The dependence of in-reactor UO2 densification on temperature and microstructure

The in-reactor changes in size of sintered UO₂ are analyzed by superposing matrix swelling and pore shrinkage. At first pore shrinkage dominates and results in densification, an effect which has been known for a few years. With regard to shrinkage mechanisms one should distinguish between very fine pores and coarser pores, the latter being responsible for the majority of total porosity in well sintered UO₂. For this coarser porosity a two-step mechanism is postulated: first, the generation of vacancies by the fission fragments traversing the pores, second, the migration of these vacancies to effective sinks (grain boundaries) producing densification. Based on this assumption the dependence of densification on fission rate, temperature, pore size distribution and grain size is evaluated. There is a transient temperature above which the generation of vacancies is rate controlling and below which the vacancy migration becomes the rate controlling mechanism. At temperatures much lower than the transient temperature no densification should be observed.     

In-pile densification of intergranular porosity in oxide fuels

A model has been developed to predict intergranular densification. The model treats densification due to both thermal diffusion of point defects and pore destruction due to fission fragment passage through the pores. The model has been programmed and that program has been combined with the previously reported swelling and gas release program. Comparisons were made between the model predictions and swelling data of Freshley et al. and Banks on UO₂ and data on ThO₂ obtained by Waldman and Spahr. Comparisons were also made between the model and pore closure data on UO₂ obtained by Ross.     

A mechanism for the sintered density decrease of UO2–Gd2O3 pellets under an oxidizing atmosphere

A mixture of UO₂ and Gd₂O₃ powders was pressed into compacts and sintered under various atmospheres ranging from reducing to oxidizing gases. The sintered density of UO₂–10 wt% Gd₂O₃ pellets decreases with increasing oxygen potential of the sintering atmosphere. Dilatometry and X-ray diffraction studies indicate that the delay of densification takes place between 1300°C and 1500°C, along with the formation of (U,Gd) O₂. A very large solubility of Gd₂O₃ in UO₂ relative to the reverse solubility might cause Gd ions to diffuse into UO₂ so directionally that new pores are produced at the places of Gd₂O₃ particles. The new pores may be difficult to shrink and thus lead to the density decrease under an oxidizing atmosphere but not under a reducing atmosphere, because a driving force for the shrinkage of new pores may be smaller under an oxidizing atmosphere than under a reducing atmosphere.     

The effect of titania on grain growth and densification of sintered UO2

The effect of additions of up to 0.33 wt % titania on the grain growth and densification of UO₂ has been studied. It is shown that the solubility of titania in UO₂ lies between 0.07 and 0.13 wt % at 1650°C in hydrogen and that the grain growth rate is proportional to the concentration of added titania up to the solubility limit, remaining constant thereafter. Titania in excess of the solubility limit forms a liquid eutectic with UO₂. This eutectic, which has a solidification temperature in the 1600–1620° C range, inhibits grain growth at temperatures below 1600°C but can enhance it at higher temperatures where the eutectic is liquid. TiO₂ is not as effective as the lower oxides in promoting grain growth.     

Some observations of density and porosity changes in UO2 fuel irradiated in water-cooled reactors

A technique has been developed for the hot-cell measurement of the apparent density of irradiated UO₂ fuel after extraction from a fuel pin. A single determination is accurate to $\text{± 3 \%}$ at the 95 % confidence limit. The method has been applied to fuel irradiated in thermal neutron fluxes in the Winfrith SGHWR and in the Halden BWR. Material has been examined at ratings of 1–51 W/g and in the burn-up range $\text{0.09–5.79 × 10}{}^{20}\text{fissions/cm}$. It is concluded that pellets with peak temperatures below 1100°C densify during irradiation, but at higher temperatures the pellets begin to swell. Fuel micrography has shown that the densification is principally due to the loss of micropores with a temperature dependency given by an activation energy of 5200 cal/mol. Above 1000°C the densification is masked by the formation and growth of intergranular fission gas bubbles, whose volume may exceed that of the manufactured pores which have sintered. In solid fuel pellets central swelling did not balance densification in the cooler rim until the fuel centre temperature exceeded 1700°C.     

Dimensional Changes in Irradiated (Th,U)O2

Effects of irradiation on the dimension and microstructure in (Th,U)O₂ pellets were examined by measurements of lattice parameter and bulk density changes, and observations of pore structures. The concentrations of fission-induced defects and the damage volume were estimated by a simple model. Both macroscopic and microscopic dimensional changes were found to increase initially with fission dose and then fall off. The difference between macroscopic and microscopic ingrowths increased with dose, suggesting that fission-induced interstitials would cluster or go to sinks and the concentration of vacancies would be in excess of that of interstititials. The damage volume for vacancies was estimated to be about 1x10^?22m³·fiss.^?1, and almost agreed with that for fission Xe release. Observations of the pore structure indicated that the volume fraction of pores smaller than 2–3 μm decreases with irradiation and the distribution of pore size shifts toward the larger side.     

