Segregation of P and S to frequently occurring grain boundaries of Cu: single atoms and cooperative effects

Abstract

Materials design and performance prediction relies on detailed knowledge of the distribution of solutes that can affect the materials properties. Here we report a study on the distribution and mechanisms of interaction of S and P atoms at four relevant grain boundaries (GBs) of fcc Cu: Σ3, Σ5, Σ9 and Σ11. Segregation site preference was investigated for single atoms and compared to the case where impurities segregate as pairs. Both the driving force for segregation—local minima—and the interactions between impurities at the GBs—global minima—have been investigated. An analysis of geometric and electronic structure effects in segregation was performed.Single S-atoms bind more strongly to GB sites than single P-atoms. For all GBs the driving force for segregation decays fast with distance from the planes and reaches the bulk values already at ≈ 4 Å. In the near vicinity of the GBs, with increased concentration, the interactions between S-atoms are mostly attractive, while for the same sites the interactions between P-atoms are mostly repulsive. S-atoms are capable of displacing P-atoms and the accumulation of P is not favorable at the GB planes, while the accumulation of S is favorable. We also performed geometric and electronic structure analyses using symmetry quantifying indicators and developed a descriptor of electronic structure effects called “impurity projected density of states (DOS)” for analyzing the bonding between the impurities and the Cu matrix. Overall, segregation is favored by an increase in the asymmetry of the segregation sites. S binds more asymmetrically to those sites preferring an off-center position while P-atoms bind more symmetrically adopting a central position. At GBs with the same excess volume, S-atoms bind stronger than P-atoms and fitting functions that describe these trends were obtained. The balance between bonding states, antibonding states, and the covalent contributions to the bonding between the impurities and the copper matrix are at the origin of the observed preferences.