Numerical study of grain boundary diffusion in nanocrystalline materials

Diffusion in nanocrystalline materials is becoming an increasingly important topic. The analysis of diffusion profiles obtained in nanocrystalline materials with enhanced grain boundary diffusion, however, is not straightforward since assumptions made in the deviation of the conventional models are often not fulfilled. In this contribution numerical diffusion studies are performed in order to investigate effects caused by the high density of interfaces in nanocrystalline material. A continuum model based on the 2D 2-nd Pick's law was solved by means of the finite element method. This allows us to analyze diffusion profiles for different geometrical situations such as a single boundary, square grains with the grain size of 80 nm and 25 nm and geometries comprising differently oriented boundaries of the average length of 30 nm. The analysis was carried out for different diffusion lengths corresponding to Harrison type A and type B kinetic regimes. For the isolated boundary a very good agreement was achieved in comparison with the classical Whipple's solution. For nanocrystalline material, however, considerable errors can occur when analyzing the averaged diffusion profiles in the conventional Harrison type A and B kinetics.