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Anharmonic contributions to ab initio computed thermodynamic material properties / Albert Glensk ; Gutachter Prof. Dr. rer. nat. Wolf Gero Schmidt, Gutachter Prof Dr. rer. nat. Jörg Neugebauer, Gutachter Prof. Dr. Michael Finnis. Paderborn, 2016
Inhalt
Acknowledgements
Abstract
Contents
1 Introduction: Ab initio thermodynamics
2 Theory
2.1 Entropic quantities and their relation to ensemble averages from molecular dynamics
2.2 From the many-body problem to density functional theory
2.2.1 Born-Oppenheimer approximation
2.2.2 Density functional theory
2.2.3 Kohn-Sham equations
2.3 Approximate theories of lattice vibrations
2.3.1 Independent harmonic oscillators — The Einstein crystal
2.3.2 Debye and Grüneisen Approximation
2.3.3 Harmonic and Quasiharmonic Approximation
2.3.4 Methods beyond the quasiharmonic approximation
2.4 Solving lattice vibrations numerically exactly
2.4.1 Many-body perturbation theory
2.4.2 Thermodynamic Integration
2.4.3 UP-TILD
3 Methodological developments
3.1 Efficient sampling of anharmonic contributions in bulk systems
3.1.1 Analysis of harmonic lattice dynamics at high temperatures
3.1.2 Local Anharmonic (LA) approximation
3.1.3 Comparison of reference potentials
3.2 Fully ab initio description of point defects at high temperatures
3.2.1 The Arrhenius model for defect formation
3.2.2 High temperature lattice vibrations in the defect and bulk supercell
3.2.3 Entropy of the defect
4 Results: Impact of anharmonicity on the thermodynamics of selected material systems
4.1 Fcc elements: A wide range study
4.1.1 Anharmonic free energy contributions in LDA and GGA
4.1.2 Effects on derived quantities: Heat Capacity, Expansion
4.2 Beyond standard DFT: RPA up to melting
4.3 Binary systems: From Mg and Si to Mg2Si
4.4 Point Defects
4.4.1 Including anharmonic contributions to defect formation
4.4.2 Mono- and divacancy interpretation of vacancies in Al and Cu
4.4.3 Gibbs energies and entropies of defect formation
4.4.4 Breakdown of the Arrhenius law and implications
5 Summary and Outlook
A Supplement
A.1 Rewriting the quasiharmonic total energy
A.2 Local Anharmonic approximation
A.3 Details of calculations on bulk systems
Bibliography
List of Publications
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