Phase diagrams of titanium and titanium oxide at high pressure

The nature of bonding in titanium (Ti) and, in particular, titanium oxide (TiO2) are of significant interest since TiO2 forms a superhard material.~ Using density-functional theory-based ab-initio computations, we have investigated the structural phase transitions of both Ti and TiO2 at high pressure. For titanium, the hexagonal close-packed (hcp), hexagonal ($\omega )$, distorted hcp ($\gamma )$, distorted bcc ($\delta )$, body-centered cubic (bcc), faced-centered cubic (fcc) and simple cubic (sc) structures were studied up to a pressure of~ $\sim $ 200 GPa. The structural phase transition sequence is as follows: hcp -$>{\rm g}\omega ->{\rm g}\gamma ->{\rm g}\delta ->$ bcc, in good agreement with both experimental and theoretical results. Furthermore, we test the stability of bcc to other cubic and close-packed phases (fcc, sc, and hcp) and find that bcc is the most stable structure of Ti under pressures between 156 and $\sim $200 GPa. For titanium oxide, rutile, anatase, columbite, baddeleyite, fluorite, pyrite, brookite, and cotunnite structures were also studied under high compression. For both Ti and TiO2, our transition pressures compare well with previous studies.