High-pressure elastic anisotropy and superconductivity of hafnium: A first-principles calculation

The elastic anisotropy and superconductivity upon hydrostatic compression of α, ω, and β Hf are investigated using first-principle methods. The results of elastic anisotropies show that they increase with increasing pressure for α and ω phases, while decrease upon compression for β phase. The calculated superconducting transition temperatures are in excellent agreement with experiments. Electron-phonon coupling constants (λ) are increasing with pressure for α and ω phases, while decreasing for β phase. For β phase, the large values of λ are mainly due to the obvious TA1 soft mode. Under further compression, the TA1 soft vibrational mode will disappear gradually.