First-principles theory of Ta up to 10 Mbar pressure: Structural and mechanical properties

Fundamental high-pressure structural and mechanical properties of Ta have been investigated theoretically over a wide pressure range, 0$-$10 Mbar, by means of ab initio electronic-structure calculations. The calculations are fully relativistic and use a state-of-the-art treatment of gradient corrections to the exchange-correlation potential and energy within density-functional theory. The calculated zero-temperature equation of state for bcc Ta is in good agreement with diamond-anvil-cell measurements up to 750 kbar and with reduced shock data to 2.3 Mbar. The crystal-structure stability among bcc, fcc, hcp, and $A15\mathrm{}$ phases has been studied as a function of compression and the observed ambient-pressure bcc phase is found to be thermodynamically stable throughout the entire 0–10 Mbar range. At the upper end of this range, a metastable fcc phase develops with positive elastic moduli and a decreasing fcc$-$bcc energy difference, suggesting that at even higher pressures above 10 Mbar, fcc Ta will become stable over the bcc phase. Elastic constants, the $H$- and $N$-point zone-boundary phonons, and the ideal shear strength have also been calculated for bcc Ta up to 10 Mbar pressure. The elastic moduli and phonons are in good agreement with experiment at ambient pressure and remain real and positive for all compressions studied, demonstrating that the bcc phase is mechanically stable in this regime. The calculated elastic constants validate the assumed pressure scaling of the shear modulus in the Steinberg-Guinan strength model of Ta, while the calculated values of ideal shear strength provide an upper bound to the high-pressure yield stress.