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Ab-Initio thermoelasticity and the physical origin of the anomalous thermal expansion in W-Re alloys Accurate calculations of the thermal expansion coefficient (CTE) from first-principles with explicit treatment of lattice vibrations are nowadays widely used. However, simpler models like the Debye-Grüneisen (DG) model are highly appreciated for reducing computational cost and making thermodynamics also feasible for methods where explicit phonon calculations are not accessible. Furthermore, simpler models for calculating vibrational free energies enable us to predict temperature dependent elastic constants of low symmetry crystals being computationally very demanding when using advanced methods like density functional perturbation theory (DFPT). In order to validate the applicability of the different approaches we study the alloy system W-Re which is of particular importance for high temperature applications especially because of its low CTE. Alloying with Re results in a higher ductility but experiments also show an increase in CTE. To obtain the thermal expansion the two main contributions to the Helmholtz free energy, the internal energy and the vibrational free energy are calculated. The internal energy is obtained via density functional theory and alloying is simulated using the virtual crystal approximation which is widely used and efficient in calculating elastic properties as well as the lattice dynamics of alloys. To obtain the vibrational part of the free energy on the one hand we use the DG model and on the other hand DFPT as implemented in the VASP code. We show that the standard DG model fails to predict the change in CTE with alloying composition while our DFPT calculations reproduce the trend observed in experiment. To give an insight into the physical origin of the failure of the DG model we use the phonon dispersion obtained via DFPT to investigate the impact of alloying on the phonon softening towards the zone boundary and in the long wavelength limit. Finally, we present a modification of the standard DG model which is able to predict the right trend with a strong reduction in computation time compared to DFPT. |