Fission Gas Diffusion Research Articles

Release of unstable fission products from defective fuel rods to the coolant of a PWR

An analysis method has been developed to predict the contents of unstable fission products in the coolant of a PWR containing defective fuel rods under steady-state operating conditions. It takes into account the relevant physical processes, such as fuel pellet oxidation, enhancement of fission gas diffusivity due to fuel oxidation, and migration of fission products from the fuel-to-clad gap to the coolant by a first-order rate process. With the shape of grains treated as tetrakaidecahedron, the transport of fission products from the fuel matrix to the grain boundaries and formation of fission gas bubbles on grain boundaries are described by White and Tucker's model. In addition, the fraction of fission gas bubbles on grain boundaries interlinked to open surfaces is determined with the use of the Monte Carlo technique. Transport of the fission products from the gap to the coolant is assumed to occur by a first-order rate process. Comparison with experimental data shows that the present method predicts reasonably well the R B ratios for defective fuel rods with intermediate linear heating rates and underpredicts for fuel rods with very high or low linear heating rates.

Fission gas release during grain growth in a microstructure with a distribution of grain sizes

Fission gas diffusion from a microstructure with a distribution of grain sizes undergoing grain growth is analyzed. Hillert's theory is used to describe the evolution in grain morphology, during which some grains enlarge while others shrink and may even disappear. Limiting cases of Booth release (when only diffusion occurs) and Malen release (when grain-boundary sweeping is dominant) are derived for a body with a distribution of grain sizes. The moving boundary diffusion equation that couples the diffusion and sweeping mechanisms is derived. The grain-size distribution is divided into 25 groups for which the diffusion equations are solved numerically for the average intragranular gas concentration. The results are compared to existing single-grain-size models which, in all cases, overpredict the fractional release. Depletion of intragranular fission gas provides a source for migration via grain boundaries to the free surface.

Evaluation of Fission Gas Release in High-Burnup Light Water Reactor Fuel Rods

Research to define the behavior of Zircaloy-clad light water reactor (LWR) UO[sub 2] fuel irradiated to high burnup levels was conducted as part of the High Burnup Effects Program (HBEP). The HBEP was a 12-yr program that ultimately acquired, characterized, irradiated, and examined after irradiation 82 LWR fuel rods ranging in rod-average fuel burnup from 22 to 69 MWd/kgM with a peak pellet burnup of 83 MWd/kg M. A principal emphasis of the HBEP was to evaluate the effect of high burnup on fission gas release. It was confirmed that fission gas release remained as dependent on design and irradiation history parameters at high burnup levels as at low to moderate burnup levels. One observed high-burnup effect was the development of a burnup-dependent microstructure at the fuel pellet surface when pellet-edge burnup exceeded 65 MWd/kgM. This low-temperature rim region' was characterized by a loss of optically definable grain structure, a high volume of porosity, and diffusion of fission gas from the UO[sub 2] matrix to the porosity. Although the rim region has the potential for enhanced fission gas release, it is concluded that no significant enhancement of rod-average fission gas release at high burnup levels was observed for the examinedmore » fuel rods.« less

A model for calculating fission gas diffusion in annealing experiments

An analytical treatment has been developed to calculate the diffusive release of fission gas in high-temperature annealing experiments. This model is based on a more general approach for treating the previous irradiation conditions. A square-root to linear dependence on the anneal time is predicted for the release fraction depending on whether the fuel samples are trace-irradiated or from high-burnup commercial rods.

Effects of additives and the oxygen potential on the fission gas diffusion in UO2 fuel

Diffusion coefficients, D, of 133Xe have been measured in the temperature range 1000–1600°C for UO2, 0.5 wt% Nb2O5-UO2 and 0.2 wt% TiO2-UO2 with the irradiation dose of 1.2 × 1017fissions/cm3 (4 MWd/t U), by means of a post-irradiation annealing technique. In addition, the effect of the oxygen potential on the diffusion coefficient for UO2 has been examined at 1400°C over the range of −560 to −390 kJ/mol. The diffusion coefficients are enhanced by the doping of Nb2O5 and TiO2 by a factor of about 50 and 7, respectively. The results for the three specimens at the oxygen potentials corresponding to a constant PH2O/PH2 ratio of 1.1 × 10−3 are as follows: D(cm2/s) = 4.0 × 10−8exp(−264(kJ/mol)/RT) for UO2, D(cm2/s) = 4.6 × 10−5exp(−306(kJ/mol)/RT) for 0.5 wt% Nb2O5-UO2, D(cm2/s) = 5.0 × 10−7exp(−272(kJ/mol)/RT) for 0.2wt% TiO2-UO2. The diffusion coefficient for undoped UO2 is increased by a factor of about 3 when increasing the oxygen potential from −556 to −391 kJ/mol at 1400°C. Over this range of the oxygen potential, the corresponding O/U ratio changes from 2.000 to 2.001. The present tendency is in agreement with previously reported results on cation self-diffusion and diffusion controlled phenomena such as creep and grain growth in undoped and additive doped UO2 fuels.

