The structural and electronic properties of oxygen vacancies (V-Ox) and titanium interstitials (Ti-(i)) in the bulk of the rutile and anatase forms of TiO2 have been investigated with LSD-GGA+U ab initio simulations. In particular, formation energies of the charged and neutral forms of the V-Ox and Ti-(i) defects as well as the corresponding vertical and thermodynamic transition levels have been estimated. The achieved results can reconcile the apparent inconsistency of experimentally observed deep donor levels with the n-type conductivity observed in reduced TiO2. They show indeed that both defects give rise to vertical transition levels about 1 eV below the conduction band (CB), in agreement with experimental measures, and to thermodynamic transition levels close to the CB. That is, these defects behave as deep donors, when looking at vertical transitions, and as shallow donors, when the effects of the structural relaxations are taken into account. A major part of the explanation of this behavior is played by the polaron-like character of the defect states, which was already noted, but not deepened, in literature. Finally, it is shown that the application of the U correction to both Ti and O species gives qualitatively similar results, but with a better agreement to experimental findings, with respect to the application to Ti only. The former approach gives pretty similar results, for both rutile and anatase bulk properties, to those coming from HSE hybrid functional calculations

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Paths of tetragonal states between two phases of a material, such as bcc and fcc, are called Bain paths. Two simple Bain paths can be defined in terms of special imposed stresses, one of which applies directly to strained epitaxial films. Each path goes far into the range of nonlinear elasticity and reaches a range of structural parameters in which the structure is inherently unstable. In this Letter we identify and analyze the general properties of these paths by density functional theory. Special examples include vanadium, cobalt, and copper, and the epitaxial path is used to identify an epitaxial film as related uniquely to a bulk phase. [S0031-9007(97)03190-6] PACS numbers: 64.70. Kb, 61.50.Ks, 62.20.Dc Pseudomorphic epitaxy of a cubic or tetragonal (001) film typically results in a strained tetragonal structure. If the stresses on the tetragonal state vanish and also the state corresponds to a local minimum of energy with respect to tetragonal deformations, the structure will be called a tetragonal phase. Such a phase will be stable or metastable, depending on whether it has the lowest energy compared to other minima. Frequently metals have two tetragonal phases; sometimes both are cubic, e.g., bcc and fcc Na and Rb [1,2]; sometimes one is cubic and the other phase is tetragonal, e.g., Ti and V [2,3]. They can, of course, also have phases with other structures; e.g., Ti also has a hcp phase.Many paths can go from one tetragonal phase to the other. If the geometries along such a path have tetragonal symmetry and if they connect bcc and fcc phases, the paths have been called Bain paths [4]. A purpose of the present work is to define and discuss a particular Bain path which will be called the epitaxial Bain path (EBP). The EBP is produced by isotropic stress or strain in the (001) plane of tetragonal phases accompanied by vanishing stress perpendicular to the plane, such as pseudomorphic epitaxy produces on an (001) cubic or tetragonal film. Epitaxy provides a valuable means of stabilizing metastable phases and of putting phases under very large strains, both tensile and compressive in the plane of the epitaxy. The EBP of a material identifies the phase that has been strained, checks quantitatively the elastic behavior, which can be highly nonlinear, and predicts which phase of the material will form on a given substrate. Thus, in order to understand the properties of epitaxial films and new materials, the knowledge of the EBP is indispensable.A different Bain path has long been discussed, particularly by Milstein [1], in which uniaxial stress is applied to a tetragonal state along the ͓001͔ axis accompanied by zero stress in the (001) plane; this path is conveniently called the uniaxial Bain path (UBP). We compare the two paths, EBP and UBP, which are both physically realizable. We show that both have the same lowest possible maximum energy or barrier energy of all Bain paths between the two tetragonal phases. However, the EBP has a special value in relating strained tetragonal structures produced by epita...

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