the absence of complicating processes such as irradiation-induced bubble destruction and fission gas resolution. Bubble-like features are frequently observed in straight lines and it has always been assumed that these were nucleated in the wake of energetic fission fragments and served as nuclei for bubble growth. However, most of these bubbles do not grow significantly and viable intra-granular bubbles are nucleated at much lower densities. At the temperature and pressure that these form, the xenon and krypton are above their critical points and the elements are supercritical fluids. However, bubble growth occurs at temperatures and pressures much greater than the critical points and the gases may be treated with simple equations of state such as those by Clausius or Van der Waals. Of greater importance is the fact that the large Van der Waals forces in these atoms generated by fluctuations in the electron dispositions lead to extensive adsorption on the inner surfaces of the bubbles and vacancy capture by the bubbles can lead to the diffusive loss of fission gas atoms resulting in bubble growth at slight over-pressure conditions. A diffusion model based on Langmuir Adsorption has been developed and shown to be consistent with the out-of-pile annealing studies.

Dislocations in naturally deformed olivine: Example of a mylonitic peridotite

We have investigated the microstructure of naturally deformed olivine (chemically equilibrated at 1000 °C) by conventional transmission electron microscopy and electron tomography. The peridotite specimen, from Oman ophiolite, has a mylonitic microstructure with remnant, strongly deformed, millimetric porphyroclasts co-existing with small newly formed olivine grains generated by dynamic recrystallization. Imaging by transmission electron microscopy reveals that both newly formed grains and porphyroclasts display [100] and [001] dislocations activity. Subgrain boundaries are composed of either [100] or [001] dislocations. The characterization of this natural sample also permits to identify sporadic [100] dislocation loops, rare [010] dislocation, infrequent melt, and intragranular bubbles or along subgrain boundaries. Electron tomography permits to identify several glide planes, which are similar to previous observations acquired on experimentally deformed polycrystalline olivine, more importantly electron tomography also permits to evidence combination of glide, climb and mixed climb (dislocation moving in an intermediate plane between the plane of glide plane and the plane of pure climb). Our study further infers the diversity of linear defects responsible for plastic deformation of olivine at lithospheric conditions.

Oriented intra-granular bubble transport due to coupling of pinned bubble growth and dislocation climb

The intra-granular fission gas release during post-irradiation annealing tests cannot be predicted if bubble motion is not taken into account. Indeed, without irradiation, the equilibrium between trapping and re-solution is completely shifted in favor of trapping, the dynamic resolution due to fission spikes no longer existing. Moreover, the sink strength of the population of intragranular bubbles is greater by a factor ∼1000 than the sink strength of the grain surface. Trapped in supposedly immobile bubbles, the gas would not escape from the grain, which is in contradiction with experimental observations. Several alternative scenarios involving bubble movement emerged to explain the observed fission gas release. The purpose of our work is to assess these scenarios using simulation. In a previous article, it was demonstrated that neither the movement of bubbles in a vacancy gradient, nor the Brownian movement of bubbles, nor the combination of them, could explain the large fission gas release obtained during post-irradiation annealing in our reference experiment. This demonstration was performed using a mesoscale model, called BEEP, where individual bubbles are described, along with the diffusion of vacancies from each bubble to the other, as well as from the free surface. In this paper, we extend the BEEP model to assess the role of dislocations in interaction with highly pressurized bubbles. It is concluded that a mechanism of dislocation climb coupled with the growth of highly pressurized pinned bubbles may explain the large intra-granular fission gas release in annealing conditions.

Restructuring in high burn-up pressurized water reactor UO2 fuel central parts: Experimental 3D characterization by focused ion beam—scanning electron microscopy

Focussed ion beam - scanning electron microscope (FIB-SEM) 3D examination was conducted on three standard UO2 and one Cr doped UO2 high burn-up pressurized water reactor (PWR) fuel samples. This work complemented other microanalysis examination, including an electron backscattered diffraction (EBSD) work on the polished surface. A parallel article giving the EBSD results was submitted simultaneously. Together, they found, in all the central area of these high burn-up samples: (i) a restructuring of the initial grains into smaller sub-grains forming low angle boundaries and with crystal orientations around that of their parent grains; and (ii) intragranular bubbles mostly situated on these low angle boundaries. The FIB-SEM 3D examination showed how such inter-sub-grain bubbles start as small compact but also small lenticular bubbles, similar to typical small intergranular lenticular bubbles. With increasing burn-up, these lenticular bubbles get thicker and locally interlink to form more complex bubbles. However, no long distance networks, between the sub-grains or between the original grains, were found. Such networks could have been a path for part of the fission gases to reach the grain boundaries, the grain edges (the intersection line of three grain boundaries), and the rod free volumes. These FIB-SEM 3D examinations brought details on the intragranular and intergranular bubbles situation for each studied volume. The distribution of the intragranular bubbles according to their sizes and shapes was exposed. The central restructuring, studied in this work, is likely to play a role in the increase of the fission gas release fractions at high burn-up. This work is an incentive to study further this restructuring and the bubbles formed, combining different approaches.

