First-principles calculations of phase transition, elastic modulus, and superconductivity under pressure for zirconium.

The elasticity, dynamic properties, and superconductivity of α, ω, and β Zr upon compression are investigated by using first-principles methods. Our calculated elastic constants, elastic moduli, and Debye temperatures of α and ω phases are in excellent agreement with experiments. Electron-phonon coupling constant λ and electronic density of states at the Fermi level N (EF) are found to increase with pressure for these two hexagonal structures. For cubic β phase, the critical pressure for mechanical stability is predicted to be 3.13 GPa and at P = 4 GPa the low elastic modulus (E =31.97 GPa) can be obtained. Besides, the critical pressure for dynamic stability of β phase is achieved by phonon dispersion calculations to be ∼26 GPa. Over this pressure, λ and N (EF) of β phase decrease upon further compression. Our calculations show that the large value of superconducting transition temperature Tc at 30 GPa for β Zr is mainly due to the TA1 soft mode. Under further compression, the soft vibrational mode will gradually fade away. [ABSTRACT FROM AUTHOR]