Thermodynamic Properties of Rutile $$(\hbox {TiO}_{2})$$ ( TiO 2 ) Within the Phonon Calculations

Electron-phonon coupling in d -electron solids: A temperature-dependent study of rutile TiO2 by first-principles theory and two-photon photoemission

“…In addition to the above discussed atomic contribution to the band-energy renormalization by thermal phonon excitation, the lattice expansion makes an additional contribution that quantitatively affects the temperature dependence of the t 2g to e g transition energy, and is likely to be important in other d-electron bands that are affected by crystal-field splitting and have anharmonic phonon modes. In our calculation of the temperature-dependent structure of TiO 2 , the a and c lattice parameters are found to increase by 0.02 Å as the temperature is increased from 0 to 600 K, due to anharmonic interatomic potentials, in good agreement with the literature [105,106]. The lattice expansion does not, however, change the discussed qualitative behavior, but only causes the t 2g to e g transition energy to shrink additionally by −0.076 eV, when temperature is increased from 0 to 600 K [63].…”

“…and have anharmonic phonon modes. In our calculation of the temperature-dependent structure of TiO 2 , the a and c lattice parameters are found to increase by 0.02 Å as the temperature is increased from 0 to 600 K, due to anharmonic interatomic potentials, in good agreement with the literature [105,106]. The lattice expansion does not, however, change the discussed qualitative behavior, but only causes the t 2g to e g transition energy to shrink additionally by −0.076 eV, when temperature is increased from 0 to 600 K [63].…”

Thermal Conductivity of Rutile and Anatase TiO2 from First-Principles

“…For both the harmonic and anharmonic IFCs we used a 3 × 3 × 3 supercell of the 6-atom (12-atom) cell of rutile (anatase), sampling the Brillouin zone with a 4 × 4 × 4 (4 × 4 × 2) grid of k-points. This supercell sizes yield dispersion relations in good agreement with previously published results 39,40. We use the Phono3py code53 to generate the inequivalent atomic displacements required to compute the IFCs and to calculate the thermal conductivity beyond the standard Relaxation Time Approximation (RTA),…”

“…The thermal properties of TiO 2 have received comparatively less attention, but they are important both from a fundamental standpoint and for applications related to thermal management and thermoelectricity. [25][26][27][28][29][30][31] Experimentally, the thermal conductivity of rutile was Touloukian et al 37 A few theoretical works have studied the elastic and thermal properties of anatase and rutile from first principles, [38][39][40] computing the phonon dispersions, the heat capacity, and the Grüneisen parameter. Regarding the thermal conductivity, however, the only available first principles results are based on the Cahill-Pohl model, 41,42 which allows obtaining the so-called minimum thermal conductivity from harmonic properties, while a full solution of the phonon Boltzmann Transport Equation (BTE) that includes anharmonic effects is still missing.…”

“…This supercell sizes yield dispersion relations in good agreement with previously published results. 39,40 We use the PHONO3PY code 53 to generate the inequivalent atomic displacements required to compute the IFCs and to calculate the thermal conductivity beyond the standard relaxation time approximation (RTA), obtaining the direct solution of the BTE due to Chaput 54,55…”