A vast number of materials properties and phenomena are regulated by diffusion. However, diffusion coefficients from experiments and calculations are far from complete. Here, we report a compilation of vacancy formation energies ( ), vacancy migration energies ( ), vacancy activation energies ( ), vacancy concentrations (C Va ), and vacancy-mediated self-diffusion coefficients (D Va ) as a function of temperature for 82 pure elements in bcc, fcc, and hcp structures by means of a comprehensive first-principles study. We assess the accuracy of four exchange-correlation (X-C) functionals for first-principles calculations, including the local density approximation (LDA), two generalized gradient approximations (PW91 and PBE), andPBEsol  the focus of the present work. To gain temperature-dependent diffusion properties, transition state structure searches are performed by the climbing image nudged elastic band

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A method based on thermodynamic modeling was developed to determine optimal amounts of Hf additions to Al 2 O 3-forming, γ-γ NiCrAl alloys. The alloy ability to maintain Hf in solution was set by the Hf concentration required to form HfO 2 at the oxygen activity defined by the alloy/Al 2 O 3 equilibrium. This Hf tolerance decreased with increasing temperature and increased with increasing γ fraction. The latter was due to the higher solubility of Hf in γ , compared to γ. The validity of the procedure was evaluated by oxidizing a series of NiCrAl-Hf alloys in dry air at 1000-1200 • C. The experimental results followed the predicted trends, although the Hf tolerance tended to be overestimated. The applicability of the criterion, and potential routes for improved predictability, were discussed by considering the influence of the compositional changes occurring at the metal surface during the transient and steady-state stages of the oxidation process.

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