Elastic properties play a key role in science and technology as they characterize the mechanical and thermodynamical behavior of a material. Although mechanical properties may even strongly depend on the material’s microstructure, they are determined by interactions happening on the atomistic scale. Thus, computational solid-state theory based on quantum-mechanics can provide insight which is crucial for the understanding of the materials’s macroscopic behavior. The main goal of this thesis is the development and implementation of a scheme toreliably compute elastic properties of crystalline materials from first principles.
Elastic properties are either characterized by elastic constants, which are the components of the elastic tensor, or by elastic moduli, which are the corresponding averaged quantities. Elastic constants can be defined by a Taylor expansion of the free energy or stress in terms of the crystal deformation, i.e., the strain. The coefficients of the Taylor series provide the elastic constants of different order.
To calculate elastic constants, one has to compute the total energy or stress of the deformed crystal. A well suited quantum-mechanical framework for doing so is density-functional theory (DFT) which was employed in the present work. We use state-of-the-art DFT codes for energy and stress calculations. We investigate second-order elastic constants choosing prototype materials for all crystal lattice types, and third-order elastic-constants for prototypes of cubic, hexagonal, and rhombohedral crystals, respectively.
Besides this general implementation in terms of symmetry, we place emphasis on the evaluation of numerical energy and stress data. We propose a new recipe to obtain elastic constants out of ab initio calculations in the most reliable manner. All the work has been collected in the software package called ElaStic. ElaStic is utilizing either the full-potential all-electron codes exciting and WIEN2k or the pseudo-potential plane-wave code Quantum ESPRESSO. It provides the elastic compliances tensor and applies the Voigt and Reuss averaging procedure in order to obtain bulk, shear, and Young moduli as well as the Poisson ratio for polycrystalline samples.