First-principles investigation of brittle cleavage fracture of fe grain boundaries

The first-principles discrete variational method, within the framework of density-functional theory, is employed to study the process of Fe grain boundary brittle cleavage and surface formation. The calculated results show that the main changes in this process take place in the fracture bonds and surface bonds. The strength of fracture bonds is weakened rapidly with an increase of the separation distance d, and decreased to zero when d is equal to about 10.0 a.u. The strength of surfaces bonds with the surface bond angle θ<45° is increased greatly, but that of surface bonds with the surface bond angle θ>45° changes small. The separation energy is increased with the increase of separation d when d is in the region of 0.0<d<10.0 a.u., and it does not change when d>10.0 a.u. in the process of fracture. This indicates that the system will absorb energy in the process of brittle cleavage fracture. The density of states is increased in the region near the Fermi level E_F, and is decreased in the region about -10 to -3 eV with the increase of separation d. Some electrons are transferred from the lower-energy level to the higher level in the process. These electrons come mainly from the atoms near to fracture plane, which means that the atoms in the surface region have higher energy than those in the grain boundary.