BEAF - a computer program for analysis of light water reactor fuel rod behavior

BEAF - a computer program for analysis of light water reactor fuel rod behavior was developed. The BEAF code, which is appropriate for on-line prediction of fuel rod behavior, can analyze fuel rod thermal and mechanical behaviors using the axisymmetric, plane strain approximation and finite difference method to realize a fast running time. In the mechanical analysis, a new cracked pellet compliance model is introduced, in which pellet cracking and crack healing, pellet initial relocation, modified elastic moduli of a cracked fuel pellet, and stress dependent hot pressing are considered. Adding to those capabilities, fission gas flow and diffusion in the fuel-clad gap are analyzed to take into account the slow fission gas dilution effect on the gap conductance during power ramp.

Evaluation of LWR fuel rod behavior under operational transient conditions

To evaluate the effects of fission gas flow and diffusion in the fuel-cladding gap on fuel rod thermal and mechanical behaviors in light water reactor (LWR) fuel rods under operational transient conditions, computer sub-programs which can calculate the gas flow and diffusion have been developed and integrated into the LWR fuel rod performance code BEAF. This integrated code also calculates transient temperature distribution in the fuel-pellet and cladding. The integrated code was applied to an analysis of Inter Ramp Project data, which showed that by taking into account the gas flow and diffusion effects, the calculated cladding damage indices predicted for the failed rods in the ramp test were consistent with iodine-SCC (Stress Corrosion Cracking) failure conditions which were obtained from out-of-reactor pressurized tube experiments with irradiated Zircaloy claddings. This consistency was not seen if the gas flow and diffusion effects were neglected. Evaluation were also made for the BWR 8 × 8 RJ fuel rod temperatures under power ramp conditions.

LIFE-GCFR: A computer code for predicting Gas-Cooled Fast-Reactor fuel performance

The fuel-pin modeling code, LIFE-GCFR, has been developed to predict the thermal, mechanical, and fission-gas behavior of Gas-Cooled Fast-Reactor (GCFR) fuel rods under normal operating conditions. Starting with the Liquid-Metal Fast-Breeder-Reactor (LMFBR) code, LIFE-3, a number of modifications and additions were made to the mixed-oxide fuel models in the code to make the description of fuel behavior more physically realistic for both LMFBR and GCFR applications. These include: a more predictive grain growth model, a creep model which is valid for both primary and secondary creep, a stress-dependent crack-healing model, a more realistic solid-fission-product swelling rate, and the addition of the GRASS-SST fission-gas model (modified for fast reactor application). Then the following options were added to incorporate specific design features of the GCFR: helium coolant properties, heat transfer coefficients for smooth and ribbed cladding sections, and a model for the axial diffusion of fission gases from the fuel to the pressure-equalization system (PES). LIFE-GCFR predictions were checked against experimental observations for a wide range of irradiation conditions. The overall good agreement between predictions and experimental results indicates that LIFE-GCFR is capable of realistically predicting the thermal, mechanical, and fission-gas behavior of mixed-oxide fuel under GCFR and LMFBR operating conditions. The reference GCFR fuel-element design was analyzed with the verified LIFE-GCFR code for steady-state histories, power-cycling histories, and the off-normal event of blockage of the PES system. The results of the calculations indicate that the GCFR fuel has adequate design margins under anticipated operating conditions.

