A broken-bond model for grain boundaries in face-centered cubic metals

The interrelation between the number of nearest-neighbor atomic bonds broken upon formation of a grain boundary in an fcc metal and the related zero-temperature boundary energy is investigated by atomistic simulation. Using both a Lennard–Jones and an embedded-atom-method potential, the structures and energies of symmetrical and asymmetrical tilt and twist boundaries are determined. As in free surfaces, a practically linear relationship between the nearest-neighbor miscoordination per unit area of the grain boundary and the related interface energy is obtained. The so-called random-boundary model, in which the interactions across the interface are assumed to be entirely randomized, is shown to provide a basis for understanding the role of broken bonds in both high-angle grain boundaries and free surfaces, thus naturally permitting the analysis of ideal cleavage-fracture energies. A detailed study of low-angle boundaries shows that only the dislocation cores—but not their strain fields—give rise to broken bonds. The complementarity between the dislocation model of Read and Shockley for low-angle boundaries and a broken-bond model for high-angle boundaries is thus elucidated.