Phase diagram of Ti metal at high pressure

Using density-functional theory based ab-initio computations, we have investigated the hexagonal close-packed (hcp) and the hexagonal ($\omega )$ structures titanium (Ti), and find good agreement with experiment. The hcp phase yields an equation of state of a zero pressure volume V$_{0}$ = 17.37 ( 0.02) {\AA}$^{3}$, an isothermal bulk modulus K$_{0}$= 111.9 ( 0.2) GPa, and its pressure derivative K$_{0}$' = 3.60 ( 0.02). Furthermore, the $c/a$ ratio for both phases increases with increasing pressure. Additionally, the calculated transition pressure from hcp to $\omega $ phase compares well with the experimental results with the $\omega $ phase more stable than the hcp phase at pressures greater than $\sim $ 5 GPa.