Thermodynamics and elastic properties of Ta from first-principles calculations

Within the framework of the quasiharmonic approximation, the thermodynamics and elastic properties of Ta, including phonon density of states (DOS), equation of state, linear thermal expansion coefficient, entropy, enthalpy, heat capacity, elastic constants, bulk modulus, shear modulus, Young's modulus, microhardness, and sound velocity, are studied using the first-principles projector-augmented wave method. The vibrational contribution to Helmholtz free energy is evaluated from the first-principles phonon DOS and Debye model. The thermal electronic contribution to Helmholtz free energy is estimated from the integration over the electronic DOS. By comparing the experimental results with the calculation results from the first-principles and Debye model, it is found that the thermodynamic properties of Ta are depicted well by the first-principles. The elastic properties of Ta from the first-principles are consistent with the available experimental data.