The movement of lenticular pores in UO2 nuclear fuel elements

A simple theory is developed which describes the motion of lenticular pores in a temperature gradient and takes into account evaporation and condensation rates in the pore surfaces. This mechanism, rather than diffusion within the pore, is likely to govern the pore motion if the pores are filled with helium, and it also gives the experimentally favoured $\text{T}{}^{\mathrm{<mtext>?</mtext><mtext>5</mtext><mtext>2</mtext>}}$ temperature-dependent factor in the pore velocity. Experimental velocities for UO₂ are reproduced quite well by the theory provided that the O/U ratios were slightly greater than 2 in the hot pore region. At temperatures around 2000 K the latter ratio is critical in giving the equilibrium vapour pressure in the pore and hence the pore velocity.     

Controlled porosity reactor fuel

Thermally stable UO₂ reactor fuel pellets have been obtained using volatile additive pore formers and high activity powders. Various additives, including uranyl and ammonium salts, have been studied, nearly all of which appear similar in effect. Due to the inherently small percentage of fine pores (<2 μm dia.) present and large grain size of pellets made by this process, it is expected that the fuel will exhibit excellent irradiation stability. Density can be controlled reproducibly by varying the amount of pore former such that fuels suitable for either LWR's or fast reactors can be prepared. The size fraction of additive does not affect the thermal response of the pellet. The size distribution of the pores can be controlled within fine limits.     

Multiphysics coupled modeling of light water reactor fuel performance

A fuel performance code for light water reactors called CityU Advanced Multiphysics Nuclear Fuels Performance with User-defined Simulations (CAMPUS) was developed. The CAMPUS code considers heat generation and conduction, oxygen diffusion, thermal expansion, elastic strain, densification, fission product swelling, grain growth, fission gas production and release, gap heat transfer, mechanical contact, gap/plenum pressure with plenum volume, fuel thermal and irradiation creep, cladding thermal and irradiation creep and oxidation. All the equations are implemented into the COMSOL Multiphysics finite-element platform with a 2D axisymmetric geometry of a fuel pellet with cladding. Comparisons of critical fuel performance parameters for UO₂ fuel using CAMPUS are similar to those obtained from BISON, ABAQUS and FRAPCON. Additional comparisons of beryllium doped fuel (UO₂-10%volBeO) with silicon carbide, instead of Zircaloy as cladding, also indicate good agreement. The capabilities of the CAMPUS code were further demonstrated by simulating the performance of oxide (UO₂), composite (UO₂-10%volBeO), silicide (U₃Si₂) and mixed oxide ((Th_0.9,U_0.1)O₂) fuel types under normal operation conditions. Compared to UO₂, it was found that the UO₂-10%volBeO fuel experiences lower temperatures and fission gas release while producing similar cladding strain. The U₃Si₂ fuel has the earliest gap closure and induces the highest cladding hoop stress. Finally, the (Th_0.9,U_0.1)O₂ fuel is predicted to produce the lowest fission gas release and a lower fuel centerline temperature when compared with the UO₂ fuel. These tests demonstrate that CAMPUS (using the COMSOL platform) is a practical tool for modeling LWR fuel performance.     

Enhanced thermal conductivity oxide nuclear fuels by co-sintering with BeO: II. Fuel performance and neutronics

The fuel rod performance and neutronics of enhanced thermal conductivity oxide (ECO) nuclear fuel with BeO have been compared to those of standard UO₂ fuel. The standards of comparison were that the ECO fuel should have the same infinite neutron-multiplication factor k_inf at end of life and provide the same energy extraction per fuel assembly over its lifetime. The BeO displaces some uranium, so equivalence with standard UO₂ fuel was obtained by increasing the burnup and slightly increasing the enrichment. The COPERNIC fuel rod performance code was adapted to account for the effect of BeO on thermal properties. The materials considered were standard UO₂, UO₂ with 4.0 vol.% BeO, and UO₂ with 9.6 vol.% BeO. The smaller amount of BeO was assumed to provide increases in thermal conductivity of 0, 5, or 10%, whereas the larger amount was assumed to provide an increase of 50%. A significant improvement in performance was seen, as evidenced by reduced temperatures, internal rod pressures, and fission gas release, even with modest (5-10%) increases in thermal conductivity. The benefits increased monotonically with increasing thermal conductivity. Improvements in LOCA initialization performance were also seen. A neutronic calculation considered a transition from standard UO₂ fuel to ECO fuel. The calculation indicated that only a small increase in enrichment is required to maintain the k_inf at end of life. The smallness of the change was attributed to the neutron-multiplication reaction of Be with fast neutrons and the moderating effect of BeO. Adoption of ECO fuel was predicted to provide a net reduction in uranium cost. Requirements for industrial hygiene were found to be comparable to those for processing of UO₂.     

