A practical coarse-grained formula for classical mobility of interstitial helium diffusion in BCC W and Fe

Helium diffusion in metals is the basic requirement of nucleation and growth of bubble, which gives rise to adverse degradation effects on mechanical properties of structural materials in reactors under irradiation. Multi-scale modeling scheme has been developed to study effects of helium on the long-term microstructural evolution. However, the implementation of Arrhenius law based on the quasi-equilibrium reaction process is not appropriate to predict the migration behavior of helium in metals due to low-energy barrier. A coarse-grained formula is required to incorporate the non-equilibrium nature, e.g., the dissipative friction coefficient $\gamma$. In this paper, we derive an analytical expression for $\gamma$ based on a coarse-grained model of Brownian motion upon a periodic potential, in terms of dissipative feature of the thermal excitations in the many-body dynamical system by constructing an adiabatic relaxation process, which is then confirmed by a numerical example of vacancy migration in BCC W. Then the many-body dynamics simulations are performed for helium migration in BCC W and Fe, where the classical mobility are obtained and in good agreement with the data from experiments and other calculations. Finally, we propose a coarse-grained formula for the helium migration in BCC W and Fe, i.e., Eq.(47) in the context, using the calculated parameters from the adiabatic relaxation simulations. This work would help to develop a new multi-scale modeling scheme for effects of helium in metals, as well as the atomistic reactions with low-energy pathways in materials science.