Modeling mesoscale fission gas behavior in UO2 by directly coupling the phase field method to spatially resolved cluster dynamics

Fission gas release within uranium dioxide nuclear fuel occurs as gas atoms diffuse through grains and arrive at grain boundary (GB) bubbles; these GB bubbles grow and interconnect with grain edge bubbles; and grain edge tunnels grow and connect to free surfaces. In this study, a hybrid multi-scale/multi-physics simulation approach is presented to investigate these mechanisms of fission gas release at the mesoscale. In this approach, fission gas production, diffusion, clustering to form intragranular bubbles, and re-solution within grains are included using spatially resolved cluster dynamics in the Xolotl code. GB migration and intergranular bubble growth and coalescence are included using the phase field method in the MARMOT code. This hybrid model couples Xolotl to MARMOT using the MultiApp and Transfer systems in the MOOSE framework, with Xolotl passing the arrival rate of gas atoms at GBs and intergranular bubble surfaces to MARMOT and MARMOT passing evolved GBs and bubble surface positions to Xolotl. The coupled approach performs well on the two-dimensional simulations performed in this work, producing similar results to the standard phase field model when Xolotl does not include fission gas clustering or re-solution. The hybrid model performs well computationally, with a negligible cost of coupling Xolotl and MARMOT and good parallel scalability. The hybrid model predicts that intragranular fission gas clustering and bubble formation results in up to 70% of the fission gas being trapped within grains, causing the increase in the intergranular bubble fraction to slow by a factor of six. Re-solution has a small impact on the fission gas behavior at 1800 K but it has a much larger impact at 1000 K, resulting in a twenty-times increase in the concentration of single gas atoms within grains. Due to the low diffusion rate, this increase in mobile gas atoms only results in a small acceleration in the growth of the intergranular bubble fraction. Finally, the hybrid model accounts for migrating GBs sweeping up gas atoms. This results in faster intergranular bubble growth with smaller initial grain sizes, since the additional GB migration results in more immobile gas clusters reaching GBs.

Modeling intra-granular fission gas bubble evolution and coarsening in uranium dioxide during in-pile transients

The description of intra-granular fission gas behavior during irradiation is a fundamental part of models used for the calculation of fission gas release and gaseous swelling in nuclear fuel performance codes. The relevant phenomena include diffusion of gas atoms towards the grain boundaries coupled to the evolution of intra-granular bubbles. While intra-granular bubbles during normal operating conditions are limited to sizes of a few nanometers, experimental evidence exists for the appearance of a second population of bubbles during transients, characterized by coarsening to sizes of tens to hundreds of nanometers and that can significantly contribute to gaseous fuel swelling. In this work, we present a model of intra-granular fission gas behavior in uranium dioxide fuel that includes both nanometric fission gas bubble evolution and bubble coarsening during transients. While retaining a physical basis, the developed model is relatively simple and is intended for application in engineering fuel performance codes. We assess the model through comparisons to a substantial number of experimental data from SEM observations of intra-granular bubbles in power ramp tested uranium dioxide samples. The results demonstrate that the model reproduces the coarsening of a fraction of the intra-granular bubbles and correspondingly, predicts gaseous swelling during power ramps with a significantly higher accuracy than is allowed by traditional models limited to the evolution of nanometric intra-granular bubbles.

Multiscale Mesoscale Modeling of Porosity Evolution in Oxide Fuels

Abstract The behavior of fission gas, notably accommodation within intra- and intergranular bubbles, influences the macroscopic properties and overall performance of oxide fuels. This work discusses progress to capture key fission gas-related phenomena with modern mesoscale techniques: the interaction of grain growth and irradiation by a phase-field crystal (PFC) method; overpressurized intragranular bubble migration in a vacancy gradient by a linearized phase-field model; and intergranular bubble interlinkage and percolation by the included phase model (IPM). An outlook on the impact of these models for the investigation of unit mechanisms of fission gas behavior and integration of them into fuel-performance codes is presented.