Thermal Conductivity of UO2-BeO Pellet

Beryllium oxide(BeO)-doped (0.3, 0.6, 0.9, 1.2 and 13.6 wt%) UO₂ pellets were fabricated to evaluate the effects of BeO precipitate shape on thermal conductivity. Precipitate distributions were of two types: BeO precipitated almost continuously along a grain boundary (designated BeO continuous type) and spherical BeO randomly dispersed within the matrix (designated BeO dispersed type). Thermal diffusivity was measured by a laser flash method and thermal conductivity was evaluated. The thermal conductivity increased with the BeO content. The thermal conductivity of the BeO continuous type was higher than that of the BeO dispersed type at lower temperatures, while their difference became smaller at higher temperatures. The thermal conductivities of UO₂-1.2 wt% BeO at 1,100K were higher than that of UO₂ by about 25 % for the BeO continuous type and by about 10 % for the BeO dispersed type. The thermal conductivities of both types were expressed by a semi-empirical equation as a function of volume fraction and shape of the BeO precipitates.     

Computer simulations of non-congruent melting of hyperstoichiometric uranium dioxide

Detailed models of UO_2+x at very high temperatures incorporating the effects of non-congruent melting have been developed to support the design and analysis of experimental work related to nuclear safety. Models based on both the Stefan formulation and phase field approach are implemented using recently published material properties. Simulations compare well with laser flash experiments performed on UO_2+x. This work has application in modelling centreline melting of defective fuel which may occur due to the reduced thermal conductivity and lower incipient melting temperature associated with fuel oxidation.     

Thermal Diffusivities and Thermal Conductivities of UO2-Gd2O3

Thermal diffusivities of samples of UO₂ and UO₂ doped with 3, 5, 7 and 10 w/0 Gd₂O₃ were measured over the temperature range of 298~2,023 K by a laser flash method. Then thermal conductivities were calculated from them. The thermal conductivity decreased with increasing Gd₂O₃ content at low temperatures, while it was independent of Gd₂O₃ content at high temperatures. An expression of the thermal conductivity was proposed for (U, Gd)O₂ solid solution as a function of Gd₂O₃ content and temperature by applying Klemens' model.     

Irradiation-induced creep of mechanically blended porous UO2-PuO2 fuel

With regard to the behaviour of fast breeder reactor fuel, irradiation creep of mechanically blended, porous U_natO₂-15% PuO₂ was investigated. Some results for UO₂ are also quoted to clarify the dependence of creep rate on stress and temperature. The sintered density of the UO₂-PuO₂ samples amounted to 86% TD and 93,5% TD, their irradiation temperatures were between 300 and 1000°C, the stress in the samples at 15 and 40 MN/m², the fission rates between 2.5 and $\text{5 × 10}{}^{\mathrm{?9}}$ f/(U + Pu)-atom · s, and the maximum burnup at about 1%. The creep rates of UO₂-PuO₂ are much higher than previously measured on UO₂ of high density, but there was a good correspondence of the stress and temperature dependence. The difference of the creep rates cannot be explained only by the porosity of the UO₂-PuO₂ samples. Therefore the PuO₂ portion of the fuel, whose distribution is heavily inhomogeneous, is treated as additional “effective” porosity. By this means a suitable interpretation is obtained for the results below about 650°C. At higher temperatures, UO₂-PuO₂ of 86% TD showed a rapid initial densification up to about 93% TD, apparently together with a simultaneous homogenization of the fission-density distribution. The results measured could be interpreted without considering an influence of the Pu-content as such.     

The kinetics of actinide redistribution by vapor migration in mixed oxide fuels (II). By pores

The migration velocity of a closed lenticular pore in hyperstoichiometric mixed oxide fuel has been calculated, and the U/Pu ratio of the solid near the moving pore has been determined. Pore migration in mixed oxides differs from the analogous process in pure stoichiometric urania in that the composition as well as the temperature of the two faces of the pore are different. It was found that pore migration is not as effective a mechanism of actinide redistribution as vapor transport along cracks. The velocity of the pores in (U_0,8Pu_0,2) O_{2 + x} is $\text{～3}\text{1}\text{2}$ times faster than that in pure UO₂.     

Thermal conductivity of uo2 and u4o9 from 100 to 300 k

The thermal diffusivities of UO₂ and U₄O₉ were measured by the laser flash method at temperatures ranging from 100 to 300 K. The phonon mean free path and the thermal conductivity were calculated from the obtained thermal diffusivity data and the heat capacity. The structure of the u₄o₉ is closely related to the UO₂ structure with an excess oxygen atom per unit cell in U₄O₉. As the excess oxygen atoms increase the anharmonicity of the lattice vibration, the phonon mean free path in U₄O₉ decreases. Therefore, the thermal conductivity of U₄O₉ is much lower than that of UO₂ and increases slightly with increasing temperature due to the rise in heat capacity.     

The ratio of grain boundary energy to surface energy of nuclear ceramics as determined from pore geometries

Several workers have derived high grain-boundary to surface energy ratios from measurement of the geometries of pores located at grain boundaries. The values (of more than unity) are two to three times greater than those calculated from the geometries of interactions of free surfaces with grain boundaries, and, in the case of irradiated UO₂, have been attributed to fission-product segregation effects. This work has confirmed previous observations of pore geometries and led to similar data for unirradiated and irradiated nuclear ceramics. It has been found that irradiation has no clear effect on pore geometries and hence it is concluded that fission-product segregation is not a significant factor. The work suggests that the theories used to derive energy ratios from pore geometries need modification.