A Monte Carlo method that was based upon random walk theory was used to simulate diffusivity by assuming that interstitial impurities jumped to neighboring sites. The jump probability along a grain boundary was greater than that in the lattice of a grain interior. The crossing point of grain boundaries had a smaller jump probability to neighboring sites on the grain boundary than into the lattice. The simulated results were found to support the so-called grain boundary cross effect upon the grain size dependence of H diffusion in polycrystalline Al. The diffusivity exhibited a peak at a critical grain size. The peak reflected 2 conflicting effects of grain boundaries. One was the enhancement of diffusion along grain boundaries. The other was the suppression of diffusion by trapping at grain boundary junctions.

M.Ichimura, Y.Sasajima: Japanese Journal of Applied Physics, 1996, 35[1-1A], 186-90