Electronic origin of grain boundary segregation of Al, Si, P, and S in bcc-Fe: combined analysis of ab initio local energy and crystal orbital Hamilton population

Abstract

In steel, P and S cause serious grain boundary (GB) embrittlement, which is associated with high segregation energies. To investigate the origins of such high segregation energies of P and S, we applied the combination of ab initio local energy analysis and crystal orbital Hamiltonian population (COHP) analysis for the GB segregation of Al, Si, P, and S in bcc-Fe, which can provide local energetic and bonding views of segregation behavior of each solute, associated with the replacement between solute–Fe and Fe–Fe bonding at GB and bulk sites. The local energy analysis revealed that GB segregation of such solutes is mainly caused by the difference between local energy changes of Fe atoms adjacent to a solute atom in the GB and bulk sites, and that the local energy change of each Fe atom depends on the solute–Fe interatomic distance with a unique functional form for each solute species. The COHP analysis showed that such distance dependency of the Fe-atom local energy change is caused by that of solute–Fe bonding interactions, relative to the Fe–Fe ones, governed by the valence atomic-orbital characters of each solute species. P and S have smaller extents of atomic orbitals and larger numbers of valence electrons; thus, they greatly lower the local energies of Fe atoms at interatomic distances shorter than the bulk first-neighbor one, and they greatly increase those of Fe atoms at longer interatomic distances around the bulk second-neighbor one. Thus, high segregation energies of P and S occur at GB sites with short first-neighbor distances and reduced coordination numbers within the bulk second-neighbor distance. The GB embrittlement by P and S was also discussed by this local-bonding viewpoint. The combination of local energy and COHP analyses can provide novel insights into the behavior of solute elements in various materials.