Modelling intragranular fission gas release in irradiation of sintered LWR UO2 fuel

A model for the release of stable fission gases by diffusion from sintered LWR UO₂ fuel grains is presented. The model takes into account intragranular gas bubble behaviour as a function of grain radius. The bubbles are assumed to be immobile and the gas migrates to grain boundaries by diffusion of single gas atoms. The intragranular bubble population in the model at low burn-ups or temperatures consists of numerous small bubbles. The presence of the bubbles attenuates the effective gas atom diffusion coefficient. Rapid coarsening of the bubble population in increased burn-up at elevated temperatures weakens significantly the attenuation of the effective diffusion coefficient. The solution method introduced in earlier papers, locally accurate method, is enhanced to allow accurate calculation of the intragranular gas behaviour in time varying conditions without excessive computing time. Qualitatively the detailed model can predict the gas retention in the grain better than a more simple model.     

Computer modeling of steady state fission gas behavior in carbide fuels

A model for the simulation of long-term, steady-state fission gas behavior in carbide fuels is formulated. It is assumed that fission gas release occurs entirely through gas atom diffusion to grain boundaries and cracks. Fission gas bubbles are assumed to remain stationary and to grow as the net result of gas atom precipitation into the bubbles from the matrix solid and gas atom re-solution from the bubbles into the matrix. Furthermore, assuming that local gas atom redistribution process in the immediate neighborhood of a bubble is very rapid, the bubble size is assumed to correspond to the equilibrium size that maintains exact balance between the rate of gas atom re-solution and that of gas atom precipitation.The model also treats the effect of attachment between bubbles and second-phase precipitates; the experimentally observed faster growth rate of precipitate bubbles is simulated using a reduced re-solution parameter for precipitate bubbles. With the grain matrix assumed to be spherical, the model allows the computation of the radial distribution of the intragranular bubbles and the gas atom concentration in the matrix.The flux of gas atoms arriving at the grain boundary is computed. The continual growth of grain boundary bubbles, resulting from the accumulation of gas atoms on the grain boundary, leads to grain boundary interlinkage and all gas atoms that subsequently reach the grain boundary are assumed to be released. Similarly, all gas atoms generated following the interlinkage of intragranular bubbles are also assumed to be immediately released.Application of the model indicates that fission gas swelling is largely due to intragranular bubbles. Grain boundary bubbles, although very large in size, contribute little to fission gas swelling and the contribution from gas atoms in solid solution in the matrix is even less significant.Physical parameters entering the model were assigned numerical values that closely represent the physical characteristics of the irradiation samples. Careful comparisons between the results of sensitivity studies and the experimental data readily identify the re-solution parameter to have the strongest influence on the results predicted by the code and that the grain size, and not the temperature, is the dominant factor affecting gas release.When allowance is made for the uncertainties of the experimental data, the predicted fission gas swelling also correlates well with experiment. The spread in the fuel swelling data, however, indicates that fuel cracking, and not fission gas swelling alone, very often contributes significantly to the fuel external dimensional changes. The linear fission gas swelling rate prediceted by the model exhibits almost a linear variation with temperature. This result correlates well with the linear swelling rate obtained from experimental swelling data if immersion density data alone are used, in order to eliminate the sources of uncertainties associated with fuel cracking.     

Swelling and gas release in oxide fuels during fast temperature transients

A previously reported intergranular swelling and gas release model for oxide fuels has been modified to predict fission gas behavior during fast temperature transients. Under steady state or slowly varying conditions it has been assumed in the previous model that the pressure caused by the fission gas within the gas bubbles is in equilibrium with the surface tension of the bubbles. During a fast transient, however, net vacancy migration to the bubbles may be insufficient to maintain this equilibrium. In order to ascertain the net vacancy flow, it is necessary to model the point defect behavior in the fuel. Knowing the net flow of vacancies to the bubble and the bubble size, the bubble diffusivity can be determined and the long range migration of the gas out of the fuel can be calculated. The model has also been modified to allow release of all the gas on the grain boundaries during a fast temperature transient.The gas release predicted by the revised model shows good agreement to fast transient gas release data from an EBR-II TREAT H-3 (Transient Reactor Test Facility) test. Agreement has also been obtained between predictions using the model and gas release data obtained by Argonne National Laboratory from out-of-reactor transient heating experiments on irradiated UO₂. It was found necessary to increase the gas bubble diffusivity used in the model by a factor of thirty during the transient to provide agreement between calculations and measurements. Other workers have also found that such an increase is necessary for agreement and attribute the increased diffusivity to yielding at the bubble surface due to the increased pressure.     

