Effective Diffusion Energy Barriers with the Boltzmann Distribution Assumption

We derived revised effective diffusion energy barriers following the Boltzmann distribution assumption for impurity atoms in a bulk material under the impact of various kinds of point defects to reveal the insights of migration mechanisms. The effective diffusion energy barriers of copper impurities in bulk zirconium were calculated through the first principle method under the presented hypothesis. Our results (ΔE|| =1.27 eV, ΔE⊥=1.31 eV) agreed well with the experimental results (ΔE|| =1.54 eV, ΔE⊥=1.60 eV), which validated bulk diffusion as the major mechanism for copper diffusion in zirconium. The effective diffusion energy barriers could be used for estimating whether the defects will accelerate the diffusion or slow them down by acting as traps of the impurity atoms. On the other hand, the first principle results of the impurity diffusion via defects could be further used as inputs of larger scale computational simulations, such as MC (Monte Carlo) or Phase Field calculations.