First-principles study of lattice dynamics ofTiO2in brookite and cotunnite structures

Abstract

The zone-center phonons and dielectric properties of orthorhombic brookite and cotunnite structures ${\mathrm{TiO}}_{2}$ were studied in the framework of density functional perturbative theory. The dielectric properties of brookite and anatase structures are similar. The calculated static dielectric permittivity of brookite is found to be slightly higher than that of anatase, but far lower than that of the rutile structure. This is in contrast with the recent experimental report on brookite flowers. Our study suggests that the static dielectric constant of cotunnite structure is smaller than those of rutile and brookite structures. We obtained the full phonon band structure and elastic properties of these structures. The bulk modulus and Debye temperature of brookite are intermediate between those of the anatase and rutile structures. The obtained value of 301 GPa for the bulk modulus of cotunnite is in good agreement with the stiffness of the material reported experimentally. Because of the similarity in $z$-direction packing of the ${\mathrm{TiO}}_{6}$ tetrahedron between brookite and rutile structures, the elastic constants associated with the $z$-polarized movement of atoms in brookite are similar to those of the rutile structure. The elastic constants of brookite associated with the movement of the atoms in $x$-$y$ plane, are similar to the corresponding constants in anatase and rutile structures. This demonstrates the similarity between the packing character of the brookite structure with both anatase and rutile structures. So, the lattice dynamics of brookite is intermediate between those of anatase and rutile polymorphs. The calculated phonon density of states of cotunnite shows that it is stable at ambient pressure.