The (111) twin-boundary and stacking-fault energies of aluminum and palladium were investigated using the all-electron total-energy linear muffin-tin orbital method based upon the local-density approximation. Fault energies were determined by comparing the total energies obtained for the same-size super-cells for each of two cases (with and without fault). The calculated values of the twin, intrinsic and extrinsic fault energies, 130 (97), 270 and ∼330mJ/m2 for aluminum (palladium) wegenerally 30% larger than the experimental data. This discrepancy between calculated and observed values was attributed to the neglect of relaxation, to the effect of the (finite) size of the super-cell (at most 28 atoms/cell), and/or to the use of the local-density approximation. The calculated results appeared to confirm the correctness of the empirical relationship 2Etw≃ESF, where Etw and ESF were the twin and stacking-fault energies, respectively.

Twin-Boundary and Stacking-Fault Energies in Al and Pd. J.Xu, W.Lin, A.J.Freeman: Physical Review B, 1991, 43[3], 2018–24