Ab initio modeling of interactions of P, H, S, S with grain boundaries in $\alpha$-iron

The results of modeling from the first principles of interaction of non-metallic impurities of interstitial (H, C) and substitutional (P, S) with grain boundaries in $\alpha$-iron are presented. The modeling has been conducted within the framework of the density functional theory (DFT) by the full-potential linearized augmented plane waves (FP LAPW) method with consideration to the generalized gradient approximation (GGA'96) in the WIEN2k software package. Three grain boundaries of the slope $\Sigma3 (111)$, $\Sigma5 (210)$ and $\Sigma5 (310)$ are studied. The supercells of the tilt grain boundaries using the coincidence site lattice model is constructed. The values of the energy characteristics of various grain boundaries with impurities are influenced by a number of factors, namely, the volume of the Voronoi polyhedron per impurity, magnetic moments, and the symmetry of the surrounding matrix. The results show that symmetric grain boundaries $\Sigma3 (111)$ and $\Sigma5 (310)$ are embrittled by phosphorus, hydrogen, and sulfur, while carbon strengthens interatomic bonds at the grain boundary, which coincides with the data available in the work. In the case of an asymmetric grain boundary $\Sigma5 (210)$, phosphorus and hydrogen weaken bonds at the grain boundary, while sulfur strengthens them. This is primarily explained by the geometry of the surrounding matrix. The magnetic moments at the impurity atoms are very small and, in most cases, are antiparallel to the magnetic moments at the neighboring Fe atoms.