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We investigated the relative stability and structural properties of Al-Cu intermetallic compounds using the density-functional theory (DFT) with different approximations. We reveal the importance of the on-site Coulomb repulsion of Cu 3d electrons on the energetics and structural properties of Al-Cu compounds of free-electron nature. The finite-temperature effect was included by accounting for the vibrational free energy within the Debye model. The present study shows that θ-Al2Cu is the ground state phase, agreeing with the experimental observations in the literature. The DFT + U approach could be useful to predict accurate formation energies of other Cu-containing precipitates in high-strength Al-alloys.

Practical and reliable methods for theoretically determining the properties of B, C, N, and O in bcc iron have been explored by systematic DFT calculations. The energies of solution and migration, and the elastic strain fields due to the solute atom have been evaluated by supercell calculations under various conditions. By applying correction for spurious elastic interaction of the solute atom with its images in the periodic supercells, reasonable estimates of the solution energy have been obtained without employing very large supercells. The correction turned out unimportant for the migration energy, as it modifies the energies of the stable position and the saddle-point similarly. The lambda tensor, which uniquely characterizes the strain field induced by a solute atom, has been evaluated for the four species of various configurations, first through the force-dipole tensor obtained in zero-strain calculations, and second from changes in supercell dimensions in zero-stress calculations. The two procedures give similar results that typically differ by a few per cent from each other. The computed values for C and N in octahedral interstitial sites are comparable to experimental values. When experimental data become available for B and O, these evaluations will resolve the as-yet contentious location of these atomic species in bcc iron.