Energetics of Ideal Grain Boundary Fracture in Iron and the Thermodynamic Criterion of Impurity Embrittlement

ABSTRACTModeling of grain boundary (GB) relaxation during ideal fracture, and the fracture energetics of a Σ3 (111) GB in Fe was performed using the modified Finnis-Sinclair semi-empirical method, and utilizing the so-called “environment-sensitive embedding energies” of impurity atoms, introduced earlier by the author. The calculations were done for both the clean GB, and GB with the following impurity atoms: H, B, C, N, O, P and S. The ideal fracture was modeled by separating the two halves of crystal normal to the GB, step-wise, minimizing the total crystal energy at every step. The interplanar distances were varied, while the Fe interatomic spacing within the hexagonal planes was held fixed. When the distance between the two crystal halves: one with the impurity and another without, exceeded the interatomic interaction cut-off radius (3.6 Å), two different free surfaces - with and without the impurity - emerged. The GB and surface energies were found both for the pure Fe, and that with impurity atoms at the GB or free surface. Both the (111) GB energy and the (111) surface energy of pure Fe agree well with experimental data and results of previous semi-empirical modeling. In general, the correlation between the embrittling/ cohesion enhancing effect of impurities in GB and the difference between the GB and free surface energies agrees with the thermodynamic criterion of embrittlement.