Re-solution effects and fission gas swelling in UO2

A fission gas swelling model is proposed which enables one to calculate swelling in the vicinity of grain boundary networks and in imperfection-free regions. The grain boundary swelling requires a knowledge of the gas accumulation and the reaction-rate at the boundary. The gas accumulation was calculated by deriving a modified form of Fick's second law wherein it was assumed that because of re-solution effects the in-pile diffusion coefficient can be described as a function of the gas concentration but is independent of the actual operating time. Reaction-rates for bubbles at grain boundaries were derived in the manner discussed by de Jong and Koehler in their treatment of vacancy clustering. The results indicate that there is a grain size of about 10⁻⁴ cm for which the swelling is a maximum, which increases somewhat with irradiation temperature and with depletion at a constant temperature. The results enable one to predict the swelling and the mean radii of both intergranular and intragranular bubbles. Mean bubble radii predicted using the re-solution swelling model are in reasonable agreement with radii obtained from electron micrographs of irradiated UO₂ fuel samples. It is argued that gas bubble migration is the predominant means by which gas atoms arrive at grain boundaries at irradiation temperatures above about 900°C.     

Simulation of non-equilibrium fission gas behaviour during fast thermal transients

A code for predicting the behavior of non-equilibrium fission gas in oxide fuel elements undergoing fast thermal transients is developed. A new variable, the equilibrium variable (EV), is introduced which, together with bubble radius r, completely specifies a fission gas bubble with respect to its size and equilibrium condition. The code is used to simulate the measurements in two TREAT transients with peak temperatures of 2477 and 2000 K. The computations are in fair agreement with the observations for bubbles smaller than 964 Å in diameter, but not for the larger bubbles. In all simulations, bubbles that grew during the heat-up phase of the transient were found to be “frozen” at a larger than equilibrium size during the cooldown phase of the transient. This phenomenon can significantly affect posttransient swelling and gas release. It is also found that the assumption of equilibrium can introduce considerable error in the computed bubble distribution, swelling and gas release at the end of as well as at post fast thermal transients; for example, the non-equilibrium model releases more gas. The code is also used to simulate the H3 TREAT transient as analyzed by Stahl and Patrician (initial temperature equal to 785 K with a maximum of 2393 K attained in 4.2 seconds, maximum thermal gradient of 10 000 K/cm and grain diameter of 4 to 10 μm) using the ideal gas as well as the Van der Waal's equations of states. The gas inventory at the start of the transient is assumed to be at equilibrium in the smallest radius group (6.2 Å), and the initial bubble concentration is assumed to be 1.2 × 10¹⁹/cc. Release rate is found to be strongly dependent upon grain size and initial bubble concentration; a 4 micron diameter grain releases about 95% of the gas retained at the start of the transient, while 6 and 10 micron grains release 68% and 20% respectively. When the initial bubble concentration is reduced by a factor of 16 for the 10 micron grain, fractional release increases to 62%. Gas release is found to result primarily from small bubbles ( ).     

Phase-field modeling of gas bubbles and thermal conductivity evolution in nuclear fuels

A phase-field model was developed to simulate the accumulation and transport of fission products and the evolution of gas bubble microstructures in nuclear fuels. The model takes into account the generation of gas atoms and vacancies, and the elastic interaction between diffusive species and defects as well as the inhomogeneity of elasticity and diffusivity. The simulations show that gas bubble nucleation is much easier at grain boundaries than inside grains due to the trapping of gas atoms and the high mobility of vacancies and gas atoms in grain boundaries. Helium bubble formation at unstable vacancy clusters generated by irradiation depends on the mobilities of the vacancies and He, and the continuing supply of vacancies and He. The formation volume of the vacancy and He has a strong effect on the gas bubble nucleation at dislocations. The effective thermal conductivity strongly depends on the bubble volume fraction, but weakly on the morphology of the bubbles.     

Electron Microscope Observations of Gas Bubbles in Neutron Irradiated Al-Li Alloys

The electron microscope has been used to observe the behavior of He gas bubbles in neutron irradiated Al-Li alloys. In the case of high He concentration, the gas bubbles were observed as small white or black dots in specimens as irradiated. The bubbles initiated appreciable growth upon heating to 400°C. They precipitated preferentially along the subgrain boundaries and dislocations, as well as along the grain boundaries. The size of the bubbles, observed in a specimen heated to 550°C, ranged from about 10 Å to 1 μ.

