Breakdown of the Arrhenius Law in Describing Vacancy Formation Energies: The Importance of Local Anharmonicity Revealed by Ab initio Thermodynamics

We study the temperature dependence of the Gibbs energy of vacancy formation in Al and Cu from T = 0 K up to the melting temperature, fully taking into account anharmonic contributions. Our results show that the formation entropy of vacancies is not constant as often assumed but increases almost linearly with temperature. The resulting highly nonlinear temperature dependence in the Gibbs formation energy naturally explains the differences between positron annihilation spectroscopy and differential dilatometry data and shows that nonlinear thermal corrections are crucial to extrapolate high-temperature experimental data to T = 0 K. Employing these corrections-rather than the linear Arrhenius extrapolation that is commonly assumed in analyzing experimental data-revised formation enthalpies are obtained that differ up to 20% from the previously accepted ones. Using the revised experimental formation enthalpies, we show that a large part of the discrepancies between DFT-GGA and unrevised experimental vacancy formation energies disappears. The substantial shift between previously accepted and the newly revised T = 0 K formation enthalpies also has severe consequences in benchmarking ab initio methods against experiments, e. g., in deriving corrections that go beyond commonly used LDA and GGA exchange-correlation functionals such as the AM05 functional.