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

TL;DR

This study uses first-principles calculations to explore phase transitions, elastic properties, and superconductivity in zirconium's different phases, revealing pressure-dependent behaviors and mechanisms behind superconductivity.

Contribution

It provides detailed first-principles insights into the elastic, dynamic, and superconducting properties of zirconium phases under pressure, including stability thresholds and transition mechanisms.

Findings

Elastic constants agree with experiments for $ ext{α}$ and $ ext{ω}$ phases.

Low elastic modulus of 31.97 GPa at 4 GPa in $eta$ phase.

Superconducting transition temperature peaks at 30 GPa due to TA1 soft mode.

Abstract

The elasticity, dynamic properties, and superconductivity of $\alpha$, $\omega$, and $\beta$ Zr 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 $N$(\emph{E}$_{\rm{F}}$) 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 \emph{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 $\mathtt{\sim}$26 GPa. Over this pressure, $\lambda$ and $N$(\emph{E}$_{\rm{F}}$) of $\beta$ phase decrease upon further compression. Our calculations show that the large value of superconducting transition temperature $\emph{T}_{\rm{c}}$ 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.