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

The elasticity, dynamic properties, and superconductivity of alpha, omega, and beta Zr upon compression are investigated by using first-principles methods. Our calculated elastic constants, elastic moduli, and Debye temperatures of alpha and omega phases are in excellent agreement with experiments. Electron-phonon coupling constant lambda and electronic density of states at the Fermi level N (E(F)) are found to increase with pressure for these two hexagonal structures. For cubic beta 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 beta phase is achieved by phonon dispersion calculations to be similar to 26 GPa. Over this pressure, lambda and N (EF) of beta phase decrease upon further compression. Our calculations show that the large value of superconducting transition temperature T(c) at 30 GPa for beta Zr is mainly due to the TA1 soft mode. Under further compression, the soft vibrational mode will gradually fade away. (C) 2011 American Institute of Physics. [doi:10.1063/1.3556753]