J. Rest

Dynamics of irradiation-induced grain subdivision and swelling in U3Si2 and UO2 fuels

Abstract 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 UO2 and U3Si2 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.

An alternative explanation for evidence that xenon depletion, pore formation, and grain subdivision begin at different local burnups☆

Abstract In order to interpret the recent observation that xenon depletion, pore formation, and grain subdivision occur successively at increasing local burnups, a rate-theory-based model is used to investigate the nucleation and growth of cavities during low-temperature irradiation of UO 2 in the presence of irradiation-induced interstitial-loop formation and growth. Consolidation of the dislocation structure takes into account the generation of forest dislocations and capture of interstitial dislocation loops. The loops accumulate and ultimately evolve into a low-energy cellular dislocation structure. The cell walls have been previously identified as recrystallization nuclei. The calculations indicate that nanometer-size bubbles are associated with this cellular dislocation structure while the observed micron-size bubbles are presumed to be either preexisting pores deformed by adjacent grains and/or new pores formed in the new recrystallized grain-boundary junctions. Subsequent to recrystallization, gas released from the recrystallized grains feeds the preexisting pores and the recrystallized grains may appear to form a preferential concentration of subdivided grains around the growing pores. This picture is illustrated in a sequence of photomicrographs of irradiated U 3 O 8.

Modeling the behavior of Xe, I, Cs, Te, Ba, and Sr in solid and liquefied fuel during severe accidents☆

Abstract This paper describes the primary physical/chemical models recently incorporated into a mechanistic code (FASTGRASS) for the estimation of fission product release from fuel, and compares predicted results with test data. The theory of noble gas behavior is discussed in relation to its effect on the release behavior of I, Cs, Te, Ba, and Sr. The behavior of these fission products in the presence of fuel liquefaction/dissolution and grain-growth phenomena is presented, as is the chemistry of Sr, Ba, I, and Cs. Comparison of code predictions with data indicates the following trends. Fission product release behavior from solid fuel strongly depends on fuel microstructure, irradiation history, time at temperature, and internal fuel rod chemistry. Fuel liquefaction/dissolution, fracturing, and oxidation also exert a pronounced effect on release during fuel rod degradation. For low burnup fuel (e.g., TMI-2), appreciable fission product retention in previously liquefied fuel can occur due to the low concentration of fission products, and the limited growth of bubbles in the liquefied material. Many of the calculations described in this paper were made with a version of FASTGRASS developed for use on a personal computer (IBM compatibile).

The effect of irradiation-induced gas-atom re-solution on grain-boundary bubble growth

The rim region of high-burnup fuels is characterized by an exponential growth of intergranular porosity. In particular, the understanding of the dynamics of irradiation-induced recrystallization and subsequent gas-bubble swelling requires a quantitative assessment of the nucleation and growth of grain-boundary bubbles. Calculations of bubble growth on the grain boundaries of irradiated nuclear fuels at relatively low temperatures have, in general, been performed under the assumption that these bubbles are not appreciably affected by irradiation-induced gas-atom re-solution. In contrast, matrix bubbles are strongly affected by this bubble shrinkage mechanism and as a consequence are generally two to three orders or more of magnitude smaller than the grain-boundary bubbles. A variational method is used to calculate diffusion from a spherical fuel grain. The junction position of two trial functions is set equal to the bubble gas-atom knock out distance. The effect of grain size, gas-atom re-solution rate and diffusivity, gas-atom knock out distance, and grain-boundary bubble density on the growth of intergranular bubbles is studied, and the conditions under which intergranular bubble growth occurs are elucidated.

An improved model for fission product behavior in nuclear fuel under normal and accident conditions

Abstract A theoretical model for the prediction of the behavior of the gaseous and volatile fission products in nuclear fuels under normal and transient conditions has undergone substantial improvements. The major improvements have been in the atomistic and bubble diffusive flow models, in the models for the behavior of gas bubbles on grain surfaces, and in the model for iodine solubility. The theory has received extensive verification over a wide range of fuel operating conditions, and can be regarded as a state-of-the-art model based on our current level of understanding of fission product behavior. Because of existing uncertainties in both materials properties and mechanisms of fission product response, any verified mechanistic description of fission product release entails assumptions in these areas. The diffusivity of fission gas bubbles during transient conditions, the effect of irradiation induced grain boundary gas-atom re-solution on intragranular diffusive flow rates, and the effect of iodine solubility on iodine release rates are aspects of fission product behavior that are currently clouded with uncertainty. The assumptions that have been made in the theory have been evaluated and are discussed in relation to the model verification, uncertainties in the existing data base, and other theoretical descriptions of fission product behavior.

Kinetics of fission-gas-bubble-nucleated void swelling of the alpha-uranium phase of irradiated U-Zr and U-Pu-Zr fuel☆

Abstract Bias-driven growth of voids is identified as a major swelling mechanism in the α-uranium phase of irradiated U-Pu-Zr metal fuels being developed at Argonne National Laboratory for the Integral Fast Reactor (IFR). The trends in U-Pu-Zr swelling data prior to fuel/cladding contact can be interpreted in terms of unrestrained void swelling. It is theorized that the swelling mechanisms at work in the α-uranium phase can be modeled by single-vacancy and single-interstitial kinetics, thus avoiding the use of complicated defect-interaction terms required for the calculation of void nucleation. A mechanistic model is presented wherein gas bubbles that are formed on α/δ phase boundaries during the incubation period act as potential nuclei for cavities. The model has the capability to predict both gas-bubble-driven swelling (overpressurized cavities) and bias-driven void swelling (underpressurized cavities), as well as the transition from one swelling mechanism to the other. The results of this study demonstrate that the relatively long incubation times characteristic of IFR swelling and gas release can be understood in terms of a reduced gas-bubble nucleation rate on the α/δ phase boundaries, i.e., the α/δ phase boundary lamellae are less efficient gas-bubble incubators than normal high angle grain boundaries. Results obtained with the model are compared with U-10Zr and U-19Pu-10Zr deformation data, and with high purity uranium swelling data.

