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

Abstract

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.

Machine learning and atomistic origin of high dielectric permittivity in oxides

“…PBEsol functional 54 with Hubbard U correction 55 was used. U=3 eV was applied to d electrons in transition metals, except for Ti and Sc, where U=0 was used 14 , and U=5 eV was applied to f electrons in rare earths. Projector-augmented wave (PAW) method was used to treat core electrons.…”

“…Projector-augmented wave (PAW) method was used to treat core electrons. Recommended PAW potentials were employed for all elements except Ti, where valence 4 "Ti" potential was found to better represent the vibrational and optical properties of titanium dioxide 14 . The k point grid density of 3000 k points•atom (approximately corresponding to a distance of 0.2 Å −1 between the k points) was used for the integration over the Brillouin zone.…”

“…Our previous theoretical analysis 8 confirmed intrinsic permittivity boosting in co-doped rutile and other substituted paraelectric titanates, and also showed that the effect can be accounted for by the lattice mechanism. It was found that the boosting is due to the softening of the active phonon mode by the local strain 14 from impurities, and a simple descriptor in the form of the maximum Ti-O bond length was proposed 8 . The descriptor was found heuristically; finding such descriptors is generally challenging and largely depends on luck and intuition.…”