Fuel swelling due to retained fission gas and thermal effects during high temperature transients

Fuel swelling of previously irradiated pressurized-water-reactor-type fuel rods tested under power-cooling-mismatch conditions is due to retained fission gas and thermal effects within the film boiling region. In this paper empirical correlations for fuel swelling are presented, and mechanisms contributing to the observed swelling and the applicability of an analytical fission gas behavior computer code (GRASS-SST) to fuel swelling are evaluated. Major contributors to fuel swelling are fuel melting and expansion, expansion of solid fuel, fission gas bubble coalescence, fission gas diffusion to grain boundaries, and change in surface tension of fuel upon melting. The contributions to fuel swelling of solid fission products and the effects of cladding contraction and wall thinning on rod swelling are also included. The overall empirically-calculated fuel swelling values and the GRASS-SST code calculated values are compared with measured values. The agreement between measured and empirically calculated fuel swelling is generally close. Fuel swelling due to retained fission gas during the film boiling transient, as calculated by the GRASS-SST code, was found to be in good agreement with experimental results.

Doping UO 2 with niobia — Beneficial or not?

The anticipated benefits of large grains in Cr2O3-doped UO2 pellets include improved mechanical and fission gas retention properties. To support the assessment of fission gas release (FGR) from doped pellets, the impact of doping on fission gas diffusivity for in-reactor conditions must be understood. In this work, we tackle this issue by informing the fission gas model within the BISON fuel performance code using material models developed at the atomic scale. The investigation of intra-granular fission gas diffusivity in Cr2O3-doped UO2 is carried out by adapting a cluster dynamics model that, accounting for UO2 thermochemistry, is capable of describing Xe diffusion under irradiation in undoped UO2 as the starting point. Using a thermodynamic analysis, it is shown that in stoichiometric UO2 with additions of Cr2O3, the oxygen potential is defined by the Cr-Cr2O3 two-phase equilibrium. Using the cluster dynamics model, the predicted Xe diffusivity in doped UO2 was significantly increased in both the intrinsic and irradiation-enhanced regimes compared to undoped UO2, as a result of higher concentrations of uranium and oxygen vacancies, respectively. This is a consequence of the more oxidizing conditions at high temperature, and more reducing conditions at low temperature, as a result of doping. Arrhenius functions have been fitted to the cluster dynamics results to enable implementation of the new diffusivities in the BISON fission gas behavior model. BISON simulations were carried out, showing the competing effects of the enlarged grains and the new fission gas diffusivity model, which act to suppress and enhance fission gas release, respectively. The new physics-informed model was validated against in-reactor experimental measurements under normal operation. Additionally, benchmarking was carried out for power ramp conditions. The predicted fission gas release agreed well with the experimental data, showing noticeable improvements over the standard UO2 model.

A microstructure-dependent model for fission product gas release and swelling in UO 2 fuel

A model for the release of fission gas from irradiated UO 2 fuel is presented. It incorporates the relevant physical processes: fission gas diffusion, bubble and grain boundary movement, intergranular bubble formation and interlinkage. In addition, the model allows estimates of the extent of structural change and fuel swelling. In the latter, contributions of thermal expansion, densification, solid fission products, and gas bubbles are considered. When included in the ELESIM fuel performance code, the model yields predictions which are in good agreement with data from UO 2 fuel elements irradiated over a range of water-cooled reactor conditions: linear power outputs between 40 and 120 kW m −1, burnups between 10 and 300 MW h(kg U) −1, and power histories including constant, high-to-low and low-to-high power periods. The predictions of the model are shown to be most sensitive to fuel power (temperature), the choice of diffusion coefficient for fission gas in UO 2, and burnup. The predictions are less sensitive to variables such as fuel restraint, initial grain size and the rate of grain growth.

Influence of defects on rare-gas diffusion in solids

The diffusion of 133Xe in CsI was studied as an aid to understanding rare gas diffusion in more complex systems, such as nuclear reactor fuels. Diffusion at low gas concentrations and negligible radiation damage levels was measured by growing single crystals of CsI containing radioactive 133I which decayed to 133Xe (T12 = 20.8 h). Both the time rate of release and temperature dependence of the rare gas diffusion coefficient were consistent with classical diffusion solutions, giving: D = D0 exp (−Q/kT), D0 = (0.57+2.30−0.43) cm2/sec, Q = (1.01 ± 0.04) eV.Crystals containing high concentrations of defects exhibited trapping of the rare gas and anomalous diffusion kinetics. Trapped gas atoms tended to stabilize the defects and prevent their annealing during heating. Diffusion of fission gas recoiled into CsI specimen surface layers from an external fissionable source obeyed classical diffusion solutions at low fission recoil concentrations, while at high concentrations, radiation damage created traps which decreased gas diffusion rates. These traps differed significantly from natural defects in trap concentration, gas atom binding energies, and annealing characteristics. Increasing the gas concentration independent of radiation damage also lowered rare gas diffusion coefficients, showing that formation of small gas atom clusters also produced trapping. The results showed that classical rare gas diffusion could be obtained under ideal conditions and that distinctive trapping behavior with different characteristics could be associated with the presence of natural defects, radiation damage, and high gas concentration.

