Faculty of Materials Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam.
J Phys Condens Matter. 2012 Oct 10;24(40):405501. doi: 10.1088/0953-8984/24/40/405501. Epub 2012 Sep 6.
The anatase-rutile phase transformation of TiO(2) 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-TiO(2) 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).
本研究采用密度泛函理论（DFT）方法研究了 TiO(2)体材料的锐钛矿-金红石相转变。根据采用 Perdew-Burke-Ernzerhof（PBE）交换相关泛函和 Vanderbilt ultrasoft 赝势进行的计算，锐钛矿相比金红石相更稳定，这与实验观察结果不一致。因此，采用 DFT + U 方法从基于电子结构的总能量计算预测二氧化钛的正确结构稳定性。通过用 U 从 3 到 10 eV 研究金红石的能带结构，确定 Hubbard U 项的值。在 U = 5 eV 时，得到金红石的理论能带隙为 3.12 eV，与报道的实验能带隙非常吻合。因此，我们选择 DFT + U 方法（U = 5 eV）使用新开发的固态力引导弹性带（ss-NEB）方法来研究转变途径，从而得到一个中间体过渡结构，该结构比锐钛矿相高 9.794 eV/四个 TiO(2)。当使用电荷密度分析检查过渡态中的 Ti-O 键时，发现有七个 Ti-O 键（在锐钛矿单元胞的 24 个键中）断裂，这一结果与先前的实验研究（Penn 和 Banfield 1999 Am. Miner. 84 871-6）非常吻合。
