Calculation of elastic and thermodynamic properties of Mo, Ta, and W under high pressures and temperatures

In this work, the elastic and thermodynamic properties of the refractory metals molybdenum, tantalum, and tungsten under high pressures and temperatures were studied within the scope of density functional theory. Thermal expansion, isotherms, shock adiabats, elastic constants, sound velocities, and melting curves for these metals were calculated. Our calculations were done with a quasiharmonic approximation based on phonon spectrum calculations at zero temperature and with the classical mean-field potential model that approximately accounts for the anharmonic effects. It was determined how anharmonicity influenced the physical characteristics of Mo, Ta, and W. Its impact was found to be stronger in Mo and W, thus improving agreement between calculated and experimental results. As for Ta, its thermodynamic characteristics of interest were adequately reproduced both by the quasiharmonic approximation and by the mean-field potential model. The mean-field potential model demonstrated its high efficiency in the calculation of the properties of Mo, Ta, and W at pressures up to at least 0.6 TPa. It is simple and less time-consuming even compared to the quasiharmonic approximation that was used in this work.