金红石TiO_2中本征缺陷扩散性质的第一性原理计算

基于密度泛函理论的爬坡弹性带方法,对金红石相二氧化钛晶体中钛间隙、钛空位、氧间隙、氧空位4种本征缺陷的扩散特征进行了研究.对比4种本征缺陷在晶格内部沿不同扩散路径的过渡态势垒后发现,缺陷扩散过程呈现出明显的各向异性.其中,钛间隙和氧间隙沿[001]方向具有最小的扩散势垒路径,激活能分别为0.505 eV和0.859 eV;氧空位和钛空位的势垒最小的扩散路径分别沿[110]方向和[111]方向,激活能分别为0.735 eV和2.375 eV.

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 (Ti_I), titanium vacancy (V_ti), oxygen interstitial (O_I) and oxygen vacancy (V_O) 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 3×3×4 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 (P4₂/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 Ti_I and O_I. As for V_Ti and V_O, 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, Ti_I 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 Ti_I, O_I 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 V_O 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, V_Ti 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 Ti_I 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.