The coupled kinetics of grain growth and fission product behavior in nuclear fuel under degraded-core accident conditions☆

Abstract The theoretical FASTGRASS-VFP model has been used in the interpretation of fission gas, iodine, and cesium release from (1) irradiated high-burnup LWR fuel in a flowing steam atmosphere during high-temperature, in-cell heating tests (performed at Oak Ridge National Laboratory) and (2) trace-irradiated LWR fuel during severe-fuel-damage (SFD) tests (performed in the PBF reactor in Idaho). A theory of grain boundary sweeping of gas bubbles has been included within the FASTGRASS-VFP formalism. This theory considers the interaction between the moving grain boundary and two distinct size classes of bubbles, those on grain faces and on grain edges, and provides a means of determining whether gas bubbles are caught up and moved along by a moving grain boundary or whether the grain boundary is only temporarily retarded by the bubbles and then breaks away. In addition, as FASTGRASS-VFP provides for a mechanistic calculation of ultra- and intergranular fission product behavior, the coupled calculation between fission gas behavior and grain growth is kinetically comprehensive. Results of the analyses demonstrate that intragranular fission product behavior during both types of tests can be interpreted in terms of a grain-growth/grain-boundary-sweeping mechanism that enhances the flow of fission products from within the grains to the grain boundaries. The effect of fuel oxidation by steam on fission product and grain growth behavior is also considered. The FASTGRASS-VFP predictions, measured release rates from the above tests, and previously published release rates are compared and differences between fission product behavior in trace-irradiated and in high-burnup fuel are highlighted.

A generalized model for radiation-induced amorphization and crystallization of U3Si and U3Si2 and recrystallization of UO2

Abstract A rate-theory model of radiation-induced amorphization and crystallization of U3Si during ion irradiation has been generalized to include U3Si2 and UO2. The generalized model has been applied to ion-irradiation and in-reactor experiments on U3Si and U3Si2 and provides an interpretation for the amorphization curve (dose required to amorphize the material as a function of temperature), for the ion-radiation-induced nanoscale polycrystallization of these materials at temperatures above the critical temperature for amorphization, as well as for the role of the small crystallites in retarding amorphization. An alternative mechanism for the evolution of recrystallization nuclei is described for a model of irradiation-induced recrystallization of UO2 wherein the stored energy in the UO2 is concentrated in a network of sinklike nuclei that diminish with dose due to interaction with radiation-produced defects. The sinklike nuclei are identified as cellular dislocation structures that evolve relatively early in the irradiation period. The complicated kinetics involved in the formation of a cellular dislocation network are approximated by the formation and growth of subgrains due to the interaction of shock waves produced by fission-induced damage to the UO2.

Precipitation kinetics of rare gases implanted into metals

Abstract A rate-theory approach is used to interpret observations on the precipitation of Kr, Xe, and Ar injected into Ni at temperatures between 25 and 560 °C. At temperatures of 400 °C or higher, the implanted Kr precipitates evolve into a bi-modal size distribution containing small solid precipitates and an additional population of larger, faceted bubbles. The calculations explore the dependence of the Kr bi-modal size distribution on the maximum size of the solid Kr precipitates and on the bubble mobility. The sensitivity of the calculated size distribution to gas-atom diffusivity and gas-bubble nucleation rate is also investigated. The analysis suggests that the swelling in these high gas production rate experiments is primarily gas driven, and that during the irradiation whereas the large bubbles move by surface diffusion, the small, solid Kr precipitates are immobile. The relevance of the Kr-Ni interaction on the solid Kr precipitate size cutoff, and differences in behavior between implanted Kr, Xe, and Ar are discussed.

Validation of mechanistic models for gas precipitation in solids during postirradiation annealing experiments

Abstract A number of different phenomenological models for gas precipitation in solids during postirradiation annealing experiments have been proposed. Validation of such mechanistic models for gas release and swelling is complicated by the use of data containing large systematic errors, and phenomena characterized by synergistic effects as well as uncertainties in materials properties. Statistical regression analysis is recommended for the selection of a reasonably well characterized data base for gas release from irradiated fuel under transient heating conditions. It is demonstrated that an appropriate data selection method is required in order to realistically examine the impact of differing descriptions of the phenomena, and uncertainties in selected materials properties, on the validation results. The results of the analysis show that the kinetics of gas precipitation in solids depend on bubble overpressurization effects and need to be accounted for during the heatup phase of isothermal heating experiments. It is shown that if only the total gas release values (as opposed to time-dependent data) were available, differentiation between different gas precipitation models would be ambiguous. The observed sustained increase in the fractional release curve at relatively high temperatures after the total precipitation of intragranular gas in fission gas bubbles is ascribed to the effects of a grain-growth/grain-boundary sweeping mechanism.