Elastic and thermal properties of the TiO(2) lattice in anatase and rutile phases were studied in the framework of density functional perturbation theory within the local density approximation (LDA) and generalized-gradient approximation (GGA). The full elastic constant tensors of the polymorphs were calculated by linear fits to the acoustic branches of the phonon band structure near the center of the first Brillouin zone in symmetry directions of the crystals. It was observed that the elastic constants within the GGA are in better agreement with experiment. In addition, the Born effective charges, dielectric tensor, heat capacity, mean sound velocity and Debye temperature were calculated. The heat capacity at room temperature and the Debye temperature within the LDA are in better agreement with the experimental results. Therefore, using the phonon band structure and the density of states, one can obtain the important mechanical and thermal properties of materials.

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We have performed first-principles calculations of hydrogen doping in anatase TiO 2 . Neutral and charged defects in interstitial and substitutional (for oxygen) positions have been considered, at concentrations between 0.125 and 0.03125 nH/nTi. A region of stability has been found for positively charged interstitial hydrogen, at realistic conditions of temperature and pressure. For example, at a partial pressure of hydrogen of 0.01 atm and a Fermi energy 2.3 eV above the top of the valence band, this defect is stable up to ∼500 K. Remarkably, at the highest concentration, metastable ordered substitutional neutral hydrogen leads to the appearance of bandlike states at the bottom of the conduction band, which lead to a band gap narrowing by 1 eV. On the contrary, in the presence of disorder or at lower concentration the neutral defects yield only localized defect states, located 0.7−0.9 eV below the bottom of the conduction band. Finally, the electronic structure of charged defects is very similar to that of pure anatase. These results explain the discrepancies observed in experiments as due to different concentrations and charge states, and suggest that a high concentration of neutral hydrogen in oxygen vacancies could be of interest for photocatalytic applications.

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