Universität Stuttgart
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Item Open Access Accurate electronic free energies of the 3d, 4d, and 5d transition metals at high temperatures(2017) Zhang, Xi; Grabowski, Blazej; Körmann, Fritz; Freysoldt, Christoph; Neugebauer, JörgFree energies of bulk materials are nowadays routinely computed by density functional theory. In particular for metals, electronic excitations can significantly contribute to the free energy. For an ideal static lattice, this contribution can be obtained at low computational cost, e.g., from the electronic density of states derived at T = 0 K or by utilizing the Sommerfeld approximation. The error introduced by these approximations at elevated temperatures is rarely known. The error arising from the ideal lattice approximation is likewise unexplored but computationally much more challenging to overcome. In order to shed light on these issues we have computed the electronic free energies for all 3d, 4d, and 5d transition elements on the ideal lattices of the bcc, fcc, and hcp structures using finite-temperature density-functional theory. For a subset of elements we have explored the impact of explicit thermal vibrations on the electronic free energies by using ab initio molecular dynamics simulations. We provide an analysis of the observed chemical trends in terms of the electronic density of states and the canonical d band model and quantify the errors in the approximate methods. The electronic contribution to the heat capacities and the corresponding errors due to the different approximations are studied as well.Item Open Access Calculating free energies of point defects from ab initio(2018) Zhang, Xi; Grabowski, Blazej; Hickel, Tilmann; Neugebauer, JörgThe formation and lifetime of point defects is governed by an interplay of kinetics and thermodynamic stability. To evaluate the stability under process conditions, empirical potentials and ab initio calculations at T 1⁄4 0 K are often not sufficient. Therefore, various concepts to determine the full temperature dependence of the free energy of point defects with ab initio accuracy are reviewed. Examples for the importance of accurately describing defect properties include the stabilization of vacancies by impurities and the non-Arrhenius behaviour of vacancy formation energies due to anharmonic lattice vibrations.Item Open Access Temperature dependence of the stacking-fault Gibbs energy for Al, Cu, and Ni(2018) Zhang, Xi; Grabowski, Blazej; Körmann, Fritz; Ruban, Andrei V.; Gong, Yilun; Reed, Roger C.; Hickel, Tilmann; Neugebauer, JörgThe temperature-dependent intrinsic stacking fault Gibbs energy is computed based on highly converged density-functional-theory (DFT) calculations for the three prototype face-centered cubic metals Al, Cu, and Ni. All relevant temperature-dependent contributions are considered including electronic, vibrational, magnetic, and explicit anharmonic Gibbs energy contributions as well as coupling terms employing state-of-the-art statistical sampling techniques. Particular emphasis is put on a careful comparison of different theoretical concepts to derive the stacking fault energy such as the axial-next-nearest-neighbor-Ising (ANNNI) model or the vacuum-slab approach. Our theoretical results are compared with an extensive set of previous theoretical and experimental data. Large uncertainties in the experimental data highlight the necessity of complementary parameter-free calculations. Specifically, the temperature dependence is experimentally unknown and poorly described by thermodynamic databases. Whereas calphad derived data shows an increase of the stacking fault energy with temperature for two of the systems (Cu and Ni), our results predict a decrease for all studied systems. For Ni, the temperature induced change is in fact so strong that in the temperature interval relevant for super-alloy applications the stacking fault energy falls below one third of the low temperature value. Such large changes clearly call for a revision of the stacking fault energy when modeling or designing alloys based on such elements.