High pressure-temperature phase diagram and equation of state of titanium

Abstract

The high pressure-temperature behavior of titanium has been studied with x-ray diffraction in resistively heated and laser-heated diamond anvil cells up to 200 GPa and $\ensuremath{\sim}3500$ K. The stability fields of $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ti},\ensuremath{\omega}\text{\ensuremath{-}}\mathrm{Ti},\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Ti},\ensuremath{\gamma}\text{\ensuremath{-}}\mathrm{Ti}$, and $\ensuremath{\delta}\text{\ensuremath{-}}\mathrm{Ti}$ have been determined in this range. $\ensuremath{\gamma}\text{\ensuremath{-}}\mathrm{Ti}$ and $\ensuremath{\delta}\text{\ensuremath{-}}\mathrm{Ti}$, which had been evidenced earlier under nonhydrostatic compression, are also observed in helium pressure transmitting medium. Equation-of-state parameters are proposed for $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Ti}$ and $\ensuremath{\omega}\text{\ensuremath{-}}\mathrm{Ti}$ at 300 K, and $\ensuremath{\beta}\text{\ensuremath{-}}\mathrm{Ti}$ at high temperature. The stability fields of the $\ensuremath{\alpha},\ensuremath{\omega},\ensuremath{\gamma}$, and $\ensuremath{\delta}$ phases are also studied using the projector-augmented wave method based on density-functional theory. Using the relevant core radius to avoid overlapping between atomic spheres, and relaxing cells and atomic positions, we show that all those phases have a stability domain at 0 K. We explain why $\ensuremath{\gamma}\text{\ensuremath{-}}\mathrm{Ti}$ and $\ensuremath{\delta}\text{\ensuremath{-}}\mathrm{Ti}$ were calculated to be unstable in earlier works. In addition, a new phase, called ${\ensuremath{\delta}}^{\ensuremath{'}}$-Ti, which is a distortion of $\ensuremath{\delta}\text{\ensuremath{-}}\mathrm{Ti}$, is predicted to form between 80 and 120 GPa and below $\ensuremath{\simeq}200$ K.