Structure-energy correlation for grain boundaries in F.C.C. metals—III. Symmetrical tilt boundaries

Abstract

The correlation between the structure and zero-temperature energy of symmetrical tilt grain boundaries (STGBs) in f.c.c. metals is investigated using two embedded-atom-method potentials (for Cu and Au) and a Lennard-Jones potential fitted for Cu. Similar to free surfaces, misorientation phase space associated with these simple planar defects consists of only two degrees of freedom, namely those associated with the GB plane. The sampling of this two-dimensional phase space in terms of the stereographic triangle shows energy cusps as its corners and along its edges. These cusps are shown to arise from GB geometries with particularly small planar unit cells. Similar to free surfaces, a good correlation is found between the number of broken nearest-neighbor bonds per unit area and the GB energy. Also, as in our earlier study of twist boundaries, a practically linear relationship is found between the GB energy and volume expansion at the boundary. Finally, a comparison with twist boundaries shows that the STGBs represent the endpoints of the energy vs twist-angle curves. This enables a direct comparison of the properties of twist and tilt boundaries.