One-dimensional modeling of bulk cationic interdiffusion in mixed oxides (U,Pu)O2 and analysis of homogenization within a microstructure using a finite difference method

This paper deals with the cationic interdiffusion phenomena, which take place during the solid state sintering of nuclear fuel mixed oxides. The latter promote the cationic homogenization required in order to avoid high burn-up areas during irradiation. It is necessary to understand this phenomenon so as to obtain homogeneous oxides at the end of the manufacturing process. Bulk interdiffusion is studied as it is crucial in the sintering of a multicomponent material. As such, Ficks laws for multicomponent systems are used and the effect of cross-terms of the diffusion matrix is highlighted. The concentration profiles of uranium and plutonium are plotted versus time in order to analyze and understand the evolution of each elemental concentration within the grains of the material. Elemental concentrations of U and Pu are computed under the assumption of a fast displacement of O in thermodynamic equilibrium with the local cationic composition of the sample. Deviation from stoichiometry is calculated on the basis of a Calphad-type thermochemical model of (U, Pu)O$_2±x$ solid solution. The results showed that each diffusing element has reached the mean value of the samples at the end of the simulation, which corresponds to the end of the sintering plateau. We observed a good agreement between the experimentally obtained concentration profiles involving pellets corrected for intergranular diffusion, and those obtained in this study. Speciation into ionic species is carried out at the end of the simulations showing the electroneutrality of our material. As grain size is an important parameter influencing the homogenization during sintering, a quantitative analysis of the homogenization phenomenon is also carried out varying this parameter, with a homogeneity criterion for the distribution of U or Pu. The results showed that the time required to reach a significant homogenization is longer as some of the crystallites are larger.