Modelling intra-granular bubble movement and fission gas release during post-irradiation annealing of UO2 using a meso-scale and spatialized approach

The effective diffusion theory, which is generally used in the modelling of base-irradiation of nuclear fuel, cannot predict the intra-granular fission gas release during post-irradiation annealing tests. From this discrepancy between experiments and usual theory, several alternative scenarios emerged. The purpose of this work is to model these scenarios, as mechanistically as possible, and to distinguish those that could really explain the observations. The difficulty is that the fission gas bubbles in irradiated UO2 are extremely small and numerous (mean distance between nano-bubble centers is only of the order of 10–20 nm) while the grain radius is about 5μm. A new spatialized mesoscale model was developed where individual bubbles are described, along with the diffusion of vacancies from each bubble to the other, as well as from the free surface. Random movement and coalescence of the bubbles have also been included in the model. Based on this principal, two scenarios, and the combination of those, could be assessed: (a) the movement of bubbles in a vacancy gradient, and (b) the Brownian movement of bubbles. It was demonstrated that neither of these two scenarios, nor the combination of them, could explain the large fission gas release obtained during post-irradiation annealing in our reference experiment. This encourages us to consider additional mechanisms, involving dislocations for instance, that could explain the high fission gas release.

Multiscale modeling of fission gas behavior in U3Si2 under LWR conditions

In this work, we present a model of fission gas behavior in U3Si2 under light water reactor (LWR) conditions for application in engineering fuel performance codes. The model includes components for intra-granular and inter-granular behavior of fission gases. The intra-granular component is based on cluster dynamics and computes the evolution of intra-granular fission gas bubbles and swelling coupled to gas diffusion to grain boundaries. The inter-granular component describes the evolution of grain-boundary fission gas bubbles coupled to fission gas release. Given the lack of experimental data for U3Si2 under LWR conditions, the model is informed with parameters calculated via atomistic simulations. In particular, we derive fission gas diffusivities through density functional theory calculations, and the re-solution rate of fission gas atoms from intra-granular bubbles through binary collision approximation calculations. The developed model is applied to the simulation of an experiment for U3Si2 irradiated under LWR conditions available from the literature. Results point out a credible representation of fission gas swelling and release in U3Si2. Finally, we perform a sensitivity analysis for the various model parameters. Based on the sensitivity analysis, indications are derived that can help in addressing future research on the characterization of the physical parameters relative to fission gas behavior in U3Si2. The developed model is intended to provide a suitable infrastructure for the engineering scale calculation of fission gas behavior in U3Si2 that exploits a multiscale approach to fill the experimental data gap and can be progressively improved as new lower-length scale calculations and validation data become available.

An effective numerical algorithm for intra-granular fission gas release during non-equilibrium trapping and resolution

Fission gas release and gaseous swelling in nuclear fuel are driven by the transport of fission gas from within the fuel grains to grain boundaries (intra-granular fission gas release). The process involves gas atom diffusion in conjunction with trapping in and resolution from intra-granular bubbles, and is described mathematically by a system of two partial differential equations (PDE). Under the assumption of equilibrium between trapping and resolution (quasi-stationary approximation) the system can be reduced to a single diffusion equation with an effective diffusion coefficient. Numerical solutions used in engineering fuel performance calculations invariably rely on this simplification. First, we investigate the validity of the quasi-stationary approximation compared to the solution of the general system of PDEs. Results demonstrate that the approximation is valid under most conditions of practical interest, but is inadequate to describe intra-granular fission gas release during rapid transients to relatively high temperatures such as postulated reactivity-initiated accidents (RIA). Then, we develop a novel numerical algorithm for the solution of the general PDE system in time-varying conditions. We verify the PolyPole-2 algorithm against a reference finite difference solution for a large number of randomly generated operation histories including prototypical RIA transients. Results demonstrate that PolyPole-2 captures the solution of the general system with a high accuracy and a low computational cost. The PolyPole-2 algorithm overcomes the quasi-stationary approximation and the concept of an effective diffusion coefficient for the solution of the intra-granular fission gas release problem in nuclear fuel analysis.

