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

Abstract

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.

Specific Heat Capacity of TiO2 Nanoparticles

“…In addition, imposing the surface effect on the polymorphs results in decreasing the phonon frequency values. As the TiO 2 polymorphs exhibit positive Gruneisen parameter [13,14], lowering the phonon frequency is equivalent to an increase in the unit cell volume. Consequently, the difference between C V and C P grows more rapidly as a function of temperature for smaller particles.…”

“…The bulk structure phonon calculations for three natural polymorphs of TiO 2 were carried out [13,14] in the formalism of density functional perturbative theory (DFPT) [15,16]. The calculations were performed using QuantumEspresso package [17].…”

“…The energy cutoff was 44 Ry. The k-point mesh in energy calculations was 4×4×4 for all of the polymorphs, while the mesh used for calculation of the interatomic force constants was 4×4×4 (2×2×2) in the case of rutile and anatase (brookite) structures [13,14]. Using phonon DOS, one can obtain the heat capacity of the bulk by the following formula:…”

Soft phonon modes in rutileTiO2

“…Effects of temperature and pressure on the static dielectric constants, frequencies of Raman active modes and Grüneisen parameters were addressed by capacitance measurements and Raman scattering and a particularly strong dependence on both pressure and temperature was found for the A 2u mode and related to structural and anharmonic contributions [3,4]. Ab initio lattice dynamics calculations using density functional perturbation theory (DFPT) were used to calculate phonon frequencies, Born effective charges and the dielectric permittivity [1,[5][6][7]. These calculations emphasize the importance of the mixed covalent ionic bonding of s and d orbitals, which is linked to its large polarizability due to long-range Coulomb interactions between the ions.…”

X-Ray Diffraction Analysis of Residual Stress in Thin Polycrystalline Anatase Films and Elastic Anisotropy of Anatase

“…[22][23][24][25] Proper accounting for crystal elastic anisotropy is often a critical aspect of the method. By contrast to the rutile phase, the single-crystal elastic constants (ECs) of which are well known, [31,32] the experimental single-crystal ECs of anatase are unknown to the authors (in References [33] through [35] are not specified either). Lack of this information can discourage the XRD stress analysis of anatase films or lead to incorrect results.…”