First-principles calculations of grain boundary theoretical shear strength using transition state finding to determine generalized gamma surface cross sections

We present a first-principles calculation of the theoretical shear strength of the Al{Σ}3(112{}) tilt boundary. Here we replace the usual {γ} surface (defined by rigid atomic translations parallel to the boundary) by a ``generalized {γ} surface'' that includes complex cooperative atomic motions occurring at the grain boundary during shear. Transition-state-finding techniques are well suited for calculations of generalized {γ}-surface cross sections. The transition states, saddles on the {γ} surface, occur during grain-boundary sliding and at grain-boundary dislocations.