First-principles study of the relations between the elastic constants, phonon dispersion curves, and melting temperatures of bcc Ta at pressures up to 1000 GPa

The possibility to relate analytically elastic shear modulus to melting temperature in the framework of Lindemann melting criterion is investigated here in the particular case of the body-centered cubic phase of tantalum, which is identified as a problematic case. Equation of state, elastic constants, and full phonon dispersion curves (PDCs) are first gathered for a wide pressure range using density functional theory and its perturbation within the generalized gradient approximation. A global fair agreement is found with previous experimental studies. Anomalies in PDCs tend to disappear with compression. Various equivalent Debye temperatures theta(D)(n) are then deduced and compared for increasing compression. The initial Debye model for atomic vibration is found to stand well above 120 GPa. Under this pressure a possibly significant difference up to 10% is found between elastic Debye temperature theta(D)(-3) and theta(D)(-2) required in Lindemann melting criterion. As for all the theoretical melting curves proposed in the past, the one found here using theta(D)(-2,V) completely overpasses the melting curve established by static measurements in diamond anvil cells, but agrees well with the shock melting experiment available. This fact is extensively discussed in terms of evolution of PDCs and explaining hypotheses to be tested in the future are proposed.