Micro- and Macroscopic Numerical Analyses on Effect of Repulsive Exclusion Zones on Interstitial Particle Diffusivity in Bcc Lattice Based on Diffusion Path Network Model

The effects of hydrogen repelling substitutional atoms towards interstitial hydrogen diffusivity is one of the important information for understanding the hydrogen embrittlement phenomena in steel. We present a comparative numerical study on the effect of repulsive exclusion zones on interstitial particle diffusivity in bcc lattice based on the diffusion path network (DPN) model using two computational methods of the macroscopic Fick's law and the microscopic random walk Monte-Carlo (RWMC) approaches. Since the diffusion phenomena using the atomistic DPN model can be analogized with the macroscopic diffusion phenomena in a porous medium, we have attempted to extend the physical picture of such transport to the Fick's law constructed with the compositions weighted by the hopping motion probabilities. In order to identify the specific individuality of diffusing particles such as hydrogens in steel within the model, it is necessary to quantitatively derive the hopping probabilities consisting of vibration frequencies and activation barriers along the diffusion pathway. In this study, we have therefore investigated the rationality and the performance of the proposed model based on the Fick's law by analyzing the "ratio" of the time-independent diffusion coefficients induced by the difference in network topology by comparing both micro- and macroscopic simulations. From some numerical experiments, we have found that the effective diffusivity considering the porosity and the tortuosity in a porous medium can be evaluated with both methods. We have also discussed the advantages and disadvantages of both micro- and macroscopic methods, especially when analyzing the diffusion phenomena of hydrogen atoms in steel.