During sliding, the grain-boundary energy depended upon the atomic structures produced during the relative translation of the 2 grains. The variation of the grain-boundary energy within the 2-dimensional boundary unit-cell constituted the grain-boundary γ-surface. Maxima in the slope of the γ-surface determined the sliding resistance: the stress required to move the system over the lowest saddle-points along a particular path within the boundary unit-cell. The results of an atomistic study of the γ-surfaces for 2 types of boundary in a face-centered cubic metal were reported. One of the boundaries was Σ = 11, <110>{131}; which was a low-energy boundary and had a simple γ-surface with a single stable configuration located at the corners and centre of the boundary unit-cell. The resistance to sliding was determined by chain-of-states methods along 4 shear vectors connecting equivalent states within the boundary unit-cell. It was found to be very high in all cases. The asymmetrical Σ = 11 <110>{252}-{414} grain-boundary had a higher grain-boundary energy, and its γ-surface was much more complex; with distinctly different structures appearing at various locations in the boundary unit-cell. At certain locations, more than one structure was found for the asymmetrical grain-boundary. Although complex, a chain-of-states calculation along one path across the boundary unit-cell suggested that the shear strength of this grain boundary was also quite high. Extrinsic grain-boundary dislocations were found to lower the resistance to shear considerably and, therefore, played the same role in the shear of grain boundaries as did glide dislocations in slip of the lattice. The existence of multiple configurations had significant implications for the interaction of lattice dislocations with grain boundaries, for the core structures of grain boundary dislocations, for the temperature-dependence of grain-boundary properties and for grain-boundary sliding resistance.

The Relation between Grain-Boundary Structure and Sliding Resistance. R.G.Hoagland, R.J.Kurtz: Philosophical Magazine A, 2002, 82[6], 1073-92