Anatase–rutile phase transformation of titanium dioxide bulk material: a DFT + U approach

Abstract

The anatase–rutile phase transformation of TiO2 bulk material is investigated using a density functional theory (DFT) approach in this study. According to the calculations employing the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional with the Vanderbilt ultrasoft pseudopotential, it is suggested that the anatase phase is more energetically stable than rutile, which is in variance with the experimental observations. Consequently, the DFT + U method is employed in order to predict the correct structural stability in titania from electronic-structure-based total energy calculations. The Hubbard U term is determined by examining the band structure of rutile with various values of U from 3 to 10 eV. At U = 5 eV, a theoretical bandgap for rutile is obtained as 3.12 eV, which is in very good agreement with the reported experimental bandgap. Hence, we choose the DFT + U method (with U = 5 eV) to investigate the transformation pathway using the newly-developed solid-state nudged elastic band (ss-NEB) method, and consequently obtain an intermediate transition structure that is 9.794 eV per four-TiO2 above the anatase phase. When the Ti–O bonds in the transition state are examined using charge density analysis, seven Ti–O bonds (out of 24 bonds in the anatase unit cell) are broken, and this result is in excellent agreement with a previous experimental study (Penn and Banfield 1999 Am. Miner. 84 871–6).