Ultrastiff cubic TiO2 identified via first-principles calculations

Electronegativity Force Field for Prediction of Elastic Moduli

Macroscopic elastic moduli (i.e., bulk modulus and shear modulus) of covalent crystals are mainly determined by microscopic structures and stiffnesses. Herein, the microscopic bond and angle force constants of covalent crystals were parameterized from their atomic electronegativities, which is named the electronegativity force field (EFF). Based on this force field, the elastic moduli of covalent crystals can be directly obtained by molecular mechanics calculations. The calculated moduli for various covalent crystals are generally consistent with first-principles calculations, while the computational cost is reduced by several orders of magnitude, indicating the accuracy and efficiency of the EFF. Finally, we found 25 ultrahigh-modulus crystals with a bulk modulus greater than 350 GPa, which demonstrates that this force field can be used for screening of ultrahigh-modulus materials from numerous crystal candidates.

Atomic stiffness for bulk modulus prediction and high-throughput screening of ultraincompressible crystals

Determining bulk moduli is central to high-throughput screening of ultraincompressible materials. However, existing approaches are either too inaccurate or too expensive for general applications, or they are limited to narrow chemistries. Here we define a microscopic quantity to measure the atomic stiffness for each element in the periodic table. Based on this quantity, we derive an analytic formula for bulk modulus prediction. By analyzing numerous crystals from first-principles calculations, this formula shows superior accuracy, efficiency, universality, and interpretability compared to previous empirical/semiempirical formulae and machine learning models. Directed by our formula predictions and verified by first-principles calculations, 47 ultraincompressible crystals rivaling diamond are identified from over one million material candidates, which extends the family of known ultraincompressible crystals. Finally, treasure maps of possible elemental combinations for ultraincompressible crystals are created from our theory. This theory and insights provide guidelines for designing and discovering ultraincompressible crystals of the future.

Polymorphs of Titanium Dioxide: An Assessment of the Variants of Projector Augmented Wave Potential of Titanium on Their Geometric and Dielectric Properties

Titanium dioxide (TiO₂) is one of the important functional materials owing to its diverse applications in many fields of chemistry, physics, nanoscience, and technology. Hundreds of studies on its physicochemical properties, including its various phases, have been reported experimentally and theoretically, but the controversial nature of relative dielectric permittivity of TiO₂ is yet to be understood. Toward this end, this study was undertaken to rationalize the effects of three commonly used projector augmented wave (PAW) potentials on the lattice geometries, phonon vibrations, and dielectric constants of rutile (R-)TiO₂ and four of its other phases (anatase, brookite, pyrite, and fluorite). Density functional theory calculations within the PBE and PBEsol levels, as well as their reinforced versions PBE+U and PBEsol+U (U = 3.0 eV), were performed. It was found that PBEsol in combination with the standard PAW potential centered on Ti is adequate to reproduce the experimental lattice parameters, optical phonon modes, and the ionic and electronic contributions of the relative dielectric permittivity of R-TiO₂ and four other phases. The origin of failure of the two soft potentials, namely, Ti_pv and Ti_sv, in predicting the correct nature of low-frequency optical phonon modes and ion-clamped dielectric constant of R-TiO₂ is discussed. It is shown that the hybrid functionals (HSEsol and HSE06) slightly improve the accuracy of the above characteristics at the cost of a significant increase in computation time. Finally, we have highlighted the influence of external hydrostatic pressure on the R-TiO₂ lattice, leading to the manifestation of ferroelectric modes that play a role in the determination of large and strongly pressure-dependent dielectric constant.

High-Pressure Phase Diagram of the Ti-O System

Titanium oxides are technologically important compounds. The chemistry of the Ti-O system is quite rich, largely because of the multiple oxidation states that titanium atoms can take. In this work, using a combination of variable-composition evolutionary crystal structure prediction (USPEX code) and data mining (Materials Project), we predicted all of the stable titanium oxides in the pressure range 0-200 GPa and found that 27 compounds can be stable at different pressures. We resolved contradictions between previous works and predicted four hitherto-unknown stable phases: P2₁/c-TiO₃, I4/mmm-Ti₃O₂, Imm2-Ti₅O₂, and R3̅-Ti₁₂O₅. We also showed that the high-pressure P6̅m2-TiO phase is an electride.

