R.J. White

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 resistometric study of ageing in Nimonic alloys. I. PE16

The Nimonic alloy PE16 is a candidate for use in a radiation environment in fast reactors. Williams and Fisher have investigated void-swelling in this alloy and have found it to be dependent upon the γ precipitate present. In order to investigate the dependence of precipitation upon heat-treatment, the variation of the electrical resistivity with time on ageing PE16 at various temperatures between 580°C and 780°C has been measured. To account for the observed variation, a model based on nucleation and growth of γ precipitates has been developed. This model allows for different scattering cross sections, and hence specific resistivities, of particles in small and large clusters. The rate constants for nucleation and growth are found to follow the usual Arrhenius behaviour with activation energies of 1.11 eV and 1.83 eV respectively. Specimens aged at different temperatures for varying times t, were viewed in the electron microscope. The observations have indicated that the precipitate diameter varies as (K2t)12, where K2 is the growth rate constant.

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 effect of stress on the incubation and growth of voids

Abstract The influence of stress on void growth at high temperatures through its effect on the thermal emission of vacancies from internal sources has been included in numerical solutions of swelling for several years. In this paper we formulate this stress effect into an analytical expression which describes both the incubation and subsequent growth of cavities in an irradiated material under stress.

Unstable fission product release from UO2 irradiated at high temperature

Abstract A model of the release of unstable gaseous and volatile fission products from UO2 nuclear fuel during irradiation is developed. By considering the physical processes controlling the release of those atoms produced remote from the outer surface of the fuel an effective diffusion coefficient has been defined for the transport of the radioactive species along the partially connected grain-edge porosity. The magnitude of this coefficient is shown to be sensitively dependent upon the volume of grain-edge porosity and example calculations are discussed.

The role of quenched-in vacancies in the ageing of nimonic alloys

Abstract Diffusion controlled coarsening theory has been applied to the resistance maximum observed during the ageing of two Nimonic alloys (PE16 and 80A). The position of the resistance maximum is shown to be strongly dependent on the rate of loss of the quenched-in vacancy supersaturation. In both alloys the principal vacancy sink is the dislocation network. The kinetics of vacancy loss have been modified to include the effect of solute-vacancy complexes in the diffusive process. Estimates are made of the efficiency of the retention of the vacancies quenched-in at the solution treatment temperature and these are shown to be in good agreement with the observed values of the vacancy supersaturation in these alloys.

The effect of foil surfaces on the loss of point defects from electron irradiated metal foils

Abstract The diffusion equations which describe the point defect distributions in electron irradiated metal foils have been solved by a computer iterative technique.

Enhanced vacancy lifetimes in the Nimonic alloys: PE16 and 80A

Abstract The variation of resistance during isothermal ageing of the two Nimonic alloys PE16 and 80A has been analysed in terms of a simple model based on the nucleation and growth of γ particles, which includes an exponential decay of the excess vacancy population, quenched-in during the pre-ageing heat-treatment of the alloys. Both the PE16 and the 80A results have been successfully described using this model and the values of vacancy lifetime derived have been compared with theoretical estimates, for diffusion to grain boundaries, dislocations and precipitates. We have shown that values of activation energy deduced from the variation of time to the resistance maximum as a function of inverse ageing temperature depend upon the vacancy lifetime. To obtain meaningful values for activation energy, this dependence must be included in the analysis.

Interstitial loop growth in irradiated thin foils

Abstract In order to understand the behaviour of materials in an irradiation environment, a knowledge of the interaction between point defects and dislocations is essential. It has been shown previously that using the rate theory continuum method, the loss of defects to the foil surface being accounted for through a smeared-out foil surface sink strength, measurements of interstitial loop growth rate in irradiated thin foils can yield such information. The present work describes a scheme for loop growth in a thin foil, based on the rate theory continuum model, which accounts directly for defect loss to the foil surface. A set of simultaneous time-dependent equations for defect concentrations and loop growth are solved numerically on a finite number of equally-spaced mesh points in the foil. Account is taken of loop overlap onto neighbouring mesh points and of loop intersection with the foil edge. Loop growth measurements in copper have been analysed with this scheme and values deduced for vacancy migration energy and dislocation bias.