M.O. Tucker

A new fission-gas release model

Abstract The release of unstable fission products from irradiated UO 2 fuel is shown to be a sensitive function of many inter-related factors. The poly-granular-aggregate model for unstable gas release assumes that the release of fission products from the interior regions of UO 2 fuel occurs, firstly, by direct diffusion to grain boundaries and, secondly, by gaseous diffusive transfer through an intermittently open grain-edge tunnel network. During the early stages of irradiation a saturated network of grain-face lenticular porosity is established by the precipitation of stable fission-gas atoms. Lenticular bubbles which nucleate near to the grain edges—junctions of the three grains—will move to a lower free energy configuration on those edges and take up a triangulated cigar shape. Continued stable gas collection inflates these bubbles to a point of interlinkage beyond which point the fission gases are vented and tunnel collapse, by means of surface diffusion away from regions of high curvature, into a string of cigar-shaped bubbled occurs. This process is repeated many times until the resulting grain-edge tunnel “pinches off” in the centre of the tunnel resulting in bubbles at the grain corners—the junction of four grains. The re-inflation of these grain-corner bubbles—tetrahedra with spherical faces—results in a permanently interlinked network of tunnels which are unconditionally stable and can resist further collapse. Using simple arguments, we demonstrate that the interlinkage times for bubble strings and the pinch-off times for tunnels effectively delay the passage of fission products from the fuel interior to the exterior and that this mechanism may be viewed as an effective diffusion process. The arrival rate of atoms into the tunnel network may be by direct diffusion or indirectly from the grain-face lenticular porosity. In the latter case some radioactive decay may have occurred, depending on the length of time spent in that porosity. The nett arrival rate into the grain-edge or corner porosity—both direct and indirect—is treated as an effective generation rate. Because the swelling rate of fuel depends on this growth and collapse of porosity it is clear that the swelling rate and hence ultimately the release rate of unstable fission products depends critically on the stable fission-gas release. In turn, the release of stable fission gases depends on the irradiation-induced resolution-controlled diffusion from the UO 2 grains. A model incorporating the Speight-Turnbull stable gas release model, the grain edge-corner swelling model and the Tucker-White percolation diffusion model from a polygranual aggregate is shown to account well for the experimental findings of Turnbull and Friskney on release rates of I 131 , I 133 , Xe 133 , Xe 138 , Kr 88 from 1.46% enriched stoichiometric UO 2 . It is shown that uncertainties in ratings of ± 5% and in fuel temperature of ± 25°C are unlikely to seriously limit the accuracy of the predictions for unstable release rates, and it is proposed that the model be used to reinterpret the Turnbull-Friskney experiments to yield “second generation” estimates of diffusion coefficients.

The effect of irradiation-induced re-solution on fission gas release

Abstract A finite-difference technique is used to compute exact solutions to the diffusion equation describing fission gas release from UO2 nuclear fuel during steady reactor operation. The resolution of gas atoms from grain-boundary bubbles is treated in two alternative ways, and the results of the parallel calculations compared. Predictions of gas release using simple analytical models are compared with the numerical results and are found in general to describe the process very accurately.

A simple description of interconnected grain edge porosity

A simple model describing the structure of grain edge porosity in irradiated UO 2 is developed which is in good agreement with more accurate calculations. Because it involves far less computation, the model is very useful in treating fuel swelling during fission gas release.

A fracture criterion for nuclear graphite

Abstract Measurements of tensile and flexural strength of a nuclear graphite using small bar specimens are reported. A theoretical model of failure is described in which critical defects are assumed to be associated with cleaved large coke particles. It is further assumed that these subcritical cracks can only extend by the cleavage of small particles which surround them. The size of the critical flaws is defined on the basis of linear elastic fracture mechanics. The model predicts the observed variation in flexural strength in three- and four-point bending as the knife edge spacings are varied. It slightly overestimates the observed ratio of tensile-to-bend strength, and this is thought to be due to some of the simplifying assumptions made in the models formulation. The potential of the model for use in engineering applications is discussed.

Relative growth rates of fission-gas bubbles on grain faces

Abstract A diffusional model of a population of grain-face fission-gas bubbles in UO2 under high-temperature irradiation has been used to investigate the effect of bubble-to-bubble size variations on the development of the population. The results are used to interpret the observed characteristic grain face porosity and to justify the use of uniformly sized bubble distributions in the modelling of gas release and swelling in UO2 fuel.

Partitioning behaviour of oxygen in steam-oxidized Zircaloy

Abstract A model has been developed which describes the high temperature partitioning behaviour of oxygen in Zircaloy. The growth kinetics of the oxide/α and α/β layers are derived from a consideration of the material continuity requirements at the respective phase boundaries. It is shown that the rate of advance of the α/β interface in specimens of finite thickness will deviate from parabolic behaviour, a departure attributable to the progressive approach of the total oxygen content in the β phase towards its saturation value. This conclusion is significant since determination of the oxygen profile in the β phase is dependent on reliable evaluation of the α/β interface advance kinetics. The validity of the model is tested by comparing the observed oxide/α and α/β interface growth rates with those derived using basic oxygen diffusion and solubility data in conjunction with total oxygen uptake kinetics.

The transfer of fission gas between grain faces and edges in UO2

Abstract A simple diffusion model is used to investigate the preferential motion of grain-boundary bubbles in UO 2 during high-temperature irradiation, caused by bubble-to-bubble variations in fission-gas pressure. The results are used to explain the observed development of grain-boundary porosity as irradiation proceeds, and a simple but realistic model of this process is suggested.

The release of unstable fission products from UO2 during irradiation

A theoretical model describing the release of unstable gaseous and volatile fission products from irradiated UO2 fuel is developed. The extent of interconnectivity of grain-edge tunnel pores is determined in order to assess the likelihood of an unstable atom reaching the exterior of the fuel before decaying. The model behaviour is compatible with experimental observation, and the effects of grain size, restraint pressure and temperature within the fuel are discussed.

The growth of grain edge porosity in irradiated UO2

A steady-state diffusion model of the growth of grain boundary porosity during fission gas release from UO2 fuel is developed. It is used to demonstrate that the observed growth of grain edge porosity, which would normally be expected to sinter, can occur through its interaction with the developing population of lenticular bubbles on the grain faces.

Oxide/α and α/β phase interface advance kinetics in steam oxidised zircaloy-2

Abstract Weight gain kinetics and phase interface advance measurements on specimens of zircaloy-2 oxidised at temperatures between 1030° and 1400°C are presented. The observed positions of the oxide/alpha and alpha/beta interfaces are compared with the predictions of a diffusion model of the process. Using previously recommended oxygen diffusion coefficients, agreement between theory and experiment is obtained at temperatures above 1100°C when oxygen saturation of the beta phase promotes isothermal growth of alpha phase incursions during oxidation. At temperatures below 1100°C, incursion growth occurs only on quenching. Agreement between prediction and observation is then obtained by excluding the alpha phase component which precipitates onto the isothermally formed alpha/beta boundary during quenching from the oxidation temperature.