The effects of Mo and Pd segregation on the cohesion of the Fe $\Sigma 3\left(111\right)\mathrm{}$ grain boundary are investigated by using the first-principles full-potential linearized augmented-plane-wave total-energy–atomic-force method with the generalized gradient approximation. Based on the Rice-Wang model, our total energy calculations show that Mo has a significant beneficial effect on the Fe grain-boundary cohesion, while Pd behaves as a weak embrittler. An analysis of the geometry optimization indicates that Mo has a moderate atomic size to fit well in the grain-boundary hole, whereas Pd introduces a larger perturbation on the atomic structure near the grain boundary. The elastic energy associated with the Mo and Pd segregation is estimated with a rigid environment approximation. It is found that both Mo and Pd introduce a beneficial volume effect. Studies of the electronic structures show that its strong bonding capability makes Mo a cohesion enhancer $\left(-0.90\mathrm{eV}\right)$ for the Fe $\Sigma 3\left(111\right)\mathrm{}$ grain-boundary. By comparison, its weak bonding capability leads Pd to be a weak embrittler $(+0.08\mathrm{}\mathrm{eV}).\mathrm{}$ Our first-principles quantum-mechanical results support the main idea of the atomistic theories in that the elemental cohesive energy difference between the substitutional element and the host element plays an important role in determining its effect on the grain-boundary cohesion. However, the numerical results for Pd, which has a similar elemental cohesive energy to that of Fe, point to the importance of the role played by the volume effect. It is expected that in a lower-angle Fe grain boundary which has a larger grain-boundary volume expansion, Pd can possibly become a cohesion enhancer.

• Received 21 December 1999

DOI:https://doi.org/10.1103/PhysRevB.62.6208