Comparative study on structural, electronic, optical and mechanical properties of normal and high pressure phases titanium dioxide using DFT

In this paper, a Self-consistent Orthogonalized linear combination of atomic orbitals (OLCAO) technique with a generalized gradient approximation such as Perdew–Burke–Ernzerhof Solid (GGA-PBE SOL) has been used to scrutinize the structural, optical, electronic and mechanical properties of normal pressure phase (Anatase and Rutile) and high pressure phase i.e., cubic (Fluorite and Pyrite) TiO2. Electronic and optical properties of normal pressure phases of TiO2 are also investigated using (Meta) MGGA-Tran and Blaha (TB09) and obtained results are a close approximation of experimental data. It is seen that the virtually synthesized structural parameter for cubic and tetragonal phases of TiO2 are consistent with experimental and theoretical data. From the effective mass of charge carriers (m*), it can be observed that pyrite TiO2 is having lower effective mass than the fluorite and hence shows higher photocatalytic activity than fluorite. Furthermore, it is seen that fluorite is more dense than anatase, rutile and pyrite TiO2. From the theoretical calculations on the optical properties, it can be concluded that optical absorption occursin the near UV region for high and normal pressue phases of TiO2. Again from the reflectivity characteristics R(ω), it can be concluded that TiO2 can be used as a coating material. Elastic constants, elastic compliance constants, mechanical properties are obtained for anatase, rutile, fluorite and pyrite TiO2. A comparison of the results with previously reported theoretical and experimental data shows that the calculated properties are in better agreement with the previously reported experimental and theoretical results.

Searching for new TiO₂ crystal phases with better photoactivity

Using the recently developed stochastic surface walking global optimization method, this work explores the potential energy surface of TiO2 crystals aiming to search for likely phases with higher photocatalytic activity. Five new phases of TiO2 are identified and the lowest energy phase transition pathways connecting to the most abundant phases (rutile and anatase) are determined. Theory shows that a high-pressure phase, α-PbO2-like form (TiO2II) acts as the key intermediate in between rutile and anatase. The phase transition of anatase to rutile belongs to the diffusionless Martensitic phase transition, occurring through a set of habit planes, rutile(101)//TiO2II(001), and TiO2II(100)//anatase(112). With regard to the photocatalytic activity, three pure phases (#110, pyrite and fluorite) are found to possess the band gap narrower than rutile, but they are unstable at the low-pressure condition. Instead, a mixed anatase-TiO2II phase is found to have good stability and narrower band gap than both parent phases. Because of the phase separation, the mixed phase is also expected to improve the photocatalytic performance by reducing the probability of the electron-hole pair recombination.

DFT+U calculations of crystal lattice, electronic structure, and phase stability under pressure of TiO2 polymorphs

This work investigates crystal lattice, electronic structure, relative stability, and high pressure behavior of TiO(2) polymorphs (anatase, rutile, and columbite) using the density functional theory (DFT) improved by an on-site Coulomb self-interaction potential (DFT+U). For the latter the effect of the U parameter value (0 < U < 10 eV) is analyzed within the local density approximation (LDA+U) and the generalized gradient approximation (GGA+U). Results are compared to those of conventional DFT and Heyd-Scuseria-Ernzehorf screened hybrid functional (HSE06). For the investigation of the individual polymorphs (crystal and electronic structures), the GGA+U/LDA+U method and the HSE06 functional are in better agreement with experiments compared to the conventional GGA or LDA. Within the DFT+U the reproduction of the experimental band-gap of rutile/anatase is achieved with a U value of 10/8 eV, whereas a better description of the crystal and electronic structures is obtained for U < 5 eV. Conventional GGA∕LDA and HSE06 fail to reproduce phase stability at ambient pressure, rendering the anatase form lower in energy than the rutile phase. The LDA+U excessively stabilizes the columbite form. The GGA+U method corrects these deficiencies; U values between 5 and 8 eV are required to get an energetic sequence consistent with experiments (E(rutile) < E(anatase) < E(columbite)). The computed phase stability under pressure within the GGA+U is also consistent with experimental results. The best agreement between experimental and computed transition pressures is reached for U ≈ 5 eV.

Structural stability of TiO2 at high pressure in density-functional theory based calculations

A new study on the pressure-induced phase transitions of TiO(2) has been performed using all-electron density-functional theory based computations with the projector augmented wave and the linearized augmented plane wave methods considering five experimentally observed structures. The static results yield a picture that is consistent with experiments, i.e., phase transitions with pressure are predicted as rutile --> monoclinic baddeleyite (MI) --> orthorhombic I (OI) --> cotunnite (OII) on compression, and OII --> OI --> MI --> columbite (TiO(2)II) on decompression. The elasticities of these five polymorphs are compared. Except for the baddeleyite structure, which is considerably softer than the other polymorphs, all phases show a zero pressure bulk modulus in the range of 200-240 GPa, consistent with compression results and the single crystal elastic constant; on the basis of these results we can say that the cotunnite phase is not a superhard TiO(2) polymorph as has been suggested previously. We further find that the rutile and columbite structures are energetically very similar, with the columbite structure favored slightly. All polymorphs are predicted as insulating with comparable band gaps (∼1.7-2.3 eV). Crystal field splitting for the Ti 3d electronic states leads to two distinct conduction bands in rutile and TiO(2)II for energies smaller than 8 eV, while there is a single conduction band for the other high pressure structures.

First-principles elastic and thermal properties of TiO2: a phonon approach

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.