Molecular dynamics study on effects of grain boundary on hydrogen behavior in bcc-Fe

Abstract

Tritium is one of the main sources for nuclear fusion reactor. However, when tritium penetrates into the structural material and is accumulated, the material becomes brittle. This phenomenon is called hydrogen embrittlement. In this research, we focus on bcc-Fe, because it is a base material of reduced activation ferritic/martensitic (RAFM) steel. In a perfect crystal of bcc-Fe, hydrogen cannot easily dissolve in the material because H atom is more unstable in a perfect bcc-Fe than in a H molecule. However, when defects are involved, H atom becomes stable and trapped near the defects. Regarding diffusivity of H atoms, defects make the energy barrier of diffusion for H atoms increase. Thus, once H atoms are trapped near defects, it is hard to diffuse out. Among several defects, grain boundary (GB) has a significant impact on hydrogen behavior, but its effect has not been clearly understood because of its complexity. Therefore, in this study, we investigate the GB effects on the solubility and diffusivity of hydrogen in bcc-Fe via a molecular dynamics (MD) simulation for the symmetric tilt Σ19b, <111> 46.8˚, {5 -3 -2} GB.

It is found that H atoms are trapped around the GB and the binding energy of hydrogen at GB is weakly dependent on the hydrogen concentration at the GB. For diffusivity of hydrogen at the GB, there are fast or slow diffusion paths and it is related to the densely packed directions or open space direction at GB. This means that the GB makes diffusion anisotropic due to its atomic configuration, and the GB not only acts as a trap but also provides a fast diffusion path along the GB. In the direction where the GB acts as a trap, the effective diffusion coefficient of hydrogen increases as hydrogen concentration increases. This can be explained by trapping effect by the GB. On the other hand, in the direction of open space where the GB provides a diffusion path, the increase in hydrogen concentration leads to the decrease in the effective diffusion coefficient. This dependence can be explained by blocking effect on the GB. Based on these results, a thermodynamic model for the GB effects on hydrogen behavior can be modelled.

However, for establishing a thermodynamic model on hydrogen diffusivity, more accurate diffusion coefficient is needed to reduce the error of the effective diffusion coefficient predicted by the thermodynamic model. Therefore, we analyzed the cause of an error in diffusion coefficient obtained by Einstein diffusion equation. The diffusion of hydrogen and carbon impurities in a perfect bcc-Fe was investigated as examples. It is known that, even though increasing the sampling number to reduce the statistical error in MD, we cannot obtain fully linear mean square displacement as a function of time (MSD(t)) at the beginning. In this study, it is found that vibration effect and negative correlated jump effect make the non-linearity in MSD(t). The fraction of negative correlated jump which makes the non-linearity in MSD(t) depends on temperature. We suggest an effective method to reduce those effects and make the MSD(t) graph linear, which would make it possible to calculate the diffusion coefficient more accurately.