The shape of the bubbles in the specimen heated to 400°C was hexagonal or octagonal in the two-dimentional projection and a polyhedral image of the larger bubbles was clearly observed. The number of planes that bound the polyhedral bubble increased with increasing temperature of heating. Spherical bubbles were also observed.     

Spaltgasfreisetzung in Keramischen Brennstoffen Bei Reaktor-Zyklen-Betrieb

Gas release kinetics have been calculated in terms of a bubble migration model; different release mechanisms are assumed to operate in various temperature ranges. It is assumed that fission gas is taken up by a bubble immediately after its formation and that the bubble becomes freed after passing the distance between the point of formation and a grain boundary (or, in the model, a zone boundary). The amount of gas released can be obtained by summing over all gas bubbles which can reach the grain boundary in the course of a specified time interval.In the operation of reactor cycles, one can use the assumption that the gas components from the different cycles do not mutually influence each other in respect of gas release; on the basis of this the total gas release can be calculated. The distribution of gas bubbles is calculated, so that for each cycle the position of the bubbles is known; this can then be used for the next cycle as the starting point for those gas bubbles which have not been released in the preceding cycle. If for each cycle start one represents the as yet unreleased gas in terms of a homogeneous gas distribution, this approximation offers computational simplifications but underestimates the gas release for low-temperature irradiation.     

The effect of gas bubbles on grain coarsening in gold foils

The interaction of small (≈ 3 nm radius) gas bubbles with migrating boundaries has been investigated using vapour-deposited gold foils, with and without implanted helium. No bubble sweeping by moving boundaries is observed; this is consistent with the rate of bubble migration being determined by the nucleation of steps on the faceted surfaces of the bubbles. Despite their relative immobility, the bubbles have no measurable effect on boundary migration, suggesting that the bubble-boundary interaction is weak. In contrast, surface grooves appear to be effective barriers to boundary motion in thin samples.     

Fission gas disposition in decay heat environment

A computer code is developed to model fission gas disposition in UO₂ fuel during nearly isothermal heating, as would result from decay heat. The intragranular analysis, random diffusion model, uses a spatial solution for random migration and bubble coalescence. Nonequilibrium bubble growth and interactions between bubbles as well as nonequilibrium bubblegrain boundary interactions are considered. In the intergranular analysis, grain growth is allowed until tunnels have formed; this is set at 6% grain edge swelling. Grain face bubbles are assumed uniform in size and distribution. Grain edge tunnels are approximated in toroidal geometry. The model (a system of two grains, one shrinking and one growing but with total volume conserved; each grain originally contained 50% of the total fission gas) is applied to a “postulated” LMFBR accident condition involving a slow “nearly isothermal” heating of the fuel. The intragranular release is computed at 3.4% without grain growth, but at 14% with grain growth. Intragranular release is found to be dominated by grain growth.The analysis was applied also to the FGR-34 transient of HEDL. It is pointed out, however, that in the FGR-34 experiment thermal gradients were present whereas in the present code, only isothermal heating is considered. In spite of this significant difference between the modeled and the observed thermal state of the fuel, the comparison was carried out with a purpose to examine the existence of nonequilibrium attractive forces, between bubbles and grain boundaries, which were suggested by HEDL as perhaps responsible for the bubble denuding observed on both sides of the grain boundary. The computations did demonstrate the existence of nonequilibrium conditions, but the computed intragranular bubble radii, with only random diffusion as the operative mechanism, were well below the reported values. It is likely that this descrepancy between computed and observed bubble radii is due to (1) the presence in FGR-34 tests of thermal gradients, which would make bubble biased migration operative, and/or (2) the possibility of very strong enhancement, significantly more than two orders of magnitude, of the diffusion coefficient due to the prevailing nonequilibrium bubble conditions. The present code treats nonequilibrium conditions, but contains no physical mechanism for diffusion enhancement.     

