Atomistic, generalized Peierls-Nabarro and analytical models for (1Â 1Â 1) twist boundaries in Al, Cu and Ni for all twist angles

We present a systematic study of the structure and energy of (1 1 1) twist boundaries in face-centered cubic Al, Cu and Ni for all twist angles from atomistic, generalized Peierls-Nabarro and analytical approaches. The results show that we can successfully classify all (1 1 1) twist boundaries into three types: low-angle grain boundaries (LAGBs), near-twin grain boundaries (NTGBs) and those intermediate between the two (IAGBs). The generalized Peierls-Nabarro model provides an accurate description of the structure and energy of the LAGBs and NTGBs based upon perfect crystal and twin reference states, respectively. While the generalized Peierls-Nabarro model provides a reasonable description of the grain boundary structure and energy well beyond the classical low-angle boundary regime, it fails when the dislocation cores overlap. To describe the twist boundary energy for all twist angles, we analytically interpolate between the LAGB and NTGB regimes using no adjustable parameters - only properties of the dislocations, the stacking fault and twin energies, and perfect crystal properties. We demonstrate that the new, analytical expression for grain boundary energy over the entire twist angle range is extremely accurate for Al, Cu and Ni compared to atomistic simulation results.