Si segregation at Fe grain boundaries analyzed by ab initio local energy and local stress

Using density-functional theory calculations combined with recent local-energy and local-stress schemes, we studied the effects of Si segregation on the structural, mechanical and magnetic properties of the Σ3(1 1 1) and Σ11(3 3 2) Fe GBs formed by rotation around the [1 1 0] axis. The segregation mechanism was analyzed by the local-energy decomposition of the segregation energy, where the segregation energy is expressed as a sum of the following four terms: the local-energy change of Si atoms from the isolated state in bulk Fe to the GB segregated state, the stabilization of replaced Fe atoms from the GB to the bulk, the local-energy change of neighboring Fe atoms from the pure GB to the segregated GB and the local-energy change of neighboring Fe atoms from the system of an isolated Si atom in the bulk Fe to the pure bulk Fe. The segregation energy and value of each term greatly depends on the segregation site and Si concentration. The segregation at interface Fe sites with higher local energies in the original GB configurations naturally leads to higher segregation-energy gains, while interface sites with lower local energies can lead to larger energy gains if stronger Si-Fe interactions occur locally in the final segregated configurations. The high Si concentration reduces the segregation-energy gain per Si atom due to the local-energy increases of Si atoms neighboring to each other or through the reduction in the number of stabilized Fe atoms per Si atom as observed in a Si dimer in bulk Fe. In the Si-segregated GBs, Si-Fe bonds enhance local Young's moduli and tend to suppress the interface weakening, while the GB adhesion is slightly reduced. And Fe atoms contacting Si atoms have reduced magnetic moments, due to Si-Fe sp-d hybridization interactions.