Surface and Grain Boundary Interdiffusion During the Sintering of Mixed Oxides Fuels—A Finite Volume Method Simulation

Sintering is a key step of the manufacturing process of mixed oxides fuels (U,Pu)O₂ used in the nuclear reactors. This step is characterized by several physical phenomena including interdiffusion mechanisms, which help to improve cationic homogenization at the end of manufacturing process. This study deals with the numerical study of interdiffusion mechanisms at surfaces and grain boundaries that occur during the sintering of mixed oxides fuels. For this purpose, two 3D grains already into contact at the initial time are constructed and meshed using GMSH software [1]. The physical model relies upon Onsager law [2] according to the framework of the linear thermodynamics of irreversible processes giving the flux corresponding to each mechanism. The flux are written as a function of the chemical potential gradient of the diffusing element, and the Onsager coefficient. The system considered in this framework is the ternary U-Pu-O system. According to Fick's equations for multicomponent diffusion, only two elements should be considered, namely uranium and plutonium, because it is well known that the diffusion of oxygen is faster than that of uranium and plutonium. Thus, the fluxes are written for uranium and plutonium only. The solid solution is assumed to be ideal so that the chemical potential can be written in a simplified way as µ_U = µ_0(U) + RT ln (C_U) and µ_Pu = µ_0(Pu) + RT ln (C_Pu). Due to the additivity of the chemical and mechanical part of the free Gibbs energy of the system, after formulating fluxes for each interdiffusion mechanism, they are added to the stress-dependent flux, already programmed into a model dealing with the sintering of two single-constituent grains. Concerning the surface and grain boundary fluxes divergence calculations, the finite volume method is used for the 2D curved surfaces and the Diffpack [3] library is used for the numerical implementation. It emerges that matter conservation is a challenge when many interdiffusion mechanisms are involved. It also appears that taking into account surface and grain boundary interdiffusion mechanisms in addition to volume interdiffusion accelerates the homogenization phenomenon.<br/>[1] C. Geuzaine et J. F. Remacle, « A three-dimensional final element mesh generator with built-in pre- and post-processing facilities. », <i>International Journal for Numerical Methods in Engineering</i>, oct. 2013.<br/>[2] J. Philibert, <i>Diffusion et transport de matière dans les solides</i>, Les éditions de Physique.<br/>[3] H. P. Langtanten, <i>Computational Partial Differential Equations</i>, tome 2.