The release of fission gas from nuclear fuels during temperature transients

The fractional release of rare gas atoms from a spherical grain of uranium dioxide containing a uniform concentration of gas atoms and intragranular bubbles is calculated for short-duration temperature transients and post-irradiation annealing. The released fraction is shown to reach a small maximum value which is dependent only on the grain size, gas atom concentration and intragranular bubble distribution. The analysis therefore may be applied to any fuel material providing these parameters are known. The conclusion therefore is that during a brief temperature transient, only a very small fraction of gas will be released from grain interiors to grain boundaries. Consequently the majority of gas released into the free volume of a pin will come from gas already residing on grain boundaries and released by mechanical cracking; the fractional gas release is small and should not cause undue concern. The calculations do not cover the case of fuel melting.     

Modeling of fission gas swelling in LWR UO2 fuel under irradiation

An understanding of the behavior of fission gas in uranium dioxide (UO₂) fuel is necessary for the prediction of the performance of fuel rods under irradiation. A mechanistic model for matrix swelling by the fission gas in LWR UO₂ fuel is presented. The model takes into account intragranular and intergranular fission gas bubbles behavior as a function of irradiation time, temperature, fission rate and burn-up. The intragranular bubbles are assumed to be nucleated along the track of fission fragments, which play the dual role of creator and destroyer of intragranular bubbles. The intergranular bubble nuclei is produced until such time that a gas atom is more likely to be captured by an existing nucleus than to meet another gas atom and form a new nucleus. The capability of this model was validated by a comparison with the measured data of fission gas behavior such as intragranular bubble size, bubble density and total fuel swelling. It was found that the calculated intragranular bubble size and density are in reasonable agreement with the measured results in a broad range of average fuel burn-ups 6–83 GW d/tU. Especially, the model correctly predicts the fuel swelling up to a burn-up of about 70 GW d/tU.     

The development of grain-face porosity in irradiated oxide fuel

The predominant mode of fission gas release occurs through atomic diffusion to the grain boundaries. In oxide fuels the fission gases initially precipitate as an array of small lenticular bubbles of circular projection. The arrival of additional gas and vacancies causes these bubbles to grow and coalesce into fewer, larger bubbles. Depending on the irradiation conditions and temperatures, these bubbles may develop either as circular lenticular pores or as extended multi-lobed pores. Eventually the pores may intersect the grain edges where pathways may be formed which enable the gas to migrate to the outer geometry of the fuel and hence to the gap and the pin free volume. Recent extensive PIE campaigns on irradiated fuels have provided a large database of inter-granular porosity development and, from these, models of bubble growth, coalescence, morphological relaxation and venting have been developed.     

On the rate theory model for fission-gas behaviour in nuclear fuels

The rate theory model of the homogeneous nucleation and subsequent growth of intragranular fission gas bubbles has been extended to allow for the inclusion of very much larger bubbles. A simple treatment of the behaviour of grain-boundary gas is included in the present model, which allows for the re-solution of gas from intergranular bubbles. The effect of varying the model parameters and of including bubble mobility in the theory have been considered and it is concluded that the dominant parameters for gas release are temperature, grain size, re-solution rate and bubble migration and coalescence.     

弥散型燃料的裂变气体行为研究

探讨了弥散型燃料中对辐照肿胀有重要影响的裂变气体的行为机理。裂变气体原子聚集成气泡引起燃料相肿胀,气泡的尺寸分布是影响辐照肿胀的重要因素。决定气泡生长的裂变气体的行为机理主要有：裂变气体原子的产生和热扩散迁移,气泡的成核和聚合长大,气泡内气体原子的重溶,燃料相的辐照亚晶化等过程。燃料中各种尺寸的气泡浓度随时间的变化率可用气泡生长的动力学速率方程组来描述。当裂变密度较高时,辐照产生的缺陷引起燃料相的     

Effect of non-equilibrium fission gas and fuel creep on swelling and release in irradiated carbide fuels

The code UCSWELL was developed to simulate fission gas behavior in carbide fuels. In the present work, one of the limiting assumptions in UCSWELL - that matrix gas bubbles are in equilibrium with gas atom concentration - is removed and non-equilibrium matrix fission gas bubbles are allowed, but with relaxation to equilibrium by means of vacancy diffusion and thermal and radiation-induced creep of the fuel. For a given grain size, the difference in swelling between equilibrium and non-equilibrium with relaxation bubble fission gas treatment increases with decreasing irradiation temperature. At a given temperature, the non-equilibrium effect is more pronounced for larger grain fuel. This is to be expected because the creep rate (and hence the rate at which bubbles grow to an equilibrium size) decreases as temperature decreases and/or as grain size increases. At temperatures, where the creep rate is grain size insensitive, grain size remains important to the equilibrium process in so far as the grain boundary is a source of vacancies to the non-equilibrium bubbles. While the difference in these quantities is at the most on the order of 20% for the steady operating conditions considered, it is anticipated that the non-equilibrium effects become more pronounced during reactor overpower and undercooling transients.     

