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

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 ~3500 K. The stability fields of ${α}{{-}}Ti,{ω}{{-}}Ti,{β}{{-}}Ti,{γ}{{-}}Ti$, and ${δ}{{-}}Ti$ have been determined in this range. ${γ}{{-}}Ti$ and ${δ}{{-}}Ti$, which had been evidenced earlier under nonhydrostatic compression, are also observed in helium pressure transmitting medium. Equation-of-state parameters are proposed for ${α}{{-}}Ti$ and ${ω}{{-}}Ti$ at 300 K, and ${β}{{-}}Ti$ at high temperature. The stability fields of the ${α},{ω},{γ}$, and ${δ}$ 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 γ-Ti and δ-Ti were calculated to be unstable in earlier works. In addition, a new phase, called δ^'-Ti, which is a distortion of δ-Ti, is predicted to form between 80 and 120 GPa and below 200 K.