# Insights into Hydrogen Diffusion Characteristics and Interactions with Vacancy in Fe Crystal Lattices from First-Principles Calculations

## TL;DR

This study uses first-principles calculations to explore how hydrogen diffuses in iron crystal lattices and how vacancies affect this process.

## Contribution

The paper provides new insights into hydrogen diffusion and interactions with vacancies in different iron crystal structures using first-principles calculations.

## Key findings

- Hydrogen atoms prefer different interstitial sites in α-Fe, γ-Fe, and ε-Fe crystals, affecting their diffusion behavior.
- Vacancy defects in iron crystals increase hydrogen atom attraction, promoting bubble nucleation and altering diffusion pathways.
- Hydrogen diffusion is most efficient in α-Fe, followed by γ-Fe and ε-Fe, with vacancies creating higher energy barriers for diffusion.

## Abstract

Hydrogen embrittlement is defined as the phenomenon wherein materials undergo sudden degradation in mechanical properties due to the ingress of hydrogen atoms, and its occurrence is closely linked to hydrogen diffusion behavior. Here, first-principles calculations are employed to systematically investigate the hydrogen diffusion characteristics of both perfect and vacancy-containing α-Fe, γ-Fe, and ε-Fe crystal structures. The dissolution energies of hydrogen atoms in perfect α-Fe, γ-Fe, and ε-Fe crystals were calculated at different interstitial sites and transition states along various pathways. Hydrogen atoms preferentially occupy tetrahedral interstitial sites in α-Fe crystals, with diffusion occurring between two nearest-neighbor tetrahedral interstitial sites. In γ-Fe crystals, hydrogen atoms favor octahedral interstitial sites, diffusing along paths from octahedral sites to tetrahedral sites and then to other octahedral sites. In ε-Fe crystals, hydrogen atoms preferentially occupy octahedral interstitial sites and diffuse along pathways between nearest octahedral interstitial sites. The hydrogen diffusion coefficients calculated based on the Arrhenius equation follow the order α-Fe > γ-Fe > ε-Fe, indicating that hydrogen atoms diffuse most readily in α-Fe crystals. Notably, examination of the relationship between the interatomic distance and interaction energy in α-Fe reveals that hydrogen atoms have difficulty aggregating and forming hydrogen molecules within defect-free α-Fe crystals. However, introducing vacancy defects increases the mutual attraction between hydrogen atoms, thereby facilitating hydrogen bubble nucleation. Furthermore, the introduction of vacancy defects in α-Fe, γ-Fe, and ε-Fe alters the preferential occupancy sites and diffusion pathways of hydrogen because of vacancy trapping effects. Compared with diffusion in perfect crystals, hydrogen atoms must overcome substantially higher energy barriers to escape vacancy trapping and diffuse into defect-free lattice regions.