High-pressure structural phases of titanium dioxide

Various phases of Ti${\mathrm{O}}_2$ are studied using the ab initio plane wave approach with soft pseudopotentials. Under pressure when the unit cell reduces in volume rutile is found to change into a columbite ($\alpha$-Pb${\mathrm{O}}_2$) phase and in turn into a baddeleyite structure with an associated slight increase in the bulk modulus. The bulk modulus of the baddeleyite phase depends upon the locations of the oxygen atoms in the unit cell. Although not nearly as hard as diamond, we suggest such a material could have hardness approaching that of boron nitride. The property of a fluorite phase that is often considered to derive from the baddeleyite phase and as yet not identified is also investigated.