Kinetic Modeling of Grain Boundary Diffusion: The Influence of Grain Size and Surface Processes

Based on rate equations, the kinetics of atom adsorption, desorption, and diffusion in polycrystalline materials is analyzed in order to understand the influence of grain boundaries and grain size. The boundary conditions of the proposed model correspond with the real situation in the electrolytes of solid oxide hydrogen fuel cells (SOFC). The role of the ratio of grain boundary and grain diffusion coefficients in perpendicular and parallel (to the surface) concentration profiles is investigated. In order to show the influence of absolute values of grain and grain boundary diffusion coefficients, we select four different cases in which one of the diffusion coefficients is kept constant while the others vary. The influence of grain size on diffusion processes is investigated using different geometrical models. The impact of kinetic processes taking place on the surface is analyzed by comparing results obtained assuming the first layer as a constant source and then involving in the model the processes of adsorption and desorption. It is shown that surface processes have a significant influence on the depth distribution of diffusing atoms and cannot be ignored. The analytical function of overall concentration dependence on grain and grain boundary volume ratio (V_g/V_gb) is found. The solution suggests that the concentration increases as a complementary error function while V_g/V_gb decreases.