First-principles calculations of the crystal structures, bulk moduli, and relative stabilities of seven known and hypothetical ${\mathrm{TiO}}_2$ polymorphs (anatase, rutile, columbite, baddeleyite, cotunnite, pyrite, and fluorite structures) have been carried out with the all-electron linear combination of atomic orbitals (LCAO) and pseudopotential planewave (PW) methods. The anatase versus rutile relative phase stability at 0 K and zero pressure has been investigated using high-quality basis sets and carefully controlled computational parameters. From the optimal crystal structures obtained with the Hartree-Fock theory at various pressures, the bulk modulus and phase transition pressures of various high-pressure polymorphs have been derived at the athermal limit. In most cases, the calculated unit cell data agree to within 2% of the corresponding experimental determination. Complete predicted structural data (unit cell constants and fractional atomic coordinates) are presented for the baddeleyite and pyrite forms. The calculated bulk moduli are within 10% of the most reliable experimental results. Both the all-electron LCAO and pseudopotential PW methods predict anatase to be more stable than rutile at 0 K and ambient pressure. The computed anatase-columbite, rutile-columbite, columbite-baddeleyite, and baddeleyite-cotunnite phase transitions appear in the same order as observed in experiments, and the transition pressures agree semiquantitatively with those measured. The pyrite and fluorite structures are predicted to be less stable than other polymorphs at pressures below 70 GPa in agreement with experiments. Finally, the elastic properties, compressibilities and phase transformations of the various polymorphs are discussed in terms of simple models based on the behavior of the constituent Ti-O polyhedra under compression.

• Received 4 January 2002

DOI:https://doi.org/10.1103/PhysRevB.65.224112