A procedure for the construction of Voronoi polyhedra

Hydrogen embrittlement caused by hydrogen segregation at grain boundaries (GBs) is the most serious issue in the development of high-strength steels, but the mechanisms behind this process are still not well understood. The GB segregation behavior of hydrogen in body-centered cubic (bcc)-Fe polycrystals was comprehensively analyzed based on the interatomic potentials derived from first-principles calculations. Considering that the atomic structure of GBs is almost independent of the grain size, the GBs in polycrystals were modeled as nano-polycrystalline GBs with random orientations. The segregation energies of hydrogen for ∼17 million interstitial sites in this GB model were calculated. From these segregation energies, the effective segregation energy for the polycrystalline GB at thermal equilibrium under various temperature and hydrogen content conditions were determined, and the validity of the calculation method was verified by comparing the results with experimental data. The relationship between the segregation energy of hydrogen at each segregation site and the surrounding local atomic environment was used to identify the major hydrogen segregation sites at the atomic level, and the changes in the crystal structure near the GB that dominated segregation were clarified. The effective segregation energies at the polycrystalline GBs were in the range of −0.48 to −0.42 eV, which are in good agreement with the experimentally reported binding energy of hydrogen at GBs of bcc-Fe polycrystals (−0.52 eV). The major hydrogen segregation sites were octahedral sites with Voronoi volumes larger than 7.0 Å3, and the segregation energy was mainly due to the uniaxially distorted crystal structure in the short-axis direction of octahedral sites. Our findings and the developed calculation method contribute to the understanding of the hydrogen segregation behavior and hydrogen embrittlement mechanism in polycrystalline metallic materials.