Grain Boundary Migration and Growth of Gas Bubbles in Neutron Irradiated Al-Li Alloys

The electron microscope has been used to observe the behavior of He gas bubbles in cold-worked Al-Li alloys upon post-irradiation heating. The bubbles appeared occasionally along the grain boundary in the Al-2.7w/0 Li specimen irradiated to 4.1×10¹⁹ n/cm² and then heated to about 300°C. Upon heating to higher temperatures, up to 450 °C, the bubbles in the specimen grew along with the gradual growth of the recrystallized grains. When the bubbles reached sizes of 0.3~0.6 μ, upon heating to 500°C, the grain boundaries migrated, leaving the bubbles detached from them. In the Al-0.4w/0 Li specimen, the bubbles migrated out of the specimen surface, along with the grain boundary, upon heating to the temperatures above 450°C. The grain sizes of the irradiated Al-2.7w/0 Li specimen heated for 1 hr to 450°C were smaller than in unirradiated specimen heated for 1 hr to 400°C.

In the displacement of grain boundary caused by grain growth, the gas bubbles are swept together to form larger bubbles until they reach a certain critical size. And as the bubbles become larger, they detach from the moving boundary. The bubbles impede the grain boundary movement, but do not suppress it completely. The bubbles found on the grain boundaries differed in shape from the bubbles that had grown in the grain interior.     

The growth of sub-critical bubbles on grain boundaries

A coalescence model is developed for the production of creep cavity nuclei. Small pre-existing bubbles situated in the grain boundary are swept by the dislocations responsible for grain-boundary sliding. The bubble motion induced by the dislocations results in bubbles continuously impinging and coalescing. The distribution of bubble sizes is calculated and the nucleus spacing is found for that part of the distribution with sizes above the critical radius. The spacing of nuclei is related to the high-temperature creep ductility of irradiated metals.     

充氚不锈钢中氦泡长大行为的加热效应

以室温贮存经历的充氚不锈钢试样为研究对象,计算了充氚不锈钢中氚、氦浓度的深度分布,利用透射电镜观察了充氚不锈钢在加热过程中氦泡的演化行为。结果表明:在氚压0.131MPa、780℃充氚8h后,不锈钢中氚在深度方向分布均匀,平均浓度为110μL/L;在空气室温环境下放置6a后,不锈钢中氚衰变的氦浓度在深度方向分布均匀,平均浓度为60μL/L;对充氚不锈钢加热处理后,在550℃/1h时效即可观察到氦泡;在950℃/1h和1050℃/1h时效时,氦泡明显长大,大的可达100nm,小的可达30nm,在晶界、晶内和位错处均可见氦泡。     

Nucleation of helium bubbles on dislocations,dislocation networks and dislocations in grain boundaries during 600 MeV proton irradiation of aluminium

High-purity aluminium (99.9999%) was irradiated with 600 MeV protons with a damage rate of $\text{3.5 × 10}{}^{\mathrm{?6}}\text{dpa/s}$. Irradiation with 600 MeV protons produces helium and hydrogen at the rate of 140 and 615 appm per dpa, respectively. Specimens irradiated at temperatures in the range 116 to 318 °C to doses in the range 0.04 to 5 dpa were examined in a transmission electron microscope (TEM). The TEM investigation has shown that helium bubbles are formed on dislocations in the grains as well as dislocations in the grain boundaries. Dislocation nodal points whether present in dislocation walls or in grain boundaries are found to be the most favourable sites for bubble nucleation. The mean diameter of the bubbles on individual dislocation lines are found to be larger than those for the bubbles in the matrix. The bubble size and density on grain boundaries vary from boundary to boundary. The size of these bubbles on the boundaries is larger than or equal to the size of those in the matrix. It is suggested that helium atoms once arrived at a dislocation remain bound to the dislocation line but at the same time remain mobile within the dislocation core; the bubble nucleation behaviour in the core would thus be affected by the core structure of the different dislocations. An estimate of the effective helium diffusion in the dislocations relative to that in the lattice has been made on the basis of the measured bubble parameters and the width of the bubble-denuded zone along dislocation lines; the diffusion coefficient of helium in the dislocations is found to be about the same as that in the lattice.