Rare Gas Diffusion in Cesium Iodide: Use of Fission Recoil Doping Techniques

Diffusion of radioactive 133Xe in single crystals of CsI was measured using two techniques for introducing Xe: a homogeneous doping method in which 133Xe was introduced through the decay of homogeneously distributed 133I, and a recoil doping technique in which 133Xe was recoiled into the specimen from an external fissionable source. The results for both techniques were consistent with a classical diffusion model and with each other. The diffusion coefficient was given by: where D0= 0.57 ± 2.30 cm2/sec, and Q= 1.01 ± 0.04 ev. The results show that classical gas diffusion applies in simple systems under ideal conditions, in contrast to the complex behavior frequently observed in fission gas diffusion studies with nuclear reactor fuels. The results also show that the recoil doping method may be a valid technique for the study of rare gas diffusion in nonfissionable solids, and that diffusion does not appear to be enhanced along the fission fragment track.

The release of some non-gaseous fission products from CaF 2, UO 2 and ThO 2

The release of certain non-gaseous fission products (Br, Rb, Cs from ion-bombarded UO 2 and ThO 2 sinters; I, Te, Ba/La from fission-recoil labelled CaF 2 single crystals) from materials with the fluorite structure was studied. The concentration of Br, Rb, and Cs was varied by using two ion doses. In most experiments, several mass transport processes contributed to the release. Release compatible with volume diffusion was found for Rb and Cs in ThO 2 at the lower bombardment dose of 3 × 10 13 ions/cm 2; release occurred at temperatures similar to those for fission gas diffusion and yielded activation enthalpies of about 100 ± 7 kcal/mole, similar to those for fission gas diffusion or uranium self-diffusion. All other releases were complex. In contrast to gas release work, no trapping was found at the high bombardment dose of 1.5 to 2 × 10 16 ions/cm 2: Release of bromine was not affected and release of Rb and Cs occurred at lower temperatures than the release at lower dose. If most of the Br or Rb was near the surface of ThO 2 sinters, an enhanced release at low temperatures was observed. Release of Br from ThO 2 was faster when the samples were annealed in hydrogen than when annealed in air. All this indicates that various factors can influence the release of these non-gaseous fission products including surface reactions (e.g. vaporization), the location of the diffusing ion with respect to the surface, the concentration of the diffusing species and the presence of radiation damage.

The emission of long-lived gaseous fission products from a small hole in the cladding of a reactor fuel element

A general expression is derived to show the effect of fuel element and hole dimensions on the diffusion of long-lived fission gases from a small hole in a reactor fuel-element can. This expression is combined with a simplified source-term to yield the corresponding reactor coolant activity levels. Results are given for the particular cases of 5·3 day 133Xe, 9·2 hr 135Xe, 4·4 hr 85 m Kr and 2·8 hr 88Kr diffusing from a hole in the canning of a Calder-type fuel element. The effects of variations in hole radius and in hole length are presented graphically. It is shown that the ratio of the activities 133Xe: 135Xe: 85 m Kr: 88Kr increases from 2:1:04:1 for bare uranium to 78000:460:06:1 for fission products diffusing through a hole of small radius. Other factors effecting fission-gas activity levels in the coolant are also considered.

The effect of surface evaporation on diffusion measured by isotopic exchange reactions

The influence of evaporation on measurements of diffusion by the heterogeneous isotopic exchange technique has been examined. A standard solution for diffusion involving moving boundaries has been adapted and used to analyse our results. Our measurements on bromine diffusion in potassium bromide show that evaporation of the crystal influences the diffusion measurement at surprisingly low temperatures. This conclusion also seems to apply to many of the reported isotopic exchange measurements and to measurements of fission gas diffusion made by the gas release method. Based on this study a criterion is suggested to decide when the solution with evaporation should be applied. It is further shown that if there is appreciable evaporation it is not in general correct to use the method of measuring diffusion coefficients on one specimen at successive temperatures. For this procedure to be used the velocity of evaporation and the diffusion coefficient must have the same temperature dependence.