Microstructure investigations of U3Si2 implanted by high-energy Xe ions at 600 °C

The microstructure investigations on a high-energy Xe-implanted U3Si2 pellet were performed. The promising accident tolerant fuel (ATF) candidate, U3Si2, was irradiated by 84 MeV Xe ions at 600 °C at Argonne Tandem Linac Accelerator System (ATLAS). The characterizations of the Xe implanted sample were conducted using advanced transmission electron microscopy (TEM) techniques. An oxidation layer was observed on the sample surface after irradiation under the ∼10-5 Pa vacuum. The study on the oxidation layer not only unveils the readily oxidation behavior of U3Si2 under high-temperature irradiation conditions, but also develops an understanding of its oxidation mechanism. Intragranular Xe bubbles with bimodal size distribution were observed within the Xe deposition region of the sample induced by 84 MeV Xe ion implantation. At the irradiation temperature of 600 °C, the gaseous swelling strain contributed by intragranular bubbles was found to be insignificant, indicating an acceptable fission gas behavior of U3Si2 as a light water reactor (LWR) fuel operating at such a temperature.

A model describing intra-granular fission gas behaviour in oxide fuel for advanced engineering tools

The description of intra-granular fission gas behaviour is a fundamental part of any model for the prediction of fission gas release and swelling in nuclear fuel. In this work we present a model describing the evolution of intra-granular fission gas bubbles in terms of bubble number density and average size, coupled to gas release to grain boundaries. The model considers the fundamental processes of single gas atom diffusion, gas bubble nucleation, re-solution and gas atom trapping at bubbles. The model is derived from a detailed cluster dynamics formulation, yet it consists of only three differential equations in its final form; hence, it can be efficiently applied in engineering fuel performance codes while retaining a physical basis. We discuss improvements relative to previous single-size models for intra-granular bubble evolution. We validate the model against experimental data, both in terms of bubble number density and average bubble radius. Lastly, we perform an uncertainty and sensitivity analysis by propagating the uncertainties in the parameters to model results.

Bubble evolution in Kr-irradiated UO2 during annealing

Transmission electron microscopy observation of Kr bubble evolution in polycrystalline UO2 annealed at high temperature was conducted in order to understand the inert gas behavior in oxide nuclear fuel. The average diameter of intragranular bubbles increased gradually from 0.8 nm in as-irradiated sample at room temperature to 2.6 nm at 1600 °C and the bubble size distribution changed from a uniform distribution to a bimodal distribution above 1300 °C. The size of intergranular bubbles increased more rapidly than intragranular ones and bubble denuded zones near grain boundaries formed in all the annealed samples. It was found that high-angle grain boundaries held bigger bubbles than low-angle grain boundaries. Complementary atomistic modeling was conducted to interpret the effects of grain boundary character on the Kr segregation. The area density of strong segregation sites in the high-angle grain boundaries is much higher than that in the low angle grain boundaries.

On the effect of irradiation-induced resolution in modelling fission gas release in UO2 LWR fuel

Irradiation resolution of gas atoms and vacancies from intra- and intergranular bubbles in sintered UO2 fuel was studied by comparing macroscopic models with a more mechanistic approach. The applied macroscopic models imply the resolution rate of gas atoms to be proportional to gas concentration in intragranular bubbles and at grain boundary (including intergranular bubbles). A relation was established between the macroscopic models and a single encounter of an energetic fission fragment with a bubble. The effect of bubble size on resolution was quantified. The number of resoluted gas atoms per encounter of a fission fragment per bubble was of the same order of magnitude for intra- and intergranular bubbles. However, the resulting macroscopic resolution rate of gas atoms was about two orders of magnitude larger from intragranular bubbles. The number of vacancies resoluted from a grain face bubble by a passing fission fragment was calculated. The obtained correlations for resolution of gas atoms from intragranular bubbles and grain boundaries and for resolution of vacancies from grain face bubbles were used to demonstrate the effect of irradiation resolution on fission gas release.

Bubble morphology in U3Si2 implanted by high-energy Xe ions at 300 °C

The microstructure modifications of a high-energy Xe implanted U3Si2, a promising accident tolerant fuel candidate, were characterized and are reported upon. The U3Si2 pellet was irradiated at Argonne Tandem Linac Accelerator System (ATLAS) by an 84 MeV Xe ion beam at 300 °C. The irradiated specimen was then investigated using a series of transmission electron microscopy (TEM) techniques. A dense distribution of bubbles were observed near the range of the 84 MeV Xe ions. Xe gas was also found to accumulate at multiple types of sinks, such as dislocations and grain boundaries. Bubbles aggregated at those sinks are slightly larger than intragranular bubbles in lattice. At 300 °C, the gaseous swelling strain is limited as all the bubbles are below 10 nm, implying the promising fission gas behavior of U3Si2 under normal operating conditions in light water reactors (LWRs).

