Calculating free energies of point defects from ab initio

Zhang, Xi; Grabowski, Blazej; Hickel, Tilmann; Neugebauer, Jörg

doi:10.1016/j.commatsci.2018.02.042

Cited by 50 publications

(27 citation statements)

References 107 publications

(146 reference statements)

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“…The anharmonic free energies F ah α (V , T ) were computed using the two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD) approach [10,36]. The required interatomic potentials were parameterized by the embedded atom method (EAM) utilizing the MEAMfit code [37].…”

Section: B Methodological Detailsmentioning

confidence: 99%

Temperature dependence of the stacking-fault Gibbs energy for Al, Cu, and Ni

et al. 2018

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The 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.

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Section: B Methodological Detailsmentioning

confidence: 99%

Temperature dependence of the stacking-fault Gibbs energy for Al, Cu, and Ni

et al. 2018

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“…In this expression G perf = min V [F ah + F el-vib + F qh + F el + E 0 + pV ], and c vac is the equilibrium concentration of vacancies, which has been computed from the Arrhenius ideal solution model introduced in Eqn. (11). To compute G vac , the vacancy part (G − G perf ) is referenced to the quasiharmonic system:…”

Section: Application To Zrcxmentioning

confidence: 99%

Fast anharmonic free energy method with an application to vacancies in ZrC

et al. 2019

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We propose an approach to calculate the anharmonic part of the volumetric-strain and temperature dependent free energy of a crystal. The method strikes an effective balance between accuracy and computational efficiency, showing a ×10 speed-up on comparable free energy approaches at the level of density functional theory, with average errors less than 1 meV/atom. As a demonstration we make new predictions on the thermodynamics of substoichiometric ZrCx, including vacancy concentration and heat capacity.

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“…The notation for the lattice constants (a start -a end ,δa; a 1 ,a 2 ) means that the mesh is going from a start to a end in steps of δa, with additional lattice constants a 1 and a 2 . The term F ah was calculated using an adapted version of the two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD) method [59,60]. We had to adapt the method because of frequent jumps of the vacancy at temperatures above ≈1000 K, which made the use of the quasiharmonic reference in the first thermodynamic integration of the TU-TILD method impracticable.…”

Section: B Total Energy Electronic and Quasiharmonic Contributionmentioning

confidence: 99%

Temperature dependence of the Gibbs energy of vacancy formation of fcc Ni

et al. 2018

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Quantum-mechanical calculations are used to determine the temperature dependence of the Gibbs energy of vacancy formation in nickel. Existing data reveal a discrepancy between the high-temperature estimates from experiments and low-temperature approximations from density functional theory. Our finite-temperature calculations-which include the effects of magnetism and fully interacting phonon vibrations-demonstrate that this discrepancy is mostly caused by the previously neglected explicit anharmonic contribution.

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Calculating free energies of point defects from ab initio

Cited by 50 publications

References 107 publications

Temperature dependence of the stacking-fault Gibbs energy for Al, Cu, and Ni

Temperature dependence of the stacking-fault Gibbs energy for Al, Cu, and Ni

Fast anharmonic free energy method with an application to vacancies in ZrC

Temperature dependence of the Gibbs energy of vacancy formation of fcc Ni

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