Effects of carbon on Fe-grain-boundary cohesion: First-principles determination

The cohesive properties of the C/FeΣ3(111) grain boundary are investigated by means of the direct determination of the difference in binding energies of C in grain-boundary and free-surface environments. The atomic force approach based on the full-potential linearized augmented plane-wave method is used to optimize the atomic structure for the clean and C-segregated grain-boundary and free-surface systems. The ω phase structure obtained in a previous grain-boundary cluster calculation is found to be only a metastable state that is 0.72 eV/cell (0.81 J/${\mathrm{m}}^2$) higher in energy than the distorted bcc ground state. The calculated binding-energy difference (i.e., Δ${\mathit{E}}_{\mathit{b}}$-Δ${\mathit{E}}_{\mathit{s}}$) is -0.61 eV/adatom, which is a theoretical demonstration that C is a cohesion enhancer in the Fe grain boundary. Comparisons with earlier results obtained for B, S, and P show that the number of hybridized p electrons and the resulting spatial anisotropy of bonding with the surrounding Fe atoms is the key factor determining the relative embrittling or cohesion enhancing behavior of a metalloid impurity. © 1996 The American Physical Society.