Density functional theory calculation of diffusion mechanism of intrinsic defects in rutile TiO2

Diffusion mechanisms of four intrinsic point defects in rutile TiO2, titanium interstitial (TiI), titanium vacancy (Vti), oxygen interstitial (OI) and oxygen vacancy (VO) are studied in the framework of density functional theory with quantum ESPRESSO suite. Diffusion processes are simulated by defect movement between two stable atomic configurations through using the climbing image nudged elastic band (CI-NEB) method. The initial and final atomic structure in the minimum energy path (MEP) are constructed with 3 x 3 x 4 perfect supercell matrix of 216 atoms. Considering that oxygen atoms build up TiO6 octahedron and half of the octahedral centers are occupied by Ti atoms in rutile, interstitial defect is constructed by adding one Ti or O atom to the empty oxygen octahedral center, and vacancy defect is constructed by removing one atom from crystal lattice grid. Structural relaxation is performed before performing the NEB calculation with gamma k point sampling in irreducible Brillouin zone with an energy cutoff of 650 eV. As rutile TiO2 has tetragonal symmetry (P4(2)/mnm), the diffusion channel along the [100] direction is equivalent to the [010] direction. Then, the diffusion paths along the direction parallel to c axis ([001] direction) and perpendicular to the c axis ([100] or [110] direction) are chosen to find the minimum diffusion energy path of TiI and OI. As for VTi and VO, diffusion paths are established from the vacancy site to nearest lattice site of the same kind. Calculation results exhibit significant anisotropy of energy barrier and diffusion mechanism. Of all defect species, TiI diffusion along the [001] direction through interstitial mechanism has the lowest activation barrier of 0:5057 eV. In addition, diffusions along the [100] and [110] direction through kick-out mechanism show higher energy barriers of 1:0024 eV and 2:7758 eV, respectively. Compared with TiI, OI shows small barrier discrepancy between different diffusion directions, which is 0:859 eV along [001] and 0:902 eV along [100] direction. For vacancy defects, diffusion can occur only through the vacancy mechanism. The activation barrier energy of symmetrically inequivalent diffusion path of VO is 0:735 eV along the [110] direction, 1:747 eV along the [001] direction, and 1:119 eV from the TiO6 apex site to the equator site. On the other hand, VTi has two inequivalent paths with much larger diffusion energy barriers: 2:375 eV along the [111] direction and 3:232 eV along the [001] direction. In summary, the TiI interstitial diffusion along the [001] direction (parallel to the c axis) has the lowest activation barrier in rutile TiO2, which is in excellent agreement with former experimental and theoretical data.