Twin-boundary and stacking-fault energies in Al and Pd

The (111) twin-boundary and stacking-fault energies of aluminum and palladium were investigated with use of the all-electron total-energy linear muffin-tin orbitals method based on the local-density approximation. Fault energies are determined by comparing the total energies obtained for the same-size supercells for each of two cases (with and without fault). The calculated values of the twin, intrinsic, and extrinsic fault energies, 130±15 (97±5), 270±50, and ∼330 ergs/${\mathrm{cm}}^2$ for aluminum (palladium) are generally 30% larger than experiment. This discrepancy between the calculated and observed values may be attributed to the neglect of relaxation, the effect of the (finite) size of the supercell (at most 28 atoms/cell), and/or the use of the local-density approximation. Our calculated results appear to verify the correctness of the empirical relationship 2${\mathit{E}}_{\mathrm{tw}}$≃${\mathit{E}}_{\mathrm{SF}}$, where ${\mathit{E}}_{\mathrm{tw}}$ and ${\mathit{E}}_{\mathrm{SF}}$ are the twin and stacking-fault energies, respectively.