Gaseous swelling of U3Si2 during steady-state LWR operation: A rate theory investigation

Rate theory simulations of fission gas behavior in U3Si2 are reported for light water reactor (LWR) steady-state operation scenarios. A model of U3Si2 was developed and implemented into the GRASS-SST code based on available research reactor post-irradiation examination (PIE) data, and density functional theory (DFT) calculations of key material properties. The reliability of the model was examined by performing sensitivity analysis of the key parameters. Simplified peripheral models were also introduced to capture the fuel-cladding interaction. The simulations identified three regimes of U3Si2 swelling behavior between 390K and 1190K. Under typical steady-state LWR operating conditions where U3Si2 temperature is expected to be below 1000K, intragranular bubbles are dominant and fission gas is retained in those bubbles. The consequent gaseous swelling is low and associated degradation in the fuel thermal conductivity is also limited. Those predictions of U3Si2 performance during steady-state operations in LWRs suggest that this fuel material is an appropriate LWR candidate fuel material. Fission gas behavior models established based on this work are being coupled to the thermo-mechanical simulation of the fuel behavior using the BISON fuel performance multi-dimensional finite element code.

Linearization-based method for solving a multicomponent diffusion phase-field model with arbitrary solution thermodynamics

This article describes a phase-field model for an isothermal multicomponent, multiphase system which avoids implicit interfacial energy contributions by starting from a grand potential formulation. A method is developed for incorporating arbitrary forms of the equilibrium thermodynamic potentials in all phases to determine an explicit relationship between chemical potentials and species concentrations. The model incorporates variable densities between adjacent phases, defect migration, and dependence of internal pressure on object dimensions ranging from the macro- to nanoscale. A demonstrative simulation of an overpressurized nanoscopic intragranular bubble in nuclear fuel migrating to a grain boundary under kinetically limited vacancy diffusion is shown.

Fission products behaviour during a power transient: Their inventory in an intragranular bubble

The behaviour of fission products is a key issue during Anticipated Operational Occurrences (AOOs) or Condition II transients or accidental sequence for nuclear fuel. Here we characterized how fission products behaved inside chromium doped UO2 pellet during a power ramp. At the pellet centre fission products have left the UO2 lattice and can be found in bubbles. The composition of the bubbles was determined using an original experimental methodology. The existence of separated precipitates made of metallic fission products for the one, and volatile fission products for the other, was evidenced. This result is discussed with regards to the behaviour of fission products during a power ramp.

Development of the MFPR model for fission gas release in irradiated UO2under transient conditions

The fission gas release microscopic model of the mechanistic code MFPR is further developed for modelling of enhanced release from irradiated UO2 fuel under transient conditions of the power ramp tests, along with the microstructure evolution characterised by the formation of a new population of large intragranular bubbles with a rather wide size distribution (from 30 to 500 nm), observed in transient-tested UO2 fuel samples. Implementation of the additional microscopic mechanisms results in a notable improvement of the code predictions (in comparison with the previous code version) for the fractional gas release in the Riso ramp tests with three different hold times of 3, 40 and 62 h at the terminal linear power of ≈40 kW/m.

Grain Subdivision Fission Gas Swelling Model for UO2

ABSTRACTUnder high burnup UO2 fuel pellets can experience high burnup structure (HBS) at the rim also known as rim effect. The HBS is exceptionally porous with fine grain sizes. HBS increases the swelling further than it would have achieved at a larger grain size. A theoretical swelling model is used in conjunction with a grain subdivision simulation to calculate the swelling of UO2. In UO2 the nucleation sites are at vacancies and the bubbles are concentrated at grain boundaries. Vacancies are created due to irradiation and gas diffusion is dependent on vacancy migration. In addition to intragranular bubbles, there are intergranular bubbles at the grain boundaries. Over time as intragranular bubbles and gas atoms accumulate on the grain boundaries, the intergranular bubbles grow and cover the grain faces. Eventually they grow into voids and interconnect along the grain boundaries, which can lead to fission gas release when the interconnection reaches the surface. This is known as the saturation point. While the swelling model used does not originally incorporate a changing grain size, the simulation allows for more accurate swelling calculations by introducing a fractional HBS based on the temperature and burnup of the pellet. The fractional HBS is introduced with a varying grain size. Our simulations determine the level of swelling and saturation as a function of burnup by combining an independent model and simulation to obtain a more comprehensive model.