Elastic stability ofβ-Tiunder pressure calculated using a first-principles plane-wave pseudopotential method

Abstract

The elastic moduli ${c}^{\ensuremath{'}}$ and ${c}_{44}$ of $\ensuremath{\beta}\text{-Ti}$ with respect to external pressure $P$ (up to about 138 GPa) are calculated with a first-principles plane-wave pseudopotential method. The accuracy of the calculations regarding the plane-wave cut-off energy, $k$-point mesh, and transferability of the pseudopotentials is carefully tested. It is found that the critical pressure beyond which $\ensuremath{\beta}\text{-Ti}$ satisfies the elastic stability conditions is about 60 GPa. The Mulliken population analysis shows that both $s$ and $p$ electrons transfer to the $d$ orbitals with increasing pressure, however, the number of $s$ electrons starts to increase when the pressure exceeds about 70 GPa. The number of $d$ electrons at the critical pressure is about 2.96, in perfect agreement with the critical number of $d$ electrons for a stable bcc Ti-V alloy, which demonstrates the correlation between the stability of bcc metals and their $d$ orbital occupation. The bonding charge density calculations show charge accumulation on the $d\ensuremath{-}{t}_{2g}$ orbitals under high pressure, which may improve the elastic stability of $\ensuremath{\beta}\text{-Ti}$.