Density-functional study of the pressure-induced phase transitions in Ti at zero Kelvin

Abstract

The pressure-induced stable and metastable phase transitions of Ti at 0 K were studied by first-principles density-functional calculations. With the pressure from the equation of state fitting or extracted directly from first-principles calculations, we predicted that the 0 K phase transition sequence of Ti is $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\beta}$, which is different from the theoretic predictions in the literature. We also found that the $\ensuremath{\delta}$ phase is not stable under hydrostatic compression. The obtained stable $(\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\beta})$ and metastable $(\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\beta})$ phase transition pressures are in a good agreement with the experimental results. We found that the equation of state based on different fitting schemes can introduce significant errors in predicting the transition sequence of Ti. Our calculations also show that only under $\ensuremath{-}8.0\text{ }\text{GPa}$, the $\ensuremath{\beta}$ phase exhibits magnetism. However, it is energetically not stable with respect to the $\ensuremath{\alpha}$ and $\ensuremath{\omega}$ phases at low pressures.