Ab initio thermoelasticity of crystals at extremes

This thesis presents the study of the second-order elastic constants (ECs) of body centered cubic (BCC) refractory metals tungsten and molybdenum, and of the hexagonal close-packed (HCP) beryllium at extreme conditions (high temperature and high pressure), using density functional perturbation theory (DFPT) within the quasi-harmonic approximation (QHA). Some preliminary results are also presented for tantalum. Moreover, we present the thermodynamic properties including the equation of states (EOS), phonon dispersion, thermal expansion (TE), bulk modulus, heat capacity and average Gruneisen parameter which are calculated by density functional theory (DFT) implemented in Quantum ESPRESSO. We find a reasonable agreement with available experiments with some exceptions discussed in the thesis. In general, the temperature dependent QHA ECs show a better description compared with quasi static approximation (QSA) ECs. The latest experimental sound velocity measurements on tungsten support our findings. For beryllium, the accuracies of various approximations on crystal structure (zero static internal stress approximation (ZSISA) and volume-constrained zero static internal stress approximation (V-ZSISA)), or on elastic constants (QHA versus QSA) which are widely applied in ab initio thermodynamic calculations are quantified in detail. A numerical approach is given to compute the ECs in presence of internal relaxations when the free energy is minimized with respect to the strain. An alternative GPU acceleration for plane waves pseudopotentials electronic structure codes designed for systems that have small unit cells but require a large number of k points to sample the Brillouin zone, such as metals, is presented. All phonon calculations in the thesis have benefited from this implementation in thermo_pw. As a side product of this work, the PAW pseudo potentials of tungsten have been updated in pslibrary.