The (111) twin-boundary and stacking-fault energies were investigated using the all-electron total-energy linear muffin-tin orbitals method based upon the local-density approximation. The fault energies were determined by comparing the total energies obtained for the same size of super-cell for each of two cases (with and without fault). The calculated values of the twin, intrinsic and extrinsic fault energies, 130, 270 and 330mJ/m2 were generally 30% higher than the experimental value. This discrepancy between calculated and observed values was attributed to the neglect of relaxation, the effect of the finite size of the super-cell (at most 28atoms/cell) and/or the use of the local-density approximation. The calculated results appeared to verify the empirical relationship, ES = 2ET, where ET and ES were the twin and stacking-fault energies, respectively.

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